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Regional cyclical behaviour and sensitivity in Canada, 1919-1973 Blain, Larry 1977

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REGIONAL CYCLICAL BEHAVIOUR AND SENSITIVITY IN CANADA,1919-1973 by LARRY A. BLAIN B.A., U n i v e r s i t y of B r i t i s h Columbia, 1969 M.A., Car l e t o n U n i v e r s i t y , 1971 A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENT FOR THE DEGREE OF DOCTOR OF PHILOSOPHY i n THE FACULTY OF GRADUATE STUDIES i n the Department of ECONOMICS We accept t h i s t h e s i s as conforming to the r e q u i r e d standard THE UNIVERSITY OF BRITISH COLUMBIA March,.1977 (8) . Larry,A. B l a i n , 1977 In presenting th is thes is in p a r t i a l fu l f i lment of the requirements for an advanced degree at the Un ivers i ty of B r i t i s h Columbia, I agree that the L ibrary sha l l make it f ree ly ava i l ab le for reference and study. I fur ther agree that permission for extensive copying of this thesis for scho la r ly purposes may be granted by the Head of my Department or by his representat ives . It is understood that copying or publication of th is thes is for f i nanc ia l gain sha l l not be allowed without my writ ten permission. Department of c ^ > ^ O C c The Un ivers i ty of B r i t i s h Columbia 2075 Wesbrook P l a c e Vancouver, Canada V6T 1W5 Research, supervisor: D. C. Paterson ABSTRACT This Thesis i n v e s t i g a t e s " s h o r t - r u n " economic cycles i n Canadian regions over the p e r i o d 1919-1973. There are a number of r e a d i l y a v a i l a b l e monthly and q u a r t e r l y t i m e - s e r i e s which represent the e s s e n t i a l aspects o f "general economic a c t i v i t y " i n the various regions ( B r i t i s h Columbia, the P r a i r i e s , Ontario, Quebec and the Ma r i t i m e s ) . These data are used to describe the p a t t e r n o f c y c l i c a l behaviour i n Canada's regions and to analyze the r e g i o n a l mechanism by which United States business c y c l e s are t r a n s m i t t e d i n t o Canada. Two q u a n t i t a t i v e methods are used - the " e p i s o d i c " method (fashioned a f t e r the approach of the N a t i o n a l Bureau of Economic Research) and the s p e c t r a l a n a l y t i c method. These areas of i n v e s t i g a t i o n are d i r e c t e d at two c h a r a c t e r i s t i c s o f Canadian development with which Canadian economists have long been concerned. The f i r s t i s the p e r s i s t e n c e o f r e g i o n a l d i s p a r i t i e s ; the a p p l i c a t i o n i n t h i s study o f the seldom-used monthly and q u a r t e r l y t i m e - s e r i e s provides new i n s i g h t to the short-run s t a b i l i t y , and changes i n s t a b i l i t y over time, o f Canada's r e g i o n a l economies. The second c h a r a c t e r i s t i c i s that at l e a s t u n t i l World War I there has e x i s t e d a very strong tendency f o r s p e c i f i c regions to p l a y c e n t r a l r o l e s as l o c a t i o n s f o r the production o f n a t i o n a l l y - i m p o r t a n t export goods at d i f f e r e n t periods o f time, suggesting an economic s e n s i t i v i t y between f o r e i g n , r e g i o n a l and n a t i o n a l economies which i s summarized by the s t a p l e theory o f Canadian economic growth. However, since the F i r s t World War there has been f o r various reasons a considerable although gradual e v o l u t i o n i n r e g i o n a l economic s t r u c t u r e which may have a l t e r e d the mechanism of c y c l i c a l transmis-s i o n among regions. Moreover, modern treatments o f f l u c t u a t i o n s i n the i n a t i o n a l economy over the p e r i o d 1919-1973 suggest t h a t i n many ways Canadian c y c l i c a l behaviour i s but a f u n c t i o n of corresponding behaviour i n the United S t a t e s . When the postwar p e r i o d i s compared with the interwar p e r i o d a d e c l i n e can be observed i n Canada's s e n s i t i v i t y to f l u c t u a t i o n s i n the general economic a c t i v i t y o f the United States but t h i s d e c l i n e has remained l a r g e l y unexplained because o f the obvious complexity of the economic linkages between the two c o u n t r i e s . By examining the e v o l u t i o n of s e n s i t i v i t y among Canada's heterogeneous regions much l i g h t i s shed upon the question of d e c l i n i n g Canadian s e n s i t i v i t y . The o v e r a l l evidence from the r e g i o n a l t i m e - s e r i e s suggests that i n a broad sense d i s p a r i t i e s i n r e g i o n a l f l u c t u a t i o n s are r a t h e r l a r g e . On balance, the Canadian regions adhere to a common, b a s i c p a t t e r n i n economic f l u c t u a t i o n s i n that episodes, found i n the n a t i o n a l i n d i c a t o r s are u s u a l l y found i n the r e g i o n a l i n d i c a t o r s and tend to have a s i m i l a r average d u r a t i o n . However, there the s i m i l a r i t y ends although there was a s u r p r i s i n g l y uniform strength i n the s h o r t e r "subcycle", e s p e c i a l l y i n the postwar p e r i o d . The a b i l i t y o f business c y c l e s to e x p l a i n the t o t a l v a r i a t i o n i n economic i n d i c a t o r s i s markedly d i f f e r e n t among regions - i n B r i t i s h Columbia and Ontario the c y c l e i s stronger than the r e g i o n a l average and i n the Maritimes and P r a i r i e s i t i s weaker. A l s o , w i t h i n the common r e g i o n a l - n a t i o n a l p a t t e r n i n f l u c t u a t i o n s s i g n i f i c a n t d i f f e r e n c e s i n t i m i n g are apparent; c e r t a i n regions seem to c o n s i s t e n t l y lead or l a g the n a t i o n a l economy. Indeed, there are s i g n i f i c a n t d i f f e r e n c e s between the c y c l i c a l behaviours of Ontario and Quebec even though the economic linkages which transmit cycles between the two regions are strong. During the interwar p e r i o d Canadian regions were g e n e r a l l y s e n s i t i v e to business c y c l e f l u c t u a t i o n s i n the United S t a t e s , although B r i t i s h Columbia, i i Ontario and Quebec were more c l o s e l y attuned to the United States economy than e i t h e r the P r a i r i e s or Maritimes. The v a r y i n g l e v e l s o f r e g i o n a l -USA correspondence i n d i c a t e that the tran s m i s s i o n o f cycl e s from the United States does not occur s i m i l a r l y i n a l l r e g i o n s , although i n each case the v o l a t i l i t y i n r e g i o n a l business c y c l e s i s l e s s than that o f the United S t a t e s . The evidence f o r the interwar p e r i o d suggests that the mechanism by which United States business c y c l e s are tra n s m i t t e d i n t o Canada i s charac-t e r i z e d by a tendency f o r Ontario to be s e n s i t i v e to both the Rest-of-Canada and the United S t a t e s ; Ontario a l s o appears to be the most v o l a t i l e r e g i o n , p a r t i c u l a r l y during the 1930s. This r e s u l t i s c o n s i s t e n t w i t h the view that because Ontario i s l i k e l y a net exporter of c a p i t a l goods and consumer durables to the other regions then a c y c l i c a l i n s t a b i l i t y i n the marginal p r o p e n s i t y t o import i n the other regions might s t a b i l i z e these regions while at the same time d e s t a b i l i z i n g the Ontario economy. When the postwar and interwar periods are compared, s e v e r a l important changes are observed i n the tr a n s m i s s i o n mechanism. While c y c l e s are s t i l l t r a n s m i t t e d from the United States to the Canadian regions there i s a n o t i c e a b l e d e c l i n e i n the s i g n i f i c a n c e o f t h i s s e n s i t i v i t y , w i t h the l a r g e s t reductions o c c u r r i n g i n Quebec and B.C., and a smaller r e d u c t i o n o c c u r r i n g i n O n t a r i o . There have al s o been d e c l i n e s i n r e g i o n a l correspondence to the Rest-of-Canada, which have been of approximately the same order o f magnitude i n each r e g i o n . To some extent the weakened i n t e r r e g i o n a l c o r r e s -pondence may have r e s u l t e d from weakened r e g i o n a l s e n s i t i v i t y to the United States but, ne v e r t h e l e s s , the r e d u c t i o n i n regional-USA s e n s i t i v i t i e s i n the postwar p e r i o d suggests a change i n the r e g i o n a l mechanism o f c y c l i c a l t r a n s -m i s s i o n , p a r t i c u l a r l y i n t h a t Ontario i s a stronger t r a n s m i t t e r o f United i i i States f l u c t u a t i o n s than formerly. Thus, the t r a d i t i o n a l view that economic c y c l e s are t r a n s m i t t e d from "staple-producing" regions to C e n t r a l Canada, e s p e c i a l l y Ontario, has apparently become l e s s appropriate since World War I I . i v TABLE OF CONTENTS TABLE OF CONTENTS i LIST OF TABLES i i i Chapter 1 INTRODUCTION 1 1.1 The Topic 1 1.2 The H i s t o r i c a l Problem 5 1.3 An Economic Region Defined U 2 PATTERNS AND DISPARITIES IN REGIONAL CYCLES 16 2.1 I n t r o d u c t i o n 16 2.2 Methods of Cycle I d e n t i f i c a t i o n 19 2.2.1 Regional Time Se r i e s Data 25 2.3 Important C y c l i c a l Frequency Bands 27 2.3.1 Seasonal V a r i a t i o n 31 2.3.2 Subcycles 34 2.3.3 Business Cycles 39 2.4 Regional Leads and Lags 54 2.4.1 Average Regional Leads and Lags 56 2.4.2 U n i f o r m i t y o f Regional Leads and Lags 64 2.4.3 C l u s t e r i n g of Regional Turning Points 66 2.5 Summary of Major E m p i r i c a l Results 68 APPENDIX 2A 76 1. S p e c t r a l A n a l y s i s 76 2. The E p i s o d i c Method 79 APPENDIX 2B 82 APPENDIX 2C 83 APPENDIX 2D 90 3 THE RELATIONSHIP BETWEEN REGIONAL AND NATIONAL CYCLES 103 3.1 I n t r o d u c t i o n 103 3.2 Method 104 3.3.1 Regional-National Cross Spectra 106 3.3.2 E l a s t i c i t y R e s u l t s 113 3.3.3 Regional D i s p a r i t i e s i n Correspondence and Cross Relative-Amplitude 117 APPENDIX 3A 122 1. Cr o s s - S p e c t r a l A n a l y s i s 122 2. The E l a s t i c i t y Approach 128 v APPENDIX 3B 131 4 REGIONAL CYCLICAL SENSITIVITY IN THE NORTH AMERICAN FRAMEWORK 135 4.1 I n t r o d u c t i o n 135 4.2 Methods o f Comparing Regional C y c l i c a l S e n s i t i v i t i e s 143 4.2.1 Data and Data Manipulations 143 4.2.2 Methods i n Drawing Conclusions 145 4.3 Regional C y c l i c a l S e n s i t i v i t y 150 4.3.1 Regional-ROC Cross Spectra 150 4.3.2 Regional-USA and ROC-USA Cross-Spectra 156 4.3.3 A Note on the Feedback Test 163 4.3.4 C l a s s i f i c a t i o n of Each Region According to I t s S e n s i t i v i t y R e l a t i o n s h i p w i t h ROC, USA 165 APPENDIX 4A 208 APPENDIX 4B 210 5 REGIONAL SENSITIVITY OVER TIME: A COMPARISON WITH CANADA-USA SENSITIVITY ANALYSIS 221 5.1 I n t r o d u c t i o n 221 5.2 The Change i n Canada-USA C y c l i c a l S e n s i t i v i t y Since 1919 222 5.3 Changes i n Regional S e n s i t i v i t y 229 5.4 Determinants of Changes i n C y c l i c a l S e n s i t i v i t y 237 6 REGIONAL AND NATIONAL CYCLES AND SENSITIVITY: A SUMMARY OF CONCLUSIONS 257 6.1 I n t r o d u c t i o n 257 6.2 N a t i o n a l I m p l i c a t i o n s of the Evidence on Regional C y c l i c a l Behaviour 257 6.3 The Regional Mechanism of C y c l i c a l Transmission 260 BIBLIOGRAPHY 266 CHART 141 v i LIST OF TABLES Table 2.1 Ranking of Regions by S p e c t r a l Density Estimates at Annual Frequencies 33 2.2 I n d i c a t o r s i n which there are S i g n i f i c a n t Subcycle Peaks; By Subperiod, by Region 38 2.3 Estimated Average P e r i o d i c i t y i n the Business Range 41 2.4 D i f f e r e n c e Between Longest and Shortest Estimated Regional Average P e r i o d i c i t y , by I n d i c a t o r and Subperiod ( i n Months) 44 2.5 Cases of Non-Correspondence Episodes 46 2.6 Regional E/C R a t i o s , "Unique Episodes" Omitted 48 2.7 I n t e r r e g i o n a l Comparison of Business Cycle E/C R a t i o s ; "Unique" Episodes Omitted 49 2.8 Intertemporal P a t t e r n of Regional E/C Ratios 51 2.9 I n t e r r e g i o n a l Comparison of R e l a t i v e C o n t r i b u t i o n of Business Cycle Frequencies 53 2.10 Regions i n which at Least Two-Thirds of I n d i c a t o r s Show Recurring Results 57 2.11 Average Regional Leads and Lags; C r o s s - S p e c t r a l A n a l y s i s 61 2.12 Uniformity: Averaged Over a l l I n d i c a t o r s 65 2.13 Ranking of Subperiods by C l u s t e r i n g 67 2.14 C l u s t e r i n g : S p e c t r a l Method 69 Appendix 2B B l Regional Turning Points 82 Appendix 2C CI S p e c t r a l Density Estimates at Annual Frequencies 83 C2 Subcycle Peaks i n Estimated S p e c t r a l Density Functions 84 C3 I n t e r r e g i o n a l Comparison of Business Cycle E/C R a t i o s ; "Unique" Episodes Included 85 C4 Relative Contribution of Business Cycle Frequencies To Explanation of Total Variance in the Regional Indicators 86 C5 Average Regional Leads and Lags: Episodic Method 87 C6 Uniformity: Normalized Variance 88 C7 Clustering: Episodic Method 89 C8 Ratio of Irregular to Cyclical (Smoothed) Components 90 3.1 Coherence, Canada Vs. Each Region 1° 7 3.2 Phase, Canada Vs. Each Region 1 0 8 3.3 Gain, Canada Vs. Each Region 109 3.4 Regional Orderings by Regional-National Correspondence and Cross Relative-Amplitude 116 Appendix 3B Bl Correspondence and Cross Relative-Amplitude by the Elasticity Approach 131 4.1 Classification of Regions by Sensitivity Relationships 147 4.2 Coherence, ROC Vs. Each Region 151 4.3 Phase, ROC Vs. Each Region 152 4.4 Gain, ROC Vs. Each Region 153 4.5 Coherence, Each Region, ROC Vs. USA 157 4.6 Phase, Each Region, ROC Vs. USA 158 4.7 Gain, Each Region, ROC Vs. USA 159 4.8 Comparison of Regional-ROC and Regional-USA Coherence I 6 0 4.9 B.C., Sensitivity Classification, Each Indicator and Time Period I 6 7 4.10 Prairies, Sensitivity Classifications, Each Indicator and Time Period I 7 4 4.11 Ontario, Sensitivity Classifications, Each Indicator and Time Period 181 viii 4.12 Ontario Vs. Quebec Cross-Spectral Results 189 4.13 Quebec, Sensitivity Classifications, Each Indicator and Time Period 196 4.14 Maritimes, Sensitivity Classifications, Each Indicator and Time Period 200 Appendix 4B Bl Cross-Correlations, Region Vs. ROC 2 1 0 B2 Cross-Correlations, ROC Vs. USA 2 1 1 B3 Cross-Correlations, Regions Vs. USA 2 1 2 B4 Cross-Correlations, Ontario Vs. Quebec 2 l3 5.1 Changes in Canada-USA Sensitivity; Interwar to Postwar Periods 2 2 ? 5.2 Changes in Regional Sensitivity; Interwar to Postwar Periods 230 5.3 Regional Business Gross Fixed Capital Formation as a Proportion of Regional Personal Income 246 LIST OF FIGURES 1 Examples of Estimated Spectra 29 i x ACKNOWLEDGEMENT I should l i k e to extend my thanks to Don Paterson f o r h i s undaunted e f f o r t s to make an economic h i s t o r i a n out of me. Throughout my graduate years at UBC h i s guidance was generous and i n c i s i v e ; as Chairman o f my Thesis committee he was demanding but p a t i e n t . I a l s o thank John Cragg f o r many h e l p f u l i n s i g h t s and p a r t i c u l a r l y Gideon Rosenbluth, a masterful economist and teacher upon whom I have leaned h e a v i l y i n t h i s t h e s i s . Sebastian, Russ, P h i l , Bernie and e s p e c i a l l y Linda are f r i e n d s who t o l e r a t e d a man and h i s tome. I appreciate the support o f the Canada Council and more r e c e n t l y the Research Department o f the Bank o f Canada. I am als o g r a t e f u l f o r the very capable t y p i n g o f Yvonne Rowe. I dedicate t h i s work to Mom and Dad and t o , as H a r r i s put i t , the "Golden Years" at UBC. CHAPTER ONE INTRODUCTION 1.1 The Topic This thesis investigates economic cycles i n Canadian regions over the period 1919-1973.1 There are a number of r e a d i l y available monthly and quarterly time-series which represent e s s e n t i a l aspects of "general economic a c t i v i t y " i n the various regions; these include a broad measure of economic a c t i v i t y (bank debits), plus indicators of r e a l output (employment and freight carloadings), investment (construction contracts),• prices (the consumer price index) and the c r u c i a l housing sector (dwelling s t a r t s ) . 2 Our i n i t i a l concern i s to establish h i s t o r i c a l f a c t s and to determine the dimensions of any regional d i s p a r i t i e s i n the c y c l i c a l behaviour of these indi c a t o r s . Questions of i n t e r e s t are, f i r s t , what regional cycles can be i d e n t i f i e d , and, second, how do the cycles compare among regions and with the Canadian national economy i n terms of (a) timing, (b) t h e i r average duration (period) and (c) the contribution of each c y c l i c a l component to the explanation of the t o t a l variance i n each time-series. In Chapter Two, i n t e r r e g i o n a l and regional-national comparisons are made f o r each region and, also, intertemporal comparisons are made between subperiods - which are roughly 1919-1940, 1945-1959 and 1960-1973. Quantitative methods include both the "episodic" method (fashioned a f t e r the approach of the National Bureau 2 of Economic Research) and the spectral a n a l y t i c method.3 Third, we ask: what i s the r e l a t i o n s h i p between regional and national c y c l i c a l behaviour i n terms of "correspondence", timing and amplitude?* In Chapter Three, t h i s relationship i s examined for those fluctuations i n economic a c t i v i t y which f a l l within the range of "business cycle" frequencies. 5 F i n a l l y , we examine the s e n s i t i v i t y r e l a t i o n s h i p of each regional economy to the rest of the Canadian economy and to the United States economy. In Chapter Four, regions are c l a s s i f i e d according to the type of s e n s i t i v i t y which characterizes the economic i n t e r r e l a t i o n s h i p between each region and the rest of the North American economy; t h i s involves not only interregional but also regional-USA comparisons of correspondence, leads/lags and amplitude. Regression and cross-spectral analysis are used to make the comparisons, changes i n regional s e n s i t i v i t y over time are examined i n Chapter Five. Since s e n s i t i v i t y i s defined by the strength (correspondence), timing (lead/lag) and nature (amplitude) of an intereconomy relationship, i t therefore also implies a causal r e l a t i o n s h i p between economies; the problem of distinguishing economic "causality" from economic "feedback" becomes central to the analysis. To a great extent we r e l y upon differences i n timing as indicating - • c a u s a l i t y but of course such inferences are always subject to suspicion. Two economies that are correspondent, or correlated, may both be 3 r e a c t i n g t o a t h i r d economy and i n f a c t have no economic l i n k a g e s w i t h each other. In t h i s case t h e i r r e l a t i o n s h i p with each other would r e f l e c t n e i t h e r c a u s a l i t y nor feedback and any l e a d s or l a g s between them would then be i r r e l e v a n t . Moreover, even i t t h e r e are s t r o n g l i n k a g e s between two economies the l e a d i n g economy need not be " c a u s i n g " the l a g g i n g economy - a l i n k a g e i n the e x p e c t a t i o n s of f u t u r e events, f o r example, co u l d imply the o p p o s i t e c o n c l u s i o n : one p o s s i b i l i t y i s t h a t an expected a g r i c u l t u r a l boom on the P r a i r i e s c o u l d i n c r e a s e farmers' demands upon the c a p i t a l goods i n d u s t r i e s of O n t a r i o i n advance o f t h e i r a c t u a l i n c r e a s e i n income. These are not new problems and they und e r l y most econometric work - but n e v e r t h e l e s s the a b i l i t y o f econometricians t o d e t e c t c a u s a l r e l a t i o n s should never be o v e r s t a t e d . Thus, i n the a n a l y s i s t h a t f o l l o w s we can o n l y assume t h a t i n g e n e r a l l e a d s and l a g s between correspondent economies are h i n t i n g a t a c a u s a l mechanism. Wherever p o s s i b l e we i n t e r p r e t the evidence so as t o account f o r the d i f f e r e n c e s i n r e g i o n a l c y c l i c a l behaviour, o r the change i n such behaviour over time. In each chapter the accumulated evidence i s summarized and, f i n a l l y , i n Chapter S i x we d i s c u s s the i m p l i c a t i o n s of the evidence f o r the a n a l y s i s of n a t i o n a l c y c l e s and s e n s i t i v i t y . We ask: are the dimensions of r e g i o n a l d i s p a r i t y i n c y c l i c a l behaviour so l a r g e t h a t n a t i o n a l c y c l e s f a i l t o r e p r e s e n t the p a t t e r n of economic a c t i v i t y i n any of the component 4 r e g i o n s ? In other words, i s r e g i o n a l c y c l i c a l behaviour such t h a t t o g a i n i n s i g h t about economic a c t i v i t y i n Canada we must analyze each r e g i o n , p l a c i n g l i t t l e r e l i a n c e upon n a t i o n a l aggregates. A l s o , does the evidence suggest a c o n s i s t e n t p a t t e r n of r e g i o n a l d i s p a r i t y i n c y c l i c a l behaviour? Furthermore, what i s the " r e g i o n a l mechanism" by which United S t a t e s c y c l e s are t r a n s m i t t e d i n t o Canada and has t h i s mechanism changed over time? Can changes over time i n Canadian c y c l i c a l s e n s i t i v i t y be e x p l a i n e d by changes i n the s e n s i t i v i t y r e l a t i o n s h i p between regions or between r e g i o n s and the U n i t e d S t a t e s ? The t h r u s t of t h i s i n v e s t i g a t i o n i s towards making g e n e r a l i z a t i o n s about r e g i o n a l c y c l i c a l behaviour i n Canada. Con c l u s i o n s are formulated i n terms of the "dimensions of r e g i o n a l d i s p a r i t i e s " or "changes i n d i s p a r i t i e s over time" or "the r a n k i n g of r e g i o n s " , e t c . I d e a l l y , a r e g i o n a l d i s p a r i t y i n a p a r t i c u l a r i n d i c a t o r would be i d e n t i f i e d u s i n g a process of aggregation from s m a l l "subregions" i n t o l a r g e r aggregates: as long as t h e components behave s i m i l a r l y , the a g g r e g a t i o n would cont i n u e . I f , say, p r o v i n c e s were aggregated i n t h i s way, the d i s p a r i t y would be measured at t h a t p o i n t where the p r o v i n c e s had been a l l o c a t e d i n t o " s i m i l a r - b e h a v i n g " r e g i o n s . Our p r a c t i c a l procedure i s t o always use the same f i v e r e g i o n s and t o i d e n t i f y d i s p a r i t i e s by comparing each r e g i o n t o e i t h e r a r e g i o n a l average o r to Canada as a whole. To g e n e r a l i z e 5 c o n c l u s i o n s about a r e g i o n using a l l the t i m e - s e r i e s , we seek a consensus o f evidence over a l l the a v a i l a b l e i n d i c a t o r s . S i n c e a l a c k of such rec u r r e n c e can l e a d to ambiguous evidence, we c o n t i n u a l l y examine the robustness of our r e s u l t s by a p p l y i n g d i f f e r e n t but (we hope) supporting methods to the same or r e l a t e d q u e s t i o n s . F o r example, both the e p i s o d i c and s p e c t r a l methods d e s c r i b e the c y c l i c a l behaviour i n a t i m e - s e r i e s and both the " e l a s t i c i t y " (regression) approach and c r o s s - s p e c t r a l a n a l y s i s compare the c y c l i c a l behaviour i n the t i m e - s e r i e s of two economies. Moreover, other r e g i o n a l and n a t i o n a l data ( u s u a l l y annual) t o g e t h e r w i t h secondary source m a t e r i a l s are employed, where p o s s i b l e , t o f u r t h e r support and c l a r i f y the r e s u l t s . 1-2 The H i s t o r i c a l Problem The areas of i n v e s t i g a t i o n o u t l i n e d above are d i r e c t e d a t two c h a r a c t e r i s t i c s of Canadian development w i t h which Canadian economists have l o n g been concerned. The f i r s t c h a r a c t e r i s t i c i s t h a t a t l e a s t u n t i l World War I t h e r e e x i s t e d a very s t r o n g tendency f o r d i f f e r e n t r e g i o n s t o play c e n t r a l r o l e s as l o c a t i o n s f o r the p r o d u c t i o n of n a t i o n a l l y -important export goods a t d i f f e r e n t p e r i o d s of time. This suggests a c a u s a l r e l a t i o n s h i p between f o r e i g n demand, r e g i o n a l supply and n a t i o n a l growth; i t f u r t h e r suggests an economic s e n s i t i v i t y between f o r e i g n , r e g i o n a l and n a t i o n a l 6 economies which i s o f t e n analyzed w i t h i n the framework of the s t a p l e theory of Canadian economic growth.* To e l a b o r a t e , i n the s i m p l e s t form of the s t a p l e theory "... the fundamental assumption ... i s t h a t s t a p l e exports a r e the l e a d i n g s e c t o r of the economy and s e t t h e pace f o r economic growth." 7 Although the r e l a t i o n s h i p between the growth of s t a p l e exports and the growth of per c a p i t a income i s undoubtedly complex, n e v e r t h e l e s s an i n t e r p r e t a t i o n of Canadian economic growth which i s based upon the impact of the production of s t a p l e exports suggests t h a t changes i n income would be c l o s e l y r e l a t e d t o changes i n the value of s t a p l e p r o d u c t i o n . T h i s i m p l i e s both s h o r t and long run s e n s i t i v i t y of the Canadian to f o r e i g n economies v i a the export s e c t o r . Caves and Holton (19 59) argue p e r s u a s i v e l y t h a t the s t a p l e s framework has s h o r t - r u n i m p l i c a t i o n s due i n l a r g e p a r t t o the p o s s i b l e l i n k between exports and r e l a t e d domestic investment (and businessmen's e x p e c t a t i o n s ) ; 8 a l s o , s p e c i a l i z a t i o n of p r o d u c t i o n on s t a p l e e xports i m p l i e s a dependence on f o r e i g n markets f o r imports of manufactured consumer durables and c a p i t a l goods. Thus, i n s t a p l e -producing economies the s h o r t - r u n income m u l t i p l i e r (and a c c e l e r a t o r ) r e l a t i o n s h i p s can be s t r o n g l y i n f l u e n c e d by s h o r t - r u n movements i n the balance of t r a d e . Throughout Canadian h i s t o r y t h e r e has been a tendency f o r the p r o d u c t i o n of s t a p l e exports t o be l o c a l i z e d i n p a r t i c u l a r r e g i o n s ; thus, t o e x p l a i n Canadian economic 7 growth the staple framework requires an important regional dimension - as MacKintosh (1939) and more recently Scott (1965) have pointed out. Since proponents (for example, Watkins (1963)) of the staple view stress the importance of linkages between staple exports and the t o t a l economy, they are therefore c e n t r a l l y concerned with the importance of regional linkages that can widen and transmit the impact of increased staple production from a region to the national economy. The lo c a t i o n of natural resources and such factors as t a r i f f protection have implanted i n Canada's regions a d i v e r s i t y of economic structures which can allow through backward and forward linkages the transmission of economic growth and fluctuations. That i s , the impact of changes i n foreign demand upon "outlying" staple-producing regions (such as the P r a i r i e region during the years of the "Wheat Economy") can be transmitted to the (tariff-protected) manufacturing sectors of Central Canada, p a r t i c u l a r l y Southern Ontario - indeed, t h i s type of regional transmission was one of the goals of the National Policy, although i t s success i n t h i s regard has never been established. Moreover, i n t e r r e g i o n a l transmission of demand fo r manufactured goods and derived demands f o r factors (labour and capital) could r e s u l t from either short-run or long-run changes i n the foreign demand for staple exports. Thus, the staple approach emphasizes not only the impact of changes i n foreign demand (and/or regional supply) upon the 8 3 t a p l e - p r o d u c i n g r e g i o n but a l s o the t r a n s m i t t e d impact upon the n a t i o n a l economy. However, s i n c e the F i r s t World War t h e r e have been c o n s i d e r a b l e although gradual changes i n r e g i o n a l economic s t r u c t u r e so t h a t we can l e g i t i m a t e l y b r i n g i n t o q u e s t i o n t h i s view of the r o l e of Canadian r e g i o n s i n the mechanism by which the Canadian economy i s s e n s i t i v e t o f o r e i g n f l u c t u a t i o n s . During the i n t e r w a r p e r i o d , the determinants of r e g i o n a l - n a t i o n a l economic r e l a t i o n s h i p s i n Canada underwent s i g n i f i c a n t changes due to s h i f t s i n the balance of power between the f e d e r a l and p r o v i n c i a l governments, r e o r g a n i z a t i o n of the i n t e r n a t i o n a l economy as a r e s u l t of the Great War, s h i f t s i n r e l a t i v e export p r i c e s , improved t r a n s p o r t a t i o n systems and t e c h n o l o g i c a l i n n o v a t i o n s p a r t i c u l a r l y i n resource-based i n d u s t r i e s . 9 A l s o , s i n c e 1919 the Canadian economy has become more d i v e r s e i n terms of i n d u s t r i a l s t r u c t u r e and, furthermore, the c r u c i a l export s e c t o r has experienced changes i n both o r i e n t a t i o n and composition. Trade with t h e United States has i n c r e a s e d i n importance w h i l e , w i t h i n t o t a l e x p o r t s , a g r i c u l t u r a l products have become l e s s important and exports of f o r e s t r y products, m e t a l l i c m i n e r a l s , n o n - m e t a l l i c m i n e r a l f u e l s and motor v e h i c l e s have become more important. Thus, the concept of a few s t a p l e goods dominating the p a t t e r n of n a t i o n a l growth may have become l e s s r e l e v a n t . But how much so? What i s the modern r e g i o n a l - n a t i o n a l s e n s i t i v i t y 9 r e l a t i o n s h i p , how has i t evolved over the course of these structural changes and does i t c a l l for a new, updated view of dynamic behaviour i n the Canadian economy? The economic indicators alluded to i n the previous section can shed much l i g h t upon the nature of interregional transmission. For example, fluctuations i n bank debits r e f l e c t changes i n general economic a c t i v i t y and i n the general demand for goods and services; the employment index approximates changes i n r e a l output and hints at interregional labour migration; construction contracts suggest c a p i t a l flows; f r e i g h t carloadings also approximate changes i n r e a l output and the CPI indicates changes in prices. In addition we ask: i n terms of c y c l i c a l s e n s i t i v i t y what are the regional implications of the s t r u c t u r a l changes i n the national economy? Modern treatments of fluctuations i n the national economy over the period 1919-1973 suggest that i n many ways Canadian c y c l i c a l behaviour i s but a function of corresponding behaviour i n the United States; also, when the postwar period i s compared with the interwar period a decline can be observed i n the s e n s i t i v i t y of the Canadian economy to fluctuations i n the general economic a c t i v i t y of the United S t a t e s . 1 0 What, then, i s the new r o l e of Canadian regions i n the mechanism by which United States fluctuations are transmitted into Canada? Has the decline i n Canadian s e n s i t i v i t y , which has been attributed to such factors as the increased importance of government 10 expenditures and the decreased importance of exports i n GNE, 1 1 o c c u r r e d with s i m i l a r impact i n the v a r i o u s regions o r , a l t e r n a t i v e l y , can the decreased n a t i o n a l s e n s i t i v i t y be e x p l a i n e d by p a r t i c u l a r d e c l i n e s i n s p e c i f i c r e g i o n s ? The second c h a r a c t e r i s t i c of development concerns the p e r s i s t e n c e s i n c e the F i r s t World War of r e g i o n a l d i s p a r i t i e s i n per c a p i t a income and output, and r a t e s of unemployment. Much r e s e a r c h has been d i r e c t e d a t measuring, e x p l a i n i n g and monitoring these d i s p a r i t i e s . 1 2 The s t u d i e s attempt i n t e r r e g i o n a l or r e g i o n a l - n a t i o n a l comparisons of these aspects of t h e (short and long run) behaviour of Canadian r e g i o n a l economies. T h i s study w i l l i n c r e a s e our understanding of r e g i o n a l d i s p a r i t i e s i n Canada by a n a l y s i n g two other a s p e c t s of r e g i o n a l economic behaviour; namely, r e g i o n a l c y c l e s and r e g i o n a l c y c l i c a l s e n s i t i v i t y t o the r e s t of the North American economy. Thus, our focus i s upon movements i n the r e g i o n a l economies ; - as r e f l e c t e d by economic i n d i c a t o r s - and not upon r e l a t i v e l e v e l s . In examining each of the above que s t i o n s we make (a) i n t e r r e g i o n a l comparisons of c y c l i c a l behaviour w i t h i n e i t h e r the i n t e r w a r or postwar p e r i o d s , and (b) i n t e r t e m p o r a l comparisons o f behaviour f o r a g i v e n r e g i o n . Although r e g i o n a l s t r u c t u r a l change has o c c u r r e d w i t h i n the subperiods, we n e v e r t h e l e s s c l a i m t h a t i t i s meaningful t o compare r e g i o n a l c y c l i c a l behaviour between subperiods; we a r e i n t e r e s t e d i n e s t a b l i s h i n g the g e n e r a l o r s e c u l a r 11 changes i n regional behaviour, and the "average" d i s p a r i t i e s i n regional behaviour which prevail over f a i r l y lengthy periods of time (21 years i n the interwar period 1919-1939, 15 years i n the "postwar I 1 period 1946-1959 and 14 years in the postwar II period 1960-1973) . 1.3 An Economic Region Defined I t i s necessary to provide some precision to the d e f i n i t i o n of an economic region used in t h i s study. The l i t e r a t u r e on t h i s topic i s vast but an economic region i s best defined by the p a r t i c u l a r problem at hand. Two types of regional d e f i n i t i o n s could be relevant to t h i s study. The f i r s t i s based upon the concept of homogeneity. I f a given structural c h a r a c t e r i s t i c has greater s i m i l a r i t y within a certain geographic area than outside the area, then the area may be considered an economic region. With t h i s type of d e f i n i t i o n the selected geographic area i s generally a p o l i t i c a l l y - d e f i n e d area (for which economic data might be available) and the selection of the s t r u c t u r a l c h a r a c t e r i s t i c i s quite a r b i t r a r y (to s u i t the purpose at hand). The second type of d e f i n i t i o n i s based upon the concept of f u n c t i o n a l i t y or behaviour. If a given indicator of economic a c t i v i t y (selected to s u i t the purpose at hand) behaves d i f f e r e n t l y i n one geographic area as opposed to another, then the two areas might be considered d i s t i n c t regional economies. 12 Since t h i s study i s concerned with d e s c r i b i n g economic behaviour, the b e h a v i o u r a l d e f i n i t i o n i s adopted and t h i s r a i s e s s e v e r a l i n t e r e s t i n g p o i n t s . The v a r i o u s aspects of c y c l i c a l behaviour which are t o be compared i n t e r r e g i o n a l l y i n t h i s study are the same aspects of behaviour which d e f i n e the r e g i o n s . Thus, i f f o r the p r e s e l e c t e d ( p o l i t i c a l l y -defined) f i v e Canadian r e g i o n s i t i s hypothesized t h a t there e x i s t s i g n i f i c a n t d i s p a r i t i e s i n c y c l i c a l behaviour, then the n u l l h y p o t h e s i s must be t h a t t h e r e i s a c t u a l l y o n l y one l a r g e (national) r e g i o n . However, i f s i g n i f i c a n t d i s p a r i t i e s are uncovered, i t does not f o l l o w by the b e h a v i o u r a l d e f i n i t i o n the p r e s e l e c t e d r e g i o n s are a c t u a l l y economic r e g i o n s . F u r t h e r geographic d i s a g g r e g a t i o n of the p r e s e l e c t e d r e g i o n s c o u l d prove t h a t w i t h the same b e h a v i o u r a l i n d i c a t o r the d i s p a r i t i e s between the s m a l l e r r e g i o n s a r e even more pronounced. A.s mentioned above, the c o r r e c t approach would be t o s t a r t w i t h the s m a l l e s t geographic area f o r which the i n d i c a t o r i s a v a i l a b l e and then t o enlarge the areas u n t i l s i g n i f i c a n t i n t e r r e g i o n a l d i s p a r i t i e s occur. However, t h i s i s simply too g r e a t a chore t o warrant the e f f o r t here, although i t c o u l d be argued t h a t such a technique should be a p p l i e d t o the P r a i r i e and Maritime provinces t o determine whether they have been (geo g r a p h i c a l l y ) aggregated too f a r and t o O n t a r i o and Quebec t o determine whether they have been (g e o g r a p h i c a l l y ) aggregated enough. T h i s would d e f i n i t e l y 13 be an area for further research i f the empirical investigation of t h i s study proves f r u i t f u l . F i n a l l y , the use ot the behavioural d e f i n i t i o n points to a problem area i n the analysi s which follows i n l a t e r chapters. Without a st r u c t u r a l d e f i n i t i o n of an economy the l i n k between the observed regional behaviour and the underlying economic structure can only be assumed. If the behaviour of the region i s attributed to i t s economic structure then conclusions concerning the determinants of the behaviour may be i n error to the extent that the regional structure i s geographically heterogeneous, f o r i n t h i s case the st r u c t u r a l data are averaged over the heterogeneous subregions and the l i n k between economic structure and economic behaviour becomes more tenuous. Again, t h i s i s a p a r t i c u l a r l y relevant concern i n analysing the P r a i r i e s because i n Alberta the importance of agriculture has diminished at a greater pace than i n Saskatchewan or Manitoba. There i s also a source of error when Prince Edward Island i s included with Nova Scotia and New Brunswick, or when Northern Ontario and Quebec are combined with the Southern portions of the two provinces. On the other hand, putting the Yukon and Northwest T e r r i t o r i e s i n with B r i t i s h Columbia probably does not create much d i s t o r t i o n , given the importance of mining throughout the region. 14 FOOTNOTES The regions are B.C., the P r a i r i e s , Ontario, Quebec and the Maritimes. Newfoundland i s not included i n the post-World War II period, and the Yukon and Northwest T e r r i -t o r i e s are included with B r i t i s h Columbia. The data a r e discussed i n Section 2, Chapter Two-A c l a s s i c example of the NBER method i s Burns and Mi t c h e l l [ 1947], "Correspondence" i s the strength of the relat i o n s h i p as measured by coherence and cor r e l a t i o n c o e f f i c i e n t s . Cross relative-amplitude compares the amplitudes of two time series a f t e r accounting f o r differences i n units or absolute magnitude. Business cycles are defined i n Section 2.2, Chapter Two. For a generally accepted statement of t h i s theory, see Watkins [ 1 963 ]. Watkins (196 3). 8 Caves and Holton (1959, Chapter Three). 15 See the r e p o r t of The Royal Commission on D o m i n i o n - P r o v i n c i a l R e l a t i o n s [1940, pg. 125]. The l i t e r a t u r e on Canadian-United S t a t e s c y c l i c a l s e n s i t i v i t y i s reviewed i n S e c t i o n 5.1 of Chapter F i v e . For example, see Rosenbluth [1958], Green [1971] and Mclnnis [1968] analyse r e g i o n a l d i s p a r i t i e s i n per c a p i t a income. Anderson [1966] and Chernick [1966] analyse i n t e r n a l m i g r a t i o n p a t t e r n s . T h i r s k [1972] deals w i t h r e g i o n a l i n f l a t i o n and unemployment, while Paraskeva-poulos [1974] d i s c u s s e s r e g i o n a l manufacturing output over time. S e n s i t i v i t y a n a l y s i s has been done by Swan [1972] on the r e g i o n a l - n a t i o n a l demand f o r labour and by Denton [1966] on the r e g i o n a l response t o n a t i o n a l unemployment l e v e l s . 16 CHAPTER TWO PATTERNS AND DISPARITIES IN REGIONAL CYCLES 2.1 Introduction Throughout history the regional economies of Canada have displayed d i s t i n c t dynamic economic c h a r a c t e r i s t i c s . Canadian economic historians have examined the d i s p a r i t i e s i n many •'long-run" aspects of regional economic development, but l i t t l e p r e cision has ever been given to d i s p a r i t i e s i n regional c y c l i c a l behaviour. In Chapters Two and Three regional cycles are examined i n order to establish the dimensions of regional differences i n several aspects of c y c l i c a l behaviour. This chapter focuses upon d i s p a r i t i e s i n the timing and average duration of regional cycles, while Chapter Three i s directed at d i s p a r i t i e s i n amplitude. The f i r s t step i s to i d e n t i f y cycles in the regional economies over the period 1919-1973. In the Canadian and United States economies a variety of c y c l i c a l frequencies has been detected; the presence of a "business cycle" of 2-5 year period i s the most generally accepted. 4 Although less conclusive, there i s evidence of 12-20 year "long-swings", espe c i a l l y i n pre-1914 time-series, and 15-19 month "sub-cycles" i n the post-1945 period. 2 In t h i s study, the shorter cycles - business-cycles, subcycles and seasonal cycles - are examined i n Canadian regional time series data. Two ways of describing the c y c l i c a l behaviour i n a time series are by the "episodic" approach and by spectral analysis. The former method i s usually associated with the 17 National Bureau of Economic Research and involves marking o f f each c y c l i c a l episode i n a seasonally-adjusted time series by i d e n t i f y i n g i t s turning points (peak, trough, e t c . ) . Spectral analysis, on the other hand, estimates the contribution of each of a wide range of c y c l i c a l frequency bands to the explanation of the t o t a l variance i n the s e r i e s . 3 Both methods can provide information on the timing and average duration of important cycles. Section 2.2 outlines these methods and includes a short description of avai l a b l e data. Appendix 2A elaborates upon the technical d e t a i l of the methods and Appendix 2D elaborates upon the data and data manipulations. In using the spectral method, a "spectrum" i s estimated for each regional time series (Section 2.3). These spectra w i l l hopefully shed l i g h t upon several i n t e r e s t i n g questions. F i r s t , are the regional spectra anything d i f f e r e n t from "white noise"; that i s , can we say that any frequency bands are important r e l a t i v e to others i n explaining the t o t a l variance in the series? Second, are c y c l i c a l frequencies i n the business cycle, subcycle and seasonal range of equal r e l a t i v e importance i n the various regions? F i n a l l y , does t h i s r e l a t i v e importance change over the interwar (1919-1940), postwar I (1945-1959) and postwar II (1960-1973) subperiods? In the episodic description of c y c l i c a l behaviour, the average duration of expansions i s the average i n t e r v a l from 18 i d e n t i f i e d trough to i d e n t i f i e d peak, while the average duration of contractions i s the average i n t e r v a l from peak to trough and the average duration of complete episodes i s measured from either peak-to-peak or trough-to-trough. From annals of regional "business cycle" turning points recorded i n Appendix 2B, these measures are calculated from detrended regional time series over each of the three above-mentioned subperiods (Section 2.3). The estimates of average duration are then compared with the spectral estimates of " r e l a t i v e l y important frequencies" (Section 2.3). Here we ask: are the two approaches mutually supportive i n describing s i m i l a r business cycle p e r i o d i c i t y ? Then, using the turning point data s p e c i f i c episodes can be compared between regions. We ask: to what extent have Canadian regions experienced the same c y c l i c a l episodes? Furthermore, do r a t i o s of the average duration of expansions to contractions ("E/C" ratios) suggest that, on average, fluctuations observed in regional economies indicate "stationary" time s e r i e s , that i s , detrended series i n which variance and autocovariance are independent of time? Also, i f regional E/C r a t i o s are calculated using only those episodes which are also i d e n t i f i e d i n the Canadian series, they provide useful information about the nature of regional leads and lags at turning points. F i n a l l y , Section 2.4 i s concerned with the timing of regional fluctuations. I f , for a given time-series 19 indicator, each regional series i s compared to the national, s e r i e s , then both the above-mentioned approaches can determine which, i f any, regions are consistently "leading" or "lagging" the national economy. This evidence i s used i n l a t e r analysis of regional c y c l i c a l s e n s i t i v i t y but i s also useful here in t e s t i n g for patterns in c y c l i c a l behaviour. For example, with the episodic approach one can examine "uniformity" - measured for a given time-series i n a p a r t i c u l a r subperiod as the variance over a l l turning points i n a region* s leads or lags - and " c l u s t e r i n g " - measured from a p a r t i c u l a r turning point i n a national time-series indicator by the variance i n regional leads and lags. An increase over time i n a region's uniformity suggests the emergence of a more stable lead/lag r e l a t i o n s h i p between the region and the national economy. This, in turn, may indicate increased s t a b i l i t y i n the mechanisms by which fluctuations are transmitted either to or from the region. When the c l u s t e r i n g measures are averaged over a l l the episodes i n a subperiod, the average indicates the extent to which fluctuations i n the national economy occur at the same time i n the various regions. An increase in clustering over time might then r e f l e c t a closer regional integration of the Canadian economy. 2.2 Methods of Cycle I d e n t i f i c a t i o n 20 There are two basic problems encountered in i d e n t i f y i n g cycles. One i s due to aggregation and the other to decomposition: a) Aggregation An "economic flu c t u a t i o n " may be defined i n terms of a single aggregate, such as Gross National Product or a l t e r n a t i v e l y i n terms of "general economic a c t i v i t y " which implies a broadly-based movement in economic variables that cannot be described consistently over time by any single economic i n d i c a t o r . With the l a t t e r d e f i n i t i o n , the one adopted here, an "aggregation" problem arises due to the d i f f i c u l t y i n drawing conclusions about the c y c l i c a l behaviour of the economy as a whole from the c y c l i c a l behaviour of a va r i e t y of economic i n d i c a t o r s . One approach to the problem i s to base conclusions upon either (a) a reference cycle i n "general business a c t i v i t y " , constructed from a relevant set of " s p e c i f i c " cycles i n in d i v i d u a l indicators, each indicator having equal weight, or (b) recurrence of si m i l a r r e s u l t s over a set of s p e c i f i c cycles. Whether or not a reference cycle i s actually constructed depends upon the number of indicators which are available over a s u f f i c i e n t l y long time period i n monthly or quarterly form. 4 In general, episodic examinations of business cycles have employed reference cycles (using Canadian data: Chambers [ 1958a, 1964], Hay [1966 ], White [ 1967 ], Waterman [1973] and Beckett [1961]), while long-swing tests and 2 1 spectral analysis of business cycles have used the "recurrence of s i m i l a r r e s u l t s " c r i t e r i o n (on Canadian business cycles: Rosenbluth [1957, 1973], on Canadian long swings: Harkness [1969] and Daly [1965], and on B.C. business cycles: Blain, Paterson and Rae [1974]). In t h i s study the s c a r c i t y of r e a d i l y available monthly or quarterly regional indicators dictates the use of the l a t t e r c r i t e r i o n ; as a r e s u l t , the p o s s i b i l i t i e s of ambiguous evidence on regional "general business a c t i v i t y " are greater than i f there were s u f f i c i e n t data to construct a reference cycle. b) Decomposition Since an economic time-series generally includes four basic dynamic components - seasonality, trend, c y c l i c a l fluctuations and i r r e g u l a r fluctuations - a problem arises i n decomposing the fluctuating time-series i n t o i t s component parts. Seasonality and trend can be estimated and thus removed from the series but the d i s t i n c t i o n between c y c l i c a l and i r r e g u l a r components remains a r b i t r a r y ; that i s , fluctuations which recur within a given (arbitrary) range of p e r i o d i c i t y are considered c y c l i c a l . Spectral analysis assumes that a time series i s composed of cycles at a wide range of frequency bands which resemble regular, wave-like, trigonometric functions with random amplitude at each frequency. The amplitudes are estimated by estimating simultaneously the contribution of each frequency band to 22 the explanation of the t o t a l variance i n the time series. If the contribution of a given band of frequencies can be considered "important" or s i g n i f i c a n t r e l a t i v e to the contributions of other frequency bands, then t h i s band of frequencies may be considered "an important cycle". Furthermore, an observed fluctuation of a period which f a l l s within the average period defined by t h i s band may be considered a "regular" or c y c l i c a l f l u c t u a t i o n , while fluctuations ot a period outside the band may be considered " i r r e g u l a r " fluctuations. In the episodic approach the average duration of (business) cycles i s estimated as the average elapsed time between i d e n t i f i e d turning points. The c r i t e r i a used to i d e n t i f y the turning points (see Appendix 2A) i n e f f e c t d i s t i n g u i s h regular (cyclical) from i r r e g u l a r fluctuations; f o r example, c y c l i c a l peaks must i n general be at l e a s t two years apart (to distinguish business cycles from subcycles) but exceptions must be allowed - such as the episode of 1920-1921. Thus, the d i s t i n c t i o n can be ambiguous since with the episodic method there i s no easy way by which the contribution of various c y c l i c a l frequencies to t o t a l variance can accurately be measured. As a r e s u l t , spectral analysis i s conceptually a preferable method for dealing with the decomposition problem, although for p r a c t i c a l reasons i t i s useful to compare the spectral estimates of "important" frequencies with the average durations estimated 23 with, the episodic approach. One reason i s that with spectral analysis there i s an estimation problem of " i n t e r -frequency leakage" (discussed i n Appendix A) that can make i t d i f f i c u l t to sort out the contributions of the various frequency bands to t o t a l variance. Also, spectral analysis i s data-intensive r e l a t i v e to the episodic technique i n that with the former technique the length of a time-series constrains the range of p e r i o d i c i t i e s which can be examined with any degree of accuracy. For example, i n analysing the business cycle i t i s only with the episodic method that the 1945-1973 postwar period can be subdivided i n t o two postwar periods (1945-1959 and 1960-1973); t h i s approach enables more refined analysis of time patterns i n regional c y c l i c a l behaviour. As mentioned, seasonality and trend are relevant to the decomposition problem. I t i s important i n sp e c t r a l analysis to f i r s t "detrend" the time-series so as to reduce the problem of interfrequency leakage and to improve the approximation of the series to the " s t a t i o n a r i t y " condition - the condition that mean, variance and autocovariance are independent of time. The detrending methods adopted i n this study, harmonic regression and growth rate transformation, are further discussed i n the technical appendix. Since the contribution to the explanation of t o t a l variance i s estimated f o r a l l frequency bands simultaneously, preliminary seasonal-adjustment of the time-series i s not 24 e s s e n t i a l , although leakage from the annual to other frequencies can create a problem i n interpreting the spectrum. With the episodic method the data are detrended and seasonally-adjusted, since both trend and seasonality can effect the i d e n t i f i c a t i o n of business cycle turning points. Furthermore, by comparing the lengths of expansions to contractions i n detrended series, one can examine the extent to which economic fluctuations do not follow regular, wave-like patterns. This s t a t i s t i c i s c r u c i a l to interpreting the spectra since the l e s s a flu c t u a t i o n i s wave-like, the l e s s l i k e l y w i l l a peak occur i n a spectrum. The timing of c y c l i c a l episodes i s also a part of i d e n t i f y i n g cycles. In l a t e r chapters the timing of regional cycles r e l a t i v e to national, United States or Rest-of-Canada (the nation minus a pa r t i c u l a r region) cycles becomes an i n t e g r a l part of the explanation of c y c l i c a l s e n s i t i v i t y and inter-economy causal r e l a t i o n s h i p s . However, i n t h i s chapter the timing of national cycles i s merely a base from which interregional and intertemporal comparisons can be made i n order to determine patterns i n regional c y c l i c a l behaviour. Estimating f o r each region the regional-national cross-spectrum for a given indicator produces an estimate of the phase differences (in radians) between regions at different c y c l i c a l frequencies as compared with the national cycle. When transformed to the time domain, the estimate of phase 25 measures the average l e a d / l a g between two economies at each frequency, and enables determination of the t i m e - o r d e r i n g of r e g i o n a l business c y c l e s . 5 The i n t e r t e m p o r a l p a t t e r n of r e g i o n a l t i m e - o r d e r i n g can then be examined by e s t i m a t i n g the phase r e l a t i o n s h i p s by subperiods (1919-1940, 1945-1973). The e p i s o d i c approach pro v i d e s a d d i t i o n a l , s i m i l a r i n f o r m a t i o n and a l s o allows more d e t a i l e d s u b p e r i o d a n a l y s i s (1945-1973 can be broken i n t o 1945-1959, 1960-1973). This method a l s o uses the n a t i o n a l i n d i c a t o r as a base; lea d s or l a g s between the r e g i o n a l and n a t i o n a l t u r n i n g p o i n t s are averaged over the subperiod to o b t a i n a comparable s t a t i s t i c t o phase - although the s t a t i s t i c s are not s t r i c t l y comparable s i n c e the t u r n i n g p o i n t averages are c a l c u l a t e d a t o n l y two p o i n t s i n each episode, the peak and the trough, w h i l e e s t i m a t i n g phase i n v o l v e s every p o i n t i n every episode. 2.2.1 Regional Time S e r i e s There are a l i m i t e d number of r e g i o n a l monthly or q u a r t e r l y economic i n d i c a t o r s a v a i l a b l e over a s u f f i c i e n t l y l o n g p e r i o d t o permit the i d e n t i f i c a t i o n of c y c l i c a l behaviour. Four monthly s e r i e s e x i s t from th e e a r l y 1920s; a l l are a v a i l a b l e from at l e a s t 1921 or can be extended backwards t o 1919 or 1921 by o t h e r r e l a t e d s e r i e s whose c y c l i c a l behaviour one can assume t o be approximately s i m i l a r to the extended i n d i c a t o r . The extended i n d i c a t o r s 26 are an index of employment (1921-1973), the value of construction contracts (1919-1972), f r e i g h t carloadings (1921-1973) and bank debits (1919-1940, 1945-1973).* Also available are the value of r e t a i l trade (1935-1966), commercial f a i l u r e s (1919-1973), dwelling s t a r t s (1947-1973) and the consumer price index (1949-1973).7 A f u l l d escription of sources, coverage, content and methods of extension and l i n k i n g i s i n Appendix D. These indicators cover a wide range of economic a c t i v i t y ; a l l were used by either Chambers, Beckett or Waterman i n the construction of t h e i r reference cycles of Canadian "general business a c t i v i t y " . 8 Chambers and Beckett point out that the construction contract series i s often a leading indicator of reference cycle turning p o i n t s . 9 Also, Beckett finds that the employment index, f r e i g h t carloadings and bank debits are, i n general, coincident with the reference cycle. 4° Several points about the time-series should be noted. Bank debits are to deposit accounts (excluding inter-bank transfers) and t h i s series along with f r e i g h t carloadings provide a broad measure of regional economic a c t i v i t y . Bank debits should be our best monthly in d i c a t o r of the impact of fluctuations i n agriculture upon the P r a i r i e economy (and also the extent to which agriculture fluctuations are transmitted to other regions). The employment index, on the other hand, i s from the establishment survey - which 27 excludes agriculture - and i t i s therefore a more s p e c i f i c indicator of output fluctuations i n the nonfarm economy. Also, we can only assume that fluctuations i n the consumer price index represent fluctuations i n a more complete index of prices such as the GNE deflator, which includes the prices of exports and c a p i t a l goods. F i n a l l y , we might note that the construction contracts series has a wide coverage i n that i t includes both r e s i d e n t i a l and nonresidential contracts. The construction contracts, bank debits and especially the commercial f a i l u r e s series have very strong i r r e g u l a r components; with monthly regional data t h i s i s anticipated since the variance in such data i s generally large when the economy i s small. This problem renders the commercial f a i l u r e s series useless for cycle i d e n t i f i c a t i o n at the regional l e v e l even though i t may be a r e l i a b l e indicator at the national l e v e l . 1 1 I t i s , however, possible to i d e n t i f y cycles i n construction contracts and bank debits but only a f t e r applying a 13-term moving average to the seasonally-adjusted, detrended series. If the r a t i o of the i r r e g u l a r component to the c y c l i c a l (smoothed) component i s calculated, the r a t i o s are highest f o r the construction contracts and bank debits s e r i e s . 1 2 The r a t i o s f o r each indi c a t o r are i n Table 8, Appendix C. 2.3 Important C y c l i c a l Frequency Bands 28 Evidence i s now presented on the contribution of c y c l i c a l frequency bands to the explanation of t o t a l variance i n the regional time series. Since i t i s expected that important cycles are to be found i n the frequency ranges corresponding to "business cycles", subcycles and seasonality, the evidence on each type of cycle i s presented i n turn. The spectral density function (the "power" spectrum) i s estimated for each regional indicator and the presence of medium to large peaks i n the log of the spectra indicate important cycles at an average p e r i o d i c i t y which corresponds to the p e a k s . T h e o r e t i c a l l y , a test of the hypothesis that p a r t i c u l a r frequencies are important r e l a t i v e to others i n explaining t o t a l variance i s a t e s t against the hypothesis that the series contains nothing but white noise. However, s t a t i s t i c a l s i g n i f i c a n c e tests for such a hypothesis are as yet only crudely developed.** Furthermore, following Granger's [1966] suggestion that the spectrum for an economic variable w i l l t y p i c a l l y be downward sloping as i n Figure 1 (b), the relevant hypothesis to test for determining important cycles becomes one involving comparison of the r e l a t i v e contributions of d i f f e r e n t frequency bands. The type of comparison adopted here i s Hatanaka and Howrey's "two-tailed t e s t " ; i f a r e l a t i v e peak occurs i n the spectrum then i t may be concluded that the frequencies corresponding to the peak are r e l a t i v e l y important i n explaining t o t a l variance.* s However, the 29 Log of Power Spectrum Figure 1 E X A M P t E S OF ESTIMATED S P E C T R A (Detrendea Data) ( a ) ->freq. 7 7 , 2 Granger's"typical shape" I d ) ^ 3 6 */\Z "Large"business cycle peak A (e) ->freq. ->freq. ^ 3 6 n T/12 Medium-absolute "business cycle peak ( f ) ->freq. ' 7 3 6 "/I2 Medium' business cycle peak ->freq. 'Slight" business cycle peak >freq. 30 peaks themselves may be of varying i n t e n s i t y and, thus, four types of peaks are defined; Figures 1(c)-(f) suggest a c r i t e r i o n f or distinguishing varying l e v e l s of c y c l i c a l importance. Spectra with "large", "medium-absolute" or "medium" peaks are interpreted as indicating important (and sign i f i c a n t ) c y c l i c a l frequencies. Also, i f a peak i s centered on the j t h frequency, 51 (where n i s the length of n the time s e r i e s ) , then the peak i s said to l i e i n a wider band defined by the frequencies "CM) and Ithll I n n n other words, since each frequency at which the spectrum i s estimated i s actually a frequency band, a peak encompasses a range of bands; that i s , i t includes more than one frequency. For any frequency the strength of c y c l i c a l contribution can be compared between regions by c a l c u l a t i n g the regional mean and regional standard deviation of estimated regional spectral d e n s i t i e s . The frequencies of i n t e r e s t here are business cycles, subcycles and seasonal variations; since each type of cycle encompasses a range of frequency bands at which the spectral density density function i s estimated, the spectral density estimates are averaged over t h i s range, 0 such that r. i s the average spectral density estimate for reqion i at frequencies within the e range. 1 6 The mean and standard deviation are calculated over the f i v e regions for a given indicator as 31 - e i l e r = r L r • a 5 i = l 1 r 4 i = l To examine the p o s s i b i l i t y that there are regional d i s p a r i t i e s i n the contribution of a given range of frequency (bands) 9 , to the explanation of t o t a l variance i n e _e e a regional time se r i e s , the i \ are compared with r . i f r i - e exceeds r by ° r i n a given series we conclude that i n region i frequency 6 i s a "stronger" cycle than indicated by the regional average. The reverse holds i f ^ exceeds r e by CTr-i Although at least one region must f a l l outside one standard deviation from the mean, by examining a l l the time-series indicators f o r recurrence of similar results we can thus i d e n t i f y d i s p a r i t i e s i n regional c y c l i c a l behaviour. Note that for each indicator t h i s crude comparison i s between each region and an unweighted regional average; comparing a region with Canada would be a comparison with a weighted average - and t h i s type of comparison would be misleading i n capturing the magnitude of regional d i s p a r i t i e s since the larger regions would tend to dominate the Canadian t o t a l . 2.3.1 Seasonal Variation We f i r s t estimate with spectral analysis the contribution of seasonal v a r i a t i o n to the explanation of t o t a l variance i n each regional time series. The annual range i s , i n general, defined by p e r i o d i c i t i e s of 11.5-12.8 months. 32 In every estimated spectral density function the most pronounced peak corresponds to the seasonal v a r i a t i o n ; spectral estimates at t h i s frequency for series which contain very strong seasonality are often of the same order of magnitude as those of the very low frequencies. Moreover, peaks are also evident at higher frequency bands which are harmonics of the seasonal v a r i a t i o n . The spectral estimates reveal a pronounced v a r i a b i l i t y over regions, subperiods and indicators i n terms of the strength of the seasonal component. When the dimensions of regional d i s p a r i t y are examined by cal c u l a t i n g the r. (Table 1 , e Appendix C), the ranking of regions by r varies f o r d i f f e r e n t indicators and subperiods. For example, Ontario has the weakest seasonal component i n employment and postwar bank debits, but i s ranked much higher for interwar bank debits and construction contracts. However, i n terms of " s i g n i f i c a n t " deviations of regional from average regional behaviour, some generalizations can be made. In Table 2 . 1 the regions are ranked using the comparison procedure outlined i n the previous section. For every indicator and every subperiod, the P r a i r i e s either approximate or exceed the regional average. Ontario and B.C. tend to have a weaker seasonal component; only Ontario interwar construction contracts and (possibly) B.C. postwar freight carloadings have seasonal components s i g n i f i c a n t l y stronger Table 2.1 RANKING OF REGIONS BY SPECTRAL DENSITY ESTIMATES AT ANNUAL FREQUENCIES 1 (Ranked R e l a t i v e t o Regional Mean, Highest t o Lowest) F r e i g h t D w e l l i n g Range Employment Index Bank Debits C o n s t r u c t i o n C o n t r a c t s C a r l o a d i n g s S t a r t s CPI T o t a l P e r i o d Interwar Postwar (I) ( 2 ) ~ (3) (2) (3) (1) (2) (3) (1) (2) (3) (3) (3) r 6+0 <r? PRA, MAR PRA PRA, (MAR) PRA PRA PRA (PRA) PRA PRA, QUE PRA QUE, (BC) MAR MAR CONT) (PRA) BC, QUE e -e r, <r -ex BC, MAR, (BC), QUE MAR, ONT BC, QUE ONT, QUE QUE, MAR ONT, QUE BC, CMAR) QUE QUE (MAR) QUE (BC), ONT BC MAR BC (PRA)(ONT) MAR, (BC) BC (BC) (ONT) ONT, PRA QUE, PRA QUE BC.ONT ONT, (MAR) BC, MAR MAR, (BC) BC ONT (ONT) The t e s t i s c a r r i e d out on the data detrended by both t e c h n i q u e s . I f the r e s u l t s vary a c c o r d i n g t o the t r e n d s p e c i f i c a t i o n , the r e g i o n i s p l a c e d i n b r a c k e t s at each rank. D e t a i l e d r e s u l t s are i n Table 1, Appendix C. MAR = M a r i t i m e s ; QUE = Quebec; ONT = O n t a r i o ; PRA = P r a i r i e s ; BC = B r i t i s h Columbia 34 than the regional average. Quebec and the Maritimes approximate the average i n most cases. There are few recognizable intertemporal patterns to the regional d i s p a r i t i e s ; i n B.C. the seasonal component seems to be gaining i n significance in comparison with seasonality i n the Canadian series, but t h i s can be concluded only tenuously. Also, both B.C. and Quebec experienced an absolute increase i n the spectral estimates at the annual frequency between the interwar and postwar periods; t h i s i s general over almost every i n d i c a t o r . In conclusion, the estimated spectral density functions o f f e r the following implications about regional seasonality: (a) with the exception of the very low frequencies, seasonal va r i a t i o n contributes more to the explanation of t o t a l variance than cycles of any other p e r i o d i c i t y , (b) i n general, the P r a i r i e region has the strongest, and Ontario and B.C. the weakest seasonal c y c l i c a l components; Quebec and the Maritimes usually do not d i f f e r s i g n i f i -cantly from the regional average, (c) between the interwar and postwar periods the seasonal component i n Quebec and B.C. has become stronger r e l a t i v e to other frequencies. 2.3.2 Subcycles On many occasions since 1919, there have been periods of economic expansion which have experienced temporary, or 35 minor, setbacks which are usually r e f l e c t e d i n decreased rates of economic growth. The setbacks are more pronounced i n some indicators than i n others and, as a r e s u l t , turning points in a reference cycle do not imply that a turning point would be i d e n t i f i e d i n any p a r t i c u l a r indicator. Furthermore, whether or not the "s u b c y c l i c a l " slackening of economic growth experienced in many indicators during 1927, 1935, 1947, 1951 and 1963 should be i d e n t i f i e d as reference cycle episodes has been a source of debate and accentuates the problem of s u b j e c t i v i t y i n the episodic-type method. 1 7 Also, Ruth Mack has suggested that subcycles can be explained i n terms of fluctuations i n inventories and durable goods manufactures. 1 8 This implies a degree of th e o r e t i c a l independence between business cycles and subcycles. Given the decision-making problem i n the episodic approach alluded to above, i t i s useful to examine the estimated spectra for evidence of a subcycle component. Mack's t h e o r e t i c a l propositions imply that some indicators w i l l have stronger subcycle components than others and that t h i s would be reinforced over regions by d i s p a r i t i e s i n regional economic structure. For example, an indicator of the volume of general economic a c t i v i t y such as the employment index should contain a stronger subcycle component i n Ontario as opposed to the P r a i r i e region due to 36 Ontario's r e l a t i v e concentration of economic a c t i v i t y on manufacturing. I t turns out that there are many subcycle peaks to be found i n the estimated spectra (detailed r e s u l t s are i n Table 2, Appendix C). Using the significance c r i t e r i a outlined i n Section 2.3, the peaks imply that r e l a t i v e to neighbouring frequency bands the subcycle frequencies account for a disproportionate amount of the explanation of t o t a l variance i n the series and are therefore "important" cycles. However, i n absolute terms the spectral estimates at subcycle frequencies tend to be s l i g h t l y lower than at the business cycle frequencies and considerably lower than at the annual frequencies or at the very lowest frequencies. e Furthermore, c a l c u l a t i n g the r r a t i o to f a c i l i t a t e i n t e r r e g i o n a l comparison of subcycle strength i s prohibited by the proximity of the frequency range to the annual range i n the estimated spectra. The absolute magnitude of the subcycle peaks appears to be largely determined through interfrequency leakage from the size of the annual peak; thus, regions are compared by the types of peaks that occur i n the estimated spectra at subcycle frequencies. Of a possible 15 cases (5 regions; 3 indicators continuous from 1919 or 1921), i n 13 cases a medium-absolute or a large subcycle peak was found i n the spectral density f u n c t i o n s . 1 9 For the interwar period (5 regions; H indicators) only 1 of 20 cases indicated s i g n i f i c a n t 37 s u b c y c l i c a l behaviour,- while i n the postwar period (5 regions; 6 indicators) 16 of 30 cases indicated significance.zo Table 2.2 shows that t h i s r e s u l t i s general over a l l regions; subcycles appear to be much more s i g n i f i c a n t i n the postwar period. The evidence presented i n Table 2.2 o f f e r s l i t t l e support for the Mack view of subcycles. F i r s t , the strongest evidence of subcycle peaks i s found in the indicators which le a s t r e f l e c t inventory-adjustment behaviour; namely, construction contracts and dwelling s t a r t s . Freight carloadings and bank debits are more general indicators but subcycles, while s i g n i f i c a n t , are less apparent. The employment index i s probably the indicator most'closely attuned to the behaviour of real output yet here the evidence for subcycles i s very weak. Al t e r n a t i v e l y , the lack of subcycle behaviour i n the consumer price index i s consistent with the Mack theory. Second, no generalization about the effect of regional economic structure on the strength of subcycle behaviour can be made; no region seems to have stronger subcycle behaviour than any other region. Although average p e r i o d i c i t y of important cycles cannot be precisely s p e c i f i e d by spectral analysis, for most indicators and regions average subcycle p e r i o d i c i t y l i e s between 18 and 30 months - a p e r i o d i c i t y somewhat longer than Mack's 15-19 months determined for U.S. data over the Table 2 . 2 INDICATORS IN WHICH THERE ARE SIGNIFICANT SUBCYCLE PEAKS; BY SUBPERIOD, BY REGION 1 B.C. (1) ( 2 ) oo Interwar Postwar  M . - C o n s t . C o n t r a c t s F r e i g h t C a r l o a d i n g s D w e l l i n g S t a r t s (1) P r a i r i e s ( 2 ) Employment Index Bank D e b i t s C o n s t . C o n t r a c t s (1) O n t a r i o ( 2 ) Bank D e b i t s C o n s t . C o n t r a c t s F r e i g h t C a r l o a d i n g s D w e l l i n g S t a r t s (1) Quebec Co n s t . C o n t r a c t s M a r i t i m e s ( 2 ) Bank D e b i t s C o n s t . C o n t r a c t s D w e l l i n g S t a r t s (1) ( 2 ) C o n s t . C o n t r a c t s D w e l l i n g S t a r t s Bank D e b i t s 1 D e t a i l e d r e s u l t s are i n T a b l e 2, Appendix C. but i s g e n e r a l l y between 1 year/6 months and Frequency v a r i e s somewhat over r e g i o n s and i n d i c a t o r s 2 y e a r s / 6 months. 39 1875-1959 period.z i This f a c t , together with the lack of evidence found here i n support of Mack's theory of inventory fluct u a t i o n s , strongly suggests that the extreme v a r i a b i l i t y found i n the p e r i o d i c i t y of fluctuations which are, on average, i n the business cycle range of 3-5 years i s such that there are s u f f i c i e n t episodes between 18 and 30 month p e r i o d i c i t y to r e s u l t i n the subcycle peaks. Moreover, since the 18-30 month range of frequency bands includes the f i r s t harmonics of frequencies situated at the upper end of the 3-5 year business cycle range, i t i s also possible that these peaks simply r e f l e c t the strength of the lower business cycle frequency bands. These seem the most palatable explanations of the evidence presented thus far. Further analysis of p e r i o d i c i t y i s included i n the next section and w i l l shed further l i g h t on the question of subcycles. 2.3.3 Business Cycles The two main sources i n which Canadian short-run economic fluctuations are i d e n t i f i e d using the episodic approach are White [1967] and Waterman [1973], White synthesises Chambers [1958a, 196U,] and Hay [1966] and determines that f o r the 1873-1965 period the average duration of c y c l i c a l fluctuations i n a reference cycle based upon seasonally-adjusted but not detrended time series varies from 50 months for 1873-1896, to 59 months for 1919-40 1938, to 51 months for 1946-1965. 2 2 However, Waterman concludes that the average duration of c y c l i c a l episodes, 1947-1969, i s only 29 months. 2 3 Such a large discrepancy i s l a r g e l y accounted for by the inc l u s i o n of several minor cycles into Waterman's reference c y c l e . 2 4 The r a t i o s of the duration of expansionary to contractionary phases (the E/C ratios) calculated from the White reference cycle are 1.86 fo r 1919-1938 and 2.67 for 1946-1966. The Waterman reference cycle i s derived from detrended time series and the r a t i o for 1947-1969 i s 0.99. " This l a t t e r r e s u l t adds c r e d i b i l i t y to the s t a t i o n a r i t y assumption which underlies spectral analysis. The top s i x rows of Table 2.3 present the p e r i o d i c i t y estimates of t h i s study f o r "important cycles" i n the Canadian economy using both spectral analysis and the episodic approach. Since there are an i n s u f f i c i e n t number of time series to construct a reference cycle, d i r e c t comparison with White's or Waterman's p e r i o d i c i t y estimates i s impossible. The series used in t h i s study suggest an average duration i n Canada ranging between 41 and 50 months fo r the interwar period and 36 and 5 3 months fo r the postwar period. The discrepancy between White's and Waterman's expansion-contraction r a t i o points out the s e n s i t i v i t y of the r e s u l t s to detrending; as one would expect, the r a t i o s f o r Canada i n Table 2.3 are considerably lower than White's Table 2.3 ESTIMATED AVERAGE PERIODICITY IN THE BUSINESS CYCLE RANGE (A l l periodicity estimates in months) Interwar Period Periodicity Canada (1) Employment Index (2) Construction Contracts (3) Bank Debits (4) Freight Carloadings (5) Dwelling Starts (6) Consumer Price Index B.C. (1) " Employment Index (2 ) Construction Contracts (3) Bank Debits (4) Freight Carloadings (3) Dwelling Starts (6) consumer Price Index Prairies t l ) Employment Index (2 ) Construction Contracts (3) Bank Debits (4) Freight Carloadings (5j Dwelling Starts (6) Consumer Price index Ontario ( l j Employment Index (2) Construction Contracts (3) Bank Debits (4) Freight Carloadings (5) Dwelling Starts (0) Consumer Price Index Q u e b e c (1) Employment Index ( 2) Construction Contracts (3) Bank Debits CO Freight CarloadInge (5) Dwelling StartB (6) Consumer Price Index M a r i t i m e s (2 ) (3) (It) (5) (6) Employment Index Construction Contracts Bank Debits, Freight Carloadings Dwelling StartB Consumer Price Index Analysis 35-48 n.a. n.a. n.a. n.a. n.a. n.a. 35-44 n.a. n.a. 35-44 n.a. n.a. 31-40 35-42 n.a. n.a. Episodic Method (5) 50 Ul U8 US 1*9 U6 52 56 1*1 1*1 i*a 1*8 111 1*3 52 1*5 1*0 1.3 1*3 1*8 39 32 1*0 Ratio of Expansionary to Contractionary Phaaes 1.21* 1.22 0.77 1.1*7 1.11 2-55 1.07 1-35 Postwar Period Periodicity Spectral EpIsooTc Analys: 1.38 2.21 1.06 1-53 1.81* 1.99 1.32 0.93 1.61 1.1*2 1.63 1.96 2.17 2.21 1.1*5 1.19 35-59 U8-60 1*3-58 50-66 1*0-50 37-60 35-50 1*8-60 1*3-58 31-1*0 39-60 31-50 1*8-60 (5) 53 36 39 37 1*8 1*1 1*4 33 1*0 1*2 36 36 37 35 1*1 1*2 37 1*3 1*3 1*5 1*2 36 1*0 1*1 1*3 39 36 36 1.1 37 39 35 1*2 43 37 1*1* Ratio of Expansionary to Contractionary Phases m 1.21 1.02 1.31 1.20 1.1*7 1-95 1.31 1.30 1-93 1.76 2.83 2.70 1.1*1 2-39 1.79 1.12 2.16 0.97 1.23 0.60 1-95 1-52 O.98 1-93 1.25 1.81 1.81 0.83 1-75 1.90 1.1*1* 1.29 2.21 1.16 2.28 2.36 Periodicity Episodic Method " T H — 1*6 »3 1*6 31* 38 1*0 1.9 1*2 1*1 * 1*1 36 33 1.5 1*0 38 1*0 1*6 36 1*5 1.2 36 Ul 1*6 1*9 1.3 1*1 31. 1*0 1.5 "*5 ".5 39 <»5 37 1*9 Postwar II Ratio ol' Expansionary to Contractionary Phases TBI 1.05 0.86 0.91 1.61 0.85 0.99 2.11 3.36 0.89 1.37 3.18 2.56 1.09 1.61 1.63 1.32 3.29 2.37 1.13 2.22 1.80 1-59 1.32 1.35 1.01 1.21 1.78 1.02 2.50 2.17 l . l l * 0.66 1.07 0.83 3.U8 3.1.0 Periodicity Episodic Ratio of ... Method to Contractionary Phases " (9) fioT-^ 67 28 30 M 60 37 1*0 21* 39 52 32 35 1*1 26 U4 "•7 34 UO 52 U6 U2 32 Uo 37 37 35 32 39 Ul 29 35 28 39 Ul 37 39 l.UU 1.18 1.61 O.96 2.15 2.7U 1.21 1.57 1.22 2.27 1.03 2.81 1.70 1-73 2.11 0.79 1.86 2.31 1-37 0.6U 1.92 1.32 1.00 2.52 1.26 2.32 1-91 0.7U 1.32 1.86 1.67 2.58 2.56 1.1*0 1.U7 1-53 1 Spectral estimates Riven only when there Is a relative peak ln the business cycle ranjje. Peaks are required ln both detrendinc versions before being recorded as a significant peak. 42 for the interwar period and are much closer to Waterman's than White's for the postwar period. In several time series indicators, rather pronounced interregional d i s p a r i t i e s are found in the episodic estimates of average duration. Furthermore, of the complete set of regional indicators, i n only 15 of 55 estimated spectra are s i g n i f i c a n t peaks found i n the business cycle frequency range. However, i n 11 of the 15 cases i n which there are " s i g n i f i c a n t " spectral peaks, the episodic estimate of average duration f a l l s within the range of frequencies defined by the spectral peak. Thus, the two methods tend to reinforce each other i n i s o l a t i n g the important cycles, although the absence of s i g n i f i c a n t peaks i n the majority of estimated spectra suggests that business cycle frequencies are of no greater importance than neighbouring frequencies i n explaining t o t a l variance in the regional time series. Furthermore, very few spectra contain both business cycle and subcycle peaks. This evidence undermines the suggestion of the previous section, that the subcycle peaks r e f l e c t e d business cycle strength because of a f i r s t harmonic r e l a t i o n s h i p . Apparently, variance i n the duration of episodes (as defined by i d e n t i f i e d turning points) l i m i t s the prospect of any p a r t i c u l a r frequency band within the business cycle range accounting f o r a disproportionate share of the t o t a l variance i n the time se r i e s . However, the lack of peaks i s also consistent with 43 the problem of interfrequency leakage emanating from the very low frequencies. Undoubtedly both factors are relevant: the p r a c t i c a l solution i s to (a) treat the episodic estimates as being precise estimates of average p e r i o d i c i t y , but also (b) define the business cycle p e r i o d i c i t y as encompassing a f a i r l y wide range of frequency bands when interregional (and regional-national) comparisons are drawn using cross-spectral analysis. We now make two detailed interregional comparisons; f i r s t , using the episodic estimates, average durations (and E/C ratios) are compared between regions. To f a c i l i t a t e a v a l i d comparison, eposides "unique" to p a r t i c u l a r regions are eliminated from the calculations. Here we ask: do c y c l i c a l episodes which occur i n both Canada as a whole and i n a p a r t i c u l a r region l a s t on average the same length of time? Second, with the spectral density estimates we can determine in which region the business cycle i s the most important r e l a t i v e to other frequency bands i n explaining t o t a l variance. In both cases, the analysis i s f o r the most part descriptive and serves to define the dimensions to d i s p a r i t i e s in regional c y c l i c a l behaviour. As summarized i n Table 2.4, i n the complete set of episodic estimates of average duration (Table 2.3) there are considerable differences between the longest and shortest estimates in most of the indicators, i n every subperiod. Furthermore, there i s no discernible pattern to regional 44 average durations i n any subperiod - regional ordering by average duration of cycles i s v i r t u a l l y random over indic a t o r s . Table 2.4 DIFFERENCE BETWEEN LONGEST AND SHORTEST ESTIMATED REGIONAL AVERAGE PERIODICITY, BY INDICATOR AND SUBPERIOD (IN MONTHS) Indicator Interwar Postwar I Postwar II Employment Index 4 16 15 Construction Contracts 7 3 22 Bank Debits 20 2 12 Freight Carloadings 16 11 20 Dwelling Starts n.a. 4 9 Consumer Price Index n.a. 13 11 Although these d i s p a r i t i e s suggest a degree of economic independence between the regions, one explanation of the d i s p a r i t i e s i s found i n the occasional occurrences of a region either missing an episode found i n other regions or having an extra episode not found i n other regions. In other words, fluctuations are f e l t more severely i n some regions than i n others; given our c r i t e r i a f o r i d e n t i f y i n g c y c l i c a l episodes, the severity of the fluctuations determines whether or not an episode i s marked o f f . The regional turning points recorded in Appendix B show that i n the overwhelming majority of cases the regional time series 45 w i l l contain the same episodes as are found i n the Canadian s e r i e s . There may be s l i g h t differences i n the timing of these episodes but i n large the episodes correspond over a l l regions. The complete set of non-corresponding episodes, recorded i n Table 2.5, almost t o t a l l y explains the d i s p a r i t i e s found i n the regional average durations. (Note that B.C. accounts for 12 non-corresponding episodes while no other region accounts f o r more than 7). In conclusion, there i s very l i t t l e evidence of any region having a uniformly d i f f e r e n t cycle p e r i o d i c i t y i n corresponding episodes. Amongst corresponding episodes in detrended data, regional d i s p a r i t i e s i n the E/C r a t i o point to regional d i s p a r i t i e s i n the timing of turning points. Regions with higher E/C r a t i o s for a corresponding episode should be either lagging regions at the peak or leading regions at the trough. Averaged over a number of corresponding episodes the E/C r a t i o i s thus helpful in distinguishing between (a) a regional average lead/lag which tends to occur at every point i n the cy c l e - i n d i c a t i n g a "phase s h i f t " between regions and (b) a regional average lead/lag which does not occur uniformly over the cycle - i n d i c a t i n g a timing difference which might be analysed i n terms of separate explanations for peaks and for troughs. Furthermore, E/C r a t i o s calculated from the peaks and troughs i n a l l episodes (corresponding and unique) have important implications for Table 2.5 CASES OF NON-CORRESPONDENCE EPISODES (dates marked c o n t a i n the episode) Interwar Regions which c o n t a i n an episode not found i n the Canadian s e r i e s in Employment Index C o n s t r u c t i o n C o n t r a c t s BC(1923-1924), PRA(1930) Bank Debits F r e i g h t C a r l o a d i n g s PRA(1929-1930), MAR(all 1934-1936) D w e l l i n g S t a r t s Consumer P r i c e Index Regions which are mi s s i n g an episode found i n the Canadian s e r i e s Ci2_ BC, PRA(both 1921-1922) MAR(1921-1922; 1924-1926) BC(1934-1935) BC(1922-1923), BC, 0NT(both 1926-1927) Postwar I i i i I?! Postwar I I i l l 121 PRA,QUE(1961-1962) -BC(1970-1971) BC(1954) MAR(1968-1969), QUE(1969-1970) BC, QUE, MAR(all 1945), ONT, QUE MAR(1952-1953) (1962-1963) BC(1967-1968) BC, QUE(1968) QUE(1961-1962), 0NT(1964) BC(1964-1965) QUE(1965) 47 i n t e r p r e t i n g the spectral r e s u l t s . The more the E/C r a t i o s deviate from unity, the less the business cycle component follows a smooth, wave-like pattern and, c e t e r i s paribus, the less the spectral estimate of the t o t a l variance i n the series which i s explained by t h i s component. Also, changes over time i n E/C r a t i o s indicate a p a r t i c u l a r way i n which the s t a t i o n a r i t y assumption i s being v i o l a t e d i n one or both of the series; t h i s becomes more relevant the greater the extent to which leads and lags at turning points represent a true "phase s h i f t " . 2 6 For each region, an E/C r a t i o i s calculated as an average of E/C r a t i o s i n corresponding episodes (Table 2.6). Then, using our usual method, these ra t i o s are compared to the regional average; as can be seen i n Table 2.7, the d i s p a r i t i e s follow several consistent patterns. Ontario r a t i o s are l e s s than, or not s i g n i f i c a n t l y d i f f e r e n t from, the regional average i n every indicator and subperiod. B.C. compares s i m i l a r l y with two exceptions - postwar I employment index and construction contracts. Quebec i s usually placed close to the regional average while the P r a i r i e s and the Maritimes could possibly be placed i n the "above-average" category. This evidence, together with the e a r l i e r finding that corresponding episodes have a s i m i l a r p e r i o d i c i t y in every region, suggests that regional average leads and lags w i l l not occur uniformly over each episode. The lower E/C r a t i o i n Ontario suggests either leading 48 Table 2.6 REGIONAL E/C RATIOS, "UNIQUE EPISODES" OMITTED Region Canada Interwar (a) Employment Index 1.24 (b) Const. Contracts 1.22 (c) Bank Debits 0.77 (d) Freight Carloadings 1.47 (e) Dwelling Starts (f) CPI E/C Ratio Postwar I 1.05 0.86 0.91 1.61 0.85 0.99 Postwar II 1.44 1.18 1.61 0.96 2.15 2.74 B.C. (a) Employment Index 1.31 2.11 1.12 (b) Const. Contracts 1.61 3.36 1.57 Cc) Bank Debits .36 .89 i.22 (d) Freight Carloadings -72 1.37 .52 (e) Dwelling Starts - 3.18 .90 (f) CPI . - -96 .64 Prairies (a) Employment Index 1.41 1.32 1.92 (b) Const. Contracts 2.97 1.61 1.73 (c) Bank Debits 1-79 1.63 2.11 (d) Freight Carloadings 1-86 1.32 1.41 (e) Dwelling Starts - 3.29 1.85 (f) CPI - 2.37 2.31 Ontario (a) Employment Index 1.23 0.87 1.37 (b) Const. Contracts 1.95 2.22 0.64 (<0 Bank Debits 1.95 1.93 1.92 (d) Freight Carloadings 0.75 1.59 0.84 (e) Dwelling Starts - 1-32 1.00 (f) CPI - 1.35 2.52 Quebec (a) Employment Index 1.25 (b) Const. Contracts 1-81 (c) Bank Debits 1-81 (d) Freight Carloadings 0.83 (e) Dwelling Starts (f) CPI 1.01 1.47 1.21 2.32 1.78 1.36 1.02 2.00 2.50 1.32 2.17 1.90 Maritimes (a) Employment Index 1.44 1.14 1.30 (b) Const. Contracts 1-29 0.66 0.78 (c) Bank Debits 1.48 1.87 2.56 W Freight Carloadings 1.60 1.56 1.40 (e) Dwelling Starts - 3.48 1.47 (f) CPI - 3.40 1.53 Table 2.7 INTERREGIONAL COMPARISON OF BUSINESS CYCLE E/C RATIOS; ^"UNIQUE" EPISODES OMITTED (Ranked from Highest to Lowest) Employment Index Bank Debits Construction Contracts Interwar Postwar I Postwar II (1) (2) (3) (1) (2) (3) (E/C).>(E7C)-KJ MAR BC PRA MAR PRA BC QUE, MAR 1 (E/C) (E/C)-a <(E/C).<(E/C)+C PRA, ONT PRA, QUE ONT, QUE PRA, ONT PRA, ONT PRA, ONT B C , ONT ONT, QUE BC, PRA (E/C) 1 (E/C) QUE MAR, ONT MAR QUE, MAR QUE, MAR QUE QUE PRA (E/C) <(E/C)-a BC BC BC BC BC MAR MAR ONT (E/C) Freight Carloadings Dwelling Starts Consumer Price Index  111 III Hi 121 IH 111 i n (E/C).>(E/C)*0 PAR, MAR MAR, QUE QUE MAR PAR MAR 1 (E/C) (E/C)-0 <(E/C).<(E/C)+o QUE PRA PRA, MAR PRA, QUE QUE, MAR PRA, QUE PRA, ONT (E/C) (E/C) BC (E/C). < (E/C)-o ONT, BC ONT, BC BC, ONT ONT BC, ONT B C , ONT BC (E / C ) 1 Thus, (E/C) i i s the E/C r a t i o i n the i t h region and (E/C) i s the regional mean. 50 behaviour at peaks or lagging behaviour at troughs (or b o t h ) . 2 7 This may also be true for B.C. and the inverse may be expected for the Maritimes and perhaps the P r a i r i e s . In the section on average leads/lags, those regional indicators f o r which the E/C r a t i o deviates s i g n i f i c a n t l y from the regional average w i l l be examined i n l i g h t of these predictions. Also, several observations can be made about intertemporal changes i n E/C ra t i o s . There i s no dis c e r n i b l e long-run trend apparent i n the r a t i o s i n any region. Rather, i n most regions for most indicators the r a t i o , while showing pronounced v a r i a t i o n , i s either higher or lower i n the postwar I subperiod than i n either the interwar or postwar II subperiods. In Table 2.8 the intertemporal pattern i s summarized over a l l indicators. Between the interwar and postwar I subperiods, the E/C r a t i o increases i n 3 of 4 B.C. indicators and decreases i n at l e a s t 3 of 4 indicators f o r every other region. However, between the postwar I and postwar II subperiods the table indicates unambiguous res u l t s only for B.C., the P r a i r i e s and the Maritimes. The evidence thus implies rather anomalous behaviour for B.C. i n that i t i s the only region characterized by a r e l a t i v e l y high E/C r a t i o during the postwar I subperiod; the P r a i r i e s and Maritimes show a pattern which i s c l e a r l y inverse to that of E.C., both Table 2.8 INTERTEMPORAL PATTERN OF REGIONAL E/C RATIOS L O E/C Ratios Calculated from a l l episodes Regions in which: Interwar > Postwar I Postwar I > Postwar II Interwar < Postwar I Postwar I < Postwar II Interwar < Postwar I Postwar I > Postwar II Interwar > Postwar I Postwar I < Postwar II PRA, MAR No generalization Possible BC, ONT, QUE E/C Ratios calculated with "unique" episodes removed B.C. PRA, MAR ONT, QUE 1 For a given region, the average E/C ratio for one subperiod is considered greater (less) than another i f a majority of a l l the indicators of the region experience at least a .10 increase (decrease) between the subperiods. v 52 between the interwar and postwar I subperiods and between the postwar I and postwar I I subperiods. F i n a l l y , the appendixed comparison (Table 3, Appendix C) of E/C r a t i o s calculated from a l l episodes show that these r a t i o s are often quite d i f f e r e n t from unity and are also somewhat variant (again, randomly) over subperiods; t h i s must be kept i n mind when the spectral density estimates are presented. In the second comparison, spectral r e s u l t s are used to make interregional comparisons of the contribution of regional business cycles to the explanation of t o t a l variance i n the regional time series. That i s , i n which regions are the sequence of recurring 3-5 year fluctuations the more important r e l a t i v e to other frequencies and random fluctuations? Interregional comparisons are made by c a l c u l a t i n g r i from the spectral density estimates, where 0 i s the same in each region but includes a f a i r l y wide band of frequencies - from approximately 2 year/9 month to 5 year/0 month p e r i o d i c i t y . (The evidence from the episodic approach supports t h i s d e f i n i t i o n of 8 .) Table 2.9 presents the in t e r r e g i o n a l comparison based upon the averaged Q spectral density estimates (r^) for each indicator ot each region using both detrending methods. (Detailed results are e i n Table 4 , Appendix C). As usual, r must f a l l outside one standard deviation of the mean of a l l the regions for that in d i c a t o r before being considered d i f f e r e n t from the Employment Index Total Period Interwar Postwar T I T e -r.>r+o OUT BC T 3 T our Table 2.9 IMTERKEGIQNAL COMPARISON OF RELATIVE CONTRIBUTION OF BUSINESS CYCLE FREQUENCIES 1,2 Bank Debits Construction Contracts (2) (3) (1) BC BC, (OM?) BC (2) (3) (BC), (OUT) BC, (ONT) Freight Carloadings (1) (2) (5) OUT (OUT), (QUE) (OUT) Dwelling Starts (3) BC CPI (3) BC -9 , 9-6 BC, MAR, QUE BC, QUE, r -or<r.<r +ar q u E j ^ pj^ ( p R A j PRA QUE, OKT (ONT), QUE ONT, QUE MAR (MAR), (PRA) MAR (PRA), MAR PRA (PRA), (MAR) PRA (BC), PRA (ONT), QUE BC, (QUE) BC, (ONT) BC, MAR PRA, ONT (ONT), QUE MAR MAR PRA (MAR) (QUE), MAR (ONT), (QUE) QUE PRA, (QUE) PRA PRA, (QUE) MAR (MAR) ONT, PRA MAR, QUE 1 Brackets surrounding the region indicate that the two methods of detrending lead to different results when the significance test is applied. 2 Detailed results are in Table h, Appendix C. 54 regional norm. 2 8 Using t h i s comparison, the B.C. and Ontario averaged spectral estimates are equal to or greater than the regional average for every indicator i n every subperiod; the P r a i r i e s and Maritimes are equal to or less than the regional average for every indicator i n every subperiod. The Quebec r a t i o tends t o approximate the regional average; in 1 of 13 cases over a l l indicators and subperiods i t l i e s above the average and i n 2 of 13 cases i t l i e s below the average. Thus, we conclude that business cycle frequencies tend to explain more variance i n B.C. and Ontario, and less variance in the P r a i r i e s and Maritimes. This re s u l t i s consistent with the e a r l i e r f i n d i n g that seasonality was r e l a t i v e l y more important i n the P r a i r i e s , and less important in Ontario and B.C., than i n the regional average. By d e f i n i t i o n , the t o t a l variance i n a time-series i s explained completely by an estimated spectrum. Thus, i f a l l frequencies other than those i n the business and seasonal ranges were of the same power i n every region then, i n a given region, a strong business cycle component r e l a t i v e to that of other regions would imply a r e l a t i v e l y weak seasonal component and vice versa. Although t h i s c e t e r i s paribus condition has not been established here, the l i k e l y p o s s i b i l i t y that there exists such an inverse r e l a t i o n s h i p between the power of business cycle and seasonal components i n the spectra points out a danger area i n the interpretation of spectral r e s u l t s . In Section 2.3.1 55 i t was concluded that the spectral density estimates increased (absolutely) for the seasonal variation between the interwar and postwar periods i n Quebec and B.C. The opposite occurred at the business cycle frequencies i n every region except Ontario. Thus, for these regions there has been an intertemporal change i n the r e l a t i o n between frequencies and, p a r t i c u l a r l y i n the cases of B.C. and Quebec, there i s some ambiguity as to which i s causal - the decreased power of business cycle frequencies, the increased power of seasonality, or both. This must be kept i n mind when, i n l a t e r sections, explanations are sought f o r intertemporal changes i n regional c y c l i c a l s e n s i t i v i t y or cross relative-amplitude. 2.4 Regional Leads and Lags While i n general the Canadian regions experience s i m i l a r fluctuations i n economic indicators, they do not necessarily do so at the same time. When the regions are compared to each other using the Canadian aggregate as a base, interregional differences i n the timing of fluctuations emerge. In t h i s section, three aspects of these d i s p a r i t i e s are investigated. F i r s t , i f each region's leads and lags are averaged over a set of episodes, are they consistent over a l l indicators and, i f so, which are the "leading" or "lagging" regions? Second, to what extent does each region's lead/lag vary over episodes; that i s , i s the 56 regional lead/lag "uniform" over time? F i n a l l y , t o what extent are regional turning points for a given episode "clustered"? Does t h i s c l u s tering vary over time? 2.4.1 Average Regional Leads and Lags In the episodic-type i d e n t i f i c a t i o n of turning points, the lead/lag between each regional and national turning point i s recorded and averaged over a l l corresponding episodes within a subperiod. If the average for peaks or troughs exceeds 1 month then for that indicator the region i s considered a leading r e g i o n . 2 9 These calculations are summarized i n Table 2.10 using the c r i t e r i o n that i f the region leads/lags i n at least two-thirds of a l l the indicators then i t i s considered a consistently leading region. (Detailed calculations are i n Table 5, Appendix C) . It i s obvious from these tables that f o r the interwar period the differences i n regional timing depend upon the indic a t o r under observation and that generalizations should not be made - although i t i s int e r e s t i n g to note the consistent Prairie leads i n troughs. Furthermore, examination of the turning point data i n Appendix 2B reveals many instances i n which regions behave d i f f e r e n t l y at peaks and troughs for a given indicator. Thus, f o r this subperiod, the turning points indicate strong, almost random, v a r i a t i o n over regions and indicators i n average leads and lags. What t h i s evidence r e f l e c t s for the interwar period i s that d i f f e r e n t Table 2 . 10 REGIONS IN WHICH AT LEAST TWO-THIRDS OF INDICATORS SHOW RECURRING RESULTS Interwar Postwar Postwar I Postwar II Peaks Troughs Peaks Troughs Peaks Troughs Peaks Troughs - Leading Regions - PRA BC, MAR ONT, MAR BC, MAR BC, ONT, MAR - ONT, QUE Lagging Regions - - PRA - PRA - - -Coinciding Regions QUE - ONT - ONT QUE BC Cannot Generalize BC, ONT BC, ONT QUE BC, PRA, QUE QUE PRA PRA, ONT BC, PRA PRA, MAR QUE, MAR QUE, MAR MAR 58 regions were leading, lagging or coincident i n the various episodes. As described i n Appendix 1A, only the 1920 and 1924 peaks and the 1932-1933 trough i d e n t i f i e d i n the Canadian series can be characterized by a general coincidence of turning points i n the regional indicators. Ontario led the 1921 trough while the P r a i r i e s and B.C. lagged, but the P r a i r i e s had long leads at the pre-depression peak and both the P r a i r i e s and B.C. led the 1936 peak. The Maritimes led the 1921 trough, the 1924 peak and the 19 33-34 "Roosevelt boomlet" but was lagging or coincident (depending upon the indicator) at the 1929 peak and the 1933 trough. Analysis of the postwar subperiod i s somewhat more f r u i t f u l . Over the entire postwar subperiod, and p a r t i c u l a r l y the postwar I subperiod, conclusions may be made for a l l regions except Quebec. B.C. i s characterized by consistently leading or coincident behaviour, although with a major exception i n the postwar II subperiod when B.C. lags the 1961 trough. Ontario consistently leads at troughs and tends to be coincident at peaks. The Maritimes, strangely enough, lead at both peaks and troughs, p a r t i c u l a r l y i n the postwar I subperiod (the regional indicators are lagging or coincident at the 1968 trough and the 1969 peak). With the exception of the 1969 peak, the P r a i r i e s tend to lag at peaks. However, while these results indicate some consistency over episodes and indicators i n 59 regional lead/lag relationships, they do not define t h i s r elationship very c l e a r l y ; the interwar and postwar II subperiods suggest l i t t l e consistency over indicators and even the postwar I subperiod has only two regions (B.C. and the Maritimes) which behave at a l l similarly at both peaks and troughs i n r e l a t i o n to the Canadian base. However, the d i s p a r i t i e s in behaviour between peaks and troughs are at l e a s t f a i r l y consistent with the regional d i s p a r i t i e s i n E/C r a t i o s determined i n the previous section. In Table 2.7 there are 35 cases in which a regional subperiod E/C r a t i o deviates from the regional average. Examination of the average leads and lags reveals 2 5 cases i n which the difference between the average lead or lag at peaks and at troughs i s consistent with the E/C r a t i o , that i s , i f the E/C r a t i o i s s i g n i f i c a n t l y greater than average, either (a) the region tends to lag at peaks and/or lead at troughs or (b) the lag at peaks exceeds the lag at troughs. In only 7 of the 35 cases were results inconsistent with the E/C r a t i o obtained. The implication of t h i s r e l a t i o n s h i p between E/C and average lead and lag at troughs and peaks i s that while the r e l a t i o n s h i p i s true by d e f i n i t i o n f o r a single episode i t seems to hold on average as well. Quite possibly the lack of recurrence over indicators i n regional lead/lag relationships can be attributed to the crudity of the episodic method. Leads and lags are 60 calculated from turning points which cannot be precisely i d e n t i f i e d but, even i f t h i s were not a problem, i t i s s t i l l questionable as to whether or not such differences i n timing accurately r e f l e c t differences i n the timing of regional fluctuations. The peak and trough are only two observations of an episode; t h i s may be too few to capture temporal displacement of fluctuations i n the regions. However, i t may also be true that there i s no pattern to regional leads and lags that i s consistent over a l l indicators and over both peaks and troughs; i t may be possible to characterize the lead/lag relationships i n certain time periods as being e s s e n t i a l l y random. To more f u l l y examine t h i s p o s s i b i l i t y , cross-spectral analysis i s employed to calculate the average lead/lag between each region and the Canadian economy. The average lead/lag i n t h i s case i s not an average of the leads and lags i d e n t i f i e d i n each episode but i s an average based upon every observation i n the time series. The average leads and lags estimated by the cross-spectral and episodic methods often do not agree with each other. Table 2 . 1 1 presents the regions with average leads/lags that vary s i g n i f i c a n t l y from zero according to cross-spectral analysis. Using harmonically detrended data, of the 30 cases i n which there are s i g n i f i c a n t leads/lags i n the interwar and postwar subperiods, there are only 17 instances where the lead/lag i s also s i g n i f i c a n t by the episodic method. In a l l other cases the peaks and troughs Table 2.11 Indicator Employment Index Construction Contracts Bank Debits Freight Carloadings Dwelling Starts Consumer Price Index AVERAGE REGIONAL LEADS AND LAGS; CROSS-SPECTRAL ANALYSIS Regions Leading (-) and Lagging (+) Canada1 (Lead or lag in months) Interwar Period Leading QUE (-1.22) ONT (- .51) BC (- .69) ONT (- .55) PRA (-2.46) PRA (-3.63) Lagging PRA (1.03) MAR (0.45) MAR (1.60) MAR (4.27) MAR (1.15) QUE ( .47) Postwar Period Leading MAR (-4.63) BC (-1.02) QUE (-2.03) BC (-3.94) QUE (-1.21) MAR (-2.52) BC (- .40) QUE (- .91) ONT (- .78) L a g g i n g PRA (1.43) PRA (6.19) ONT (1.22) BC (4.94) QUE (2.57) MAR (8.86). PRA (3.80) MAR (7.31) MAR (1.33) Total Period Leading MAR (-2.30) QUE (-1.95) ONT (-1.03) BC (-1.52) MAR (- .74) QUE (-1.81) Lagging PRA (5.76) BC (2.00) PRA (3.02) 1 Only average leads and lags which are significantly different from zero using the crude Granger and Hatanaka test [1964, pg.80] are lis t e d . The lead or lag is averaged over the business cycle frequencies at truncation point n/3. 2 A l l indicators have been detrended using harmonic regression. 62 e i t h e r do not both l e a d o r l a g , are not s i g n i f i c a n t l y d i f f e r e n t from zero, or c o n t r a d i c t the s p e c t r a l r e s u l t s . The l a c k of c o n s i s t e n c y between the two methods i s due predominantly t o d i f f e r e n c e s i n the magnitude of the e s t i m a t e d l e a d / l a g . In o n l y 3 cases do the methods c o n t r a d i c t each o t h e r . Although with c r o s s - s p e c t r a l a n a l y s i s g e n e r a l i z a t i o n s over a l l i n d i c a t o r s are a g a i n d i f f i c u l t to draw, s e v e r a l c o n s i s t e n t p a t t e r n s do emerge. For the i n t e r w a r p e r i o d , the Maritimes are c o n s i s t e n t l y a l a g g i n g r e g i o n , the P r a i r i e s l e a d i n bank d e b i t s and the employment index, and O n t a r i o l e a d s i n employment and c o n s t r u c t i o n c o n t r a c t s and i s c o i n c i d e n t i n the other two i n d i c a t o r s . B.C. and Quebec i n d i c a t e l i t t l e c o n s i s t e n c y over i n d i c a t o r s . For the postwar p e r i o d , two important r e v e r s a l s occur i n the p a t t e r n of r e g i o n a l leads and l a g s . F i r s t , the Maritimes become a l e a d i n g r e g i o n i n two i n d i c a t o r s f o r which i t was l a g g i n g i n the interwar p e r i o d even though i t s t i l l l a g s i n bank d e b i t s , d w e l l i n g s t a r t s and the consumer p r i c e index. T h i s r e v e r s a l i s m i r r o r e d i n the e p i s o d i c r e s u l t s , where every i n d i c a t o r showed e i t h e r an i n c r e a s e d l e a d or decreased l a g f o r both peaks and troughs between the i n t e r w a r and postwar p e r i o d . Most of the i n c r e a s e d l e a d i s accounted f o r by the postwar I subperiod; every i n d i c a t o r shows an i n c r e a s e d l e a d o r decreased l a g between the i n t e r w a r and postwar I p e r i o d s f o r both peaks and troughs. The tendency i s towards a 63 greater lag between postwar I and postwar II although there are several exceptions. 3 0 Second, i n chree of four indicators there i s a tendency for the P r a i r i e lead of the interwar period to diminish or become a s i g n i f i c a n t l a g . 3 1 This r e s u l t i s also supported by the episodic r e s u l t s . In every indicator there i s a tendency towards a greater lag i n the postwar period and, as in the Maritimes, most of the change seems to have occurred: in the postwar I subperiod. In the postwar period, B.C. and Quebec lead s i g n i f i c a n t l y or are coincident i n every indicator except bank debits, while Ontario seldom d i f f e r s s i g n i f i c a n t l y with the national base. The r e s u l t f o r B.C. i s consistent with that of the episodic method but the results for Ontario and Quebec are more d i f f i c u l t to int e r p r e t . The episodic method suggests that Ontario i s coincident at peaks but leading at troughs while the spectral results suggest that i t i s generally coincident. However, the lead at troughs i s quite short (an average of 1 .2 months for postwar I indicators and 1.0 months for postwar II indicators) and i s uniform over a l l indicators i n both postwar subperiods with the exception of construction contracts which, by both methods, indicate a s i g n i f i c a n t Ontario lag. Quebec i s similar i n that i t tends to lead or coincide at troughs but i s d i f f e r e n t i n that at peaks i t s behaviour varies widely according to both the indi c a t o r and the episode observed. The s i g n i f i c a n t leads captured by the spectral method suggest that perhaps for the 6 4 Quebec case turning points are even less representative of the r e l a t i v e timing of fluctuations than i n other regions. 2-4.2 Uniformity of Regional Leads and Lags Consistency over time i n regional leads/lags can be examined more precisely by determining the extent to which an average lead or lag i s uniform over the complete set of i d e n t i f i e d episodes within a subperiod. Does the average lead/lag indicate a difference i n timing which tends to occur i n every episode or does i t r e f l e c t an averaging of timing differences which vary over episodes? The extent of uniformity can be measured by the variance of leads and lags (from the episodic method) over episodes for a given region. The mean about which the variance i s calculated i s the average lead/lag. Detailed calculations for each indicator are i n Table 6, Appendix C. A crude method of summarizing the uniformity measures for each region i s to take the average of the variances over a l l indicators (Table 2.12). From t h i s summary i t i s clear that Ontario has a much more uniform lead/lag pattern than any other region. This r e s u l t i s general over every subperiod for both peaks and troughs. In combination with the r e s u l t obtained e a r l i e r that Ontario, on average, has short leads or i s coincident with the Canadian base, i t can now be stated that t h i s behaviour i s quite general. However, t h i s i s the only concrete r e s u l t to be obtained Table 2.12 UNIFORMITY: AVERAGED OVER ALL INDICATORS Interwar Postwar Postwar I Postwar II Peaks Troughs Peaks Troughs Peaks Troughs Peaks Troughs Maritimes 19.78 45.50 27.53 41.09 23.04 27.36 14.87 14.96 Quebec 7.06 22.60 11.83 24.86 11.63 16.38 12.54 29.43 Ontario 5.64 12.33 10.26 5.19 3.91 2.09 14.61 5.24 Prairies 47.17 35.24 27.16 28.39 19.48 8.37 20.39 18.81 B.C. 10.25 10.84 18.11 32.59 26.42 22.12 6.21 16.60 Interwar average includes employment index, construction contracts', bank debits and freight carloadings. Postwar also includes dwelling starts and the CPI. 66 here. Uniformity varies markedly over regions, indicators and subperiods, but not i n any recognizable pattern. 2.4.3 Clustering of Regional Turning Points One f i n a l aspect of regional leads and lags remains to be examined and t h i s concerns regional d i s p a r i t i e s i n timing from the point of view of each episode. For a given indicator, the variance i n regional leads and lags r e l a t i v e to the average regional lead/lag at a p a r t i c u l a r i d e n t i f i e d turning point measures the extent to which the regional turning points are "clustered" about the regional "average turning p o i n t . " 3 2 This variance i s averaged over a l l episodes i n a subperiod, and then compared with other subperiods so as to determine the intertemporal pattern of regional d i s p a r i t i e s . A decrease i n variance over time implies a greater degree of clu s t e r i n g and a convergence i n regional turning points to the regional "average turning point". (Note that a convergence in clu s t e r i n g would be independent of an increase or decrease i n the average regional lead or la g ) . In Table 2.13 the subperiods are ranked for each ind i c a t o r according to the extent of cl u s t e r i n g . (The detailed c l u s t e r i n g s t a t i s t i c s are i n Table 7, Appendix C). The Table shows that, for three of four indicators, episodes are more t i g h t l y clustered i n the interwar subperiod than i n either of the postwar subperiods. This i s 67 Table 2.13 RANKING OF SUBPERIODS BY CLUSTERING1 (Lowest rank i n d i c a t e s the l e a s t c l u s t e r i n g ) Peaks Troughs Employment Index 1-2-3 3-2-1 Cons t r u c t i o n Contracts 1-3-2 1-2-3 Bank Debits 1-2-2 1-3-2 F r e i g h t Carloadings 3-2-1 1-3-2 Dwelling S t a r t s n.a. -1-2 n.a. -1 Consumer P r i c e Index n.a. -1-2 n.a. -1 1 Variances must be d i f f e r e n t by at l e a s t 1.00 before they are given separate ranks. 68 true for both peaks and troughs. Between the postwar I and postwar II subperiods there i s no consistent pattern over indicators for either peak or trough turning points. The spectral method can also bring evidence to bear upon t h i s point. With t h i s method, leads and lags are estimated as an average over a period of time. Thus, the "spectral" measure of clustering i s the variance i n average regional leads and lags i n a subperiod, while the "episodic" measure i s an average over a subperiod of the variances in regional leads and lags where the variances are calculated f o r each episode. 3 3 The mean about which the variance i s calculated i n the spectral c l u s t e r i n g measure i s the average of the regional leads and lags which, i n spectral analysis, are themselves averages of the differences i n timing between the regions and Canada over the subperiod. 3 4 The spectral clustering s t a t i s t i c s presented i n Table 2.14 for each indicator by subperiod c l e a r l y support the episodic c l u s t e r i n g s t a t i s t i c s . For every indicator and with both methods of detrending the extent of clu s t e r i n g i s greater i n the interwar subperiod than i n the postwar subperiod - although t h i s r e s u l t i s tenuous i n bank debits and construction contracts since several of the coherences are quite low. 3 5 2.5 Summary of Major Empirical Results Table 2.14 CLUSTERING: SPECTRAL METHOD Indicator Average Regional Lead or Lag (in months) (+) indicates Canada leads the region Maritimes Quebec Ontario Prairies B.C. Average of Average Regional Leads and Lags Variance Employment Index Interwar Postwar 0.4S -4.62 -1.22 -0.64 -0.51 -0.08 1.03 1.42 -0.69 -1.02 -0.18 -0.98 0.S6 4.49 Construction Contracts Interwar Postwar 1.60 3.46 -0.3S -2.03 -0.55 1.19 -0.37 6.19 0.66 1.39 0.34 2.04 0.69 7.38 Bank Debits Interwar Postwar 4.27 8.86 1.17 2.57 1.43 1.91 -2.46 -3.23 1.66 4.94 1.21 3.01 4.61 15.65 Freight Carloadings Interwar Postwar 1.15 -2.52 0.47 -1.21 0.64 -0.20 -3.63 3.80 -0.50 -3.94 -0.41 -0.81 2.80 3.03 1 Clustering s t a t i s t i c i s the variance of average regional leads and lags, where average leads and lags are calculated at truncation point n/3 (n = number of observations), and averaged over relevant frequency bands in the business cycle range. Detrending is by harmonic regression. 3 4 2 For formula see Footnote , on previous page. 70 The h i s t o r i c a l picture of the short-run c y c l i c a l behaviour of Canadian regions indicates differences in regional fluctuations which seem rather large. Canadian regions, while adhering to a common, basic pattern i n economic fluctuations, are quite disparate i n many aspects of these fluctuations. With the possible exception of subcycles, the strength of the various c y c l i c a l components that explain the t o t a l v a r i a t i o n i n economic indicators i s markedly d i f f e r e n t over regions. Already i t can be said that the severity of fluctuations varies considerably over regions; there are many cases i n which episodes are i d e n t i f i e d i n some regions but not i n others. Even i n corresponding episodes, the r a t i o of the average duration of expansionary to contractionary phases varies over regions. Differences i n the timing of regional fluctuations are apparent; c e r t a i n regions seem to consistently lead or lag other regions. A l l of these factors suggest differences i n regional c y c l i c a l behaviour and there i s also evidence that since the interwar period some of these d i s p a r i t i e s have not remained constant. The nature of the change over time i n average leads and lags has been captured by the i n t e r e s t i n g r e s u l t concerning the c l u s t e r i n g of both regional turning points and regional "phase s h i f t s " . The timing of regional fluctuations using a l l indicators was more clustered during the interwar period 7 1 than a f t e r , but there has been no subsequent change during the postwar periods I and I I . By drawing upon the accumulated evidence on the strength of c y c l i c a l components and the p e r i o d i c i t y and timing of business cycles, the behaviour of each region can now be more f u l l y described, es p e c i a l l y in terms which are r e l a t i v e to other Canadian regions. Later chapters w i l l add to t h i s description, but i t i s appropriate at t h i s point to take stock of what has already been determined. By almost any measure Ontario i s Canada's largest economic region. Simply because of i t s weight i n determining Canadian t o t a l s one would not expect the region's behaviour to d i f f e r much from that of the national aggregate. However, i n both t h i s type of comparison and also i n comparisons with regional (unweighted) averages, several differences do emerge. In Ontario the seasonal component i s weak and the business cycle component i s strong r e l a t i v e to other regions. This d i s p a r i t y has persisted i n every subperiod since the interwar period. The sets of business cycle episodes i d e n t i f i e d i n the Ontario and Canadian economies are nearly i d e n t i c a l , with the r e s u l t that average p e r i o d i c i t y i s quite s i m i l a r i n both economies. Ontario peaks coincide c l o s e l y with Canadian peaks but short, uniform leads are found at troughs p a r t i c u l a r l y during the postwar period. When average leads and lags are estimated by the cross-spectral method, Ontario tends to be 72 coincident with the Canadian economy - t h i s i s not necessarily inconsistent with the observed leads at troughs, given t h e i r shortness and uniformity. An in t e r e s t i n g d i s p a r i t y i s found i n the E/C r a t i o s , where Ontario i s lower than average for the consumer price index, dwelling s t a r t s , f r e i g h t carloadings and postwar construction contracts and approximates the average i n bank debits and the employment index. Within the former group of indicators there are several cases of a lead at troughs and coincidence at peaks are, thus, inconsistent with what i s expected when E/C ra t i o s are low. Relative to other regions, the Pr a i r i e s have a strong seasonal component and a weak business cycle component. At the business cycle frequency the region undergoes s i g n i f i c a n t change between the interwar and postwar subperiods. During the interwar period the P r a i r i e s are, on average, a leading region but by the postwar I period a strong tendency towards an increasing lag or a diminishing lead i s established, p a r t i c u l a r l y at peaks. This change i s accompanied by a s i g n i f i c a n t reduction i n E/C r a t i o s . There i s thus an apparent inconsistency between the decline in P r a i r i e E/C r a t i o s and longer lags at peaks as opposed to troughs. However, the fact that E/C ra t i o s declined i n every region except B.C. removes the inconsistency since the P r a i r i e E/C r a t i o f e l l , on average, by less than the f a l l i n 73 other regions. In the postwar II subperiod the P r a i r i e lags are less apparent and E/C r a t i o s r i s e . The strength of the various c y c l i c a l components i n B.C. i s s i m i l a r to that of Ontario; i n r e l a t i o n to the regional average, the seasonal component i s weak and the business cycle component i s strong. Between the interwar and postwar periods the seasonal component becomes stronger and the business cycle component weaker i n r e l a t i o n to other frequencies. There i s some evidence that B.C. i s a coincident region during the interwar period - although the fa c t that B.C. has more unique and missing episodes than any other region suggests r e l a t i v e l y independent behaviour for the region and that comparison of timing between i t and other regions may be somewhat i r r e l e v a n t . In the postwar periods there are fewer cases of non-corresponding episodes and timing comparisons are more v a l i d ; through the postwar period B.C. was a leading region i n the employment index, f r e i g h t carloadings and the CPI, but lags i n bank debits and construction contracts. Also, the E/C r a t i o s follow a unique temporal pattern i n B.C. - low during the interwar period, r i s i n g i n the postwar I period and f a l l i n g thereafter. The Maritimes were a lagging region during the interwar period but the tendency towards becoming a leading region i n the postwar period i s a surprising r e s u l t worthy of close scrutiny i n following a n a l y s i s . 3 6 Another su r p r i s i n g r e s u l t 74 i s that f o r several indicators the Maritimes have the highest E/C r a t i o of a l l the regions; together the two r e s u l t s imply greater leads at troughs than peaks and t h i s i s borne out by the data. Other aspects of c y c l i c a l behaviour in the Maritimes seem to coincide more with what one might expect. Relative to other regions, seasonality i s of average strength and the business cycle component i s weak. The temporal pattern of E/C r a t i o s resembles that of the P r a i r i e s - higher during the interwar or postwar II periods. Generalizing about most aspects of c y c l i c a l behaviour i n Quebec i s impossible. Ambiguities and inconsistencies were often encountered when comparing indicators or subperiods. Seasonality and the business cycle component appear to be of average strength i n Quebec although i n several indicators and subperiods there are exceptions. As i n B.C., between the interwar and postwar periods the strength of business cycles has decreased and that of seasonality has increased, r e l a t i v e to other regions. Quebec E/C r a t i o s approximate the average, but again there are exceptions. The evidence concerning the temporal pattern of E/C r a t i o s i s similar to that of Ontario i n that the r a t i o s f o r most indicators are lower during the postwar I period than the interwar period and also i n that the change between postwar I and postwar II i s inconsistent over indicators. L i t t l e can be concluded about average leads and 75 lags i n the interwar period. In the postwar period the region i s leading or coincident with the exception o i the bank debits case. An important point which should be made here i s that even though the results for Quebec are often inconclusive i t i s rea d i l y apparent that Quebec and Ontario do not exhibit i d e n t i c a l c y c l i c a l behaviour. The d i s p a r i t i e s are s i g n i f i c a n t enough t o warrant for economic reasons t h e i r separation into two regions. 76 APPENDIX 2A Technical Notes 1. Spectral Analysis When using any econometric technique, but i n particular the spectral analytic technique, some l a t i t u d e exists in selecting estimation methods and i n deriving conclusions. This appendix i s included to precisely specify the methods used i n t h i s study. Estimating the power spectrum (the normalized spectral density function) and the cross-spectrum involves several choices. Although spectral analysis can t h e o r e t i c a l l y d i s t i n g u i s h between the contributions of each frequency band to the explanation of t o t a l variance i n a time-series, there i s a problem of interfrequency "leakage" encountered when estimating the spectrum, especially i n the neighbourhood of those frequencies which account for r e l a t i v e l y large or small proportions of t o t a l variance, and a choice arises as to how best to deal with t h i s problem. The leakage problem arises because spectrum estimators are smoothed i n order to reduce t h e i r v a r i a n c e . 3 7 The smoothing device which minimizes the leakage for non-neighbouring frequency bands i s the Parzen "window", although the p r i c e paid f o r minimized leakage with t h i s window i s greater bias i n the estimator. This implies, i n e f f e c t , that longer time-series are required using t h i s window to achieve a given degree of 77 unbiasedness. 3 8 This study employs the Parzen window and, as a r e s u l t , peaks i n the spectral density function are interpreted as including a f a i r l y wide range of frequency bands; for example, i f a peak i s centered on the j t h frequency IL (where n i s the length of the time-series), n then i n general the peak i s said to l i e i n a range defined by the iLLliand iiii!!frequency bands. n n Since f o r economic variables low frequencies t y p i c a l l y account for the greatest proportion of t o t a l variance, i t i s at these frequencies that the leakage problem i s the most severe, e s p e c i a l l y i f the time-series has not been accurately detrended. 3' Trend can be defined i n terms of low frequencies and can be removed from the data using a v a r i e t y of methods, two of which are used i n t h i s study. One i s a simple transformation of the time-series into growth rates to remove loglinear trend. The other method i s to estimate by harmonic regression a trigonometric polynomial of the form: Tft n . Trt _ 2Tft „ . 2rrt (1) X = a + 3, cos — + B. s i n — + B 7 cos + B s m — -^ J t 1 n 2 n 3 n 4 n where X i s the time-series, n i s the number of observations and t i s time. Incorporated i n t h i s d e f i n i t i o n of trend are cycles which do not repeat themselves within the time period (linear components) plus cycles the length, or one-half the length, of the time period.*o Residuals from t h i s regression become 78 the detrended time-series. This s p e c i f i c a t i o n of trend i s the most consistent with the assumptions underlying spectral analysis. The f i n a l choice to be made i n the selection of an estimation method concerns truncation points; that i s , the selection of the number of autocovariance terms to be included in the spectral estimator (or the amount of smoothing to be applied to the estimator). Increasing the truncation point i s equivalent to decreasing the amount of smoothing and has the ef f e c t of increasing the estimator's variance while reducing its bias . * 1 There i s as yet no optimization procedure which w i l l s e l e c t the truncation point to best deal with t h i s trade-off. A rule-of-thumb, suggested by Granger and Hatanaka, i s that at the truncation point n/3, where n i s the number of observations, smoothing i s , i n general, s u f f i c i e n t l y limited to allow business cycle peaks to appear i n the spectrum so long as n exceeds 200-250 observations. At t h i s truncation point the variance of the estimates may introduce spurious peaks into the spectrum but t h i s effect can be examined through a "window opening" procedure which involves re-estimating the spectrum at lower truncation points. By comparing a set of spectra estimated with a variety of truncation points, the s t a b i l i t y of i r r e g u l a r i t i e s i n the spectra can be analysed - although i t i s expected that the more pronounced peaks w i l l be found i n the spectrum estimated with the n/3 truncation point. This 79 i s the procedure followed here and conclusions concerning cycle i d e n t i f i c a t i o n are derived from the spectrum estimated with a n/3 truncation point - even though there i s no p a r t i c u l a r reason for selecting this p o i n t . * 2 2. The Episodic Method In the episodic method cycles i n i n d i v i d u a l time-series can be defined i n terms of i d e n t i f i e d peak and trough turning points. The cycle of predominant i n t e r e s t i s the business cycle. Since seasonality i s t h e o r e t i c a l l y d i s t i n c t from t h i s cycle - the turning points of the annual and business cycle need not coincide - i d e n t i f i c a t i o n i s aided by seasonally-adjusting each time-series. The method used i n t h i s study i s the X-11 variant of the Census Method II programme prepared by the United States' Department of Commerce.*3 The "additive" method i s selected and i t assumes the weights of each dynamic component i n the time-series to be constant over time. Seasonal factors are determined by a 3x5 term moving average and there are d i f f e r e n t factors for each year.** Nerlove [I960] has shown empirically that t h i s adjustment does not introduce a serious, spurious non-seasonal c y c l i c a l element into the time series. In p l o t t i n g each regional series for the purpose of i d e n t i f y i n g turning points, the series are f i r s t detrended by harmonic regression. Also, observation i s aided by 80 p l o t t i n g the detrended, seasonally-adjusted series against a series from which the " i r r e g u l a r " component i s removed by a 13-term moving average. Cycles are s t i l l i d e n t i f i e d i n the former series, but the l a t t e r , smoothed series accentuates the business cycle component (although i t may even magnify i t , as Slutsky [1937] and Bird, et. a l . [1965] have shown). Identifying turning points i n a time-series which includes both i r r e g u l a r and recurring fluctuations involves somewhat a r b i t r a r y d i s t i n c t i o n between these two components. The d i s t i n c t i o n i s surely a question of the degree to which an indicator i s affected by some stochastic disturbance which has occurred either i n t e r n a l l y or externally to the economy.4 s Thus, to compare the recurring fluctuations between regions, i t i s important to i d e n t i f y turning points consistently i n every region. To do t h i s a set of c r i t e r i a i s employed to d i s t i n g u i s h the peaks and troughs of recurring fluctuations (cycles) from i r r e g u l a r movements i n the i n d i c a t o r : * 6 (1) a peak (trough) i s i d e n t i f i e d at the observation which i s (a) the maximum (minimum) value within an approximate two year time period, and (b) above (below) the mean of the series, (2) when a peak (trough) i s l e v e l - zero detrended growth -fo r a period of time, the f i r s t occurrence, of the l e v e l i s the i d e n t i f i e d peak (trough), (3) minor cycles - where both peak and trough are on the same .81 side of the mean of the series - are i d e n t i f i e d as c y c l i c a l episodes i f they have duration and v o l a t i l i t y of the same order of magnitude as the average major cycle (where the peak i s above, and the trough below, the mean), (4) where contiguous minor cycle peaks (troughs) exist, the peak (trough) closest to the Chambers-Waterman reference cycle dating i s selected as the turning p o i n t , 4 7 (5) the month i n which the turning point occurs i s considered to be l a s t month of the previous episode. The presence of long swings i n seasonally-adjusted, detrended time-series can d i s t o r t the i d e n t i f i c a t i o n of business cycle turning points. The primary d i s t o r t i o n would be the tendency to make major cycles appear i n the series as i f they were minor cycles. Since i t would be extremely d i f f i c u l t to accurately remove long swings from the data, the alternative i s to provide i n the i d e n t i f i c a t i o n c r i t e r i a a f a i r l y wide l a t i t u d e for the i n c l u s i o n of minor cycles as i d e n t i f i e d turning points. The d i s t o r t i o n s are not expected to be very severe in the post-World War II period; for t h i s period i t i s obvious that long swings do not dominate the data and may be s t a t i s t i c a l l y i n s i g n i f i c a n t . However, the interwar period, dominated by the boom of the 1920*s and depression of the 1930s, undoubtedly includes business cycles which have been distorted i n t h i s way. 82 REGIONAL TIMING POIHTS Bugloyment Index (interwar^ Pralrlee Ontario Quebec Maritimes a^loynmt ladnj (poatvarj Prairiea tat&rlo Quebec Karltimea Canada Bank Deblta ( i n t e r w ) Pralrlea Ontario Quebec Karl times Bank Deblta (Poatvar) Prairies Ontario Quebec Karltlmea 5/19 5/19 3/19 1/20 a/19 V19 6/46 BA6 9A6 9A6 8A6 SA6 3/19 2/20 1/19 2/19 3/19 1/19 1/1*6 3A6 U A 5 l/U 2A6 11A5 Conatractlon Cont met a flntervax) are: *-6/19 Prairies 5/19 Ontario 4/19 Quebec 6/1Q Korltljaee 4/19 Canada II /10 Construction Contract* (pcatvar) Prairies Ontario Quebec Marltijaes 4/48 1/1.9 5/48 6/48 4/46 5/48 8/a 5/20 9 / » -,—5/20 6/21 4/20 3/21 11/19 7/21 6/20 6/21 5/20 1/21 1/20 6/20 8/20 3/20 12/22 9/2* 1/23 10/24 2/24 9/24 11/23 9/24 7/23 2/24 7/47 2/50 l6/46 6/50 11/48 3/50 12/47 3/50 iAe 3/50 3/48 2/50 2/52 9/51 6/51 9/52 6/51 8/21 5/28 8/46 6/V7 12/1.6 3/49 11/46 7/48 2/18 10/48 U/46 11/49 11/46 11/48 1/50 10/50 PC9 4/49 9/50 2/50 ll/l< 3/20 11/19 2/51 1/20 2/22 10/19 6/21 1/20 7/21 7/50 6/49 6/49 U/49 6A9 8A9 3/22 7/22 5/22 12/22 1/51 6/52 3/51 10/50 11/50 3/51 8/53 7/53 5/53 7/52 e/55 12/24 S/24 10/52 1/52 1/52 8/29 8/28 8/29 11/29 7/30 8/29 2/53 1/52 5/53 4/53 3/53 1/53 1/53 4/55 3/23 4/ak 12/55 11/56 u / 5 5 6/57 6/55 11/57 6/56 5/57 9/55 8/56 3/56 5/57 3/33 9/32 4/33 11/32 1/33 5/33 1/23 1/24 2/23 7/24 10/22 10/23 7/22 10/23 9/22 11/23 2/23 2/24 2/52 2/55 12/52 7/55 1/53 1/55 9/54 5/55 11/54 9/54 11/54 11/54 3/25 l l / » 8/56 10/56 5/56 5/56 8/55 5/56 9/25 5/25 5/24 4/24 4/24 6/24 6/57 5/58 1/58 MS 3/58 12/35 12/36 3/34 10/36 7/34 7/35 3/35 7/36 3/34 7/34 7/34 7/36 9/57 9/58 3/57 9/58 12/56 11/58 12/56 10/58 12/56 11/58 12/56 10/58 2/27 10/26 10/26 2/26 12/26 10/26 5/37 11/39 3/36 5/39 10/37 5/39 10/37 11/38 7/37 2/39 " 11/38 9/37 6/59 ID/61 11/59 5/60 11/59 l / d l 12/59 6/60 11/59 1/61 6/59 1 / 8 1/29 7/58 9/57 11/59 1/58 2/60 3/58 3/60 3/57 2/59 3/58 2/60 2/28 6/28 10/27 7/28 10/28 i/28 UL/sri 11A 5/28 4/29 5/28 12/28 3/61 11/61 8/60 4/61 9/60 9/6I 8/60 10/60 8/61 11/60 9/61 ins 6/69 7/2? M/29 10/29 6/29 5/61 1/63 6/61 12/62 6/62 11/61 4/63 5/63 7/62 3/61 3<§ H" 5 / » 5/v 4/32 3/29 4/33 3/29 5/32 5/34 3/35 10/34 4/35 10/34 5/35 7/54 2/35 10/34 2/35 11/60 1/62 U / 6 0 1D/6J 10/60 10/62 2/62 11/62 1/60 10/61 11/60 10/62 12/63 3/66 7/64 2/67 5/65 2/67 1/66 9/66 8/63 8/63 9/62 9/63 1/30 6/30 12/63 4/64 11/63 5/64 1/64 6/64 5/65 8/32 5/32 6/32 2/33 5/32 5/32 5/64 4/65 10/64 10/65 4/65 .3/65 2/66 6/67 6/66 2/37 1/36 V 3 7 3/37 3/37 4/37 3/68 2/69 6/68 3/68 6/67 3/68 4/68 7/68 7/68 11/66 7/68 6/66 7/68 6/66 7/6B 4/38 7/38 5/38 5/38 4/38 5/38 I/69 7/68 5/35 11/35 4/35 9/36 2/55 10/35 10/35 8/36 6/35 11/35 2/35 11/35 12/66 1/70 1/69 11/69 7/69 11/69 11/69 9/38 12/39 e/38 11/30 3/39 10/38 1/70 2/69 3/37 7/37 6/37 8/37 2/37 6/37 7/70 7/71 8/64 6/65 5/68 7/68 5/63 6/68 3/66 7/69 6/70 7/70 12/70 7/69 9/70 5/39 9/39 10/39 10/39 3/39 10/39 3/69 12/68 3/63 12/68 4/69 3/69 5/72 9/72 11/71 3/71 11/71 8/71 6/70 5/71 2/71 7/71 3/70 5/71 2/40 9/40 11/40 11/40 e/li 1/41 8/71 9/71 11/69 11/69 IO/69 12/69 1/70 Pralrlee Ontario Quebec Karltljnee canaaa 11/21 4/22 6/22 1/22 4/22 8/24 10/23 8/24 4/23 4/23 3/23 8/24 8/24 6/25 9/24 12/25 8/26 3/27 11/26 6/27 10/28 11/28 11/27 8/29 10/27 7/2? 9/27 10/21 11/29 6a 7/32 8/30 8/31 7/32 7/32 10/32 7/32 10/34 5/36 3/34 10/36 1/36 6A7 8/36 3/37 6/37 7/37 4/57 7/38 6/38 HI 9/38 11/38 2/39 Prairies Ontario Quebec Maritimes 6/45 5/45 7A6 5/46 3A7 5A6 Dwelling, starts (PostwarHQugrtcr/Yegr) 1/48 2/51 Pralrlee 3/48 4 / 5 1 Ontario • i ^ f l 3/51 Quebec 2/1,3 4 / ^ Maritimes 2/48 3/5J. C ~ " a fa |,/51 Consumer Price Index {Postwar) Pralrlee Ontario Quebec Harltljoee 1/50 1/50 1/50 2/50 1/50 2/50 9/48 10/47 11/48 6Ae 3/48 11/48 1/53 2/53 1/53 3/53 1/53 1/53 12/51 1/54 12/51 -11/51 -12/51 -12/51 -12/51 -1/50 5/50 loA9 10/49 6/49 1/50 2/53 5/53 4/53 4/53 2/53 4/53 9/54 2/52 8/52 5/52 11/52 S/52 3/51 8/52 3/51 2/55 3/55 4/56 4/56 4/56 4/56 3/55 4/56 3>55 2/55 3/55 4/56 5/56 5/56 2/56 3/56 2/56 2/56 5/58 3/58 /  3/58 /  3/56 3/58 2/53 6/53 6/53 3/53 8/52 3/53 2/58 2/58 2/58 2/58 1/56 2/56 5/59 3/59 7/59 3/59 9/58 6/59 1/54 5/54 5/54 7/54 8/56 5/54 3/56 5/54 2/60 2/60 2/60 2/60 3/62 3/60 3/61 2/60 - ' -10/55 6/56 8/56 1/62 3/62 1/61 10/60 3/62 U/fO 7/61 10/60 6/61 12/60 5/61 10/60 6/61 10/60 10/61 12/57 12/59 9/58 2/63 4/63 4/62 12/59 H/59 7/59 8/56 8/58 9/59 4/64 4/64 4/64 2/63 4/64 3.62 4/64 1/62 4/62 4/64 4/63 6/62 2/63 1/63 10/62 10/64 1/63 11/64 10/64 10/64 10/64 2/65 6/61 7/62 5/61 7/61 3/61 9/61 5/62 8/62 2/66 2/66 3/66 2/66 3/66 1/67 10/66 2/67 3/66 2/67 10/66 3/67 2/66 7/66 4/66 6/67 10/66 2/67 6/64 3/63 12/64 6/63 6/64 12/64 6/64 3/67 3/68 2/69 2/69 4/68 4/68 2/69 1/69 1/68 6/68 5/65 5/65 5/65 5/65 2/70 2/70 1/70 2/70 1/70 1/70 1/68 6/68 6/69 12/69 9/69 .6/69 2/70 6/69 12/65 11/67 11/65 5/65 12/65 11/68 11/68 11/65 8/69 11/65 11/68 4/71 2/71 3/71 4/71 2/71 4/71 3/71 10/71 12/70 12/70 2/71 12/70 5/71 5/71 5/71 7/70 5/71 5/71 1/73 4/72 1/75 2/72 1/75 1/73 11/71 11/72 8/73 2/72 7/72 2/72 2/72 5/73 6/73 V". 5/73 00 Appendix 2C Table C l 1 SPECTRAL DENSITY ESTIMATES AT ANNUAL FREQUENCIES (Truncation Point n / 3 ) -Canada B.C. Prai r i e s Ontario Quebec Maritimes Indicator Type of Detrending T o t a l Period (1) Interwar (2) Postwar (5) (1) (2) (5) (1) (2) (5) (1) (2) (3) (1) (2) (3) (1) (2) (3) Employment Index Harmonic Growth Rates • 197 -51*5 .21*9 .1*60 .200 —1*68 .228 .265 .528 —11*0 .1*80 • 525 — 200 - .866 — 100 .212 .118 -.1*82 • 195 .1*25 .527 - 5 1 1 .1*56 .5U7 Bank Debits Harmonic^ Growth Rates - -.7^1 -.665 -1 .086 - -1 .012 -1*55 -1.212 -.110 .01*0 -511* -— 610 - 7 9 2 -1.1*28 - - 7 9 0 - 7 1 6 -1.1*95 - - 5 9 6 - 7 0 5 -1.1*28 Construction Contracts Harmonic Growth Rates .1*16 - 0 9 7 - 5 5 7 .176 —250 - 5 5 5 - .876 -1.000 -1*99 -1.271* • 585 —071 - 2 7 0 .182 - 3 3 0 .189 —050 -.508 -.065 -.1*1*6 -.001 - 1 7 5 -.1*10 - .166 - 7 5 5 -.076 - .252 -305 —192 - 5 6 6 Freight Carloadings Harmonic Growth Rates .297 -.245 - .252 -.298 -.021 - .008 - 5 0 7 — 1*10 —206 -.661 • 39i* .289 -.01*7 .202 -.161 - 5 2 1 -1.11*9 -.866 - 2 7 8 - 5 9 5 .568 - 2 9 5 — I69 .1*70 .270 -61*0 - 5 5 5 - .890 -.751 -1.175 Dwelling Starts Harmonic - - —020 - - — 250 - - -.030 - - —012 - - - .070 - - - 0 5 0 CPI Harmonic _ -1.051* - - - 9 3 1 - - -I.O60 - - -1 .058 - - -1.055 - - - 8 8 6 1 Average of spectral density over 2 frequencies closest to annual frequency (.083) 2 Detrended by harmonic regression over subperiod. 00 Appendix 2C Table C2 SUBCYCLE PEAKS IN ESTIMATED SPECTRAL DENSITY FUNCTIONS (Periodicity Presented in Years/Months) Indicator Canada B.C. Prairies Ontario Periodicity Magnitude Employment Index Total Period (Harmonic) 1/0-2/0 Quebec Maritimes Periodicity Magnitude Periodicity Magnitude Periodicity Magnitude Periodicity Magnitude Interwar (Harmonic) Postwar (Harmonic) (Growth Rate) Bank Debits Interwar (Harmonic) Postwar (Harmonic) (Growth Rate) Construction Contracts 1/8-2/1 1/8-1/10 1/10-2/5 l / l O - 2 / l 1/8-2/1 Total Period (Harmonic) Z2/5-2/7 v^/lO-2/lO Interwar (Harmonic) 1/8-2/1 (Growth Rate) l/ l O - 2 / l Postwar (Harmonic) (Growth Rate) Freight Carloadings Total Period (Harmonic) Interwar (Harmonic) (Growth Rate) Postwar (Harmonic) (Growth Rate) Dwelling Starts Postwar (Harmonic) Consumer Price Index Postwar (Harmonic) 1/10-2/1 2/7-2/10 1/8 1/8 1/8-1/10 medium slight slight medium medium medium slight, large J medium slight medium medium l / 8 - l / l l medium slight slight medium 2/0-2/5 l / l O - 2 / l 2/5-2/7 1/7-1/8 2/0-2/5 I/10-2/1 /2/1-2/5 W6 - 1 / 8 2/1-2/5 1/7-1/10 1/8-1/9 1/11 1/7-1/10 2/3-2/5 1/9-2/3 1/6-1/8 medium slight slight slight large medium slight \ medium J large slight large slight large slight large slight 2/6-2/7 2/1-2/7 2/1-2/7 2/5-2/10 1/8-2/1 1/7-1/10 2/4-2/7 2/5-2/7 1/7-1/10 2/5-2/10 2/3-2/6 2/6-2/11 2/5-2/11 2/0 1/6-1/10 large slight medium medium medium medium medium medium large medium slight slight medium slight slight (5/0-3/6 Vl/lO-2/l 1/7-1/10 /2A-2/6 Vl/8-1/10 1/8-2/1 1/8-2/1 1/10-2/1 1/11-2/1 1/8-1/10 medium\ slighty 1/0-2/0 slight l / 6-l/lO 1/8-2/1 l/lO - 2/l l/lO - 2/l slight 2/5-2/7 2/1-2/7 medium large medium "\ large y medium medium medium slight large 1/8-2/10 medium 1/8-1/10 medium 2/7-2/9 1/10-2/5 1/8-2/1 /2/7-2/10 W7-2/1 1/8-2/1 1/8-2/1 l/lO - 2/l 2/5-2/10 1/7-1/8 1/6-1/9 medium medium slight slight slight medium medium large "\ large / large large medium large large large Periodicity Magnitude 2/1-2/5 medium 1/10-2/1 2/5-2/7 1/10-2/1 2A-3A Z2/5-2/9 vi/8-2/1 1/8-1/11 2/1-2/5 1/7-1/10 2/5-2/10 1/9-1/11 1/8-1/10 2/5-2/11 2/0-2/6 1/8-1/10 slight slight slight medium mediunA medium y medium slight medium large medium slight medium large slight Appendix 2C Table C3 INTERREGIONAL COMPARISON OF BUSINESS CYCLE E/C RATIOS; "UNIQUE" EPISODES INCLUDED (Ranked from Highest to Lowest) LO 00 (a) (E/C).>(E/C) +a c i 7 ? ) (c) CE/C).<(E7c)-a(i7E) (a) (b) Interwar MAR PRA, OUT QUE BC Employment Index Bank Debits Construction Contracts Postwar I PRA, OHT QUE, MAR Postwar II —Ui— PRA, MAR OHT, QUE BC QUE BC MAR Freight Carloadings Taj T3T ONT BC, PRA QUE BC PRA, ONT MAR (1) QUE OUT, MAR BC, PRA (2) BC Dwelling Starts m MAR BC, PRA QUE (3) MAR PRA, ONT PRA, ONT QUE, MAR QUE BC T3T PRA BC, QUE MAR (1) BC PRA, ONT MAR QUE (2) BC ONT, QUE PRA MAR (3) MAR BC, PRA QUE OHT Consumer Price Index MAR BC, PRA QUE 137 BC PRA, ONT QUE (c) ONT MAR QUE ONT ONT ONT MAR 1 The significance test is exactly analogous to that used in comparing spectral densities in Table 2.5-Thus, (E/C^ is the E/C ratio in the ith region and (E7C) is the regional mean. C O Appendix 2C Table Ck RELATIVE CONTRIBUTION OF BUSINESS CYCLE FREQUENCIES TO EXPLANATION OF TOTAL VARIANCE IN THE REGIONAL INDICATORS (relative to other frequencies) B.C. Prairies Ontario Indicator Type o f Total Period Detrending (l) Interwar (2) Postwar (3 ) (1 ) (2) (3) (1) (2) (3) Employment Index Harmonic Growth Rates - 0 . 2 9 - 0 . 0 3 - 0 . 1 5 -1.31 - 0 . 9 0 - 0 . 0 6 -0.61+ - 1 . 7 1 - 0 . 2 5 - . 11 - .01 - . 87 Bank Debits Harmonic Growth Rates - 0 . 1 0 - 2 . 1 5 - . 28 -- -32 -2.31+ - 0 . 5 9 - .11 - 2 . 2 1 - . 6 3 Construction Contracts Harmonic Growth Rates -0.1+6 - 0 . 1 7 - 0 . 9 9 - -35 -0.6k - 1 . 2 0 - 0 . 1 9 - 1 . 1 1 - . 80 -1.1+7 - 0 . 5 0 - 0 . 2 1 - 1 . 1 7 - 0 - 5 7 - 0 . 9 9 Freight Carloadings Harmonic Growth Rates -O.36 -1.61+ - 0 . 3 9 - 1 . 5 1 - 0 . 2 5 - 1 . 9 5 - 0 . 6 2 -I . 96 -0.83 - 1 . 8 0 -0.1+2 - 2 . 1 0 -0.21+ -1.31 - 0 . 2 3 - 1 . 2 6 - 0 . 0 9 •-1.54 Dwelling Starts Harmonic - - -O.65 - - - 0 . 8 6 - - -O.96 CPI Harmonic - - -0.32 - - 0 . 3 7 _ _ - 0 . 3 8 (1) -0.1+5 -0.62 -0.1+9 -1.51 Quebec (2) - . 0 9 - 0 . 1 1 - 0 . 2 5 - 0 . 1 5 -1.21+ ( 3 ) - 0 . 2 1 - 1 . 1 7 -2.23 - .1+6 -O.51 -1.1+3 - 0 . 5 7 - 1 - 5 9 - 1 . 0 1 -0.33 Maritimes (1 ) -0.1+1+ - 0 . 5 3 -0.31 -1.59 (2) (3 ) - 0 . 1 1 - 0 . 5 3 - - 1 . 6 0 _ - 2 . 3 8 -0.03 - . 6 9 -O.58 - . 6 1 - 0 . 7 8 - 1 . 0 7 - 0 . 0 3 - 0 . 1 2 - 1 . 5 2 -1.1+9 - - 1 . 0 9 - - 0 . 3 3 Appendix 2C Table C5 AVERAGE REGIONAL LEADS AND LAGS: EPISODIC METHOD (corresponding episodes) oo Region B.C. Prairies Ontario Quebec Maritimes Leading 1 2 2 1 1 Number of Indicators Leading and Lagging by at Least 1 Month on Average: Peaks  Interwar Postwar Lagging (2) 1 0 0 0 2 Coincide (3) 2 2 2 3 1 (1) 4 2 2 3 6 (2) 1 . 4 0 1 0 (3) 1 0 4 2 0 (1) 5 1 2 3 4 Postwar I (2) 1 4 0 2 1 Postwar II (3) 0 1 4 1 1 (1) 1 3 3 2 3 (2) 1 1 1 3 1 (3) 4 2 2 I 2 Number of Indicators Leadings and Lagging by at Least 1 Month: Troughs B.C. Prairies Ontario Quebec Maritimes (1) 2 3 2 1 2 Interwar (2) 2 1 0 1 1 (3) 0 0 2 2 1 (1) 3 1 4 3 5 Postwar (2) 1 3 1 0 0 (3) 2 2 1 3 1 CD-4 1 4 0 6 Postwar I (2) 0 2 0 0 0 Postwar II (3) 2 3 2 6 0 (1) 2 3 4 4 3 (2) 1 2 2 1 1 (3) 3 1 0 1 2 88 Appendix 2C Table C6 UNIFORMITY Maritimes (1) Employment Index (2) Construction Contracts (3) Bank Debits (4) Freight Carloadings (5) Dwelling Starts (6) Consumer Price Index Quebec (1) Employment Index (2) Construction Contracts (3) Bank Debits (4) Freight Carloadings CS) Dwelling Starts (6) Consumer Price Index Ontario Interwar Peaks Troughs 18.69 8.00 57.71 14.17 Postwar Postwar I Postwar II Peaks Troughs Peaks Troughs Peaks Troughs 7. OS 12.26 1.00 10.88 8.78 1.45 7.75 75.83 2.06 3.16 6.10 6.36 11.76 5.55 70.94 13.80 2.20 0.21 8.65 3.74 4.78 4.65 9.20 38.24 9.91 3.74 2.00 2.00 5.10 8.70 56.13 12.44 0.66 5.51 109.56 36.71 7.87 132.00 29.82 4.80 1.57 4.69 16.44 8.00 7.78 5.76 2.26 70.09 14.00 6.00** 0.08 4.57 9.83 9.17 6.71 62.59 11.25 108.89 2.50 17.16 5.50 16.60 6.76 8.62 4.12 3.SO** 22.50 8.66 - - 35.92 32.25 7.00 2.00 5.86 62.40 - 8.73 7.61 4.66 4.66 5.28 8.82 (1) Employment Index (2) Construction Contracts (3) Bank Debits (4) Freight Carloadings (5) Dwelling Starts (6) Consumer Price Index Prairies (1) Employment Index (2) Construction Contracts (3) Bank Debits (4) Freight Carloadings .-(5) Dwelling Starts (6) Consumer Price Index. B.C. Cl) Employment Index (2) Construction Contracts (3) Bank Debits (4) Freight Carloadings (5) Dwelling Starts (6) Consumer Price Index 0.0 36.69 13.16 8.45 0.22 0.63 4.00 6.10 4.16 4.07 6.80 14.95 1.50 12.66 16.16 1.32 0.87 8.63 9.45 0.47 3.00 2.37 9.87 0.39 , 0.66 0.2S 12.57 1.98 11.07 1.80 2.60 3.00 - - 6.74 3.00 0.0 ** 0.33 5.40 4.80 7.85 4.43 1.32 0.66** 0.66 2.80 9.44 • 27^13 1.34 2.63 0.61 1.42 0.66 0.65 11.83 26.94 16.32 14.55 6.75 12.71 20.24 10.14 670.84 9.52 11.32 7.66 1.71 11.25 25.72 5.01 13.74 2.41 20.26 13.48 25.60 60.80 1.50 29.81 - 2.09 5.91 2.00 1.00 4.31 9.20 18.53 3.83 2.67 4.66** 14.09 1.12 250.60 5.43 23.94 13.54 27.56 0.93 9.40 22.50** . 4.85 11.60 5.11 47.24 3.12 37.52 4.71 6.80** 0.70 1.41 4.42 14.50 5.27 14.50 1.00 13.SO 2.99 3.73 .9.80 5.00 5.18 6.40 21.50 3.00 • " • - 2.25** 11.95 2.00 0.40 2.40 25.20** - 5.40 4.38 6.93 12.69 2.57 1.50 Appendix 2C Table C7 CLUSTERING: EPISODIC METHOD oo Interwar Postwar Postwar I Postwar II Peaks Troughs Peaks Troughs Peaks Troughs Peaks Troughs Employment Index 6.24 16.56 26.81 13.94 25.76 19.57 27.86 8.30 Construction Contracts 4.99 15.01 24.86 25.11 43.76 20.84 5.95 29.37 Bank Debits 19.69 23.28 63.99 35.87 63.82 37.98 64.17 33.76 Freight Carloadings 22.70 12.21 10.49 14.83 13.92 7.34 7.05 24.20 Dwelling Starts - - 10.17 10.24 4.32 4.48 13.68 13.70 CPI - - 7.48 7.84 3.52 5.90 11.63 4.29 1 Postwar I period ends at fi r s t identified trough before 1960. Appendix 2C Table C8 O CM RATIO OF IRREGULAR TO CYCLICAL Indicator CSMOOTHED) COMPONENTS 1 Region Employment cn Interwar Index Value of Construction Contracts Bank Debits Freight Carloadings Consumer Price Index (2) Postwar Cl) (2) CD C2) CD C2) C2) B.C. 1.18 0.98 4.61* 2.64 1.81 4.85* 2.74 3.22 .95 Prairies 1.38 1.12 2.05 3.47 2.64 5.70* 2.44 2.96 .82 Ontario 0.93 0.90 3.38 5.73* 2.44 5.97* 1.76 2.42 .91 Quebec 1.41 1.01 3.97* 4.73* 2.74 5.11* 1.74 1.71 .88 Maritimes 1.22 1.64 3.24 3.55 2.19 6.75* 1.88 3.45 .95 Canada 0.59 0.90 3.37 4.17 2.40 3.48 2.39 2.53 .62 1 In the seasonally-adjusted, detrended series, this ratio i s : total variance - variance contributed by cyclical component variance contributed by cyclical component The cyclical "component" i s the smoothed series. In most cases, the smoothing procedure is a 13-term moving average. If the series i s highly irregular, a 23-tenn average i s employed. Such cases are marked with an (*). 91 APPENDIX 2D CANADIAN REGIONAL DATA AND DATA MANIPULATIONS 1. Index of Employment, monthly, 1919-1973, Canada and regions: Note; The index i s an i n d u s t r i a l composite excluding agriculture, f i s h i n g , trapping, public administration and defense. The series i s based upon the establish-ment survey (where establishments employ 20 or more persons). Manipulations: The index i s adjusted to a common (1926=100.0) base. Extension, 1919-1921, i s by "vacancies reported at month's end", compiled for major c i t i e s in the Labour Gazette. The extension i s linked to the 1922-19 73 index by a l i n k i n g factor from overlapping 1922 observations. To re-aggregate regions for the ROC series employment weights are from Employment and Payrolls, 72-002. The weights are assumed to be constant f o r the 12 months of each year; for the years i n which the weights are not published, they are interpolated. Sources: 1922-1973: DBS (1922-1973), "Employment and Average Weekly Wages and Salaries ( t i t l e v a r i e s ) " . Units: index, 1926=100.0 2. Bank Debits, monthly, 1919-1973, Canada and regions: Note: Bank debits are defined as cheques paid through banks 92 located i n various clearing house centres and charged to deposit accounts. Several regional observations are missing, 1940-1944. Manipulations: Series are extended 1919-1923 by clearing s t a t i s t i c s f o r major c i t i e s linked to the debit series by the r a t i o of clearings to debits, 1924-1927. The cle a r i n g s t a t i s t i c s are a v a i l a b l e by major c i t y i n the Monetary Times. When the cross spectra are estimated between these regional series and the United States series for the postwar period the series are seasonally-adjusted by the Census Method XII pro-gramme (see Appendix 4A) . Sources; 1924-1939: DBS (1924-1939), "Monthly Review of Eusiness S t a t i s t i c s " . 1945-1973: DBS (1945-1973), "Cheques Cashed at Clearing Centres". Units: M i l l i o n s of d o l l a r s , expressed i n logarithmic form. 3. Value of Construction Contracts, monthly, 1919-1972, Canada and regions: Manipulations: For 1919-1921 period, series i s extended by the value of building permits by major c i t y , linked by the r a t i o of contracts to permits for 1922-192 7. Building permits are avai-lable by major c i t y i n the Canada Year Book. 93 Series i s .not available f o r a l l regions afte r 1972. Sources: 1922-1940: DBS (1924-1939), "Monthly Review of Business S t a t i s t i c s " . 1940-1965: "Building Reporter", a removable section of the MacLean's Building Guide. 1966-1972: Southam Building Guide. Freight Carloadings, monthly, 1919-1966, Canada and regions: Note: Regional series are available only i n quarterly form from 1.9,67. Manipulations: Series are seasonally-adjusted by the Census Method II programme when they are used to estimate cross spectra with the United States ser i e s . Sources: 1919-1973: DBS (1919-1973), "Monthly T r a f f i c Report of the Railways of Canada". Units: Thousands of Cars. Consumer Price Index, monthly, 1949-1973, Canada and regions Note: Indexes are available 1919-1939 (Labour Gazette) for a l l items, staple foodstuffs, f u e l and l i g h t and rent by major c i t y but they are too crude to be used here. Manipulations: 1949-1973 are adjusted t o common 1949=100.0 base. Sources: 1949-1973: DBS (1949, 1973), "Prices and Price Indexes". Units: index, 1949=100.0 94 6. Number of Dwelling Starts, quarterly, 1948-1973, Canada and regions: Note: There i s some inconsistency i n the series over time due to expanding coverage. Error i s minimized by using the most recently-published observation. Sources: 19"8-1973: DBS (1948, 1973), "Housing Starts and Completions". Units: Thousands of Units. 95 FOOTNOTES TO CHAPTER TWO The l i t e r a t u r e on c y c l e i d e n t i f i c a t i o n i s f a r too v a s t t o f a c i l i t a t e exhaustive survey. The work of the NBER dominates and t y p i c a l of t h i s approach are, f o r U.S. business c y c l e s , M i t c h e l l [ 1927, 1951 ], Burns and M i t c h e l l [1947], and Moore [ 1961 , 1955 ]. Chambers-[ 1958, 1964 ], Hay [ 1966 ], White [1967], Rosenbluth [1957], Waterman [1973] and Beckett [1961] i n v e s t i g a t e Canadian business c y c l e s . Granger and Hatanaka [45, Chap. 12] and B l a i n , Paterson and Rae [1974] use s p e c t r a l a n a l y s i s t o examine bu s i n e s s c y c l e s i n the U.S. and B r i t i s h Columbia, r e s p e c t i v e l y . Kuznets [1952], Burns [1934], Burns and M i t c h e l l [1947] I s a r d [1942] and Abramovitz [1956,1959,1964] t e s t f o r "long swings" i r U.S. t i m e - s e r i e s using an e p i s o d i c approach. Daly [1965] t e s t s the Canadian data. Using s p e c t r a l a n a l y s i s , Adelman [ 1965 ], Granger and Hatanaka [ 1964], Hatanaka and Howrey [ 1968], Howrey [1968] and Harkness ["9] t e s t the U.S. data, and Harkness [1969] t e s t s the Canadian. C a l c u l a t e d average d u r a t i o n s tend t o vary a c c o r d i n g t o the i n d i c a t o r and the method used. Subcycles i n the U.S. economy are examined by Mintz [1972] and Mack [195 7, 1967]. For e x p o s i t i o n of s p e c t r a l a n a l y s i s as an econometric technique, see Granger and Hatanaka [1964] and J e n k i n s 96 and Watts [ 1968 ]. Precise s p e c i f i c a t i o n of business cycle turning points (or, i n the case of spectral analysis, precise s p e c i f i c a t i o n of autocovariances underlying the estimation of the spectral density function) requires monthly or quarterly observations i n order to capture the intrayear c y c l i c a l pattern. The problem of t e s t i n g for s t a t i s t i c a l s i g n i f i c a n c e i s discussed i n Section 2.3. The f r e i g h t carloadings series i s available only i n quarterly form, 1966-1973. Other economic time-series are available but are not considered (by t h i s author) to be r e l i a b l e indicators of general economic a c t i v i t y ; for example, sales of l i f e insurance (1924-1973). Chambers [1958], Waterman [1973], Beckett [1961]. Beckett's reference cycle covers only the 1948-1957 period. Chambers [ 1958], Beckett [1961, pg. 304-305]. Beckett [1961, pg. 304-305]. 97 1 1 The r e t a i l trade series i s also rejected because i t does not cover any two subperiods. 1 2 The r a t i o i s calculated i n the X-11 Census Method II seasonal adjustment programme. Since t h i s programme requires a time series of less than 30 years length, the r a t i o s are calculated for the interwar (approximately 1919-1940) and postwar (approximately 1945-1973) periods. 1 3 The spectra are presented i n logarithmic form so as to decentuate the effects of leakage from the low frequencies. »* Jenkins and Watts [1968, pg. 255] and Jenkins [1961]. The problem i s due to the variance-bias trade-off i n the spectral estimators. See Appendix A for discussion. l s Hatanaka and Howrey [1968]. For discussion and application see Harkness [1969] and B l a i n , Paterson and Rae [1974, Appendix A]. 1 6 In general, the business cycle band includes periods from 2 years/9 months to 5 years/0 months, and the seasonal v a r i a t i o n from 11.5 to 12.8 months. These bands can vary s l i g h t l y according to the in d i c a t o r and time period. 98 1 7 For example, Waterman [19 73, pg. 128] dates a reference cycle peak at A p r i l 1951, while Chambers [1958] omits the episode completely. i s Mack [ 1957, 1967 ]. 1 9 In a few cases, a peak i s found with one method of detrending but not with the other. For these cases the following rule i s applied: at least one of the two density functions must have a large peak before the case i s considered a s i g n i f i c a n t peak. 2 0 That more cases of si g n i f i c a n c e cx^arrred i n the t o t a l period than i n either subperiod can be accounted f o r by the greater number of degrees of freedom i n the former case. 2 * Mack [ 1967, pg. 163]. 2 2 White [ 1967, pg. 37 ]. 2 3 Calculated from Table 36 i n Waterman [1973, pg. 128]. 2 4 Chambers i d e n t i f i e s peaks i n October 1948 and May 1953. The t o t a l duration of t h i s episode i s thus 58 months. Within t h i s period Waterman includes two complete episodes. 99 This r a t i o i s calculated from Waterman's " r e l a t i v e l y r e l i a b l e reference cycle" [1973, pg. 128]. Episodes are measured between points of zero detrended growth. For several reasons, not every episode has such points and thus the r a t i o i s not calculated over every episode. Granger and Hatanaka [1964], pg. 159. 2 7 A smaller lead (lag) at troughs (peaks) than at peaks (troughs) i s also consistent. - e i 5 8 2 8 The base i s the average regional r a t i o , that i s r = — Z i \ . i = l The standard deviation i s a r 1 y f,! -e,2 2 9 I f the lead or lag i s less than 1 month, the region i s con-sidered "coincident" with the Canadian base. 3 0 Bank debits (troughs and peaks) and dwelling starts (peaks) 3 1 The P r a i r i e s lag i n the interwar period employment index but t h i s l a g increases i n the postwar period. 3 2 The variance calculated r e l a t i v e to the regional average i s , i n e f f e c t , an "unweighted" variance where each region 100 has equal weight i n determining the reference point to which the regional turning points are compared- If the variance were calculated with the Canadian turning point as a reference, t h i s would i n a sense be a "weighted" variance. 1 " 2 3 3 That i s , variance = — z a where n i s the number of episodes 2 1 5 - . 2 i n the subperiod and a = — £ ( e ^ ey where e i j i s the •* i = l 5 regional lead or lag for the i t h region and e. = I E ^ - . 3 i = l 1 5 -2 3 4 That i s , variance = ~r Z (e - E ) where ^ i s the average i = l - 1 lead or l a g of the i t h region and e = J ^ £^-3 5 Table 2.22 presents the c a l c u l a t i o n s j u s t f o r the data detrended by harmonic regression - but the conclusion i s the same using a growth rate transformation. 3 * That the Maritimes are a lagging region during the interwar period i s not confirmed by the episodic r e s u l t s . 3 7 For elaboration, see Jenkins and Watts [1968, pg. 239-240, 282], and Granger and Hatanaka [ 1964, pg. 60-64 ]. 101 Jenkins and Watts [ 1968- pg. 282 ], and Granger and Hatanaka [1964, pg. 61]. Granger [1966] points out that for economic variables low frequencies tend to have the greatest amplitude and that a graph of spectral density against frequency w i l l be down-ward sloping. See also Granger and Hatanaka [1964, Chap. 8] and Harkness [1969] for discussion of the severity of the leakage problem. On t h i s method see Granger and Hatanaka [1964, pg. 134-136]. For application, see Harkness [1969], Rosenbluth [1973] and B lain, Paterson, and Rae [1974]. Jenkins and Watts [1968, pg. 277-279]. Rosenbluth [1973] selects the same truncation point. For an application of a "window opening" procedure, see Blain, Paterson and Rae [1974, Appendix A]. See Shiskin, Young and Musgrave [1972 ] f o r a description and manual. Extreme observations (those more than 2.5 standard deviations from the estimated seasonal component) are given graduated modification when estimating the f i n a l , seasonally-adjusted 102 series. This statement, I think, aptly summarizes the currently-held t h e o r e t i c a l position on the "causes" of business cycles that has emerged from a vast l i t e r a t u r e on the subject. The c r i t e r i a are based upon those used by Waterman [1973, pg. 17-19] in h i s study of Canadian business cycles over the 1947-1969 period. However, the c r i t e r i a used by Waterman are more precise than those used i n t h i s study. The Chambers [1958] reference cycle f o r Canadian business cycles covers the 1919-1960 period while Waterman's i s f o r 1948-1969. During the overlap period, the turning points do not vary s i g n i f i c a n t l y between authors although Waterman i d e n t i f i e s a minor cycle i n the early 19 50's. Since Waterman's c r i t e r i a are closest to those of t h i s study, the Waterman dating points between 1947 and 1960 are preferred to those of Chambers. 103 CHAPTER THREE THE RELATIONSHIP BETWEEN REGIONAL AND NATIONAL CYCLES 3.1 Introduction Chapter Two reported tests f o r the existence of c y c l i c a l behaviour i n the regional economies. Where such behaviour was found, the regional d i s p a r i t i e s i n the "strength", average period and timing were measured. In t h i s chapter, two additional comparisons are made between regional and national business cycle behaviour. F i r s t , the strength of inter-economy relationships on a regional-national basis i s examined by estimating "correspondence"; second, the amplitudes of cycles in the two economies (after accounting for differences i n units or absolute magnitude) are compared by estimating cross relative-amplitude. When added to the e a r l i e r evidence these two c h a r a c t e r i s t i e s of regional c y c l i c a l behaviour provide a more substantial d e s c r i p t i o n of Canadian regional business cycles during the period 1919-1973. Each of the measures alluded to above i s estimated for every regional economic ind i c a t o r and from them the dimensions of regional d i s p a r i t i e s are determined. The regional-national comparison i s of considerable i n t e r e s t for i t s own sake i n providing a more precise description of regional c y c l i c a l behaviour than has previously been ava i l a b l e to Canadian economists. As well, the comparison provides useful a p r i o r i information to the analysis of regional c y c l i c a l s e n s i t i v i t y i n the next chapter; i n the 104 Canadian context, d i s p a r i t i e s i n regional c y c l i c a l behaviour are apt to imply d i s p a r i t i e s i n regional c y c l i c a l s e n s i t i v i t y . Thus, for each indicator mentioned i n Chapter Two for each region f o r each subperiod (interwar and postwar), cross-spectral analysis i s employed to estimate the regional-national r e l a t i o n s h i p f o r the indicator over the range of business cycle frequency bands by estimating coherence (correspondence), phase (average lead/lag) and gain (cross relative-amplitude). These estimates are accompanied by regression estimates of regional-national c o r r e l a t i o n (correspondence) and e l a s t i c i t y (cross r e l a t i v e -amplitude) to, we hope, reinforce the spectral r e s u l t s . 3.2 Method* In these regional-national comparisons, the measures alluded to above are calculated for each (detrended) regional i n d i c a t o r using regional-national cross-spectra and simple e l a s t i c i t y regressions. The national economy i s simply the base upon which int e r r e g i o n a l comparisons can be made.2 (This procedure was discussed i n Section 1.1 i n the introductory chapter). For each indicator the s t a t i s t i c s are compared so as to determine (a) whether or not there e x i s t s i g n i f i c a n t regional d i s p a r i t i e s i n business cycle behaviour, and (b) whether or not there exists a pattern to these d i s p a r i t i e s over time. Correspondence measures the strength of the r e l a t i o n s h i p between a regional and the 105 national economy and a change over time i n correspondence suggests a change over time i n the economic relationship between regions. Regional behaviour i s considered " s i g n i f i c a n t l y disparate" i f cross relative-amplitude (gain and e l a s t i c i t y ) vary s i g n i f i c a n t l y from unity or phase varies s i g n i f i c a n t l y from zero. Our use of the gain and e l a s t i c i t y s t a t i s t i c s i n t h i s way i s highly tentative and can bear a l t e r n a t i v e interpretation when the c y c l i c a l transmission process underlying the regional behaviour i s unknown. As a r e s u l t of t h i s problem, and also to avoid being misled due to "errors i n variables", a conclusion that there i s a regional d i s p a r i t y i n amplitude requires that cross relative-amplitude estimated with either series as a base d i f f e r s s i g n i f i c a n t l y from unity; these points are elaborated i n the technical Appendix 3A. Based upon these r e s u l t s , a conclusion i s then generalized for each region by t e s t i n g for recurring, s i m i l a r r e s u l t s over a l l economic indic a t o r s . If a consensus can be found, the object i s to i d e n t i f y those regions which have a d i f f e r e n t r e l a t i v e amplitude than the national economy and those regions which are "out of phase" with the national economy. Preliminary analysis of phase was presented i n 2.4.1, Chapter Two; here we present the f u l l r e s u l t s for phase, correspondence and cross r e l a t i v e -amplitude. 106 3.3.1 Regional-National Cross Spectra Cross-spectra are estimated between each Canadian indi c a t o r and i t s counterpart in each region; each time series has been detrended by harmonic regression. 3 Coherence, phase and gain estimates (Tables 3.1, 3.2 and 3.3 respectively) are averaged over the relevant range of business cycle frequency bands. Although not every time-series i s of exactly the same length, the s t a t i s t i c s are estimated over the t o t a l period (1919-1973) and both the interwar subperiod (1919-1940) and postwar subperiod (1946-1973).* A l l of the three s t a t i s t i c s show a wide v a r i a t i o n over regions, i n d i c a t o r s and time, although t h i s i s somewhat less true i n the case of gain. Coherence i s much higher f o r some indicators than f o r others; a simple ordering based upon average regional coherence, from highest to lowest, would be the consumer price index (.95), dwelling s t a r t s (.79), employment index (.74), f r e i g h t carloadings (.73), construction contracts (.55), and bank debits (.53).5 The va r i a t i o n i s further indicated by the proportion of estimates which are s i g n i f i c a n t l y d i f f e r e n t from zero. For the t o t a l period estimates, 47% are d i f f e r e n t from zero at 90% confidence and 73% exceed .6 5. By subperiods the proportions are 45% and 50% respectively for the interwar period and 50% and 63% for the postwar period. As would be expected, Quebec and Ontario account f o r a large proportion Table 3.1 COHERENCE, CANADA VS. EACH REGION Indicator Period B.C. Ontario Quebec Maritimes Regional Average Standard Deviation Employment Index Total Interwar Postwar .73* .89* .78* .58 .85* .53 .94* .98* .94* .82* .85* .73* .65* .89* .39 89.2 67.4 2.3 8.3 Construction Contracts Total Interwar Postwar .78* .61 .61 .43 .61 .57 .70* .85* .69* .81* .37 .66* .04 .14 .04 51.6 51.4 10.8 10.6 o Bank Debits Interwar Postwar .59 .47 .16 .23 .67* .69* .59 .61 .15 .69* 43.2 53.8 10.2 7.7 Freight Carloadings Total Interwar Postwar . 71* .73* .75* .41 .45 .62 .94* .97* .93* .87* .93* .76* .70* .61 .61 73.8 73.4 9.0 5.2 Consumer Price Index Postwar .94* .94* .97* .98* .92* 95.0 1.0 Dwelling Starts Postwar .82* .78* .97* .80* .57 64.4 7.4 1 2 * indicates coherence significantly different from zero at 90% confidence using Granger and Hatanaka [1964, pg. 79]. ** indicates coherence greater than .65. (2) marks cases where the estimates have been averaged over frequencies closer to 2/0-3/0 periodicity. Table 3.2 PHASE, CANADA VS. EACH REGION1 [Phase in months; (+) indicates Canada leads region] Indicator Period B.C. Prairies Ontario Quebec Maritimes Employment Index Total Interwar Postwar .13 - .69** -1.02 - .23 1.03* 1.42 .53* .51* .08 .18 -1.22* - .64 -2.30* .45 -4.62* Construction Contracts Total Interwar Postwar 2.00* .66 1.39 5.76* - .37 6.19* 1.03 • .55* 1.19 -1.95* - .35 -2.03* 2.26 1.60 3.46 Bank Debits Interwar Postwar 1.66 4.94* -2.46* -3.23 1.43 1.91 1.17 2.57* 4.27* 8.86* Freight Carloadings Total Interwar Postwar •1.52 - .50 -3.94* 3.02* -3.64* 3.80* .45* .65* .21 •1.81* .48* -1.21* - .74 1.16 -2.52* Consumer Price Index Postwar .40 .40 .78* .91* 1.33* Dwelling Starts Postwar .30 ,33 .04 .24 2.40* 1 * indicates phase s i g n i f i c a n t l y different from zero at 95%, using Granger and Hatanaka [1964, pg. 80, Table 5.1]. Table 3.3 GAIN, CANADA VS. EACH REGION Indicator Employment Index Construction Contracts Bank Debits Freight Carloadings Consumer Price Index Dwelling Starts Period B.C. Prairies Ontario Quebec Maritimes Total .81 1.47* .88 1.05 .92 Interwar .97 1.05 .93 1.12 .91 Postwar .93 1.34* .87 .96 .83 Total .95 1.30* 1.38 1.31* .17 Interwar .78 .82 .98 .69 .48 Postwar .63 .96 1.17 1.05 .23 Interwar .49* .28 .53* .50* .39 Postwar .43 .43 .55* .69 Total .91 .93 .86 1.18* .66* Interwar .90 1.19 .86 .78* .55 Postwar .94 1.03 .71* 1.37* .72 Postwar 1.02 .96 .97 1.02 .98 Postwar .64* .78 .97 .95 .88 1 Region i s base; i f gain exceeds 1.0, then national relative amplitude exceeds regional relat i v e amplitude. (*)indicates cases where gain i s s i g n i f i c a n t l y different from unity at 95% confidence when either region i s used as a base. 110 (58*) of the t o t a l number of cases of s i g n i f i c a n t coherence, while the Maritimes and P r a i r i e s account for a very small proportion (16%). The higher coherence i n the price series than the employment or freight carloadings series i s consistent with the fact that Canadian regions, i n t h e i r economic relationships with each other, are open economies with fixed exchange rates. With a high l e v e l of interdependence i n "trade", no buffering influence from a f l o a t i n g exchange rate and, also, a variety of common i n s t i t u t i o n s (such as labour unions and banks), i t follows that fluctuations i n the CPI would be sim i l a r i n each region even when our "output" variables are less closely related. The high coherences i n dwelling s t a r t s r e f l e c t s an unexpected strength i n the s i m i l a r i t y of behaviour in regional housing markets - again, t h i s may r e s u l t from such common factors as federally-administered housing p o l i c i e s and nat i o n a l l y -determined i n t e r e s t rates. The importance of int e r e s t rates i s suggested by the turning point data, where i t can be seen that regional cycles i n dwelling starts are often c o n t r a c y c l i c a l with respect to other indicators and the Canadian reference cycle. Phase estimates, transformed to the time domain, also show considerable v a r i a t i o n , ranging from a regional lead of 4.6 2 months i n the Maritimes postwar employment index to a regional lag of 8.86 months i n Maritimes postwar bank I l l debits. (Note that the lead/lag i s to be interpreted as an average lead/lag over the time period i n which the spectra are estimated). The proportion of estimates which are s i g n i f i c a n t l y d i f f e r e n t from zero i s s i m i l a r to that of coherence (5 3% of estimates based on the t o t a l period, 50% of those based on the interwar period and 47% of those based on the postwar period). Although gain estimates also vary widely, a r e l a t i v e l y low proportion are s i g n i f i c a n t l y d i f f e r e n t from unity (33% of t o t a l period estimates, 25% of interwar period estimates and 27% of postwar period estimates). Thus, i t appears that there are only a few cases of pronounced regional d i s p a r i t y i n cross r e l a t i v e -amplitude. It i s inter e s t i n g to note that the overwhelming majority (75%) of the gain estimates are less than one -implying, when s i g n i f i c a n t , greater regional than national r e l a t i v e amplitude. This i s , of course, to be expected since regional fluctuations do not occur simultaneously and as a r e s u l t the national r e l a t i v e amplitude measured at any point i n time w i l l be lower than i t would be i f the regional cycles occurred simultaneously. The r e s u l t s are quite s i m i l a r when detrending i s by a growth rate transformation. A l l of the above cross spectra were re-estimated using time-series that had been detrended i n t h i s way and although coherences tended to be lower than when the data were "harmonically" detrended, rankings of regions by regional-national coherence were not upset for 112 most indicators and time periods. When phase estimates were compared between the two detrending procedures, only 6 2% of the cases were of the same sign (where the sign implies lead or l a g ) . However, i n 82% of the instances i n which the phase estimate was s i g n i f i c a n t l y d i f f e r e n t from zero when using the harmonic regression detrending method, the estimate from the growth rate detrending was of the same sign. Thus, most of the inconsistencies between the two methods occurred when either the estimated lead/lag was very short or the coherence was very low. The gain estimates were reasonably consistent between detrending methods, although the ranking of regions by regional-national gain was occasionally d i f f e r e n t . However, i n those cases where gain was s i g n i f i c a n t l y d i f f e r e n t from unity the estimates by the two methods were quite close. Thus, a f t e r comparing the three s t a t i s t i c s produced by the two methods, the harmonic regression detrending method i s selected over the growth rate method simply because coherences are higher; conceptually, both methods involve acceptable d e f i n i t i o n s of the trend component. In conclusion, the strength of the regional-national correspondence i n the business cycle frequency range seems, i n general, to be reasonably strong but with considerable d i s p a r i t i e s over regions, indicators and time. Also, s i g n i f i c a n t regional-national phase differences have been uncovered by the evidence. The use of the gain s t a t i s t i c to 113 compare regional v o l a t i l i t i e s i s a tenuous exercise since (a) regional-national coherences are disparate and (b) the contribution of c y c l i c a l frequency bands to the explanation of t o t a l variance i n the various regional indicators i s also to some extent disparate- and both these factors can influence gain. Apart from t h i s , there are few gain estimates which by our method are s i g n i f i c a n t l y d i f f e r e n t from unity; the gain s t a t i s t i c s thus o f f e r l i t t l e i n d i c a t i o n of d i s p a r i t i e s i n the r e l a t i v e v o l a t i l i t y of regional (relative to national) fluctuations. However, i n t o t a l the evidence suggests that the regions do behave d i f f e r e n t l y and that the more det a i l e d and precise analysis on c y c l i c a l s e n s i t i v i t y in Chapter Four w i l l be quite f r u i t f u l . 3.3.2 E l a s t i c i t y Results With the e l a s t i c i t y approach we hope to reinforce the cross-spectral r e s u l t s described above. For each regional i n d i c a t o r the e l a s t i c i t y of regional with respect to national magnitudes i s calculated using the l o g - l i n e a r model s p e c i f i e d i n Appendix 3A. Detailed results including the e l a s t i c i t y , , as well as the c o r r e l a t i o n c o e f f i c i e n t , the constant and the t - s t a t i s t i c are presented i n Table 1 i n Appendix 3B. The t - s t a t i s t i c can be used to test the hypothesis that the e l a s t i c i t y i s equal to zero. However, the hypothesis that the estimated e l a s t i c i t y deviates s i g n i f i c a n t l y from unity has more relevance for t e s t i n g , for 114 i t i s t h i s t e s t which indicates whether or not regional r e l a t i v e amplitude d i f f e r s from national r e l a t i v e amplitude. As with gain, we calculate the e l a s t i c i t y using both series as the independent variable and require i n our significance t e s t that the two estimates l i e on e i t h e r side of unity. Estimates f o r which t h i s hypothesis i s accepted are marked by an a s t e r i s k . 6 Input series to these simple, log-linear regressions are detrended (by harmonic regression), seasonally-adjusted and "mean-corrected". 7 The e l a s t i c i t i e s are estimated only for the interwar and postwar periods. The estimates of correspondence and cross r e l a t i v e -amplitude using t h i s approach must be interpreted with great care. Few e l a s t i c i t y estimates deviate s i g n i f i c a n t l y from unity - indicating : a lack of pronounced regional d i s p a r i t i e s i n cross r e l a t i v e amplitude. When the c o r r e l a t i o n c o e f f i c i e n t s are compared with the coherence estimates from cross spectral analysis, i n 77% of the cases the coherence i s higher. However, the two estimators are not s t r i c t l y comparable since (a) coherence i s affected by leakage from the low frequencies while the c o r r e l a t i o n i s not, (b) coherence compares only the c y c l i c a l behaviour of two time series while the c o r r e l a t i o n c o e f f i c i e n t compares highly i r r e g u l a r fluctuations as well, and (c) coherence accounts f o r differences i n timing (average lead/lag) . Assuming the time series to be long enough, and detrended well enough, to s i g n i f i c a n t l y reduce the leakage factor, the c o r r e l a t i o n may 115 therefore be low because regional and national i r r e g u l a r fluctuations are less c l o s e l y related than the more regular movements i n economic indicators or because of differences i n timing - or, more l i k e l y , because of a combination of both factors. This i n t e r p r e t a t i o n i s further strengthened by the fact that, even i f trend has not been completely removed from the series, the e f f e c t of trend would most l i k e l y be to increase both coherence and c o r r e l a t i o n . Coherence would increase due to leakage and c o r r e l a t i o n would increase due to the presence of s i m i l a r trend i n most regional time series. However, the e l a s t i c i t y approach can s t i l l reinforce the spectral r e s u l t s i f the regional orderings of coherence and cross relative-amplitude with Canada are s i m i l a r using either method: regional orderings are more important i n t h i s analysis than absolute l e v e l s . In order to compare the two approaches, the regions are ranked by t h e i r correspondence and cross relative-amplitude f o r both estimating techniques (Table 3.4). The two measures of correspondence indicate quite s i m i l a r regional orderings; for t h i s s t a t i s t i c the spectral and e l a s t i c i t y approaches appear to reinforce each other i n r e l a t i v e terms even though correlations are generally lower than coherences. However, for cross relative-amplitude such i s not the case. The methods are not mutually r e i n f o r c i n g i n either absolute or r e l a t i v e terms. In 10 instances i n which gain varies s i g n i f i c a n t l y from unity, the e l a s t i c i t y Table 3.4 REGIONAL ORDERINGS BY REGIONAL-NATIONAL CORRESPONDENCE AND CROSS RELATIVE-AMPLITUDE (Ranking from Highest to Lowest) A. Correspondence Employment Index Construction Contracts Bank Debits Freight Carloadings Consumer Price Index Coherence Correlation Coherence Correlation Coherence Correlation Coherence Correlation Coherence Correlation Interwar Ontario* .times) /BC \Mari ^Prairies*) Ontario Quebec Prairies Mar BC Ontario* Ontario /BC "\ /PrairiesN V f r a i r i e s ) ^Quebec J Quebec* BC Maritimes* Maritimes /1)ntario*s\/'0ntarid\ / Quebec \Ouebec / I BC JBC \ Prairies* /Prairies^\ \MaritimesXVMaritimev /1)ntario*\ Quebec * ) \QuebeC BC ^thitario^ Maritimes* Maritimes Prairies* Prairies Postwar Ontario* Ontario /BC* *\ Quebec VQuebec J /BC \ Prairies* \Prairiev Maritimes* Maritimes /Ontario*\ Quebec \Quebec / /Ontario BC ( BC Grairies* \\Prairie: aritimes*/ Maritimes ) /thitario* *N Ontario VMaritimes*/ Quebec Quebec* BC Prairies* Maritimes Ontario* Ontario Orairies ) Cebec \ Quebec J /BC \ Crairies* \ \Prairiey aritimes*/ Maritimes Quebec* Quebec Ontario* /BC Vrairies Maritimes* Maritimes 2c- i^ueDec rio* /Ontario \ A (BC rie / XPrairies/ B. Cross Relative-Amplitude Gain Elasticity Gain Elasticity Gain Elasticity Gain Elasticity Gain Elasticity Interwar National Exceeds Hegional Quebec Regional Exceeds National /Ontario "\ VPrairies/ fontarioX Quebec Quebec J .BC J Quebec Postwar National Exceeds Prairies Quebec Regional Quebec Regional Exceeds - - - - /Maritime: National lOntario J Quebec Ontario \Juebec 1 Ontario B.C. 1 Estimates must differ by at least one standard deviation before regions are given separate ranks in the ordering. Regions with the same rank are surrounded by brackets. In the case of cross relative-amplitude, estimates must differ significantly from unity using either series as the exogenous variable before they can be ranked. 2 An (*) marks cases in which the regional coherence varies by at least one standard deviation from the average regional-national coherence. 117 estimates are consistent i n only three cases. The regional orderings are d i f f e r e n t with the two methods i n almost every case. These r e s u l t s suggest that i n t e r r e g i o n a l differences i n the timing of c y c l i c a l episodes and i n the strength and timing of the more i r r e g u l a r fluctuations are s u f f i c i e n t l y pronounced to cause the e l a s t i c i t y estimates to d i f f e r from the gain estimates. For the analysis of c y c l i c a l behaviour, gain i s conceptually preferable to e l a s t i c i t y because the i r r e g u l a r component and differences i n timing are taken into account; the e l a s t i c i t y estimator appears to be too crude to capture interregional differences i n cross r e l a t i v e -amplitude. 3.3.3 Regional D i s p a r i t i e s i n Correpondence  and Cross Relative-Amplitude To provide a more precise description of business cycle behaviour i n the Canadian regions, we wish to rank the regions according to the "strength" and v o l a t i l i t y of regional-national economic i n t e r r e l a t i o n s h i p s . The regions are ranked i n Table 3.4 according to the cross-spectral r e s u l t s on correspondence and cross relative-amplitude (in Tables 3.1 and 3.3). For one region to be ranked d i f f e r e n t l y from the others i n terms of correspondence, we require that regional-national coherence be at l e a s t one standard deviation above or below that of any other region. 8 Thus, the ranking i t s e l f defines a means by which 118 d i s p a r i t i e s can be defined. From the table i t i s quite c l e a r that we have found pronounced d i s p a r i t i e s i n regional-national coherence. Also, i n a par t i c u l a r i n d i c a t o r , d i s p a r i t i e s can also be isolated by comparing each regional-national coherence with the average of a l l regional-national coherences. In Table 3.4, the regions marked with an asterisk vary at least one standard deviation from the average regional-national coherence. Using either d e f i n i t i o n , d i s p a r i t i e s are evident. During the interwar period Ontario i s the region most c l o s e l y r e l a t e d to the national economy; t h i s i s r e f l e c t e d i n every indicator. The P r a i r i e s 'and Maritimes are the more independent regions; for both regions t h i s i s true i n 3 of 4 indicators with the fourth indicator i n s i g n i f i c a n t l y d i f f e r e n t from the regional average. B r i t i s h Columbia i s f o r every in d i c a t o r i n s i g n i f i c a n t l y d i f f e r e n t from the regional average, and no generalization can be made for Quebec. Thus, B.C. has only an average l e v e l of independence i n spite of the e a r l i e r observation that i t has an above-average number of non-corresponding episodes. For every region except Quebec the r e s u l t s are consistent with the influence of the region's weight i n determining the national t o t a l . While t h i s e f f e c t must be recognized, i t remains that there e x i s t varying degrees of regional independence from the national economy. 119 In the postwar, period the r e s u l t s are quite s i m i l a r . The only differences are that the Maritimes region has above-average coherence i n bank debits and that Quebec-Canada coherence has increased f o r 3 of 4 indicators i n r e l a t i o n to other regions. With these exceptions, the regional orderings have remained highly stable between time periods. The disparate l e v e l s of regional independence found i n both time periods i s an inter e s t i n g r e s u l t worthy of more investigation. The regional-ROC (Rest-of-Canada) comparisons i n the next chapter should present a clearer i n d i c a t i o n of the strength of regional i n t e r r e l a t i o n s h i p s since the influence of the regional weight i n the national t o t a l w i l l be removed. Regional d i s p a r i t i e s i n cross relative-amplitude are less pronounced. However, since the economic indicators must have a high degree of correspondence before the gain estimate becomes relevant, i n many cases the regional independence r e f l e c t e d by the coherence estimates i n e f f e c t negates the importance of cross relative-amplitude. Over a l l regions and indicators i n both subperiods there are only 10 cases i n which the gain estimate varies s i g n i f i c a n t l y from unity; 5 of these cases are from the bank debits s e r i e s . Since there are many fewer cases of gain varying s i g n i f i c a n t l y from unity than coherence varying s i g n i f i c a n t l y from zero, the implication i s that there exists a general conformity i n regional and national 120 r e l a t i v e amplitude for those instances i n which the regional and national economies are closely i n t e r r e l a t e d . When such an i n t e r r e l a t i o n s h i p does not exist, there i s of course no need to pursue an analysis of cross relative-amplitude. However, gain estimates for bank debits suggest a regional d i s p a r i t y i n relative-amplitude. Quebec and Ontario have cycles with greater r e l a t i v e amplitude than the nation i n both subperiods. B r i t i s h Columbia gain narrowly f a i l s our s i g n i f i c a n c e t e s t but nevertheless indicates some tendency towards greater r e l a t i v e amplitude than the nation. In both subperiods Ontario l i k e l y has a lower r e l a t i v e amplitude than B.C. - and t h i s d i s p a r i t y increases over time. Since the p r i n c i p a l Canadian f i n a n c i a l markets are located i n Ontario and Quebec, the r e l a t i v e v o l a t i l i t y i n B.C. i s a surprising r e s u l t which i s inconsistent with other sources of evidence i n t h i s area. For example, Arthur Burns found that the r e l a t i v e amplitude of cycles i n bank clearings f o r New York C i t y was more than double that of bank clearings outside New York C i t y . 9 In Garvey [1959], i t can be seen that the rate of turnover of demand deposits i s more v o l a t i l e i n New York C i t y than i n the 6 lar g e s t United States f i n a n c i a l centres, and more v o l a t i l e i n these 6 centres than i n the 337 "other" c e n t r e s . 1 0 This geographic " r i p p l i n g " of amplitude would presumably be the r e s u l t of stock, money and commodity markets e f f e c t i n g the f i n a n c i a l a c t i v i t y of commercial banks. Even though there i s a 121 concentration of these markets i n Toronto and Montreal, such a r i p p l e e f f e c t i s not obvious from the Canadian data, except to the extent that Quebec, Ontario and possibly B.C. have greater v o l a t i l i t y than the P r a i r i e s or the Maritimes. In summary, the evidence presented i n t h i s chapter indicates rather pronounced differences in the correspondence and timing of regional business cycles. This evidence i s based upon the cross-spectral method, with detrending by harmonic regression, and i s favored for a number of reasons over the results produced by the e l a s t i c i t y approach. Regional-national correspondence i s strongest between price as opposed to output variables, and a surprising degree of coherence was found i n the dwelling starts series, suggesting the federal influence i n regional housing markets. Since a region's weight i n the national t o t a l i s often a major determinant of regional-national correspondence, the analysis of the next chapter, i n which such influences are removed, provides an even firmer footing than i n the present chapter for drawing conclusions about differences between regions i n c y c l i c a l behaviour. 122 APPENDIX 3A TECHNICAL NOTES 1. cross-Spectral Analysis Appendix A i n Chapter Two outlined the estimation procedure adopted i n t h i s study for spectral analysis. Only a few points need be added i n specifying the use of cross-spectral analysis. Cross-spectral analysis compares two time-series by c a l c u l a t i n g , at a wide range of frequency bands, phase (average lead/lag), coherence (correspondence) and gain (cross relative-amplitude). Whereas spectral analysis i s based upon the autocovariance function, cross-spectral analysis u t i l i z e s the cross covariance function as w e l l . 1 1 The problems of leakage and the bias-variance trade-off in the estimators are, of course, s i m i l a r i n cross-spectral as i n spectral analysis. The measure of coherence between two time-series at a given frequency band i s constructed analogously to the c o r r e l a t i o n c o e f f i c i e n t i n simple regression analysis. Significance tests are available to test the hypothesis that the true coherence varies s i g n i f i c a n t l y from zero; the t e s t s are crude because the d i s t r i b u t i o n a l properties of the estimator can be as yet only crudely approximated. 1 2 The greater the length of the time-series and the less the truncation point, the greater the number of degrees of 123 freedom. A problem with the coherence estimator i s that i t i s biased, and the bias increases in d i r e c t proportion to the coherence estimate and inversely with the r a t i o of the truncation point to the length of the time-series. Furthermore, the larger the estimated phase the greater the bias i n the coherence estimate, although there w i l l be "appreciable" bias due to phase only when the truncation point i s l e s s than the lead or lag (measured i n the frequency domain). 1 3 Thus, we anticipate that the phase bias w i l l be of n e g l i g i b l e influence because the possible phase differences between the relevant economies at business cycle frequencies w i l l undoubtedly be quite short r e l a t i v e to the number of smoothing terms i n the e s t i m a t o r s . 1 4 Bias i n coherence can be l i m i t e d by using the recommended r a t i o of truncation point to length of series (a maximum of one-third) . Its e f f e c t can be examined through the window cl o s i n g procedure outlined i n Appendix A, Chapter Two. The phase s t a t i s t i c i s an estimate of average lead/lag between two time series. I t has been pointed out that the transformation of the phase estimate from the frequency to the time domain involves the i m p l i c i t assumption that the difference i n timing r e f l e c t s "pure delay" between the series and not a d i s t r i b u t e d lag mechanism. 1 5 Pure delay i s an engineering term which implies a simple s h i f t i n time between an input and an output. For example, a l i n e a r delay may be expressed as y (t) = a 0 x ( t - t 0 ) where y i s the output, 124 x i s the input and t 0 i s the length of the time delay. A l t e r n a t i v e l y , with a d i s t r i b u t e d l a g mechanism the output i s a function cf a weighted average of previous values of the input. C l e a r l y , inter-economy relationships - even those not dominated by economic feedback - are bound to be more a d i s t r i b u t e d lag than a pure delay transfer mechanism, and lags should therefore not be interpreted as pure delay. However, i n making in t e r - r e g i o n a l comparisons of the timing of regional cycles r e l a t i v e to Canada or the USA, the lag s t a t i s t i c i s s t i l l meaningful insofar as the d i s t r i b u t e d lag mechanisms are s i m i l a r i n each region. The phase estimator i s only s l i g h t l y biased. Its variance increases as coherence tends to zero, due to the increasing amount of white noise and as the r a t i o of the truncation point to the length of the time-series increases. Since i t i s even more d i f f i c u l t to obtain an approximation to the d i s t r i b u t i o n of the phase estimator than that of the coherence estimator, the confidence i n t e r v a l s for the phase estimates are quite c r u d e . H o w e v e r , for want of anything better they are used i n t h i s study to test the hypothesis that phase d i f f e r s s i g n i f i c a n t l y from zero. Technically, ,- each frequency gain represents the amp l i f i c a t i o n or attenuation of a "frequency response" function that relates an exogenous input variable to an endogenous output variable. Since we cannot claim that our gain estimates r e f l e c t such deterministic i n t e r r e g i o n a l 125 r e l a t i o n s h i p s , we must allow 'that gain may be strongly influenced by either (a) differences between the regions i n the importance of other c y c l i c a l frequencies, or (b) differences between the regions i n the extent of interfrequency leakage which emanates from the lower frequencies when estimating the power spectra. Gain i s constructed analogously to the regression c o e f f i c i e n t i n simple regression analysis and, when one series i s designated as a base, an estimated gain exceeding unity implies that the other series has r e l a t i v e l y greater amplitude at that p a r t i c u l a r frequency - i f gain i s s i g n i f i c a n t l y l e s s than unity when the tes t i s reversed and the other series i s used as a base. As a p r a c t i c a l procedure the cross-spectra r e a l l y need only be calculated once since there i s a : straightforward functional r e l a t i o n s h i p between coherence and the two gain estimates calculated using both series as a base. Carrying out each t e s t i n both directions also helps to avoid a problem that arises when there are errors i n variables. If measured values include the true value plus a stochastic component due to errors of observation, then i n the analogy of a simple, least-squares regression the regression c o e f f i c i e n t i s biased and inconsistent and, moreover, the bias w i l l be systematic i n a downward direction. 1*' Thus, i n cross-spectral analysis, a hypothesis that gain i s less than unity i s more e a s i l y accepted when there are measurement errors i n 126 the variables. However, i f the test i s carr i e d out i n both d i r e c t i o n s , there i s a much smaller p o s s i b i l i t y of being misled by such bias. F i n a l l y , i t should be noted (a) that the series are i n i d e n t i c a l units and (b) that they are normalized to account for differences i n mean i n the o r i g i n a l series (because i f the mean i n one series before trend-removal i s larger than the mean before trend-removal i n the other, then, c e t e r i s paribus, the variance w i l l be larger i n the former series a f t e r both series have been detrended). Again, comparing gain with unity i s a tenuous exercise due to the problems alluded to above. The variance of the gain estimator varies inversely with the length of the time-series and the coherence but d i r e c t l y with the truncation point.. As with the coherence and phase estimates, the s t a b i l i t y rof gain estimates can be examined by window-closing. .Significance tests for gain estimates are quite crude and a general rule i s that confidence i n t e r v a l s are smaller the greater the coherence. t« i n t h i s study, a gain estimate i s considered s i g n i f i c a n t l y d i f f e r e n t from unity i f unity i s not included within the confidence i n t e r v a l G(6) ± G(6) 2 ~ n . rl-Coh(6) v-2 '2, ~J K Coh(6) where G(6) i s the gain estimate at frequency 9; v i s the number of degrees of freedom associated with the smoothing of the 127 spectra - for the Parzen window i t i s 3.71 n/ra; f 2 v _ 2 ( 1 - a ) i s the upper 100(1-a) % point of the ? 2 v_ 2 d i s t r i b u t i o n ; and Coh i s coherence.» 9 128 2. The E l a s t i c i t y Approach The e l a s t i c i t y of an indicator i n one economy with respect to the same indi c a t o r i n another economy i s a r e l a t i v e measure of rates of change in the two economies. The e l a s t i c i t y r e l a t i o n s h i p between a region and the national economy can be represented by the following simple mode1: a where CD R j t = VVfm) " E t R.t i s an indicator for the j t h region i n period t ; N t i s the corresponding indicator for the national economy; i s a constant; a j i s the e l a s t i c i t y ; m i s a time s h i f t (lead/lag) between R. and N; and E i s an error term. 2 0 J t Since the structure of the model i s m u l t i p l i c a t i v e (log-linear) i t i s therefore estimated i n the form: 2 1 (2) l o g R.t = l o g C. + a. l o g N ( t + m ) + l o g E t This s p e c i f i c a t i o n of the e l a s t i c i t y r e l a t i o n s h i p i s not s t r i c t l y analogous to the concept of cross r e l a t i v e -amplitude measured by the gain s t a t i s t i c i n cross-spectral analysis because there i s no decomposition of f l u c t u a t i n g components. Since primary focus i s upon c y c l i c a l behaviour i n the business cycle range, the e l a s t i c i t y defined by (1) includes far too much. Thus, the indicators are detrended and seasonally-adjusted by the methods outlined i n Appendix A, Chapter Two i n order to remove the non-business cycle dynamic components. What now remains i n the time-series i s the business cycle component, the i r r e g u l a r component, and 129 perhaps a subcycle component. Since the detrending process produces a time series with an approximate zero mean, the absolute value of the minimum observation i s added to every observation to f a c i l i t a t e the log transformation. The detrended, seasonally-adjusted and "mean-corrected" series are la b e l l e d R 1 and N». Also, the time s h i f t factor (m) j implies a type of lead/lag which does not l i k e l y e x i s t and t h i s points out a c r u c i a l weakness i n the e l a s t i c i t y approach; the factor implies a uniform and not an average lead/lag but leads and lags tend not to be so uniform. To f u l l y account for differences in the timing of fluctuations the e l a s t i c i t y should be estimated at the lead/lag which produces the maximum corr e l a t i o n between R j and N. However, t r i a l and error regressions with either (a) d i f f e r e n t uniform leads and lags or (b) a time s h i f t which i s assumed to approximate the average phase (estimated with cross-spectral analysis) do not af f e c t the co r r e l a t i o n s between R^  and N to any great extent. For t h i s reason, the factor n i s simply omitted from the model.. The estimating form becomes: (3) log Rl = log + ct_. log N ! + log The c o e f f i c i e n t o.^  i s thus an estimate of the "short-run" e l a s t i c i t y between R.. and N (that i s , e R N) and i t should approximate the cross relative-amplitude estimates from cross-spectral analysis. I f a., s i g n i f i c a n t l y exceeds unity, then regional exceeds national short-run v o l a t i l i t y 130 for that i n d i c a t o r . In t h i s study, the e l a s t i c i t y i s considered to deviate s i g n i f i c a n t l y from unity i f ( e l a s t i c i t y -1.0) passes a two-tailed t - t e s t at 95% confidence. As with gain, the t e s t i s carried out twice, f i r s t with the regional series as dependent variable and then again with the regional series as independent variable. Appendix 3B Table 1 CORRESPONDENCE AND CROSS RELATIVE-AMPLITUDE BY THE ELASTICITY APPROACH 1 CANADA VS. EACH REGION e RN Constant Prairies Ontario Quebec Maritimes Constant RN Constant RN Constant RN Constant Employment Index Interwar -51 Postwar .29 Construction Contracts Interwar .30 Postwar .40 .37 11.77 •33 12.86 •15 .18 6.83 8.35 2.00 2.97 -.20 1.19 1.14* • 51 .61 • 30 .67 21.92 — 57 1.10* .90 1*7.06 .31 12.27 L H .90 .82 38.81 .1*5 14.59 .11* A 3 .85 .52 16.69 -.30 .23 •51 .51* .88 te.69 1.95 .52* .61 22.61 1.61 •59 .42 13.71 .27 •71 .63 20.20 •39 .01 - .01 .21 .07 4.37 1.00 3.28 .07 7.12 2.13 . 29 .19 8.63 3.19 - 5lt .31 11.76 1.29 .14 .03 3.21 2.11 Bank Debits Interwar Postwar .81 .62 19.68 6.24 .77 -37 11.84 21.60 .94 .87 41.97 21.95 1.21* .83 36.17 8.71 .81 .31 12.01 9«47 . 73 .26 10.75 11.60 1.20* .79 34.48 2.43 1.13* .66 24.83 4.22 .65 .40 12.64 8.54 .15 .02 2.82 12.01 Freight Carloadings Interwar .71 Postwar .15 Consumer Price Index Postwar .67 .39 12.37 .02 2.51 -.44 4.23 .72 27.62 I .97 •15 • 72 • 72 .04 2.13 6.09 .71 25.48 1.30 •79 33-17 1.64 .56 .32 IO.58 2.71 •53 .30 10.67 2.76 .76 .81 31.93 .40 .16 7.03 3.82 .86 .74 29.45 .86 1.01 .85 41.52 .20 .03 •33 .14 6.34 3.51 .21* .06 4.16 4.35 • 71 .66 24.29 1.73 1 (*) indicates el a s t i c i t y i s significantly different from unity at 95$ confidence when either series is used as the independent variable. Canada (nation) i s independent variable, e exceeding 1.0 implies regional relative amplitude exceeds national relative amplitude. RN 132 FOOTNOTES See Appendix 3A for det a i l e d technical descriptions of the procedures followed i n t h i s chapter. The f i r s t part of the Appendix d e t a i l s the cross-spectral analysis and the second part the e l a s t i c i t y approach. However, i n the tables i t i s the regional indicators which enter the cross-spectral calculations as base; t h i s means that the greater i s the gain s t a t i s t i c then the greater i s national r e l a t i v e to regional v o l a t i l i t y . For elaboration see Appendix A, Chapter Two. The precise length of each series i s given i n Appendix E, Chapter Two. These averages are calculated over the t o t a l 1919-1973 period. The t - s t a t i s t i c used for t e s t i n g t h i s hypothesis i s simply the r a t i o of the estimated e l a s t i c i t y less unity to the standard error of the estimate. See Appendix 3A. For elaboration r e f e r to the te c h n i c a l note on the e l a s t i -c i t y approach, Appendic 3A. 133 8 The standard deviation i s calculated with the average regional-national coherence as the mean. • Burns [ 1969, pg. 76-77 ], 1 0 Garvey [ 1959, pg. 22, Chart 2]. 1 1 For a good technical discussion of cross-spectral analysis, refer to Granger and Hatanaka [1964, Chap. 5-7] and Jenkins and Watts [1968, Chap. 8-9]. » 2 Jenkins and Watts [1968, pg. 398-399], 4 3 For discussion, see Jenkins and Watts [1968, pg. 375], 1 4 That i s , the series w i l l not l i k e l y require "alignment" to correct for large phase differences. See Jenkins and Watts, [ 1968, pg. 375]. i s Hause [1971 ]. •« Jenkins and Watts [ 1968, pg. 38 0]. 1 7 For a proof of t h i s statement, see Malinvaud (1970, pg. 279-383). 1 8 Jenkins and Watts [1968, pg. 434-435]. 134 J e n k i n s and Watts [1968, pg. 437]. Note t h a t n/m i s the r a t i o o f t h e number of o b s e r v a t i o n s t o the t r u n c a t i o n p o i n t . S i n c e n/m i s u s u a l l y 3 i n t h i s study, the number of degrees of freedom i s u s u a l l y 11.13. Th i s model i s adopted from B r e c h l i n g ' s [1967] model of r e g i o n a l and n a t i o n a l unemployment i n the U.K. As i n B r e c h l i n g , the model c o u l d be s p e c i f i e d i n a d d i t i v e form, where R j t = C j + ^j N(t+m)' Here the e l a s t i c i t y i s $i _ where N , R are means. However, the p r o p o r t i o n a t e J R changes i n N and R i n the m u l t i p l i c a t i v e form are c l o s e r t o t h e concept of c r o s s r e l a t i v e - a m p l i t u d e than the a b s o l u t e changes i n the a d d i t i v e form. 135 CHAPTER FOUR REGIONAL CYCLICAL SENSITIVITY IN THE NORTH AMERICAN FRAMEWORK U.1 Introduction The preceed.ing analysis has focused upon determining the dimensions of regional d i s p a r i t i e s i n various aspects of c y c l i c a l behaviour. The d i s p a r i t i e s were usually defined i n r e l a t i v e terms by comparing each region to an average of a l l regions or to the aggregate Canadian economy. Thus, the comparisons were purely descriptive and only suggested the economic r e l a t i o n s h i p between the regions. However, i t i s the purpose of t h i s chapter to provide empirical d e f i n i t i o n to a single aspect of the .interregional economic r e l a t i o n s h i p ; namely, the regional s e n s i t i v i t y to business cycles. Under the assumption that the Canadian economy i s i n general responsive to fluctuations o r i g i n a t i n g i n the United States economy, the investigation i s now directed at determining the magnitude of d i s p a r i t i e s i n the regional impact of such fluctuations and also at defining the i n t e r r e g i o n a l mechanism by which the cycles are transmitted i n t o Canada. In p a r t i c u l a r , a s p e c i a l emphasis i s placed upon the strength of transmission from the "outlying" regions ( B r i t i s h Columbia, the P r a i r i e s , the Maritimes) to Central Canada. In the introduction to t h i s study i t was stated that increased d i v e r s i f i c a t i o n i n the Canadian economy might lead to a weakness of interregional transmission of t h i s nature. 136 There are three important dimensions to a regional s e n s i t i v i t y relationship; these are, of course, i d e n t i c a l to the parameters used i n describing the regional-national r e l a t i o n s h i p , namely, correspondence, average lead/lag, and cross relative-amplitude. Since these facets of c y c l i c a l s e n s i t i v i t y are estimated with cross-spectral analysis, the technical appendix to the previous chapter describes the estimating technique used i n t h i s chapter. S e n s i t i v i t y analysis varies with the preceeding descriptive analysis i n that s e n s i t i v i t y implies causal inter-economy relationships. We assume that the c y c l i c a l r e l a t i o n s h i p between economies i s "causal" when there exists (a) s i g n i f i c a n t correspondence and (b) a s i g n i f i c a n t time la g between the economies - although the reader should note that inferences concerning causality are always subject to some suspicion (for discussion, see Section 1.1 i n the introductory chapter). The nature of the c a u s a l i t y i s further defined by cross relative-amplitude. A. dependent (sensitive) economy i s "responsive" i f i t s reaction to a transmitted cycle i s such that the r e l a t i v e amplitude of i t s fluctuations exceeds that of the economy to which i t i s linked; an opposite reaction i s termed "passive". Furthermore, defining the mechanism involves distinguishing between dire c t regional s e n s i t i v i t y to United States cycles and i n d i r e c t regional s e n s i t i v i t y transmitted through other Canadian regions. 1 The d i s t i n c t i o n can be made by comparing 137 regional s e n s i t i v i t y to the Rest-of-Canada ("ROC": the other four regions) with regional s e n s i t i v i t y to the United States. The regional-ROC comparison i s a disaggregation of the regional-national comparison and allows inferences to be drawn concerning the economic relationship between regions since the spurious influence of the region's portion of the national aggregate has been removed. It i s expected that the dimensions of d i s p a r i t i e s i n the regional-ROC comparisons w i l l exceed those of the regional-national comparisons; t h i s i s p a r t i c u l a r l y relevant to the larger economies of Ontario and Quebec. Coherences w i l l l i k e l y decrease while gain and phase need not change i n any predictable way - although the d i s p a r i t i e s should increase i n s t a t i s t i c a l s i g n i f i c a n c e . In the e a r l i e r investigation of regional c y c l i c a l behaviour, several regional-national d i s p a r i t i e s were discovered that generate testable hypotheses which can now be examined i n the wider context of the North American economy. In general, we now ask: can these d i s p a r i t i e s be accounted for i n the mechanisms by which United States fluctuations are transmitted i n t o Canada? S p e c i f i c a l l y , our analysis of the interwar period revealed that P r a i r i e indicators tended to lead national i n d i c a t o r s but, while experiencing e s s e n t i a l l y the same fluctuations as the nation, the region was also characterized by weak regional/national correspondence. Can the P r a i r i e s then be 138 characterized as a region less s e n s i t i v e to Canadian economic influence and more sensitive to international fluctuations? Also, to what extent are fluctuations i n the P r a i r i e region transmitted to other Canadian regions? During the postwar period P r a i r i e leads diminished but correspondence with Canada did not change appreciably. Does t h i s change i n regional behaviour r e f l e c t an increased and more immediate P r a i r i e s e n s i t i v i t y t o the United states economy? Such a s h i f t would of course be consistent with the change i n regional economic structure which accompanied the investment boom of the 1950s i n resource and primary manufacturing in d u s t r i e s . Also, the evidence reveals that the Maritimes lag Canada during the interwar period but tend towards leading behaviour i n the postwar period. Since t h i s change i s accompanied by some decline in regional-national correspondence, we ask: have the Maritimes experienced an increased orientation to the United States at the expense of the Rest-of-Canada? Furthermore, we have observed that c y c l i c a l behaviour i n Ontario i n terms of period, v o l a t i l i t y and timing i s quite s i m i l a r to that of the nation. Is t h i s behaviour a s t a t i s t i c a l aberration caused by Ontario's weight i n the Canadian t o t a l or are fluctuations i n t h i s region actually t y p i c a l of the Pest-of-Canada average? Are Ontario and Quebec the regions most c l o s e l y attuned, to the United States economy or i s Ontario more sensi t i v e to 139 demands by other regions ( p a r t i c u l a r l y Quebec) for c a p i t a l goods and manufactured consumer durables? If the former, i s the c y c l i c a l transmission mechanism strongest from Ontario to Quebec or vice versa and, also, does the Ontario-Quebec i n t e r r e l a t i o n s h i p dominate the linkages between these and the other three regions? F i n a l l y , does the regional-national coincidence i n c y c l i c a l timing observed f o r B.C. i n the interwar period r e s u l t from a d i r e c t s e n s i t i v i t y to the United States economy and an absence of an i n d i r e c t mechanism? Can the rather ambiguous evidence on the c y c l i c a l behaviour of B.C. i n the postwar period be made more clea r by analyzing the region within a wider, North American context? As mentioned, s e n s i t i v i t y implies c a u s a l i t y i n economic linkages. However, a p r a c t i c a l problem emerges when implying c a u s a l i t y from the lagged c y c l i c a l reaction of one economy to another. When lags are short - less than, say, 2 months - or coherence i s not exceptionally high - between, say, .65 and .80 - the cross-spectral estimate of the lag w i l l often be " i n s i g n i f i c a n t l y d i f f e r e n t from zero" even though there would seem to be a d e f i n i t e tendency towards lagging behaviour, p a r t i c u l a r l y when t h i s tendency recurs over a number of time-series i n d i c a t o r s . Thus, i t can be useful to bring more information to bear upon the lead/lag aspect of c a u s a l i t y . One source of such information i s the estimated c r o s s - c o r r e l a t i o n function, which includes for a 140 pa r t i c u l a r time series indicator the c o r r e l a t i o n between economy A and various lagged observations i n economy B and the co r r e l a t i o n between economy B and various lagged observations i n economy A. The greater the extent of economic feedback between A and B, the higher t h e i r cross-c o r r e l a t i o n at zero lag, but i f one economy tends to transmit economic fluctuations to another economy then the cros s - c o r r e l a t i o n should be higher between observations of the " s e n s i t i v e " economy and lagged values of the "transmitting" economy than vice v e r s a . 2 In other words, an observation at time period t i n the sensitive economy should be more cl o s e l y r e l a t e d to observations at t - i ( i = 1, 2 ...) i n the transmitting economy than vice versa. In addition, the timing difference should not be s p e c i f i e d at a p a r t i c u l a r lag, but rather over a range of lags. This i s because the nature of ca u s a l i t y - i f i t r e a l l y i s causality - i s not l i k e l y to be a pure delay but should also include elements of a d i s t r i b u t e d lag mechanism. Thus, comparison of the cross-correlations measures the extent of economic feedback and, where feedback i s not strong, the d i r e c t i o n of cau s a l i t y . This technique i s analogous to that used elsewhere i n examining the causal r e l a t i o n s h i p between changes in aggregate income and changes i n the money supply. 3 However, i t i s also true that simple analysis of c o r r e l a t i o n at various lags does not account for the 141 underlying c y c l i c a l behaviour i n the time-series. Comparison of cross-correlations cannot be c a r r i e d out upon business cycle frequencies i n i s o l a t i o n ; the method i s therefore less consistent with the concept of c y c l i c a l s e n s i t i v i t y than i s the estimation of phase. For t h i s reason, the feedback test i s employed only to reinforce cases i n which phase estimates narrowly f a i l the si g n i f i c a n c e t e s t . More precise explanation of the c r i t e r i a adopted in the feedback t e s t to accept or r e j e c t the hypothesis that there e x i s t s s i g n i f i c a n t feedback i s included with the presentation of the cross-spectral r e s u l t s i n Section 4.3 In the Canadian regional context, the causal mechanisms by which c y c l i c a l behaviour i s transmitted are of the types described by the simple model i n Figure 4.1 below. Economic linkages between each region, the Rest-of-Canada (ROC) and the United States r e s u l t i n four types of causal mechanisms which must be examined. The regional-USA mechanism (A) and the ROC-USA mechanism (B) are examined by estimating with cross-spectral analysis the correspondence, lead/lag and cross relative-amplitude for each regional i n d i c a t o r , i n each subperiod. S i m i l a r l y , mechanisms C and D are examined by estimating the cross-spectra between each region and i t s associated ROC, but here the potential for s i g n i f i c a n t i n t e r r e g i o n a l economic feedback i n c e r t a i n cases -p a r t i c u l a r l y between Quebec and Ontario - clouds the Figure 4.1 C ^ |Region | < D fROC~| 142 d i s t i n c t i o n between C and D-type mechanisms. Thus- when the spectral r e s u l t s are presented i n Section 4.3 there i s further discussion of the feedback problem and, also, i t i s there that the feedback t e s t i s employed to dis t i n g u i s h between C and D-type caus a l i t y . Apart from the problem of concluding c a u s a l i t y from co r r e l a t i o n and timing, the model in Figure 4.1 i s obviously a highly s i m p l i f i e d one. I t assumes that the regional-USA mechanism (A) and the ROC-USA mechanism (B) do not r e f l e c t a common correspondence to a t h i r d economy. Also, i t assumes that each Canadian region i s affected by the general economic a c t i v i t y i n the whole of the United States. Perhaps the B.C. economy i s linked c l o s e l y t o the P a c i f i c Northwest and the Maritimes to New England. If U.S. regions are characterized by disparate c y c l i c a l behaviour then our model which uses the entire U.S. economy would be mis-sp e c i f i e d . Specifying more disaggregatedinterregional models i s a d e f i n i t e area worthy of future research, but i s unfortunately outside the scope of t h i s t h e s i s . In Section 4.3.4 the r e s u l t s of the chapter are summarized i n terms of defining the inte r r e g i o n a l mechanism of c y c l i c a l transmission. This involves a discussion of the r o l e ot each region i n the transmission process. The focus upon drawing f o r each region the d i s t i n c t i o n between d i r e c t (USA) and i n d i r e c t (USA v i a ROC) c y c l i c a l s e n s i t i v i t y . Where possible, the e a r l i e r evidence from the episodic 143 approach plus data and discussion from secondary sources are employed to c l a r i f y the cross-spectral r e s u l t s . Furthermore, a taxonomy of regional s e n s i t i v i t y c l a s s i f i c a t i o n s (outlined i n 4.2.2) aids i n summarizing a l l the r e s u l t s . 4.2 Methods of Comparing Regional C y c l i c a l S e n s i t i v i t i e s Three types of comparisons have been outlined for t h i s chapter; namely, the regional-ROC, regional-USA and ROC-USA comparisons. The only empirical technique used f o r these comparisons i s cross-spectral analysis. The regional time-series indicators used are i d e n t i c a l to those used i n the regional-national comparisons; the USA and ROC series are discussed i n 4.2.1. Methods used i n drawing conclusions i n s e n s i t i v i t y analysis are discussed i n 4.2.2. This includes presentation of the taxonomy of s e n s i t i v i t y c l a s s i f i c a t i o n s . 4.2.1 Data and Data Manipulations In the regional-USA comparisons, time series s i m i l a r to the regional indicators were found i n the United States data i n four of s i x cases. None of the United States indicators required the l a t e 1910s or early 1920s extrapolation by proxy variable that was required for the Canadian regional time se r i e s . * Available over the period covered by the regional series are the value of construction contracts (1919-1972), f r e i g h t carloadings (19 19-1966), bank debits 144 (1919-1940, 1945-1973) and the consumer price index (1948-1973). An equivalent to the monthly employment index i s not to be found i n the United States data but a reasonably close proxy i s the monthly index of manufacturing employment (1919-1973) and t h i s series i s used for comparison with the Canadian regional employment indexes. Sources and data manipulations for the USA series are in Appendix 4.A, although i t should be pointed out here that for f r e i g h t carloadings and postwar bank debits series the data were seasonally-adjusted. For comparison with these series the regional dataware also adjusted. In the regional-ROC spectra the dataware- not adjusted. In order to l i m i t the scope of our analysis, regional-USA comparisons are made only between l i k e i n d i c a t o r s . This i s an important r e s t r i c t i o n as there are several i n t e r e s t i n g hypotheses which could be pursued by comparing d i f f e r e n t i n d i c a t o r s ; for example, the importance of the United States t o E r i t i s h Columbia as a market for lumber exports could be examined by comparing the U.S. dwelling starts series with indicators of general economic a c t i v i t y i n B.C. (such as bank debits or the employment index) . This would be a good to p i c for further research. Since regional-USA comparisons of dwelling starts would not provide any useful information, such comparisons are not made. The ROC series are simply the national series net of a pa r t i c u l a r region and, thus, for each region there i s a 145 corresponding ROC d e f i n i t i o n . A. problem i s encountered when the time series i s an index since the ROC observation i s then not simply the difference between the Canadian and regional observations. Instead, the ROC series i s a weighted average of the four regions which i t comprises. For the employment index, the weights used by S t a t i s t i c s Canada to determine the national index are the proportions of p r o v i n c i a l to national t o t a l employment and the same weights, aggregated where necessary into regional weights, are used i n t h i s study. 5 There are several years f o r which the weights are unavailable and for these years the weights are interpolated; the s t a b i l i t y of the weights insures that the error introduced by i n t e r p o l a t i o n i s not very large. For the consumer price index there are no weights analogous to those of the employment index and the series had to be used as a national aggregate i n the regional-ROC comparisons. 4.2.2 Methods i n Drawing Conclusions Significance i s defined i n the same way as i n the regional-national comparisons and for each region we seek a consensus of s i m i l a r r e s u l t s over every i n d i c a t o r . This evidence i s then used to define the s e n s i t i v i t y r e l a t i o n s h i p of each region i n terms of (a) the d i r e c t i o n of ca u s a l i t y i n c y c l i c a l transmission and (b) the nature of the dependent economy's reaction to a cycle transmitted from another 146 economy. The context for each region i s a three-economy system comprising a region, the Rest-of-Canada and the United States, within t h i s context we define 14 possible regional s e n s i t i v i t y relationships; a taxonomy i s presented i n Table 4.1 and i t outlines the following application of the cross-spectral estimates: (a) Coherence: The coherence between any two economies measures the strength of the linkages between them and thereby distinguishes "independence" from "interdependence". For example, a region which has i n s i g n i f i c a n t coherence with both the Rest-of-Canada (ROC) and the USA. i s c l a s s i f i e d as "independent". ( c l a s s i f i c a t i o n (1), Table 4.1). Note that t h i s does not suggest absolute inde-pendence, for i t i s conceivable that the region could be interdependent with an economy which i s outside the s p e c i f i e d three-economy system. A l t e r n a t i v e l y , a region which corresponds with ROC but not USA i s "ROC-related" ( c l a s s i f i c a t i o n (3)) or, i f i t corresponds with the USA and not ROC i t i s "USA-related" ( c l a s s i f i c a t i o n (4)). Corres-pondence with both ROC and USA i s termed " i n t e r -dependence" ( c l a s s i f i c a t i o n (9)). (b) Phase: A temporal displacement between corresponding economies i s taken to imply that one economy i s 147 Table 4.1 CLASSIFICATION OF REGIONS BY SENSITIVITY RELATIONSHIPS* Reg i o n : USA* i n s i g n i f i c a n t s i g n i f i c a n t Regional C l a s s i f i c a t i o n (1) Independent [REG I (2) USA r e l a t e d I REG I  ^- fusTl (3) ROC r e l a t e d (RE5>-fl!ixT| (4) D i r e c t l y s e n s i t i v e to USA |REG | s i g n i f i c a n t ^ < - f u S A l -responsive/passive t o USA (5) D i r e c t l y s e n s i t i v e s i g n i f i c a n t t o R O C [ R E G H R O C 1 -responsive/passive t o ROC (6) I n d i r e c t l y s e n s i t i v e JREC K-fitqcl lower - d i r e c t l y responsive/passive t o B O C - I n d i r e c t l y responsive/ p a s s i v e t o USA (7) U n i v e r s i t y s e n s i t i v e | R E G h^ JRCxTl s i g n i f i c a n t NfuSAy - d i r e c t l y responsive/passive to R O C - i n d i r e c t l y responsive/passive to USA - d i r e c t l y responsive/passive t o USA Coherence ROC:Region* ROC:USA* i n s i g n i f i c a n t s i g n i f i c a n t s i g n i f i c a n t s i g n i f i c a n t s i g n i f i c a n t s i g n i f i c a n t (8) J o i n t l y s e n s i t i v e [ R E G ] — [ R O C ! NfUSAV - j o i n t l y responsive/ passive to USA (9) Interdependent .REG HROC I lower s i g n i f i c a n t s i g n i f i c a n t s i g n i f i c a n t (10) Independent t r a n s m i t t e r IREOH ~ ~ -ROC responsive/passive t o REG (11) Transmittor -responsive/passive to USA s i g n i f i c a n t lower i n s i g n i f i c a n t s i g n i f i c a n t s i g n i f i c a n t s i g n i f i c a n t lower Region:USA' Roc:Region* >1.0/<1.0 <1.0/>1.0 <1.0/>1.0 <1.0/>1.0 and >1.0/<1.0 <1.0/>1.0 <1.0/>1.0 and >1.0/<1.0 >1.0/<1.0 >1.0/<1.0 and <1.0/>1.0 and >l'.0/<1.0 >1.0/<1.0 >1.0/<1.0 (12) D i r e c t l y s e n s i t i v e - Independent s i g n i f i c a n t IREGHRQC) -responsive/passive t o USA (13) J o i n t l y s e n s i t i v e - independent s i g n i f i c a n t lHEG_[HROpl -responsive/passive to USA (14) P a r t i a l Transmittor |REGh>f^y1 s i g n i f i c a n t -responsive/passive to USA -ROC d i r e c t l y responsive/ passive to Region -ROC i n d i r e c t l y responsive/ passive to USA i n s i g n i f i c a n t i n s i g n i f i c a n t i n s i g n i f i c a n t s i g n i f i c a n t s i g n i f i c a n t s i g n i f i c a n t >1.0/<1.0 >1.0/<1.0 >1.0/<1.0 >1.0/<1.0 Region lags USA Region lags ROC Region lags ROC lags USA. Region lags USA by more than ROC lags USA Region, ROC lags USA. Region lags ROC Region-ROC l a g i n s i g n i f i c a n t Region, ROC do not lead USA Region-ROC lag i n s i g n i f i c a n t Region leads ROC Region-USA l a g i n s i g n i f i c a n t ROC lags Region lags USE. ROC lags USA by more than Region lags USA Region lags USA Region, ROC l a g USA ROC lags USA Region leads ROC, does not lead USA >1.0/<1.0 and >1.0/<1.0 * Marks economy which i s the base i n c r o s s - s p e c t r a l a n a l y s i s . I ndicates correspondence. "* Indicates correspondence.with a s i g n i f i c a n t average lead. • •• •> Indicates a lack of correspondence. 148 reacting to another economy and i s , therefore, s e n s i t i v e to that economy. Also, s e n s i t i v i t y may be i n d i r e c t i n the sense that the o r i g i n a l impulse or disturbance originates in a t h i r d economy and i s then transmitted through one economy to another. Thus, i n c l a s s i f i c a t i o n (6), ROC i s d i r e c t l y s e n s i t i v e to the USA economy and the region i s i n d i r e c t l y sensitive to the USA. Note that the region i s also d i r e c t l y sensitive to ROC, but the s i g n i f i c a n t correspondence between the USA and ROC implies that the region i s reacting to a cycle o r i g i n a t i n g i n the USA. If the region also corresponds to the USA economy i t would be "univ e r s a l l y s e n s i t i v e " as in c l a s s i f i c a t i o n (7). A region to which there i s another economy d i r e c t l y sensitive i s a "transmitting" economy (for example, c l a s s i f i c a t i o n s (10), (11) and (1*0). (c) Gain: An economy which is- d i r e c t l y or i n d i r e c t l y sen-s i t i v e to another economy w i l l react either responsively or passively to the other economy depending upon whether gain exceeds or i s l e s s than unity (remember that gain accounts for d i f f e r -ences i n absolute magnitude between the series) , An economy can be d i r e c t l y responsive/passive to an economy to which i t i s d i r e c t l y s e n s i t i v e and 149 i n d i r e c t l y responsive/passive to an economy to which i t i s i n d i r e c t l y s e n sitive. Thus, a region which i s i n d i r e c t l y sensitive to the USA could be responsive to ROC but, because ROC reacts passively to the USA economy, i t could be i n d i r e c t l y passive with respect to the USA economy. Since we anticipate "economic feedback" i n many of our inte r r e g i o n a l systems, gain i s again calculated twice for the purposes of sign i f i c a n c e testing, once with each economy as the base. This procedure also helps to avoid being misled by the downward bias which i s l i k e l y implanted onto the gain s t a t i s t i c by "errors of observation". (For discussion see the techni c a l appendix to Chapter Three). The above c l a s s i f i c a t i o n s are determined for each in d i c a t o r f o r each region i n each time period; the results are recorded by region i n Section 4.3.4. If possible, the c l a s s i f i c a t i o n s are generalized over a l l i n d i c a t o r s for each region by the "recurrence of similar r e s u l t s " c r i t e r i o n . To f a c i l i t a t e t h i s generalization the c l a s s i f i c a t i o n s are f i r s t decided upon s t r i c t l y by s t a t i s t i c a l s i g n i f i c a n c e as outlined i n Table 4.1, but then a more subjective appraisal i s made from which cases of "almost s i g n i f i c a n t " are included. I t i s hoped that each region can be c l a s s i f i e d as 150 being generally s e n s i t i v e or transmitting, responsive or passive, etc. 4.3 Regional C y c l i c a l S e n s i t i v i t y In t h i s section, regions are c l a s s i f i e d by type of s e n s i t i v i t y according to the taxonomy outlined above. The estimates of coherence, phase and gain are presented and discussed in turn for each of the cross spectra (Sections 4.3.1 and 4.3.2). Section 4.3.3 includes a short note on the feedback t e s t and, following t h i s , Section 4.3.4 contains a description of the s e n s i t i v i t y r e l a t i o n s h i p determined for each region. 4.3.1 Regional-ROC Cross Spectra Tables 4.2, 4.3 and 4.4 present for each region, in d i c a t o r , and time period the cross-spectral estimates i n the range of relevant business cycle frequency bands (2 year/0 month to 5 year/0 month). As i n the regional-national comparisons the estimates are averages of estimates i n the relevant frequency range. We f i r s t discuss the r e s u l t s i n general terms. When compared with the regional-national estimates, the regional-ROC estimates are often affected by the removal of the region from the national series i n a predictable way. Coherence i s expected to decrease as spurious c o r r e l a t i o n i s removed; i n 81% of the cases coherence decreases, i n 61% of Table 4.2 Indicator Employment Index Construction Contracts Bank Debits Freight Carloadings 2 Consumer Price Index Dwelling Starts COHERENCE, ROC VS. EACH REGION Period B.C. Prairies Total .68** .67** Interwar .78* .73* Postwar .70* .56 Total .75* .35 Interwar .19 .56 Postwar .68** .34 Ontario Quebec Maritimes .88* .78* .69** .92* .80* .84* •84* .76* .35 •70* .71* .07 •23 .24 .17 .70* .69** .09 Interwar Postwar Total Interwar Postwar .57 . 3 9 .68* .68* .65* • 1 22 .18 .22 .23 .54 .67** .402 .78* .87* .85* •55 .25 .78* .88* .70* .38 . .67**' .66** .53 .57 Postwar . 9 4 * . 9 4 * Postwar .77* .69** .98* .98* .92* •82* .69* .53 1 2 — Table 4.3 PHASE, ROC VS. EACH REGION1 [Phase.in months; (+) indicates ROC leads region] Indicator Employment Index Period Total Interwar Postwar B.C. 1.25* • .25 • .73 Prairies - .06 1.27 1.98* Ontario - .60* - .83* .88 Quebec .99 .54 - .68 Maritimes -1.36 .33 -4.72* Construction Contracts Total Interwar Postwar 1.73* .25 2.51* 6.40* - .92 5.74* - .61 2.72 1.03 -4.39* .16 -5.12* -5.36 1.15 -4.56 LO Bank Debits Freight Carloadings Interwar Postwar Total Interwar Postwar 2.07 , 4.83*' -1 65 .96 3.78* -4.43 -4.15 2.78 -8.57 4.03* 1.66* -2.52 .73 2.19* .65 2.12 5.38* -1.79* .52 -1.16* 4.26*, -7.44*' - .81 1.04 -3.13* Consumer Price Index Postwar ..40 .40 .78* - .91* 1.33* Dwelling Starts Postwar .31 .25 .46 - .94 7.01* (*) marks cases where phase significantly different from zero at 90% confidence; (2) marks cases where the estimates have been averaged over frequencies closer to 2/0-3/0 periodicity. Cross-spectra calculated between regional and national time-series. Table 4.4 GAIN, ROC VS. EACH REGION Indicator-Employment Index Construction Contracts Period Total Interwar Postwar Total Interwar Postwar B.C. .72 .87 .78 .67 .38 .65 Prairies 1.55* 1.10 1.45* 1.05 .70 1.04 Ontario .71* .77* .60* 1.09 .44 1.01 Quebec .84 1.08 .82 .84 .42 .87 Maritimes .87 .79 .72 .28 .55 .41 Bank Debits Freight Carloadings Interwar Postwar Total Interwar Postwar • 4 92 .40 .89 .86 .87 • 2 52 .40 .78 .97 1.01 .54* .28 .63* .61* .55* • 5 72 .45 1.11 .73* 1.46* .35 .85 .60 .54 .70 Consumer Price Index Postwar 1.02 .96 .97 . 1.02 .98 Dwelling Starts Postwar .61* .73 .95 .89 .89 Region is base; i f gain exceeds 1.0, then ROC relative amplitude exceeds regional relative amplitude; (*) indicates cases where gain is significantly different from unity at 95% confidence when either (^marks cases^here^he estimates have been averaged oyer frequencies closer to 2/0-3/0 periodicity. Cross-spectra calculated between regional and national time-series. 154 the cases coherence decreases by at l e a s t .05, but i n only 11% of the cases does coherence decrease by more than .15. Phase differences are expected t o increase since a lead or lag between a region and the nation would be shortened by the influence of the region i n the national t o t a l s . However, the change i n phase should be examined only i n those regional-ROC cases where the lead/lag i s s i g n i f i c a n t l y d i f f e r e n t from zero. It not s i g n i f i c a n t l y d i f f e r e n t from zero then either (a) the two economies are coincident and there i s no reason to expect a change i n phase, or (b) the coherence i s so low that the variance i n the phase estimator makes i t unstable. Where there i s a s i g n i f i c a n t lead/lag, the phase difference i s at least as long as i n the regional-national comparison i n 82% of the cases. In a l l other cases the lead or lag decreases only s l i g h t l y . F i n a l l y , while gain takes on more meaning i n the analysis of s e n s i t i v i t y than i t d i d i n the regional-national comparisons, the estimates w i l l l i k e l y decline as a r e s u l t of the lower coherences. Apart from the influence of coherence, gain need not change i n any obvious, general way. For example, i f a region has a greater r e l a t i v e amplitude than the nation and i f t h i s r e l a t i v e l y v o l a t i l e regional component i s removed from the national s e r i e s , then one might expect that regional r e l a t i v e amplitude would exceed the ROC r e l a t i v e amplitude by more than i t exceeds the national r e l a t i v e amplitude. However, i n a more r e a l i s t i c sense the removal 155 of the region from the national series can make the ROC series quite d i f f e r e n t from the national s e r i e s ; the aggregation of the amplitudes of the regions within ROC can thus r e s u l t i n a ROC cycle of unpredictable amplitude, given the differences i n c y c l i c a l timing i n the component regions. Again, i t i s useful only t o compare cases where the regional-ROC coherence varies s i g n i f i c a n t l y from zero, because when i t does not t h i s renders the gain estimate i r r e l e v a n t . Where there i s coherence greater than .65, i n 61% of the cases gain i s lower by at l e a s t .05, i n 11% i t i s higher and i n 28% i t does not change by more than .05. For those instances i n which coherence does not decline, the decreased gain implies that regional v o l a t i l i t y i s higher r e l a t i v e to ROC than the nation. The general ( s t a t i s t i c a l ) s i g n i f i c a n c e of the regional-ROC comparison i s not that di f f e r e n t from that of the regional-national comparison. As j u s t mentioned, coherences are lower and t h i s widens the confidence i n t e r v a l s about the gain and phase estimates. The number of s i g n i f i c a n t leads or lags i s approximately the same in both comparisons, and there are a s i m i l a r number of cases of s i g n i f i c a n t gain ( s i g n i f i c a n t l y d i f f e r e n t from unity when eithe r series i s used as the base). The estimates vary widely according to the region, i n d i c a t o r or time period selected. Ontario and Quebec have the highest coherences with RCC for most i n d i c a t o r s ; again, 156 t h i s may r e f l e c t more t h e i r close i n t e r r e l a t i o n s h i p with each other than i t does t h e i r i n t e r r e l a t i o n s h i p with other regions. The phase estimates show that f o r c e r t a i n indicators Ontario leads Quebec while for others t h i s r e l a t i o n s h i p i s reversed; the i n t e r r e l a t i o n s h i p i s apparently complex. For each of the other regions the l e v e l s of regional-ROC coherences are i n general higher for the employment index, f r e i g h t carloadings, dwelling starts and the consumer price index than they are for bank debits and construction contracts. Also, there are s i g n i f i c a n t d i s p a r i t i e s i n the changes over time i n regional coherences; analysis of trends i n regional s e n s i t i v i t y i s the purpose of Chapter Five. • 3.2 Regional-USA and ROC-USA Cross-Spectra With our usual cross-spectral estimation procedure, coherence, gain and phase are estimated between each region and the United States and between each ROC series and the United States (Tables 4.5, 4.6 and 4.7). The coherence estimates indicate a s t r i k i n g r e s u l t . Canadian regions tend to correspond as c l o s e l y to each other as they do t o the United States economy. Table 4.8 emphasizes t h i s point; during the interwar period, i n almost every regional indicator, regional-ROC coherence i s at least as high as regional-USA coherence. This r e s u l t i s as strong i n f r e i g h t carloadings, which are seasonally-adjusted i n the Table 4 .5 COHERENCE, EACH REGION, ROC VS. USA [Figure in brackets is ROC vs. USA] Indicator Period B.C. Prairies Ontario Quebec Maritimes 2 Employment Index Total .75* (.66*) .38 (-70*) .68* (.70*) .72* (.65*) .47 (.69*) Interwar .82* (-79*) .54 (.81*) •80* (.77*) .80* (.77*) .74* (.79*),, Postwar .44 (.58 r .21 (.63*) .74* (.67*) .71* (.71*/ .43 2 (.73*) Construction Contracts Total .27 (.24 )l .182 (•33 ) 2 2 2 •36 (.29 ) .48 (-27 ) 2 .09 (.35 ) 2 Interwar .18 (.35 y .21 (-37 ); •32 (.35 ); .36 (.24 r .08 (-35 ), Postwar .18 (.21 ) .132 (.24 ) .27 (.19 ) .27 (.24 ) .05 2 (.25 ) Bank Debits Interwar .62 (.57 ) .39 (.57 ) .49 (.61 ) .54 (•59 ) .33 (.61 ) Postwar .17 (.30 ) .04 (.34 ) .28 (.15) .19 (.30 ) .19 (.36 ) Freight Carloadings Total •»\ (•70*)?, .162 (•77*)2 2 2 •77* (.56 f .632 (•68*)2 .72*2 (•67*)2 Interwar .57^ (.80*) .28 (.86*) .84* (.68*) .86* (.76*) .66* 2 (.77*r Postwar .50 (.79*) .41 (.80*) .85* (.69*) .57 (.77*) .48 (.77*) 3 Consumer Price Index Postwar .71*2 .71*2 .79*2 .69*2 .71*2 1 (*) indicates coherence significantly different from zero at 90% confidence using Granger and Hatanaka [ 1964, pg. 79]; (**) indicates coherence greater than .65; (2) marks cases where the estimates have been averaged over frequencies closer to 2/0-3/0 periodicity. 2 For the USA, the series is employment in manufacturing. 3 ROC-USA cannot be estimated. Table 4.6 PHASE, EACH REGION, ROC VS. USA1 [Figure in brackets is ROC vs. USA] Indicator Period B.C. Prairies Ontario Quebec Maritimes oo Employment Index Construction Contracts Bank Debits Freight Carloadings Consumer Price Index Total Interwar Postwar Total Interwar Postwar Interwar Postwar Total Interwar Postwar Postwar 1.31 1.2S 1.67 8.01 -2.07 8.55 (0.67 ) (2.57 ). (o.7s y (8.09*)' (0.45 Y (7.30 )' 0.93 (-.62 ) -5.78 (4.76 ) •23* (1.02 Y\ 1.28 ( .15 ) -1.23 (1.81*) .72 0. 79 (1.10 ) 0. .38, ( 0.87 ) 1.09 ( 2. 14 (2.39 ) 2. .24 ( 2.47 ) 3.39* ( 2, 3. 90 (0.32 ) 1. .542 ( 0.80 ) 0.42 ( 1 -5. 29 2 (6.85*)2 5. • 89 2 ( 9.S4*)2 4.86 ( 8, 0. 04 (0.24 ) 4. .41 (-0.12 y 0.47 ( o, -1. 63 (5.77*)' 6. ,622 ( 5.33 ) 4.29 ( 7. -4. 92* (0.17 ) ,54 (- .51 ) 1.09 (-1. 10. 94 (S.65*) 7. .55* ( 3.05 ) -9.38 ( 4. -1. 08 2 U.46*)2 1. ,202 ( -82 )l 1.072 ( • -5. 75* ( -91*) ,79* (- .so y .80 (- • 4. 34 (1.08 ) 1. ,54* ( 1-78 ) .68 ( 1. 2 2 2 - . 11 ,15 .15 55 ) 10 ) 96 ); 02 Y - .78 (0.71 ) 3.06 (2.33 ) - .94 (1.29 ) 4.77 (6.34*), -1.16 (0.29 )t 2.34 (S.59 Y 2.63 1.47 (-.72 ) (9.06*) 2 2 2.54* ( .85 Y 1.86 (-.06 ) .85 (1.71*) 1.24 1 (*) indicates phase significantly different from zero at 90% confidence; (2) marks cases where the estimates have been averaged over frequencies closer to the 2/0-3/0 periodicity. Estimates in months;(+) indicates USA leads region, ROC. 2 See Table 4.5, Footnote 2. 3 See Table 4.5, Footnote 4. Table 4.7 GAIN,. EACH REGION, ROC VS. USA1 [Figure in brackets is ROC vs. USA] Indicator Period B.C. Prairies Ontario Quebec Maritimes 2 Employment Index Total .80 (.64 ) .31* (.76 ) .74 (.59*) .80 (.62*) .54 (.67 ) Interwar .75 (.72 ) .49 (.77 ) .81 (.63*) .69* (.71 ) .78 (.72*) Postwar .46 (•50*r .17 (.63 r .52*2 (.39*) .72 (.38*)' .40* (.43*) Construction Contracts Total .50 (.31 )* .19 (.55 ) 2 • 4 1 2 (.41 ) 2 .45 (.40 )2 .18 (.52 ) Interwar .40 (.63 ) .51 (.63 r .55 (.69 ) .67 (.52 ) .2.1 (.65 ) Postwar .41 (.39 ) .202 (.54 ) .402 (.43 ) .43 (.40 ) .22 (.49 ) Bank Debits Interwar .89 (.61 ) .42 (.67 ) .58 (.61 ) .62 (.63 ) .54 (.66 ) Postwar .28 (.20*) .09 (.23*) .30* (.14 ) .23 (.23*) .18 (.32 ) Freight Carloadings Total . s o \ (.66 )l .202 (.79 ) 2 .782 (•46*)2 .49*2 (.65 ) 2 .942 (.60 ) Interwar .50 l (.68*) .23* (.84 ) .79 (.57*) .88 (.62*) .88 (.64*) Postwar .48 (.68*) .38 (.73 ) .95 (.49*) .39* (.79 ) .55 (.64*) 3 Consumer Price Index Postwar .942 .942 1.042 .952 .902 (2) marks cases where the estimates have been averaged over frequencies closer to the 2/0-3/0 periodicity. The USA is the base for estimating the cross-spectra; i f gain exceeds 1.0 then regional or ROC relative amplitude exceeds that of USA. The (*) indicates cases were gain is significantly different from unity at 95% confidence when either region is used as a base. See Table 4.5, Footnote 2. See Table 4.5, Footnote 3. Table 4.8 COMPARISON OF REGIONAL-ROC AND REGIONAL-USA COHERENCE B- c- P r a i r i e s O n t a r i o Quebec M a r i t i m e s Interwar Postwar T o t a l Interwar Postwar T o t a l Interwar Postwar T o t a l Interwar Postwar T o t a l Interwar Postwar T o t a l Regional-ROC Coherence FCL EMPL CC EMPL EMPL EMPL EMPL Exceeds Regional-USA CC FCL CC CC CC BD Coherence BD BD FCL FCL FCL CPI CPI I n s i g n i f i c a n t EMPL FCL FCL O D i f f e r e n c e ( D i f f e r e n c e CC P C L PCL FCL EMPL EMPL EMPL EMPL EMPL BD CC CC CC CC CC CPI BD FCL BD FCL FCL CPI BD FCL EMPL CC EMPL CC l e s s than .05) BD Regional-USA Coherence EMPL BD CC CC EMPL Exceeds Regional-ROC P^ L Coherence 1 EMPL: employment index CC : c o n s t r u c t i o n c o n t r a c t s BD : bank d e b i t s FCL : f r e i g h t c a r l o a d i n g s CPI : consumer p r i c e index. 161 USA comparisons, as i n the other in d i c a t o r s , which are not seasonally-adjusted. For the Maritimes, the r e s u l t i s stronger: correspondence i s stronger with respect to ROC than to USA in every indicator. The ordering of regions by regional-USA coherence varies according to the indicator selected; but i n general we find that B.C., Ontario and Quebec have higher coherence than the P r a i r i e s or Maritimes. During the postwar period, B.C., the P r a i r i e s and Quebec correspond more c l o s e l y t o the ROC than USA. For Ontario and the Maritimes no generalization i s possible. Also, i n the postwar period a d e f i n i t e regional ordering i n terms of correspondence with the United States emerges: Ontario c l e a r l y has the strongest correspondence, followed by Quebec, B.C., the Maritimes and the P r a i r i e s (B.C. ana the Maritimes are approximately equal). The USA tends to lead the regional economies. Over a l l regional indicators and subperiods, i n 2U% of the cases a regional lead i s indicated but there i s only one instance i n which t h i s lead i s s i g n i f i c a n t l y d i f f e r e n t from zero at 90% confidence. As expected, cycles appear to be transmitted from the USA economy to the Canadian regional economies and not vice versa. The varying l e v e l s of correspondence between the regions and the United States indicate that the transmission of United States cycles does not occur s i m i l a r l y in every region; evidence of varying l e v e l s of regional-ROC correspondence together with evidence of 162 s i g n i f i c a n t leads and lags between the regions and ROC suggests the presence of a vari e t y of regional s e n s i t i v i t y r e l a t i o n s h i p s . Also, the d i s p a r i t i e s i n the regional-USA and regional-ROC gain estimates indicate that the impact of transmitted USA cycles i s not the same i n every region, although those gain estimates s i g n i f i c a n t l y d i f f e r e n t from unity are in every instance less than unity, implying that United States' r e l a t i v e amplitude exceeds regional r e l a t i v e amplitude. However, i t appears that, i n general, the component regions of the Canadian economy tend to react ••passively" as opposed to "responsively" to business cycles o r i g i n a t i n g i n the USA economy. This r e s u l t holds during both the interwar and postwar years, although there i s i n t e r e s t i n g evidence of interperiod changes i n regional-USA gain; t h i s evidence i s to be investigated more f u l l y i n the next chapter. The general ( s t a t i s t i c a l ) s i g n i f i c a n c e of the regional-USA and ROC-USA comparisons i s of a lower order of magnitude than i s found i n the regional-ROC comparisons. As ju s t mentioned, coherences are often lower i n the regional-USA case. There are only 24% as many s i g n i f i c a n t phase estimates, and 33% as many gain estimates s i g n i f i c a n t l y d i f f e r e n t from unity. Coherence between regional and United States prices i s p a r t i c u l a r l y strong. One would expect that an important factor here would be the e x i s t i n g exchange rate regime; t h e o r e t i c a l l y , price transmission should be 163 strongest when the exchange rate i s fixed. However, even though Canada has had a lengthy period under a f l o a t i n g exchange rate regime, the period i s too short to allow us to divide the postwar period into subperiods of f i x e d and f l o a t i n g exchange rates. Moreover, Rosenbluth concluded that "... the high coherence for price fluctuations i n Canada and the United States suggest that the exchange rate f o r the two countries was i n a s i g n i f i c a n t sense fi x e d even when i t was ' f l o a t i n g ' . " 6 4.3.3 A Note on the Feedback Test As mentioned e a r l i e r , a simple feedback test i s employed to aid i n c l a r i f y i n g the directions of c a u s a l i t y underlying a s e n s i t i v i t y r e l a t i o n s h i p . For given time-series indicators i n two economies (say, regions A and B) the feedback te s t i s a comparison of CorCA^, i) with Cor(A ., B ) where Cor i s the estimated cross-correlation function and i i s the length of lag. If Cor(At, B ^ ) s i g n i f i c a n t l y exceeds Cor(At ^, Bt) - then i t can be said that, for the given indicator, region A causes region B. Of course, t h i s implication would involve the assumption that both regions are not sensitive to a t h i r d economy but with d i f f e r e n t lags. Moreover, to repeat a point made i n the introductory chapter: i n econometric work a difference i n timing can only hint at the d i r e c t i o n of c a u s a l i t y . Stronger conclusions can be obtained with greater d e t a i l i n 1 6 4 modelling, but t h i s would require data which i s unavailable. Nevertheless, we assume that " s i g n i f i c a n t feedback" between the regions i s implied by the absence of a s i g n i f i c a n t difference between the c o r r e l a t i o n functions. Two rather a r b i t r a r y choices must be made i n setting up the feedback t e s t . The f i r s t concerns the number of lags to be included in the cross-correlation functions. I f region B lagged region A by i months at every observation i n every business cycle episode, then the relevant cross-correlation f o r the feedback t e s t would be Cor(A t > B t _ i ) and C o r ( A t i , Bt) B). However, such uniform lag r e l a t i o n s h i p s do not normally e x i s t and i t i s more reasonable to compare the average of the functions over a range of lags. Since the longest lead/lag uncovered i n e a r l i e r analysis i s nine months, the average i s c a l c u l a t e d over lags from 1 to 11 months duration. Longer lags would be influenced by seasonality. The averages s t i l l may not r e f l e c t the i n t e r r e l a t i o n s h i p between business cycles i n the two regions i f the regions are i n t e r r e l a t e d at some other c y c l i c a l frequency, but t h i s problem should not be of major importance, e s p e c i a l l y with detrended data. The second choice concerns the problem of t e s t i n g the s i g n i f i c a n c e of differences between the cross-correlation functions. Since any t e s t used would be an a r b i t r a r y one, i n t h i s study the average of one function must exceed the average of the other by at least .10 before they are 165 considered " s i g n i f i c a n t l y d i f f e r e n t " . Given the t y p i c a l cross-spectra, t h i s i s a demanding te s t for reaching a conclusion of "c a u s a l i t y " as opposed to "feedback". A demanding t e s t strengthens the conclusions on s e n s i t i v i t y r e l a t i o n s h i p s . A complete l i s t i n g of the r e s u l t s of the feedback te s t f o r every i n d i c a t o r of each region i s i n Appendix 4.B. 4.3.4 C l a s s i f i c a t i o n of Each Region According to  Its s e n s i t i v i t y Relationship with ROC, USA The s e n s i t i v i t y c l a s s i f i c a t i o n s are presented for each region i n Tables 4.9-4.14. The "comments" i n the tables for each s e n s i t i v i t y c l a s s i f i c a t i o n account for the extent to which the c r i t e r i a of the taxonomy are upheld by the s t r i c t s t a t i s t i c a l s i g n i f i c a n c e tests f o r coherence, gain and phase. Since the si g n i f i c a n c e tests developed for cross-spectral analysis are f a i r l y crude, cases of "almost s i g n i f i c a n t " are included to f a c i l i t a t e a more subjective evaluation of the results i n summarizing a s e n s i t i v i t y c l a s s i f i c a t i o n over a l l indicators i n each time period for each region. Each region i s summarized i n turn. Some of the ambiguities i n the evidence are c l a r i f i e d by drawing upon information on p a r t i c u l a r episodes obtained from the turning point data (Appendix B, Chapter Two) and, i n several instances, from a d d i t i o n a l data obtained from secondary sources. 166 (1) B r i t i s h Columbia Interwar Period: For the employment index and freight carloadings B.C. corresponds s i g n i f i c a n t l y with ROC while fo r construction contracts and bank debits i t does not. B r i t i s h Columbia indicates highly independent behaviour i n construction contracts p a r t i c u l a r l y during the early 1920s; f o r example, the turning point data show that the region misses the national episode of 1921 and experiences a non-corresponding episode i n 1922-1923 (see Table 2.5). Apart from t h i s i n d i c a t o r , B.C. approximates or i s less than the regional average i n terms of s e n s i t i v i t y (coherence) to United States business cycles. Also, as i s true f o r every region, B.C. has lower amplitude than the United States. There i s l i t t l e timing difference between B.C. cycles and ROC cycles, or between B.C. cycles and USA cycles, and no obvious i n d i c a t i o n of B.C. behaving as a transmitter of United States cycles to ROC. Since B.C. i s no more correspondent with the USA than ROC, i t follows that the coincidence in timing observed between B.C. and the USA does not r e f l e c t any greater " d i r e c t s e n s i t i v i t y " of B.C. than the rest of Canada. However, i n spite of the fact that phase estimates between B.C. and ROC are also i n s i g n i f i c a n t l y d i f f e r e n t from zero, the feedback test indicates B.C. c a u s a l i t y for the employment index and f r e i g h t carloadings and the existence of s i g n i f i c a n t feedback for bank debits and construction contracts (albeit British Columbia Indicator Period Employment Index Total Interwar Postwar Construction Contracts Total Interwar Postwar Bank Debits Interwar Postwar Freight Carloadings Total Interwar Postwar Consumer Price Index Postwar Table 4.9 B.C., SENSITIVITY CLASSIFICATIONS, EACH INDICATOR AND Sensitivity Classification University sensitive Jointly sensitive ROC-related Directly sensitive to ROC Independent Directly sensitive to ROC Independent Independent ROC-related ROC-related ROC-related Jointly-sensitive PERIOD Comments BC, ROC have insignificant lag behind USA; ROC leads BC Al l lags insignificant Tendency towards "transmittor" but a l l leads, lags insignificant BC, ROC have significant lag behind USA BC lags ROC Almost "universally sensitive" Almost "directly.sensitive to ROC", as BC lags ROC ROC has significant coherence with USA ROC has significant coherence with USA; BC almost "jointly sensitive" or "partial transmittor" Almost "jointly passive to USA" Almost "partial transmittor" as BC leads ROC and BC: USA coherence is fai r l y strong Since every region corresponds with USA, ROC must also. 168 with very low coherence f o r construction contracts). There i s , thus, some evidence of B.C. serving as a transmitting region during t h i s period but, i f t h i s i s the case, then either the B.C. lead i n front of ROC must have been quite short or the transmission must have been quite weak. Either implication i s consistent with the i n s i g n i f i c a n c e of the B.C.-ROC phase estimates. The b i t s of information available to us on regional production and trade enable a crude examination of the consistency between fluctuations in foreign trade and fluctuations i n the four B.C. monthly indicators. Such a consistency would imply that the B.C. foreign trade sector was an important mechanism by which foreign cycles were transmitted into the region, although we have i n s u f f i c i e n t data to examine the exact linkage or s e n s i t i v i t y r e l a t i o n s h i p between B.C. foreign exports and United States cycles i n general economic a c t i v i t y . The gain estimates do not suggest any s i g n i f i c a n t difference between E.C. and ROC r e l a t i v e amplitudes, except possibly i n the case of bank debits, but there are several s p e c i f i c episodes i n which B.C. expansions or contractions were of a d i f f e r e n t severity than that found i n the res t of Canada. In the majority of these instances conjectures about the behaviour of the B.C. trade sector are consistent with the d i s p a r i t y between B.C. and ROC c y c l i c a l behaviour. There are several i n t e r e s t i n g 169 cases where B.C. fluctuations are also disparate with those i n the United States. An impression of r e l a t i v e amplitude i n each episode i s obtained from the seasonally-adjusted, detrended indicators which were plotted when id e n t i f y i n g c y c l i c a l turning points. These data show, f o r example, that B.C. (and the Prairies) f e l l very gradually from t h e i r 1920 peaks and that the E.C. contraction lasted u n t i l 1923. B.C. thus "misses" the United States recession of 1921. On the other hand, there i s some evidence that regions l i k e B.C. which were more dependent upon certa i n export markets experienced a more intense recession i n 1927 due to a sharper downturn i n 1926 and more d i f f i c u l t p o s s i b i l i t i e s for recovery t h e r e a f t e r . 7 The NBER i d e n t i f i e s a recession during 1927 i n t h e i r United States reference cycle (peak i n October 1926, trough i n November 1927), but investigators of Canadian cycles suggest that Canada "missed" t h i s r e c e s s i o n . 8 Of a l l the B.C. indicators only bank debits has an i d e n t i f i e d trough between l a t e 1926 and l a t e 1927, but the recession i s quite noticeable i n the other indic a t o r s . In foreign markets Canadian exports of zinc and lumber declined by 8.8% and 7.3%, respectively, between 1926 and 1927.9 Since B.C. accounted f o r almost a l l of Canadian zinc production, and the mining and lumber industries accounted f o r 23.5% and 39.1% of B.C.'s gross value added (in 1929), the impact of the export decline upon the B.C. economy i s not s u r p r i s i n g . 9 170 Furthermore, the value of B.C. gold production decreased, 1926-1927, by 22% while the Canadian value increased by 5.2%. 1 1 Chambers dates the climax of the l a t e 1920s boom i n Canada at A p r i l 1929, 2 months i n advance of the U.S. peak. The early Canadian downturn i s a t t r i b u t e d by most authors to advance downturns i n Canadian exports, p a r t i c u l a r l y wheat and newsprint. 1 2 The regional i n d i c a t o r s suggest that the contraction was the most severe i n E.C., Quebec and the P r a i r i e s . The B.C. depression, although shorter than on the P r a i r i e s , was i n many ways the most severe; t o t a l E.C. nominal wages and salar i e s f e l l by 4 7% between 192 8 and 1933, surpassing the P r a i r i e s decline of 45.3%. 1 3 Between the pre-1930 peak and the 1932-1933 trough, percentage decreases i n the employment index, bank debits, construction contracts and fre i g h t carloadings were again, the most severe i n B.C. - then the P r a i r i e s , then Quebec. The P r a i r i e i n d i c a t o r s lead the Canadian peak by up to 11 months, and t h i s i s consistent with the Canadian peak i n a g r i c u l t u r a l exports i n July 192 8. Three of four B.C. indicators were coincident with the Canadian s e r i e s , suggesting a close r e l a t i o n s h i p i n c y c l i c a l timing between B.C. and the United States. B.C.'s exports were la r g e l y affected by declines i n lumber and lumber products ( p a r t i c u l a r l y s o f t woods) from l a t e 1928, salmon exports from 1928 and zinc, lead and copper from 1928 and 1929. 1 4 171 After 1933, B r i t i s h Columbia embarked upon a period of healthy growth, stimulated by rapid growth i n the value of production and exports i n the mining industry, p a r t i c u l a r l y i n base metals, and by recovery i n lumber and lumber products. 1 5 Fluctuations i n B.C. growth rates were quite mild through to 19 37; the indicators declined s l i g h t l y during 1935 and 1936. This c y c l i c a l pattern was unlike that of Canada, where the pattern was dominated by the influence of increased wheat exports to Great B r i t a i n (in s p i t e of the appreciation i n 1931 of the Canadian d o l l a r r e l a t i v e to the pound),** the Roosevelt "boomlet" i n 1933-1934 1 7 and then the more stable but rapid growth a f t e r mid-1936. Thus, the pattern of recovery i n the Canadian regions was quite disparate, and the B.C. pattern was in many ways unique. F i n a l l y , the Canadian reference cycle turns down in mid-1937, shortly a f t e r the downturn in the United states. Exports of non-ferrous metals reach a peak 2 months before the reference c y c l e peak, while exports of wood and paper products lag i t by 2 months.*7 B r i t i s h Columbia indicators thus correspond c l o s e l y with the reference cycle peak but since the export declines were not that severe, the downturns i n each of the four monthly indicators were quite moderate and the recession less severe than i n e i t h e r Canada or the United States. An important influence on the B.C. economy was l i k e l y the "buffering" influence of rearmament i n the United Kingdom, which greatly stimulated the demand 172 f o r Canada's (and B.C.'s) base metals. The value of output from the Canadian mining industry between the Canadian reference cycle peak and trough expanded by 8% while the U.S. mining industry declined by 17% and, also, exports of non-ferrous metals as a proportion of t o t a l exports rose from 5-10% i n 1929 to 15-20% i n 1938.19 Postwar Period: In t h i s period, estimated coherence i s higher between B.C. and ROC than i t i s between B.C. and the United States. This does not indicate an increase since the interwar period i n the strength with which B.C. and ROC are in t e r r e l a t e d ; rather, i t indicates a pronounced decrease i n B.C.-USA correspondence. B.C.-POC correspondence increased dramatically i n construction contracts, but decreased s l i g h t l y i n every other indicator. There i s no s e n s i t i v i t y c l a s s i f i c a t i o n which applies to every i n d i c a t o r ; construction contracts and bank debits show B.C. s i g n i f i c a n t l y lagging ROC, while for fre i g h t carloadings B.C. i s leading s i g n i f i c a n t l y . The s e n s i t i v i t y r e s u l t s are thus ambiguous and no generalization over a l l indicators can be made. The r e s u l t s on gain are also ambiguous; i n dwelling s t a r t s B.C. has s i g n i f i c a n t l y greater r e l a t i v e amplitude than ROC, while for a l l other indicators the gain estimates are i n s i g n f i c a n t l y d i f f e r e n t from unity. As i n the interwar period, B.C. has lower r e l a t i v e amplitude than the United States. Also, i n spite of the ambiguities alluded to above, we can conclude that B.C. i s now c l e a r l y 173 l e s s c l o s e l y correspondent with the United States economy than i t was during the interwar period. since B.C.-ROC correspondence has not changed appreciably, the explanation of the decline i n B.C.-USA coherence may be that (a) B.C. exports have declined i n importance in t o t a l regional expenditure or have become re-oriented to other countries, (b) United States demand for B.C. exports has become less correspondent with indicators of United States "general economic a c t i v i t y " , or (c) economic linkages which do not operate through the trade sector (such as business expectations and c a p i t a l flows), have weakened between B.C. and the United States. Unfortuantely, there i s i n s u f f i c i e n t data available to allow examination of these hypotheses. (2) The P r a i r i e s Interwar Period: We f i n d that of a l l Canadian regions the P r a i r i e s are the most independent of the rest of the North American economy. For every i n d i c a t o r there i s weaker correspondence between the P r a i r i e s and the USA than there i s between ROC and the USA; f o r every indicator except construction contracts, Prairie-USA correspondence i s the lowest of a l l regions. Also, Prairie-ROC coherence i s the weakest of a l l regional-ROC relationships i n 3 of 4 i n d i c a t o r s , the sin g l e exception being construction contracts - for which i t i s .56, over double that of the next strongest regional-ROC construction contracts coherence. Thus, the P r a i r i e leads noticed i n both the Table 4.10 Pr a i r i e s PRAIRIES, SENSITIVITY CLASSIFICATIONS, EACH INDICATOR AND TIME PERIOD Indicator Employment Index Construction Contracts Bank Debits Period Total Interwar Postwar Total Interwar Postwar Interwar Postwar Freight Carloadings Total Interwar Postwar S e n s i t i v i t y C l a s s i f i c a t i o n ROC-related ROC-related Independent Independent Independent Independent Independent Independent Independent Independent In d i r e c t l y sensitive Consumer Price Index Comments ROC:USA coherency s i g n i f i c a n t Almost " i n d i r e c t l y s e n s i t i v e " as P r a i r i e lag behind ROC i s almost s i g n i f i c a n t Almost " i n d i r e c t l y s e n s i t i v e " as P r a i r i e significantly lags ROC Almost "ROC-related" Almost " d i r e c t l y sensitive to ROC" A l l coherences extremely weak A l l coherences extremely weak Almost " d i r e c t l y sensitive to ROC"; P r a i r i e s lag ROC Pr a i r i e s lead USA, ROC but coherences very low P r a i r i e s : ROC coherence high but not s i g n i f i c a n t Postwar Interdependent Since each region corresponds with USA, ROC must also. 175 episodic analysis and the regional-POC comparison do not seem to indicate any transmitting role for the region. The anomalous behaviour i n construction contracts suggests that, f o r some reason, construction a c t i v i t y i n the P r a i r i e s i s r e l a t i v e l y c l o s e l y t i e d t o another region, perhaps Ontario, since the int e r r e g i o n a l d i s p a r i t i e s are so pronounced with t h i s series that i t i s u n l i k e l y that any one region could be rel a t e d simultaneously to more than one other region i n the ROC aggregate. The P r a i r i e i n d i c a t o r s are c l o s e l y attuned to fluctuations i n the a g r i c u l t u r a l sector; turning points in the P r a i r i e indicators of general business a c t i v i t y are c l o s e l y related to turning points in a g r i c u l t u r a l production and exports - which generally do not conform to turning points i n Canadian indicators of general business a c t i v i t y and thereby r e s u l t i n P r a i r i e leads/lags.zo The gain s t a t i s t i c s suggest that the P r a i r i e indicators are the le a s t v o l a t i l e of a l l regions - esp e c i a l l y i n the employment index and f r e i g h t carloadings - but t h i s need not imply a lack of v o l a t i l i t y i n a g r i c u l t u r a l fluctuations. The employment index i s an " i n d u s t r i a l composite" and excludes the farm sector; as such i t w i l l not capture the f u l l impact on the t o t a l economy of fluctuations i n the a g r i c u l t u r a l sector. Furthermore, at business cycle frequency bands, the fr e i g h t carloadings series l i k e l y represents i n d u s t r i a l as opposed to a g r i c u l t u r a l economic a c t i v i t y . Nevertheless turning 176 points i n the agriculture exports series (from Chambers, 1958b) are c l o s e l y correlated to turning points i n the four monthly indicators of general economic a c t i v i t y . The linkages within the region between the i n d u s t r i a l and a g r i c u l t u r a l sectors are such that amplitude and not timing i s effected. This further suggests that with the possible exception of the bank debits series, our indicators may not f u l l y capture the transmission of agriculturally-induced fluctuations to the other regions. The phase estimates f o r 3 of 4 indicators show a s i g n i f i c a n t P r a i r i e lead ahead of ROC. The episodic results i n Chapter Two suggest a P r a i r i e lead i n 2 of 4 indicators at national peaks and i n 3 of 4 at troughs. However, the P r a i r i e s lag the 1920 peak i n the national construction contracts series as the sustained increase i n a g r i c u l t u r a l exports from 1912 to 1920 does not turn down i n chambers' s p e c i f i c cycle u n t i l l a te 1920. The reference cycle peaks i n June 1920, but the P r a i r i e s l ag the nation i n every i n d i c a t o r . The P r a i r i e s then had long leads at the pre-Depression peak, the 1932-1933 trough, and the 1936 peak. Both of these leads i n the various i n d i c a t o r s were roughly coincident with turning points i n a g r i c u l t u r a l exports: there was a peak i n J u l y 1928, 11 months i n advance of the reference cycle peak, a trough i n mid-19 32 and a peak i n l a t e 1936. The decline i n a g r i c u l t u r a l exports a f t e r mid-1928 was of course, dominated by declines in the value of 177 wheat exports; a f t e r May 1932, the value of Canadian wheat exports to Great B r i t a i n started to increase (in spite of the 19 31 appreciation of the d o l l a r r e l a t i v e to the pound). 2 1 During 1935 the stimulus of a g r i c u l t u r a l exports was limited; although grain prices rose continually from 1931 to 1937, 1935 marked the lowest volume of wheat and f l o u r exports since 1921, and t h i s resulted i n a p a r t i c u l a r l y severe setback i n the P r a i r i e s during l a t e 1934 and early 1935. 2 2 A g r i c u l t u r a l exports then recovered, but then turned down again i n l a t e 1936 i n correspondence with the recession i n the United Kingdom. This downturn preceeds the Canadian reference cycle and, also, the P r a i r i e s lead Canada i n each of the indicators of general economic a c t i v i t y . In conclusion, we have found independent c y c l i c a l behaviour i n t h i s region. Turning points are on average i n advance of t h e i r Canadian counterparts, but there i s l i t t l e support f o r the view that a g r i c u l t u r a l l y - i n d u c e d f l u c t u a t i o n s on the P r a i r i e s are transmitted with any impact into other Canadian regions although, to repeat, the lack of evidence on transmission may r e f l e c t the p o s s i b i l i t y that the P r a i r i e i n d i c a t o r s to which the ROC indicators are compared may themselves not f u l l y capture the impact of a g r i c u l t u r a l f l u c t u a t i o n s . Only i n the case of bank debits can we state with some confidence that the transmission i s weak. 178 Postwar Period: Although Prairie-ROC coherence increases s i g n i f i c a n t l y between the interwar and postwar periods for bank debits and f r e i g h t carloadings and decreases s i g n i f i c a n t l y for employment and construction contracts, i n each in d i c a t o r correspondence remains quite weak. The change i n Prairie-USA coherence i s s i m i l a r , except the bank debits coherence also declines. These changes, together with the emergence of s i g n i f i c a n t P r a i r i e lags behind ROC i n employment, construction contracts and f r e i g h t carloadings, r e s u l t i n the P r a i r i e s showing a much stronger tendency towards being " i n d i r e c t l y s e n s i t i v e " to the USA economy, although i n general the region remains "independent". For every indicator, Prairie-USA coherences are much lower than ROC-USA coherences. Cycles appear to be transmitted from the USA through ROC to the P r a i r i e s ; t h i s e f f e c t i s not strong, but i s general over a l l indicators except bank debits. The change in the status of t h i s region i s consistent with the change i n c y c l i c a l timing observed in the episodic analysis, where P r a i r i e leads of the interwar period decreased or became lags in the postwar period and p a r t i c u l a r l y the postwar I period (1945-1959) period. For most indicators Prairie-ROC or Prairie-USA coherence i s so weak that the gain s t a t i s t i c becomes d i f f i c u l t to i n t e r p r e t even though we s t i l l expect that the a g r i c u l t u r a l base of the economy might induce v o l a t i l e f l u c tuations i n the regional i n d i c a t o r s ( p a r t i c u l a r l y i n 179 bank d e b i t s ) . Indeed, there have been many intances during the postwar period when the path of the P r a i r i e economy has deviated widely from the Canadian economy. For example, with the stimulus of r i s i n g a g r i c u l t u r a l export prices, annual growth i n P r a i r i e personal income was the highest i n Canada during the 1946-1949 recovery. 2 3 Canadian a g r i c u l t u r a l exports declined by 20% i n 19 54 and, as a r e s u l t , the most severe impact of the 1954 recession was f e l t i n the P r a i r i e s . 2 * Again, a trough i n grain exports i n March 1957 resulted i n the P r a i r i e s experiencing the only regional decline i n personal income between 1956 and 1957. 2 5 As mentioned, the P r a i r i e turning points during the l a t e 1940s and 1950s tended to lag t h e i r Canadian counterparts. The major fluctuations i n the economy seem to be related to the a g r i c u l t u r a l sector; thus, the strong (foreign direct) investment linkage between the P r a i r i e s and the United States does not account i n any obvious way f o r the lags as the turning points. During the expansion of the early 1960s, rapid growth was t y p i c a l of every region but the P r a i r i e s grew the fastest, stimulated i n the early stages by large grain crops and then by production increases i n petroleum and natural gas together with booming non-r e s i d e n t i a l investment. 2* The P r a i r i e s continue t h i s v o l a t i l e growth pattern by being the weakest region i n 1967 and then the strongest i n 1968. 2 7 After the mid-1960s the P r a i r i e economic indicators become more d i f f i c u l t to 180 i n t e r p r e t due to disparate behaviour between Alberta and the other two provinces. In spite of t h i s evidence of v o l a t i l i t y , the only in d i c a t o r which has a gain s i g n i f i c a n t l y d i f f e r e n t from ROC (the employment index) suggests p a s s i v i t y i n regional amplitude. As mentioned e a r l i e r , a l i k e l y explanation i s that the employment index i s an " i n d u s t r i a l composite" and excludes the farm sector. Furthermore, to a lesser extent f r e i g h t carloadings also suggest a lack of v o l a t i l i t y in regional cycles. Again, t h i s series at the business cycle range l i k e l y represents i n d u s t r i a l as opposed to a g r i c u l t u r a l economic a c t i v i t y . Its Prairie-ROC correspondence,, together with that of the employment index, suggests that the .Prairie-ROC i n d u s t r i a l r e l a t i o n s h i p i s stronger than for other aspects of economic a c t i v i t y . (3) Ontario Interwar Period: There are two e s s e n t i a l aspects of Canadian economic structure which suggest d i f f e r e n t roles for Ontario i n the mechanism by which United States fluctuations are transmitted i n t o Canada. On the one hand, one would suspect that foreign trade, money market and investment expectations linkages would be strong between Ontario and the United States; t h i s suggests a transmitting r o l e f o r the region. A l t e r n a t i v e l y , the staple framework (see Section 1 . 2 of Chapter 1) would suggest that Ontario might be a net exporter of c a p i t a l goods and manufactured Ontario Indicator Period Employment Index Total Interwar Postwar Construction Contracts Total Interwar Postwar Bank Debits Interwar Postwar Freight Carloadings Total Interwar Postwar Consumer Price Index Table 4.11 ' ONTARIO, SENSITIVITY CLASSIFICATIONS, EACH INDICATOR Sensitivity Classification Interdependent Partial transmittor Jointly sensitive (passive to USA) Interdependent Independent Interdependent Directly sensitive to ROC Independent Directly sensitive to ROC and USA Directly sensitive to ROC and USA Jointly sensitive TIME PERIOD Comments Al l lags, leads insignificant Higher coherence between ROC:ONT than ROC:USA or ONT:USA Tendency towards "universally sensitive"; Ontario almost significantly lags ROC Tendency towards "independent transmittor"; Ontario almost significantly leads ROC Tendency towards "universally sensitive", but coherences very low Ontario lag behind ROC almost significant No significant USA lead; Ontario lags ROC Ontario lags USA; Ontario leads ROC Ontario lag behind ROC is insignificant Tendency towards "universally sensitive", as ROC:USA almost has significant coherence Almost "universally sensitive" Postwar Transmittor 182 consumer durables to the other regions; t h i s i n turn would suggest a strong s e n s i t i v i t y i n Ontario to f l u c t u a t i o n s i n the other regions. The evidence here seems s l i g h t l y more consistent with the l a t t e r than the former hypothesis. Ontario-ROC coherences are very high r e l a t i v e to other regional-ROC coherences for every i n d i c a t o r but Ontario-USA coherences are not so high; when compared with other regional-USA coherences, Ontario ranks second i n the employment index (although only . 0 2 below B.C., which ranks f i r s t ) , second i n construction contracts, t h i r d i n bank debits, and second i n f r e i g h t carloadings ( .02 below Quebec). Also, Ontario leads ROC for only the employment index; i n freight carloadings and bank debits there are s i g n i f i c a n t , short lags. This evidence together with the evidence from the feedback test which establishes that Ontario i s not a causal region f o r any i n d i c a t o r , suggests a tendency towards Ontario being c l a s s i f i e d as " d i r e c t l y s e n s i t i v e " f o r every indicator except employment. In construction contracts, coherences are very low, but there i s a tendency for Ontario to be s e n s i t i v e to both ROC and the USA. In both bank debits and f r e i g h t carloadings, the region i s sensitive to ROC, and in the l a t t e r i t i s s e n s i t i v e to the USA as well. Our method and data thus cannot unambiguously determine a s e n s i t i v i t y r e l a t i o n s h i p for Ontario other than that the region i s c l o s e l y i n t e r r e l a t e d with both ROC and the USA 183 during the interwar period. However, there i s f a i r l y strong evidence that Ontario i s a r e l a t i v e l y v o l a t i l e region since i n 3 of H i n d i c a t o r s r e l a t i v e amplitude i s s i g n i f i c a n t l y greater than ROC. To explain t h i s v o l a t i l i t y we make one tenuous conjecture. As we w i l l discuss in the next chapter, s e n s i t i v e economies can be s t a b i l i z e d through t h e i r import sectors by p r o c y c l i c a l movements i n the demand for c a p i t a l goods and consumer durables, i f these goods occupy a s i g n i f i c a n t proportion of t o t a l imports. Since we have presumed that Ontario to a greater extent than the other regions s e l l s these goods i n interregional trade, then i t follows that the Ontario economy would tend to be d e s t a b i l i z e d by the "automatic s t a b i l i z e r s " of i t s regional trading partners. The turning point data indicate that the cases where Ontario business cycle behaviour was more v o l a t i l e or d i f f e r e n t than i n ROC were i n the 19 30s. Disparate behaviour i n the 1920s i s seldom noticeable. For example, the extremely severe postwar expansion and contraction i n the Canadian reference cycle between 1919 and 1921 2 8 was pa r a l l e l l e d i n the Ontario indicators although there i s some evidence of a mild Quebec and Ontario downturn in late 1919 (both regions were l i k e l y f e e l i n g the influence of a short but s i g n i f i c a n t decrease i n national e x p o r t s ) 2 9 and, when the Canadian economy recovered with a broadly-based expansion - commencing i n early 19 22, Ontario was coincident 184 and correspondent. Furthermore, the Canadian reference cycle and the Ontario indicators together experienced the downturn of 1925 and f e l t only s l i g h t l y the 1927 recession. Although the timing of the peak i n advance of the Depression i s widely disparate over regions, Ontario ind i c a t o r s coincide with the Canadian average and, also, the contraction during the following years was of approximately equal severity i n both economies. After March 1933 Ontario was affected by the Roosevelt "boomlet" of 1933-1934, which gave temporary stimulus to non-agricultural exports, es p e c i a l l y non-ferrous metals and wood pulp, and had s i g n i f i c a n t influence upon business-attitudes and p r o f i t expectations. 3 0 Regional c y c l i c a l behaviour was quite disparate through the 1933-1936 period due to varying regional impact of the recession following the temporary 193 3 upsurge. The Ontario (and Maritime) indi c a t o r s reached peaks i n 1934 or early 1935, contracted s i g n i f i c a n t l y i n l a t e 1935 and early 1936, then expanded through 1937; the other regions reacted somewhat d i f f e r e n t l y . The Ontario expansion i n 1933-1934 was strong, l i k e l y based upon non-ferrous metals and pulp, but the ensuing contraction was also severe, l i k e l y the r e s u l t of the less rapid expansion i n manufacturing output and the lack of non-inventory investment that t y p i f i e d t h i s c y c l i c a l episode i n Canada 3 1. This recession seems a p a r t i c u l a r l y 185 good example of the strength of the Ontario-ROC trade linkage. The NBER reference cycle then dates a United states peak i n May 1937 and a trough i n June 19 38; Chambers places the Canadian peak at July 1937 and a trough i n October 1938. 3 2 While the Canadian downturn has been attributed to the United states recession, the recession was l e s s severe i n Canada because of the "buffering" influence of r e l a t i v e l y mild recession i n the.United Kingdom. 3 3 However, i n Ontario the episode was quite v o l a t i l e , the episode coinciding with Canadian exports of non-ferrous metals (to the United Kingdom) and wood and paper products, 3 4 but the downswing i n p a r t i c u l a r coincided with a weakness i n Ontario manufacturing a c t i v i t y . This decline i n manufacturing i s consistent with Chambers [1955] view that the United States recession i n s t i g a t e d a period of inventory l i q u i d a t i o n i n Canada. 3 5 Thus, i n t h i s instance the Ontario-USA linkage appears c r u c i a l . Postwar Period: During the postwar period the Ontario s e n s i t i v i t y r e l a t i o n s h i p continues to be ambiguous, but there i s some evidence that the region has increased i n importance as a transmitter of United States fluctuations. The lags of Ontario behind ROC found i n 3 of 4 interwar period indicators are a l l sharply reduced in the postwar period. The only s i g n i f i c a n t timing difference i s i n consumer prices, where Ontario leads ROC. The feedback test 186 indicates that there e x i s t s s i g n i f i c a n t Ontario-ROC feedback i n 3 indicators, and that Ontario i s a causal region i n 3 others. For every indicator except bank debits, Ontario-ROC coherence i s at lea s t as strong as any other regional-ROC coherence; the lowest Ontario-ROC coherence of these ind i c a t o r s i s .70. However, for every i n d i c a t o r , Ontario-USA coherence exceeds ROC-USA coherence; Ontario corresponds more strongly than any other region with the USA economy. The t o t a l of t h i s evidence suggests a change i n the role f o r Ontario i n the mechanism by which USA cycles are transmitted into the Canadian regions, but to describe t h i s r o l e requires some elaboration. I t has been established that Ontario-ROC and Ontario-USA coherences are r e l a t i v e l y high, that there i s an absence of s i g n i f i c a n t timing differences between Ontario and ROC, but also that there are many instances of s i g n i f i c a n t timing differences between other regions and ROC. There i s thus an apparent inconsistency i n the accumulated evidence: how can other regions lead or l a g ROC i f Ontario, the largest regional economy by f a r , has both i n s i g n i f i c a n t timing differences and strong correspondence with ROC? In other words, i f a region s i g n i f i c a n t l y leads/lags ROC then at least one other region must have an opposite timing difference with ROC -unless the leading/lagging regional economy i s small i n r e l a t i o n to other regions, i n which case i t w i l l have only minimal influence when i t i s a component of FOC as defined 187 f o r the other regions. The economies of B.C., the P r a i r i e s and the Maritimes may be considered small in r e l a t i o n to Ontario and Quebec. I t follows that i f any of these small regions had a s i g n i f i c a n t difference i n c y c l i c a l timing from ROC then, given the l i m i t e d accuracy of phase estimation i n t h i s analysis, Quebec and Ontario could have i n s i g n i f i c a n t timing differences with ROC i f these two large regions had no s i g n i f i c a n t timing differences with each other. Simultaneous c y c l i c a l timing i n the two regions would also suggest that the abnormally high Ontario-ROC and Quebec-ROC correspondence simply r e f l e c t s strong correspondence between the two regions. Also, since Quebec i s unlike Ontario i n that i t s ROC coherence exceeds i t s USA coherence f o r every i n d i c a t o r , a preliminary hypothesis i s that i n the mechanism by which USA cycles are transmitted into Canada, Ontario i s (slightly) a more transmitting region than i s Quebec, but that other regions are much less s e n s i t i v e to cycles transmitted through Ontario or Quebec than the two central regions are to each other. However, a further complicating factor i n t h i s puzzle i s the evidence that Quebec has s i g n i f i c a n t timing differences with ROC i n construction contracts, bank debits, f r e i g h t carloadings and the consumer price index. With the exception of bank debits, Quebec d e f i n i t e l y leads ROC. To analyze t h i s evidence i t i s useful to f i r s t examine more f u l l y the Quebec-Ontario i n t e r r e l a t i o n s h i p . To do t h i s , 188 cross-spectra are estimated between Ontario and Quebec for every indicator; the estimating technique i s exactly the same as for the regional-ROC comparisons. From the results of the Ontario-Quebec spectral estimation i n Table 4.12, i t i s apparent that timing differences between Ontario and Quebec are much shorter than either Ontario-ROC or Quebec-ROC timing differences. With the exception of construction contracts, a l l leads or lags are less than one month i n duration. In the construction contracts s e r i e s , Ontario-Quebec coherence i s much lower than either Ontario-ROC or Quebec-ROC coherence. Thus, for t h i s i n d i c a t o r Ontario and Quebec seem to correspond more c l o s e l y to other regions than they do to each other, Ontario lagging and Quebec leading; although a l l regional-USA coherences are exceptionally low (the highest i s .27) and the regional series are so e r r a t i c that there i s minimal transmission at most. However, due to i t s s i g n i f i c a n t lead, Quebec i s l a b e l l e d an "independent transmitter" even though the pronounced Quebec leads of the postwar period have cx^cnorred since the Centennial-Expo construction boom of the mid-196 0s; before that time, Ontario and Quebec were coincident at most turning points. In employment, bank debits and freight carloadings Ontario-ROC and Ontario-USA coherences exceed those of Quebec-ROC and Quebec-USA. In bank debits and fr e i g h t carloadings, Ontario-Quebec coherence exceeds Ontario-ROC and Quebec-ROC coherence. These r e s u l t s are consistent with Table 4.12 ONTARIO VS. QUEBEC CROSS-SPECTRAL RESULTS Indicator Time Period Coherence Phase 1 Gain Employment Index Interwar .82 1.00 .67 Postwar .76 -.20 • 72* Construction Contracts Bank Debits Freight Carloadings Consumer Pr i c e Index * Interwar .15 -5.61 .39 Postwar .50 -3.80* .84 Interwar .81 .81 1.08 Postwar .76 .78 1.18 Interwar .91 .12 1.20 Postwar .89 -.84* .75 Postwar .66 .80 .92 1 Ontario i s base f o r cross-spectral estimation; (+) indicates Ontario leads Quebec 2 Gain greater than u n i t y implies Quebec r e l a t i v e amplitude exceeds Ontario r e l a t i v e amplitude. (*) marks cases of (a) s i g n i f i c a n t deviation from zero i n phase, or (b) s i g n i f i c a n t deviation from u n i t y i n gain. 190 the transmission mechanism hypothesized in the previous paragraph. That i s , the two central regions transmit cycles i n these ind i c a t o r s more to each other than to other regions; leads/lags are very short and i n both cases the feedback t e s t (Table 4, Appendix B) indicates a very high degree of i n t e r r e g i o n a l feedback. In employment and consumer prices, both regions experience an almost simultaneous, lagged reaction to USA cycles, although in both cases Ontario i s more the transmitter. Ontario appears more c l o s e l y r e l a t e d to other regions i n i n d u s t r i a l employment than i t i s to Quebec, although the Ontario-Quebec feedback t e s t again indicates highly s i g n i f i c a n t i n t e r r e g i o n a l feedback. Thus, the economic i n t e r r e l a t i o n s h i p between Ontario and Quebec dominates the Ontario-ROC comparison; Ontario appears to be more c l o s e l y related to the USA economy than does Quebec, p a r t i c u l a r l y i n such variables as consumer prices and f r e i g h t carloadings, although i n several instances i t can be concluded that the Quebec reaction to USA cycles i s faster than that of Ontario. The immediate postwar period exemplifies the Ontario-USA r e l a t i o n s h i p . During t h i s rapid expansion, 194 7-19 53, the Canadian economy experienced two mild contractions in growth i n 194 9 and 1951. The 1948 peak was approximately coincident with peaks ) i n non-agricultural exports and the United States reference c y c l e 3 * but to some extent Canada "missed" the U.S. 191 recession of 1949 3 7; Ontario i n d i c a t o r s coincided with the national turning points and the contraction was more severe, but i n Quebec most series indicated l i t t l e c y c l i c a l a c t i v i t y through to 1953. A second instance o c c u r r e d i n the l a t e 1950s, when the Canadian economy recovered from the 1958 "slow-down" to a peak i n the various reference cycles in l a t e 1959 or early 1960, and then contracted to a trough i n early 1961. 3 8 The explanation of t h i s deceleration r e l a t i v e to the e a r l i e r postwar years was a source of great debate amongst economists at that time but, c l e a r l y , the rather massive increases i n f i x e d c a p i t a l formation i n resource industries during the early and mid-1950s were excessive i n terms of p r e v a i l i n g foreign demand f o r Canadian exports during the l a t e 1950s and early 1960s. 3 9 The Ontario indicators (and also annual growth i n personal income) declined by s l i g h t l y more than i n Quebec, 1960-1961, although i t must be noted that Ontario i n p a r t i c u l a r would have f e l t the recessionary (internal) influence of the completion i n 19 59 of construction on both the St. Lawrence Seaway and the Trans-Canada P i p e l i n e . Moreover, there are further examples of the r e l a t i v e l y close r e l a t i o n s h i p between the Ontario and United States economies i n the mid-1960s and i n 1970-1971. From the 1961 recession, growth i n Ontario progresses very evenly u n t i l 1965. Increased iron ore exports and strong domestic demand for iron and s t e e l products, chemicals and other 192 manufactured products imply a broadly-based expansion i n the Ontario economy.*© By 1963, increased foreign demand for base metals and, due to Canada's improved international competitive p o s i t i o n as a r e s u l t of devaluation, increased exports and import-competition i n manufactured products became important factors. The slowing of the U.S. economy i n early 1966, and some weakness i n the Canadian demand for autos i n 1965 and 1966 created weakness i n the Ontario economy shortly i n advance of the P r a i r i e s , Quebec and the Maritimes. More rapid growth characterized 1967 and 1968 i n both Ontario and the United States; the Ontario economy was stimulated by increased production and investments i n s t e e l and i n automobiles (as a r e s u l t of the 1965 Auto Pact).** Ontario performance during the "slowdown" was above the Canadian average i n employment, personal income, dwelling s t a r t s and non-residential c a p i t a l expenditures; Ontario exports rose by 28.3% i n nominal value between 196 7 and 1968.*2 Ontario indicators coincide quite c l o s e l y with those of Canada as a whole at the 19 68 trough even though the regional slowdown was l e s s pronounced. A l t e r n a t i v e l y , during the 1961-1968 period the c y c l i c a l pattern i n Quebec i s d i s t i n c t l y less similar to that of the United States. In Quebec, average annual growth i n personal income i s close to the Canadian average over the 1961-1965 period. The expansion of the early s i x t i e s i s quite smooth except for a short setback i n l a t e 1962 and early 1963, 193 which re s u l t s i n mild subcycles i n the employment index, bank debits and f r e i g h t carloadings. To some extent the slowdown was caused by a downturn i n dwelling s t a r t s - a downturn which lagged the Canadian downturn by two quarters. Also relevant were temporary reversals i n the production of pulp and paper (related to weak newsprint exports), clothing and t e x t i l e s . In employment and bank debits Quebec c l e a r l y lags at the 1965-1966 peak, r e f l e c t i n g the extra stimulus of Expo and related t o u r i s t expenditures. Also, the l e t t i n g of construction contracts i n preparation f o r the Centennial r e s u l t s i n a large peak i n t h i s i n d i c a t o r i n late 1965. In 1968 the economy slows down considerably and the rate of growth i n Quebec personal income, 19 67-1968, i s by f a r the weakest of a l l regions. Thus, during t h i s mild Canadian recession the major influences on r e l a t i v e Quebec performance hinge upon l o c a l f a c t o rs. F i n a l l y , the short fluctuation i n Canadian economic a c t i v i t y between early 1968 and l a t e 1970 resembled s i m i l a r behaviour i n the U.S. economy, although Canada lagged by several months in the respective reference cycles and the Canadian downturn a f t e r the e a r l y months of 1969 was quite mild i n r e l a t i o n to the U.S. downturn. A Canadian export expansion i n l a t e 1967 and early 196 8 i n response to the U.S. recovery was further strengthened by threatened and actual i n d u s t r i a l disputes i n the U.S. which increased both overseas and U.S. demand for Canadian exports of copper, 194 aluminum and s t e e l products.* 3 However, the Canadian and p a r t i c u l a r l y the Ontario employment indexes turn down sharply with the auto s t r i k e i n late 196 9. In Quebec the downturn i n 1969-1970 i s much milder and t h i s i s due e s s e n t i a l l y to the weaknesses of recovery i n 1968; p a r t i c u l a r weakness was found i n t e x t i l e s , shipbuilding and e l e c t r i c a l products.** . Furthermore, while Ontario and Canadian ind i c a t o r s are i n general coincident during t h i s episode, the Quebec indicators do not coincide; Ontario seems much more c l o s e l y attuned to the U.S. f l u c t u a t i o n . As i n the interwar period, the postwar cross-spectral r e s u l t s indicate that the Ontario region appears to have the highest r e l a t i v e amplitude of a l l Canadian regions. In employment, bank debits and freight carloadings, Ontario-ROC gain estimates are s i g n i f i c a n t l y l e s s than unity (implying that Ontario r e l a t i v e amplitude exceeds ROC r e l a t i v e amplitude) and, r e l a t i v e to other regional-ROC gain estimates, Ontario-ROC c r o s s - r e l a t i v e amplitude ranks lowest f o r every in d i c a t o r except construction contracts. That Ontario i s r e l a t i v e l y v o l a t i l e i s further supported by the Ontario-Quebec comparison; for a l l ind i c a t o r s except bank debits, Ontario r e l a t i v e amplitude exceeds Quebec r e l a t i v e amplitude. F i n a l l y , while Ontario r e l a t i v e amplitude i s le s s than USA r e l a t i v e amplitude, i t i s s t i l l greater in comparison to the USA than i s any other region. (4) Quebec 195 Interwar Period: The Quebec region during t h i s period was either independent or sensitive. For two indicators, construction contracts and bank debits, Quebec-POC coherences are quite low, and as such the region i s c l a s s i f i e d as being "independent". However, for the other i n d i c a t o r s the region was " j o i n t l y s e n s i t i v e " , although for every indicator Quebec-ROC coherence was l e s s than Ontario-ROC coherence. Quebec reacts to USA cycles i n a s i m i l a r fashion as ROC, except Quebec has s l i g h t l y higher coherence - about the same as i n the Ontario-USA comparison - and there are no s i g n i f i c a n t timing differences between Quebec and ROC. Although the feedback test indicates that Quebec i s "causal" i n the case of fr e i g h t carloadings, bank debits and construction contracts (in the l a t t e r case i t must be remembered that there i s very low coherence i n the Quebec-ROC comparison). Quebec i s generally of average v o l a t i l i t y i n terms of regional-ROC gain estimates. As i n the postwar period, Ontario-Quebec coherence i n bank debits and f r e i g h t carloadings greatly exceeds either Ontario-ROC or Quebec-ROC coherence, and the feedback test indicates s i g n i f i c a n t Ontario-Quebec economic feedback i n every indicator. The important implication here for the analysis of the Quebec economy i s that for every indicator except construction contracts the " j o i n t s e n s i t i v i t y " of the Quebec region i s predominately the r e s u l t of " j o i n t Ontario-Quebec Table 4.13 QUEBEC, SENSITIVITY CLASSIFICATIONS, EACH INDICATOR AND TIME PERIOD Quebec  Indicator Employment Index Bank Debits Freight Carloadings Period Total Interwar Postwar Construction Contracts Total Interwar Postwar Interwar Postwar Total Interwar Postwar S e n s i t i v i t y C l a s s i f i c a t i o n J o i n t l y s ensitive J o i n t l y sensitive (passive to USA) J o i n t l y sensitive Independent transmittor Independent Independent transmittor Independent Independent Transmittor J o i n t l y s e n s i t i v e P a r t i a l transmittor (passive to USA, ROC i n d i r e c t l y passive to USA) Comments Quebec:USA coherence greater than ROC:USA A l l coherences s i g n i f i c a n t Almost "transmittor", since Quebec:USA coherence i s r e l a t i v e l y high although i n s i g n i f i c a n t A l l coherences very low Almost " j o i n t l y s e n s i t i v e " Almost " i n d i r e c t l y sensitive" Almost "universally sensitive" Almost "independent transmittor" as Quebec:USA coherency i s r e l a t i v e l y low Consumer Price Index Postwar Transmittor 197 s e n s i t i v i t y " . As mentioned e a r l i e r , the turning point and other data suggest that the c y c l i c a l behaviour of Ontario deviated from ROC more i n the 1930s than the 1920s. Ontario also deviated often front Quebec during t h i s period, although the f i r s t such deviation was i n 1927, when Ontario "missed" the recession but Quebec, with greater concentration of economic a c t i v i t y i n pulp and paper than Ontario, f e l t more heavily the 9.8% decrease i n national pulp export value between 1926 and 1927.*s Quebec then preceded Ontario into the Depression, as the region was undoubtedly h i t heavily by the f a i l u r e of pulp exports to recover from the 19 26 decline and the downturn i n newsprint exports i n December 1928, although the general impact of the Depression upon the regional indicators (and personal income) was approximately the same i n both Ontario and Quebec.•* During the recovery of the mid-1930s, the Quebec pattern i n fluctuations (in the usual indicators) resembled that of Ontario except Quebec lagged somewhat and experienced a severe reduction i n growth i n early 1936 (although not i n f r e i g h t carloadings). However, i n Quebec the value of foreign exports (custom port data) increased gradually between 19 34 and early 1936, but accelerated r a p i d l y i n the l a s t 6 months of 1936. 4 7 This r i s e i n exports undoubtedly f a c i l i t a t e d the region's quick recovery from the early 1936 contraction noticed i n the employment index and construction contracts, and enabled the region to escape, to some extent, the more pronounced 198 recession f e l t i n Ontario. F i n a l l y , Quebec indicators did not decline as much as Ontario during the 19 38 downturn. Quebec experienced the l e a s t decline of any region i n 1938, despite a 17% decline i n the value of regional forestry production; the explanation may l i e i n the f a c t that the value of mining output grew, 193 7-1938, and the decline i n manufacturing was less than i n B.C. or O n t a r i o . 4 8 Postwar Period: The regional s e n s i t i v i t y of Quebec has already been discussed i n some d e t a i l i n the course of analysing Ontario. There i t was found that Ontario and Quebec transmit cycles i n bank debits and fre i g h t carloadings more to each other than to other regions. I t was pointed out that Quebec was s l i g h t l y more the transmitter i n f r e i g h t carloadings and Ontario ( s l i g h t l y ) more the transmitter i n bank debits. Since Quebec leads both ROC and Ontario i n freight carloadings i t i s termed a " p a r t i a l transmitter" for that i n d i c a t o r and, since for bank debits Quebec-USA coherence i s so much weaker than either Ontario-USA or ROC-USA coherence, Quebec i s f o r t h i s i n d i c a t o r termed "independent" but tending towards " i n d i r e c t s e n s i t i v i t y " . Both regions behave s i m i l a r l y i n construction contracts i n that coherences with ROC and the USA are approximately the same, but since Quebec-Ontario coherence i s s i g n i f i c a n t l y lower than Quebec-ROC coherence, and Quebec s i g n i f i c a n t l y leads ROC, then Quebec i s c l a s s i f i e d as an independent transmitter. Again, consumer prices tend to 199 emanate through Ontario and Quebec to the other regions, and i n employment both regions experience an almost simultaneous lagged reaction to USA cycles, although Ontario seems to be somewhat more the transmitter. As i n the interwar period, the v o l a t i l i t y of the Quebec economy i s not e a s i l y generalized from the r e s u l t s on each i n d i c a t o r . Quebec has average c r o s s - r e l a t i v e amplitude with ROC as compared to other regional-ROC estimates i n employment, construction contracts, bank debits and consumer p r i c e s . The singl e exception i s f r e i g h t carloadings, i n which Quebec indicates a pronounced p a s s i v i t y as a transmitting region. Also, from the Ontario-Quebec comparison, Quebec has lower r e l a t i v e amplitude than Ontario i n every in d i c a t o r except bank debits. As i s true for every other region, Quebec reacts passively to USA cycles i n every indicator, that i s , Quebec r e l a t i v e amplitude i s l e s s than USA r e l a t i v e amplitude. (5) The Maritimes Interwar Period: During t h i s period, the Maritimes correspond more with ROC than with the USA. Maritime-USA coherences are extremely low for bank debits and construction contracts, but are high enough to rank higher than the P r a i r i e region i n employment and fre i g h t carloadings. In f r e i g h t carloadings, and p a r t i c u l a r l y i n employment, Maritime-ROC coherences are reasonably strong; Table 4.14 Maritimes MARITIMES, SENSITIVITY CLASSIFICATIONS, EACH INDICATOR AND TIME PERIOD O C OJ Indicator Employment Index Period Total Interwar Postwar Construction Contracts Total Interwar Postwar S e n s i t i v i t y C l a s s i f i c a t i o n Interdependent J o i n t l y s ensitive Independent Independent Independent Independent Comments A l l coherences s i g n i f i c a n t . Almost "universally sensi t i v e " Almost "independent transmittor", as Maritimes lead ROC Extremely low coherences Bank Debits Interwar Postwar Independent Independent Tendency towards "universal s e n s i t i v i t y " , but coherences low Maritime lead/lag i s ambiguous Freight Carloadings Total Interwar Postwar P a r t i a l transmittor Universally sensitive Independent R0C:USA coherence exceeds that of Maritime:USA Almost " p a r t i a l transmittor" Consumer Price Index Postwar Universally sensitive Maritimes lag ROC, USA 201 f o r every other i n d i c a t o r the coherence i s either the lowest or next-to-lowest of a l l regional-ROC coherences. The region i s therefore c l a s s i f i e d as "independent" i n construction contracts and bank debits. There i s some tendency i n bank debits towards an " i n d i r e c t l y s e n s i t i v e " c l a s s i f i c a t i o n , a r e s u l t consistent with the fact that the Maritimes are i n general a sensitive region with evidence of lagged reaction i n every indicator. I t i s the low coherences which cause the s e n s i t i v i t y c l a s s i f i c a t i o n s to be di f f e r e n t over i n d i c a t o r s . There i s a clear tendency for the region to be either "independent" due to low coherences or "universally s e n s i t i v e " due to lagged reaction to both ROC and USA. Coherences are too low i n construction contracts and bank debits to enable any determination of c r o s s - r e l a t i v e amplitude with either ROC or the USA. In the employment index and fr e i g h t carloadings, even though neither gain estimate i s s i g n i f i c a n t l y d i f f e r e n t from unity, there i s a f a i r l y clear i n d i c a t i o n that cycles i n the Maritime region have low r e l a t i v e amplitude i n comparison with other regions and ROC. Postwar Period: Between the interwar and postwar periods, Maritime-ROC coherence declined for employment and construction contracts, increased f o r bank debits and remained about the same f o r freight carloadings. For every in d i c a t o r except bank debits, t h i s coherence was at lea s t as 202 low as any other regional-ROC coherence for every indicator. Thus, the Maritimes i n the postwar period replace the P r a i r i e s as being Canada's most "independent" region. S i m i l a r l y , Maritime-USA coherences decline f o r every in d i c a t o r . The very weak correspondence between the Maritimes and both ROC and the USA r e s u l t in the Maritimes having an "independent" c l a s s i f i c a t i o n for employment, construction contracts, and freight carloadings. In B.C., Quebec and Ontario, regional-ROC coherences i n bank debits declined considerably between the interwar and postwar periods, but the Maritimes became more correspondent with ROC. The region also lags ROC by over seven months, and t h i s r e s u l t i s quite surprising given that (a) the spectral r e s u l t s suggest leading behaviour i n the other indicators, and (b) the turning point data show that at every peak and trough between 1952 and 1970 the Maritimes lead Canada by at l e a s t 9 months. Also, as mentioned e a r l i e r , the bank debits series indicated a strength i n s u b c y c l i c a l f luctuations such that regional-ROC coherences are often higher at subcycle than at business cycle frequencies. At the subcycle frequencies, leads/lags which are as long as seven months may indicate s i g n i f i c a n t phase s h i f t s between two series without i n d i c a t i n g which region i s leading/lagging i n the sense of c a u s a l i t y . This seems the best int e r p r e t a t i o n : the Maritimes are considered independent i n every indicator (except p r i c e s ) . In consumer prices, the Maritimes have 203 s i g n i f i c a n t correspondence with both ROC and the USA and also lag both ROC and USA; the region i s thus "universally s e n s i t i v e " . The independence of the Maritime region can be observed throughout the postwar period. In the early postwar period, 1948-1955, Maritime economic fluctuations are markedly d i f f e r e n t from those i n Canada as a whole. Whereas the Canadian postwar recovery by almost any indicator was quite strong, the Maritimes were the weakest region. The war had provided the region with considerable economic stimulus, p a r t i c u l a r l y i n shipbuilding and i n several manufacturing i n d u s t r i e s * 9 , but the region v i r t u a l l y stagnated u n t i l some s l i g h t growth was recorded i n most in d i c a t o r s during 1950-1951; a peak was reached i n l a t e 1951 or early 1952 and the ensuing mild recession was succeeded by a period of very modest growth through to 1955. Thus, the Maritimes experience some impact from the 1951-1952 subcycle (along with B.C.) and, furthermore, leads at the peak ahead of Canada are quite pronounced. One fa c t o r which undoubtedly influenced both of these regions was the downturn marked i n February 1952 i n the exports of wood and wood products. 5 0 However, the Maritimes f e l t l i t t l e impact from the 1954 recession. With the exception of dwelling starts (which tend to move c o n t r a c y c l i c a l l y ) the national indicators reach c y c l i c a l peaks i n 1956 and troughs i n 1958. The regional 204 indicators followed a s i m i l a r pattern i n each region, but the Maritimes again l e d at the turning points, which i s consistent with the dramatic decline in Maritime (custom-port) exports i n 1956 and 1957. The rebound i n exports i n 1960 was quite strong. Apart from r i s i n g unemployment, the performance of the Maritime economy over the 1958-1960 period compares favourably with the other regions; growth i n personal income and c a p i t a l expenditures exceeds that of both Quebec and Ontario. However, the Maritimes during the f i r s t half of the 1960s had the worst economic performance of any region and although the regional turning points are approximately coincident with the Canadian turning points at the 1960-1961 trough and the 1965-1966 peak, i n the minor fluctuations between these turning points the Maritime indicators do not i n general correspond with the Canadian i n d i c a t o r s . Bank debits, construction contracts, the employment index and dwelling starts reach mild peaks i n l a t e 1961 and f r e i g h t carloadings indicate a s l i g h t (unidentified) peak at the same time. In the same way the indi c a t o r s suggest a mild trough i n l a t e 196 2 and early 1963. Following t h i s there i s s l i g h t evidence of a peak i n la t e 1964 and a trough i n mid-1965. These fluctuations are l i k e l y export-based, as the (annual) custom-port export series i s extremely v o l a t i l e through t h i s period, with peaks and troughs i n f a i r l y close conformity to these turning points - although i t i s , of course, impossible to determine 205 the province-of-origin of the exported commodities or the extent of exports from the Maritimes to other Canadian r e g i o n s . 5 1 The c o n t r a c y c l i c a l nature of the Maritime economy through t h i s period i s indicated by the f a c t that i n 1961, 1963 and 1961 Maritime per capita personal income moved closer to the Canadian average, while i n 1960, 1962 and 1965 i t moved farther from the average. 5 2 From 1966 to 1968 the Maritimes fared somewhat better i n r e l a t i o n to the Canadian average than during the early 1960s. Total c a p i t a l expenditures grew s i g n i f i c a n t l y faster than the Canadian average, p a r t i c u l a r l y i n 1967 and 1968. 5 3 However, c y c l i c a l a c t i v i t y i s quite damped during the 1966-1968 period; i d e n t i f i e d turning points represent only very mild f l u c t u a t i o n s . Then, both exports and output declined i n many sectors i n 1969 and the region continued to indicate i t s c o n t r a c y c l i c a l (relative to Canada) behaviour by recovering modestly during 1970 i n the indicators and i n fo r e s t r y production, mining, manufacturing, i n t o t a l exports. 5* Leads are again apparent. The regional-ROC spectral r e s u l t s and the above discussion thus indicate a lack of correspondent c y c l i c a l behaviour between the Maritimes and the rest of Canada. With the low Maritime-USA coherences, we must as well reject the hypothesis that " d i r e c t s e n s i t i v i t y " to the USA would account for the observed leads ahead of ROC. However, the independent and a t times c o n t r a c y c l i c a l pattern of 206 fluctuations i n the Maritimes does suggest the i n t e r e s t i n g hypothesis that federal s t a b i l i z a t i o n p o l i c i e s have been of the l e a s t benefit to t h i s region. F i n a l l y , as i n the interwar period, the low coherences p r o h i b i t analysis of gain i n most indicators even though one's impression from observing the detrended data i s that economic fluctuations i n the Maritimes are quite mild in r e l a t i o n to the national economy. Also there i s again some in d i c a t i o n i n the spectral results that Maritime r e l a t i v e amplitude i s l e s s than both ROC and USA r e l a t i v e amplitude. In summary, i n t h i s chapter we have attempted to categorize each region according to the role that i t plays i n the transmission of United states business cycles i n t o Canada. This involved f i r s t defining a taxonomy ot the various types of s e n s i t i v i t y and cycle transmission that could emerge i n a three economy system comprising a region, the P.est-of-Canada and the United States. These intereconomy systems may be misspecified to the extent that a Canadian region i s c l o s e l y correspondent with a U.S. region that i n turn does not correspond cl o s e l y with general movements i n the United States economy. Therefore, we have taken only a f i r s t step i n defining for each Canadian region the way that i t i n t e r a c t s with the r e s t of the North American economy. After "estimating" the simple models, the r e s u l t s for each region are analyzed i n some d e t a i l . Many regional s e n s i t i v i t y relationships underwent s i g n i f i c a n t 207 change between the interwar and postwar periods; explaining these changes i s the t o p i c of the next chapter. 208 APPENDIX 4A UNITED STATES DATA AND DATA MANIPULATIONS [ A l l Series from Rosenbluth (1973), with updates] Manufacturing Employment, monthly, 1919-1973, USA: Note: Series i s production workers i n manufacturing. Sources: 1919-1967: Bureau of Labour S t a t i s t i c s (1968) B u l l e t i n No. 1312-5, Pg. 46. 1967-1970: Bureau of Labour S t a t i s t i c s (1971) B u l l e t i n No. 1312-7. 1971-1973: Bureau of Labour S t a t i s t i c s (1971-1973), "Monthly Labour Review". Units: Thousands of workers. Bank Debits, monthly, 1919-1973, USA: Note: Series i s bank debits to deposit accounts, excluding inter-bank accounts. No seasonally unadjusted series i s a v a i l a b l e a f t e r 19 64. Therefore, data f o r 1946-1964 was seasonally-adjusted using the Census Method XII and then linked with the seasonally-adjusted data for 196 4-19 72. The interwar and postwar periods were detrended separately t o conform to the detrending of the Canadian data. Sources: 1919-1936: Annual Reports of the Federal Reserve Board (1934, 1937) . 1937-1973: Federal Reserve B u l l e t i n (1937-1973). 209 Units; Tens of m i l l i o n s of d o l l a r s , expressed i n logarithmic form. Value of Construction Contracts, monthly, 1919-1972. Sources; 1919-1945: Bureau of the Census (1960). " H i s t o r i c a l S t a t i s t i c s of the United States", series App. No. 22. 1946-1972: Department of Commerce (1946-1972), "Survey of Current Business" (From F.W. Dodge Corporation). Units: M i l l i o n s of d o l l a r s . Freight Carloadings, monthly, 1919-1966, USA: Note: The series i s a seasonally-adjusted index. Sources: 1919-1967: Federal Reserve B u l l e t i n (1937-1973), various issues. Units: Index, 1935-1939 = 100.0. Consumer Price Index, monthly, 1948-1973, USA: Note: The series i s an index. Sources: 1948-1973: Department of Commerce (1946-1972), "Survey of Current Business". Units: Index, 1957-1959 = 100.0. Appendix 4.B Table 1 CROSS-CORRELATIONS, REGION VS. ROC O i-H C M Indicator Employment Index Construction Contracts Bank Debits Freight Carloadings Consumer Price Index Dwelling Starts Period Total Interwar Postwar Total Interwar Postwar Interwar Postwar Total Interwar Postwar Postwar Postwar B.C. Pr a i r i e s Ontario A A A A A A Quebec A A Maritimes A A A 1 (•) indicates that an average of cross-correlations between Region t and ROC t ( t + l f t + 2 ••• exceeds average of cross correlations between ROC and Region^ ^ ... That i s , c o r r e l a t i o n from (Region^ ROC^) exceeds correl a t i o n from (Region^., R0Ct), j =1, .... This implies Region causes ROC.( (A) indicates difference i n c o r r e l a t i o n i s less than .10, and that there exists " s i g n i f i c a n t " feedback. 2 The national series i s used as a proxy f o r ROC. Appendix 4.B Table 2 CROSS-CORRELATIONS, ROC VS. USA Indicator , Employment Index Construction Contracts Period Total Interwar Postwar Total Interwar Postwar ROC.B.C. A + A ROC.Prairies A + A ROC. Ontario A + A ROC.Quebec A + A ROC.Maritimes A A Bank Debits Freight Carloadings Interwar Postwar Total Interwar Postwar (•) indicates that average of cross-correlations between USA and ROC t t , t+1, t+2 and USA That i s , c o r r e l a t i o n from (USA ROC ) exceeds correlation from (USA ROC ) i = 1 t z*j t + j t exceeds average of cross-correlations between ROCt ., 11 and th i s SUS" JiguousdrreedtrUS « *• cross-correlation does not exceed .10. 2 ROC.Region i s Canada minus Region. Indicator Period Employment Index Construction Contracts Bank Debits Freight Carloadings Consumer Price Index Total Interwar Postwar Total Interwar Postwar Interwar Postwar Total Interwar Postwar Postwar 1 Analogous to Footnote 1, Table R. Appendix 4.B Table 3 CROSS-CORRELATIONS, REGIONS VS. USA1 B- c- Prairies Ontario A A • + • + + A A A A A A A A Quebec Maritimes A A A A A 213 Appendix 4.B Table 4 CROSS-CORRELATIONS, ONTARIO VS. QUEBEC1 Indicator Time Period Cross-Correlation Employment Index Interwar A Postwar A Construction Contracts Interwar A Postwar Bank Debits Interwar A Postwar A Freight Carloadings Interwar A Postwar A Consumer Price Index Postwar A 1 (+) indicates Ontario causes Quebec. See Table 1, Appendix 4B, Footnote 1. 214 FOOTNOTES TO CHAPTER FOUR Indirect s e n s i t i v i t y might also include the s e n s i t i v i t y of an "outlying" region to c y c l i c a l behaviour endogenously-generated i n the r e s t of Canada. For a cr o s s - c o r r e l a t i o n function Cor(X t, Y t _ i ) where x i s a time series from one economy, Y i s a s i m i l a r time series i n another economy, and i ( i = 1, 2, ...) s p e c i f i e s the number of lags, t h i s amounts to comparing Cor(A t, Bt i) with Cor(A t_., Bt) . See Sims [ 1972]. The bulk of t h i s data was kindly made ava i l a b l e to the author by Professor Rosenbluth of the U.B.C. Department of Economics. The weights are i n DBS (192 2-19 39), "Employment and Average Weekly Wages and Sal a r i e s " . Rosenbluth (1973). Estimates of regional gross value-added i n 1929 by major industry d i v i s i o n s are in Green [1971, Appendix E, Table B3], 215 On the United States and Canadian turning points, see a summary i n White [1967, Appendix A, Table A1.1]. On the Canadian "recession" of 1926-1927, see Hay [1966, Pg. 363] and Caves and Holton [1959, Pg. 99]. Urquhart and Buckley [1965, Tables N7 9-81 and K153-164]. Green [1971, Appendix B, Table B3 ]. Canada Year Book, [1928]. See Chambers [ 1958b, Pg. 181], Marcus [1954, Pg. 11] and Safarian [ 1970, Pg. 107]. Compiled from the Report of the Royal Commission on Dominion-P r o v i n c i a l Relations [1940, Appendix 4, Table V]. Urquhart and Buckley [ 1965, Tables N1-50]. Urquhart and Buckley [1965, Tables K160-168, N1-26 and L265-317], The Canadian value of production and exports of copper, gold (although not exports) , lead, n i c k e l , s i l v e r and zinc a l l expanded i n very year between 193 2 and 1937. See Urquhart and Buckley [ 196 5, Tables N1-50]. Crude estimates-of the importance of each industry i n 1937 provincial "gross value-added" are available i n the Canada Year Book, 216 (1938). 1 7 Chambers [1958a] and, f o r discussion, see Marcus [1954, Pg. 115]. * a chambers [ 19 58b]. 1 9 See Brecher and Reisman [1957, Pg. 43] and, on the st r u c t u r a l change i n the export sector, see Marcus [1954, Pg. 153]. 2 0 Turning points f o r a g r i c u l t u r a l exports are i n Chambers [ 1958b]. Marcus [1954]. 2 2 Grain prices and wheat exports are i n Urquhart and Buckley [1965, Tables L98-113 and L139-146, r e s p e c t i v e l y ] . i 3 Income data are from DBS, (1924-1973), "National Accounts". Furthermore, net income received by farm operators i n Saskatchewan declined by 71% between 19 53 and 1954. DBS, (1924-1973), "National Accounts". 1 5 The decline was concentrated i n Saskatchewan and (to a lesser extent) Manitoba since Alberta, which had been by 217 far the major r e c i p i e n t of new fixed c a p i t a l formation i n the P r a i r i e s during the investment boom of the 1950s, experienced an increase i n personal income as c a p i t a l formation i n the mining, quarrying and o i l wells industries increased, 1956-1957. For mining data see Urquhart and Buckley [1965, Table E115]. The trough i n grain exports i s i d e n t i f i e d by Chambers [1958b]. Investment data i s from Department of Trade and Commerce, (1948-1973), "Public and Private Investment Survey". Growth i s measured i n personal income, DBS (1924-1973), "National Accounts"; information on the a g r i c u l t u r a l sector during the early 1960s i s i n the Bank of Canada, (1 948-1973), "Annual Reports". Wheat exports were p a r t i c u l a r l y strong after 1962, due to general increases i n in t e r n a t i o n a l food prices and to several large wheat and flou r contracts negotiated with the U.S.S.R. and Eastern European countries. The measure here i s annual growth i n personal income, DBS (1924-1973), "National Accounts". Chambers [ 19 58a]. Canadian exports were lower during October and November of 1919 than for the same months i n 1918 or 1920. DBS (1923-1939), "Monthly Report of the Trade of Canada". 218 Chambers [1958b] and Marcus [1954, Pg. 115]. On expectations, see Safarian [1970, Pg. 145]. Production data for Canada i s i n Urguhart and Buckley [1965, Section N for minerals and f u e l s , Section K for pulp and paper, Section Q f o r manufacturing]. For investment data, see Department of Trade and Commerce (1951) , "Public and Private Investment i n Canada, 1926-1951". See White [1967, Pg. 236, Table A1]. On the r e l a t i v e severity of the Canadian recession, see Marcus [1954, Pg. 153-155] and Brecher and Eeisman [1957, Pg. 42]. The r o l e of the United Kingdom i n "buffering" t h i s recession i s twofold; f i r s t , recovery i n Canada, 1936-1937, was to some extent c u r t a i l e d due to the recession from mid-1936 i n the United Kingdom which had adverse e f f e c t s on Canadian wheat exports and, second, the severity of the 1937-1938 recession i n Canada was reduced by the rearmament programme i n the United Kingdom which greatly stimulated the demand for Canada's base metals. [Marcus, (1954), Pg. 156]. Chambers [1958b]. Chambers [ 1955 ]. 2 1 9 For exports t u r n i n g p o i n t s , see Chambers [195 8b]. U n i t e d S t a t e s t u r n i n g p o i n t s are i n White [ 1967, Pg. 236 ]. In Canada, t h e growth of GNP d u r i n g the U.S. r e c e s s i o n d e c e l e r a t e d but remained p o s i t i v e . DBS (1924-1973), " N a t i o n a l Accounts". Turning p o i n t s are from Waterman [1973]. For a g e n e r a l d i s c u s s i o n of the i s s u e s c e n t r a l t o the weak-ness i n economic growth d u r i n g the l a t e 1950s, see Caves and Reuber [1969 ]. Bank of Canada (1968, 1969), "Annual Report". Bank of Canada (1968, 196 9), "Annual Report". O n t a r i o M i n i s t r y of t h e T r e a s u r y (1976) , " O n t a r i o S t a t i s t i c s , 1975", V o l . 2. Bank of Canada (1968, 1969), "Annual Report". Bank of Canada (1970), "Annual Report". On pulp e x p o r t s , see Urquhart and Buckley [1965, Tables K153-164]. 220 Newsprint exports i n 1929 exceeded those of 1928 (Urquhart and Buckley [1965, T a b l e K162 ]) , but f e l l t e m p o r a r i l l y i n e a r l y 1929. For d i s c u s s i o n see Marcus [1954, Pg. 60]. The monthly, custom-port export s e r i e s i s from Dominion Bureau of S t a t i s t i c s (1923-1939), "Monthly Report of the Trade o f Canada". The s t r u c t u r a l data i s a g a i n from the Canada Year Book, (1938, 1939). See Howland [ 1957, Pg. 64]. See Chambers [1958b, Table 1]. The custom-port e x p o r t data are i n DBS (1923-1939), "Monthly Report of t h e Trade of Canada". On r e g i o n a l income d i s p a r i t i e s , see T h i r s k [ 1972, Pg. 11]. Data i s from Department of Trade and Commerce (1951), " P u b l i c and P r i v a t e Investment i n Canada, 1926-1951". Maritime e x p o r t data i s i n E a r l [1973, Chapter F o u r ] . 221 CHAPTER FIVE REGIONAL SENSITIVITY OVER TIME: A COMPARISON WITH CANADA-USA SENSITIVITY ANALYSIS 5.1 Introduction This chapter examines the change i n regional c y c l i c a l s e n s i t i v i t y between the interwar and postwar periods. Here we ask: has the mechanism by which United States cycles are transmitted into Canada changed over time? This topic i s relevant not only to the question of the strength of int e r r e g i o n a l cycle transmission, but also to an area of empirical i n v e s t i g a t i o n with which Canadian economists have long been concerned; namely, the change i n the Canadian s e n s i t i v i t y to fluctuations i n the United States economy. From the disaggregate, regional analysis of t h i s study, the nature of the change i n aggregate, Canadian s e n s i t i v i t y should become much more cle a r , although the comparison between the change i n regional and the change i n national s e n s i t i v i t i e s i s complicated by the fact that a variety of economic i n d i c a t o r s and empirical techniques have been used to examine national s e n s i t i v i t y . The t o t a l of Canada-USA evidence suggests, at l e a s t , a very i n t e r e s t i n g hypothesis t o be examined i n t h i s study. That there has been a general decline i n Canadian-United States c y c l i c a l s e n s i t i v i t y can be only tenuously concluded, but there i s cle a r evidence, p a r t i c u l a r l y i n Rosenbluth's analysis, that there has been a a weakening of s e n s i t i v i t y i n some comparative indicators of 222 general economic a c t i v i t y . Furthermore, the observed decline i s much more pronounced in some indicators than others. I t has already been concluded i n the previous chapter that regional-USA s e n s i t i v i t y d i f f e r s i n the various regions; i t i s also observed that s e n s i t i v i t y has changed over time i n several regions and an examination of these changes in l i g h t of the Canadian-USA change should provide a f u l l e r d e f i n i t i o n and understanding of the c y c l i c a l s e n s i t i v i t y of the two national economies. 5.2 The Change i n Canada-USA C y c l i c a l S e n s i t i v i t y Since 1919 Rosenbluth [1957] examined Canadian s e n s i t i v i t y by comparing with regression techniques matched pairs of Canadian and United States amplitudes at turning points i d e n t i f i e d by the episodic method.1 The four time series indicators used included freight carloadings, railway f r e i g h t ton-miles, railway gross revenues and the manufacturfng production index. From t h i s data base, Professor Rosenbluth concluded that: "... the amplitude of the Canadian fluctuations exceeded that i n the United States before 1914, was frequently about the same i n the 19 20 ,s, was usually lower i n the 1930's and was often lower after 1946 [ t o 1956], One thus gains the impres-sion of a long-run decline i n Canadian s e n s i t i v i t y to United States fluctuations, at least up to the 223 1930's."2 Also, Brecher and Reisman [ 1957 ], i n writing f o r the Royal Commission on Canada's Economic Prospects, estimated cross relative-amplitude using the same data and turning points as Rosenbluth but with a somewhat d i f f e r e n t estimating technique. Cross relative-amplitude i s measured (simply) as the r a t i o between Canadian and United States amplitude at each turning p o i n t . 3 Their conclusion concerning the trend i n Canadian s e n s i t i v i t y i s the same as Rosenbluth's, although i t i s in t e r e s t i n g to note that for one i n d i c a t o r which i s not included i n the Rosenbluth data base, the value of construction contracts, there i s a pronounced increase i n cross relative-amplitude during contractions when 1946-1955 i s compared with either 1919-1929 or 1929-1939.* Apart from construction contracts, these important r e s u l t s were the f i r s t hints of a postwar decline i n Canadian s e n s i t i v i t y , but due to the date of writing, Rosenbluth's f i n a l conclusion was that ..."there i s , however, no agreement among the figures as to the trend between the 1930's and the postwar period." 3 In 1969 Rosenbluth expanded the analysis by including several p r i c e variables, although the time period was the same.* For these indicators the e a r l i e r conclusion was not supported; the cross relative-amplitude of long-term bond y i e l d s , common stock prices and wholesale prices was higher, 1946-54, than either 1919-29 or 1929-39.7 The Brecher-224 Reisman analysis of 1957 concurs. 8 The decline i n s e n s i v i t i t y thus seems to be t y p i c a l of only value and p a r t i c u l a r l y volume i n d i c a t o r s . Since the Rosenbluth analysis, several other studies employing s i m i l a r episodic techniques provide (limited) support f o r the "declining s e n s i t i v i t y " conclusion. Chambers [1958a] finds that the amplitude of s p e c i f i c cycles i n Canadian manufacturing employment, non-agricultural employment, manufacturing production, the value of imports, the value of exports, f r e i g h t carloadings and non-a g r i c u l t u r a l exports a l l declined between 1919-1938 and 1946-1954.9 This does not, of course, necessarily mean a change i n s e n s i t i v i t y since i t i s also true that the amplitude of United States cycles declined over the same periods and, also, there i s no accompanying measure of the correspondence aspect of s e n s i t i v i t y . White [1967] updates (to 19 65) the Chambers-Hay i d e n t i f i c a t i o n of s p e c i f i c cycle turning points and then suggests that Canadian amplitudes i n cycles i n i n d u s t r i a l production tend to be lower than United States amplitude and that postwar amplitude i s , on average, lower than i n the interwar period.>" While there i s no s p e c i f i c c a l c u l a t i o n of either cross relative-amplitude or correspondence, a crude estimate of cross relative-amplitude can be obtained from White's estimates of amplitude i n i n d u s t r i a l p roduction. 1 1 I f the average r a t i o of Canadian to United States amplitude for a l l matching episodes, 1919-225 1937, i s compared to that of 194 5-1965, i t appears that the "declining s e n s i t i v i t y " conclusion i s supported. While t h i s method i s p a r t i c u l a r l y crude the r e s u l t i s , nevertheless, consistent with what Professor Rosenbluth observed for the more immediate postwar period. By 19 72 i t became possible to analyse the postwar change i n s e n s i t i v i t y more pr e c i s e l y . Rosenbluth again tackled the question, but t h i s time he employed cross-spectral a n a l y s i s . 1 2 The i n d i c a t o r s , data manipulations, detrending procedure and estimating technique are v i r t u a l l y i d e n t i c a l to those used here; the use of cross-spectral analysis i n t h i s study i s i n large part a regional disaggregation of Rosenbluth's 1972 Canadian-United States s e n s i t i v i t y analysis. Except f o r the fact that only 4 of the 11 indicators used by Rosenbluth are avai l a b l e at the regional l e v e l , h i s r e s u l t s and those of t h i s study are quite comparable. Rosenbluth's general conclusion from the spectral study concerning the trend i n business cycle s e n s i t i v i t y was that "... the findings have confirmed the r e s u l t s of the e a r l i e r [1957] study with regard to the decline i n c y c l i c a l s e n s i t i v i t y between the interwar and post-war e r a s . " 1 3 However, t h i s conclusion i s not free of ambiguity. A decline i n correspondence (coherence) was found i n most, but not a l l , i n d i c a t o r s - an important exception was the 226 construction contracts s e r i e s . 1 5 Furthermore, with respect to cross relative-amplitude (gain) Rosenbluth concluded that "... c y c l i c a l s e n s i t i v i t y as measured by gain was lower a f t e r the Second World War than between the wars, but ... the evidence i s l e s s conclusive than i n the case of c y c l i c a l s e n s i t i v i t y as measured by coherence." 1 5 Thus, the decline i n s e n s i t i v i t y i s not found i n every indica t o r ; i t i s more general i n coherence than i n gain. Also, as Brecher and Reisman concluded i n t h e i r 19 57 study and as he concluded i n his comment at the 1969 conference on Economic S t a b i l i t y , Rosenbluth again found i n the spectral study that the decline i n s e n s i t i v i t y was more relevant to indicators of value and p a r t i c u l a r l y volume variables than i t was to p r i c e v a r i a b l e s . 1 * To best f a c i l i t a t e the comparison i n the next section between trends i n regional c y c l i c a l s e n s i t i v i t y and what has already been observed for Canada as a whole, the Rosenbluth r e s u l t s are presented i n Table 5.1 f o r the set of indicators used i n the regional analysis. From the tables of re s u l t s i n the Rosenbluth study, the re s u l t s r e i t e r a t e d here are based only upon h i s estimates i n the business cycle range of frequencies; t h i s necessitates the presentation of his r e s u l t s i n a form s l i g h t l y d i f f e r e n t from h i s own method. Also included i n Table 5.1 are the r e s u l t s of another cross-spectral study, by Bonomo and Tanner [1972]. This Table 5.1 CHANGES IN CANADA-USA SENSITIVITY; INTERWAR TO POSTWAR PERIODS CM Source: Indicator Rosenbluth [1972] Time Periods 1921-1938/1945-1971 Employment Index Construction Contracts 1919-1938/1945-1972 Bank Debits 1919-1938/1945-1972 Freight Carloadings 1919-1938/1945-1967 Coherence Bonomo and Tanner Gain 1 Indicator Time Period Coherence + Industrial Production 1919-1939/1945-1967 +.10 Gain -.05 1 For the three business cycle frequencies (3 yr./6 mo., 4 yr./8 mo., 7 yr./O mo.), the ranking of coherence and gain by subperiod must be the same for each frequency before i t i s concluded that the indicator has experienced a change i n s e n s i t i v i t y . (•) indicates an increase i n coherence or gain; (A) indicates ambiguous re s u l t s ; (-) indicates a decrease. 2 of 3 frequencies indicate a decrease 2 of 3 frequencies indicate an increase The coherence and gain estimates i n Bonono and Tanner [ 1972,, .Table C], are averaged over the relevant business cycle frequencies; that i s , over periods of 33.3 and 50 months. 228 Canadian-United States s e n s i t i v i t y analysis i s based upon only one in d i c a t o r of economic a c t i v i t y , the index of i n d u s t r i a l production. The Bonomo and Tanner method i s somewhat d i f f e r e n t from that employed by Rosenbluth and i n t h i s study, most p a r t i c u l a r l y i n that t h e i r indicators are not detrended i n advance. The authors suggest that except for seasonal cycles a comparison of postwar with interwar cross relative-amplitude ... " f a i l e d to support the hypothesis of a changing structure [ of Canadian s e n s i t i v i t y ] . " 1 7 Examination of t h e i r tabulated r e s u l t s indicates that at the relevant business cycle frequencies t h e i r conclusion i s supported by t h e i r coherence estimates but not t h e i r gain estimates. 1 8 It thus appears that for the index of i n d u s t r i a l production the r e s u l t s are ambiguous, although t h e i r method i t s e l f i s questionable given the e f f e c t that the lack of advance detrending might have on the estimates due to the problems associated with non-stationarity and interfrequency leakage. Whereas the t o t a l of the evidence suggests some decline i n postwar Canadian s e n s i t i v i t y , i t should be noted that to some extent the observed declines may be the r e s u l t of increased d i s p a r i t i e s i n the timing of regional fl u c t u a t i o n s . In Chapter Two (2.4.3) i t was shown that the "cl u s t e r i n g " of regional turning points has decreased from the interwar to the postwar periods, that i s , the d i s p a r i t i e s i n the timing of regional business cycles have 229 increased over time. This r e s u l t i s quite general and unambiguous. I t follows from t h i s r e s u l t that, even i f regional r e l a t i v e amplitudes remained constant over time, Canadian r e l a t i v e amplitude would l i k e l y decline; the fewer the number of regions which expand and contract simultaneously, the lower the aggregated, Canadian amplitude. 1 9 The c l u s t e r i n g decrease, while s i g n i f i c a n t i n every indi c a t o r , i s p a r t i c u l a r l y pronounced i n construction contracts.zo Since i t i s t h i s s e r i e s which also indicates an increase (or the l e a s t decrease) i n Canadian-United States s e n s i t i v i t y , i t follows that i n t h i s case the Canadian regional amplitudes must have experienced pronounced increases to compensate fo r the e f f e c t of the reduced c l u s t e r i n g . This hypothesis i s examined i n the next section. 5.3 Changes i n Regional S e n s i t i v i t y The change i n coherence and gain between the interwar and postwar periods f o r each region and indicator are recorded i n Table 5.2. Quite c l e a r l y , a general conclusion i s that the strength of i n t e r r e g i o n a l economic linkages has declined since the interwar period. Regional-ROC coherences decrease for almost every indicator i n each region; an exception for some regions i s the construction contracts s e r i e s , which indicates a higher regional-ROC coherence i n o to CM Table 5-2 CHANGES IH REGIONAL SENSITIVITY; INTERWAR TO POSTWAR PERIODti A. Coherence^-B.C. Prairies o Ontario Quebec Maritimes Indicator Reg:ROC Reg:USA R0C:USA Reg:ROC Reg:USA ROC:USA Reg:ROC Reg:USA ROC:USA Reg:R0C Reg:USA ROC:USA Reg:ROC Reg:USA ROC:USA Employment Index -.06 -.38 - .21 - 1 9 -33 - 1 8 - 0 8 ( - 0 6 ) - 0 6 - 1 0 -04 -.09 -.06 - U 9 - 3 1 - 0 6 Construction Contracts +.1*9 .00 - l i * —22 -.09 -13 +.47(+.35) -.05 -.16 +•25 -.09 .00 -.06 -.0? -.10 Bank Debits -.18 - 4 5 - 2 7 +.06 - 3 5 -23 - 3 7 ( - 0 5 ) - 2 1 -46 -30 -35 - 2 9 +.29 -.14 - 2 5 Freight Carloadinge -.03 -.07 —01 +.21 +.13 - 0 6 - 0 3 ( - 0 2 ) +.01 +.01 - 1 8 - 2 9 + .01 -.04 -.18 .00 1 (-) indicates decrease* B. Gain 3 B.C. Prairies 2 Ontario Quebec Maritimes Indicator SeS:R0C Reg:USA R0C:USA Reg:R0C Reg:USA R0C:USA Reg:ROC Reg:USA ROC:USA Reg:R0C Reg :USA ROC:USA Reg:ROC Reg:USA ROC:USA Employment Index -.09 -.29 —22 +.35 - 3 1 -.14 -17(+.05) -.29 - 1 6 - 2 6 +.03 - 3 3 - 0 7 - 3 8 - 2 9 Construction Contracte +.27 +.01 -24 +.34 - 3 1 -.09 +.57(+.45) -15 -.24 +.45 -.24 — 12 - 1 4 +.01 -.16 Bank Debits -.09 -.61 "-111 +.15 -31 -.44 —26(+.10) -.28 - 4 7 -.12 - 3 9 -.40 +.50 -56 - 3 4 Freight Carloadings +.01 +.18 .00 +.04 +.15 - 0 9 - 0 6 ( - 4 5 ) +.16 -.08 +•73 - 4 9 +.17 +.16 - 3 3 .00 2 The figures i n brackets are the change i n Ontario-Quebec coherence and gain. For gain, a (-) indicates a decline i n the amplitude of Quebec r e l a t i v e to Ontario cycles. 3 (-) indicates Region has increased r e l a t i v e amplitude r e l a t i v e to ROC and decreased r e l a t i v e amplitude r e l a t i v e to USA (and (-) implies ROC r e l a t i v e amplitude has decreased r e l a t i v e to USA). 231 B.C., Ontario and Quebec. This rather anomolous behaviour i n construction contracts cannot be accounted for by increases i n the strength of the business cycle component i n any of the regions; the evidence of Chapter Two has shown that the construction contracts s e r i e s , while being f o r every region a highly i r r e g u l a r s e ries, does not undergo any noticeable intertemporal changes i n the strength of the various c y c l i c a l components i n explaining t o t a l variance. The evidence for t h i s indicator suggests increased si g n i f i c a n c e in the regional i n t e r r e l a t i o n s h i p between B.C., Ontario and Quebec since the interwar period. This i s consistent with the evidence from the Ontario-Quebec comparison i n Chapter Four where coherence increased dramatically between the interwar and postwar periods. In terms of t h i s indicator Quebec leads both Ontario and ROC, while Ontario and B.C. lag ROC. We then concluded, however, that the leading behaviour of Quebec i n construction contracts has occured since the mid-1960s Centennial-Expo construction boom, when the Quebec indicator became s i g n i f i c a n t l y "out ot phase" with ROC. In every region, correspondence i n employment declines. The decline i s more acute i n the Maritimes and P r a i r i e s than i n the other regions; the decline between Ontario and Quebec i s approximately the same as between these and the other regions. Therefore, i n the postwar period fluctuations in employment i n one region have less tendency to be 232 accompanied by a f l u c t u a t i o n i n another region - even when there are time displacements. In the bank debits series there i s a pronounced weakening i n regional-ROC correspondence i n B.C., Ontario and Quebec, although there i s l i t t l e decline between Ontario and Quebec. Thus, the interregional correspondence i n bank debits has declined between Central Canada and the smaller regions. This i n d i c a t o r i s a very broad measure of economic a c t i v i t y and the weakening i n correspondence c l e a r l y r e f l e c t s a weakening of t h i s type i n the economic linkages between regions. Since the bank debits series contains a p r i c e as well as a volume component, and since we have already determined that the transmission of price changes between Canadian regions i s very strong i n the postwar period, i t follows that the weakening i n linkages i s concentrated on the r e a l side of economic a c t i v i t y . This i s further r e f l e c t e d i n the freight carloadings series where regional-ROC coherences decline i n every region except the P r a i r i e s . Again, the dramatic decline i n Quebec-ROC coherence i s not the r e s u l t of a decline i n Ontario-Quebec coherence. The change i n cross relative-amplitude (gain) estimates lead t o ambiguous r e s u l t s i n the regional-ROC comparison. Although the P r a i r i e s indicate a d e f i n i t e decrease i n amplitude r e l a t i v e to ROC, no such pattern emerges for any other region. Furthermore, i t can also be concluded that 233 there i s l i t t l e pattern to the regional-ROC changes i n coherence. Thus, while there i s some evidence of a decline over time in i n t e r r e g i o n a l correspondence, there i s no region which can be sai d to have experienced a greater decline than any other. The regional-USA evidence i s le s s ambiguous; c l e a r l y the regional-USA coherence for B.C., Quebec and the Maritimes has declined between the interwar and postwar periods. B.C. and Quebec show the most severe declines -for these regions, every indicator had a greater coherence decline than d i d the ROC-USA coherence (except, again, for B.C. construction contracts). For Ontario the opposite occurs as ROC-USA coherence declines more than Ontario-USA coherence. The evidence f o r the P r a i r i e s and Maritimes i s ambiguous. That the Ontario-USA decline i n coherence has been r e l a t i v e l y s l i g h t while the Quebec decline has been r e l a t i v e l y severe i s a very i n t e r e s t i n g r e s u l t , f o r i t again points out the d i s p a r i t i e s i n economic behaviour between these two regions. I t also suggests an increasingly more important role f o r Ontario i n the transmission of USA cycles i n t o Central Canada. The evidence on changes i n regional s e n s i t i v i t y adds further refinement to Professor Rosenbluth's investigation. In his study i t was found that Canada-USA s e n s i t i v i t y (coherence) declined, interwar to postwar, i n employment, f r e i g h t carloadings and bank d e b i t s . 2 1 The same can be said 234 f o r B.C., Quebec and the Maritimes; the r e s u l t i s not general over a l l regions because the Ontario-USA and Prairie-USA coherence i n f r e i g h t carloadings increased, p a r t i c u l a r l y i n the P r a i r i e s case. Furthermore, Rosenbluth found the construction contracts series to y i e l d ambiguous r e s u l t s ; i n t h i s study the s e n s i t i v i t y of t h i s indicator declined i n every region except B.C., although the decrease was i n general l e s s pronounced than that of any other in d i c a t o r , except for f r e i g h t carloadings i n Ontario and the P r a i r i e s . The regional-USA gain estimates are more d i f f i c u l t to i n t e r p r e t . The national freight carloadings indicator experiences l i t t l e change i n cross relative-amplitude between the interwar and postwar periods and t h i s i s consistent with Rosenbluth's r e s u l t s . 2 2 However, i n the regions there are s i g n i f i c a n t intertemporal changes; the P r a i r i e s and Ontario have an increased gain, while Quebec and the Maritimes decrease, although for the Quebec, P r a i r i e and Maritime regions the i n t e r p r e t a t i o n of t h i s r e s u l t i s ambiguous since the changes i n gain are accompanied by s i m i l a r changes i n coherence. Rosenbluth found an increase i n Canadian cross relative-amplitude i n employment and construction contracts. From t h i s study i t appears that, fo r employment, t h i s change emanated from every region except Quebec while, f o r construction contracts, i t emanated from the P r a i r i e s , Ontario and p a r t i c u l a r l y Quebec. In bank 235 debits Rosenbluth finds a decrease i n gain; i n Table 5.2 i t can be seen that t h i s change i s quite pronounced i n every region. In general terms, the ROC-USA gain estimates only suggest a decrease i n cross relative-amplitude (with the possible exception of f r e i g h t carloadings) since correspondence has also declined. However, underlying the general r e s u l t i s evidence of rather pronounced regional v a r i a t i o n in the magnitude of the decline, and also evidence that within each region the intertemporal change i n the various indicators i s quite disparate. One point which requires further explanation i s the observed lack of pronounced decline i n the s e n s i t i v i t y of construction contracts. The combined evidence on construction contracts tends to support the hypothesis stated at the end of Section 5.2 concerning the implications of the observed decrease i n c l u s t e r i n g . In Table 5.2 i t can be seen that regional-ROC gain rose quite dramatically i n every region except the Maritimes, thus o f f s e t t i n g the e f f e c t of decreased c l u s t e r i n g upon Canadian amplitude. Furthermore, construction contracts experienced the l e a s t decline in regional-USA coherences r e l a t i v e to other i n d i c a t o r s and also experienced i n B.C., Quebec and Ontario marked increases i n regional-ROC coherences. F i n a l l y , from Tables 4.2 and 4.5 in Chapter Four i t can be seen that regional-ROC and regional-USA coherences i n interwar period 236 construction contracts are extremely low r e l a t i v e to other indicators while i n the postwar period they are closer to the average of a l l i n d i c a t o r s . One possible explanation for a l l the evidence on construction contracts i s based upon the evidence that interwar coherences were so low. I t has been shown that the series contains an (exceptionally) strong i r r e g u l a r component and that the i r r e g u l a r component was as strong r e l a t i v e to other components i n the postwar period as i t was i n the interwar period. It follows that i f these i r r e g u l a r f l u ctuations i n the various regions become more c l o s e l y correspondent between the interwar and postwar periods, t h i s would be at l e a s t p a r t i a l l y r e f l e c t e d i n the coherence and gain estimates. Leads and lags would become more c l e a r l y recognizable - none of the interwar period leads and lags are s t a t i s t i c a l l y d i f f e r e n t from zero - and the c l u s t e r i n g measure could then indicate increased dispersion i n regional timing. This explanation suggests an increase i n the i n t e r r e g i o n a l linkages underlying construction a c t i v i t y . In conclusion, there appears to be strong i n d i c a t i o n that, for each region* s e n s i t i v i t y to USA business cycles has decreased since the interwar period. Although i t i s more evident i n terms of correspondence than i t i s i n terms of cross relative-amplitude, the decline i n s e n s i t i v i t y i s less pronounced i n Ontario and more pronounced i n Quebec. With the exception of the construction contracts indicator, 237 the decline i n regional-USA correspondence i n B.C., Ontario and Quebec has been accompanied by a decline i n regional-ROC correspondence. The change i n Ontario-Quebec correspondence, from the Quebec point of view, i s such that the region has become r e l a t i v e l y more correspondent to Ontario than ROC, even though coherence with Ontario and with ROC has declined absolutely i n both cases. From the Ontario point of view the change i s sim i l a r although much le s s pronounced. The implication here for the Ontario-Quebec i n t e r r e l a t i o n s h i p i s that for Quebec the extent of Ontario-Quebec interdependence has increased r e l a t i v e to Quebec-ROC interdependence, but for Ontario a change of t h i s nature i s much les s apparent. 5.4 Determinants of Changes i n C y c l i c a l S e n s i t i v i t y There are, of course, many hypotheses a v a i l a b l e to explain changes i n c y c l i c a l s e n s i t i v i t y . Our purpose here i s to suggest, i n general terms, several hypotheses which we consider to be of p a r t i c u l a r relevance to explaining changes i n Canadian regional s e n s i t i v i t y ; however, empirical examination of these hypotheses i s seriou s l y l i m i t e d by the lack of regional s t r u c t u r a l data. Correspondence between fluctuations i n two economies can r e s u l t i f between the economies there e x i s t trade, money market, investment expectations or other economic linkages and/or the two economies have correspondent linkages with 238 other economies. Most inter-economy linkages can be viewed, f o r the sensitive economy (" s e n s i t i v i t y i s defined i n 4.2.2, Chapter Four), as externally-determined portions of t o t a l autonomous expenditures. In the Canadian context, exports and autonomous investment are generally considered two of the most important intereconomy linkages and they can be viewed i n t h i s way although the proportion of t o t a l autonomous investment which i s i n f a c t externally-determined - v i a linkages i n business expectations, c a p i t a l goods prices and f i n a n c i a l markets - cannot e a s i l y be q u a n t i f i e d . 2 3 A l l these linkages are even more d i f f i c u l t to quantify i n the regional context; only the regional trade linkage could be even t e n t a t i v e l y established, given the paucity of both i n t e r r e g i o n a l and foreign (on a regional basis) trade flow data. If there were s u f f i c i e n t data, the responsiveness/passiveness of a s e n s i t i v e economy would be determined by (a) the e l a s t i c i t y of the l e v e l of a linked v a r i able with respect to external general business a c t i v i t y , (b) the e l a s t i c i t y of the sensitive economy's general business a c t i v i t y with respect to the l e v e l of the link e d v a r i a b l e and (c) the l e v e l of the linkage r e l a t i v e to t o t a l autonomous expenditures. 2* A change over time i n any of these re l a t i o n s h i p s could r e s u l t i n a change i n the nature of c y c l i c a l s e n s i t i v i t y . We now examine several of the important determinants of regional c y c l i c a l s e n s i t i v i t y , although i t should be noted 2 3 9 that regardless of the linkages between Canadian regions, the observed declines i n regional-ROC correspondence may i n general be r e l a t e d to the observed decline i n both Canadian-USA and regional-USA coherence. Canadian regions are se n s i t i v e to United States fluctuations but i f these s e n s i t i v i t i e s decline over time then the observed regional-ROC coherences w i l l a l so decline unless the i n t e r r e g i o n a l linkages have strengthened. However, the declines would probably be d i f f e r e n t i n d i f f e r e n t regions since, as we have shown, regional-USA and regional-ROC coherences are quite c l e a r l y not the same i n each region. Furthermore, the observed weakening i n regional-USA coherences suggests the hypothesis (not to be examined here) that i f several Canadian regions were cl o s e l y linked to s p e c i f i c United States regions and i f United States regions become less correspondent over time, i t follows that correspondence between Canadian regions and the U.S. aggregates might decline as well. (1) The Foreign Trade Sector In attempting to explain the postwar decline i n Canadian s e n s i t i v i t y , Rosenbluth [1973] examines two aspects of the export linkage. F i r s t , a comparison over time between the value of Canadian exports and United States railway operating revenues (an i n d i c a t o r of general economic a c t i v i t y ) tests f o r changes in the e l a s t i c i t y of Canadian 240 exports with respect to changes i n United States general economic a c t i v i t y . The declines between the interwar and postwar periods i n both coherence and gain lead him to conclude that "... i t i s l i k e l y that the way Canadian exports respond to United States fluctuations provides a part of the explanation of the changes i n s e n s i t i v i t y . . . " . The change i n the s e n s i t i v i t y of exports has occured despite two fundamental changes i n the Canadian export sector which have taken place since World War I, namely, (a) a decline i n the r e l a t i v e importance of a g r i c u l t u r a l exports - a variable which Chambers [1958b] has shown to have an i r r e g u l a r pattern r e l a t i v e to his reference dates for business cycles - and (b) an increase i n the proportion of t o t a l Canadian (presumably nonagricultural) exports which are sold to the United States (essentially at the expense of the United Kingdom). 2 5 Thus, an increase over time i n the importance of the United States within the Canadian export sector has been accompanied by a decrease i n the s e n s i t i v i t y of t o t a l Canadian exports t o United States output. The decreased export s e n s i t i v i t y would be extremely d i f f i c u l t to account for i n the national economy l e t alone the regional economies. However, one conjecture that we might make res u l t s from our observation that the P r a i r i e s have become only very s l i g h t l y more " i n d i r e c t l y s e n s i t i v e " to United States fluctuations i n the postwar period and have indicated no tendency towards an increase i n " d i r e c t 241 s e n s i t i v i t y " . Within t o t a l Canadian exports the decline over time in the importance ot a g r i c u l t u r a l products, and the increase i n non-metallic minerals, suggests increased exports to the United States as a proportion of t o t a l P r a i r i e exports. Since Prairie-USA c y c l i c a l s e n s i t i v i t y has not increased, we suggest that either (a) the linkages within the region between exports of non-metallic minerals and general economic a c t i v i t y are quite weak, or (b) the e l a s t i c i t y of these exports with respect to United States output i s quite low. A second important aspect of the export linkage concerns the l e v e l of exports as a proportion of t o t a l expenditures. Rosenbluth [1958] concluded that the observed decline in the r a t i o of merchandise exports to GNE between the interwar and early postwar periods was also consistent with declining s e n s i t i v i t y - and the importance of exports i n GNE remains approximately the same when the 1958-1973 period i s compared to the 1948-1957 period, although since 196 6 the increased trade i n motor vehicles (and parts) has caused the share of exports to increase rather d r a m a t i c a l l y . 2 6 In f a c t , Canadian merchandise exports to the United States as a proportion of Canadian GNE increases when the postwar period i s compared to the interwar p e r i o d . 2 7 Although regional trade data i s unavailable, our conjecture i s that s h i f t s over time i n the composition of Canadian exports to the United States would have encouraged 242 an increase (relative to other regions) i n the proportion of Ontario output exported to the United States. I f the Canadian annual average export composition, 1948-1965, i s compared to that of the interwar period there are increased proportions within t o t a l exports to the United states of non-ferrous metal products, iron products and chemicals -a l l of which are important sectors i n Ontario's economy. 2 8 Moreover, after 1965 Ontario-USA trade i s increased to an even greater proportion of Canada-USA trade through the l i b e r a l i z a t i o n of trade i n motor vehicles. The impact of t h i s e f f e c t i s c l e a r l y consistent with our observations (a) that Ontario has experienced the l e a s t decline of a l l regions i n c y c l i c a l s e n s i t i v i t y , (b) that Ontario has experienced an increased tendency towards "transmitting" United States fluctuations to other regions - p a r t i c u l a r l y to Quebec - and (c) that examination of p a r t i c u l a r episodes i n the postwar period revealed a s i m i l a r i t y i n c y c l i c a l behaviour between Ontario and the United States which could not be found i n any other region. Thus, t h i s evidence may p a r t i a l l y explain why c y c l i c a l s e n s i t i v i t y declined more in Quebec and B.C. than i n Ontario. Moreover, the observed decline i n regional-ROC coherences (together with our e a r l i e r abservation of decreased " c l u s t e r i n g " of regional turning points i n the postwar period) i s consistent with the view that i n t e r r e g i o n a l trade sectors have declined i n importance i n the regional economies, perhaps due to 243 i n c r e a s e d s e l f - s u f f i c i e n c y i n manufactured p r o d u c t s . However, t h i s e f f e c t should not be o v e r s t a t e d s i n c e both O n t a r i o and, t o a l e s s e r e x t e n t , Quebec - the t r a d i t i o n a l e x p o r t e r s of manufactured products t o t h e o t h e r r e g i o n s -have maintained extremely s t a b l e shares s i n c e 1951 i n the t o t a l value-added i n Canadian manufacturing i n d u s t r i e s . 2 9 To the e x t e n t t h a t the Ontario-USA t r a d e i n manufactured goods has expanded, Ontario-ROC t r a d e i n manufactured consumer and c a p i t a l goods may have d e c l i n e d . Rosenbluth then completes h i s a n a l y s i s of the t r a d e s e c t o r by examining i m p o r t s . Here the c r o s s r e l a t i v e -amplitude between Canadian imports and Canadian r a i l w a y o p e r a t i n g revenue suggests the c y c l i c a l s t a b i l i t y of the average p r o p e n s i t y t o import and, a l s o , the Canadian income-m u l t i p l i e r , t h e r e b y t e s t i n g the c y c l i c a l behaviour of the e l a s t i c i t y between Canadian g e n e r a l economic a c t i v i t y and t h e l e v e l of autonomous expenditures (which i n c l u d e s l i n k v a r i a b l e s such as e x p o r t s ) . Rosenbluth found postwar coherence and g a i n lower than i n the i n t e r w a r p e r i o d ; i m p o r t s have become l e s s s e n s i t i v e t o domestic f l u c t u a t i o n s i n economic a c t i v i t y , thus reducing the import s e c t o r s " s t a b i l i z i n g " i n f l u e n c e on domestic income and r e n d e r i n g Canada more s u s c e p t a b l e t o f o r e i g n f l u c t u a t i o n s . He then concludes t h a t ..."the behaviour of imports i s t h e r e f o r e of no h e l p i n e x p l a i n i n g reduced s e n s i t i v i t y t o U n i t e d S t a t e s fluctuations". 3° 244 There i s some evidence i n the Canadian d a t a t h a t the m a r g i n a l p r o p e n s i t y t o import behaves p r o c y c l i c a l l y due t o t h e h i g h i m p o r t - c o n t e n t o f investment g o o d s . 3 1 Thus, the c y c l i c a l s t a b i l i t y of the p r o p e n s i t y t o import would be i n c r e a s e d i f . , c e t e r i s p a r i b u s , t h e r e was (a) an i n c r e a s e i n the c y c l i c a l s t a b i l i t y of the p r o p o r t i o n of investment i n GNE (and t h e r e f o r e spending on imported investment goods i n GNE) , or (b) a decrease i n e i t h e r t h e imported investment-goods content of t o t a l investment spending or t h e p r o p o r t i o n o f t o t a l investment spending i n GNE. Thus, both (a) and (b) would c o n t r i b u t e towards i n c r e a s e d v o l a t i l i t y i n the Canadian economy. Without the n e c e s s a r y import data we cannot compare such a s p e c t s of s t r u c t u r e w i t h t h e observed changes i n r e g i o n a l c y c l i c a l s e n s i t i v i t y ; t o examine the c y c l i c a l behaviour of the import leakage would r e q u i r e not o n l y regional-USA import data but a l s o regional-ROC t r a d e d a t a . A s i m p l i s t i c view of r e g i o n a l i n d u s t r i a l s t r u c t u r e i n Canada would suggest t h a t the o n l y r e g i o n w i t h a s i g n i f i c a n t c a p i t a l goods s e c t o r would be O n t a r i o (and p o s s i b l y Quebec); t h e d e c l i n e i n the s t a b i l i z i n g i n f l u e n c e of imports n o t i c e d by Rosenbluth might t h e r e f o r e p e r t a i n more t o r e g i o n s other than O n t a r i o , s i n c e they purchase c a p i t a l goods from both the United S t a t e s and O n t a r i o . I f t h i s were the case, we would expect i n c r e a s e d regional-USA s e n s i t i v i t y f o r every r e g i o n except O n t a r i o - which i s c o n t r a r y to what we have 245 observed. Changes i n t h e import l i n k a g e , then, do not e x p l a i n the observed changes i n r e g i o n a l s e n s i t i v i t y . (2) Domestic Investment The l i n k a g e s between U n i t e d S t a t e s f l u c t u a t i o n s and Canadian domestic investment are u s u a l l y expressed i n terms o f the p r i c e s of c a p i t a l goods, the f o r m u l a t i o n of e x p e c t a t i o n s by i n v e s t o r s and t h e terms upon which investment funds can be o b t a i n e d . 3 2 However, the r o l e of investment e x p e n d i t u r e s as a t r a n s m i s s i o n mechanism i s d i f f i c u l t i s i s o l a t e e m p i r i c a l l y s i n c e the investment data cannot d i s t i n g u i s h between U n i t e d States-determined and d o m e s t i c a l l y - d e t e r m i n e d investment e x p e n d i t u r e s . Thus, the o n l y p o s s i b i l i t y f o r a n a l y s i s i s t o examine t o t a l investment expenditures and assume t h a t the d o m e s t i c a l l y - d e t e r m i n e d p o r t i o n remains c o n s t a n t over time. Rosenbluth found t h a t the e l a s t i c i t y of Canadian investment with r e s p e c t t o U n i t e d S t a t e s output was s t a b l e from t h e i n t e r w a r t o t h e postwar p e r i o d - except f o r a decrease i n s e n s i t i v i t y d u r i n g 1933-1937, which can be a t t r i b u t e d t o the s e v e r i t y of t h e d e p r e s s i o n i n Canada and t h e weak response of the Canadian economy t o reco v e r y i n the U n i t e d S t a t e s . 3 3 However, the r a t i o of p r i v a t e f i x e d investment t o Canadian GNE has i n c r e a s e d from 12.7 percent, 1921-1939, t o 18.1 percent, 1946-1973; a l s o , the importance o f (non-farm business) i n v e n t o r y investment has d i m i n i s h e d 246 s l i g h t l y , from 1.51 p e r c e n t i n the i n t e r w a r p e r i o d t o 1.38 p e r c e n t i n the postwar p e r i o d . 3 4 S i n c e the P u b l i c and P r i v a t e Investment survey does not p u b l i s h r e g i o n a l data b e f o r e 1948, we cannot examine w i t h any p r e c i s i o n the r e g i o n a l i m p l i c a t i o n s of the i n c r e a s e d importance of b u s i n e s s f i x e d c a p i t a l f ormation i n Canadian GNE. However, i t i s p o s s i b l e t o compare between r e g i o n s i n the postwar p e r i o d the p r o p o r t i o n of b u s i n e s s f i x e d c a p i t a l f o r m a t i o n i n r e g i o n a l p e r s o n a l i n c o m e . 3 5 The p r o p o r t i o n s averaged over the postwar p e r i o d ( i n T a b l e 5.3) show t h a t the importance o f investment w i t h i n our r e g i o n a l t o t a l output proxy v a r i e s w i d e l y over the v a r i o u s r e g i o n s . Table 5.3 REGIONAL BUSINESS GROSS FIXED CAPITAL FORMATION AS A PROPORTION OF REGIONAL PERSONAL INCOME* Region 1948-1959 1960-1973 194 8-1973 O n t a r i o 17. 1 14.5 15.3 Quebec 17.8 14.7 15.7 Maritimes 13.3 18.8 17.1 B.C. 22.0 21.9 22.0 P r a i r i e s 28.9 16.6 25.3 * Source: P e r s o n a l income i s from DBS (1975), " N a t i o n a l Accounts, The Annual E s t i m a t e s , 1926-1974", and investment i s from the Department of Trade and Commerce (1948-1973, " P u b l i c and P r i v a t e Investment Survey". 247 Our hypothesis i s that the higher t h i s proportion the stronger the investment linkage to the United States economy and, therefore, the stronger the regional correspondence to United States fl u c t u a t i o n s . In Chapter Four i t was concluded that i n the postwar period the regional ordering according to regional-USA correspondence was - from strongest to weakest - Ontario; Quebec; B.C. - Maritimes (about equal); P r a i r i e s . Obviously, t h i s ordering i s not the same as the ordering by investment-income proportions i n Table 5.3. The inconsistency suggests that the investment linkage i s not an important determinant i n explaining d i s p a r i t i e s i n regional s e n s i t i v i t y . The role of inventory investment may be more important. Although inventory investment only accounts for some 10 percent of t o t a l investment, i t may play a larger role than that figure suggests given i t s v o l a t i l e c y c l i c a l behaviour and the tendency f o r the r a t i o of non-farm business inventory investment to Canadian GNE to decline during c y c l i c a l contractions i n the United S t a t e s . 3 * Since inventory stocks are concentrated i n manufacturing in d u s t r i e s , i t follows that Ontario and Quebec with t h e i r r e l a t i v e concentration of economic a c t i v i t y i n manufacturing industries would have a stronger linkage to the United States economy through t h i s mechanism than would the other regions. The Central Canadian regions have the strongest correspondence with the United States and, therefore, our 248 conjecture i s that the inventory investment linkage explains a part of t h i s correspondence. The observed decline i n the r a t i o of inventory investment to GNE i s consistent with the declining c y c l i c a l s e n s i t i v i t y i n Ontario and Quebec although we do not know the extent to which inventory investment has changed i n importance within the t o t a l expenditures of these regions. (3) Government Expenditure F i n a l l y , one of the most s i g n i f i c a n t s t r u c t u r a l changes to occur i n the Canadian economy since World War I has been the increase within GNE of the share of t o t a l government expenditures on goods and services and the decrease i n the share of personal expenditures, the l a t t e r a t t r i b u t a b l e to a large decrease in the share of expenditures on nondurables and a smaller decrease i n the share of expenditures on s e r v i c e s . 3 7 This s t r u c t u r a l change may have had two ef f e c t s on Canadian c y c l i c a l s e n s i t i v i t y . F i r s t , federal government expenditures are no l e s s v o l a t i l e than private investment, but ..."only c o i n c i d e n t a l l y have [movements i n federal government expenditures ] reinforced fluctuations i n investment i n the pri v a t e s e c t o r . " 3 8 P r o v i n c i a l and municipal expenditures tend to be more stable and show l i t t l e response to fluc t u a t i o n s i n aggregate demand. Since government spending does not conform to fluctuations i n general economic 249 activity, such "automatic stabilizers" as progressive income taxation become more effective. Thus, substitution by government spending for exports and personal expenditures would tend to stabilize fluctuations in general economic activity. That i s , . . . " c y c l i c a l l y insensitive expenditures have been substituted for the more variable exports and consumer expenditures." 3 9 Although data on total government expenditures by region are unavailable, i t lik e l y follows that the regional economies would have experienced approximately similar growth in government and, therefore, experienced a similar effect upon the v o l a t i l i t y of cy c l i c a l fluctuations. Second, the increased importance of government transfer payments also would tend to increase the c y c l i c a l stability of the economy.*o Transfers are likely contracyclical due to the automatic stabilizing influence of unemployment insurance benefits and welfare payments. Again, the regional impacts of this development are l i k e l y quite similar. 2 5 0 FOOTNOTES TO CHAPTER FIVE Rosenbluth [ 1957 ]. Rosenbluth [1957, pg. 489]. Brecher and Reisman [ 1 957 ]. Brecher and Reisman, [1957, Table 14]. Rosenbluth [ 1957, pg. 491]. Rosenbluth [ 1969 ]. Rosenbluth, [ 1969, Table 2.2]. Brecher and Reisman [1957 ]. Chambers [ 1 958 ]. White [ 1967, pg. 45-50 ]. White [1967, Table 11]. Amplitude i s measured as 100 (P-T/P+T) where P and T are three month averages centered on s p e c i f i c cycle peaks and troughs. The turning points are those of Chambers, updated to 1965 by White. 251 Rosenbluth [1973]. Rosenbluth, [ 1973, pg. 28]. Rosenbluth, [ 1973, pg. 12]. Rosenbluth, [1973, pg. 15]. Rosenbluth, [ 1973, pg. 11]. Bonomp and Tanner [1972, pg. 5]. Their r e s u l t s for these frequencies are r e i t e r a t e d in Table 5.1. Given the f a c t that Canadian regional economies are of such unequal s i z e (that i s , they have widely d i f f e r e n t weights i n the national t o t a l ) , i t i s conceivable, although not l i k e l y , that regional leads and lags could change over time such that a decrease i n c l u s t e r i n g would be consistent with an increase i n Canadian amplitude. See Table 2.14 and Table 7, Appendix C i n Chapter Two. Rosenbluth [1973, Table 1]. 252 Rosenbluth [ 1973, Table 1]. This hypothesis, and the elaboration which follows, leans heavily upon the modelling of the determinants of Canadian s e n s i t i v i t y to United States business cycles by Rosenbluth [1958] and White [1967]. For discussion of the investment linkages, see Bryce [1939], Rosenbluth [1958, pg. 32] and White [ 1973, pg. 118-131, 153-190]. For elaboration of t h i s theory see Rosenbluth (1958). A g r i c u l t u r a l (plus animal) exports as an average annual percentage of t o t a l merchandise exports declined from 46.3%, 1926-1939, to 23.2%, 1948-1972. The data source for t o t a l exports i s i n the following footnote. Exports of a g r i c u l t u r a l and animal products, 1926-1939, i s i n Urquhart and Buckley [1965, Table F298]. For 1948-1972, the t o t a l of food and l i v e animal products (including seed, beverages and tobacco) from DBS (1948-1972), "Review of Foreign Trade", i s linked to the Urquhart-Buckley series using the overlapped observations, 1948-1960. Exports to the United States were, on average, 38.1% of t o t a l exports, 1919-1939, but rose to 58.4% over the 1948-1972 period. Exports to the United States, 1919-1960, are from Urquhart and Buckley [1965, Table] and 1960-1972 are from DBS (1960-1972), "Exports by Commodity". 253 During the 1921-1939 period, exports of goods and services on average comprised 25.0 percent of GNE. Then, during the 1946-1957 period, nominal merchandise exports were on average 21.8 percent of GNE. From 1958-1973 t h i s proportion remained at 21.3 percent, although i t f e l l to 19.2 percent between 1958 and 1965 and then rose to 23.4 percent, 1966-1973. The importance of motor vehicle (and parts) exports rose from 1.1 percent of t o t a l exports, 1953-1965, to 15.9 percent, 1966-1973. For 1953-1969 data, see Bank of Canada (1969), "Supplement to the S t a t i s t i c a l Summary", and for 1970-1973 see the Bank of Canada (1974), "Bank of Canada Review". For 1926-1954, see DBS (1975), "National Accounts, The Annual Estimates, 1926-1974". For 1921-1925 estimates of exports and GNP see Buckley, [1955, Table, G. H, J ] . Exports to the United States as an average annual percentage of .Canadian GNE rose from 5.1%, 1919-1939, to 10.4%, 1948-1972. For data references, see footnotes 25 and 26. Within t o t a l Canadian exports to the United States the value of ir o n , copper, ni c k e l and chemical products grew from 10.1% i n the interwar period to 16% i n the 1948-1965 period. The r a t i o exceeded 18% i n the early 1960s but declined to less than 10% i n 1973 due t o the increased share of motor vehicles. The interwar period data i s 254 an average of export shares i n 1926-1932 and 1938-39, the years f o r which export data by commodity i s available in the trade of Canada on a calendar year basis. For the postwar period, data i s from DBS (1948-1973) Exports by Commodity, 65-004. Ontario Ministry of the Treasury (1976), "Ontario S t a t i s t i c s ; 1975". Rosenbluth [ 1973 ]. Rosenbluth [1958, Pg. 482] reiterates K.W. Taylor's point that Canada the high import content of investment goods r e s u l t s i n a balance of trade d e f i c i t during expansions and a surplus during depressions. Robinson [1968] shows that the marginal propensity t o import i s greater during upswings than downswings, and White [1967] shows the p r o c y c l i c a l behaviour of (a) the investment-GNE r a t i o and (b) the import-intensive components of t o t a l investment. White [1968, pg. 118-123] summarizes evidence on the existence of arbitrage i n Canadian-United States money markets. Rosenbluth [1973, Tables 1, 3] finds high coherence between bond y i e l d s . Stock prices, which indicate expectations concerning the future rate of p r o f i t , have beer, shown to be c l o s e l y r e l a t e d between the economies by White [1967, pg. 2 5 5 124] and Rosenbluth [1973, Tables 1, 3]. White [pg. 128] also finds a close r e l a t i o n s h i p between indexes of i n d u s t r i a l material prices i n Canada and the United States. Rosenbluth [ 1958 ]. Data for 1926-1973 i s from DBS (1975), "National Accounts, the Annual Estimates, 1926-1973". For 1921-1925, see Buckley, K. [ 1955, Tables G, H, I ] . Business (gross) f i x e d c a p i t a l formation i s t o t a l c a p i t a l and repair expenditures from the Public and Private Investment survey excluding housing, government i n s t i -tutions and government departments. See Department of Trade and Commerce (1948-1973), "Public and Private Investment i n Canada". This r e l a t i o n s h i p i s calculated from Table 13 i n White [1967]. The proportion of t o t a l government expenditures on goods and services i n GNE increased from 9.4 percent, 1921-1939, to 14.8 percent i n 1965. The share of personal expen-ditures f e l l from 72.4 percent to 61.8 percent over the same period, with personal expenditures on nondurables f a l l i n g from 39.1 percent to 29.7 percent and on services f a l l i n g from 27.1 percent to 24.3 percent. Data for 1926-256 1973 i s from the DBS (1975), "National Accounts, Annual Estimates, 1926-1974", and, f o r 1921-1925, from Buckley, [ 1955, Tables G, H, J ] . White [ 1967, pg. 157]. 39 Rosenbluth [1958]. 4 0 The r a t i o of government transfers (to persons) to GNE increased from 3.5 percent, 1926-1939, to 6.8 percent, 1948-1973. Data i s from DBS (1975), "National Accounts, Annual Estimates, 1926-1974". 257 CHAPTER SIX REGIONAL AND NATIONAL CYCLES AND SENSITIVITY: A SDMMARY OF CONCLUSIONS 6.1 Introduction Our purpose i n t h i s summary i s to discuss the implications of the accumulated evidence for the analysis of national cycles and s e n s i t i v i t y . F i r s t , based upon the descriptive analysis i n Chapters Two and Three we examine the general dimensions of regional d i s p a r i t i e s i n c y c l i c a l behaviour. Does the evidence reveal consistent patterns to regional d i s p a r i t i e s i n c y c l i c a l behaviour, and does t h i s evidence then warrant a geographic disaggregation of the analysis of national c y c l i c a l behaviour? Second, from the s e n s i t i v i t y analysis of Chapters Four and Five, we offer several conjectures as to the "regional mechanism" by which United States cycles are transmitted i n t o Canada. Furthermore, can changes over time i n Canadian c y c l i c a l s e n s i t i v i t y be explained by changes i n the s e n s i t i v i t y r e l a t i o n s h i p between regions or between regions and the United States? 6.2 National Implications of the Evidence on  Regional C y c l i c a l Behaviour In general, the evidence on d i s p a r i t i e s i n regional c y c l i c a l behaviour i s highly suggestive. In most instances a concensus has been found i n the various economic 258 indicators which permits description of the general nature of the d i s p a r i t i e s between regional and national c y c l i c a l behaviour. In a broad sense the dimensions of d i s p a r i t i e s i n regional fluctuations seem rather large. We have found, on balance, that the Canadian regions adhere to a common, basic pattern of economic f l u c t u a t i o n s . Episodes found i n the national i n d i c a t o r s are usually - but not always - found i n the regional i n d i c a t o r s and tend to have a s i m i l a r average duration, but there the s i m i l a r i t y ends. The strength of the various c y c l i c a l components that explain the t o t a l v a r i a t i o n i n economic indicators i s markedly d i f f e r e n t over regions - with the possible exception of subcycles in the postwar period. In every region the annual cycle i s the most pronounced, but there are s i g n i f i c a n t regional d i s p a r i t i e s i n the strength of t h i s component r e l a t i v e to the business cycle frequencies. Within the common regional-national pattern i n fluctuations the r a t i o of the average duration of expansionary to contractionary phases varies over regions and, moreover, s i g n i f i c a n t differences i n the timing of regional fluctuations are apparent; certain regions seem to consistently lead or lag the national economy. Also, there i s tenuous evidence that the v o l a t i l i t y of regional cycles i s usually at l e a s t as great as that of Canada; when the influence of the regional weight i n the national t o t a l i s 2 5 9 removed, we found that Ontario i s the most v o l a t i l e region i n comparison with the Rest-of-Canada, although i n general Ontario i s the region whose c y c l i c a l behaviour most clos e l y resembles that of the nation. Furthermore, we found s i g n i f i c a n t differences between the c y c l i c a l behaviours of Ontario and Quebec even though the economic linkages which transmit cycles between the two regions are strong. Since the interwar period some of these d i s p a r i t i e s have not remained constant. Changes over time i n the contribution of the various c y c l i c a l components to the explanation of t o t a l variance i n the regional time-series i n d i c a t o r s was for several regions d i f f e r e n t than the intertemporal pattern i n the national economy. Regional leads/lags with respect to the Canadian economy also changed between the interwar and postwar periods; the " c l u s t e r i n g " measure - which summarizes the extent to which the regions are "out of phase" with each other - indicates that over time the d i s p a r i t i e s i n regional timing have increased. This has been accompanied by a general decline i n regional-national correspondence, although correspondence i n the postwar period remains much stronger for some economic indicators than for others. The higher coherence i n the p r i c e series than the employment or f r e i g h t carloadings series i s consistent with the fact that Canadian regions, i n t h e i r economic relationships with each other, are of open economies with f i x e d exchange rates. With regional 260 interdependence i n trade and a v a r i e t y of common i n s t i t u t i o n s (such as labour unions and banks), i t follows that f l uctuations i n the CPI would be s i m i l a r i n each region even when "output" variables are l e s s c l o s e l y r e l a t e d . The high postwar coherence in dwelling s t a r t s r e f l e c t s a s i m i l a r i t y of behaviour i n regional housing markets which may result from such common factors as federally-determined housing p o l i c i e s and nationally-determined i n t e r e s t rates -although we notice a d e f i n i t e d i s i n t e g r a t i o n i n the c l u s t e r i n g of regional-national turning points since the 196 6 trough. 6.3 The Regional Mechanism of C y c l i c a l Transmission During the interwar period Canadian regions were i n general sensitive to business cycle fluctuations i n the United States, although B.C., Ontario and Quebec were more c l o s e l y atuned to the United States economy than either the P r a i r i e s or Maritimes. Despite t h i s general s e n s i t i v i t y we also found that each region tended to correspond as c l o s e l y to fluctuations i n the Rest-of-Canada as i t does to those of the United States but, again, the l e v e l of correspondence varied quite widely over regions. The varying l e v e l s of regional-USA correspondence indicate that the transmission of cycles from the United States does not occur s i m i l a r l y i n every region; evidence of varying l e v e l s of regional-ROC correspondence together with evidence of s i g n i f i c a n t leads 261 and lags between the regions and ROC suggests a v a r i e t y of regional s e n s i t i v i t y r e l a t i o n s h i p s . Also, the d i s p a r i t i e s i n the regional-USA and regional-ROC gain estimates indicate that the impact of transmitted United States cycles i s not the same i n every region, although i n every case the v o l a t i l i t y i n regional business cycles i s l e s s than that of the United States. The evidence suggests that i n the mechanism by which United States business cycles are transmitted into Canada, there i s a tendency for Ontario to be s e n s i t i v e to both ROC and the United States; i n our indicators Ontario i s also the most v o l a t i l e region, p a r t i c u l a r l y during the 1930s, and t h i s r e s u l t i s consistent with the view that because Ontario i s l i k e l y a net exporter of c a p i t a l goods and consumer durables to the other regions then the c y c l i c a l i n s t a b i l i t y of the marginal propensity to import i n the other regions might s t a b i l i z e these regions while at the same time d e s t a b i l i z i n g the Ontario economy. The Ontario-Quebec i n t e r r e l a t i o n s h i p , e s s e n t i a l l y one of economic feedback, i s by far the dominant factor i n both the Ontario-ROC and Quebec-ROC i n t e r r e l a t i o n s h i p s . These two regions have a s i m i l a r s e n s i t i v i t y to United States fluc t u a t i o n s , but Ontario i s to a greater extent than Quebec correspondent with the other three regions; apart from d i r e c t s e n s i t i v i t y to the United States, Ontario thus has a greater s e n s i t i v i t y to fluctuations i n the Rest-of-Canada than does Quebec. 262 Also, we found the P r a i r i e s and Maritimes regions to be the most independent regions - there i s extremely weak P r a i r i e s e n s i t i v i t y to fluctuations i n the United states. Furthermore, we have found no support f o r the view that agriculturally-induced fluctuations on the P r a i r i e s are transmitted with any impact into other Canadian regions. When the postwar period i s compared with the interwar period, the transmission mechanism described above undergoes several important changes. While cycles are s t i l l transmitted from the United States to the Canadian regions and not vica versa, there i s a noticeable decline i n the s i g n i f i c a n c e of t h i s s e n s i t i v i t y , p a r t i c u l a r l y i n Quebec and B.C., and to some extent i n Ontario. There are also declines i n regional-ROC correspondences - as mentioned in the previous section - which have been of approximately the same order of magnitude i n each region. To some extent the weakened regional-ROC correspondences may r e s u l t from weakened regional-USA correspondences; moreover, the extent t o which regions are " i n phase" with each other has also declined since the interwar period and we have shown that t h i s i s consistent with the observed postwar weakening i n national s e n s i t i v i t y to United States fl u c t u a t i o n s . Nevertheless, i t remains that regional-USA s e n s i t i v i t i e s have also weakened i n the postwar period and i t i s our conjecture that these phenomena imply an evolution i n the regional mechanism of c y c l i c a l transmission. Ontario 263 i s a stronger transmittor of United States f l u c t u a t i o n s than formerly. In the postwar period Ontario corresponds more strongly with the United States than any other region and the interwar lags behind ROC have a l l sharply been reduced. Examination of p a r t i c u l a r episodes i n the postwar period reveal a s i m i l a r i t y i n c y c l i c a l behaviour between Ontario and the United States which could not be found i n any other region. Evidence of price transmission seems p a r t i c u l a r l y convincing; i n the CPI, Ontario leads ROC but lags the United States and correspondence with both ROC and the United States i s considerably stronger than for any other region. Furthermore, while the Ontario-Quebec s e n s i t i v i t y i n t e r r e l a t i o n s h i p i s s t i l l dominated by economic feedback, the change over time i n Ontario-Quebec s e n s i t i v i t y suggests that for Quebec the extent of interdependence with Ontario has increased r e l a t i v e to that with the ROC, but f o r Ontario a change of t h i s nature i s much less apparent. Thus, Ontario has to a greater extent than Quebec maintained it's correspondence with the other Canadian regions. Of a l l regions, Ontario experienced the least decline i n United States s e n s i t i v i t y ; t h i s r e s u l t provides an important q u a l i f i c a t i o n to the evidence on o v e r a l l Canada-United States s e n s i t i v i t y . The change i n the s e n s i t i v i t y of Ontario i s consistent with s h i f t s over time i n the i n d u s t r i a l composition of Canadian exports to the United States which increase, r e l a t i v e to other regions, the 264 proportion of regional output exported to the United States. Furthermore, while the weakening noticed by Rosenbluth i n the s e n s i t i v i t y of Canadian exports to general economic a c t i v i t y i n the United States cannot be attributed to the p a r t i c u l a r r e g i o n a l trade sectors, i t appears that i n Ontario t h i s e f f e c t has had the l e a s t impact. However, the impact may have been greater i n the P r a i r i e s ; even though P r a i r i e exports to the United States have l i k e l y experienced a dramatic increase in the postwar period, the region has not had an accompanying increase i n dir e c t s e n s i t i v i t y to United States fluctuations i n general economic a c t i v i t y . Ontario-ROC trade i n c a p i t a l goods and consumer durables has possibly declined i n importance, but Ontario s t i l l remains the region with the highest r e l a t i v e -amplitude. Our conjecture i s that there i s s t i l l a d e s t a b i l i z i n g influence upon Ontario due to the "automatic s t a b i l i z i n g " influence i n the other regions from c y c l i c a l i n s t a b i l i t y in the marginal propensity to import goods from Ontario. Furthermore, i f there has been a decline i n the importance of Ontario-ROC trade, then the increased transmitting behaviour i n Ontario may be due to transmission mechanisms apart from the trade linkage. Apart from the above q u a l i f i c a t i o n s , the decline in regional-USA s e n s i t i v i t i e s i s undoubtedly explained by the same factors which have caused Canadian-USA s e n s i t i v i t y to decline. The most important of these factors appear to be 265 r e l a t e d to increased government involvement i n the economy i n the form of increased shares i n GNP of both government expenditures on goods and services and transfer payments. As yet there appear to be no s i g n i f i c a n t regional differences i n the impact of t h i s e f f e c t . 266 BIBLIOGRAPHY 1. BOOKS AND ARTICLES Abramovitz, M. (1956). "Resource and Output Trends in the United States since 1870". Abramovitz, M. (19 59). Statement i n the United States Congress, Jo i n t Economic Committee, "Employment, Growth, and the Price Level", Hearings (86th Congress, 2nd Session), Part I I , 411-465. Abramovitz, M. (1964). "Evidence of Long Swings i n Aggregate Construction Since the C i v i l War", Occasional Paper No. 90, National Bureau of Economic Research (New York). Adelman, I. (1965). "Long Cycles - Fact or A r t i f a c t " , American Economic Review 55, 444-463. Anderson, I. (1966). "Internal Migration i n Canada, 1921-1961", Economic Council of Canada, Staff Study No. 13, (Ottawa). Beckett, W.A. (1961). "Indicators of C y c l i c a l Recessions and Revivals i n Canada", i n G.H. Moore, ed., "Business Cycle Indicators", National Bureau of Economic Research, (New York) . Bird , R.C, Desai, M.J., Enzler, J . J . and Taubman, P.J. (1965). "Kuznet's Cycles' i n Growth Rates: The Meaning", Inter-national Economic Review 6, 229-239. Bl a i n , L., Paterson, D.C. and Rae, J.D. (1974). "The Regional Impact of Economic Fluctuations During the Interwar Period: The Case of B r i t i s h Columbia", Canadian Journal of Economics 7, 381-401. Bonomo, V. and Tanner, J.E. (197 2). "Canadian S e n s i t i v i t y t o Economic Cycles i n the United States", Review of Economics and S t a t i s t i c s 54, 1-8. Brecher, I. and Reisman, S.S. (1 957). "Canada-United States Economic Relations", Royal Commission on Canada's Economic Prospects, (Ottawa). Brechling, F. (1967). "Trends and Cycles i n B r i t i s h Regional Unemployment", Oxford Economic Papers 19, 1-21. Bryce, R.N. (1939). "The E f f e c t s on Canada of I n d u s t r i a l Fluctuations i n the United States", Canadian Journal of Economics and P o l i t i c a l Science 5, 37 3-386. Buckley, K. (1955). "Capital Formation i n Canada, 1896-1930", Canadian Studies i n Economics, (Toronto). Burns, A.F. (1934). "Production Trends i n the United States 267 Since 1870", National Bureau of Economic Research, (New York). Burns, A.F. and M i t c h e l l , W.C. (1947). "Measuring Business Cycles", National Bureau of Economic Research, (New York). Burns, A.F. (1969). "The Business Cycle i n a Changing World", National Bureau of Economic Research, (New York). Caves, R.E. and Holton, R.H. (1959). "The Canadian Economy: Prospect and Retrospect", (Cambridge: Harvard). Caves, R. and Reuber, G. (1969). "Canadian Economic Pol i c y and the Impact of International C a p i t a l Flows", (Toronto). Chambers, E.J. (1955). "The 1937-1938 Recession i n Canada", Canadian Journal of Economics and P o l i t i c a l Science 21, 284-306. Chambers, E.J. (1958a). "Canadian Business Cycles Since 1919", Canadian Journal ot Economics and P o l i t i c a l Science 24, 166-189. Chambers, E.J. (1958b). "Canadian Business Cycles and Merchandise Exports", Canadian Journal of Economics and P o l i t i c a l Science 24, 406-410. Chambers, E.J. (1964). "Late 19th century Business Cycles i n Canada", Canadian Journal of Economics and P o l i t i c a l Science 30, 391-412. Chernick, S.E. (1967). "Interregional D i s p a r i t i e s i n Income", Economic Council, S t a f f Study No. 14, (Ottawa). Daly, D.J. (1965). "Long Cycles and Recent Canadian Experience", Royal Commission on Banking and Finance, Appendix Volume, (Ottawa). Denton, F.T. (1966). "An Analysis of Interregional Differences i n Manpower U t i l i z a t i o n and Earnings", Economic Council of Canada, Staff Study No. 15, (Ottawa). E a r l , J.F. (1973). "The A t l a n t i c Provinces: Protection and Free Trace", A t l a n t i c Provinces Economic Council. Garvey, G. (1959) . "Deposit Velocity and Its Significance", Federal Reserve Board of New York, (New York) . Granger, C.W.J, and Hatanaka, M. (1964). "Spectral Analysis of Economic Time Series", Princeton Studies i n Economics, (Princeton). 268 Granger, C.W.J. (1966). "The Typical Shape of an Economic Variable", Econometrica 34, 150-161. Green, A.G. (1971). "Regional Aspects of Canada's Economic Growth", Canadian Studies i n Economics, (Toronto). Harkness, J.P. (1969). "A Spectral Analytic Test of the Long Swing Hypothesis i n Canada", Review of Economics and S t a t i s t i c s 50, 429-436. Harkness, J.P. (1969). "Long Swings", Review of Economics and S t a t i s t i c s 51, 94-96. Hatanaka, M. and Howrey, E.P. (1969). "Low Frequency Vari a t i o n i n Economic Time Series", Kyklos 22, 752-766. Hause, J.C. (1971). "Spectral Analysis and the Detection of Lead-Lag Relations", American Economic Review 61, 289-298. Hay, K.A.J. (1966). "Early Twentieth Century Business Cycles i n Canada", Canadian Journal of Economics and P o l i t i c a l Science 32, 354-365. Howland, R.D. (1957). "Some Regional Aspects of Canada's Economic Development", Royal Commission on Canada's Economic Prospects, (Ottawa). Howrey, E.P. (196 8). "A Spectrum Analysis of the Long Swing Hypothesis", International Economic Review 9, 228-259. Isard, W. (1942). "A Neglected Cycle: The Transport Building Cycle", Review of Economics and S t a t i s t i c s 24, 149-158. Jenkins, G.J. (1961). "General Considerations i n the Analysis of Spectra", Technometrics 3, 221-228. Jenkins, G.M. (1963). "Cross-Spectral Analysis and the Estimation of Linear Open Loop Transfer Functions", i n M. Rosenblatt, ed., "Time Series", (New York). Jenkins, G.M. and Watts, D.G. (1968). "Spectral Analysis and i t s Applications", (Haden-Day). Kuznets, S. (1952). "Long Term Changes In the National Income of the United States Since 1870", i n S. Kuznets, ed., "Income and wealth", Series I I , (Cambridge). Mack, R. (1957). "Notes on Subcycles i n Theory and Practice", American Economic Review 47, 161-174. Mack, R. (1967). "Information, Expectations and Inventory 269 Fluctuations", National Bureau of Economic Research, (New York). Mackintosh, W.A. (1939). "The Economic Background of Dominion-P r o v i n c i a l Relations", Appendix I I I , Report of the Royal Commission on Dominion-Provincial Relations, (Ottawa). Malinvaud, E. (1970). " S t a t i s t i c a l Methods of Econometrics", Second E d i t i o n , (North-Holland: New York). Marcus, E. (1954). "Canada and the International Business Cycle, 1927-1939", (New York). Mclnnis, M. (1968). "The Trend of Regional Income D i f f e r e n t i a l s i n Canada", Canadian Journal of Economics 1, 440-470. Mintz, I. (1972). "Dating American Growth Cycles", i n V. Xarnowitz, ed., "The Business Cycle Today", National Bureau of Economic Research, (New York) . M i t c h e l l , W.C. (1927). "Business Cycles: The Problem and i t s Setting", National Bureau of Economic Research, (New York). M i t c h e l l , W.C. (1951). "What Happens During Business Cycles", National Bureau of Economic Res search, (New York) . Moore, G.H. (1955). "Diffusion Indexes, Rates of Change and Forecasting", The American S t a t i s t i t i a n 9, 13-17. Moore, G.H. (1961). "Leading and Confirming Indicators of General Business Changes", i n G.H. Moore, ed., "Business Cycle Indicators", National Bureau of Economic Research, (New York). Nerlove, M. (1964). "Spectral Analysis of Seasonal Adjustment Procedures", Econometrica 32, 241-286. Paraskevopoulos, C.C. (1974). "Regional Growth Patterns i n Canadian Manufacturing Industry: An Application of S h i f t and Share Analysis", Canadian Journal of Economics 7, 121-125. "Report of the Royal Commission on Dominion-Provincial Relations, Book 1, Canada; 1867-1939", (1940). Robinson, T. R. (1 968). "Canada's Imports and Economic S t a b i l i t y " , Canadian Journal of Economics 1, 401-428. Rosenblatt, H. (1968). "Spectral Evaluation of BLS and Census Revised Seasonal Adjustment Procedures", Journal of the American S t a t i s t i c a l Association 63, 472-501. 270 Rosenbluth, G. (1957). "Changes i n Canadian S e n s i t i v i t y to United States Business Cycles", Canadian Journal of Economics and P o l i t i c a l Science 23, 480-503. Rosenbluth, G. (1958). "Changing Structural Factors i n Canada's C y c l i c a l S e n s i t i v i t y , 1903-1954", Canadian Journal of Economics and P o l i t i c a l Science 24, 21-43. Rosenbluth, G. (1 969). "Comments (on D.J. Daly)", M. Bronfen-brenner, ed., "Is the Business Cycle Obsolete", (New York: Wiley). Rosenbluth, G. (1973). "Twentieth Century Business Cycles i n Canada and the United States", Discussion Paper 98, Department of Economics, University of B r i t i s h Columbia. Safarian, A.E. (1970). "The Canadian Economy i n the Great Depression", (Toronto). Scott, A.D. (1965). "Policy for Declining Regions" A Theoretical Approach" i n W.D. Wood and R.S. Thoman, eds. "Queenjs University Conference on Areas of Economic Stress i n Canada", (Kingston) . Shearer, R.A. (editor) (1971). "Trade L i b e r a l i z a t i o n i n a Regional Economy: Studies of the Impact of Free Trade on B r i t i s h Columbia", Private Planning Association of Canada, (Toronto). Shiskin, J . , Young, A. and Musgrave, J.C. (1967). "The X-11 Variant of the census Method II Seasonal Adjustment Programme", Bureau of The Census Technical Paper No. 15 (revised), United States Department of Commerce, (Washington). Sims, CA. (1972) . "Money, Income and Causality", American Economic Review 62, 540-552. Slutsky, E. (1937). "The Summation of Random Causes as a Source of C y c l i c Processes", Econometrica 5, 105-146. Swan, N.M. (1972). "Differences in the Response of the Demand fo r Labour t o Variations i n Output Among Canadian Regions", Canadian Journal of Economics, 5, 3 73-3 85. Thirsk, W. (1972). "Regional Dimensions of I n f l a t i o n and Unemployment", Prices and Incomes Commission, (Ottawa). Urquhart, M.C. and Buckley, K.A.H. (1965). " H i s t o r i c a l S t a t i s t i c s of Canada", (Toronto). Waterman, A.M.C. (1973). "The Measurement of Economic Fluc-tuations i n Canada", Staff Study, Prices and Incomes 271 Commission, (Ottawa). Watkins, M.H. (1963). "A Staple Theory of Economic Growth Canadian Journal of Economics and P o l i t i c a l Science 2 141-158. White, D.A. (1967). "Business Cycles i n Canada, Economic Council of Canada", Staff Study No. 17, (Ottawa). 272 2. STATISTICAL SOURCES Annual Reports of the Federal Reserve Board (1934, 1937). Bank of Canada (1948-1973), "Annual Report", (Ottawa). Bank of Canada, (1969), "Supplement to the S t a t i s t i c a l Summary", (Ottawa). Bank of Canada (1974), "Bank of Canada Review", (Ottawa). Bureau of the Census (1960), " H i s t o r i c a l S t a t i s t i c s of the United States", Series App. No. 22, (Washington). Bureau of Labour S t a t i s t i c s (1 968), B u l l e t i n No. 1312-5. Bureau of Labour S t a t i s t i c s (1971), B u l l e t i n No. 1312-7. Bureau of Labour S t a t i s t i c s (1971-1973), "Monthly Labour Review", (Washington). Canada Year Book (1919-1939). Department of Commerce (1946-1972), "Survey of Current Business", (Washington). Department of Labour (1919-1922), "Labour Gazette", (Ottawa). Department of Trade and commerce (1948-1973), "Public and Private Investment i n Canada", (Ottawa). Department of Trade and Commerce (1951), "Public and Private Investment i n Canada, 1926-1951", (Ottawa). Dominion Bureau of S t a t i s t i c s (1919-1973), "Monthly T r a f f i c Report of the Railways of Canada", 52-002, (Ottawa). Dominion Bureau of S t a t i s t i c s (1922-1973), "Employment and Average Weekly Wages and Salaries ( t i t l e v a r i e s ) " , (Ottawa). Dominion Bureau of S t a t i s t i c s (1 923-1939), "Monthly Report of the Trade of Canada", (Ottawa). Dominion Bureau of S t a t i s t i c s (1924-1939), "Monthly Review of Business S t a t i s t i c s " , 11-003, (Ottawa). Dominion Bureau of S t a t i s t i c s (1924-1973a), "National Accounts", 13-201, (Ottawa). Dominion Bureau of S t a t i s t i c s (1945-1973), "Cheques Cashed at Clearing Centres", 61-001, (Ottawa). 273 Dominion Bureau of S t a t i s t i c s (1948-1972), "Review of Foreign Trade", 65-205, (Ottawa). Dominion Bureau of S t a t i s t i c s (1948-1973), "Housing Starts and Completions", 64-002, (Ottawa). Dominion Bureau of S t a t i s t i c s (1949-1973), "Prices and Price Indexes", 62-001, (Ottawa). Dominion Eureau of S t a t i s t i c s (1960-1972), "Exports by Commodity", 65-004, (Ottawa). Dominion Bureau of S t a t i s t i c s (1975), "National Accounts; The Annual Estimates, 1926-1974", 13-531 Occasional, (Ottawa). Federal Reserve B u l l e t i n (1937-1973). MacLean's Building Guide (1940-1965) (Southam: Toronto). Monetary Times (1919-1927) (Southam: Toronto). Ontario Ministry of the Treasury 1976), "Ontario S t a t i s t i c s ; 1975", Volume 2, (Toronto). Southam Building Guide (1966-1972) (Southam: Toronto). 

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