UBC Theses and Dissertations

UBC Theses Logo

UBC Theses and Dissertations

The impact of United States final demand on Canadian production : an input-output study Horner, Leslie William Keith 1967

Your browser doesn't seem to have a PDF viewer, please download the PDF to view this item.

Item Metadata

Download

Media
831-UBC_1967_A8 H58.pdf [ 6.78MB ]
Metadata
JSON: 831-1.0104793.json
JSON-LD: 831-1.0104793-ld.json
RDF/XML (Pretty): 831-1.0104793-rdf.xml
RDF/JSON: 831-1.0104793-rdf.json
Turtle: 831-1.0104793-turtle.txt
N-Triples: 831-1.0104793-rdf-ntriples.txt
Original Record: 831-1.0104793-source.json
Full Text
831-1.0104793-fulltext.txt
Citation
831-1.0104793.ris

Full Text

THE IMPACT OP UNITED STATES FINAL DEMAND ON CANADIAN PRODUCTION AN INPUT-OUTPUT STUDY by LESLIE WILLIAM KEITH HORNER B.A., University of B r i t i s h Columbia, 1963* A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF ARTS i n the department of-ECONOMICS We accept t h i s thesis as conforming to the required standard • THE UNIVERSITY OF BRITISH COLUMBIA A p r i l , 1967 I n p r e s e n t i n g t h i s t h e s i s i n p a r t i a l f u l f i l m e n t of the requirements f o r an advanced degree a t the U n i v e r s i t y of B r i t i s h Columbia, I agree t h a t the L i b r a r y s h a l l make i t f r e e l y a v a i l a b l e f o r reference and study. I f u r t h e r agree t h a t p e r m i s s i o n - f o r extensive copying of t h i s t h e s i s f o r s c h o l a r l y purposes may be granted by the Head of my Department or by h i s r e p r e s e n t a t i v e s . I t i s understood t h a t copying or p u b l i c a t i o n o f t h i s t h e s i s f o r f i n a n c i a l g ain s h a l l not be allowed without my w r i t t e n p e r m i s s i o n . Department of JZ. C-SYXCTYTVLC r The U n i v e r s i t y of B r i t i s h Columbia Vancouver 8, Canada - i i -ABSTRACT I n t h i s t h e s i s , the impact o f U n i t e d S t a t e s f i n a l demand on Canadian demand and p r o d u c t i o n i s i n v e s t i g a t e d u s i n g an i n t e r r e g i o n a l i n p u t - o u t p u t model. F i r s t , the s i m p l e L e o n t i e f I n p u t - o u t p u t model i s c o n s i d e r e d . I t i s a d i s a g g r e g a t e d model o f the p r o d u c t i o n s e c t o r o f an economy t h a t a l l o w s a s e t o f i n d u s t r y o u t p u t s t o be e x p r e s s e d as a f u n c t i o n o f a c o r r e s p o n d i n g s e t o f i n d u s t r y f i n a l demands. I t improves on o t h e r o u t p u t d e t e r m i n a t i o n models by a d m i t t i n g t h a t i n d u s t r y o u t p u t s are i n t e r d e p e n d e n t . However, i t r e q u i r e s the a s s u m p t i o n of f i x e d p r o d u c t i o n c o e f f i c i e n t s . N e x t , the e x t e n s i o n o f the model t o i n c o r p o r a t e i n t e r -r e g i o n a l t r a d e i s c o n s i d e r e d . S e v e r a l models are d e s c r i b e d t h a t d e t e r m i n e the i n d u s t r y o u t p u t s o f each o f a group o f r e g i o n s as f u n c t i o n s of the i n d u s t r y f i n a l demands i n a l l r e g i o n s . A model i s s e l e c t e d t h a t d i f f e r s from a l l of t h e s e , not i n i t s e s s e n t i a l a l g e b r a i c s t r u c t u r e , but I n the method by wh i c h i t i s a p p l i e d . I n the s i m p l i f i e d form i n wh i c h i t i s used i n t h i s s t u d y , i t r e q u i r e s t h a t Canada's merchandise e x p o r t s t o the U n i t e d S t a t e s be r e c l a s s i f i e d a c c o r d i n g t o the i n d u s t r y schemes o f the Canadian and American i n p u t - o u t p u t t a b l e s . The main advantage of the model over the o t h e r i n t e r r e g i o n a l models c o n s i d e r e d i s t h a t i t a l l o w s the i n p u t - o u t p u t t a b l e s o f the I n d i v i d u a l r e g i o n s t o be used i n t h e i r o r i g i n a l form. - i i i -Using the model, two questions are investigated. F i r s t , how do equal expenditures on the various components of United States f i n a l demand - Consumption, Fixed investment, Federal Government purchases, and State and l o c a l government purchases -compare i n t h e i r impact on Canadian demand and output ? Second, i n the period 1956 to I 9 6 0 , did v a r i a t i o n i n the l e v e l and pattern of United States f i n a l demand tend to aggravate f l u c t u a t i o n s i n Canadian demand, output, and net exports ? Several r e s u l t s are obtained. With reference to the f i r s t question, Investment expend-i t u r e i s found to have considerably greater impact on Canadian demand and production than any of the other components of United States demand. The wide d i s p a r i t y i n impact i s l a r g e l y explained by the concentration of Canadian exports to the United States on a few commodities. Concerning the second question, i t i s concluded that v a r i a t i o n s i n both the l e v e l and pattern of United States f i n a l demand helped to generate f l u c t u a t i o n s i n the growth of Canadian demand and.output. By contrast, the f l u c t u a t i o n of United States f i n a l demand tended to damp:--- flu c t u a t i o n s i n Canadian net exports. - i v -TABLE OF CONTENTS page LIST OF TABLES v i CHAPTER I INTRODUCTION 1 I I INTRODUCTION TO INPUT-OUTPUT ANALYSIS 5 1. The Nature of the Open Leontief Model 6 2. Limitations of the Open Leontief Model 18 III INPUT-OUTPUT ANALYSIS AND FOREIGN TRADE .27 1. Analysis of Foreign Trade With the Simple Leontief Model 27 2. Extension of the Simple Leontief Model 32 IV THE EXPORT RECLASSIFICATION MODEL 44 1. The Export R e c l a s s i f i c a t i o n Model 44 2. A Restricted Form of the Model 46 V APPLICATION OF THE MODEL: DATA AND PROCEDURE 50 1. The Data 50 2. Application of the Model to the Canadian and United States Data 54 3 . Estimation of the Parameters and Solution of the Model 57 VI THE IMPACT OF UNITED STATES FINAL DEMAND ON CANADIAN PRODUCTION AND TRADE 60 1. Comparison of the E f f e c t s of One B i l l i o n Dollar Increases i n United States F i n a l Demand 60 2. The C y c l i c a l E f f e c t of United States F i n a l Demand on Canadian Output and the Canadian Balance of Merchandise Trade 66 VII CONCLUSIONS 86 BIBLIOGRAPHY 90 APPENDICES A DETAILED RESULTS 93 - V -p a g e B C L A S S I F I C A T I O N OF 1958 EXPORTS FROM CANADA TO T H E U N I T E D S T A T E S ACCORDING TO T H E CANADIAN AND U N I T E D S T A T E S INDUSTRY SCHEMES 99 C T H E T E C H N I Q U E USED I N U P D A T I N G T H E CANADIAN I N P U T - O U T P U T M A T R I C E S 107 D P R I C E D E F L A T I O N OF T H E CANADIAN E X P O R T V E C T O R 109 - v i -LIST OF TABLES page NUMBER I The Leontief Transactions Table 9 I I Selected Input-Output Flows and Co e f f i c i e n t s 17 I I I Comparison of the Aggregate E f f e c t s of Increases i n Four Components of United States F i n a l Demand, 1958 61 IV The Concentration of Induced Output and 1958 Exports Among Canadian Industries 63 V Output Generated i n P a r t i c u l a r Canadian Industries by One B i l l i o n Dollar Increases i n United States F i n a l Demand; 1958 Exports to The United States by Industry 65 VI Growth i n United States F i n a l Demand, 1957-1960 68 VTI Comaprison of the Aggregate E f f e c t s of One B i l l i o n Dollar Increases i n Types of United States Personal Consumption Expenditure 71 VIII Comparison of Annual Growth Rates: United States F i n a l Demand and Induced Canadian Exports 75 IX Comparison of Annual Growth Rates: Canadian F i n a l Demand With and Without Induced Exports 76 X Comparison of Annual Growth Rates: The Output of Selected Export Industries With and Without the Output Generated by United States F i n a l Demand 78 XI Growth of Canadian Merchandise Exports With and Without Induced Exports 83 XII Growth of Canadian Net Exports With and Without Induced Net Exports 84 XIII Postulated Increases i n United States F i n a l Demand Sk XIV Induced Increases i n United States A c t i v i t y Levels 95 ' XV Induced Increases i n Canadian Exports 96 XVT Induced Increases i n Canadian A c t i v i t y Levels 97 XVII Induced Increases i n Canadian Imports 98 - v i i -NUMBER XVIII Allocated Exports to the United States, 1958 XIX Canadian Exports to the United States, 1958; C l a s s i f i c a t i o n i n t o Elements T . . XX Canadian Exports to the United States, 1958; Canadian Industry C l a s s i f i c a t i o n XXI Canadian Exports to the United States, 1958; United States C l a s s i f i c a t i o n XXII Derivation of Export Price Indexes for the Canadian Industries FIGURE 1 The E f f e c t of Induced Output on the Annual Growth of Selected Export Industries CHAPTER I INTRODUCTION The close economic r e l a t i o n s h i p between Canada and the United States has long been a subject of discussion and concern i n Canada. I t has been argued that so many important economic decisions i n Canada are dictated by p o l i c i e s or conditions e x i s t i n g i n the United States that Canada has l i t t l e economic or p o l i t i c a l autonomy. Two separate questions are involved i n evaluating such a claim. F i r s t , does United States ownership of Canadian industry imply that c i t i z e n s of the United States are responsible for many decisions that d i r e c t l y a f f e c t Canada's p o l i t i c a l posture or economic development ? Second, to what extent do the high l e v e l s of commodity and c a p i t a l flows between the countries make the Canadian economy sensitive to changes i n economic conditions i n the United States ? In t h i s paper, some of the f a c t o r s bearing on the second question are examined. A model i s developed which w i l l y i e l d estimates of the amount of Canadian output generated by various l e v e l s and patterns of United States f i n a l demand. Thus i t may be used to investigate the impact of c y c l i c a l v a r i a t i o n s i n United States demand on Canadian production a c t i v i t y . The model may also be used to estimate changes i n the l e v e l s of Canadian exports and imports a t t r i b u t a b l e to a change i n - 2 -United States f i n a l demand, and by subtraction, the primary e f f e c t of the change on the Canadian merchandise balance of trade. However, the model y i e l d s only a p a r t i a l answer to the question of Canadian s e n s i t i v i t y to economic condit-ions i n the United States. I t can not be used to estimate changes i n the l e v e l s of Canadian Consumption and Investment that r e s u l t from changes i n United States f i n a l demand; nor can i t be used to predict changes i n Canadian output a t t r i b u t -able to the influence of Canadian-American c a p i t a l flows on Canadian i n t e r e s t rates. Within the area of enquiry l i m i t e d by the nature of the model, several r e s u l t s are obtained. 1 . Of equal aggregate expenditures on the four major components of United States f i n a l demand - Personal con-sumption, Investment, Federal Government expenditure, and State and l o c a l government expenditure - the Investment expenditure has much the strongest impact on Canadian aggre-gate demand and output. The prime reason for the wide v a r i a t i o n i n e f f e c t among these demand components i s the concentration of Canadian exports to the United States on a small number of products. 2. For the period 1956 to i 9 6 0 , the l e v e l of Canadian exports generated by United States f i n a l demand grew at a rate that fluctuated i n phase with, but more widely than the growth rate of United States aggregate demand i t s e l f . Thus, s h i f t s i n the composition of United States demand acted to - 3 -exaggerate the Impact of f l u c t u a t i o n s i n i t s l e v e l . 3. The growth rate of induced Canadian demand also varied i n phase with the observed f l u c t u a t i o n s i n the growth of Canadian f i n a l demand, and therefore contributed to them. In other words, the dependence of Canadian aggregate demand on United States business a c t i v i t y had a c y c l i c a l l y d e s t a b i l -i z i n g e f f e c t on Canadian economic growth. 4. This conclusion regarding the transmission of business cycles did not apply u n i v e r s a l l y to the growth of output of important Canadian export i n d u s t r i e s . 5. Variations i n United States f i n a l demand had a s t a b i l i z i n g e f f e c t on f l u c t u a t i o n s i n the Canadian balance of merchandise trade. This resulted from the f a c t that import f l u c t u a t -ions dominated export f l u c t u a t i o n s i n determining the growth of Canadian net exports. The model used to obtain these r e s u l t s i s an extension of the simple Leontief Input-Output model. That model deter-mines the set of industry outputs required by a corresponding set of f i n a l demands. In doing so i t recognizes e x p l i c i t l y the interdependence of industry output l e v e l s . I t i s based on the assumption that the production of a unit of an industry's output w i l l require as inputs, f i x e d amounts of the outputs of other i n d u s t r i e s . In other wrjrds i t assumes constant production, or input-output,coefficients. By assuming,in addition, that exports from Canada con-s t i t u t e a f i x e d proportion of the t o t a l supply of each - 4 -industry's output i n the United States, the simple Leontief model i s extended so that the set of Canadian industry outputs required by a set of United States f i n a l demands may be deter-mined. This i s e s s e n t i a l l y the same model as that proposed by R. J. Wonnacott"*" i n which the sets of both Canadian and United States industry outputs are r e l a t e d simultaneously to the combined set of f i n a l demands. The advantage of t h i s variant of the Wonnacott model i s that i t i s easier to apply and update -while s a c r i f i c i n g very l i t t l e i n pre c i s i o n . The paper may be divided i n t o two parts, the f i r s t being concerned with the development of the model, and the second with i t s a p p l i c a t i o n . The nature of the simple Leontief model i s elaborated i n Chapter I I . In Chapter I I I i t s extension to include foreign trade i s discussed, and i n Chapter IV the model to be used i s described. The data and procedure used i n apply-ing the model are discussed i n Chapter V. In Chapter VI the r e s u l t s are developed and i n Cha/pter VTI they are summar-iz e d and evaluated. 1. R. J . Wonnacott, Canadian-American Dependence: An i n t e r -industry Analysis of Production and Prices, Amsterdam; The North-Holland Publishing Company, 1 9 6 1 . - 5 -CHAPTER I I INTRODUCTION TO INPUT-OUT ANALYSIS The Leontief Input-Output model i s an attempt to put some aspects of general equilibrium theory i n t o computationally workable form. In i t s basic open construction i t i s con-cerned only with the production side of economic a c t i v i t y and does not deal ivith the determination of f i n a l demand. The basis of the model i s a set of accounting i d e n t i t i e s which describes the i n t e r - i n d u s t r y flow of goods and services i n a p a r t i c u l a r economy. The i d e n t i t i e s are transformed into equations with the a i d of a c r i t i c a l assumption. Then the set of equations may be used as a disaggregated model of the technological structure of the economy. In p a r t i c u l a r , i n d i v i d u a l industry output l e v e l s may be simultaneously determined as functions of the industry f i n a l demands. The model's main advantage over p a r t i a l equilibrium analysis i s that i t recognizes and i s capable of dealing with the interdependence^ of industry output l e v e l s . That i s , i t e x p l i c i t l y accounts f o r the e f f e c t s of changes i n the f i n a l demand for one product on the output l e v e l s of others. S i m i l a r l y , i t s main advantage over aggregative analysis i s that i t admits that aggregate input and output l e v e l s are affected by the composition of f i n a l demand. On the other hand, the model has d e f i n i t e l i m i t a t i o n s which r e s t r i c t i t s power of pr e d i c t i o n and range of ap p l i c a t i o n . - 6 -The nature of the model and I t s l i m i t a t i o n s w i l l now be considered i n more d e t a i l . 1. The Nature of the Open Leontief Model Three stages of construction of an open Leontief model may be i d e n t i f i e d . They are (a) the transactions table, (b) the d i r e c t requirements matrix, and (c) the t o t a l require-ments matrix. The discussion w i l l follow these stages. (a) The Transactions Table The transactions table i s b u i l t from a set of accounting i d e n t i t i e s which describe the pattern of i n t e r -industry flows of goods and services for a c e r t a i n time period. Two steps must be taken at the outset i n b u i l d i n g a set of such flows. F i r s t , the multitude of i n d u s t r i e s i n the economy must be c l a s s i f i e d i n t o a workable number of sectors (also c a l l e d i n d u s t r i e s ) . The number chosen i s a r b i t r a r y from a t h e o r e t i c a l standpoint and i n practice w i l l depend l a r g e l y on what i s desired of the model, what data i s a v a i l a b l e , and what resources of time and money are available for the compilation of the table. Regardless of the number of sectors, the guiding p r i n c i p l e of c l a s s i f i c a t i o n i s that the i n d u s t r i e s within each sector should have, as f a r as possible, the same kinds and combinations of inputs and outputs. In t h i s way a necessary assumption of the a n a l y t i c a l model i s approximated. In theory, each sector must produce a single homogeneous product to ensure that changes i n a sector output, however caused, w i l l always require the same combination of inputs. - 7 _ The causes and eff e c t s of heterogeneous sector outputs w i l l be discussed i n the second part of t h i s chapter. Second, a common unit should be adopted to express the physical flows so that inputs and outputs of d i s s i m i l a r goods may be combined. This step i s not s t r i c t l y necessary. Physical units may be used as long as the units within each equation are consistent. However, a common unit s i m p l i f i e s both the analysis and exposition. The unit chosen i s a do l l a r ' s worth of product. The use of t h i s value unit makes i t important to express a l l subsequent flows i n the prices p r e v a i l i n g i n the period of ap p l i c a t i o n of the model. Otherwise, an increase of say f i f t y percent i n the price of a product would appear to r e s u l t i n a f i f t y percent increase i n the physical flow of that product. With these steps ta£en, the two sets of accounting i d e n t i t i e s may be defined. Let: N = the number of producing sectors, X^ = the output of sector i , x^. = the output of sector i used by sector j , . V. = the primary inputs to sector j , and Y. = the output of sector i d i s t r i b u t e d d i r e c t l y to f i n a l users. - 8 -Then the sets of i d e n t i t i e s are: U = 1 3 • • • } N) ( 2 . 1 ) + Y. x ( i = 1 N) ( 2 . 2 ) The f i r s t demands that the output of each sector be i d e n t i c a l to the sum of the inputs to i t from the N prod-ucing sectors, plus primary inputs. The l a t t e r , also c a l l e d value added, are considered to come from sector N + 1 . They generally include imports, i n d i r e c t taxes, and depreciat-ion, as well as payments to households i n the form of wages and s a l a r i e s , i n t e r e s t and dividends, and net p r o f i t s of unincorporated businesses. The second requires that the output of each sector be d i s t r i b u t e d either as inputs to other sectors or d i r e c t l y to f i n a l users. The f i n a l output, Y^ , i s generally shown as the sum of outputs to the basic National Accounts categories of f i n a l demand:- Personal consumption expenditure, Gross private f i x e d c a p i t a l formation, Net inventory change, Exports, and Government expenditures on goods and services. The system of flows for the whole economy may be portrayed i n a transactions table where the inputs to each section ( i d e n t i t y 2 . 1 ) are shown as columns, and the outputs ( i d e n t i t y 2 . 2 ) as rows. In Table I, an example i s given for N = 3 . - 9 -T A B L E I THE LEONTIEF TRANSACTIONS TABLE Producing Sectors 3. 4 Using Sectors 1 2 3 • 4 X 12 X l ? X l x 2 1 , x 2 2 x 2 3 y 2 X 2 X 3 2 X 5 3 Y 3 3 \ V 2 V 3 ? v . 3=1 J X l X 2 X 3 i = l 1 V^=Y^ represents inputs of value added directly-required by f i n a l users. An example would be Government payments to c i v i l servants. N+l N+l . N . . The aggregates E V. , E Y.. , and £ X, (not shown) j=l J 1=1 1 k=l * warrant explanation. In National Accounts terminology, N+l- N+l E V. i s Gross National Product j E Y. i s Gross National j=l J 1=1 1 Expenditure. Thus the i d e n t i c a l macro-economic variables, aggregate income and aggregate demand, are obtainable from the transactions table. The grand t o t a l of the sector outputs, N E X, , includes both f i n a l and intermediate'outputs. For k=l K t h i s reason i t does not give a d i r e c t i n d i c a t i o n of the l e v e l of economic performance and has no counterpart i n t r a d i t i o n a l - 1 0 -aggregative analysis. (b) Direct Requirements Matrix As a f i r s t step i n moving from the descriptive transactions table to a system capable of y i e l d i n g p r e d i c t -ions, the c o e f f i c i e n t s a. . are introduced. i j Let: x. . a i j = yr1 = 1>--" N) ( 2-3) Thus the c o e f f i c i e n t . a. . i s defined as the amount of product i d i r e c t l y required i n the production of one u n i t o f product j . Introduction of the a. . does not change the substa.nce of the systems ( 2 . 1 ) and ( 2 . 2 ) . They are s t i l l sets of i d e n t i t i e s that describe interindustry flows i n the accounting period. However, i f the nature of the a. . , the V. , and the Y. are s p e c i f i e d , two sets of i j 0__ i  simultaneous equations are produced. They are: N X. = Z a X + V. ( j = l , . . . , N ) ( 2 . 4 ) j i = i X J J «J and X = 5 a . X + Y ( i = l , . . . , N ) ( 2 . 5 ) 1 j=l " " 1 Here the X. are unknowns which depend on the a. . and, i n r i j t h e i r respective systems, on the V. and Y. . I t i s also apparent that the systems represent a set of production functions. In ( 2 . 4 ) , industry output l e v e l s are related to input l e v e l s . In a more general form, t h i s set of functions would be - 11 -In equations (2.5) on the other hand, t o t a l industry outputs are shown as functions of output for f i n a l use. The usual Leontief model i s of the type (2.5). Never-theless, i n the s p e c i f i c a t i o n of the a^j , the requirements of the t r a d i t i o n a l production function, (2 . 4 ) or (2.6), are of importance. The only universal requirement i s that i t e x h i b i t s diminishing returns when any of i t s inputs are 2 varied alone. In addition to t h i s requirement, the q u a l i t y of l i n e a r homogeneity i s usually a t t r i b u t e d to production functions. This means that a l l terms i n the function are of the same ( f i r s t ) order. In general, P J.(Xx l j.,Xx 2.,...,Xx N j,XV j) = X r P J ( x l j J x 2 j , . . . , x N J , V J ) (2.7) f o r homogeneity, with r = 1 for l i n e a r homogeneity. Linear homogeneity thus implies that i f the input quantities are a l l doubled, the quantity of output w i l l double; that i s , i t implies constant returns to scale. This assumption i s made f o r the sake of both s i m p l i c i t y and p l a u s i b i l i t y . Linear homogeneous functions are r e l a t i v e l y easy to work with mathematically. Moreover, t h e i r i m plication of constant returns to scale i s acceptable. 2. In terms of equation (2.6) t h i s means that (for continuous production functions ) 0 A k < 0 ( i = 1,...,N). 9 x i k 3. This i s discussed i n section 2.b of t h i s chapter. - 12 -Of a l l l i n e a r homogeneous production functions, that involving constant input c o e f f i c i e n t s i s the simplest, and t h i s i s L e o n t i e f s c r i t i c a l assumption. In systems ( 2 . 4 ) and ( 2 . 5 ) "the a. . are taken as constant and the set of general production functions, ( 2 . 6 ) , becomes X. = minimum 3 f f L l ?M 3 Zl) ( j = 1,...,N) ( 2 . 8 ) a U a 2 J a N j v j V i th Here v. = ^ i s a constant input c o e f f i c i e n t for the N + 1 sector. I t w i l l be noted that since the functions are discontinuous, the condition of diminishing returns cannot be stated i n i t s usual form. Instead a stronger condition holds. When the l e v e l of any input, x. . , i s increased so that the r a t i o -—^ i s greater than the minimum of the other 1 J X k i input r a t i o s , say — ^ , then the input of product: i X i i x k i represented by — ^ - — — p r o d u c e s no increase i n output. a i J ®kj ~ With the Leontief assumption of constant a. . s system x j ( 2 . 5 ) becomes a set of N l i n e a r equations i n N unknowns. I t may now be written as: X^ - a^X^ - aj_2^2~* * " ~ a i i ^ i ~ * * * _ aiN^N = ^ i ^ = ^" )"' 3^^ or ~ a i l ^ l ~ a i 2 ^ 2 ~ ' ' ,+ ^ ~ a i i ^ i ~ * ' ' ~ aiN^N = ^ i ^  = ( 2 . 9 ) The N x N array of the c o e f f i c i e n t s of t h i s system i s c a l l e d the d i r e c t requirements matrix . Nov;, providing the equations - 13 -are independent (no equation i s a l i n e a r combination of the .4 others), the can be simultaneously determined i n terms of the Y i . To complete the derivation of t h i s s t r u c t u r a l model of the economy i t only remains to be shown that the r e s u l t i n g industry output l e v e l s w i l l be. meaningful. S p e c i f i c a l l y , any set of non-negative f i n a l demands must generate a set of non-negative industry outputs. I t has been demonstrated by D. Hawkins and H.A. Simon that a set of conditions on the production c o e f f i c i e n t s are necessary and s u f f i c i e n t to ensure t h i s r e s u l t . T h e Hawkins-Simon conditions are: |a| > 0 where the |a| are a l l the p r i n c i p l e minors of the array of c o e f f i c i e n t s i n system ( 2 . 9 ) - In the extreme case of single element minors, the requirement i s that 1 - a ^ > 0 . These conditions require that i n a l l industries together and i n every sub-group of i n d u s t r i e s , the production of a unit of each product, i , w i l l require, directly, and i n d i r e c t l y , l e s s than a unit of i . In other words, a l l ind u s t r i e s and groups of in d u s t r i e s must be s e l f - s u s t a i n i n g . I f these conditions were not met the system would be unstable since increasing the f i n a l demand f o r , say, product i would r e s u l t i n a proportionally greater deficiency of i t . 4. F a i l u r e to meet t h i s condition would mean that the out-puts (or inputs) of an industry were of the exact pattern of another industry or combination of in d u s t r i e s . Since the industries i n the model are each defined as producing a single homogeneous product, the industry i n question would be redundant. 5. D. Hawkins and H.A. Simon,"Note: Some conditions of Macro-economic S t a b i l i t y " , Econometrica, XXX ( 1963) , pp, 90-110. - 14 -That the Hawkins-Simon conditions are i n f a c t met by the production c o e f f i c i e n t s i s e a s i l y demonstrated. For example, consider a system of two sectors (or second order p r i n c i p a l minor of larger system). The conditions require: ( i ) 1 - a n > 0 , ( i i ) 1 - agg > 0 3 a n d > 0 ( i i i ) (1. - - a 1 2 " a21 ^ " a22^ i . e . , ( l - a-j^)(l - ^22) ^ a12 a21 " Now, except i n the improbable cases -where there i s a negative value added or where a l l values added are zero, the sum of the elements i n each column of the production c o e f f i c i e n t s matrix xvill be no greater than one, and at l e a s t one sum w i l l be l e s s than one. Therefore, a n d a l l + a21 < 1 a12 + a22 - 1 o r a 2 1 < (1 - a n 1 ) 11 o r a 1 2 < (1 - a p p ) 22' From these i n e q u a l i t i e s i t can be seen by inspection that ( i ) , ( i i ) , and ( i i i ) are s a t i s f i e d . The demonstration may e a s i l y be extended to systems of more than two sectors. This discussion indicates a f i n a l a t t r i b u t e of the Leontief assumption of constant input c o e f f i c i e n t s . Apart from y i e l d i n g a simple model with pl a u s i b l e production functions, i t y i e l d s a system f o r which a stable solution e x i s t s . - 1 5 -(c) The Total Requirements Matrix. At t h i s point i t w i l l be convenient to represent the system and solution i n terms of matrices and to continue the discussion i n t h i s form. The system described i n ( 2 . 9 ) . may be written as: X - aX = Y or (I - a)X = Y (2 .10) , Here X and Y are N- element column vectors of the X^ and Y^ , and a i s an N x N matrix of the a ^ . I i s an N t h order i d e n t i t y matrix (that i s , a square matrix with ones on the diagonal and zeros elsewhere). I f the equations of ( 2 . 9 ) or (2 .10) are independent, (I - a) i s non-singular and i t s inverse y (I - a ) ~ \ e x i s t s . This means that a unique solution of industry output l e v e l s may be found f o r each Y . The solution i s written:. X = (I - a ) - 1 Y (2.11) and since the Hawkins-Simon conditions are met, X >_ 0 . The inverse, (I - a ) " 1 , i s the t o t a l requirements matrix. I t s t y p i c a l element, b. . , represents the- t o t a l — — ——— i j amount of product i required d i r e c t l y and i n d i r e c t l y i n the production of a unit of f i n a l output of product j . Since the nature of the t o t a l requirements c o e f f i c i e n t s i s key to the a p p l i c a t i o n of the model, i t w i l l be discussed i n more d e t a i l . - 16 -The inverse may he described by means of the i d e n t i t y : (I - a ) " 1 = I + a + a 2 + a? + . . . 7 (2 .12) When t h i s expression i s used f o r (I - a)""*" , the c o e f f i c i e n t s may be expressed as follows: b.,,(i t 0") = a. . + \ a. a . + £ § a . k a a +... 10 i j k = 1 i k Ko l = 1 k = 1 xK k-C ^ . • _ , N N N b i i = 1 + a i i \ t ± &±^± a i k a k ^ a U + * • * (2 .13) A t o t a l requirements c o e f f i c i e n t , b. . , can therefore be represented as the sum of the d i r e c t requirements c o e f f i c i e n t , a. . , and a series of cross-product terms of diminishing importance. The l a t t e r represent i n d i r e c t flows whose degree of circuitousness i s defined by the number of terms i n the cross-product. For example, the terms a.^ a^ . (k = 1,...,N) describe the requirement of product i embodied i n a l l the d i r e c t inputs to industry o" • As an example, consider the c o e f f i c i e n t s of three 8 industries i n the Canadian Input-output matrices f o r 19^9• 7. The i d e n t i t y depends on the convergence of the series since, multiplying both sides by (1-a) y i e l d s : L e f t Side: (I - a)(I - a ) " 1 = I Right Side: (I - a)(I + a + a2+...) = I + a + a 2 + 8? +.. 2 3 — 3. "~ cl - ct — £L 8. See D.B.S. Publication No. 13-513, Supplement to the • Inter-Industry Flow of Goods and Services, Canada, 1949, Ottawa: Queen's Prin t e r , 19&0, Tables 1, 2, and 3 . - 17 -The i n d u s t r i e s chosen a r e : (2) F o r e s t r y , (24) Paper p r o d u c t s , and (25) P r i n t i n g , p u b l i s h i n g and a l l i e d i n d u s t r i e s . The r e l e v a n t i n t e r - i n d u s t r y t r a n s a c t i o n s , d i r e c t c o e f f i c i e n t s , and i n v e r s e c o e f f i c i e n t s a r e t a b l e d below. .TABLE I I SELECTED INPUT-OUTPUT FLOWS AND COEFFICIENTS I n d u s t r i e s F l o w s and C o e f f i c i e n t s x. 10 10 2,24 215.6 223512 226139 24 , 2 5 68.2 ,195808 ,198423 2,25 .045350 S e v e r a l o b s e r v a t i o n s may be made from t h i s t a b l e . The o u t p u t o f f o r e s t r y p r o d u c t s used d i r e c t l y by the paper i n d u s t r y i s 215.6 m i l l i o n d o l l a r ' s w o r t h or about 22.35 % o f the paper i n d u s t r y i n p u t s . The d i r e c t o u t p u t o f f o r e s t r y t o the p r i n t -i n g i n d u s t r y i s n e g l i g i b l e o r z e r o . The t o t a l r e q u i r e m e n t s c o e f f i c i e n t s b 2 g l f and b 2 2 + 2 ^ a r e o n l y s l i g h t l y g r e a t e r t h a n the c o r r e s p o n d i n g d i r e c t c o e f f i c i e n t s (about 0.0026 i n each c a s e ) . Thus, l i t t l e f o r e s t r y o u t p u t i s used i n d i r e c t l y by the paper i n d u s t r y , and l i t t l e paper used i n d i r e c t l y by p r i n t i n g . However, b 2 ^ i s s u b s t a n t i a l l y g r e a t e r t h a n &. „- so t h e r e i s a ' s i g n i f i c a n t i n d i r e c t r e q u i r e m e n t f o r 2,0 - 18 -f o r e s t r y products by p r i n t i n g . One would suspect that t h i s i n d i r e c t flow would occur l a r g e l y through inputs of paper to p r i n t i n g . This suggestion i s supported by the f a c t that b 2 2 ^ = .045350 i s l i t t l e greater than a 2 24' a24 25 = (.223512)(.195808) = .043765. This example i l l u s t r a t e s the nature of the inverse, or t o t a l requirements, c o e f f i c i e n t s . However, because of i t s very s i m p l i c i t y i t can not i l l u s t r a t e the usefulness of a simultaneous solution for industry output l e v e l s . I t i s i n sectors, such as chemicals or metal products, which have a much greater d i v e r s i t y of inputs and outputs that the i n d i r e c t flows become important. When complex industries such as these are examined, the advantages of the Leontief simultaneous solution over p a r t i a l equilibrium analysis become apparent. As well as these advantages, the input-output- model has several important l i m i t a t i o n s . These are considered next. 2. Limitations of the Open Leontief Model Weaknesses i n the Input-Output model w i l l be discussed under three headings: (a) the problem of industry c l a s s i f i c -ation, (b) t h e o r e t i c a l implications of the assumption of constant c o e f f i c i e n t s , and (c).the neglect of/induced changes i n f i n a l demand. (a) The problem of industry c l a s s i f i c a t i o n The aim of industry c l a s s i f i c a t i o n i s to produce sectors whose outputs are e f f e c t i v e l y homogeneous. This i s achieved by constructing the sectors from industries whose input - 19 -c o e f f i c i e n t s are i d e n t i c a l or whose output l e v e l s vary i n exact proportion i n response to any change i n f i n a l demand. Only i n these two cases are heterogeneous sector outputs consistent with constant input c o e f f i c i e n t s . In the attempt to approach t h i s i d e a l , i n d u s t r i e s are c l a s s i f i e d by establishment, the smallest business unit f o r which the necessary s t a t i s t i c s are generally av a i l a b l e . Thus establishments are m i l l s , f a c t o r i e s , etc. and there may be many establishments within a firm. The establishments combined to form a sector are chosen so that t h e i r input l e v e l s or output l e v e l s are l i k e l y to vary i n proportion. As a r e s u l t , sectors commonly consist of establishments that either produce commodities with similar uses, or handle a p a r t i c u l a r material at successive stages of production. The E l e c t r i c a l apparatus^ industry i s an example of the former type; the Metal mining, smelting and r e f i n i n g industry, an example of the l a t t e r . However-, success i n producing e f f e c t i v e l y homogeneous sector outputs i s l i m i t e d i n the end by the frequent impossi-b i l i t y of i s o l a t i n g single commodities that correspond to •single production processes. Not only do most establishments produce several d i s s i m i l a r products, but some products are produced i n two or more d i f f e r e n t i n d u s t r i e s . Important examples of the l a t t e r case are f e r t i l i z e r , which i s produced i n both chemical f e r t i l i z e r and metal mining and smelting establishments, and advertising,which i s an output of publish-ing, radio and T.V., and business services establishments. - 20 -This problem can not be solved by aggregation techniques because of i t s double-edged nature. A f i n e r c l a s s i f i c a t i o n lightens the problem of multi-product i n d u s t r i e s but aggra-vates the problem of products that belong to more than one sector. The r e s u l t i n g r e s t r i c t i o n on the a b i l i t y to define sectors with e f f e c t i v e l y homogeneous outputs l i m i t s the p l a u s i b i l i t y of constant production c o e f f i c i e n t s . Further l i m i t a t i o n s are discussed i n the following section. (b) Implications of the Constant C o e f f i c i e n t s Assumption The c r i t i c a l Leontief assumption e n t a i l s three assertions that contradict t r a d i t i o n a l mocroeconomic theory: constant returns to scale f o r i n d u s t r i e s , no substitution, and no technological change. In the main, these implications must be accepted as f a i l u r e s of the model and attention centred on the extent to which they damage i t s p r e d i c t i v e power. Constant returns. The most d i r e c t assertion i s that industry output w i l l vary proportionally with the l e v e l of inputs, providing input composition i s not varied. In opposition to t h i s , t r a d i t i o n a l theory asserts that i n many instances, the i n d i v i s i b i l i t y of some of the factors of production w i l l lead to increasing returns to scale. In defense of constant returns i t may be noted that the argument for increasing returns applies l e s s at the industry l e v e l than at the l e v e l of the firm since i t depends on the existence of p a r t i c u l a r , p a r t i a l l y - u t i l i z e d f a c t o r s . Also, - 21 -the factors usually described as r e l a t i v e l y i n d i v i s a b l e are plant and machinery, and technical and managerial s k i l l s , which are not included among the d i r e c t inputs of the Leontief Q model. For these reasons, the implication of constant returns to scale i s not considered to be a s i g n i f i c a n t weak-ness of the model. No substitution.. The second assertion implied i n the assumption of constant production c o e f f i c i e n t s i s that the methods of production w i l l not change i n the face of changes i n the r e l a t i v e prices of inputs. One of the basic tenets of microeconomic theory, on the other.hand, i s that r a t i o n a l producers w i l l t r y to employ inputs to the l e v e l s where t h e i r marginal products equal t h e i r respective marginal costs. I f t h i s i s true, changing r e l a t i v e p r i c e s must c e r t a i n l y r e s u l t i n s u b s t i t u t i o n among inputs and hence, changing input c o e f f i c i e n t s . Since r e l a t i v e p r i c e changes occur i n response to changing f i n a l demands - the very changes analysed by the Leontief model - the denial of sub s t i t u t i o n could be a serious l i m i t a t i o n . The soundest defense of the input-output model's neglect of substitution was suggested by Leontief when he f i r s t advanced the model. He argued that i t i s the magnitude of the e f f e c t , rather than the f a c t of substitution that i s important. 9. This introduces a more serious problem regarding the use-fulness of the production c o e f f i c i e n t s . I t i s discussed i n section ( c ) . - 22 -He said: Insofar as the proportions i n which the separate factors can be combined within the same production function . . . are variable, these proportions w i l l most probably vary with every change i n t h e i r r e l a t i v e p r i c e s . This t h e o r e t i c a l proposition . . . i s beyond dispute. I t i s , however, not the fundamental v a l i d i t y of the p r i n c i p l e of s u b s t i t u t -ion but i t s quantitative significance which i s important from the point of view of empirical analysis.ID His conclusion with regard to the e f f e c t of r e l a t i v e price changes on h i s input c o e f f i c i e n t s was that the r e s u l t i n g •errors " l i e within r e l a t i v e l y narrow limits"."'""'" Leontief's empirical conclusion may be r a t i o n a l i z e d by arguing that i n c a p i t a l - i n t e n s i v e , t echnologically sophisticated economies such as those of Europe and North America, production methods leave very l i t t l e room fo r v a r i a t i o n i n input proportions, at l e a s t i n the short run. This argument, while s u f f i c i e n t to j u s t i f y empirical a p p l i c a t i o n of the model, does not deny the f a c t that substitution i n response to r e l a t i v e price changes i s a p o s s i b i l i t y which may l i m i t i t s p r e d i c t i v e power. No technological change. The t h i r d assertion inherent i n the assumption of constant c o e f f i c i e n t s i s that of an unchanging technology. I t i s the most obviously v i o l a t e d but, at the same time, the easiest to deal with. Ah innovation which changes the nature of i n d u s t r i a l processes or encourages the use of d i f f e r e n t raw materials c l e a r l y i n v a l i d a t e s 10. W.W. Leontief, The Structure of the American Economy,  1919-1939, Second e d i t i o n , New York, Oxford University Fress, 1950, p. 201. 11. . Loc. c i t . - 23 -production c o e f f i c i e n t s derived before the change. This implies that Leontief matrices n a t u r a l l y tend to become l e s s useful as time passes. Since these matrices t y p i c a l l y take six or seven years to produce, th e i r deterioration i n accuracy presents a serious problem. For example, when 1956 industry outputs were estimated using the input-output c o e f f i c i e n t s for 19^9) a weighted-average error of about eight percent was I P found. A p a r t i a l solution to the problem of technological change has been found i n updating the input-output matrices. Two approaches to updating have been used. The f i r s t consists of incorporating known technological changes into the d i r e c t requirements matrix. I f , f o r example, product k replaces product 1 as an input to the j t h industry, the c o e f f i c i e n t s a, . and a . are altered to account for the change. This simple correction i n the d i r e c t c o e f f i c i e n t s matrix w i l l , of course, r e s u l t i n several, possibly many, changed c o e f f i c i e n t s i n the inverse matrix. The second approach i s used to improve the accuracy of input-output r e s u l t s without i n v e s t i g a t i o n of p a r t i c u l a r technological changes. Production c o e f f i c i e n t s are altered i n such a way that the r e s u l t i n g equations are made consistent with independently estimated vectors of both f i n a l demand and industry outputs for the year i n question. This method may be applied i n several ways, ranging from the mult i -1^ 5 p l i c a t i o n of each row of a by a pr o p o r t i o n a l i t y constant, v 12. See T. I. Matuszewski, P. R. P i t t s , and J. A. Sawyer, "L'Ajustement Periodique des Systemes de Relations Inter-i n d u s t r i e l l e s , Canada, 1949-1958," Econometrica, xxxi (1963) , p.94. 13. ' Ibid., p.96. - 24 -to employing a l i n e a r programme to minimize the sum of changes 14 i n i n d i v i d u a l c o e f f i c i e n t s . In addition, the second approach may be used i n conjunction with the f i r s t when a few changes i n technology are outstanding. Matuszewski, Sawyer and P i t t s have demonstrated that these techniques are success-f u l i n ma t e r i a l l y reducing forecast errors. They compared the forecasts of o r i g i n a l and updated matrices to estimated f i n a l demands and industry outputs for a t h i r d year close to the year to which the matrices are updated. They found, for example, that updating the 1949 Canadian matrix to conform to to 1956 data reduced the weighted-average error of predictions o f 1958 industry outputs from 11.69 % to 5 . 4 6 % . 1 5 I t may be concluded that while technological change i s c e r t a i n l y an important source of forecast error, i t s e f f e c t s can be at l e a s t p a r t l y accounted for by updating the Leontief matrices. (c) The neglect of induced changes i n f i n a l demand. The f i n a l set of l i m i t a t i o n s i s only i n d i r e c t l y con-cerned with the nature of input c o e f f i c i e n t s . The open Leontief model i s based on the assertion that a change i n f i n a l demand w i l l r e s u l t i n predictable changes i n the l e v e l s o f the industry outputs and primary inputs. No consideration 14. T. I. Matuszewski, P. R. P i t t s , and J. A. Sawyer, "Linear Programming Estimates of Changes i n Input C o e f f i c i e n t s " , Canadian Journal of Economics and P o l i t i c a l Science, XXX ( 1964) , pp. 203-210. 15. T. I. Matuszewski, P. R. P i t t s , and J . A. Sawyer, "L'Ajustement Periodique des Systemes de Relations Inter-i n d u s t r i e l l e s , Canada 1949-1958", Econometrica, XXXI ( 1963) , p. 9 3 , 99-- 25 -i s given to the p o s s i b i l i t y that secondary changes i n f i n a l 16 demand i t s e l f may also r e s u l t . In macro-economic theory, on the other hand, i t i s concluded that s i g n i f i c a n t consumption and investment expenditures w i l l be induced by a change i n aggregate demand. To begin with, a stable r e l a t i o n s h i p has been demonstrated to e x i s t between aggregate personal consumption expenditure and aggregate income. Thus an increment of aggregate income i s expected to r e s u l t i n a c e r t a i n smaller increment of aggre-gate consumption. Since any change i n aggregate f i n a l demand i s at the same time a change i n aggregate income, i t follows that such a change w i l l r e s u l t i n successive increments of consumption expenditure. This i s c a l l e d the m u l t i p l i e r e f f e c t . S i m i l a r l y i t has been concluded that an increase i n f i n a l demand w i l l r e s u l t i n additional investment expenditure. This conclusion i s based on the assumption that a stable r e l a t i o n s h i p exists between the l e v e l of f i n a l output and the stock of c a p i t a l necessary to produce i t . I f the necessary c a p i t a l stock depends on the l e v e l of f i n a l demand, then increases i n c a p i t a l stock, or investment, w i l l be required by changes i n f i n a l demand. This i s the accelerator e f f e c t . In f a i l i n g to recognize m u l t i p l i e r and accelerator e f f e c t s , the open Leontief model neglects induced changes i n f i n a l demand. 16. This i s true only of the open Leontief model. Closed models have been developed to include p r e c i s e l y these e f f e c t s . - 26 -Other things being equal, the changes i n industry output l e v e l s obtained as solutions of the model w i l l be under-estimates. At the same time, without induced investment, i t could also happen that some.or a l l of the solution outputs would not be f e a s i b l e . This p o s s i b i l i t y places an obvious l i m i t a t i o n on the increases i n f i n a l demand that may be examined using the model. To sum up, t h i s chapter has introduced the Open Leontief or Input-Output model, an extension of which i s developed and used i n t h i s paper. The model i s b u i l t from the actual physical transactions of the production units of an economy for a p a r t i c u l a r i n t e r v a l of time. These transactions are f i r s t expressed i n value units and c l a s s i f i e d as inputs or outputs of a workable number of i n d u s t r i e s . Then the assumption of constant input c o e f f i c i e n t s i s introduced to transform the descriptive scheme into a simple mathematical model that r e l a t e s industry output l e v e l s to the l e v e l and pattern of f i n a l demands. The assumptions necessary to b u i l d the model i n t h i s form were seen, i n several instances, to be imperfectly attained or to involve contradictions with expected economic behaviour. The e f f e c t of these problems on predictions obtained from the model were suggested. In the case of the model's denial of tech-n o l o g i c a l change, methods of improving the predictions were indicated. The following chapter discusses the extension of the input-output model to analyse the s t r u c t u r a l e f f e c t s of foreign trade. - 27 -CHAPTER II I  INPUT-OUTPUT ANALYSIS AND FOREIGN TRADE Foreign trade i n goods and services plays an important part i n determining the l e v e l and pattern of production i n most countries. Accordingly, commodity trade i s generally included in;the Leontief model, and the e f f e c t s of changes i n trade patterns are often the subject of input-output analysis. This chapter f i r s t discusses the treatment of trade i n the simple Leontief model and then the extension of the model to consider more than one country or region. 1. Analysis of Foreign Trade with the Simple Leontief Model. In the simple input-output system, exports are considered as a category of f i n a l demand and therefore autonomous. Imports, on the other hand, may be treated i n a va r i e t y of ways. I f import l e v e l s are not desired as r e s u l t s of the model, imports may simply be c l a s s i f i e d as negative elements of f i n a l demand. Al t e r n a t i v e l y , they may be treated as inputs with constant input c o e f f i c i e n t s . In t h i s case import l e v e l s are determined i n the solution of the domestic a c t i v i t y l e v e l s . In the l a t t e r case, where import l e v e l s are explained, there are two p r i n c i p a l methods of defining the model. Since both of these w i l l be observed l a t e r i n the paper, i t w i l l be useful to outline them here. - 2 8 -F i r s t , t w o c l a s s i f i c a t i o n s o f i m p o r t e d c o m m o d i t i e s m u s t b e d e f i n e d . C o m p e t i t i v e i m p o r t s a r e t h o s e f o r w h i c h t h e r e i s a n e q u i v a l e n t c o m m o d i t y p r o d u c e d d o m e s t i c a l l y . N o n - c o m p e t i t i v e i m p o r t s a r e t h o s e , l i k e t r o p i c a l f o o d s i n C a n a d a , f o r w h i c h t h e r e i s n o d o m e s t i c e q u i v a l e n t . I n b o t h m o d e l s , n o n -c o m p e t i t i v e i m p o r t s a r e d i s t r i b u t e d t o u s i n g i n d u s t r i e s a n d f i n a l d e m a n d . T h e y may b e s h o w n e i t h e r a s a r o w o r m a t r i x o f i n p u t s . I n t h e l a t t e r c a s e t h e r o w s o f t h e i m p o r t m a t r i x i d e n t i f y t h e i r i n d u s t r i e s o f o r i g i n . I n t h e t r e a t m e n t o f c o m p e t i t i v e i m p o r t s , h o w e v e r , t h e t w o m o d e l s d i f f e r . I n M o d e l I , c o m p e t i t i v e i m p o r t s a r e t r e a t e d i n t h e same way a s n o n - c o m p e t i t i v e i m p o r t s . The l e v e l o f t o t a l c o m p e t i t i v e i m p o r t s i n e a c h i n d u s t r y i s r e l a t e d t o t h e o u t p u t o f u s i n g i n d u s t r i e s b y a n N x N m a t r i x o f c o n s t a n t c o e f f i c i e n t s . , The m o d e l i s N X i " j ^ a i j X j = Y i M . - ? m. . X . = ( i = 1 , . . . , N ) (3.1) w h e r e : X ^ = t h e t o t a l d o m e s t i c o u t p u t o f p r o d u c t i , = t h e f i n a l demand f o r d o m e s t i c a l l y p r o d u c e d i , a. .= t h e a m o u n t o f d o m e s t i c a l l y p r o d u c e d i r e q u i r e d i n t h e p r o d u c t i o n o f a u n i t o f p r o d u c t j , M ^ = t h e i m p o r t l e v e l o f p r o d u c t i , Y ^ = t h e f i n a l demand f o r i m p o r t s o f p r o d u c t i a n d m. .= t h e a m o u n t o f p r o d u c t i r e q u i r e d i n t h e d o m e s t i c p r o d u c t i o n o f a u n i t o f p r o d u c t j . - 29 -The m. . are assumed constant. In matrix form, the systems are (I - a)X = Y (3.2) M - mX = Y*4 M where X,Y,M, and Y are N element column vectors whose M t y p i c a l elements are X^ , Y^ , , and Y^ , and a and m +• w are N order square matrices with t y p i c a l elements a. . and m. . . Using the r e s u l t shown i n (2.12), the following solut-ions are obtained X = (I - a ) _ 1 Y (3.3) M = m(I - a ) " 1 + Y M In Model I I , each competitive import i s considered as an input to the domestic industry which produces the same product. Each of the basic equations of the model describes the d i s t r i b -ution of the t o t a l supply (domestic and imported) of a product. Competitive import l e v e l s are determined by constant c o e f f i c i e n t s r e l a t i n g them to the t o t a l supply of each of the commodities. Using t h i s method i t i s unnecessary to consider the imports of any product as being d i s t i n c t from the domestic product. At the same time, the a b i l i t y to i d e n t i f y the amount of any imported product used by a p a r t i c u l a r industry i s sa c r i f i c e d . ' 1 1. The d i s t r i b u t i o n of imported products i s available only under the a r t i f i c i a l assumption that they are demanded by users i n the same proportions as th e i r domestic counterparts. - 30 -The equations of the model are A N A A A X i -O4 a u XJ = Y i ( i = 1,...,N) ( 3 . 4 ) M. = m. X. 1 1 1 where X^ = X^ + , the t o t a l supply of product i , I = Y_. + Y" , 1 1 A a. . = (a. . + m. .) , known only i n t o t a l , and _ . A m. = M./X. , the share, assumed constant, of the t o t a l supply of product i accounted for by imports. In matrix form the systems are - A A (I - a)X = Y (3 .5) M = mX A A A i n which X , Y , and M are N-element column vectors, a th A i s an N order square matrix of the a. . «, and m i s an N order diagonal matrix of the nL . The solutions are X = (I - a ) - 1 Y A A { 5 - 6 ) M = m(I - a ) " 1 Y In both of these methods of treating competitive imports, non-technical assertions are i m p l i c i t i n the assumption of constant input-output c o e f f i c i e n t s . In Model I, the assump-ti o n of constant production c o e f f i c i e n t s requires that the imported input of product i used by industry j be a constant proportion of industry j's t o t a l requirements of product i . - 3 1 -I f M. . i s the flow of imported product I to industry j , then M., ./X. . must he constant. In Model I I , on the other i j i J hand, the t o t a l imports of product i , M^, must maintain A 2 a constant proportion of the t o t a l supply of i , X^ . Both these implications are unfortunate because the argument against input substitution i s a technological one that does not apply to any question of the share of a market held by various suppliers. whether or not one of the methods i s superior to the other has not been demonstrated conclusively. Backcast tests made with Canadian data showed that Model I yielded s l i g h t l y more 2 . A purely technical c o e f f i c i e n t involving imports would show the t o t a l supply product i required for the domestic production of a unit of j . Thus, x. . + M. . a ± d - x — -The input-output c o e f f i c i e n t s of Model I and Model I I may be re l a t e d to the technical c o e f f i c i e n t s , a. . , as follows: xj x. . .. Model I a. . = = a . . . i — xj X- xj M.. • x. . + M. . i j' , M o d e l 1 1 •- - hi • '• TTT x X. J For further discussion see: C. P. Modlin and G. Rosenbluth, "The Treatment of Foreign and Domestic Trade and Trans-portation Charges i n the Leontief Input-Output Table", Economic A c t i v i t y Analysis (ed. 0. Morganstern), New York: John Wiley and Sons, Inc., 1954. and T. I. Matuszewski, P.R. P i t t s , and J. A. Sawyer, "Alter-native Treatments of Imports i n Input-Output Models - A Canadian Study," Journal of the Royal S t a t i s t i c a l Society Series A. CXXVI (lQh>^,\. ™ . inr,_it^5~ :  - 32 -accurate predictions than Model I I . More detailed import s t a t i s t i c s are required i n Model I than i n Model II so no strong preference can be indicated a p r i o r i . With a simple Leontief model that incorporates foreign trade flows using an appropriate method, several questions may he investigated. For example, the e f f e c t s of d i f f e r e n t l e v e l s and patterns of exports on i n d u s t r i a l output may be examined. Again, using either of Model I or I I , the import content of u various categories of f i n a l demand may be estimated. As well as having implications regarding the l e v e l and structure of domestic production a c t i v i t y , t h i s question i s of i n t e r e s t i h i n v e s t i g a t i n g balance of payments determinants. 2. , E x t e n s i o n o f the S i m p l e L e o n t i e f Model The next l o g i c a l step i n input-output trade analysis i s to t r y and explain the l e v e l and composition of the export vector. Since exports are imports of other counties, they can be re l a t e d to foreign a c t i v i t y l e v e l s and foreign f i n a l 3. T. I. Matuszewski, P. R. P i t t s , and J. A. Sawyer, " A l t e r -native Treatments of Imports i n Input-Output Models: A Canadian Study", Journal of the Royal S t a t i s t i c a l Society, Series A, CXXVI (1963), p. 425. ~~ 4. For discussion and examples of t h i s type of analysis, see: ( i ) R. E. Caves, "The Inter-Industry Structure of the Canadian Economy", Canadian Journal of. Economics and  P o l i t i c a l Science, XXIII (1957), pp. 313-330. T i l T. I. Matuszewski, P. R. P i t t s , and J. A. Sawyer, The Impact of Foreign Trade on Canadian Industries, 1956", Canadian Journal of Economics and P o l i t i c a l Science, XXXI (1965), PP. 206-221. - 33 -demands by the methods of section 1. This procedure allows changes i n domestic a c t i v i t y l e v e l s to be related to changes i n f i n a l demand i n foreign countries. Such a model may therefore be used to examine the i n t e r n a t i o n a l transmission of business cycles. This question has t r a d i t i o n a l l y been investigated by aggregative analysis based on foreign trade m u l t i p l i e r s . In such analysis, the aggregate l e v e l of imports i s r e l a t e d to national income by an import function which recognises that the change i n imports produced by a change i n income may-vary according to the i n i t i a l income l e v e l , but does not recognise that the induced change i n imports w i l l vary with the composition of the income change. That i s , a country's marginal prop-ensity to import i s assumed constant f o r any given l e v e l of income. Exports are either taken as autohonous or r e l a t e d to the national income of another country (where the other country usually represents an amalgamation of a l l the f i r s t country's trading partners). The equilibrium national income of the f i r s t country i s then determined by the necessary equality of exports and imports, i f no c a p i t a l imports or exports are allowed, or by the equality of domestic investment 5. The explanation of other autonomous vectors of f i n a l demand i s also a natural step and r e s u l t s i n a f u l l y or p a r t i a l l y closed model. However, such models are seldom used i n empirical studies because the necessary assumptions of unchanging patterns of consumption and investment expend-i t u r e s are l e s s tenable than the assumptions of constant production or import c o e f f i c i e n t s . - 34 -plus exports and savings plus imports. The comparative advantages and disadvantages of the input-output approach to the transmission of business cycles p a r a l l e l those of simple Leontief analysis as compared to analysis of domestic aggregates. The input-output approach admits that the r e l a t i o n s h i p of changes i n import l e v e l s to changes i n domestic f i n a l demand depends i n part on the composition of the f i n a l demand change. On the other hand, i t neglects the secondary e f f e c t s of changes i n income. Several input-output models have been developed that may be used to analyse the transmission of national income changes through i n t e r n a t i o n a l trade. Three of these w i l l be i n t r o -duced here. (a) Leontief's Interregional Analysis L e o n t i e f s i n t e r r e g i o n a l input-output model i s one example 7 of such a model. While i t i s described i n terms of regions within a national economy, there are no t h e o r e t i c a l objections to considering the regions as national economies and the over-a l l system as the description of a world or trading bloc economy. The basis of the model i s a d i v i s i o n of the sector outputs in t o regional and national goods. The former are products, 6. For a more de t a i l e d discussion of foreign trade m u l t i p l i e r models see: C . P . Kindleberger, International Economics, Revised E d i t i o n , Homewood: R. D. Irwin, 1958, Chapter 10. 7. W. W. Leontief et a l . , Studies i n the Structure of the  American Economy. New York: Oxford University Press, 1953', pp. 93-115. - 35 -such as m i n e r a l s and a g r i c u l t u r a l p r o d u c t s , which a r e consumed In the r e g i o n where they a r e p r o d u c e d . The l a t t e r a r e p r o d u c t s w h i c h a r e t r a d e d among r e g i o n s . These a r e p r e d o m i n a n t l y d u r a b l manufactured goods. The s t r u c t u r e o f the n a t i o n and the r e g i o n s i s d e t e r m i n e d by: ( 1 ) the f i n a l demands f o r each p r o d u c t i n each r e g i o n , ( 2 ) a m a t r i x of n a t i o n a l p r o d u c t i o n c o e f f i c i e n t s , w h i c h i s assumed t o a p p l y t o each r e g i o n as w e l l , and (3) a s e t o f c o e f f i c i e n t s d e t e r m i n i n g the p r o p o r t i o n o f the o u t p u t of each i n t e r r e g i o n a l good produced i n each r e g i o n . I n L e o n t i e f s n o t a t i o n , m i n d u s t r i e s a r e d e f i n e d w i t h 1 = l , . . . , h r e p r e s e n t i n g the r e g i o n a l ones and g = h+l,...,m r e p r e s e n t i n g the n a t l o n a l ones. N e x t , n r e g i o n s a r e d e f i n e d w i t h r e g i o n a l o u t p u t s i d e n t i f i e d by a p r e f i x e d s u b s c r i p t j = l , . . . , n . Thus f o r the m n a t i o n a l o u t p u t s t h e r e c o r r e s p o n d nm r e g i o n a l o u t p u t s ^X^ . S i m i l a r l y , t h e r e a r e nm f i n a l demands, Y j 1 The s t r u c t u r a l p a r a m e t e r s a r e : ( k = 1,...,m) , and (g = h+l,...,m ; j = l , . . . , n ) The a c t i v i t y l e v e l s a r e d e t e r m i n e d i n t h r e e s t a g e s . F i r s t the n a t i o n a l o u t p u t o f each p r o d u c t i s found by X ± = S b i k Y k ( i = l , . . . , m ) . (5.7) K . = l * i k a X g - 36 -where the a r e the t o t a l r e q u i r e m e n t s c o e f f i c i e n t s - the elements o f ( I - a ) - 1 . Now, g i v e n , the r e g i o n a l o u t p u t s o f the n a t i o n a l p r o d u c t s a r e d e t e r m i n e d . Thus, j X g = X g ( g = h+1, ...,m ; j = 1, ...,n) ( 3 . 8 ) F i n a l l y , the r e g i o n a l o u t p u t s of r e g i o n a l goods a r e de t e r m i n e d u s i n g s u b - m a t r i c e s o f b o t h the d i r e c t r e q u i r e m e n t s m a t r i x a , -1 and the t o t a l r e q u i r e m e n t s m a t r i x , ( I - a) . Thus, ,X = ? a . o - ' n ^ + £ b , k ' i Y k ( 1 = l , . . . , h ; j = l , . . . , n ) J 1 g=h+l l & 0 g k = l **• J K ( 3 . 9 ) S i n c e the n a t i o n a l f i n a l demands a r e t o t a l s o f the r e g i o n a l f i n a l demands and s i n c e the n a t i o n a l and r e g i o n a l i n p u t - o u t p u t m a t r i c e s a r e i d e n t i c a l , the r e g i o n a l i n d u s t r y o u t p u t s of l o c a l and t r a d e d goods w i l l be c o n s i s t e n t . The s t r o n g e s t p o i n t o f L e o n t i e f s model i s t h a t i t encompasses the' p r o d u c t i o n o f a complete s e t o f r e g i o n s o r n a t i o n s . I t t a k e s a n o t h e r s t e p towards the i d e a l g e n e r a l e q u i l i b r i u m model i n r e c o g n i z i n g i n t e r d e p e n d e n c y i n the o u t p u t l e v e l s o f a l l the r e g i o n s i n a t r a d i n g group. I n a d d i t i o n , once the r e g i o n a l f i n a l demand v e c t o r s a r e e s t i m a t e d and the c l a s s o f t r a d e d goods d e f i n e d , i t i s a r e l a t i v e l y easy model t o d e a l w i t h . However, t h e r e a r e some drawbacks t o the model which a r e p a r t i c u l a r l y s e r i o u s i n the c o n t e x t o f p r o d u c t i o n f o r i n t e r n a t i o n a l t r a d e . The a p p l i c a t i o n o f a s i n g l e c l a s s i f i c a t i o n o f t r a d e d and l o c a l p r o d u c t s t o a l l r e g i o n s i s an o v e r s i m p l i f i c -a t i o n w h i c h s h o u l d r e s u l t i n an u n d e r e s t i m a t i o n o f the amount o f I n t e r r e g i o n a l t r a d e . Second, t h e r e i s o n l y a p a r t i a l - 37 -explanation of i n t e r r e g i o n a l trade flows. The regional pattern of production f o r trade i s determined by fixed supply patterns, and there i s no means of p r e d i c t i n g trade between p a r t i c u l a r regions. In a more r e a l i s t i c model, the quantities of traded goods supplied by any region would depend on the regional d i s t r i b u t i o n of demand. Third, and perhaps the most important l i m i t a t i o n of the model, i s the uniform technology attributed to the nation and each of i t s regions. When input-output c o e f f i c i e n t s are estimated for each region i n d i v i d u a l l y , more r e a l i s t i c r e l a t i o n s between regional f i n a l demand vectors and t h e i r input and. import requirements may be derived. Like the others, t h i s l i m i t a t i o n would be e s p e c i a l l y serious i f the model were used to investigate the e f f e c t s on national outputs of i n t e r n a t i o n a l trade. (b) The Interregional Models of Isard and Moses 8 In t h i s section models designed by Walter Isard and 9 Leon N. Moses are introduced. They are discussed together because they are e s s e n t i a l l y the same model. They d i f f e r only i n the procedure used i n deriving regional import c o e f f i c i e n t s . Both models follow L e o n t i e f s interregional model i n using a uniform production matrix f o r a l l regions. Thus they are better 8. W. Isard, "Interregional and Regional Input-Output Analysis: A Model of a Space Economy," Review of Economics and  S t a t i s t i c s , XXXIII, 1951, PP. 3TS -'"3287"" 9. L. N. Moses, "The S t a b i l i t y of Interregional Trading Patterns and Input-Output Analysis," The American  Economic Review, XLV, 1955, PP. 803 - 532. - 38 -s u i t e d f o r i n t r a n a t i o n a l t h a n i n t e r n a t i o n a l a n a l y s i s . On the o t h e r hand, they d i f f e r from the L e o n t i e f model by r e l a t i n g the e x p o r t s o f each r e g i o n t o the i m p o r t r e q u i r e m e n t s of the o t h e r i n d i v i d u a l r e g i o n s . F o r i n s t a n c e , i n s t e a d o f assuming t h a t r e g i o n one s u p p l i e s s i x t y p e r c e n t o f the t o t a l i r o n and s t e e l r e q u i r e m e n t s of the n a t i o n , t h e s e models might assume t h a t r e g i o n one s u p p l i e s f i f t y p e r c e n t o f r e g i o n t w o 1 s i r o n and s t e e l r e q u i r e m e n t s , e i g h t y p e r c e n t o f r e g i o n t h r e e ' s r e q u i r e -ments, e t c . The t r a d e p a r a m e t e r s a r e s t i l l r i g i d but t h e y i n c o r p o r a t e a l o c a t i o n a l f a c t o r and a r e t h e r e f o r e more r e a l i s t i c than L e o n t i e f s s u p p l y c o e f f i c i e n t s . Moreover, i t i s u n n e c e s s a r y i n t h e s e models t o d e f i n e c l a s s e s o f t r a d e d and l o c a l goods. The model i s d e v e l o p e d u s i n g the I s a r d p r o c e d u r e f o r . t r e a t i n g r e g i o n a l i m p o r t s . A f t e r w a r d s the Moses v a r i a n t w i l l be d i s c u s s e d w i t h r e f e r e n c e t o the same e q u a t i o n s . C o n s i d e r a system o f R r e g i o n s , e a c h w i t h " N i n d u s t r i e s . L e t : a.. . = the amount o f d o m e s t i c a l l y produced i r e q u i r e d J i n the p r o d u c t i o n o f a. u n i t o f j" (These p a r a -meters a p p l y t o a l l r e g i o n s . ) , X = the o u t p u t of i n d u s t r y i i n the k o n r e g i o n , 1 and, Y k = the f i n a l demand f o r the o u t p u t o f 1 1 t h produced i n the k r e g i o n . F i r s t , the f i n a l demand of each r e g i o n i s p a r t i t i o n e d i n t o e x p o r t s t o the o t h e r r e g i o n s and a r e s i d u a l . The r e s i d u a l i n c l u d e s any e x p o r t s t o r e g i o n s o u t s i d e the system. - 39 -Thus Y* = E + F* . (3 .10) 1 1=1 1 1 w here E^' r e p r e s e n t s the e x p o r t s o f p r o d u c t 1 t o r e g i o n l and F^ r e p r e s e n t s a l l o t h e r f i n a l demands f o r the o u t p u t o f 1 produced i n r e g i o n k . Ne x t , the i n t e r r e g i o n a l e x p o r t demands a r e r e l a t e d t o p r o d u c t i o n a c t i v i t y i n the i m p o r t i n g id k£ r e g i o n s . I n the I s a r d model,import c o e f f i c i e n t s , S. . , a r e d e f i n e d by E*1 = 1 sH + f k ^ ( 3 . H ) 1 j = l 1 J J k/ Thus, d e s c r i b e s the amount o f p r o d u c t i im p o r t e d from r e g i o n k t h a t i s r e q u i r e d i n the p r o d u c t i o n of a u n i t o f kk p r o d u c t j i n r e g i o n i . Note t h a t S. . w i l l be z e r o . S i m i l a r l y , f 1 ^ d e s c r i b e s the amount o f i , im p o r t e d from r e g i o n k , t h a t i s demanded d i r e c t l y by f i n a l u s e r s i n r e g i o n I . F o r s i m p l i c i t y i t i s c o n s i d e r e d t o be i n c o r p o r a t e d i n F^ I n ( 3 . 1 0 ) . W i t h these d e f i n i t i o n s , t he d i s t r i b u t i o n o f the r e g i o n a l i n d u s t r y o u t p u t s may be e x p r e s s e d i n the f o l l o w i n g s e t of e q u a t i o n s . X* = E a. .X1? + E E S*'r X^ + F* ( i = l , . . . , N ; k = l,... 1 j = l 1 0 J <-=io=i J J (3 .12) L e t : a = the N o r d e r m a t r i x c f the • . S^1 = the N t h o r d e r m a t r i x o f the c o e f f i c i e n t s , t h a t d e s c r i b e r e q u i r e m e n t s o f r e g i o n k's p r o d u c t s i n r e g i o n X . X = the N- element column v e c t o r o f the X^ ^ , and k lr F = the N— element column v e c t o r o f the F£ - 40 -Then, i n m a t r i x form, (3 .12) i s X k = a X k + S k l X 1 + . . . + S k R X R + F k (k = 1, • • . ,R) or ( I - a ) X k - S U X 1 . . . . - S l c ¥ B F l £ . (k = 1 , . . . ,H) T a k i n g R = 3 as an example, (3.13) may be w r i t t e n ( I - a) - s 1 2 ' - s 1 3 1 " F ( I - a) ' - S 2 3 X 2 = F 2 - S 3 2 ( I - a) F 3 L e t L be the parameter m a t r i x , which i n g e n e r a l w i l l (3.13) 2 2 N R e l e m e n t s , and X and F ,, column v e c t o r s w i t h s u b v e c t o r s :J X k and F k . Then LX = F (3.14) S i n c e L i s square and n o n - s i n g u l a r i t s i n v e r s e e x i s t s . T h e r e f o r e the i n d u s t r y / o u t p u t s i n each r e g i o n may be w r i t t e n as l i n e a r f u n c t i o n s o f the r e g i o n a l f i n a l demands by X = L " x p (3.15) F i n a l l y , as l o n g as v a l u e added ( e x c l u d i n g i m p o r t s ) i s s t i l l n o n - n e g a t i v e f o r each r e g i o n a l i n d u s t r y , the Hawkins-Simon c o n d i t i o n s w i l l be met. F o r F > 0 , the X k w i l l be p o s i t i v e The model d e v e l o p e d by Leon Moses d i f f e r s o n l y i n the d e r i v a t i o n of the im p o r t c o e f f i c i e n t s , S. k£ 10 I n I s a r d ' s model, t h e y a r e d e r i v e d under the a s s u m p t i o n t h a t the • - . 4 1 -t h 1 o u t p u t o f each r e g i o n i s d i s t i n c t from the c o r r e s p o n d i n g o u t p u t s o f the o t h e r r e g i o n s . That i s , the t e c h n i q u e d e s c r i b e d i n Model I i s used i n r e l a t i n g i m p o r t l e v e l s t o k-f l e v e l s of domestic o u t p u t . I n c o n t r a s t , the S^^ i n Moses' system i n v o l v e an.assumption t h a t i s v e r y s i m i l a r t o t h a t of 10 Model I I . Imports are c o n s i d e r e d t o be s u b s t i t u t a b l e f o r d o m e s t i c p r o d u c t s and a r e d i s t r i b u t e d among u s i n g i n d u s t r i e s and f i n a l demand I n the same p r o p o r t i o n s as the domestic o u t -p u t s . E q u a t i o n (3.11) becomes E ^ = X? = m ^ a. ,Xl. + m * M ' (3.16) l i i l i j j i i k-t Here the nu ar e c o e f f i c i e n t s r e l a t i n g the i m p o r t s o f i from k t o the d o m e s t i c o u t p u t s o f 1 i n r e g i o n I . Thus = m*1 a. . 1 0 1 -^O i n the Moses model. The m ^ F f a r e e q u i v a l e n t t o the f k ^ i l i n ( 3 . 1 1 ) . An advantage o f t h i s model over the I s a r d model k X i s t h a t the m. may be e s t i m a t e d w i t h g r e a t e r ease and a c c u r -Kl acy than I s a r d ' s The a l g e b r a o f the I s a r d and Moses models (systems ( 3 . 1 3 ) , ( 3.14), and ( 3 . 1 5 ) ) i s b a s i c t o the Wonnacott model d i s c u s s e d 10. I n Model I I i m p o r t s a r e r e l a t e d t o the t o t a l s u p p l y r a t h e r t h a n the d o m e s t i c s u p p l y o f competing I n d u s t r y o u t p u t s . I f t h i s p r o c e d u r e were used i n an Isard-Moses model the r e s u l t i n g p r e d i c t i o n s would be i d e n t i c a l ' t o those o b t a i n e d i n the Moses v a r i a n t . To use the p r o c e d u r e o f Model I I , the X. and a.. would have t o be r e d e f i n e d i n terms o f i j t o t a l s u p p l y . The S m a t r i c e s would become d i a g o n a l m a t r i c e s o f c o e f f i c i e n t s r e l a t i n g the Imports o f any commodity t o i t s t o t a l s u p p l y i n the i m p o r t i n g r e g i o n . - 42 -n e x t and t o the model a c t u a l l y used i n t h i s p a p e r . These models d i f f e r from the Isard-Moses model o n l y i n t h e i r methods o f d e f i n i n g the t r a d e and p r o d u c t i o n m a t r i c e s . ( c ) The Wonnacott Model. The t h i r d i n t e r r e g i o n a l model t o be d i s c u s s e d was d e v e l o p e d by R. J . W o n n a c o t t . 1 1 I t s main d e p a r t u r e from the Isard-Moses model i s t h a t i t i n c o r p o r a t e s d i f f e r e n t p r o d u c t i o n m a t r i c e s 12 f o r each r e g i o n . F o r t h i s r e a s o n i t i s a s u p e r i o r model w i t h w h i c h t o i n v e s t i g a t e the i n t e r d e p e n d e n c e of r e g i o n a l o u t -p u t s a t an i n t e r n a t i o n a l l e v e l . The model may be e x p r e s s e d by the e q u a t i o n s (3.13) i f the ( I - a) s u b - m a t r i c e s a r e changed t o ( I - a k ) (k = 1,...,R). The S k ^ i n Wonnacott's model a r e d e r i v e d u s i n g Moses' a s s u m p t i o n t h a t S k ^ = mk^. a f • + m k^ F[ . Wonnacott developed h i s model i n terms o f two r e g i o n s , Canada and the U n i t e d S t a t e s . To r e p r e s e n t the Canadian and American t e c h n o l o g i e s i n m a t r i c e s t h a t would f i t i n t o the I s a r d -Moses system, he ag g r e g a t e d the i n p u t - o u t p u t m a t r i c e s o f each of the c o u n t r i e s so as t o make t h e i r s e c t o r d e f i n i t i o n s conform as c l o s e l y as p o s s i b l e . S t a r t i n g w i t h a f o r t y - t w o s e c t o r 11. R. J . Wonnacott, Canadian-American Dependence: An I n t e r -i n d u s t r y A n a l y s i s of P r o d u c t i o n and P r i c e s , - Amsterdam: The N o r t h - H o l l a n d P u b l i s h i n g Company, 1961. 12. Wonnacott a l s o d e v e l o p e d a method o f h a n d l i n g c a p a c i t a t e d i n d u s t r i e s i n h i s model. See C h a p t e r IV of h i s book. - 43 -Canadian i n p u t - o u t p u t t a b l e and a f o u r hundred and f i f t y -s e c t o r U n i t e d S t a t e s t a b l e , he produced s e p a r a t e t h i r t y - f i v e s e c t o r t a b l e s . Thus w h i l e the Wonnacott model i s v e r y s i m i l a r t o an Isard-Moses model, the ' s t a t i s t i c a l p r o c e d u r e n e c e s s a r y t o a p p l y i t i s q u i t e d i f f e r e n t . . The t h r e e i n t e r r e g i o n a l models i n t r o d u c e d i n t h i s c h a p t e r have the common purpose of y i e l d i n g s i m u l t a n e o u s s o l u t i o n s f o r r e g i o n a l i n d u s t r y o u t p u t ' l e v e l s as f u n c t i o n s o f r e g i o n a l f i n a l demands. They a l l r e c o g n i z e the i n t e r d e p e n d e n c y o f i n d u s t r y o u t p u t l e v e l s i n any group o f r e g i o n s w h i c h t r a d e t o g e t h e r . I n L e o n t i e f s i n t e r r e g i o n a l model, the o u t p u t s of a r e g i o n depend on i t s f i n a l demands and the a g g r e g a t e f i n a l demands of the system of r e g i o n s . I n the Isard-Moses and Wonnacott models, a r e g i o n ' s o u t p u t s depend on the f i n a l demands of each I n d i v i d u a l r e g i o n . As w e l l as the b a s i c L e o n t i e f a s s u m p t i o n of c o n s t a n t prod-u c t i o n c o e f f i c i e n t s , the models assume f i x e d s u p p l y c o e f f i c i e n t s f o r r e g i o n a l i m p o r t s . Depending on the n a t u r e o f the a c t u a l r e g i o n s under e x a m i n a t i o n , the l a t t e r a s s u m p t i o n i s l i k e l y t o be l e s s r e a l i s t i c than the f o r m e r . F i n a l l y , the i n t e r r e g i o n a l models p a r a l l e l the s i m p l e L e o n t i e f model i n t h e i r n e g l e c t o f i n d u c e d changes i n the Investment and P e r s o n a l consumption components of f i n a l demand. The model t o be used i n t h i s paper i s e l a b o r a t e d i n the n e x t c h a p t e r . I t i s a v a r i a n t o f Wonnacott's model and t h e r e f o r e s h a r e s most of the s t r e n g t h s and weaknesses of the models d e s c r i b e d above. - 44 -CHAPTER IV THE EXPORT RECLASSIFICATION MODEL The aim o f t h i s paper i s t o i n v e s t i g a t e the dependence of Canadian i n d u s t r y o u t p u t s on American f i n a l demand. F o r the i n v e s t i g a t i o n a model i s d e v e l o p e d t h a t I s s i m i l a r t o the Wonnacott model. However, i t I s a p p l i e d i n a d i f f e r e n t way and has some s i m p l i f y i n g r e s t r i c t i o n s p l a c e d on I t . S e c t i o n ( l ) o f t h i s c h a p t e r d e s c r i b e s the model i n i t s g e n e r a l form, and s e c t i o n (2) d e t a i l s the r e s t r i c t i o n s t h a t a r e i n t r o d u c e d t o f a c i l i t a t e i t s e m p i r i c a l a p p l i c a t i o n . 1. The E x p o r t R e c l a s s i f i c a t i o n Model The purpose of the model i s t o r e l a t e the i n d u s t r y o u t -p u t s o f r e g i o n s w i t h s e p a r a t e i n p u t - o u t p u t t a b l e s , w i t h o u t h a v i n g t o r e c o n s t r u c t those t a b l e s a c c o r d i n g t o a u n i f o r m c l a s s i f i c a t i o n system. The method used i s t o b u i l d t r a d e m a t r i c e s t h a t r e l a t e the e x p o r t s o f one r e g i o n , c l a s s i f i e d a c c o r d i n g t o I t s i n d u s t r y scheme, t o the i n d u s t r y I n p u t s of a n o t h e r , c l a s s i f i e d d i f f e r e n t l y . I f the p r o d u c t i o n m a t r i x o f r e g i o n k has M s e c t o r s and t h a t of r e g i o n 1 has N , k£ then the t r a d e m a t r i x S w i l l have M rows and N columns When the p r o d u c t i o n and t r a d e m a t r i c e s a r e a r r a y e d i n the manner of the I s a r d - M o s e s and Wonnacott systems (see the - 45 -example f o l l o w i n g ( 3 . 1 3 ) ) , i t i s found t h a t the c o e f f i c i e n t m a t r i x , L , i s s q u a r e . Moreover, L w i l l n o r m a l l y be found t o be n o n - s i n g u l a r and t o obey the Hawkins-Simon c o n d i t i o n s so the system w i l l y i e l d a p o s i t i v e s o l u t i o n v e c t o r o f r e g i o n a l i n d u s t r y o u t p u t s f o r p o s i t i v e v e c t o r s o f f i n a l demand. T h i s model has a d i s t i n c t advantage over Wonnacott's model i n t h a t the t a s k of a p p l y i n g i t t o a c t u a l d a t a i s e a s i e r . G r e a t e r a c c u r a c y i s a l s o t o be e x p e c t e d s i n c e t r a d e d a t a a r e g e n e r a l l y found i n more d e t a i l t h a n i s a v a i l a b l e i n i n p u t -o u t p u t t a b l e s o r the w o r k i n g p a p e r s used i n b u i l d i n g them. C l e a r l y the advantages o f the e x p o r t r e c l a s s i f i c a t i o n model w i l l be p a r t i c u l a r l y n o t i c a b l e f o r systems i n v o l v i n g t h r e e o r more r e g i o n s . B e f o r e r e s t a t i n g the model i n a r e s t r i c t e d form i t w i l l be c o n v e n i e n t t o e x p r e s s i t i n a s l i g h t l y s i m p l e r n o t a t i o n . T h i s i s p o s s i b l e because o n l y two r e g i o n s a re i n v o l v e d i n the a p p l i c a t i o n . The n o t a t i o n d e f i n e d here w i l l be used t h r o u g h -out the r e s t o f the p a p e r . L e t : M = the number o f s e c t o r s i n the Canadian i n p u t - o u t p u t t a b l e , N = the number o f s e c t o r s i n the U n i t e d S t a t e s i n p u t -o u t p u t t a b l e , x = the v e c t o r o f Canadian a c t i v i t y l e v e l s , X = the v e c t o r o f U n i t e d S t a t e s a c t i v i t y l e v e l s , e = the v e c t o r o f Canadian e x p o r t s t o the U n i t e d S t a t e s , f = the v e c t o r o f a l l o t h e r f i n a l demands f o r o u t p u t s produced i n Canada, y = e + f = the t o t a l f i n a l demand f o r Canadian o u t p u t s , - 46 -E = the v e c t o r o f American e x p o r t s t o Canada, F = the v e c t o r o f a l l o t h e r f i n a l demands f o r p r o d u c t s of U n i t e d S t a t e s i n d u s t r i e s (As i n the Isard-Moses and Wonnacott models F w i l l i n c l u d e any e x p o r t s t o Canada from the U n i t e d S t a t e s t h a t a r e a l l o c a t e d d i r e c t l y t o f i n a l demand. ' I n t h i s model, i t w i l l be assumed t h a t t h e r e a r e no such e x p o r t s . T h i s a s s u m p t i o n i s made f o r theUemand f o r Canadian o u t -p u t s , f , as w e l l ) , Y = a = A J E + F = the t o t a l f i n a l demand f o r o u t p u t s o f U n i t e d S t a t e s i n d u s t r i e s , the M o r d e r m a t r i x o f Canadian i n p u t - o u t p u t c o e f f i c i e n t s , ' the c o r r e s p o n d i n g N o r d e r I n p u t - o u t p u t m a t r i x f o r the U n i t e d S t a t e s , the M x N m a t r i x d e s c r i b i n g the p a t t e r n of Canadian e x p o r t s r e q u i r e d by u n i t a c t i v i t y l e v e l s o f U n i t e d S t a t e s i n d u s t r i e s , and K = the N x M m a t r i x d e s c r i b i n g the p a t t e r n o f U n i t e d S t a t e s e x p o r t s r e q u i r e d f o r u n i t o u t p u t l e v e l s o f C anadian i n d u s t r i e s . W i t h t h e s e d e f i n i t i o n s , ( 3 . I 3 ) becomes (4.1) ( I - a) - J X f -k ( I - A)_ F The s o l u t i o n (X = L - 1 F i n the n o t a t i o n X X ( I - a) -K • - J ( I " A) -1 f -1 f F (4.2) 2. A R e s t r i c t e d Form o f the Model I n the a p p l i c a t i o n o f t h i s p a p e r , o n l y the s o l u t i o n v a l u e s o f the Canadian a c t i v i t y l e v e l s , x , a r e o f i n t e r e s t . So t h a t t h e y may be i s o l a t e d , the I n v e r s e o f (4.2) i s e x p r e s s e d i n - 47 -mm am X X terms of i t s s u b - m a t r i c e s . 1 I n t h i s form, (4.2) i s [ ( I - a ) - J ( l - A ) _ 1 K ] - 1 [ ( I - a J - J C l - A r ^ r ^ I - A ) - 1 [ ( l - A ) - K ( l - a ) " 1 J ] " 1 K ( I - a ) " 1 [ ( I - A ) - K ( I - a ) _ 1 J ] " h F ( 4 . 5 ) -Now o n l y the f i r s t system of e q u a t i o n s need be c o n s i d e r e d . The Canadian a c t i v i t y l e v e l s a r e e x p r e s s e d as f u n c t i o n s o f Canadian and American f i n a l demands'by x = [ ( I - a J - J C l - A ) " 1 ^ ] " ^ + [ ( I - a ) - J ( I - A ) " 1 K ] " 1 J ( I - A ) " 1 F (4.4) Such a s o l u t i o n r e c o g n i z e s t h a t a change i n the l e v e l o r p a t t e r n o f the f i n a l demand of e i t h e r c o u n t r y has n o t o n l y a d i r e c t e f f e c t on t h a t c o u n t r y ' s a c t i v i t y l e v e l s , but an i n f i n i t e c h a i n o f i n d i r e c t e f f e c t s on the a c t i v i t y l e v e l s o f b o t h c o u n t r i e s . I n o r d e r t o reduce the d a t a r e q u i r e m e n t s i n the e m p i r i c a l a p p l i c a t i o n o f the model, i t i s assumed t h a t U n i t e d S t a t e s a c t i v i t y l e v e l s a r e not r e s p o n s i v e t o changes i n Canadian i n d u s t r y o u t p u t l e v e l s . That i s , the e f f e c t s on U n i t e d S t a t e s 1. I f B l l B12 B21 B22 ( I - a) - J -K ( I - A) n -1 then ( I - a) - J -K ( I - A) B. 11 B 12 B 21 B 22 I 0 0 I where the I are i d e n t i f y m a t r i c e s of o r d e r M and o r d e r N r e s p e c t i v e l y . From t h i s system the B . may be e a s i l y o b t a i n e d . • i j - 4 8 -i n d u s t r y o u t p u t s o f induced changes i n Canadian i m p o r t s a r e n e g l e c t e d . T h i s a s s u m p t i o n i s i n c o r p o r a t e d i n the model by p o s t u l a t i n g K = 0 . System ( 4 . 4 ) may now be w r i t t e n x = ( I - a ) _ 1 f + ( I - a ) _ 1 J ( I - A ) _ 1 F . F u r t h e r m o r e , no changes w i l l be p o s t u l a t e d f o r the v e c t o r o f Canadian f i n a l demands, f . A c c o r d i n g l y , the model i n the r e s t r i c t e d form d e s i r e d i s V x = ( I - a ) _ 1 J ( I - A ) _ 1 F ( 4 . 5 ) I t might be argued t h a t the n e g l e c t o f the I n d i r e c t e f f e c t s o p e r a t i n g t h r o u g h Canadian i m p o r t s I s a s e r i o u s o m i s s i o n . However, the e f f e c t s o m i t t e d a r e l e s s d i r e c t and t h e r e f o r e l e s s l i k e l y t o be s i g n i f i c a n t than e f f e c t s produced p by the s t i m u l a t i o n o f t h i r d c o u n t r y a c t i v i t y l e v e l s . A g r e a t e r i n c r e a s e i n a c c u r a c y would p r o b a b l y be o b t a i n e d by g e n e r a l i z i n g the r e s t r i c t e d model t o more r e g i o n s t h a n by i n c o r p o r a t i n g the I n d i r e c t e f f e c t s g e n e r a t e d by Canadian i m p o r t s . The model found i n ( 4 . 5 ) i s s t a t e d i n v e r y g e n e r a l terms. I n p a r t i c u l a r , the n a t u r e o f J i s l a r g e l y u n s p e c i f i e d . F o r 2. The r e s t r i c t e d form o f the e x p o r t r e c l a s s i f i c a t i o n can be s i m p l y a l t e r e d t o i n c l u d e such e f f e c t s . L e t : a = the t h i r d c o u n t r y ' s p r o d u c t i o n m a t r i x , o f o r d e r P , G = the M x p t r a d e m a t r i x t h a t r e l a t e s C anadian e x p o r t s t o the t h i r d c o u n t r y t o the l a t t e r ' s a c t i v i t y l e v e l s , and H = the P * N t r a d e m a t r i x t h a t r e l a t e s t h i r d - c o u n t r y e x p o r t s t o U n i t e d S t a t e s a c t i v i t y l e v e l s . Then x = ( l - a ) _ 1 [ J + G ( I - a ) - 1 H ] ( I - A ) _ 1 F - 49 -example, In the present formulation, imports could be treated according to eith e r of Model I, Model I I , or the Moses variant of Model I I . The precise d e f i n i t i o n of the trade matrix, J , w i l l depend l a r g e l y on the nature of the input-output tables of the two economies. Therefore, i t w i l l be discussed i n the next chapter which examines the data and procedure used In constructing the empirical model. - 50 -CHAPTER V APPLICATION OF THE MODEL: DATA AND PROCEDURE In t h i s c h a p t e r , the s o u r c e s and n a t u r e o f the d a t a a r e f i r s t examined. Then the a p p l i c a t i o n of the model t o t h i s d a t a i s d e s c r i b e d , a n d f i n a l l y , t h e p r o c e d u r e f o l l o w e d i n e s t i m a t i n g the pa r a m e t e r s and o b t a i n i n g s o l u t i o n s i s d i s c u s s e d . 1. The Data Three b a s i c groups o f d a t a a r e d i s c u s s e d h e r e : the American and Canadian i n p u t - o u t p u t t a b l e s , and Canadian e x p o r t s t o the U n i t e d S t a t e s . ( a ) The U n i t e d S t a t e s I n p u t - O u t p u t T a b l e s The U n i t e d S t a t e s i n p u t - o u t p u t t a b l e s used i n t h i s p a p e r a r e found on page 33 o f the September 1965 i s s u e o f Survey o f  C u r r e n t B u s i n e s s , a p u b l i c a t i o n o f the U n i t e d S t a t e s Department of Commerce, O f f i c e o f B u s i n e s s E c o n o m i c s . 1 The i n f o r m a t i o n c o n t a i n e d i n t h i s r e f e r e n c e i s based on d a t a f o r the y e a r 1958 and c o n s i s t s o f : 1. These t a b l e s - w i t h i m p o r t s t r e a t e d not as p r i m a r y i n p u t s b u t as n e g a t i v e e l e m e n t s o f f i n a l demand - a l s o appear i n an a r t i c l e by W. W. L e o n t i e f i n the A p r i l 1965 i s s u e o f S c i e n t i f i c A m e r i c a n . - 51 -( i ) a t r a n s a c t i o n s t a b l e c o n s t r u c t e d t o agree w i t h N a t i o n a l A c c o u n t s d a t a , ( i i ) a p r o d u c t i o n c o e f f i c i e n t s m a t r i x , ( i i i ) a t o t a l r e q u i r e m e n t s , o r i n v e r s e , m a t r i x , and ( i v ) a t a b l e d e f i n i n g the p r o d u c t i o n s e c t o r s o f the p r e c e d i n g t a b l e s by r e f e r e n c e t o codes found i n the 1957 e d i t i o n o f the U n i t e d S t a t e s S t a n d a r d  I n d u s t r i a l C l a s s i f i c a t i o n Manual. The t r a n s a c t i o n s t a b l e and d i r e c t and t o t a l r e q u i r e m e n t s m a t r i c e s a r e c o n s t r u c t e d u s i n g e i g h t y - t w o p r o d u c i n g s e c t o r s . There a r e a l s o dummy s e c t o r s (namely: (83) S c r a p , Used and Secondhand Goods, (84) Government I n d u s t r y , (85) R e s t o f the World I n d u s t r y , (86) Household I n d u s t r y , and (87) I n v e n t o r y V a l u a t i o n A d j u s t m e n t ) , and a V a l u e added row. The p r i n c i p a l use o f the dummy s e c t o r s i s t o r e c o r d payments f o r s e r v i c e s shown I n the N a t i o n a l A c c o u n t s as f i n a l demand w h i c h do not b e l o n g t o any o f the e i g h t y - t w o i n d u s t r i e s . Examples a r e payments t o d o m e s t i c s e r v a n t s and, most i m p o r t a n t , payments t o c i v i l s e r v a n t s a t a l l l e v e l s o f government. F i n a l demand i n the t r a n s a c t i o n s t a b l e , i s shown as the sum o f s i x component v e c t o r s . These a r e : ( i ) P e r s o n a l consumption e x p e n d i t u r e s , ( i i ) . G r o s s p r i v a t e f i x e d c a p i t a l f o r m a t i o n , ( i i i ) Net i n v e n t o r y change, ( l v ) Net e x p o r t s , ( v ) F e d e r a l Government p u r c h a s e s , and ( v i ) S t a t e and l o c a l government p u r c h a s e s . - 52 -The f l o w s shown i n the t r a n s a c t i o n s t a b l e a r e v a l u e d a t p r o d u c e r s ' p r i c e s . T h i s means t h a t t r a d e and t r a n s p o r t m argins a r e e x c l u d e d from the s a l e s o f any s e c t o r . These margins a r e shown as payments by the p u r c h a s i n g s e c t o r d i r e c t l y t o the t r a d e and t r a n s p o r t s e c t o r . I n d i r e c t t a x e s l e s s s u b s i d i e s a r e a l s o e x c l u d e d from s e c t o r o u t p u t s . They a r e i n c l u d e d as p r i m a r y i n p u t s i n the v a l u e added row. Im p o r t s a r e shown as a p r o d u c t i v e s e c t o r - i n d u s t r y 80. S i n c e i m p o r t s a r e a c t u a l l y a p r i m a r y i n p u t , i n d u s t r y 80 has o u t p u t s t o a l l o t h e r s e c t o r s and f i n a l demand, but no i n p u t s from o t h e r s e c t o r s . The o u t p u t o f the i m p o r t i n d u s t r y i s an a g g r e g a t i o n o f c o m p e t i t i v e and n o n - c o m p e t i t i v e i m p o r t s which a r e t r e a t e d i n d i f f e r e n t ways. N o n - c o m p e t i t i v e i m p o r t s a r e shown as i n p u t s t o u s i n g I n d u s t r i e s and f i n a l demand. No breakdown by o r i g i n a t i n g i n d u s t r y i s p u b l i s h e d so the i n p u t o f n o n - c o m p e t i t i v e i m p o r t s i n t o any i n d u s t r y w i l l t y p i c a l l y be an a g g r e g a t i o n of i m p o r t s from s e v e r a l , u n i d e n t i f i e d f o r e i g n i n d u s t r i e s . C o m p e t i t i v e i m p o r t s a r e a l l o c a t e d a c c o r d i n g t o Model I I i n C h a p t e r I I I . They a r e t r a n s f e r r e d t o i m p o r t - c o m p e t i n g , I n d u s t r i e s and t h e r e a r e no i n p u t s o f c o m p e t i t i v e i m p o r t s r o u t e d d i r e c t l y t o f i n a l demand. T h i s means t h a t the t y p i c a l a c t i v i t y l e v e l , , d e s c r i b e s the t o t a l s u p p l y o f o u t p u t i I n the U n i t e d S t a t e s . S i m i l a r l y , the p r o d u c t i o n c o e f f i c i e n t s A i n m a t r i x A = [A ] d e s c r i b e the d i r e c t r e q u i r e m e n t s o f - 53 -d o m e s t i c and i m p o r t e d p r o d u c t i p e r u n i t of t o t a l s u p p l y o f p r o d u c t j . To emphasize t h i s the U n i t e d S t a t e s i n p u t - o u t p u t e q u a t i o n s w i l l he r e w r i t t e n u s i n g the n o t a t i o n f o r t o t a l s u p p l y I n t r o d u c e d i n C h a p t e r I I I . Thus, the system i s w r i t t e n X = ( I - A) F . (b) The Canadian I n p u t - O u t p u t T a b l e s The b a s i c s o u r c e f o r i n f o r m a t i o n on the n a t u r e o f the Canadian i n p u t - o u t p u t t a b l e s i s Dominion Bureau o f S t a t i s t i c s p u b l i c a t i o n number 13-513, Supplement t o the I n t e r - i n d u s t r y Flow  of Goods and S e r v i c e s , Canada 1949. I t c o n t a i n s , u s i n g 1949 d a t a : ( i ) a t r a n s a c t i o n s t a b l e i n t e g r a t e d w i t h the , N a t i o n a l A c c o u n t s , ( i i ) a d i r e c t r e q u i r e m e n t s m a t r i x , ( i i i ) an I n v e r s e o r t o t a l r e q u i r e m e n t s m a t r i x , and ( i v ) a t a b l e d e f i n i n g the p r o d u c i n g s e c t o r s i n terms o f the codes found i n the 1948 e d i t i o n o f the Canadian S t a n d a r d I n d u s t r i a l C l a s s i f i c a t i o n Manual. F o r t y - t w o s e c t o r s a r e d e f i n e d i n the Canadian t a b l e s . As i n the U n i t e d S t a t e s t a b l e s , a l l f l o w s a r e e x p r e s s e d i n p r o d u c e r s ' p r i c e s . An updated i n v e r s e and i m p o r t r e q u i r e m e n t s m a t r i x a r e a l s o a v a i l a b l e . They were p r e p a r e d by T. I . M a t u s z e w s k i , P. R. P i t t s , p and J . A. Sawyer f o r the C a r t e r R o y a l Commission on T a x a t i o n . 2. A copy o f t h e s e updated m a t r i c e s , on IBM punch c a r d s , was s u p p l i e d by Dr. G. R o s e n b l u t h . - 54 -The method o f u p d a t i n g i n v o l v e d a c o m b i n a t i o n o f the two approaches suggested i n s e c t i o n 2.b o f Ch a p t e r I I . I t i s e l a b o r a t e d I n Appendix C. The updated i n v e r s e m a t r i x a p p l i e s t o the y e a r 1959- The i m p o r t r e q u i r e m e n t s m a t r i x i s a p r o d u c t o f the updated i n v e r s e and an i m p o r t c o e f f i c i e n t s m a t r i x , m , wh i c h i s updated t o 1 9 5 6 . 3 ( c ) Canadian E x p o r t s t o the U n i t e d S t a t e s , 1958 The p r i n c i p a l s o u r c e s o f i n f o r m a t i o n on Canadian e x p o r t s t o the U n i t e d S t a t e s were Trade o f Canada volumes I and I I , p u b l i s h e d a n n u a l l y by the Dominion Bureau o f S t a t i s t i c s , ( p u b l i c a t i o n number 6 5 - 2 0 2 ) . A l s o used was The Canadian  B a l a n c e o f I n t e r n a t i o n a l Payments (Dominion Bureau o f S t a t i s t i c s p u b l i c a t i o n number 6 7 - 2 0 1 ) . E x p o r t s a r e l i s t e d i n commodity groups i n f a i r d e t a i l i n Trade o f Canada, volume I , and i n much g r e a t e r d e t a i l i n volume I I . 2. A p p l i c a t i o n o f the Model t o the Canadian and U n i t e d S t a t e s Data The s t a t i s t i c a l a p p l i c a t i o n o f the model i n v o l v e s the s e l e c t i o n o f a base y e a r and the d e r i v a t i o n o f the t r a d e c o e f f i -c i e n t s , J . , i n terms o f the r e s t o f the d a t a . 3. The i m p o r t c o e f f i c i e n t s m a t r i x f o l l o w s Model I i n a l l o c a t -i n g a l l i m p o r t s t o u s i n g i n d u s t r i e s . - 55 -An i n p u t - o u t p u t model p r o v i d e s an a c c u r a t e d e s c r i p t i o n of the r e l a t i o n between i n d u s t r y o u t p u t s and f i n a l demand o n l y i n the p e r i o d f o r which the p r o d u c t i o n c o e f f i c i e n t s a r e e s t i m a t e d . F o r t h i s r e a s o n i t i s i m p o r t a n t t h a t the i n p u t - o u t p u t systems used t o r e p r e s e n t the Canadian and American t e c h n o l o g i e s s h o u l d a p p l y t o y e a r s as c l o s e t o g e t h e r as p o s s i b l e . F o r t h i s a p p l i -c a t i o n , 1958 was chosen as the base y e a r , and the u p d a t e d Canadian p r o d u c t i o n c o e f f i c i e n t s (base y e a r 1959) were assumed t o d e s c r i b e Canadian t e c h n o l o g y i n 1958. The f i r s t and most i m p o r t a n t s t e p i n d e r i v i n g the t r a d e c o e f f i c i e n t s was t o d e c i d e how U n i t e d S t a t e s i m p o r t s from Canada sho u l d be r e l a t e d t o U n i t e d S t a t e s a c t i v i t y l e v e l s . I t was assumed t h a t a l l Canadian e x p o r t s a r e s u b s t i t u t a b l e f o r American d o m e s t i c o u t p u t s . A c c o r d i n g l y , the l e v e l o f e x p o r t s o f each commodity was r e l a t e d t o the t o t a l s u p p l y , X , o f the e q u i v -a l e n t o u t p u t i n the U n i t e d S t a t e s . T h i s method was chosen by r e a s o n o f i t s s i m p l i c i t y , and because the s i m i l a r i t y o f geography and t e c h n o l o g y i n the two c o u n t r i e s makes the assump-t i o n o f s u b s t i t u t a b l e o u t p u t s p l a u s i b l e . A f i n a l p roblem i n the a p p l i c a t i o n o f the model was posed by the u n i t s i n which the Canadian commodity f l o w s were e x p r e s s e d . The Canadian o u t p u t r e q u i r e m e n t s i n the updated i n v e r s e m a t r i x were e x p r e s s e d i n d o l l a r ' s w orths a t 1949 p r i c e s . I n c o n t r a s t , the e x p o r t s t o the U n i t e d S t a t e s used t o d e r i v e the were v a l u e d a t 1958 p r i c e s . Two methods were a v a i l a b l e by w h i c h t o s t a n d a r d i z e t h e s e u n i t s ; the i n v e r s e c o e f f i c i e n t s c o u l d be a d j u s t e d so t h a t t h e y would be e x p r e s s e d i n 1958 d o l l a r ' s w o r t h s , - 56 -o r the e x p o r t v a l u e s c o u l d be d e f l a t e d t o 1949 p r i c e s . The second method was chosen because i t was f e l t t h a t e x p o r t p r i c e r e l a t i v e s would be more a c c u r a t e than d o m e s t i c p r i c e r e l a t i v e s . Domestic p r i c e l e v e l s t e n d t o be ob s c u r e d by i n t r a - f i r m t r a n s f e r s o f i n t e r m e d i a t e p r o d u c t s a t non-market p r i c e s . I n the l i g h t o f these d e c i s i o n s , Canadian e x p o r t s may be r e p r e s e n t e d as f u n c t i o n s o f U n i t e d S t a t e s a c t i v i t y l e v e l s by e, = § 2 J , , X . ( 1 = 1 , . . . , 4 2 ) (5.1) j = l 1 J J where J = the amount o f Canadian output 1 , i n 1949 i J Canadian d o l l a r s ' w o r t h s , t h a t i s i n c l u d e d i n a 1958 U n i t e d S t a t e s d o l l a r s ' w o r t h o f the t o t a l s u p p l y o f U n i t e d S t a t e s o u t p u t j . The J a r e assumed t o be c o n s t a n t over changes i n the A X and ov e r changes i n the r a t e o f exchange o f Canadian and U n i t e d S t a t e s d o l l a r s . The l a t t e r a s s u m p t i o n i s o f p a r t i c u l a r i m p o r t a n c e i f , as i n t h i s p a p e r , the a n a l y s i s i s extended beyond the base y e a r of the model. The J a r e d e f i n e d i n terms of 13 p h y s i c a l f l o w s ( o r d o l l a r s ' w o r t h s a t base y e a r p r i c e s ) so th e y a r e not d i r e c t l y a f f e c t e d by a c h a n g i n g exchange r a t e . x However, I t i s q u i t e p o s s i b l e t h a t a change i n exchange r a t e would p r e c i p a t e changes i n the p h y s i c a l c o e f f i c i e n t s . An example might be s h i f t s i n t h e p r o p o r t i o n o f the t o t a l s u p p l y o f a p r o d u c t a c c o u n t e d f o r by i m p o r t s . T h i s p o s s i b i l i t y i s n e g l e c t e d i n the model. - 57 -3. E s t i m a t i o n o f the Parameters and S o l u t i o n of the Model The p r o c e d u r e f o l l o w e d i n e s t i m a t i n g the J and o b t a i n i n g s o l u t i o n s o f the model may be d i v i d e d i n t o f o u r s t e p s . F i r s t , the l i s t o f 1958 Canadian e x p o r t s t o the U n i t e d S t a t e s was c l a s s i f i e d a c c o r d i n g t o b o t h the Canadian and U n i t e d S t a t e s i n d u s t r y schemes. The aim was t o produce an a r r a y o f ele m e n t s , , where T. • = the q u a n t i t y of 1958 Canadian e x p o r t s t o the U n i t e d 1* } S t a t e s t h a t b e l ongs a s o u t p u t s t o b o t h the i t h Canadian and j ^ h American s e c t o r s . They a r e e x p r e s s e d i n Canadian d o l l a r ' s worths a t 1958 p r i c e The method o f c l a s s i f i c a t i o n i s d i s c u s s e d f u l l y i n Appendix B. B r i e f l y i t i n v o l v e d m a t c h i n g the d e s c r i p t i o n s of commodity groups o f e x p o r t s w i t h the coded d e s c r i p t i o n s i n the Sta n d a r d I n d u s t r i a l C l a s s i f i c a t i o n - M a n u a l o f each c o u n t r y . The coded e x p o r t s were then a l l o c a t e d t o p a i r s o f i n d u s t r i e s u s i n g the c l a s s i f i c a t i o n t a b l e s p r o v i d e d i n each s e t o f i n p u t - o u t p u t d a t a By a g g r e g a t i n g the e x p o r t s a l l o c a t e d t o each p a i r o f i n d u s t r i e s l i -the a r r a y o f T ^ j was produced 4. From the T- • , the v e c t o r o f 1958 e x p o r t s ( i n 1958 Canadian d o l l a r s ) c o n f o r m i n g t o e i t h e r c l a s s i f i c a t i o n i s e a s i l y o b t a i n e d . C l a s s i f i e d a c c o r d i n g t o the Canadian 82 scheme, the e x p o r t s a r e e. = £ T., ( j = 1,...,42) . 1 j - 1 1 J and a c c o r d i n g t o the U n i t e d S t a t e s scheme - 4 2 ej = T±i U = 1,....,82). V e c t o r s e = [eL] and e = [e.] , and the non-zero f . . a r e shown i n Appendix B. - 58 -Second, c o e f f i c i e n t s t were o b t a i n e d from '13 ' i j £ ( i = 1,...,42; j = 1 , . . . , 8 2 ) Now Canadian e x p o r t s v a l u e d a t 1958 p r i c e s c o u l d be e x p r e s s e d i n terms o f U n i t e d S t a t e s a c t i v i t y l e v e l s by 82 A ' . ' • e = E t . . X. ( i = 1 , . ..,42) 3=1 1 0 3 o r i n m a t r i x form by e = TX where T = [ t ] . (5.2) '. The t h i r d s t e p was t o e x p r e s s the v e c t o r o f e x p o r t s , e , i n terms o f 1949 p r i c e s . A d i a g o n a l m a t r i x , p , o f e l e m e n t s , , was e s t i m a t e d w i t h 5 p = the e x p o r t p r i c e o f Canadian o u t p u t I i n 1949 . . 1 the e x p o r t p r i c e o f Canadian o u t p u t I i n 195^ The v e c t o r o f Canadian e x p o r t s a t 1949 p r i c e s , e , c o u l d t h e r e f o r e be found by e = p e (5*3) Moreover, combining ( 5 . 2 ) and ( 5 . 3 ) y i e l d s e = pT$ so the t r a d e m a t r i x J was o b t a i n e d by e s t i m a t i n g s e p a r a t e l y the p arameters o f p and T . The f i n a l s t e p i n a p p l y i n g the model was t o o b t a i n s o l u t i o n v e c t o r s o f Canadian o u t p u t s and i m p o r t s f o r p o s u l t a t e d v e c t o r s o f U n i t e d S t a t e s f i n a l demand. The c a l c u l a t i o n s were made w i t h 5. The e s t i m a t i o n o f t h e s e e x p o r t p r i c e r e l a t i v e s i s d e s c r i b e d i n Appendix D. - 59 -the IBM 7040 computer a t the U n i v e r s i t y o f B r i t i s h Columbia Computing C e n t r e . The r e l a t i v e l y s i m p l e c a l c u l a t i o n s 82 A e. = p. t . . X . were w r i t t e n i n t o the programme so t h a t . i t would be u n n e c e s s a r y f o r the e n t i r e p and T m a t r i c e s t o be s t o r e d i n the computer. To c a l c u l a t e the Canadian i m p o r t s g e n e r a t e d by the p o s t u l a t e d v e c t o r s of U n i t e d S t a t e s f i n a l demand, the Canadian i n v e r s e m a t r i x was r e p l a c e d by the im p o r t — • -1 r e q u i r e m e n t s m a t r i x , m(I - a) - 60 -CHAPTER V I THE IMPACT OF UNITED STATES PINAL DEMAND  ON CANADIAN PRODUCTION AND TRADE The model de v e l o p e d i n Ch a p t e r I V i s used t o i n v e s t i g a t e the impact on the Canadian economy o f changes i n the l e v e l and p a t t e r n o f U n i t e d S t a t e s f i n a l demand. Of p r i m a r y i n t e r e s t i s the e f f e c t on C a n a d i a n • f i n a l demand and the out p u t o f . Canadian i n d u s t r i e s , h u t the e f f e c t on Canada's b a l a n c e o f merchandise t r a d e i s a l s o examined. The i n v e s t i g a t i o n i s p r e s e n t e d i n two p a r t s . The f i r s t p a r t compares the e f f e c t s o f a b i l l i o n d o l l a r s w o r t h o f each o f the major components o f U n i t e d S t a t e s f i n a l demand. An att e m p t i s made t o i s o l a t e the f a c t o r s c h i e f l y r e s p o n s i b l e f o r the d i f f e r e n c e s i n the l e v e l s o f Canadian o u t p u t and . Imports g e n e r a t e d . The second p a r t examines t h e e f f e c t o f c y c l i c a l changes i n U n i t e d S t a t e s f i n a l demand on the growth of Canadian f i n a l demand and o u t p u t , and on the b a l a n c e o f merchandise t r a d e . 1. Comparison of the E f f e c t s o f One B i l l i o n D o l l a r I n c r e a s e s  i n U n i t e d S t a t e s F i n a l Demand '. Ta b l e X I I I i n Appendix A p r e s e n t s v e c t o r s r e p r e s e n t i n g a b i l l i o n d o l l a r s w o r t h of each o f • t h e f o u r major components of U n i t e d S t a t e s f i n a l demand: P e r s o n a l consumption e x p e n d i t u r e , C , Gross p r i v a t e f i x e d c a p i t a l f o r m a t i o n . ( I n v e s t m e n t ) , I , F e d e r a l Government e x p e n d i t u r e , G , and S t a t e and l o c a l g o v e r n -- 61 -ment expenditure, G It should be observed that not a l l of • S the b i l l i o n d o l l a r s applies to the eighty-two producing sectors. This i s p a r t i c u l a r l y evident i n the vectors of government expenditure where the payments of wages and s a l a r i e s to govern-ment exployees i s important. Tables XIV, XV, XVI, and XVII i n Appendix A exhibit the vectors of United States output, and Canadian exports, output, and imports that are generated by the one b i l l i o n d o l l a r f i n a l expenditures. The sum of the elements, or aggregate, of each of these vectors i s shown i n Table I I I below. TABLE I I I COMPARISON OF THE AGGREGATE EFFECTS OF INCREASES  IN FOUR COMPONENTS OF UNITED STATES FINAL' DEMAND, 1958 Increase i n : C I G G _F _S ( m i l l i o n s of d o l l a r s ) United States f i n a l demand3 1000.00 1000.00 1000.00 1000.00 United States output 3 1933.19 2281.27 1384.92 1142.57 Canadian exports* 3 4 .18 8.55 4.29 4 .09 Canadian output 7.69 15.37 7 .60 7 .25 Canadian Imports .37 .87 .44 .36 a. United States d o l l a r s ; 1958 prices b. Canadian d o l l a r s ; 1949 p r i c e s . - 62 -Two i n t e r e s t i n g o b s e r v a t i o n s may be made from these r e s u l t s . F i r s t , Canadian demand and o u t p u t a r e s t i m u l a t e d t o a much g r e a t e r degree by U n i t e d S t a t e s Investment e x p e n d i t u r e than by any o f the o t h e r e x p e n d i t u r e s . Second, the r a t i o s between the agg r e g a t e v a l u e s o f i n d u c e d Canadian e x p o r t s ( o r o u t p u t ) and induced U n i t e d S t a t e s o u t p u t v a r y c o n s i d e r a b l y . I n p a r t i c u l a r , a d o l l a r s ' w o r t h o f U n i t e d S t a t e s o u t p u t g e n e r a t e d by an i n c r e a s e i n P e r s o n a l consumption e x p e n d i t u r e r e q u i r e s a r e l a t i v e l y s m a l l i n c r e a s e i n Canadian e x p o r t s and o u t p u t . B o t h t h e s e o b s e r v a t i o n s s u g g e s t t h a t the i n d u s t r y compos-i t i o n o f i n d u c e d U n i t e d S t a t e s o u t p u t i s i m p o r t a n t i n d e t e r m i n -i n g the e x t e n t t o w h i c h Canadian o u t p u t i s s t i m u l a t e d . The r e a s o n f o r t h i s may be i n v e s t i g a t e d b y - o b s e r v i n g the impact o f the I n c r e a s e s i n U n i t e d S t a t e s f i n a l demand on p a r t i c u l a r C anadian i n d u s t r i e s . T a b l e I V shows the p e r c e n t o f t o t a l i n d uced Canadian o u t -put t h a t i s acc o u n t e d f o r by the f i v e , and t e n , most a f f e c t e d I n d u s t r i e s . I n s i m i l a r f a s h i o n , the i n d u s t r y c o n c e n t r a t i o n o f e x p o r t s i s shown. - 63 -TABLE IV THE CONCENTRATION OP INDUCED OUTPUT AND  1958 EXPORTS AMONG CANADIAN INDUSTRIES. P e r c e n t of T o t a l Accounted f o r by: Top F i v e I n d u s t r i e s Top Ten I n d u s t r i e s Canadian Output Generated by U.S. F i n a l Demand Component: C 53.4 74.5 I 56.3 75.7 G P 57.4 77 .6 'V 6 0 . 8 7 9 . 2 C a n a d i a n E x p o r t s , 1958 72.5 8 6 . 8 I t i s ap p a r e n t from t h e s e f i g u r e s t h a t the o u t p u t g e n e r a t e d by each type of U n i t e d S t a t e s f i n a l e x p e n d i t u r e i s c o n c e n t r a t e d on a r e l a t i v e l y s m a l l number of Canadian i n d u s t r i e s . The top f i v e o f the f o r t y - t w o i n d u s t r i e s produce between f i f t y and s i x t y p e r c e n t o f the t o t a l i n d u c e d Canadian o u t p u t s , the top t e n between s e v e n t y - f i v e and e i g h t y p e r c e n t . The e x p l a n -a t i o n may be found i n the c o n c e n t r a t i o n o f e x p o r t s on a few p r o d u c t s , f o r i t i s even g r e a t e r . I n T a b l e V the i n d u s t r i e s w i t h h i g h induced o u t p u t s and h i g h 1958 e x p o r t s a r e i d e n t i f i e d . From t h i s t a b l e i t may be observed t h a t , d e s p i t e the d i s s i m i l a r i t y of the U n i t e d S t a t e s - 6 4 -f i n a l demand v e c t o r s , the same few e x p o r t i n d u s t r i e s a r e the ones most s t r o n g l y stimulated." 1" . Moreover, they a r e not the same i n d u s t r i e s t h a t a r e s t i m u l a t e d most by o v e r - a l l Canadian f i n a l demand. I n the 1949 Canadian i n t e r i n d u s t r y s t u d y f o r example, f i v e o f the top t e n i n d u s t r i e s ranked by v a l u e o f out-put a r e not common t o any o f the r a n k i n g s i n T a b l e V. The top t e n a r e : T r a n s p o r t a t i o n , s t o r a g e and t r a d e ( 3 8 ) , S e r v i c e i n d u s t r i e s ( 4 2 ) , C o n s t r u c t i o n ( 3 7 ) , A g r i c u l t u r e ( l ) , F i n a n c e , i n s u r a n c e and r e a l e s t a t e ( 4 1 ) , T r a n s p o r t a t i o n equipment ( 2 9 ) , Paper p r o d u c t s ( 2 4 ) , I r o n and s t e e l p r o d u c t s , n.e.s. ( 2 8 ) , C l o t h i n g ( t e x t i l e and f u r ) ( 2 1 ) , and Meat p r o d u c t s ( 7 ) . C o n s i d e r a t i o n of the i n d u c e d o u t p u t s In p a r t i c u l a r Canadian i n d u s t r i e s l e a d s t o the c o n c l u s i o n t h a t the e f f e c t o f an I n c r e a s e i n U n i t e d S t a t e s f i n a l demand on Canadian agg r e g a t e o u t p u t depends l a r g e l y on the degree t o w h i c h a c e r t a i n few e x p o r t I n d u s t r i e s are s t i m u l a t e d . A t the same t i m e , I t e x p l a i n s why the l e v e l o f a g g r e g a t e Induced Canadian output s h o u l d be so s e n s i t i v e t o the p a t t e r n of U n i t e d S t a t e s o u t p u t r e q u i r e m e n t s and f i n a l demands. 1. A n o t a b l e e x c e p t i o n i s the T r a n s p o r t a t i o n , s t o r a g e and t r a d e i n d u s t r y (number 3 8 ) . F o r each v e c t o r o f U n i t e d S t a t e s f i n a l demand i t i s ranked i n the top f i v e i n d u s t r i e s a c c o r d -i n g t o i n d u c e d o u t p u t ; h u t i t has no e x p o r t s . O t h e r i n d u s t r i e s w i t h h i g h induced o u t p u t s b u t low e x p o r t s a r e : F o r e s t r y ( 2 ) , I r o n and s t e e l p r o d u c t s ( 2 8 ) , E l e c t r i c power, gas and water ( 4 0 ) , and P r o d u c t s of p e t r o l e u m and c o a l ( 3 4 ) . 2. Dominion Bureau of S t a t i s t i c s , number 13-513, Supplement t o the I n t e r - I n d u s t r y Flow of Goods and S e r v i c e s , Canada, 194~9 T a b l e 1. - 65 -TABLE V OUTPUT GENERATED IN PARTICULAR CANADIAN INDUSTRIES BY ONE  BILLION DOLLAR INCREASES IN UNITED STATES FINAL DEMAND; 1958 EXPORTS TO THE UNITED STATES BY INDUSTRY (thousands o f d o l l a r s ) Rank Type o f U n i t e d S t a t e s F i n a l E x p e n d i t u r e . 1958 E x p o r t s t o the U.S. C I Industry Output Generated Ind. Out. Gen. Ind. Out. Gen. Ind. Out. Gen. Ind. Exports 1 (24) 1867 (4) 2783 (4) 213? (24) 1120 (24) 846 ,235 2 (1) 742 (23) 2016 (24) 984 (4) 1090 (4) 620,664 3 (4) 532 (24) 1682 (38) 512 (23) 1074 (23) 273,157 4 (38) 530 (38) 1084 (35) 435 (2) 617 (1) 183,284 5 (2) 440 (2) 1081 (23) 375 (38) 509 (27) 90,335 6 (5) 353 (28) 724 (29) 367 (35) 318 (3) 88,080 7 (35) 352 (27) 712 (40) 339 (33) 271 (35) 80,284 8 (40) 297 (40) 523 (2) 317 (40) 265 (33) 79,780 9 (2?) 285 (33) 516 (5) 273 (5) 264 (5) 75,744 10 (34) 236 (35) 504 (28) 265 (34) 216 (14) 68,290 Key t o I n d u s t r i e s : ( l ) A g r i c u l t u r e , (2) F o r e s t r y , ( 3 ) F i s h i n g and t r a p p i n g , (4) M e t a l m i n i n g and s m e l t i n g ana r e f i n i n g , (5) C o a l , crude p e t r o l e u m and n a t u r a l gas, (14) A l c o h o l i c b e v e r a g e s , (23) Wood p r o d u c t s ( e x c e p t f u r n i t u r e ) , (24J Paper* p r o d u c t s , (27) A g r i c u l t u r a l implements,.(2 8 ) I r o n and s t e e l p r o d u c t s , n.e.s., (29) T r a n s p o r t a t i o n equipment, (33) N o n - m e t a l l i c m i n e r a l p r o d u c t s , (34) ' P r o d u c t s of p e t r o l e u m and c o a l , (35) C h e m i c a l s and a l l i e d p r o d u c t s , (38) T r a n s -p o r t a t i o n , s t o r a g e and t r a d e , (40) E l e c t r i c a l power, gas and v;ater. - 66 -2. The C y c l i c a l E f f e c t of U n i t e d S t a t e s F i n a l Demand on Canadian Output and the Canadian B a l a n c e of Merchandise Trade I n t h i s s e c t i o n the i n v e s t i g a t i o n i s c a r r i e d a s t e p f u r t h e r . U s i n g observed a g g r e g a t e v a l u e s o f the components of U n i t e d S t a t e s f i n a l demand f o r a p e r i o d of s e v e r a l y e a r s , the model i s used t o e s t i m a t e the a n n u a l v a l u e s of Induced Canadian e x p o r t s , i n d u c e d o u t p u t and in d u c e d net e x p o r t s ( i n d u c e d e x p o r t s l e s s i n d u c e d i m p o r t s ) . Then the an n u a l f l u c t u a t i o n s i n growth of the l a t t e r a g g r e g a t e s a re compared w i t h f l u c t u a t i o n s i n the growth o f the c o r r e s p o n d i n g Canadian a g g r e g a t e s t o de t e r m i n e whether t h e y were s t a b i l i z i n g o r d e s t a b l i z i n g o ver the p e r i o d . I f , f o r i n s t a n c e , the an n u a l growth o f in d u c e d Canadian e x p o r t s f l u c t u a t e d i n phase w i t h the growth o f t o t a l Canadian f i n a l demand, i t c o u l d be c o n c l u d e d t h a t v a r i a t i o n i n the growth o f U n i t e d S t a t e s f i n a l demand had a d e s t a b i l i z i n g e f f e c t on Canadian f i n a l demand. The a c c u r a c y of i n p u t - o u t p u t p r e d i c t i o n s has been shown t o d e c l i n e f a i r l y r a p i d l y as y e a r s d i s t a n t from the base y e a r a r e c o n s i d e r e d . F o r t h i s r e a s o n the a n a l y s i s i s l i m i t e d t o the f i v e y e a r p e r i o d 1956 t o i 9 6 0 , c e n t r e d on the base y e a r , 1958. S i n c e the a n a l y s i s c o v e r s a s h o r t span o f time and makes use o f a n n u a l f i n a l demand d a t a , i t i s c o n v e n i e n t t o d i s c u s s annual r a t h e r than s t r i c t l y c y c l i c a l f l u c t u a t i o n s . F o r t u n a t e l y the y e a r s c o n s i d e r e d were c h a r a c t e r i z e d by pronounced f l u c t u a t -i o n s i n the growth o f demand. The v a l u e s f o r 1956" t o i 9 6 0 o f the v a r i o u s components o f U n i t e d S t a t e s Gross N a t i o n a l Expend-i t u r e ( h e r e i n a f t e r GNE) are p r e s e n t e d i n Table V I . From the s e - 67 -v a l u e s , the a n n u a l growth i n GNE i s c a l c u l a t e d f o r 1957 t o i 9 6 0 . These growth r a t e s a r e shown i n T a b l e V I and p l o t t e d i n the appended f i g u r e as w e l l . • Prom the g r a p h . I t i s a p p a r e n t ' t h a t the r a t e o f growth of f i n a l demand f l u c t u a t e d over a c y c l e whose p e r i o d a l m o s t e x a c t l y c o i n c i d e d w i t h the f o u r y e a r s 1957 t o i 9 6 0 . Between m i d - p o i n t s I n the c y c l e i n 1957 and i 9 6 0 , the r a t e o f growth of f i n a l demand d e c l i n e d t o a low p o i n t I n 1958 and r o s e t o a peak i n 1959. As a r e s u l t i t i s p r o b a b l y f a i r t o I n v e s t i g a t e the c y c l i c a l b e h a v i o r o f f i n a l demand u s i n g a n n u a l v a r i a t i o n s i n i t s growth. The c y c l i c a l b e h a v i o r o f U n i t e d S t a t e s f i n a l demand r e f e r s t o v a r i a t i o n i n i t s l e v e l and i n d u s t r y c o m p o s i t i o n . The l a t t e r i s a p proximated here by c o n s i d e r i n g the v a r i a t i o n i n the r e l a t -i v e w e i g h t s of major e x p e n d i t u r e components. W i t h the e x c e p t i o n o f P e r s o n a l consumption e x p e n d i t u r e (see b e l o w ) , no v a r i a t i o n s a r e c o n s i d e r e d i n the p a t t e r n of demand w i t h i n any of the e x p e n d i t u r e c l a s s i f i c a t i o n s . T h i s means t h a t an i n c r e m e n t o f , say, F e d e r a l Government e x p e n d i t u r e i s assumed t o have the same i n d u s t r y p a t t e r n as t o t a l F e d e r a l Government expend I t u r e i n the base year,' 1958. T h i s a s s u m p t i o n a d m i t t e d l y weakans the p r e d i c t i v e power o f the model b u t s h o u l d n o t be u n t e n a b l e i f the i n c r e m e n t s c o n s i d e r e d a r e s m a l l i n r e l a t i o n t o t o t a l expend-i t u r e i n the base y e a r . T a b l e V I can be used t o compare the a n n u a l i n c r e m e n t s of the v a r i o u s f i n a l demand components t o t h e i r 1958 a g g r e g a t e v a l u e s . The c o n d i t i o n t h a t the changes be s m a l l i n r e l a t i o n t o the 1958 t o t a l s i s met f o r a l l c l a s s i f i c a t i o n s but Net i n v e n t o r y change and Net e x p o r t s . F o r these components, the a n n u a l i n c r e m e n t s a r e t y p i c a l l y d ouble or t r i p l e the 1958 t o t a l s . - 68 -TABLE VI GROWTH IN UNITED STATES FINAL DEMAND, 1956-1960 1956 1957 1953 1959 i 9 6 0 ( b i l l i o n s of d o l l a r s ; 1958 p r i c e s ) P e r s o n a l Consumption E x p e n d i t u r e - d u r a b l e s 41 . 0 41.5 37.9 4 3 . 7 4 4 . 9 - n o n - d u r a b l e s 1 3 6 . 2 1 3 8 . 7 140 .2 146.9 149.7 - s e r v i c e s 104 . 1 1 0 3 . 0 112 . 0 1 1 6 . 3 1 2 1 . 6 T o t a l P e r s o n a l Consumption Exp. 231 .4 238. ? 290.1 3 0 7 . 3 3 1 6 . 2 Gross P r i v a t e F i x e d C a p i t a l Exp. 6 9 . 3 67.6 6 2 . 4 6 8 . 8 6 8 . 9 Federal Government E x p e n d i t u r e 4 9 . 7 5 1 . 7 5 3 . 6 5 2 . 5 51 . 4 State and Local Government Exp. 3 5 . 6 3 7 . 6 4 0 . 6 42.2 43.5 SUBTOTAL: (F = C+I+G^+G,,) F — 5 — 4 3 6 . 2 4 4 5 . 1 446 . 7 4 7 0 . 8 4 8 0 . 0 Net I n v e n t o r y Change 4 . 3 1 .2 -1.5 4 . 8 3 . 5 Net E x p o r t s 5 . 0 6 . 2 2 . 2 0 . 3 4 . 3 Gross N a t i o n a l E x p e n d i t u r e (GNE) 4 4 5 . 1 452.5 4 4 7 . 3 4 7 5 . 9 437.3 Annual Growth i n GNE 6,4 - 5 . 2 2 8 . 6 1 1 . 9 Annual Growth, i n F 8 . 9 1 .6 24 . 1 9 . 2 , A n n u a l Growth ( b i l l i o n s ) GNE F (=C+I+G p +G s) 1957 1958 1959 I960 S o u r c e : Survey o f C u r r e n t B u s i n e s s , August, 1965, p.27. N o t e : F i g u r e s do not alwa y s add t o t o t a l s due t o r o u n d i n g . I t would not be r e a s o n a b l e t o assume t h a t the 1958 i n d u s t r y p a t t e r n s o f the e x p e n d i t u r e would be good e s t i m a t o r s o f the impact on i n d u s t r y o u t p u t s o f the changes i n t h e i r l e v e l s . T h e r e f o r e , t h e s e components o f U n i t e d S t a t e s GNE a r e o m i t t e d •3 from c o n s i d e r a t i o n . F o r the p u r p o s e s of t h i s i n v e s t i g a t i o n , U n i t e d S t a t e s f i n a l demand i s d e f i n e d as the sum o f P e r s o n a l consumption e x p e n d i t u r e , Gross p r i v a t e f i x e d c a p i t a l f o r m -a t i o n , F e d e r a l Government e x p e n d i t u r e , and S t a t e and l o c a l government e x p e n d i t u r e , ( i . e . , F = C+I+G +G ) The r e s u l t o f n e g l e c t i n g Net i n v e n t o r y change and Net e x p o r t s i s t o s i g n i f i c a n t l y u n d e r s t a t e the c y c l i c a l f l u c t u a t i o n of U n i t e d S t a t e s a g g r e g a t e demand. The growth o f f i n a l demand w i t h and w i t h o u t t h e s e components i s compared i n T a b l e V I and the appended c h a r t . The a n n u a l f l u c t u a t i o n i n growth r a t e i s more pronounced f o r GNE tha n f o r f i n a l demand, F , a t b o t h the t r o u g h and peak o f the c y c l e . The average change i n an n u a l growth r a t e , ^ A , i s used as a measure o f the a m p l i t u d e o f each o f the f l u c t u a t i o n s . Comparing the degree o r a m p l i t u d e of the v a r i a t i o n s i n t h i s way shows t h a t u s i n g F i n s t e a d o f 3. There i s a n o t h e r argument f o r n e g l e c t i n g Net e x p o r t s . I t I s composed t o a l a r g e e x t e n t of e x p o r t s t o Canada w h i c h , depend on Canadian a c t i v i t y l e v e l s , the s o l u t i o n v a r i a b l e s o f the model. 4. The average change i n a n n u a l growth r a t e , A , i s an average of t he d e c l i n e s i n a n n u a l growth i n 1957-1958 and 1959-I96O and the i n c r e a s e i n a n n u a l growth i n 1958-1959, summed w i t h -out r e s p e c t t o s i g n . F o r GNE, A = l ( - 5 . 2 ) - 6 . 4 1 + I28.6 - ( - 5 . 2 )1 + 1 1 1 . 9 - 28.6| = 20.7 b i l l i o n d o l l a r s . I t i s used t o measure a m p l i t u d e here because i t does not r e q u i r e the d e f i n i t i o n o f a t r e n d i n the r a t e o f growth. - 70 -GNE u n d e r s t a t e s the c y c l i c a l f l u c t u a t i o n i n U n i t e d S t a t e s f i n a l demand by a p p r o x i m a t e l y t h i r t y - e i g h t p e r c e n t . (A = $20.7 b i l l i o n f o r GNE and $14 .9 b i l l i o n f o r F) O b v i o u s l y , the impact of the c y c l i c a l v a r i a t i o n i n U n i t e d S t a t e s b u s i n e s s c o n d i t i o n s on the Canadian economy w i l l a l s o be s i g n i f i c a n t l y u n d e r e s t i m a t e d . On the o t h e r hand, an improvement i n the a b i l i t y o f the model t o r e f l e c t the c y c l i c a l b e h a v i o r o f U n i t e d S t a t e s f i n a l demand i s o b t a i n e d by u s i n g t h r e e s u b - c l a s s i f i c a t i o n s o f P e r s o n a l consumption e x p e n d i t u r e s . The s u b - c l a s s e s a r e e x p e n d i t u r e on: d u r a b l e s , n o n - d u r a b l e s , and s e r v i c e s . I t i s p o s s i b l e t o s e p a r a t e P e r s o n a l consumption e x p e n d i t u r e s i n t o t h e s e t h r e e t y p e s because i n d u s t r y d i s s a g g r e g a t i o n s a r e a v a i l -a b l e f o r them t h a t conform t o the s e c t o r d e f i n i t i o n s o f the 5 U n i t e d S t a t e s i n p u t - o u t p u t m a t r i c e s . U n f o r t u n a t e l y no such d i s s a g g r e g a t i o n s a re p u b l i s h e d f o r the major components o f Investment o r government e x p e n d i t u r e s . I n T a b l e V I I , the aggre g a t e e f f e c t s on Canadian e x p o r t s , o u t p u t , and Imports o f e x p e n d i t u r e s o f one b i l l i o n d o l l a r s on each o f the t h r e e t y p e s o f consumption a r e compared t o the c o r r e s p o n d i n g e f f e c t s f o r 1958 t o t a l P e r s o n a l consumption e x p e n d i t u r e . 5. Survey o f C u r r e n t B u s i n e s s , October 1965, P'13, T a b l e 3. - 71 -TABLE V I I COMPARISON OF AGGREGATE EFFECTS OF ONE BILLION DOLLAR  INCREASES IN TYPES OF UNITED STATES PERSONAL CONSUMPTION EXPENDITURE . 1958 D u r a b l e s N o n - d u r a b l e s S e r v i c e s T o t a l I n c r e a s e i n ( m i l l i o n s o f d o l l a r s ) U n i t e d S t a t e s P e r s o n a l Consumption E x p e n d i t u r e 3 - 1 , 0 0 0 . 0 0 1 ,000.00 1 ,000.00 1 ,000.00 Canadian E x p o r t s 1 3 5.68 5.63 I . 8 5 4.18 Canadian Output 1 3 1 0 . 2 8 10.44 3-38 7.69 Canadian I m p o r t s 1 3 .57 .49 .16 .37-a. U n i t e d S t a t e s d o l l a r s ; 1958 p r i c e s . b. Canadian d o l l a r s ; 1949 p r i c e s . I t was a p p a r e n t from the r e s u l t s o f s e c t i o n 1 o f t h i s c h a p t e r t h a t the c y c l i c a l impact o f s h i f t s i n the c o m p o s i t i o n o f U n i t e d S t a t e s f i n a l demand w i l l depend t o a g r e a t e x t e n t on s h i f t s between Investment and any of the o t h e r t h r e e c a t e -g o r i e s o f e x p e n d i t u r e . These r e s u l t s show t h a t a s t r o n g c y c l i c a l e f f e c t might a l s o a r i s e from s h i f t s between p u r c h a s e s o f s e r v i c e s and m a t e r i a l s , w i t h i n the P e r s o n a l consumption c a t e -g o r y o f demand. W i t h t h i s b ackground, f o u r q u e s t i o n s w i l l be i n v e s t i g a t e d : ( a ) How d i d s h i f t s i n the l e v e l and c o m p o s i t i o n o f U n i t e d S t a t e s f i n a l demand compare i n t h e i r e f f e c t s on the - 72 -l e v e l o f in d u c e d Canadian demand? (b) D id v a r i a t i o n s I n i n d u c e d Canadian demand a g g r e v a t e or dampen Canadian b u s i n e s s c y c l e s ? ( c ) What e f f e c t s d i d the f l u c t u a t i o n s i n U n i t e d S t a t e s f i n a l demand have on the growth o f output i n p a r t i c u l a r Canadian i n d u s t r i e s ? (d) D id v a r i a t i o n s i n i n d u c e d n et e x p o r t s a g g r a v a t e o r dampen f l u c t u a t i o n s i n Canadian n et e x p o r t s ? a • The r e l a t i v e e f f e c t on Canadian demand o f c y c l i c a l s h i f t s i n the l e v e l and c o m p o s i t i o n o f U n i t e d S t a t e s f i n a l demand. To i s o l a t e the e f f e c t o f c y c l i c a l v a r i a t i o n i n the p a t t e r n o f U n i t e d S t a t e s demand, i t i s o n l y n e c e s s a r y t o compare the f l u c t u a t i o n s i n the growth r a t e o f i n d u c e d Canadian f i n a l demand w i t h the f l u c t u a t i o n s i n t h e growth o f U n i t e d S t a t e s demand. I f the i n d u s t r y c o m p o s i t i o n o f U n i t e d S t a t e s demand were unchanged o v e r the p e r i o d , the p a t t e r n and a m p l i t u d e o f the v a r i a t i o n s i n the two growth r a t e s would be i d e n t i c a l . I n o r d e r t o compare changes i n v a r i a b l e s t h a t a r e e x p r e s s e d i n d i f f e r e n t u n i t s , the changes a r e f i r s t e x p r e s s e d as p e r c e n t a g e s . T a b l e V I I I shows the v a l u e s o f U n i t e d S t a t e s f i n a l demand and in d u c e d Canadian e x p o r t s f o r 1956 t o i 9 6 0 , and the a n n u a l p e r c e n t a g e growth i n these two v a r i a b l e s f o r 1957 t o i 9 6 0 . I n the appended c h a r t , the f l u c t u a t i o n s i n growth r a t e s a r e compared g r a p h i c a l l y . I t i s i m m e d i a t e l y a p p a r e n t t h a t the p e r c e n t a g e growth r a t e of in d u c e d Canadian e x p o r t s v a r i e d more w i d e l y t h a n t h a t o f U n i t e d S t a t e s f i n a l demand. V a r i a t i o n i n t h e c o m p o s i t i o n o f U n i t e d S t a t e s a g g r e g a t e demand t h e r e f o r e - 73 " T A B L E V I I I C O M P A R I S O N O F A N N U A L G R O W T H R A T E S : U N I T E D S T A T E S F I N A L D E M A N D A N D I N D U C E D C A N A D I A N E X P O R T S 1956 1957 1958 1959 I960 U n i t e d S t a t e s F i n a l Demand ( F ) a 436.2 445.1 446.7 470.8 480.0 Induced Canadian E x p o r t s * 3 2145 2171 2142 2277 2309 Growth i n U n i t e d S t a t e s F i n a l Demand {%) Growth i n Induced Canadian E x p o r t s {%) 2.04 1.22 .36 -.74 5.40 6.30 1.95 1.41 a. B i l l i o n s o f U n i t e d S t a t e s d o l l a r s ; 1958 p r i c e s . b. m i l l i o n s o f Canadian d o l l a r s ; 1949 p r i c e s . Annual Growth U.S. F i n a l Demand (F) Induced Canadian E x p o r t s 1957 1958 1959 " i 9 6 0 - ih -r e i n f o r c e d the e f f e c t s o f v a r i a t i o n s i n i t s l e v e l . C a l c u l a t i n g the average change i n a n n u a l g r o w t h , A , f o r b o t h v a r i a b l e s y i e l d s 3 .38$ f o r U n i t e d S t a t e s f i n a l demand and 4 .63$ f o r induced e x p o r t s . I n o t h e r words, v a r i a t i o n i n the l e v e l o f U n i t e d S t a t e s demand e x p l a i n e d s e v e n t y - t h r e e p e r c e n t , and v a r i a t i o n i n i t s c o m p o s i t i o n t w e n t y - s e v e n p e r c e n t , o f the a m p l i t u d e o f f l u c t u a t i o n s I n in d u c e d Canadian e x p o r t s . Induced e x p o r t s , and t h e i r a n n u a l growth r a t e s , were a l s o c a l c u l a t e d u s i n g the i n d u s t r y p a t t e r n o f t o t a l P e r s o n a l con-sumption e x p e n d i t u r e s i n s t e a d o f the p a t t e r n s o f e x p e n d i t u r e s on d u r a b l e s , n o n - d u r a b l e s , and s e r v i c e s . Thus e s t i m a t e d , induced e x p o r t s v a r i e d w i t h an a m p l i t u d e o f 4 . 3 8 $ . T h i s means t h a t s h i f t s among the f o u r major components o f demand e x p l a i n e d twenty-one p e r c e n t o f the v a r i a t i o n i n the growth o f induced Canadian e x p o r t s w h i l e s i x p e r c e n t was accounted f o r by v a r i a t i o n among the t h r e e t y p e s o f P e r s o n a l consumption expend-i t u r e . b. The e f f e c t of v a r i a t i o n s i n induced Canadian e x p o r t s on  the growth o f Cana d i a n a g g r e g a t e demand.6 The ann u a l growth r a t e s o f i n d u c e d and t o t a l Canadian f i n a l demand a r e devel o p e d and compared i n Table I X and i t s appended c h a r t . The f i r s t q u e s t i o n t o be answered by t h i s 6. The q u e s t i o n of t r a n s m i s s i o n o f b u s i n e s s c y c l e s i s d i s c u s s e d I n terms o f aggre g a t e demand r a t h e r than a g g r e g a t e o u t p u t because the l a t t e r s t a t i s t i c was not r e a d i l y a v a i l a b l e and i s n o t g e n e r a l l y used i n d i s c u s s i n g economic f l u c t u a t i o n s . - 75 -comparison I s whether or not the an n u a l growth r a t e s o f the two a g g r a g a t e s v a r i e d I n phase over the f o u r y e a r s . S i n c e t h e y d i d i t may be c o n c l u d e d t h a t the f l u c t u a t i o n s i n induced e x p o r t s r e i n f o r c e d the f l u c t u a t i o n s 'in Canadian f i n a l demand. The c y c l i c a l b e h a v i o r of f i n a l demand i n the U n i t e d S t a t e s had a d e s t a b l i z i n g e f f e c t on Canadian economic growth i n the p e r i o d c o n s i d e r e d . The s t r e n g t h of t h i s d e s t a b l i z i n g e f f e c t can be e s t i m a t e d -by comparing the a m p l i t u d e , o f f l u c t u a t i o n s i n Canadian f i n a l demand - w i t h and w i t h o u t the induced e x p o r t s . The average change i n an n u a l growth, A , was 376 m i l l i o n f o r a c t u a l Canadian f i n a l demand, and 292 m i l l i o n f o r Canadian f i n a l demand l e s s i n d u ced e x p o r t s . The f l u c t u a t i o n i n Canadian e x p o r t s generated by the f l u c t u a t i o n i n the l e v e l and c o m p o s i t i o n o f U n i t e d S t a t e s f i n a l demand accounted f o r $84 m i l l i o n o r twenty-two, p e r c e n t o f the a m p l i t u d e o f the f l u c t u a t i o n i n Canadian f i n a l demand. T h i s i s q u i t e a r e m a r k a b l e c o n c l u s i o n f o r two r e a s o n s . F i r s t , the f l u c t u a t i o n i n U n i t e d S t a t e s f i n a l demand i s s u b s t a n t i a l l y under-s t a t e d . Second, averaged over the p e r i o d c o n s i d e r e d , the induced e x p o r t s a ccounted f o r o n l y n i n e p e r c e n t o f Canadian aggregate demand. c. A comparison o f the growth i n induced and t o t a l • C a n a d i a n  o u t p u t f o r s i x e x p o r t i n d u s t r i e s . The v a l i d i t y of the c o n c l u s i o n t h a t U n i t e d S t a t e s f i n a l demand had a d e s t a b l i z i n g e f f e c t on Canadian economic growth can be t e s t e d by comparing the growth p a t t e r n s o f induced and t o t a l o u t p u t f o r p a r t i c u l a r i n d u s t r i e s . S i x e x p o r t i n d u s t r i e s a re - 76 -COMPARISON OF ANNUAL GROWTH RATES: CANADIAN FINAL DEMAND WITH AND WITHOUT INDUCED EXPORTS 1956 1957 1958 1959 I960 ( m i l l i o n s o f d o l l a r s ; 1949 p r i c e s ) Induced Canadian E x p o r t s 2145 2171 2142 2277 2309 Canadian F i n a l Demand 23,811 24,117 24,397 25,342 25,849 Canadian F i n a l Demand l e s s Induced E x p o r t s 21,666 21,946 22,250 23,065 23,540 Growth i n Canadian F i n a l Demand 306 280 945 507 Growth i n Canadian F i n a l Demand l e s s Induced E x p o r t s 280 304 815 475 Annual Growth ( m i l l i o n s ) Canadian F i n a l Demand Canadian F i n a l Demand l e s s Induced E x p o r t s - 77 -c o n s i d e r e d : Paper p r o d u c t s (number 2 4 ) , Wood p r o d u c t s (23). M e t a l m i n i n g and s m e l t i n g and r e f i n i n g ( 4 ) , I r o n and s t e e l p r o d u c t s , n.e.s. (28), C h e m i c a l s and a l l i e d p r o d u c t s (35), and A g r i c u l t u r e ( l ) . The growth of induced and t o t a l o u t p u t i s c o n s i d e r e d because e s t i m a t e s of the growth of i n d u s t r y o u t p u t a r e a v a i l a b l e and because the o u t p u t induced by a d o l l a r s w o r t h o f f i n a l demand v a r i e s c o n s i d e r a b l y among i n d u s t r i e s . The v a l u e s o f in d u c e d and t o t a l o u t p u t f o r 1956 t o i960 a r e shown i n T a b l e X. A l s o shown I s the a n n u a l growth i n output w i t h and w i t h o u t the o u t p u t g e n e r a t e d by U n i t e d S t a t e s f i n a l demand. I n F i g u r e 1, the growth r a t e s a r e compared g r a p h i c a l l y . A t f i r s t g l a n c e , the r e s u l t s o f t h i s i n v e s t i g a t i o n appear t o d e t r a c t from the s t r e n g t h o f the c o n c l u s i o n reached i n s e c t i o n ( b ) . I t i s found t h a t o u t p u t g e n e r a t e d by U n i t e d S t a t e s demand was d e s t a b i l i z i n g i n t h r e e c a s e s and s t a b i l i z i n g i n t h r e e . However, i n the t h r e e cases\where i n d u c e d o u t p u t was s t a b i l i z i n g (Wood p r o d u c t s , C h e m i c a l s , and A g r i c u l t u r e ) I t may be observed t h a t the f l u c t u a t i o n i n the growth of the i n d u s t r y o utput i s out of phase w i t h the f l u c t u a t i o n i n b o t h Canadian and U n i t e d S t a t e s f i n a l demand. The i n d u c e d e x p o r t demand t h e r e f o r e tended t o a g g r a v a t e v a r i a t i o n i n the growth of i n d u s t r i e s whose ou t p u t v a r i e d c y c l i c a l l y , and dampen v a r i a t i o n i n those whose o u t p u t s v a r i e d c o u n t e r - c y c l i c a l l y . d. The impact o f v a r i a t i o n i n U n i t e d S t a t e s f i n a l demand on  Canada's b a l a n c e o f merchandise t r a d e . Canada's b a l a n c e o f merchandise t r a d e i s the d i f f e r e n c e between T o t a l M erchandise E x p o r t s and T o t a l Merchandise Imports - 78 -TABLE X COMPARISON OF ANNUAL GROWTH RATES; THE OUTPUT OF SELECTED EXPORT INDUSTRIES  WITH AND WITHOUT THE OUTPUT GENERATED  BY UNITED STATES FINAL DEMAND ( m i l l i o n s o f d o l l a r s ; 1949 p r i c e s ) 1. Paper P r o d u c t s 1956 1957 1958 1959 i 9 6 0 Induced o u t p u t 7 3 6 751 7 4 6 792 805 T o t a l o u t p u t 3 1503 1478 1 4 7 9 1579 1619 Net o u t p u t ( T o t a l l e s s i n d u c e d ) 767 727 7 3 3 787 814 Growth i n t o t a l o u t p u t "25 1 100 4 0 Growth i n net ou t p u t - 4 0 6 54 27 i i . Wood p r o d u c t s ( e x c e p t f u r n i t u r e ) 1956 1957 1958 1959 i 9 6 0 Induced o u t p u t 280 280 272 293 297 T o t a l o u t p u t 3 871 802 832 861 857 Net o u t p u t 591 522 560 568 560 Growth I n t o t a l o u t p u t -69 30 29 -4 Growth i n net o u t p u t -69 38 8 -8 - 79 -TABLE X ( C o n t i n u e d ) ( m i l l i o n s o f d o l l a r s ; 1949 p r i c e s ) i i i . M e t a l M i n i n g and S m e l t i n g and R e f i n i n g 1956 1957 1958 1959 i 9 6 0 Induced o u t p u t .495 499 487 518 522 T o t a l o u t p u t 3 972 1095 1161 1296 1273 Net o u t p u t 477 596 674 778 751 Growth i n t o t a l o u t p u t 123 66 135 -23 Growth i n net o u t p u t 119 78 104 -27 i v . I r o n and S t e e l P r o d u c t s , n.e.s. 1956 1957 1958 1959 i 9 6 0 Induced o u t p u t 129 130 125 135 137 T o t a l o u t p u t 3 480 461 424 486 453 Net o u t p u t 351 331 299 351 316 Growth i n t o t a l o u t p u t -19 -37 62 -33 Growth i n net o u t p u t -20 -32 52 -35 v. Ch e m i c a l s and A l l i e d P r o d u c t s 1956 1957 1958 1959 i 9 6 0 Induced o u t p u t 168 171 170 180 182 T o t a l o u t p u t 3 477 500 541 568 599 Net o u t p u t 309 329 371 388 417 Growth i n t o t a l o u t p u t 23 41 27 31 Growth i n net o u t p u t 20 42 17 29 - 80 -TABLE X ( C o n t i n u e d ) ( m i l l i o n s o f d o l l a r s ; 1949 p r i c e s ) v i . A g r i c u l t u r e 1956 1957 1958 1959 i 9 6 0 Induced o u t p u t 233 238 239 251 256 T o t a l o u t p u t 3 1785 1480 1577 1578 1612 Net o u t p u t 1552 1242 1338 1327 1356 Growth i n t o t a l o u t p u t -305 97 1 34 G r o w t h , i n net ou t p u t -310 96 -11 29 a. Source: DBS 61-505, Indexes o f R e a l Domestic P r o d u c t  by I n d u s t r y of O r i g i n , 1935-61, p.67. - 81 -FIGURE 1 THE EFFECT OF INDUCED OUTPUT ON THE ANNUAL  GROWTH OF SELECTED EXPORT INDUSTRIES ( m i l l i o n s of d o l l a r s ; 194-9 p r i c e s ) 1957 1958 1959 I960 1957 1958 1959 I960 Paper p r o d u c t s Wood p r o d u c t s M e t a l m i n i n g I r o n and s t e e l p r o d u c t s C h e m i c a l s A g r i c u l t u r e T o t a l Canadian o u t p u t Net Canadian o u t p u t ( t o t a l l e s s induced} - 82 -f o r any p e r i o d and w i l l be r e f e r r e d t o as net e x p o r t s . T o t a l M e r c h a n d i s e E x p o r t s i n c l u d e s the e x p o r t s o f most goods and s e r v i c e s b u t d i f f e r s from T o t a l C u r r e n t R e c e i p t s i n the e x c l u s i o n o f i t e m s such as Gold p r o d u c t i o n a v a i l a b l e f o r e x p o r t , T r a v e l e x p e n d i t u r e s , I n t e r e s t and d i v i d e n d s , F r e i g h t and s h i p p i n g , and I n h e r i t a n c e s and i m m i g r a n t s f u n d s . The i n i t i a l impact o f U n i t e d S t a t e s f i n a l demand on the Canadian b a l a n c e of t r a d e i s the g e n e r a t i o n o f induced e x p o r t s and i n d u c e d i m p o r t s , and by s u b t r a c t i o n , the g e n e r a t i o n o f i n d u c e d n e t e x p o r t s . The c y c l i c a l e f f e c t on the Canadian t r a d e b a l a n c e of dependence on U n i t e d S t a t e s f i n a l demand w i l l be e s t i m a t e d by comparing the growth o f Canadian net e x p o r t s w i t h the growth o f n e t e x p o r t s e x c l u d i n g induced net e x p o r t s . F i r s t , T a b l e X I compares the growth of Canadian e x p o r t s w i t h and w i t h o u t i n d u c e d e x p o r t s . I t may be observed t h a t the e f f e c t o f the induced e x p o r t s was t o make t o t a l Canadian e x p o r t s f l u c t u a t e c y c l i c a l l y . T a b l e X I I and the appended c h a r t p r e s e n t the growth of Canadian net e x p o r t s w i t h and w i t h o u t Induced net e x p o r t s . I t appears t h a t the f l u c t u a t i o n i n i n d u c e d net e x p o r t s dampened the f l u c t u a t i o n I n net e x p o r t s . The e x p l a n a t i o n o f t h i s r e s u l t i s t h a t the a m p l i t u d e o f v a r i a t i o n i n the l e v e l o f Canadian i m p o r t s was much g r e a t e r t h a n the a m p l i t u d e of e x p o r t v a r i a t i o n . (A was $557 m i l l i o n f o r i m p o r t s and $ 6 4 m i l l i o n f o r e x p o r t s . ) S i n c e the f l u c t u a t i o n s I n i m p o r t s were c y c l i c a l , the f l u c t u a t i o n s i n n e t e x p o r t s were c o u n t e r - c y c l i c a l . As a r e s u l t , t h e y were - 83 -TABLE XI GROWTH OF CANADIAN MERCHANDISE EXPORTS WITH• AND WITHOUT INDUCED EXPORTS Induced e x p o r t s T o t a l M e r c h a n d i s e E x p o r t s 3 Growth i n induced e x p o r t s Growth i n t o t a l e x p o r t s Growth i n : t o t a l e x p o r t s l e s s i n d u c e d e x p o r t s 1956 1957 1958 1959 i 9 6 0 ( m i l l i o n s of d o l l a r s ; 1949 p r i c e s ) 2145 2171 2142 2277 2309 4117 4167 4189 167 26 50 24 -29 22 51 4331 135 142 7 4527 32 196 164 a.- Source DBS 67-201, The Canadian B a l a n c e o f I n t e r - n a t i o n a l Payments ( a n n u a l ) , T a b l e 2, p. 8 . The f i g u r e s are d e f l a t e d t o 1949 p r i c e s u s i n g i n d e x e s found i n DBS 65-205, Review o f F o r e i g n Trade ( a n n u a l ) , T a b l e XX. Annual Growth ( m i l l i o n s ) T o t a l e x p o r t s E x p o r t s l e s s i n d u ced e x p o r t s 1957 1958 1959 I960 - 84 -TABLE XII GROWTH OF CANADIAN NET EXPORTS WITH AND WITHOUT INDUCED NET EXPORTS Induced n e t e x p o r t s Canadian n e t e x p o r t s ' 1956 1957 1958 1959 I960 ( m i l l i o n s of d o l l a r s ; 1949 p r i c e s ) 1947 1966 1943 2065 2096 -937 -668 -274 -666 -393 Growth i n induced net e x p o r t s Growth i n Canadian net e x p o r t s Growth i n .-Canadian net e x p o r t s l e s s i n d u ced n e t e x p o r t s 19 269 250 -23 394 417. 122 -392 -514 31 273 242 a. Induced net e x p o r t s = induced Canadian e x p o r t s l e s s i n d u c e d Canadian i m p o r t s . b. Net e x p o r t s = t o t a l C a n a d i a n - e x p o r t s l e s s t o t a l C a n a d i a n i m p o r t s . - 85 -dampened by the c y c l i c a l f l u c t u a t i o n s i n induced net e x p o r t s . I n the f i n a l c h a p t e r , t h e s e r e s u l t s are summarized and t h e i r p r o b a b l e b i a s d i s c u s s e d . - 86 -CHAPTER V I I  CONCLUSIONS ( The f o l l o w i n g c o n c l u s i o n s were drawn from the r e s u l t s o b t a i n e d i n a p p l y i n g the i n p u t - o u t p u t model t o Canadian and American d a t a f o r 1956 t o i960. -1. Of e q u a l e x p e n d i t u r e s on the f o u r major components o f U n i t e d S t a t e s f i n a l demand, Gro s s p r i v a t e f i x e d c a p i t a l f o r m a t i o n , or Investment, had much the g r e a t e s t i m p act on Canadian a g g r e g a t e . demand and p r o d u c t i o n . There was r e l a t i v e l y l i t t l e d i f f e r e n c e i n e f f e c t between e x p e n d i t u r e s on the o t h e r t h r e e components. The main f a c t o r c o n t r i b u t i n g t o the wide d i v e r g e n c e between the impact of Investment and the o t h e r ' components was the c o n c e n t r a t i o n of Canadian e x p o r t s on a. r e l a t i v e l y s m a l l number o f p r o d u c t s . 2. The e f f e c t on the Canadian economy of c y c l i c a l f l u c t u a t i o n s i n the l e v e l o f U n i t e d S t a t e s f i n a l demand was r e i n f o r c e d by v a r i a t i o n i n the r e l a t i v e w e i g h t s of i t s major components. I n p a r t i c u l a r , the r e l a t i v e w e i g h t of Investment e x p e n d i t u r e tended t o d e c l i n e d u r i n g p e r i o d s of demand c o n t r a c t i o n , and r i s e d u r i n g p e r i o d s o f e x p a n d i n g demand. C y c l i c a l v a r i a t i o n i n the share o f P e r s o n a l consumption e x p e n d i t u r e devoted t o d u r a b l e goods was a l s o a c o n t r i b u t i n g f a c t o r . ,3. The r a t e o f growth o f Canadian e x p o r t s .generated by U n i t e d S t a t e s f i n a l demand f l u c t u a t e d I n phase w i t h the r a t e o f growth - 87 -o f t o t a l Canadian f i n a l demand. T h e r e f o r e , the f l u c t u a t i o n s i n i n d u c e d e x p o r t s c o n t r i b u t e d t o the f l u c t u a t i o n s i n Canadian a g g r e g a t e demand. Indeed, i t was e s t i m a t e d t h a t twenty-two p e r c e n t o f the a m p l i t u d e of the a n n u a l f l u c t u a t i o n s i n Canadian demand was a t t r i b u t a b l e t o t h e c y c l i c a l b e h a v i o r o f U n i t e d S t a t e s f i n a l demand. 4. F l u c t u a t i o n s i n the l e v e l and p a t t e r n of U n i t e d S t a t e s demand a g g r a v a t e d f l u c t u a t i o n s i n the growth of o u t p u t o f some Canadian i n d u s t r i e s and dampened tho s e of o t h e r s . The d i r e c t i o n o f e f f e c t depended on whether or not the i n d u s t r y growth r a t e v a r i e d i n phase w i t h the o v e r - a l l growth o f the Canadian and American economies. F l u c t u a t i o n s i n growth were r e i n f o r c e d i n the Paper p r o d u c t s , M e t a l m i n i n g , and I r o n and s t e e l I n d u s t r i e s , and dampened i n the Wood p r o d u c t s , C h e m i c a l s , and A g r i c u l t u r e i n d u s t r i e s . 5. C y c l i c a l f l u c t u a t i o n s I n the Canadian b a l a n c e o f merchandise t r a d e were dampened by f l u c t u a t i o n s i n the e x p o r t s and i m p o r t s g e n e r a t e d by U n i t e d S t a t e s f i n a l demand. The r e a s o n f o r t h i s was t h a t f l u c t u a t i o n s i n Induced e x p o r t s dominated the growth o f i n d u c e d net e x p o r t s w h i l e i m p o r t f l u c t u a t i o n s dominated the growth o f t o t a l Canadian n et e x p o r t s . I n the d e r i v a t i o n of the model and i n i t s a p p l i c a t i o n , s e v e r a l a s sumptions were i n t r o d u c e d . I n t h i s f i n a l s e c t i o n the e f f e c t o f r e l a x i n g these a s s u m p t i o n s i s s u g g e s t e d . - 88 -1. The n e g l e c t e d f a c t o r most d i r e c t l y a f f e c t i n g the c o n c l u s -i o n s i s the impact of c y c l i c a l changes i n the l e v e l s o f Net i n v e n t o r y change and Net e x p o r t s . I t i s c e r t a i n t h a t the . n e g l e c t o f t h e s e components o f U n i t e d S t a t e s demand r e s u l t e d I n a s u b s t a n t i a l u n d e r s t a t e m e n t of the t r a n s m i s s i o n o f b u s i n e s s c y c l e s from the U n i t e d S t a t e s t o Canada. 2. Changes were not c o n s i d e r e d i n t h e i n d u s t r y c o m p o s i t i o n o f the components of U n i t e d S t a t e s f i n a l demand. The e f f e c t o f such changes c o u l d have been e i t h e r c y c l i c a l l y s t a b i l i z i n g o r d e s t a b i l i z i n g and c o u l d be q u i t e i m p o r t a n t , p a r t i c u l a r l y . w i t h r e g a r d t o the o u t p u t s of i n d i v i d u a l C anadian i n d u s t r i e s . 3. Changes I n the Canadian e x p o r t share o f the t o t a l U n i t e d S t a t e s s u p p l y o f any i n d u s t r y o u t p u t were n e g l e c t e d . A g a i n , I t i s d i f f i c u l t t o p r e d i c t what the e f f e c t o f r e l a x i n g t h i s r e s t r i c t i o n might be. 4. S i m i l a r l y , changes i n i n d u s t r y I n p u t c o e f f i c i e n t s t h a t m ight r e s u l t from n o n - c o n s t a n t r e t u r n s t o s c a l e , s u b s t i t u t i o n , o r t e c h n o l o g i c a l change were n e g l e c t e d . Moreover, the p o s s i b -i l i t y of e r r o r a r i s i n g from n o n - c o n s t a n t p r o d u c t i o n c o e f f i c i e n t s was enhanced by the f a c t t h a t 1958, the base y e a r of the s t u d y , was a y e a r i n w h i c h the r a t e o f economic growth d e c l i n e d s h a r p l y . Any v a r i a b i l i t y i n p r o d u c t i o n a l t e r n a t i v e s s h o u l d have been f u l l y e x p l o i t e d i n such a y e a r , w h i c h s u g g e s t s t h a t 1958 i n t e r -i n d u s t r y t r a n s a c t i o n s may have been poor d a t a on w h i c h t o base p r o d u c t i o n c o e f f i c i e n t s f o r o t h e r y e a r s . - 8 9 -5. F i n a l l y , no changes were considered i n Canadian Personal consumption and Investment expenditures i n response to changes i n the l e v e l of United States f i n a l demand. Again, t h i s i s a factor that would increase the s e n s i t i v i t y of the Canadian economy to changes i n United States business conditions. Consideration of these neglected factors leads to the conclusion that the impact of fluctuations i n United States f i n a l demand on Canadian f i n a l demand and industry outputs i s under-estimated In t h i s i n v e s t i g a t i o n . Neglect of the f i r s t and l a s t factors d e f i n i t e l y imparted a strong conservative bias to the r e s u l t s , while the d i r e c t i o n of errors due to neglect of the other factors was probably mixed. - 90 -BIBLIOGRAPHY I. Unpublished Material 1 . Updated Canadian inverse and import matrices, punched on IBM cards, with accompanying technical notes by T. I. Matuszewski, P. R. P i t t s , and J . A. Sawyer. I I . Government Publications A . Publications of the Dominion Bureau of S t a t i s t i c s , Ottawa: Queen's P r i n t e r . 1. No. 12-501, Standard I n d u s t r i a l C l a s s i f i c a t i o n  Manual, 1948. 2 . No. 13-513, Supplement to the Inter-Industry Flow of Goods and~ Services, Canada, 19~4"9T"l9"60. 3 . No. 62-002, Prices and Price Indexes (annual). 4. No. 65-201, Trade of Canada, Volume I, Summary, (annual). 5 . No. 65-202, Trade of Canada, Volume I I , Exports, (annual). 6. No. 65-205, Review of Foreign Trade (annual). 7. No. 67-201, The Canadian Balance of International  Payments (annualT^ 8. Canada Year Book (annual). B. Other 1. Executive Office of the President, Bureau of the Budget, Standard Ind u s t r i a l C l a s s i f i c a t i o n Manual, 1957. 2. United States Department of Commerce, Office of Business Economics, Survey of Current Business: - ."The National Income and Product Accounts of the United States: Revised Estimates, 1929-64," August, 1965, P.6. - "The Transactions Table of the 1958 Input-Output Study and Revised Direct and Total Requirements Data," September, 1965, p .33« "Personal Consumption Expenditures in the 1958 Input-Output Study," October, 1965, P - 7 . - 91 -I I I . Books. 1. . Allen, R.D.G., Mathematica1 Economics, Second E d i t i o n , London: MacMillan and Company Ltd., 1956. 2. Kindleberger, C.P., International Economics, Revised E d i t i o n , Homewood: R. D. Irwin, 195b. 3 . Leontief, W.W, The Structure of the American Economy, 1919-1939, Seconded i t ion, New York: Oxford University Press, I§"51. 4 . , et a l , Studies in the Structure of the American Economy, New York: Oxford University Press, 7 ~ 5 . Morgenstern, 0 . (ed.), Economic A c t i v i t y Analysis, New York: John Wiley and Sons, Inc., 1954. 6 . National Bureau of Economic Research, Input-Output Analysis: An Appraisal, Studies i n Income and Wealth, XVIII, Princeton University Press, 1955. 7. Wonnacott, R.J., Canadian-American Dependence: An  Interindustry Analysis of Production and Prices, Amsterdam: The North-Holland Publishing Company, 1961. IV. Journal A r t i c l e s . 1. Caves, R.E., "The Inter-Industry Structure of the Canadian Economy," Canadian Journal of Economics and . P o l i t i c a l Science, T H T T T I 9 5 7 ) , PP. 3~13-330~ • 2. Degen, R.A., "U.S. Recessions and Selected Imports," Canadian Journal of Economics and P o l i t i c a l Science, • XXV (1959) , PP. 1«0=T89: . 3 . Dorfman, R., "The Nature and Significance of Input-Output," Review of Economics and S t a t i s t i c s , XXXVI (1954), pp". 121-133. 4 . Hawkins, D. and Simon, H.A., "Note: Some Conditions of Macroeconomic S t a b i l i t y , " Econometrica, XVII ( 1949) , pp. 245-248. 5. ' Isard W., "Interregional and Regional Input-Output Analysis: A Model of a Space Economy," Review of  Economics and S t a t i s t i c s , XXXIII (1951) , PP. 318-328. 6. Leontief, W.W., "Output, Employment, Consumption, and Investment," Quarterly Journal of Economics, LVIII • (1944) , pp. 2^31^. - 92 -Leontief, W.W., "Exports, Imports, Domestic Output and Employment,".Quarterly Journal of Economics, LX (1946) , pp. 175-193. , "The Structure of the U.S. Economy," S c i e n t i f i c American, A p r i l , 1965. Matuszewski, T.I., P i t t s , P.R., and Sawyer, J.A., "Alternative Treatments of Imports i n Input-Output Models: A Canadian Study," Journal of the Royal  S t a t i s t i c a l Society, Series A, CXXVI (1963), PP. 410-432. , "Interindustry Estimates of Canadian Imports, 1949-1958," Canadian P o l i t i c a l  Science Association, Conference on S t a t i s t i c s , 1961 - Papers, University of Toronto Press, 19~5~3, pp. 1~40-167. , "L'Ajustement Periodique des Systemes de Relations I n t e r - I n d u s t r i e l l e s , Canada, 1949-1958," Econometrica, XXXI (1963) , PP. 90-110. ' , "Linear Programming Estimates of Changes i n Input C o e f f i c i e n t s , " Canadian Journal of  Economics and P o l i t i c a l Science, XXX (1954), pp. 20~3-210. , "The Impact of Foreign Trade on Canadian Industries, 1956," Canadian Journal of  Economics and . P o l i t i c a l Science, XXXI U 9 b 5 T , pp. 206-221. Moses, L.N., "The S t a b i l i t y of Interregional Trading Patterns and Input-Output Analysis," The American Economic Review, XLV ( 1955) , PP. 803-H527 Rosenbluth, G., "Changes i n Canadian S e n s i t i v i t y to U.S. Business Fluctuations," Canadian Journal of Economics and P o l i t i c a l Science, XXXIII r195TT~PP• 480-503. , "Changing Structural Factors in Canada's C y c l i c a l S e n s i t i v i t y , 1903-54," Canadian Journal of  Economics and P o l i t i c a l Science, XXIVT^58T7~PPT~2"1 - 4 3 . Sawyer, J.A., "Measurement of Inter-Industry Relation-ships i n Canada," Canadian Journal of Economics and P o l i t i c a l Science, XXI ( 1 9 5 5 ) , PP• 4b0-497. - 93 -APPENDIX A DETAILED RESULTS The p o s t u l a t e d v e c t o r s o f U n i t e d S t a t e s f i n a l demand a r e shown i n T a b l e X I I I . They are o b t a i n e d from v e c t o r s p u b l i s h e d on page 39 Qf S u r v e y of C u r r e n t B u s i n e s s , September 1965. The elements o f each o f the p u b l i s h e d v e c t o r s a r e m u l t i p l i e d by a c o n s t a n t f a c t o r t o make them t o t a l one b i l l i o n d o l l a r s . The v e c t o r o f P e r s o n a l consumption e x p e n d i t u r e i s r e p r e s e n t e d by C ; I r e p r e s e n t s the v e c t o r o f Gross p r i v a t e f i x e d c a p i t a l f o r m a t i o n , G_ t h e v e c t o r o f F e d e r a l Government p u r c h a s e s , and Gg the v e c t o r o f S t a t e and l o c a l government p u r c h a s e s . T a b l e s XIV, XV, XVI, and X V I I show the v e c t o r s o f U n i t e d S t a t e s a c t i v i t y l e v e l s , C a n a d i a n e x p o r t s , Canadian a c t i v i t y l e v e l s , and Canadian i m p o r t s g e n e r a t e d by the p o s t u l a t e d v e c t o r s o f U n i t e d S t a t e s f i n a l demand. I n a l l t a b l e s , the f i g u r e s may not add t o the t o t a l s due t o r o u n d i n g . TABLE X I I I POSTULATED INCREASES IN UNITED STATES FINAL DEMAND [P] ( t h o u s a n d s of U n i t e d S t a t e s d o l l a r s ; 1958 p r i c e s ) INDUSTRY G ~ F 1 . L I V E S T O C K + L I V E S T O C K P R O D U C T S 2 . O T H E R A G R I C U L T U R A L P R O D U C T S 3 . F O R E S T R Y + F 1 S H E R Y P R O D U C T S 4 . A G R I C U L T U R A L . , F O R E S T R Y + F I S H E R Y S E R V I C E S 5 . I R O N * F E R R O A L L O Y O R E S M I N I N G 6 . N O N F E R R O U S M E T A L . O R E S M I N I N G 7 . C O A L . M I N I N G 8 . C R U D E P E T R O L E U M + N A T U R A L G A S 9 . S T O N E + C L A Y M I N I N G Q U A R R Y I N G I 0 . C H E M I C A L + F E R T I L 1 2 E R M I N E R A L . M I N I N G I I . N E W C O N S T R U C T I O N 12 . M A I N T E N A N C E - H R E P A I R C O N S T R U C T I O N 13 . O R D N A N C E + A C C E S S O R 1 E S 1 4 . F O O D + K I N D R E D P R O D U C T S 1 5 . T O B A C C O M A N U F A C T U R E S 1 6 . B R O A D + N A R R O W F A B R I C S , Y A R N + - T H R E A D 1 7 . M I S C . F A B R I C A T E D T E X T I L E P R O D U C T S 1 8 . A P P A R E L 19 . M I S C . F A B R I C A T E D T E X T I L E P R O D U C T S 2 0 . L U M B E R * W O O D P R O D S . . E X C E P T C O N T A I N E R S . 21 . W O O D E N C O N T A I N E R S 2 2 . H O U S E H O L D F U R N I T U R E 2 3 . O T H E R F U R N I T U R E + F I X T U R E S 2 4 . P A P E R + A L L I E D P R O D S . , E X C E P T C O N T A I N E R S 25 . P A P E R B O A R D C O N T A I N E R S t B O X E S 2 6 , P R I N T I N G t P U B L l S H I N G 2 7 . C H E M I C A L S t S E L E C T E D C H E M I C A L P R O D U C T S 28 . P L A S T I C S + S Y N T H E T I C M A T E R I A L S 29 . D R U G S . C L E A N I N G + T O I L E T P R E P A R A T I O N S 3 0 . P A I N T S * A L L I E D P R O D U C T S 31 . P E T R O L E U M R E F I N I N G +R E L A T E D I N D U S T R I E S 32 . R U B B E R + M I S C E L L A N E O U S P L A S T I C S P R O D U C T S 3 3 . L E A T H E R T A N N I N G + l N D U S T R I A L L E A T H E R P R O D S . 3 4 . F O O T W E A R + O T H E R L E A T H E R P R O D U C T S 35 , G L A S S * G L A S S P R O D U C T S 36 . S T O N E + C L A Y P R O D U C T S 3 7 . P R I M A R Y I R O N + - S T E E L M A N U F A C T U R I N G 3 8 . P R I M A R Y N O N F E R R O U S M E T A L S M A N U F A C T U R I N G 3 9 . M E T A L C O N T A I N E R S 4 0 . H E A T I N G , P L U M B I N G + - S T R U C T U R A L M E T A L P R O D S _ _ 41 . S T A M P I N G S , S C R E W M A C H I N E P R O D U C T S - H 3 0 L T S 4 2 . O T H E R F A B R I C A T E D M E T A L P R O D U C T S 43 . E N G I N E S + T U R B I N E S 4 4 . F A R M M A C H I N E R Y + E Q U I P M E N T 45 . C O N S T R U C T I O N , M I N I N G + O I L F I E L D M A C H I N E R Y 4 6 . M A T E R I A L S H A N D L I N G M A C H I N E R Y + E Q U I P M E N T 47 . M E T A L W O R K I N G M A C H I N E R Y + E Q U I P M E N T 4 8 . S P E C I A L I N D U S T R Y M A C H I N E R Y + E Q U I P M E N T 4 9 . G E N E R A L I N D U S T R I A L M A C H I N E R Y + - E O U I P M E N T 5 0 . M A C H I N E S H O P P R O D U C T S . 51 . O F F I C E . C O M P U T I N G + A C C O U N T I N G M A C H I N E S 5 2 . S E R V I C E I N D U S T R Y M A C H I N E S 5 3 . E L E C T R I C I N D U S T R I A L E Q U I P M E N T R A P P A R A T U S 5 4 . H O U S E H O L D A P P L I A N C E S 5 5 . E L E C T R I C L I G H T I N G + W l R I N G E Q U I P M E N T 5 6 . R A D I O , T . V . - f C O M M U N I C A T I O N E Q U I P M E N T 57 . E L E C T R O N I C C O M P O N E N T S A C C E S S O R I E S 58 . M I S C E L L A N E O U S E L E C T R I C A L M A C H I N E R Y + S U F P U E 5 9 . M O T O R V E H I C L E S f E Q U I P M E N T 6 0 . A I R C R A F T + P A R T S 61 . O T H E R T R A N S P O R T A T I O N E Q U I P M E N T 62 . S C I E N T I F I C t C O N T R O L L I N G I N S T R U M E N T S 6 3 . O P T I C A L . O P H T H A L M I C t P H O T O G R A P H 1 C E Q U I P T . 6 4 . M I S C E L L A N E O U S M A N U F A C T U R I N G 65 . T R A N S P O R T A T l O N t W A R E H O U S I N G 6 6 . C O M M U N I C A T I O N S - E X C E P T R A D I O V f . V . 67 . R A D I O * T . V . B R O A D C A S T I N G 68 . E L E C T R I C , G A S . W A T E R t S A N I T A R Y S E R V I C E S 69 . W H O L E S A L E + R E T A I L T R A D E . 7 0 . F I N A N C E - * I N S U R A N C E 71 . R E A L E S T A T E * R E N T A L 7 2 . H O T E L S - P E R S O N A L f - R E P A I R S E R V I C E S 7 3 . B U S I N E S S S E R V I C E S 74 . R E S E A R C H + D E V E L O P M E N T 7 5 . A U T O M O B I L E R E P A I R * S E R V I C E S 76 . A M U S E M E N T S 7 7 . M E D I C A L E D U C A T I O N S E R V I C E S 7 8 . F E D E R A L G O V E R N M E N T E N T E R P R I S E S 79 . S T A T E + L O C A L G O V E R N M E N T E N T E R P R I S E S 8 0 . G R O S S I M P O R T S O F G O O D S + S E R V I C E S 81 . B U S I N E S S T R A V E L , E N T E R T A I N M E N T - f G I F T S 8 2 . O F F I C E S U P P L I E S D U M M Y I N D U S T R I E S '  7 2 7 8 8374 969 9 0 0 59 3 545 157755 14652 2 4 5 5 2561 38491 3796 514 8 3 3 3 445 2 9 2 3 131 8429 734 34 12783 63_ 2 5 0 2 5 4513 8988 448 738 66 38 _241__ 858 1307 434 28 107 66 2 0 0 852 52 8329 1079 4699 514 896 . 31720 9 3 2 5 0 3 1203 1613 8743 29851 13476 2 7 7 8 6 2 1 2 2 3 9 40737_ "137763 32597 6509 15125 11247 70492 2179 1076 13290 592346 721 2 0 2 0 12790 8 3 3 8 0 160 JU3_48_ 2661 9232 2 6 7 6 7 21141 5642 18480 2 3 5 2 9 16845 16284 " 15307 25917 1491 401 16172 4 3 3 1330 5 7 3 0 0 5738 " 1 8 8 8 1 " 8527 2 6 1 3 4472 8126 5802 60056 T 9 3 7 8 ~ 2 5 6 - 5 6 2 0 0 2 0 - 2 5 5 7 8 4 0 3582 187 2 0 5 _ 63216 2 0 1 6 9 42355 989 9 3 3 75 746 1922 - 1 1 2 _ 37 466 485 1343 9 3 1717 13807 9 3 2481 56. . 13545 2201 429 37 9 3 2107 6156 317 r698~ 2126 4459 9 3 1493 2537 3190 5 6 0 3731 765_ 1399 1194 3396 392 317 2 6 0 6 6 4366 1679 5710 121264 _ "12221 10243 2556 672 2 6 8 4 9 3153 6492 12034 19 2 0 9 0 4590 9179 96597 2407 336 2164 1045 2108 5 0 6 9 6 8 0 5 3 ( t 3 t 7 5 ) 1381 368719 2 7 2 667 1505 - 2 9 S 2 9 6 2 9 7 5 3 0 ' 8 2 3 1 4 99 6706 2 2 3 25 2 2 6 8 1406 3107 147 42 67 5967 9 4 1 8 1850 49 99 25 — 1 2 3 1135 74 4 2 0 519 1234 123 741 123 __864 2 1 9 5 519 123 25 197 1529 815 10799 9 3 8 2121 371 4414 9911 4685 11982 .4512 _ 4 7 1 0 _ 5 7 4 5 2146 13683 2 4 0 7 - 1 0 8 4 7668 1653 148 7 4 3255 478755 TOTAL 1 0 0 0 0 0 0 1000000 1 0 0 0 0 0 0 1000000 - 95 " T A B L E X I V INDUCED I N C R E A S E S I N U N I T E D S T A T E S A C T I V I T Y L E V E L S [x = ( i - A)-1F] ( t h o u s a n d s o f U n i t e d S t a t e s d o l l a r s ; 1958 p r i c e s ) INDUSTRY C I G G ~ P ~ s 1 . L I V E S T O C K S I V E S T O C K P R O D U C T S 8 1 6 6 3 5 7 0 0 5 3 5 0 5622 2 . O T H E R A G R I C U L T U R A L P R O D U C T S 61443 10725 2 5 9 2 6 7 3 5 0 3 . F O R E S T R Y + F 1 S H E R Y P R O D U C T S 32 05 5887 - 1 4 6 5 3240 4 . A G R I C U L T U R A L . . F O R E S T R Y+ F I S H E R Y S E R V I C E S 4341 9 5 5 1998 - 1 121 5 . 1 R O N * F E R R O A L L O Y O R E S M I N I N G 1379 7432 2 9 6 4 271 3 6 . . N O N F E R R O U S M E T A L . O R E S M I N I N G 1181 5632 8745 231 1 7 . C O A L . M I N I N G 51 17 6582 3195 5137 8 . C R U D E P E T R O L E U M * N A T U R A L . G A S 2 6 9 7 9 15690 15679 15475 9 . S T O N E + C L A Y M I N I N G Q U A R R Y I N G 13SS 1211 1 2 4 7 6 6565 1 0 . C H E M I C A L + F E R T I L I Z E R M I N E R A L M I N I N G 9 0 3 1063 1 376 1175 I I . N E W C O N S T R U C T I O N — 5 9 2 3 4 6 63216 "297530 12 . M A I N T E N A N C E + R E P A I R C O N S T R U C T I O N 3 5 2 9 0 147 09 29834 9 0 5 8 3 13 . O R D N A N C E + A C C E S S O R 1 E S 1124 2 0 9 0 75507 5 0 4 H . F O O D r K I N D R E D P R O D U C T S 211325 10551 7961 13877 1 5 . T O B A C C O M A N U F A C T U R E S 18530 485 295 213 1 6 . B R O A D 4 - N A R R O W F A B R I C S . Y A R N f T H R E A D 33698 5 3 2 4 6296 3884 1 7 . M I S C . F A B R I C A T E D T E X T I L E P R O D U C T S 6941 375 3 2 0 5 0 1419 1 8 . A P P A R E L 48045 1309 1946 3252 1 9 . M I S C . F A B R I C A T E D T E X T I L E P R O D U C T S 6 8 4 2 1312 2 7 6 6 612 2 0 . L U M B E R O O D P R O D S . . E X C E P T C O N T A I N E R S 8066 60991 10546 32851 21 . W O O D E N C O N T A I N E R S 1134 897 497 " " 398 " 2 2 . H O U S E H O L D F U R N I T U R E 8878 7009 2 2 9 3 3529 2 3 . O T H E R F U R N I T U R E r F I X T U R E S 7 3 0 159S7 1 369 4627 2 4 . P A P E R S A L L I E D P R O D S . . E X C E P T C O N T A I N E R S 24691 2 1 7 4 9 12803 14668 2 5 . P A P E R B O A R D C O N T A I N E R S t B O X E S 9 2 8 0 6642 3925 3466 2 6 . P R I N T I N G t P U B L I S H I N G 31875 2078 0 14027 21209 2 7 . C H E M 1 C A L S * - S E L E C T E D C H E M I C A L P R O D U C T S 2 2 2 4 8 23236 32765 2 2 0 0 6 28 . P L A S T I C S + S Y N T H E T 1 C M A T E R I A L S 9349 8 5 6 9 6149 4765 29 . D R U G S . C L E A N I N G + T O I L E T P R E P A R A T I O N S 18902 2 4 4 3 5049 6 3 3 0 3 0 . P A I N T S - * A L L I E D P R O D U C T S 3371 5 8 4 3 3129 6908 31 . P E T R O L E U M R E F I N I N G ' R E L A T E D I N D U S T R I E S 4 3 9 2 3 2 6 6 8 5 2 7 0 2 9 " "26184 32 R U B B E R ^ M I S C E L L A N E O U S P L A S T I C S P R O D U C T S 14928 1771 1 12246 8 8 0 5 3 3 . L E A T H E R T A N N 1 N G + l N D U S T R 1 A L L E A T H E R P R O D S . 2811 425 289 176 3 4 . F O O T W E A R + O T H E R L E A T H E R P R O D U C T S 10246 372 662 2 0 2 35 . G L A S S + G L A S S P R O D U C T S 5 1 8 8 5119 2618 2538 3 6 . S T O N E D - C L A Y P R O D U C T S 5241 6261 1 11782 32909 3 7 . P R I M A R Y I R O N + - S T E E L M A N U F A C T U R I N G 2 1 0 0 6 123031 45251 43491 3 8 . P R I M A R Y N O N F E R R O U S M E T A L S M A N U F A C T U R I N G 9 8 3 0 52628 42053 2 0 9 0 2 3 9 . M E T A L C O N T A I N E R S 6097 1285 1324 1170 4 0 . H E A T I N G , P L U M B 1 N G + S T R U C T U R A L M E T A L P R O D S . 3305 77415 10483 3 5 9 4 0 41 . S T A M P I N G S , S C R E W M A C H I N E P R O D U C T S + B O L T S 6017 15690 12593 4522 4 2 . O T H E R F A B R I C A T E D M E T A L P R O D U C T S 9 6 2 5 32092 14477 13128 4 3 . E N G 1 N E S t T U R B I N E S 1603 16273 8085 1170 4 4 . F A R M M A C H 1 N E R Y + E Q U I P M E N T 1175 3 0 0 4 0 1 354 1091 45 . C O N S T R U C T I O N , M I N I N G + O I L F I E L D M A C H I N E R Y 8 8 2 2 8 5 6 4 3526 2 9 9 0 4 6 . M A T E R I A L S H A N D L I N G M A C H 1 N E R Y+ E Q U I P M E N T 2 5 6 10128 3 5 1 3 3139 47 . M E T A L W O R K I N G M A C H 1 N E R Y + E Q U 1 P M E N T 2 3 9 8 28681 14065 2352 4 8 . S P E C I A L I N D U S T R Y M A C H 1 N E R Y + E Q U 1 P M E N T 1140 2 7 4 0 4 .2015 1700 4 9 . G E N E R A L I N D U S T R I A L M A C H 1 N E F ! Y + E Q U 1 P M E N T 1862 33685 10746 4135 S O . M A C H I N E S H O P P R O D U C T S 1604 538 0 11667 2319 51 . O F F I C E . C O M P U T I N G t A C C O U N T 1 N G M A C H I N E S 1832 1991 1 3 2 2 0 3617 5 2 . S E R V I C E I N D U S T R Y M A C H I N E S 1934 2 0 7 8 3 2 9 7 5 2 6 3 4 5 3 . E L E C T R I C I N D U S T R I A L E Q U 1 P M E N T » A P P A R A T U S 8863 46361 1 5 3 5 9 5032 5 4 . H O U S E H O L D A P P L I A N C E S 9 3 9 3 6553 4 5 6 4 2 1 6 3 5 S . E L E C T R I C L I G H T I N G + W1 R I N G E Q U I P M E N T 2 6 6 8 13473 6 2 0 3 6602 5 6 . R A D I O , T .V.-f C O M M U N I C A T I O N E Q U I P M E N T 6727 21241 45928 2 8 4 9 57 . E L E C T R O N I C C O M P O N E N T S A C C E S S O R I E S 3266 8007 19184 1366 58 . M I S C E L L A N E O U S E L E C T R I C A L M A C H 1 N E R Y + S U P P U E S 2 8 5 8 5 0 5 4 4376 1941 5 9 . M O T O R V E H I C L E S + - E Q U I P M E N T 52 3 42 91817 2 0 2 8 8 18553 6 0 . A 1 R C R A F T + P A R T S 1715 11164 2 0 6 0 9 8 " 1031 61 . O T H E R T R A N S P O R T A T I O N E Q U I P M E N T 3 9 9 3 23218 14737 2142 62 . S C I E N T I F I C t C O N T R O L L 1 N G I N S T R U M E N T S 3878 15462 2 0 3 5 5 4731 63 . O P T I C A L , O P H T H A L M I C ' P H O T O G R A P H 1 C E Q U 1 P T . 3 2 9 6 3936 4636 1098 6 4 . M I S C E L L A N E O U S M A N U F A C T U R I N G 14389 9 7 8 8 4 0 8 9 7931 65 . T R A N S P O R T A T I O N + W A R E H O U S 1 N G 727 86 74666 56 416 44337 66 . C O M M U N I C A T I O N S - E X C E P T R A D I O + T . V . 245 53 16370 9165 9 9 6 4 6 7 . R A D I O < - T . V . B R O A D C A S T I N G . 3515 3774 1928 2 7 4 8 6 8 . E L E C T R I C , G A S . W A T E R 1 - S A M I T A R Y S E R V I C E S 55525 2 4 1 8 0 21075 2 6 0 7 0 69 . W H O L E S A L E + R E T A I L T R A D E . 2 6 4 6 9 2 168750 52672 61455 70 . F I N A N C E * I N S U R A N C E 79154 2 5 6 8 0 t 2 1 7 6 18567 71 . R E A L E S T A T E + R E N T A L 190945 51937 22139 23555 ' 7 2 . H O T E L S - P E R S O N A L t R E P A I R S E R V I C E S 3 8 6 6 0 4899 7461 4375 7 3 . B U S I N E S S S E R V I C E S 5S6 07 6099 8 30831 4 3 9 7 3 7 4 . R E S E A R C H + O E V E L O P M E N T 324 416 9 7 0 7 0 171 75 . A U T O M O B I L E R E P A 1 R+ S E R V I C E S 2 2 9 06 8573 5684 6625 7 6 . A M U S E M E N T S 17289 1964 1622 - 2 2 0 7 7 . M E D I C A L E D U C A T I O N S E R V I C E S . 73847 2461 13343 8969 7 8 . F E D E R A L G O V E R N M E N T E N T E R P R I S E S 10733 6065 4329 5 0 8 0 7 9 . S T A T E + L O C A L G O V E R N M E N T E N T E R P R I S E S 12596 0351 6 6 5 3 5165 8 0 . G R O S S I M P O R T S O F G O O D S + S E R V I C E S 44085 34170 7 1 0 3 0 16670 81 . B U S I N E S S T R A V E L . E N T E R T A I N M E N T + G I F T S 14916 17835 10960 7 8 C 3 8 2 . O F F I C E S U P P L I E S 2 8 7 3 2 3 7 3 2811 4562 TOTAL 1933187 228127 3 1384924 1142569 TABLE XV INDUCED INCREASES IN CANADIAN EXPORTS [e = J ( l - A ) ~ F l (thousands of Canadian ' do l l a r s ; 1949 prices) INDUSTRY C I *F *S 1 Agriculture 539 57 103 47 2 Forestry 3-1 237 41 128 3 Fishing, hunting and trapping 146 267 - 6 7 146 k Metal mining & smelting & refining 492 2623 2033 1031 5 Coal, crude petroleum & natural gas 178 107 104 104 6 Non-metal mining & prospecting 26 69 25 40 7 Heat products 162 8 6 11 8 Dairy products 1 • - - -9 Fish processing 31 2 1 2 10 Fruit and vegetable preparations 3 _ _ _ 11 Grain B i l l produetc 17 1 1 1 12 Bakery products 10 - - 1 13 Carbonated beverages - - - -U Alcoholic beverages 205 10 8 13 15 Confectionery end sugar refining 2 - - -16 Miscellaneous food preparations 17 1 1 1 17 Tobacco and tobacco products - — _ _ 16 Rubber products 5 6 4 3 19 Leather products 14 2 1 1 20 Textile products (except clothing) 18 8 5 3 21 Clothing (textile and fur) 6 1 1 1 22 Furniture _ _ _ 23 Wood products (except furniture) 247 I 8 5 6 321 1000 24 Paper products 1564 1378 811 929 25 Printing, publishing 4 allied ind 7 4 3 4 26 Priaary iron and steel 23 134 49 47 27 Agricultural implements 28 707 32 26 28 Iron & steel products, n.e.s. 48 177 67 41 29 Transportation equipment 18 43 196 7 30 Jewellery & silverware _ __2_ 1 1 1 31 Non-ferrous cstal products, n.o.s.. 42 223 177 8 9 -32 Electrical apparatus & supplies 10 24 40 5 33 Non-metallic mineral products 42 404 80 216 34 Products of petroleum & coal 8 13 7 7 35 Cheaicals and allied products 140 136 188 131 36 Misc. Esnufacturing industries 13 17 17 8 37 Construction — 38 Transportation, storage & trade - _ _ 39 Ccaamnication — _ _ — 40 Electric power, gas & water 84 36 32 39 u Finance, insurance & real estate 42 Service industries - — _ TOTAL 4178 8556 4289 4086 - 97 -TABLE XVI INDUCED INCREASES IN CANADIAN ACTIVITY LEVELS  [x = ( I - a ) " 1 J ( l - A ) - 1 F ] (thousands of Canadian d o l l a r s ; 1949 prices) INDUSTRY 1 Agriculture 2 Forestry 3 Fishing, hunting and trapping 4 Metal dining & smelting & refining 5 Coal, crude petroleum & natural gas 6 Non-metal mining & prospecting 7 Meat products 8 Dairy products 9 Fish processing a 10 Fruit and vegetable preparations 11 Grain mill products 12 Bakery products 13 Carbonated beverages 14 Alcoholic beverages 15 Confectionary and sugar refining 16 Miscellaneous food preparations 17 Tobacco and tobacco products 18 Rubber products 19 Leather products 20 Textile products (except clothing) 21 Clothing (textile and fur) 9 15 11 7 22 Furniture 4 8 5 4 23 Wood products (except furniture) 285 2016 375 1074 24 Paper products 1867 1682 984 1120 25 Printing, publishing & allied ind 32 49 27 27 26 Primary iron and steel 91 459 155 118 27 Agricultural implements 32 712 33 27 28 Iron & steel products, n.e.s. 202 724 265 197' 29 Transportation equipment 134 306 367 123 30 Jewellery & silverware 4 5 2 3_ 31 Non-ferrous cstal products, n.e.s. 66 292 224 i l 6 32 Electrical apparatus & supplies 66 153 121 63 33 Non-metallic mineral products 88 516 135 271 34 Products of petrolevm & coal 236 457 223 216 35 Chemicals and allied predicts 352 504 435 318 36 Misc. manufacturing industries 37 61 34 30 37 Construction 79 148 77 72 38 Transportation, storage 4 trade 530 1084 512 509 39 Coamunic&tioa 49 90 44 46 40 Electric power, gas & water _§97 5J?3______239 ?65_ 41 Finance, insurance k real eotate 119 204 104 99 42 Service Industries , 98 187 101 89 TOTAL 7689" 15373 7600 7254 c I . —F 742 171 164 118 440 1081 317 617 159 271 -66 149 532 2783 2137 1090 353 439 273 264 68 I85 74 98 195 24 19 21 2 1 - -33 3 2 3 4 1 — -,89 17 16 12 10 1 - • 1 211 11 ~8 14 4 1 - -40 6 4 5 34 90 37 24 23 11 5 4 74 82 37 39 - 98 -TABLE XVII INDUCED INCREASES IN CANADIAN IMPORTS  fm = i n ( I - a ) " 1 J ( l - A ) " 1 F ] c I 2* 15 7 6 5 4 22 12 1 — - -6 31 17 10 76 . 133 67 67 7 22 9 11 5 2 2 1 1 1 _ _ 1 — - -(thousands of Canadian d o l l a r s ; 194-9 prices) INDUSTRY ' 1 Agriculture 2 Forestry 3 Fishing, hunting and trapping 4 Metal mining & smelting & refining 5 Coal, crude petroleum & natural gas 6 Non-setal mining & prospecting 7 Meat products 6 Dairy products 9 Fish processing 10 Fruit and vegetable preparations 11 Grain a i l l products 12 Bakery products 13 Carbonated beverages 14 Alcoholic beverages 15 Confectionary end sugar refining 16 Miscellaneous food preparations 17 Tobacco and tobacco products 16 Rubber products 19 Leather products 20 Textile products (except clothing) 21 Clothing (textile and fur) 22 Furniture 23 Wood products (except furniture) 24 Paper products 25 Printing, publishing & allied ind 26 Priaary iron and steel 27 Agricultural ijraplements 28 Iron & steel products, n.e.s. 29 Transportation equipment 30 Jewellery & silverware 31 Non-ferrous metal pro&icts, n.e.c 32 Electrical apparatus & supplies 33 Non-jsatallic mineral pro diets 34 Products of petroleum & cc&l 35 Choaicals and allied products 36 Misc. nanufacturing industries 37 Construction 38 Transportation, storage & trade 39 Cossaainication 40 Electric power, gas & water. 1 - - • -1 1 1 1 2 5 2 2 1 1 - -21 . 25 9 13 2 12 9 5 — 1 - -6 29 6 13 19 22 12 14 1 2 1 1 15 72 24 15 4 4 1 -29 139 44 31 20 43 47 18 1 2 1 1 6 24 16 9 r~ 12 10 5 9 24 10 11 14 42 28 19 43 63 46 35 4 8 4 4 49 112 64 52 2 4 2 2 41 Finance, insurance & real aetata 42 Service industries ' TOTAL 371 866 444 359 - 99 -APPENDIX B CLASSIFICATION OF 1958 EXPORTS FROM CANADA TO THE  UNITED STATES ACCORDING TO THE CANADIAN AND . UNITED STATES INDUSTRY SCHEMES The appendix f i r s t d i s c u s s e s the d e r i v a t i o n o f a l l o c a t e d  e x p o r t s ( i . e . , e x p o r t s t h a t can be m e a n i n g f u l l y a s s i g n e d t o e x p o r t i n d u s t r i e s ) from b a l a n c e o f payments d a t a . Second, the p r o c e d u r e used i n c l a s s i f y i n g the a l l o c a t e d e x p o r t s i s d e s c r i b e d . As i n d i c a t e d i n the t e x t , the e x p o r t d a t a and i n f o r m a t i o n r e g a r d i n g i n d u s t r y c l a s s i f i c a t i o n a r e t a k e n from seven s o u r c e s . They a r e : (1) D.B.S., 67-201, The Canadian B a l a n c e o f I n t e r n a t i o n a l  Payments, a n n u a l . (11) D.B.S., 65-201, Trade o f Canada, v o l . I , a n n u a l , ( i i i ) D.B.S., 65-202, Trade o f Canada, v o l . I I , a n n u a l , ( i v ) D.B.S., 12-501, S t a n d a r d I n d u s t r i a l C l a s s i f i c a t i o n  Manual, 1948 e d i t i o n , ( v ) U n i t e d S t a t e s S t a n d a r d I n d u s t r i a l C l a s s i f i c a t i o n  Manual, 1959. ( v i ) D.B.S., 13-513, Supplement t o the I n t e r - I n d u s t r y Flov; of Goods and S e r v i c e s , Canada 1949, p. 26, T a b l e 10, " I n d u s t r i a l C l a s s i f i c a t i o n F o r the 1949 T a b l e o f I n t e r - I n d u s t r y Flow o f Goods and S e r v i c e s " . - 100 -( v i i ) "The T r a n s a c t i o n s T a b l e o f the 1958 I n p u t - O u t p u t Study and R e v i s e d D i r e c t and T o t a l Requirements Data" Survey o f C u r r e n t B u s i n e s s , September, 1965, p. 83 , T a b l e : " I n d u s t r y Numbering f o r the 1958 I n p u t - O u t p u t S t u d y " . 1. D e r i v a t i o n of A l l o c a t e d E x p o r t s . The t a b l e on page 102 shows the r e l a t i o n of 1958 a l l o c a t e d  e x p o r t s t o the U n i t e d S t a t e s t o T o t a l Merchandise E x p o r t s t o  the U n i t e d S t a t e s and t o T o t a l C u r r e n t R e c e i p t s . F o l l o w i n g the pr o c e d u r e used i n the Canadian i n p u t - o u t p u t s t u d y of 1949} the e x p o r t v a l u e s i n the A g r i c u l t u r e and F i s h p r o c e s s i n g i n d u s t r i e s were reduced by 1 0 . 6 $ . I n a l l o t h e r i n d u s t r i e s the F.O.B. p o i n t o f shipment v a l u a t i o n used i n Trade o f Canada was t a k e n as e q u i v a l e n t t o p r o d u c e r s 1 p r i c e s . On the o t h e r hand, two d e p a r t u r e s were made from the d e f i n -i t i o n o f a l l o c a t e d e x p o r t s used i n the 1949 s t u d y . Gold p r o d u c -t i o n a v a i l a b l e f o r e x p o r t was e x c l u d e d because i t c o u l d not be assumed t o v a r y w i t h U n i t e d S t a t e s f i n a l demand. I t s i n c l u s i o n would have d i s t o r t e d o u t p u t p r e d i c t i o n s f o r the i m p o r t a n t I n d u s t r y , M e t a l m i n i n g and s m e l t i n g and r e f i n i n g ( i n d u s t r y 4 ) . Second, f r e i g h t e x p o r t s were e x c l u d e d from a l l o c a t e d e x p o r t s because t h e y c o u l d not be m e a n i n g f u l l y l i n k e d t o a c o m p e t i t i v e 2 U n i t e d S t a t e s i n d u s t r y . 1. D.B.S., 13-513, Supplement t o the I n t e r - I n d u s t r y Flow o f  Goods and S e r v i c e s , Canada, 1949, p. 19. 2. I f t h e y were p a r t i c u l a r l y d e s i r e d i n an a p p l i c a t i o n o f the model, they c o u l d perhaps be r e l a t e d t o t o t a l e x p o r t s t o the U n i t e d S t a t e s . - 101 -TABLE XVIII  ALLOCATED EXPORTS TO THE UNITED STATES, 1958 ( m i l l i o n s of Canadian d o l l a r s ; 1958 p r i c e s ) T o t a l C u r r e n t R e c e i p t s 6579 T o t a l C u r r e n t R e c e i p t s from the U n i t e d S t a t e s 4010 LESS: G o l d p r o d u c t i o n a v a i l a b l e f o r e x p o r t 160 T r a v e l e x p e n d i t u r e s 309 I n t e r e s t and d i v i d e n d s 100 F r e i g h t and s h i p p i n g 206 I n h e r i t a n c e s and Immigrants funds 47 A l l o t h e r c u r r e n t r e c e i p t s 280 T o t a l M erchandise E x p o r t s t o the U n i t e d S t a t e s ( p e r D.B.S. 67-201) 2908 LESS: R e - e x p o r t s 86 Adjustment -6 T o t a l M e r c h a n d i s e E x p o r t s t o the U n i t e d S t a t e s ( p e r D.B.S. 65-201) 2828 LESS: U n a l l o c a t e d i t e m s 29 ( s e t t l e r s e f f e c t s , g i f t s , c o n t r a c t o r s o u t f i t s , a l l o t h e r a r t i c l e s ) Trade margins i n A g r i c u l t u r e (1) and F i s h P r o c e s s i n g (9) 23 T o t a l A l l o c a t e d E x p o r t s t o the U n i t e d S t a t e s 2776 - 102 -2. The I n d u s t r y C l a s s i f i c a t i o n o f A l l o c a t e d E x p o r t s . T h i s s e c t i o n d e s c r i b e s the p r o c e d u r e used t o o b t a i n the f l o w s , /T , ( i = 1,...,42; j = 1,...,82), common t o p a i r s o f C a n a d i a n and U n i t e d S t a t e s i n d u s t r i e s . F i r s t , 1958 e x p o r t s t o the U n i t e d S t a t e s were l i s t e d from Trade o f Canada, v o l . I (pp. 235-239). I n t h i s s o u r c e they a r e b r o k e n down i n t o n i n e major commodity g r o u p s , each of whi c h i s f u r t h e r r e f i n e d i n t o twenty o r t h i r t y s ub-groups. Second, each of the sub-groups was matched w i t h one o r more S t a n d a r d I n d u s t r i a l C l a s s i f i c a t i o n ( o r S.I.C.) code numbers f o r b o t h the Canadian and U n i t e d S t a t e s c l a s s i f i c a t i o n s . T h i s was the most d i f f i c u l t and most i m p o r t a n t o p e r a t i o n . I t was done by r e f e r i n g t o the p r o d u c t i n d e x and the d e t a i l e d i n d u s t r y d e s c r i p t i o n s I n the S.I.C. manuals. At the same t i m e , t h e c l a s s i f i c a t i o n t a b l e s ( s o u r c e s v i and v i i ) were used t o a l l o c a t e the e x p o r t s t o p a i r s o f i n d u s t r i e s a c c o r d i n g t o t h e i r a s s i g n e d S.I.C. numbers. Some o f the sub-groups o f commodities were found t o b e l o n g t o two o r more i n d u s t r i e s i n e i t h e r o r b o t h of the i n p u t - o u t p u t c l a s s i f i c a t i o n s . I n th e s e c a s e s , Trade o f Canada, v o l . I I was used t o o b t a i n a f i n e r breakdown o f the e x p o r t s . These . d e t a i l e d e x p o r t i t e m s were t h e n a s s i g n e d t o i n d u s t r i e s i n the same way as were the commodity sub-groups. There were a few i n s t a n c e s where e i t h e r the commodity d e t a i l o r I n d u s t r y d e s c r i p t i o n s were i n a d e q u a t e . Here i t was n e c e s s a r y - 10^ -t o make ass u m p t i o n s about the n a t u r e o f the e x p o r t s . F o u r examples are d e s c r i b e d below: ( i ) F u r s k i n s . T h i s p r o d u c t c o u l d be an e x p o r t of f u r farms ( p a r t o f i n d u s t r y 1) o r o f F i s h i n g , h u n t i n g and t r a p p i n g ( 3 ) . The t o t a l v a l u e was a s s i g n e d t o I n d u s t r y 1. ( i i ) H i d e s and S k i n s . They a r e not mentioned i n e i t h e r S.I.C. Manual. They were assumed t o be p r o d u c t s o f the a b b a t o i r and t h e r e f o r e o f Meat p r o c e s s i n g - ( C a n a d i a n i n d u s t r y 7; U n i t e d S t a t e s i n d u s t r y 1 4 ) . ( i l l ) S c r a p . ( m o s t l y s c r a p m e t a l s ) . These were assumed t o be p r o d u c t s o f the P r i m a r y i r o n and s t e e l i n d u s t r i e s ( C a n a d i a n , 28; U n i t e d S t a t e s 3 7 ) . ( i v ) F u r n i t u r e . Here the e x p o r t c l a s s i f i c a t i o n i s not as d e t a i l e d as the U n i t e d S t a t e s i n d u s t r y c l a s s i f i c a t i o n . A l l f u r n i t u r e e x p o r t s were r o u t e d t o the Household f u r n i t u r e i n d u s t r y ( 2 2 ) , and none t o Other f u r n i t u r e and f i x t u r e s ( 2 3 ) . F i n a l l y , w i t h a l l the commodity e x p o r t s a l l o c a t e d t o Canadian and American i n d u s t r i e s , the elements T were c a l c u l a t e d by a g g r e g a t i n g t h e e x p o r t v a l u e s a s s i g n e d t o each p a i r o f i n d u s t r i e s . The non - z e r o elements T. a r e l i s t e d i n T a b l e X I X f o l l o w -i j • • ing. I n T a b l e s X X and X X I the e x p o r t s a r e shown c l a s s i f i e d a c c o r d i n g t o the Canadian and U n i t e d S t a t e s i n d u s t r y schemes. - 104 -TABLE XIX CANADIAN EXPORTS TO THE UNITED STATES, 1958 CLASSIFICATION INTO ELEMENTS, f l . __L 1 0 (Canadian d o l l a r s ; 1958 prices) l , l 4 a 7 ,14 8 ,14 9 , l 4 a 10 ,14 11 ,14 12 ,14 14,14 15 ,14 16 ,14 35 ,14 36 ,14 1 7 , 1 5 2 0 , 1 6 2 0 , 1 7 2 1 , 1 8 2 , 2 0 2 3 , 2 0 Element Value - l , l a 1 0 6 , 0 1 2 , 7 9 3 1 , 2 * 7 1 , 8 0 3 , 2 2 7 6 , 2 7 , 5 0 5 , 8 7 3 3 , 3 8 8 , 0 7 9 , 8 9 6 8 1 , 0 6 2 , 3 0 4 4 , 6 3 5 , 8 2 4 , 8 8 1 5 , 7 2 , 6 9 9 , 8 5 2 5 , 8 73 ,043 ,757 6 , 9 1 0 , 6 5 9 , 7 7 4 3 3 , 9 48 , 167,316 6 , 1 0 2 , 9 1 0 , 4 2 6 2 8 , 1 3 6 , 0 7 7 3 5 , 1 3 1 7 , 2 1 7 5 , 4 6 7 , 7 7 4 6 1 , 4 8 0 , 5 1 3 5 0 5 , 8 9 9 12 ,700 , 884 8 3 5 , 3 1 9 4 , 1 6 3 , 3 8 4 2 , 3 1 7 , 6 6 0 6 8 , 2 8 9 , 6 7 5 4 6 7 , 4 7 0 5 ,541 ,544 866 ,849 4 9 2 , 6 2 8 7 0 , 0 6 1 1 , 1 1 7 , 1 3 4 5 , 3 6 6 , 0 0 8 1 , 2 7 9 , 0 7 8 4 0 , 3 0 0 , 6 8 1 2 7 2 , 5 9 7 , 7 3 1 Element Value Element Value 2 3 , 2 1 5 5 9 , 3 3 8 2 8 , 4 5 8 0 7 , 7 7 4 2 2 , 2 2 2 2 1 , 8 7 5 28 ,46 2 1 4 , 7 0 0 24,24 846 , 156,107 2 8 , 4 7 1 , 1 5 8 , 2 1 5 24 ,25 7 9 , 1 6 8 28 ,48 2 , 2 1 3 , 6 3 5 2 5 , 2 6 3 , 2 9 9 , 7 2 6 2 8 , 4 9 664 ,954 3 5 , 2 7 7 3 , 2 9 9 , 5 6 0 2 8 , 5 0 4 , 8 0 6 , 5 4 5 3 5 , 2 8 1 ,366 ,849 2 8 , 5 1 5 , 8 3 4 , 9 8 1 3 5 , 2 9 3 , 3 7 7 , 8 3 9 2 8 , 5 2 14 ,266 3 5 , 3 0 1 , 3 5 5 , 2 1 0 3 2 , 5 3 1 0 , 6 7 3 3 4 , 3 1 1 8 , 3 2 1 9 , 3 3 1 9 , 3 4 3 3 , 3 5 3 , 2 0 9 , 0 8 0 3 , 9 1 6 , 8 5 7 5 , 2 8 2 , 4 4 5 1 , 0 9 5 , 8 2 9 8 9 9 , 1 2 1 2 8 , 5 4 3 2 , 5 4 3 2 , 5 5 3 2 , 5 6 3 2 , 5 8 2 8 , 5 9 2 9 , 5 9 1 6 , 7 2 3 1 3 , 8 8 3 9 7 , 5 3 4 5 , 0 3 6 , 6 7 9 2 , 9 1 3 , 0 0 8 17,717 ,540 9 , 224 , 5 8 8 3 3 , 3 6 2 6 , 3 7 2 8 , 3 7 3 4 , 3 7 4 , 3 8 31 ,38 28 ,40 28 ,41 3 0 , 7 1 3 , 6 3 6 2 6 , 5 8 2 , 1 5 ! 3 ,048 ,119 1 , 5 4 5 , 5 7 0 5 0 3 , 7 7 6 , 6 9 5 51 , 946 ,544 2 0 3 , 6 9 9 5 5 , 7 4 5 2 9 , 6 0 2 9 , 6 1 3 6 , 6 2 3 6 , 6 3 20 ,64 21 ,64 30 ,64 36 ,64 40 ,68 : 1 4 , 9 7 7 , 0 9 6 9 4 5 , 8 0 1 2 , 3 7 1 , 0 3 2 1 , 1 9 2 , 9 0 2 5 , 1 7 7 7 8 1 , 4 1 5 9 4 3 , 1 5 6 3 , 446 ,055 3 0 , 5 6 1 , 3 1 3 28 ,42 31 ,42 5,630 , 442 6 8 1 , 9 9 9 Total 2,776 ,398,208 2 8 , 4 3 1 3 6 , 5 0 5 27 ,44 9 0 , 3 3 4 , 8 0 9 ad.iusted for trade margins. Elements - 105 -TABLE XX CANADIAN EXPORTS TO THE UNITED STATES, 1958 CANADIAN INDUSTRY CLASSIFICATION (Canadian d o l l a r s ; 1958 prices) INDUSTRY VALUE 1 Agric vulture 183,283,794 2 Forestry 40,300,681 3 Fishing, hunting and trapping 88,079,896 4 Metal mining & smelting & r e f i n i n g . 620,663,880 5 Coal, crude petroleum & natural gas '75,743,609 6 Non-metal mining & prospecting 21,076,073 7 Meat products 61,480,513 8 Dairy products 505,899 9 Fish processing 12,700,884 10 F r u i t and vegetable preparations 835,319 11 Grain m i l l products ~- 4,163,384 12 Bakery products 2,317,660 13 Carbonated beverages -14 Alcoholic beverages 68,289,675 15 Confectionery and sugar r e f i n i n g 467,470 16 Miscellaneous food preparations , 5,541,544 17 Tobacco and tobacco products 70,061 18 Rubber products 3,916,857 19 Leather products 6,378,274 20 T e x t i l e products (except clothing) 6,488,319 21 Clothing ( t e x t i l e and fur) " - - - - - - 2,060,493 22 Furniture 221,875 23 Wood products (except furniture) 273,157,069 24 Paper products 846,235,275 25 P r i n t i n g , publishing & a l l i e d i n d 3,299,726 26 Primary i r o n and s t e e l 26,582,151 27 A g r i c u l t u r a l implements 90,33^,809 28 Iron & s t e e l products, n.e.s. 42,529,880 29 Transportation equipment 25,147,485 30 Jewellery & silverware : _..943,156„. 31 Non-ferrous metal products, n.e.s. 52,628,543 32 E l e c t r i c a l apparatus & supplies 8,071,777 33 Non-metallic mineral products 79,780,073 34 Products of petroleum & coal . 4,754,650 35 Chemicals and a l l i e d products 80,283,524 36 Misc. manufacturing industries • 7,502,617 37 Construction 38 Transportation, storage & tradci ; . :' 39 Communication -40 E l e c t r i c power, gas & water_ _ : 29>5I°1,.313_ 41 Finance, insurance & r e a l estate -42 Service industries TOTAL 2,776,398,208 - 106 -TABLE . XXI CANADIAN EXPORTS TO THE UNITED STATES, 1958  UNITED STATES CLASSIFICATION (Canadian d o l l a r s ; 1958 prices) INDUSTRY VALUE i z 3 4 5 6 7 8 9 10 11 12 13 14 IS 16 17 18 19 2 0 21 22 2 3 2 4 2S 26 27 28 29 30 31 32 33 34 35 36 37 38 39 4 0 41 42 43 44 45 46 47 48 49 50 51 52 S3 5 4 S5 56 57 58 59 60 61 62 6 3 64 , 65 66 67 68 , 69 70 71 . 72 73 7 4 . 75 76 77 78 79 80 81 . 8 2 . . L I V E S T O C K * ! . I V E S T O C K P R O D U C T S . O T H E R A G R I C U L T U R A L P R O D U C T S F O R E S T R Y + F 1 S H E R Y P R O D U C T S . A G R I C U L T U R A L , F O R E S T R Y+ F I S H E R Y S E R V I C E S . I R O N * F E R R O A L L O Y O R E S M I N I N G . N O N F E R R O U S M E T A L O R E S M I N I N G . C O A L M I N I N G . C R U D E P E T R O L E U M * N A T U R A L G A S . S T O N E + C L A Y M I N I N G Q U A R R Y I N G . C H E M I C A L + F E R T I L I Z E R M I N E R A L M I N I N G . N E W C O N S T R U C T I O N . M A I N T E N A N C E + R E P A I R C O N S T R U C T I O N . O R D N A N C E + A C C E 5 S O R I E S . F O O D * K I N D R E D P R O D U C T S . T O B A C C O M A N U F A C T U R E S . B R O A D + N A R R O W F A B R I C S . Y A R N + T H R E A D • M I S C . F A B R I C A T E D T E X T I L E P R O D U C T S . A P P A R E L . M I S C . F A B R I C A T E D T E X T I L E P R O D U C T S L U M B E R + W O O D P R O D S . , E X C E P T C O N T A I N E R S . W O O D E N C O N T A I N E R S . H O U S E H O L D F U R N I T U R E . O T H E R F U R N l T U R E t F I X T U R E S . P A P E R + A L L I E D P R O D S . , E X C E P T C O N T A I N E R S . P A P E R B O A R D C O N T A I N E R S + B O X E S . P R I N T l N G t P U B L I S H I N G C H E M I C A L S + S E L E C T E D C H E M I C A L P R O D U C T S P L A S T I C S + S Y N T H E T I C M A T E R I A L S D R U G S , C L E A N I N G + T O 1 L E T P R E P A R A T I O N S P A I N T S + A L L I E D P R O D U C T S -. P E T R O L E U M R E F I N I N G + R E L A T E D I N D U S T R I E S R U B B E R + M I S C E L L A N E O U S P L A S T I C S P R O D U C T S • L E A T H E R T A N N I N G + l N D U S T R I A L L E A T H E R P R O D S . . F O O T W E A R * O T H E R L E A T H E R P R O D U C T S . G L A S S + G L A S S P R O D U C T S . S T O N E + - C L A Y P R O D U C T S . P R I M A R Y I R O N f S T E E L M A N U F A C T U R I N G . P R I M A R Y N O N F E R R O U S M E T A L S M A N U F A C T U R I N G . M E T A L C O N T A I N E R S . H E A T I N G , P L U M B I N G + S T R U C T U R A L M E T A L P R O D S . -• S T A M P I N G S , S C R E W M A C H I N E P R O D U C T 5 * B O L T S . O T H E R F A B R I C A T E D M E T A L P R O D U C T S . E N G I N E S * T U R B I N E S . F A R M M A C H I N E R Y + E Q U I P M E N T . C O N S T R U C T I O N , M I N I N G + O I L F I E L D M A C H I N E R Y . M A T E R I A L S H A N D L I N G M A C H I N E R Y + E Q U I P M E N T . M E T A L W O R K I N G M A C H I N E R Y + E Q U I P M E N T . S P E C I A L I N D U S T R Y M A C H I N E R Y + E Q U I P M E N T . G E N E R A L I N D U S T R I A L M A C H I N E R Y + E Q U I P M E N T . M A C H I N E S H O P P R O D U C T S _ O F F I C E . C O M P U T I N G + A C C O U N T I N G M A C H I N E S S E R V I C E I N D U S T R Y M A C H I N E S E L E C T R I C I N D U S T R I A L E Q U I P M E N T + A P P A R A T U S H O U S E H O L D A P P L I A N C E S E L E C T R I C L I G H T I N G + W l R I N G E Q U I P M E N T R A D I O , T . V . + C O M M U N I C A T I O N E Q U I P M E N T E L E C T R O N I C C O M P O N E N T S A C C E S S O R I E S M I S C E L L A N E O U S E L E C T R I C A L M A C H I N E R Y + S U F P U E S M O T O R V E H I C L E S + E Q U I P M E N T A I R C R A F T + P A R T S _ O T H E R T R A N S P O R T A T I O N E Q U I P M E N T S C I E N T I F I C + C O N T R O L L I N G I N S T R U M E N T S O P T I C A L . O P H T H A L M I C + P H O T O G R A P H I C E Q U I P T . M I S C E L L A N E O U S M A N U F A C T U R I N G T R A N S P O R T A T I O N + W A R E H O U S I N G C O M M U N I C A T I O N S - E X C E P T R A D I O + T . V . R A D I O + T . V . B R O A D C A S T I N G E L E C T R I C , G A S . W A T E R + S A N I T A R Y S E R V I C E S W H O L E S A L E + R E T A I L T R A D E . F I N A N C E " * I N S U R A N C E _ R E A L E S T A T E + R E N T A L H O T E L S - P E R S O N A L + R E P A I R . S E R V I C E S B U S I N E S S S E R V I C E S R E S E A R C H + D E V E L O P M E N T A U T O M O B I L E R E P A I R+ S E R V I C E S A M U S E M E N T S M E D I C A L E D U C A T I O N S E R V I C E S F E D E R A L G O V E R N M E N T E N T E R P R I S E S S T A T E + L O C A L G O V E R N M E N T E N T E R P R I S E S G R O S S I M P O R T S O F G O O D S + S E R V I C E S B U S I N E S S T R A V E L , E N T E R T A I N M E N T + G I F T S O F F I C E S U P P L I E S 106012793 7 9309 1 0 0 8 8 0 7 9 8 9 6 8 1 0 6 2 3 0 4 358248B1 2 6 9 9 8 5 2 7 3 0 4 3 7 5 7 58827 090 2910426 2 3 2 9 4 163129599 70061 1117134 5 3 6 6 0 0 8 1279078 312898 412 " 5 5 9 3 3 8 " 221875 846156107 79168 3299726 7 3 2 9 9 5 6 0 1366849 3377839 1355210 3209 080 39168S7 5282445 1095829 899121 3 0 7 1 3 6 3 6 3 1 1 7 5 8 4 0 555723239 2 0 3 6 9 9 55745 6312441 136505 9 0 3 3 4 8 0 9 8 0 7 7 7 4 2 1 4 7 0 0 1158215 2 2 1 3 6 3 5 664954 4 8 0 6 5 4 5 _ 5834981 ? 14226 10673 3 0 6 0 6 9 7 5 3 4 5036 679 2 9 1 3 0 0 8 2 6 9 4 2 1 2 8 _14977096 945 801 2371 032 1192902 5175803 30561 313 TOTAL 2,776,398,208 - 107 -APPENDIX C THE TECHNIQUE USED IN UPDATING THE  CANADIAN INPUT-OUTPUT MATRICES The u p d a t i n g p r o c e d u r e used by T. I . M a t u s z e w s k i , P. R. P i t t and J . A. Sawyer i n o b t a i n i n g t h e 1959 d i r e c t r e q u i r e m e n t s m a t r i x i s made more complex by t h e f a c t t h a t the 1949 m a t r i x was upda t e d t o a p p l y t o 1956 and t h e r e s u l t i n g m a t r i x updated t o 1959* The i m p o r t m a t r i x was u p d a t e d t o 1956 b y a method q u i t e s i m i l a r t o t h a t used f o r the p r o d u c t i o n m a t r i x , so i t s u p d a t i n g w i l l n o t be d e s c r i b e d . Two methods were combined i n u p d a t i n g the 1949 d i r e c t 49 r e q u i r e m e n t s m a t r i x , a y , t o 1956. The f i r s t method used was t o r e - e s t i m a t e c o e f f i c i e n t s i n d i v i d u a l l y . T h i s was done f o r s e v e r a l c o e f f i c i e n t s ( e i g h t i n t he p r o d u c t i o n m a t r i x ) t h a t d e s c r i b e d p r o c e s s e s a f f e c t e d by two i m p o r t a n t t e c h n o l o g i c a l changes. The changes c o r r e c t e d f o r were the s h i f t f r o m n a t u r a l t o s y n t h e t i c f i b r e s i n t e x t i l e s and c l o t h i n g , and the s h i f t f r o m m a n u f a c t u r e d t o n a t u r a l gas. The second method used by Sawyer was the t h e o r e t i c a l l y l e s s sound b u t n e v e r t h e l e s s e f f e c t i v e one o f m u l t i p l y i n g each row 49 o f a ^ by a c o n s t a n t p r o p o r t i o n a l i t y f a c t o r . The f a c t o r g e n e r a l l y used i s 1 1 - 108 -where o and 1 a r e t h e base y e a r and c u r r e n t y e a r r e s p e c t -i v e l y . I t r e p r e s e n t s the r a t i o between two e s t i m a t e s o f the i n t e r m e d i a t e o u t p u t o f p r o d u c t i . The f i r s t e s t i m a t e i s made by d i r e c t N a t i o n a l A c c o u n t s e s t i m a t e s o f i n d u s t r y o u t p u t and f i n a l demand. The second e s t i m a t e i s made by a p p l y i n g the o l d p r o d u c t i o n c o e f f i c i e n t s , a ? . , t o the new e s t i m a t e d t o t a l o u t p u t s , X ^ ; The p r o p o r t i o n a l i t y f a c t o r a c t u a l l y used was a m o d i f i c a t i o n o f the one shown, d e s i g n e d t o a v o i d i n f l u e n c i n g the p r e v i o u s l y • r e - e s t i m a t e d c o e f f i c i e n t s . The f l o w s t o be r e p r e s e n t e d by the.-t. i n d e p e n d e n t l y e s t i m a t e d c o e f f i c i e n t s were t e m p o r a r i l y s e t e q u a l t o z e r o and the f a c t o r a p p l i e d t o the r e m a i n i n g f l o w s . Thus t h 49 the c o e f f i c i e n t t h a t was a p p l i e d t o the i row o f a . • was , x 5 6 . y 5 6 _ C 5 6 d 5 = 1 1 1  1 y2 a 4 9 x 5 6 where the C;?^ r e p r e s e n t s t h e b l o c k e d f l o w s i n t h e i ^ * 1 row. The a p p l i c a t i o n o f t h e two methods was com p l e t e d by p l a c i n g 56 49 th e i n d e p e n d e n t l y e s t i m a t e d c o e f f i c i e n t s i n d^ a ^ where 56 S6 d i s t h e d i a g o n a l m a t r i x o f dr . , 59 F i n a l l y , a was formed u s i n g t h e second method a l o n e so t h a t ' N a59 . d59 a56 59 where the p r i n c i p a l elements o f a r e . Q x 5 9 59 d 5 9 = i »± ( . = 1 • k 2 ) 42 56 59 E aj° xf 0=1 J J - 109 APPENDIX D PRICE DEFLATION OF THE CANADIAN EXPORT VECTOR T h i s a p p e n d i x e x p l a i n s how t h e Pj_ , the d i a g o n a l elements o f P , were o b t a i n e d . The p r i m a r y source o f i n f o r m a t i o n was D.B.S. Number 65-205, Review o f F o r e i g n Trade, a n n u a l , T a b l e XX " P r i c e s o f Domestic E x p o r t s by Groups and S e l e c t e d Commodities" The p r i c e s i n t h i s t a b l e a r e i n d e x e s based on the y e a r 1948. 58 I f P^ i s the i n d e x f o r e x p o r t commodity k f o r 1958, t h e n p 5 8 _ 1958 p r i c e x , m n  P k ~ 1948 p r i c e X 1 0 0 * ° • A c c o r d i n g l y , the f i r s t s t e p i n d e r i v i n g p^ was t o combine th e 1949 and 1958 e x p o r t commodity p r i c e i n d e x e s o b t a i n i n g P k 9  P k = — P 5 8 r k N e xt the commodity i n d e x e s , P , were a l l o c a t e d t o Canadian k i n d u s t r i e s . I n most c a s e s the i n d e x o f a s i n g l e commodity ( o r commodity group) was c o n s i d e r e d s u f f i c i e n t t o r e p r e s e n t the p r i c e e x p e r i e n c e o f an e x p o r t i n d u s t r y . F o r t h e s e i n d u s t r i e s , P i = P k . Such was the c a s e , f o r i n s t a n c e , w i t h w h i s k y ( i n d u s t r y 1 4 ) , l e a t h e r ( 1 9 ) , and f a r m m a c h i n e r y ( 2 7 ) . I n othe c a s e s , commodity i n d e x e s were a g g r e g a t e d t o o b t a i n the i n d u s t r y i n d e x . Here, 1958 e x p o r t v a l u e s t a k e n from Trade o f Canada were used t o w e i g h t the commodity i n d e x e s . F o r t h e s e - 110 -i n d u s t r i e s p. = £ P,V, where V. i s the 1958 e x p o r t v a l u e i k = 1 K. k o f commodity k , and I the number o f commodity i n d e x e s a g g r e g a t e d . The p r o d u c t s o f a few i n d u s t r i e s were n o t e x p l i c i t i n the Review o f F o r e i g n Trade t a b l e and, f o r most o f t h e s e , d o m e s t i c i n d e x e s were used. The source o f th e s e i n d e x e s was D . B . S . number 6 2 - 0 0 2 , P r i c e s and P r i c e I n d e x e s , a n n u a l , "Wholesale P r i c e Index Numbers Showing Component D e t a i l (1935-39'= 1 0 0 . 0 ) " . I t i s T a b l e I V i s e d i t i o n s c o v e r i n g the y e a r s t o 1952 and T a b l e I I I i n l a t e r e d i t i o n s . A g a i n the r a t i o o f two i n d e x e s was used t o r e l a t e 19^9 p r i c e s t o 1958 p r i c e s . F i n a l l y , f o r the p r o d u c t s : - uranium ( 4 ) , and e l e c t r i c power and n a t u r a l gas ( 4 0 ) , no p r i c e i n f o r m a t i o n c o u l d be f o u n d f o r y e a r s p r i o r t o 1958. I n the f i r s t case t h i s i s because i n f o r m a t i o n on uranium e x p o r t s was c l a s s i f i e d b e f o r e 1958. I n the second i t i s because e x p o r t s b e f o r e 1957 o r 1958 were i n s i g n i f i c a n t . F o r t h e s e c o m m o d i t i e s , a p r i c e * d e f l a t o r o f 100.0 was assumed. The v a l u e s and d e r i v a t i o n o f the i n d e x e s p^ ( i = 1,..,42) are shown i n T a b l e X X I I f o l l o w i n g . - I l l -T A B L E X X I I DERIVATION OF EXPORT PRICE INDEXES FOR THE CANADIAN INDUSTRIES Component Commodities . Industry Price Index. Source (and Indexes) 1 100.8 (a) barley (140.0), oats (106.8), rye (142.4), wheat (126.2), dairy cattle (80.7), slaughter cattle (93.8), fur skins (93.6), eggs (142.9) 2 81.5 (a) pulpwood 3 74.9 (a) f i s h 4 80.4 (a) iron ore (77.7), aluminum (66.9), copper (83.7), lead (190.3), s i l v e r (85.2), platinum (133.7), zinc (138.9), nickel (52.6); (c) uranium (100.0) 5 81.8 (a) coal (78.4); (b) petroleum (81.9) 6 97.0 (a) asbestos (68.2); (b) lime and cement (96.8), stone (99.4) 7 81.5 (a) beef and veal, fresh 8 88.4 (a) milk processed 9 74.9 (a) fish 10 99.3 (b) miscellaneous foods 11 127.5 (a) wheat flour 12 127.5 (a) wheat flour 13 - no exports 14 93-0 (a) whisky 15 94.5 (b) sugar 16 99.3 (b) miscellaneous foods 17 87.3 (a) tobacco 18 64.2 (a) rubber 19 71.2 (a) leather 20 71.3 (a) fibres and textiles - 112 -TABLE X X I I ( c o n t i n u e d ) Industry Price Index Source Component Commodities 21 71.3 (a) fibres and t e x t i l e s 22 96.2 (a) planks and blocks 23 94.2 (a) planks and blocks (96.2), shingles (72.4), plywood (100.6) 24 78.8 (a) woodpulp (86.3), newsprint (76.0) 25 76.0 (a) newsprint 26 79.5 (a) pig iron, ferro-alloys -•  27 66.9 (a) farm machinery 28 75.4 (a) machinery (non-farm) 29 77.4 (a) autos, trucks, and parts 30 85.2 (a) s i l v e r 31 81.4 (a) aluminum (66.9), copper (83.7), lead (190.3), zinc (138.9) 32 86.7 (a) miscellaneous manufacturing 33 66.0 (a) abrasives (61.4), asbestos (68.2) 34 80.4 (a) coal (78.4) 35 91.5 (a) chemicals and f e r t i l i z e r s 36 86.7 (a) miscellaneous manufacturing 37 - no exports 38 - no exports 39 - no exports 40 100.0 (c) electric power and natural gas 4 1 - no exports 42 - no exports Key to Sources (a) Review of Foreign Trade (b) Prices and Price Indexes (c) No price information for years previous to 1958. 

Cite

Citation Scheme:

        

Citations by CSL (citeproc-js)

Usage Statistics

Share

Embed

Customize your widget with the following options, then copy and paste the code below into the HTML of your page to embed this item in your website.
                        
                            <div id="ubcOpenCollectionsWidgetDisplay">
                            <script id="ubcOpenCollectionsWidget"
                            src="{[{embed.src}]}"
                            data-item="{[{embed.item}]}"
                            data-collection="{[{embed.collection}]}"
                            data-metadata="{[{embed.showMetadata}]}"
                            data-width="{[{embed.width}]}"
                            async >
                            </script>
                            </div>
                        
                    
IIIF logo Our image viewer uses the IIIF 2.0 standard. To load this item in other compatible viewers, use this url:
http://iiif.library.ubc.ca/presentation/dsp.831.1-0104793/manifest

Comment

Related Items