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UBC Theses and Dissertations

The demand for durables, nondurables, services and the supply of labour in Canada : 1946-1969 Gussman, Thomas Keith 1972

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THE DEMAND FOR DURABLES, NONDURABLES, SERVICES AND THE SUPPLY OF LABOUR IN CANADA: 1946 - 1969 b y THOMAS KEITH GUSSMAN B . A . , U n i v e r s i t y o f B r i t i s h C o l u m b i a , 1970 A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF ARTS i n t h e D e p a r t m e n t o f E c o n o m i c s We a c c e p t t h i s t h e s i s as c o n f o r m i n g t o t h e r e q u i r e d s t a n d a r d THE UNIVERSITY OF BRITISH COLUMBIA A u g u s t , 1972 In present ing th i s thes i s in p a r t i a l f u l f i lmen t of the requirements for an advanced degree at the Un iver s i t y of B r i t i s h Columbia, I agree that the L ib ra ry sha l l make i t f r ee l y ava i l ab le for reference and study. I fu r ther agree that permission for extensive copying o f th i s thes i s fo r s cho la r l y purposes may be granted by the Head of my Department or by h i s representat ives . It is understood that copying or pub l i c a t i on o f th i s thes i s f o r f i nanc i a l gain sha l l not be allowed without my wr i t ten permiss ion. Department of , Economics The Un iver s i t y of B r i t i s h Columbia Vancouver 8, Canada Date August 30, 1972 A B S T R A C T A G e n e r a l i z e d L e o n t i e f I n v e r s e I n d i r e c t U t i l i t y F u n c t i o n a n d i t s e s t i m a t i o n a r e d i s c u s s e d ; a d a t a b a s e c o m p a t i b l e w i t h t h e r e q u i r e m e n t s o f t h e f u n c t i o n i s c r e a t e d , and we a t t e m p t t o e s t i m a t e p o s t w a r C a n a d i a n p r e f e r e n c e s ( f o r c o n s u m p t i o n w i t h and w i t h o u t t h e s i m u l t a n e o u s s u p p l y o f l a b o u r ) . The p a r a m e t e r s o f t h e f u n c t i o n a r e e s t i m a t e d i n a t w o - s t a g e ( g e n e r a l i z e d ) l e a s t s q u a r e s p r o c e d u r e due t o Z e l l n e r [ 1 9 6 1 ] . The e m p i r i c a l r e s u l t s i n d i c a t e t h a t t h e f u n c t i o n a l f o r m b e h a v e s r a t h e r w e l l and o u r e s t i -mated e x p e n d i t u r e s h a r e s and e l a s t i c i t i e s o f s u b s t i t u t i o n be tween goods seem t o c o n f o r m t o o u r t h e o r e t i c a l e x p e c t a t i o n s . i i TABLE OF CONTENTS Page L I S T OF TABLES v C h a p t e r I. INTRODUCTION . . 1 I I . A REVIEW OF THE LITERATURE . . 3 A . The L i n e a r E x p e n d i t u r e S y s t e m (LES) 3 B . The G e n e r a l i z e d L i n e a r E x p e n d i t u r e S y s t e m 4 C . The Demand f o r D u r a b l e Goods 6 D. The I n d i r e c t U t i l i t y F u n c t i o n 10 I I I . GENERALIZED LEONTIEF PREFERENCES AND THEIR ESTIMATION. .16 A . A G e n e r a l i z e d L e o n t i e f U t i l i t y F u n c t i o n .16 B . E c o n o m e t r i c s i n B r i e f . . 20 I V . DATA: CONCEPTS AND SOURCES. . 23 A . The T r e a t m e n t o f D u r a b l e Goods . . -. 23 1. S t o c k s 23 2. I n i t i a l S t o c k s 24 3. The D u r a b l e Goods 25 a . C l o t h i n g 25 b . M o t o r V e h i c l e s 26 c . O t h e r D u r a b l e s 28 d . H o u s i n g 30 i . R e s i d e n t i a l L a n d 31 i i . D w e l l i n g s .35 i i i . P r o p e r t y T a x e s 39 B . The Rate o f I n t e r e s t R e l e v a n t t o Consumer E x p e n d i t u r e D e c i s i o n s 39 C . R e n t a l P r i c e s 42 D. Nondurab l e s 44 i i i i v C h a p t e r Page E . S e r v i c e s 44 1. M e d i c a l C a r e and H e a l t h S e r v i c e s 45 F . The S u p p l y o f L a b o u r 46 A p p e n d i x t o C h a p t e r IV 48 V . REGRESSION R E S U L T S : MODEL NO. 1 — CONSUMPTION ONLY. . 71 D i s c u s s i o n 77 V I . REGRESSION R E S U L T S : MODEL NO. 2 — CONSUMPTION AND LEISURE . . 79 V I I . CONCLUSIONS 86 BIBLIOGRAPHY 91 LIST OF TABLES Table Page IV-1 Aggregate Stock Series 49 IV-2 Canada: Population and Employment 50 IV-3 Durables: Purchase P r i c e Indexes 51 IV-4 Durables: Discount Rate and Average Property Tax Rate. . 52 IV-5 Durables: Rental P r i c e s . 55 IV-6 Nondurables: Purchase P r i c e Indexes 56 IV-7 Per Capita Quantity S e r i e s . 57 IV-8 Consumption Model: 'Normalized' P r i c e s 58 IV-9 Annual Wage B i l l s and Hours Worked 59 IV-10 Sources Used to Calculate the Rate of Tax on Labour Earnings . . 60 IV-11 Labour: Hours, Tax and Wages 61 IV- 12 Consumption and Le i s u r e : 'Normalized' Pr i c e s 62 Computer Programs Used i n Computations: DELTA To Calcu l a t e A Depreciated stock Series 63 LF To Calculate the Terms of the Generalized Leontief U t i l i t y Function . . 64 SIGUNN To Calculate 'Pseudo' — E l a s t i c i t i e s of S u b s t i t u t i o n . . 66 SIGNORM To Calcu l a t e E l a s t i c i t i e s of S u b s t i t u t i o n ( a . . ) For Market^Demands . . 68 MS HA RE To Calcu l a t e Estimated Market Shares 70 V- l Estimated C o e f f i c i e n t s f o r Consumer Preferences . . . . . 72 V-2 F i t t e d Market Shares . 74 V-3 E l a s t i c i t i e s of S u b s t i t u t i o n . 75 v vi Table Page VI-1 Estimated C o e f f i c i e n t s f o r Consumer Preferences 79 VI-2 F i t t e d Market Shares 82 VI-3 E l a s t i c i t i e s of Su b s t i t u t i o n 83 VII-1 I n d i r e c t U t i l i t y Function 89 \ A C K N O W L E D G E M E N T It would be grossly unfair to proceed without f i r s t paying tribute to a long l i s t of people who have unselfishly offered ideas and criticisms throughout the formative stages of this thesis. Among these, Professors Robert Evans, John Helliwell, Ronald Shearer, William Stanbury, and Dan Usher were constantly plagued by my queries and deserve a note of thanks for their suggestions and patience. My committee, consisting of my supervisor, Professor Erwin Diewert, and Professors Terence Wales and Alan Woodland, somehow managed to endure the trial-and-error process that is inr herent in the data game, and hopefully, they have emerged relatively un-scarred. I owe them an especial debt of gratitude. Professor Diewert"s theories and teachings are self-evident in my work, and without him I would quite likely have been unable to work on the present topic, namely, the simul-taneous estimation of consumer demand and labour supply functions. It is important to emphasize that a l l persons mentioned should not be associated with any errors, since I alone am responsible. The typing of the manuscript (especially the interpretation of my handwriting!) was no small task, and Susan Aizenman, whose " c l i f f hanger" style has erupted many an ulcer, came through in fine style with eleven minutes to spare before the deadline. In typing the final draft, my wife, Natalie, provided an inspiration to us by incessantly talking so as to prevent our sleeping on the job. Finally, I wish to acknowledge the Department of Manpower and Immigration (Ottawa) for financial support. v i i CHAPTER I INTRODUCTION In t h e l i t e r a t u r e o f a p p l i e d consumer t h e o r y , s e v e r a l a t t e m p t s h a v e b e e n made t o a p p r o x i m a t e t h e p a r a m e t e r s o f " t h e " u t i l i t y f u n c t i o n u n d e r l y i n g t h e e x p e n d i t u r e p a t t e r n s o b s e r v e d i n a p a r t i c u l a r c o u n t r y . M o s t n o t a b l y , t h e works o f S t o n e ( G r e a t B r i t a i n ) ; H o u t h a k k e r and T a y l o r ( U . S . A . ) ; P o l l a k a n d Wales ( U . S . A . ) ; S c h w e i t z e r ( C a n a d a ) , a n d W a l e s (Canada) have b e e n a t t e m p t s t o e s t i m a t e t h e p r e f e r e n c e map u n d e r l y i n g demands emergent f r o m an i n h e r e n t m a x i m i z a t i o n o f some p a r t i c u l a r f u n c t i o n s u b j e c t t o an income o r b u d g e t c o n s t r a i n t . A t t i m e s , t h e demand f u n c t i o n s h a v e b e e n l i n e a r r s e m i - l o g a r i t h m i c ; d o u b l e - l o g a r i t h m i c ; o r e v e n i n v e r s e s e m i - l o g a r i t h m i c . Some o f t h e s e f u n c t i o n s h a v e c o n s t a n t e l a s t i c i t i e s o f s u b s t i t u t i o n , w h i l e o t h e r s a d m i t t h e p o s s i b i l i t y o f an a r b i t r a r y e l a s t i c i t y o f s u b s t i t u t i o n b e t w e e n e a c h p a i r o f g o o d s . Whatever t h e f u n c t i o n a l f o r m , t h e s e s t u d i e s have e a c h c o n t r i b u t e d t o t h e l i t e r a t u r e . In a s i m i l a r f a s h i o n , t h e p r e -s e n t s t u d y a t t e m p t s t o e s t i m a t e t h e " t y p i c a l " C a n a d i a n c o n s u m e r ' s u t i l i t y map i n a f o r m a l i z e d r e v e a l e d p r e f e r e n c e f ramework . We make u s e o f t h e i n -d i r e c t u t i l i t y f u n c t i o n and assume a n o n - h o m o t h e t i c G e n e r a l i z e d L e o n t i e f f u n c t i o n a l f o r m due t o D i e w e r t [7 ; 1971] w h i c h i s q u a d r a t i c i n t h e s q u a r e r o o t s o f t h e p a r a m e t e r s (Ln t h e consumer c a s e p r i c e s ) . F rom t h e d e r i v e d demand e q u a t i o n s , we e s t i m a t e t h e p r e f e r e n c e s i n a g e n e r a l i z e d l e a s t s q u a r e s p r o c e d u r e . 1 2 Our model has several p i t f a l l s , among which i s the problem of d e a l -ing with aggregate data and a r b i t r a r i l y d i v i d i n g a l l q u a n t i t i e s by popula-t i o n to approximate per-capita shares. C l e a r l y , whether we evenly d i s t r i -bute c a p i t a l stock and expenditure by person or by family, we are not ob-t a i n i n g a true p i c t u r e of personal expenditure. As i s well-known, s t a t i s -t i c a l d i f f i c u l t i e s may a r i s e i n such a framework. However, since a sur-vey of alt f a m i l i e s i n the data universe i s i n f e a s i b l e , we work with what i s a v a i l a b l e . Another shortcoming i n t h i s study i s the exclusion of personal savings from the model; here, savings i s an exogenous d e c i s i o n and i s thus not determined as a d e c i s i o n v a r i a b l e along with expenditures and labour supply. The good features, however, ought to, at l e a s t i n part, compensate f o r the omissions. We are hopeful that' the i n c l u s i o n of a more d e t a i l e d a l l o c a t i o n of expenditure i n the current period, the treatment of consumer durables i n a user-cost framework, and the simultaneous estimation of the demand f o r "dis-work" (leisure) so that the labour supply d e c i s i o n i s endo-genous to the system, w i l l prove to be u s e f u l . Chapter II b r i e f l y reviews other studies i n consumer theory. Chapter I I I o u t l i n e s the Generalized Leontief Function, i t s properties and the process used to estimate i t s unknown parameters. CHAPTER I I A REVIEW OF THE LITERATURE A . THE LINEAR EXPENDITURE SYSTEM (LES) From the S t o n e - G e a r y u t i l i t y f u n c t i o n , ^ " we may d e r i v e demand e q u a -t i o n s i n w h i c h e x p e n d i t u r e on e a c h g o o d i s a l i n e a r homogeneous f u n c t i o n o f income and a l l p r i c e s . F o r t h i s r e a s o n t h e mode l i s known as ( S t o n e ' s ) l i n e a r e x p e n d i t u r e s y s t e m . A t y p i c a l S t o n e - G e a r y u t i l i t y f u n c t i o n i s : n U = E B. l o g ( X . - v . ) ( I I - l ) i-1 1 1 1 where i s a q u a n t i t y ; 0 < 8. < 1; — I f o r a l l i n The f u n c t i o n i s o n l y d e f i n e d when ( X ^"Y^) > 0 . T h i s f u n c t i o n i s 2 d i r e c t l y a d d i t i v e , a n d t h e r e s u l t a n t demand s y s t e m i s : N p . X . = p . Y . + B. • (Y - Z p . Y . ) ( i = l , . . . , N ) ( I I -2) 1 1 1 1 1 j=i 3 3 The p o i n t s b r o u g h t o u t h e r e a r e b a s i c a l l y c o n d e n s e d f r o m G o l d b e r g e r ' [18] s u p e r l a t i v e s u r v e y o f consumer demand t h e o r y ( i . e . , r e t h e S t o n e - G e a r y f u n c t i o n ) . 2 G o l d b e r g e r [18; p . 45] shows t h i s a l g e b r a i c a l l y . 4 where y = xncome; p = p r i c e o f i t h g o o d . G o l d b e r g e r o f f e r s a u s e f u l i n t e r p r e t a t i o n : G i v e n income y and p r i c e s p ^ , . . . / P n / t n e consumer f i r s t p u r c h a s e s "minimum r e q u i r e d q u a n t i t i e s " o f e a c h g o o d : o f g o o d 1,. . .,y o f g o o d n . A t t h e g i v e n p r i c e s , t h i s c o s t s £ p . Y . » w h i c h may be t e r m e d " s u b s i s t e n c e i n c o m e . " He i s 3 3 3 l e f t w i t h y-Sp_.Yj/which may be t e r m e d " s u p e r n u m e r a r y i n c o m e " ; t h i s he d i s t r i b u t e s among t h e goods i n t h e p r o p o r t i o n s ( 3 ^ , . . . 3 n -(The B 's a r e t h u s i d e n t i f i e d w i t h . . . m a r g i n a l b u d g e t s h a r e s . . . ) R e c a l l t h a t t h e u t i l i t y f u n c t i o n i s d e f i n e d o n l y f o r ( ^ " Y ^ ) > 0 ( i = l , . . . , n ) ; i t makes no p r e d i c t i o n a b o u t t h e b e h a v i o u r o f a consumer f o r whom y - p . Y . = Ep . ( q . - Y . ) < 0 s i n c e he c a n n o t a f f o r d 3 3 3 3 3 3 3 t o a c q u i r e Y ^ » - • * ' Y a t t h e g o i n g p r i c e s . O f c o u r s e , t h e r e i s no need t o i n t e r p r e t t h e y as b a r e m i n i m a , b u t t h i s p a r -t i c u l a r f o r m o f u t i l i t y f u n c t i o n o n l y r e q u i r e s t h a t (x.-y.)X3 a n d y - E p . y . > 0. 1 1 j 3 3 One f u r t h e r p o i n t t o n o t e i s t h a t t h e r e c a n be no i n f e r i o r goods i n t h e L E S . S t o n e , e i t h e r by h i m s e l f o r i n c o n j u n c t i o n w i t h o t h e r s , h a s e s t i -mated t h i s LES e x t e n s i v e l y u s i n g B r i t i s h d a t a . B . THE GENERALIZED L INEAR EXPENDITURE SYSTEM Wales [37], f o l l o w i n g work done j o i n t l y w i t h P o l l a k - ( i n t h e U n i t e d S t a t e s ) , e s t i m a t e s a generalized l i n e a r e x p e n d i t u r e m o d e l o f t h e demand f o r n o n d u r a b l e s i n C a n a d a . The u t i l i t y f u n c t i o n i s assumed t o be o f 3 G o l d b e r g e r [18; p . 47]. 5 t h e f o r m : n where U(x ) = ( E a . ( x . - b . ) a ) 1 / a (II-3) i-1 1 1 1 a . > 0; l x . - b . > 0; i i — a < 1; x .> 0. l— The u t i l i t y - m a x i m i z i n g p r o c e s s y i e l d s demand f u n c t i o n s o f t h e f o r m : n n x . = b . + [ ( a . / p . ) ° / 2 ( a . / p . ) C p . ] * (y - E p . b . ) (II-4) 1 1 j = i 3 3 3 j = 1 3 3 where > 0; x . - b . > 0 l i x . > 0 l c = e l a s t i c i t y o f s u b s t i t u t i o n . As Wales p o i n t s o u t , t h e s y s t e m d i f f e r s f r o m t h e LES b a s i c a l l y i n t h a t ( i ) m a r g i n a l b u d g e t s h a r e s a r e p r i c e d e p e n d e n t r a t h e r t h a n c o n s t a n t ; 4 and ( i i ) p a r t i a l e l a s t i c i t i e s o f s u b s t i t u t i o n be tween any p a i r o f supernumer -a r y q u a n t i t i e s ( x £ ~ b ^ ) w h i c h e q u a l 1 i n t h e L E S , a r e e q u a l t o c i n t h e W a l e s s y s t e m . 4 I n t h e p r e s e n t s t u d y , t h e s e e l a s t i c i t e s a r e d e n o t e d as d . . , ID 6 For estimation purposes, a "habit formation" concept is adopted as a dynamic specification; this i s achieved by allowing the b's to depend on 5 previous consumption. The empirical work is carried out under various stochastic specifi-cations on the broad consumption aggregates of food, clothing, shelter and miscellaneous. The results deem a proportional habit model inconsistent with the underlying utility function, but are consistent with a linear (lagged) habit model. In his conclusions, Wales suggests that while the added feature of the estimation of c (the elasticity of substitution be-tween pairs of supernumerary quantities) in 'the generalized LES does make the system more flexible, the results are not significantly different enough to warrant using the generalized LES rather than the LES when a large number of goods or observations are involved, given that the generalized model carries with i t computational difficulties. C. THE DEMAND FOR DURABLE GOODS Since one of the interesting features of the current study is a reason-ably thorough treatment of consumer durables, i t will prove useful to examine other approaches to the demand for durables. ;Stone and Rowe [35; 1957] first proposed a simple, testable dynamic theory of demand (for durables). The demand for "perishables" (nondurable Wales [37; p. 473]: "This means that the utility functions are no longer separable over time and that the demand equations should be obtained assuming intertemporal utility maximization. We avoid this complication by assuming that the consumer is unaware that his future preferences change as a function of his current behaviour." 7 goods and s e r v i c e s ) i s a s p e c i a l c a s e i n w h i c h one o f t h e p a r a m e t e r s ( o b -v i o u s l y t h e r a t e o f d e p r e c i a t i o n ) goes t o i t s l i m i t . B a s i c a l l y , g r o s s e x -p e n d i t u r e on a d u r a b l e g o o d may b e decomposed i n t o an a d d i t i o n t o t h e o p e n -i n g s t o c k ( i . e . , an i n v e s t m e n t ) and a f l o w o f c o n s u m p t i o n ( i . e . , what i s u s e d up d u r i n g t h e p e r i o d ) . T h e a u t h o r s assume a r e d u c i n g - b a l a n c e d e p r e c i -a t i o n f o r m u l a and t h u s t h e amount u s e d up (u) w i l l be 1/nth o f t h e o p e n i n g s t o c k ( s ) . A c c o r d i n g l y , ( i ) Q = v + u S Q ( i i ) u = — + — (Q r e p r e s e n t s t o t a l . _ _ _. n m , t i i - b ) p u r c h a s e s o r g r o s s i n v e s t m e n t a n d v n e t i n v e s t m e n t ) m ^ 1 . s + — — v n ( m - l ) m-1 H e r e , — i s t h a t p r o p o r t i o n o f t h e c u r r e n t p e r i o d p u r c h a s e s Q w h i c h m i s u s e d u p . G e n e r a l l y , i t i s assumed t h a t m > n and n > 1. T h e c l o s i n g s t o c k (Es) e q u a l s t h e o p e n i n g s t o c k (s) p l u s n e t i n v e s t m e n t (v) (Es = s + v ) . "The c r u c i a l f e a t u r e o f t h e t h e o r y i s a d i s t i n c t i o n b e t w e e n t h e o p e n -i n g s t o c k , s , and t h e e q u i l i b r i u m s t o c k , s * , w h i c h i s assumed t o d e p e n d on c o n s u m e r s ' i n c o m e s a n d p r i c e s . " I t i s assumed t h a t n e t i n v e s t m e n t i s u n d e r -t a k e n t o r e d u c e t h e gap (between s and s * ) by a p r o p o r t i o n ? ^ . Thus n v = — ( s * - s ) ( I I -6 ) n where r i s t a k e n t o be t h e r a t e o f s t o c k a d j u s t m e n t . S t o n e and Rowe [35; p . 425] 8 T h i s method o f s t o c k ^ a d j u s t m e n t has b e e n p o p u l a r i n s t u d i e s c o n -d u c t e d t h r o u g h o u t t h e 1 9 6 0 ' s . T h e a u t h o r s g i v e t h e b e s t summary i n t h e i r own w o r d s : . . . T h e t h e o r y employs a r e d u c i n g b a l a n c e d e p r e c i a t i o n f o r m u l a w i t h a d e p r e c i a t i o n r a t e t h a t i s c o n s t a n t o v e r t i m e , a c o n c e p t o f e q u i l i b r i u m c o n s u m p t i o n w h i c h d e p e n d s , a p a r t f r o m a r e s i d u a l t r e n d , o n c u r r e n t income and t h e c u r r e n t p r i c e s t r u c t u r e and an i n v e s t m e n t r e l a t i o n s h i p d e s i g n e d t o n a r r o w a n d , u n d e r s t a b l e c o n d i t i o n s , e v e n t u a l l y t o e l i m i n a t e t h e d i f f e r e n c e be tween e q u i l i b r u m and a c t u a l s t o c k s . ^ Q A d i s t i n g u i s h e d g r o u p o f C h i c a g o e c o n o m i s t s f o r m e d i n 1954 c o n d u c t e d a s e r i e s o f s t u d i e s on t h e c y c l i c a l p r o c e s s i n t h e U n i t e d S t a t e s . I n p a r t i c u -l a r , t h e s e s t u d i e s f o c u s on t h e d u r a b l e s s e c t o r s i n c e t h e w i d e f l u c t u a t i o n s i n d u r a b l e s demand make t h a t s e c t o r a " d a n g e r s p o t " ( i n w h i c h w i d e c y c l i c a l s w i n g s c o u l d i n i t i a t e ) . T h u s , as H a r b e r g e r p u t s i t , " a n u n d e r s t a n d i n g o f t h e m e c h a n -i s m s d e t e r m i n i n g c h a n g e s i n t h e demand f o r d u r a b l e goods i s i m p o r t a n t f o r 9 e s t i m a t i n g t h e p r o b a b l e e f f e c t s o f p r o p o s e d s t a b i l i z a t i o n s c h e m e s . " T h e s e s t u d i e s , r a n g i n g f r o m r e f r i g e r a t o r s t o n o n - f a r m h o u s i n g , h a v e b e e n c o l l e c t e d i n [21a] and e d i t e d b y H a r b e r g e r . One o f t h e ma in f e a t u r e s i s t h e t r e a t m e n t o f t h e s t o c k demand v e r s u s f l o w demand p r o b l e m . T h e r e r e -m a i n s , h o w e v e r , t h e c o n c e p t o f a " d e s i r e d " s t o c k t o w h i c h consumers w i l l s u p p o s e d l y a d j u s t . Many p r o b l e m s a r e p o i n t e d o u t and a t t e m p t s a r e made t o S t o n e and Rowe [35; p . 4 4 1 ] . 8 A . C . H a r b e r g e r , R. F . M u t h , M. C . B u r s t e i n , G . C . Chow, Z . G r i l i c h e s , and Y . G r u n f e l d . See r e f e r e n c e [ 2 1 a ] . 9 H a r b e r g e r ( E d . ) , [ 2 1 a ] , p . v . 9 t r e a t s u c h p r o b l e m a r e a s as t h o r o u g h l y as p o s s i b l e g i v e n t h e c o n s t r a i n t o f i m p r e c i s e d a t a ( r e l a t i v e t o t h e r e a s o n a b l y e x a c t d a t a a v a i l a b l e , f o r e x a m p l e , i n t h e a r e a o f wheat c o n s u m p t i o n ) . As H a r b e r g e r p o i n t s o u t : . . . I f c a r s o f a l l ages r e a l l y h a v e t h e same s e r v i c e y i e l d , t h e a g g r e g a t e s e r v i c e y i e l d o f t h e e x i s t -i n g s t o c k o f c a r s w o u l d be m e a s u r e d by t h e i r number; i f , on t h e o t h e r h a n d , t h e s e r v i c e y i e l d o f i n d i v i d u a l c a r s i s p r o p o r t i o n a l t o t h e i r v a l u e , t h e s e r v i c e y i e l d o f t h e s t o c k w o u l d be m e a s u r e d b y i t s a g g r e g a t e v a l u e . 1 0 T h u s , i f a u t o m o b i l e d e p r e c i a t i o n were a c o n s t a n t d o l l a r amount e a c h y e a r , t h i s w o u l d be an i n d i c a t i o n t h a t t h e f l o w o f s e r v i c e s was a p p r o x i -m a t e l y t h e same f o r c a r s o f d i f f e r e n t v i n t a g e s , and t h e "numbers" measure w o u l d be more s u i t a b l e . I f , h o w e v e r , (which i s t h e more l i k e l y c a s e ) d e p r e -c i a t i o n were a c o n s t a n t p e r c e n t a g e o f t h e v a l u e o f t h e s t o c k , t h e " a g g r e g a t e v a l u e " measure w o u l d be p r e f e r a b l e . E v e n a t t h a t , e i t h e r measure i s o n l y a r o u g h a p p r o x i m a t i o n , s i n c e m a i n t e n a n c e c o s t s h a v e t h e a b i l i t y t o r a i s e t h e c a p a c i t y o f t h e e x i s t i n g s t o c k . T h u s , a t b e s t , we c a n o n l y g e t an a p p r o x i -m a t i o n t o " t h e " s t o c k o f a p a r t i c u l a r d u r a b l e . The o v e r a l l c o n t r i b u t i o n o f t h i s c o l l e c t i o n o f s t u d i e s i s a c a r e f u l s i f t i n g o f t h e e v i d e n c e i n o r d e r t o o b t a i n answers t o c e r t a i n b r o a d q u e s t i o n s i n t h e a r e a o f d u r a b l e s demand. More r e c e n t l y , H o u t h a k k e r and T a y l o r [25] and S c h w e i t z e r [33] h a v e u n d e r t a k e n h i g h l y d i s a g g e g a t e d e c o n o m e t r i c consumer demand s t u d i e s i n t h e U n i t e d S t a t e s and C a n a d a r e s p e c t i v e l y . The b a s i c d y n a m i c m o d e l i s a g a i n I t h e ( e q u i l i b r i u m ) s t o c k - a d j u s t m e n t c o n c e p t and d e p r e c i a t i o n o f d u r a b l e s i s assumed t o be o f t h e d e c l i n i n g - b a l a n c e f o r m . The demand e q u a t i o n s f o r n o n -H a r b e r g e r ( E d . ) , [ 2 1 a ] , p . 5 . 10 d u r a b l e s a r e o f t h e same fo rm a s t h o s e f o r d u r a b l e s w i t h t h e c o n c e p t o f s t o c k a d j u s t m e n t r e p l a c e d by t h a t o f h a b i t f o r m a t i o n . As p o i n t e d o u t b y H o u t h a k k e r , t h e s t o c k may be p s y c h o l o g i c a l i n s t e a d o f , o r as w e l l a s , p h y s i c a l . T o t a l p e r s o n a l consumer e x p e n d i t u r e i s t a k e n t o be t h e b u d g e t c o n s t r a i n t , a n d a s e t o f demand e q u a t i o n s c o n s i s t e n t w i t h u t i l i t y maximir-z a t i o n i s e s t i m a t e d . In t h e e n d , t h e s e demand e q u a t i o n s a r e u s e d t o make p r o j e c t i o n s . I n t h e U . S . s t u d y [25], p r i c e s a r e f o u n d t o p l a y a modes t r o l e r e l a t i v e t o income i n d e t e r m i n i n g c o n s u m p t i o n . " I f income i s h i g h e n o u g h , i t i s p o s s i b l e f o r n e a r l y a l l c o m m o d i t i e s t o become s u b j e c t t o h a b i t f o r -m a t i o n . " 1 1 The b a s i c c o n c l u s i o n i s t h a t t h e dynamic m o d e l i s , f o r t h e most p a r t , h e r e t o s t a y . D. THE INDIRECT U T I L I T Y FUNCTION The t r a d i t i o n a l s t u d i e s have one common b a s e ; a l l o f them, h a v i n g assumed an a r b i t r a r y f o r m f o r t h e u t i l i t y f u n c t i o n , m a x i m i z e t h i s u t i l i t y f u n c t i o n s u b j e c t t o a b u d g e t c o n s t r a i n t a n d u s e t h e a l g e b r a i c s o l u t i o n f o r d e r i v e d demand e q u a t i o n s as a b a s i s f o r e s t i m a t i o n . "The p r o b l e m w i t h t h i s ' 12 a p p r o a c h i s t h a t i f one assumes a ' f l e x i b l e ' f u n c t i o n a l f o r m f o r t h e u t i l i t y f u n c t i o n , t h e d e r i v e d demand f u n c t i o n s a r e e i t h e r i m p o s s i b l e t o d e r i v e a l g e -13 b r a i c a l l y o r a r e e x t r e m e l y n o n - l i n e a r i n t h e unknown p a r a m e t e r s . " 11[25; p . 305]. 12. . i . e . , c a p a b l e o f p r o v i d i n g a s e c o n d o r d e r a p p r o x i m a t i o n t o an a r b i -t r a r y t w i c e d i f f e r e n t i a b l e u t i l i t y f u n c t i o n . The c o r r e s p o n d i n g d e r i v e d demand f u n c t i o n s w i l l be a p p r o x i m a t e d t o t h e f i r s t o r d e r . ( D i e w e r t [9; p . 47]). 13 Ibid., p p . 19-20. 11 Under c e r t a i n a s s u m p t i o n s and r e g u l a r i t y c o n d i t i o n s , a much e a s i e r method f o r o b t a i n i n g a s y s t e m o f d e r i v e d demand f u n c t i o n s i s a v a i l a b l e — 14 n a m e l y , t h e i n d i r e c t u t i l i t y f u n c t i o n a p p r o a c h . Whereas t h e d i r e c t u t i l i t y f u n c t i o n U=U(x) i s d i f f i c u l t t o e s t i m a t e , t h e i n d i r e c t u t i l i t y f u n c t i o n [which shows t h e maximum u t i l i t y t h e consumer c a n a c h i e v e g i v e n " i n c o m e " (Y) and p r i c e s ( p ) ] , c a n be r e a d i l y e s t i m a t e d i f we impose a n o r m a l i z a t i o n . In t h i s s t u d y , we w i l l work w i t h p r i c e s normalized by i n c o m e ; we s h a l l c a l l t h e s e n o r m a l i z e d p r i c e s v^ = p ^ / Y . T h u s n g(v ) E max (u (x): £ v . x . <_ 1} ( I I -7 ) w . r . t . i = i 1 1 x > o where g = i n d i r e c t u t i l i t y f u n c t i o n ; x = c o n s u m e r ' s c h o i c e v a r i a b l e s ( q u a n t i t i e s ) ; 0_ = a z e r o v e c t o r ; E v . x . = b u d g e t c o n s t r a n t . ,15 „ „ , 1 6 D i e w e r t [9 ; p . 2 0 ] , f o l l o w i n g t h e work o f S h e p h a r d and Hanoch d e m o n s t r a t e s t h a t f rom t h e d u a l i t y b e t w e e n d i r e c t and i n d i r e c t u t i l i t y f u n c -t i o n s we may i n f a c t c a l c u l a t e the u t i l i t y f u n c t i o n U(x ) as t h e s o l u t i o n t o D i e w e r t [ 7 ] ; [ 9 ] ; [ 1 0 ] ; [ 1 2 ] . 1 5 R . W. s h e p h a r d , Theory of Cost and Production Functions ( P r i n c e t o n , N.J.: P r i n c e t o n U n i v e r s i t y P r e s s , 1970) t r e a t s t h e i n d i r e c t u t i l i t y f u n c t i o n i n t h e a p p e n d i x . 16 " G i o r a H a n o c h , " G e n e r a t i o n o f New P r o d u c t i o n F u n c t i o n s T h r o u g h D u a l -i t y , " mimeo ( 1 9 7 0 ) . 12 t h e f o l l o w i n g p r o b l e m : n U(x) = min w . r . t . v > 0 i = l ( I I -8 ) The b r i e f o u t l i n e w h i c h f o l l o w s i s e s s e n t i a l l y c o n d e n s e d f r o m Hanoch [ 2 1 a a ] , S h e p h a r d [ 3 3 3 ] , and D i e w e r t [9 ; p . 2 1 ] . " I f t h e d i r e c t u t i l i t y f u n c t i o n U i s n o n - n e g a t i v e , c o n t i n u o u s , q u a s i -c o n c a v e , and n o n - d e c r e a s i n g i n t h e components o f X , t h e n t h e i n v e r s e i n d i r e c t u t i l i t y f u n c t i o n , h ( v ) = 1 / g ( v ) , w i l l have t h e same p r o p e r t i e s a s t h e u t i l i t y 17 f u n c t i o n and v i c e v e r s a . " N o n - n e g a t i v i t y i s s e l f - e x p l a n a t o r y . The n o n - d e c r e a s -1 2 1 2 xng r e q u i r e m e n t means t h a t i f x >_ x , t h e n f (x ) >_ f (x ) . Q u a s i c o n c a v i t y (a weaker f o r m o f c o n c a v i t y ) i s o b t a i n e d when the l e v e l s e t s L ( x ) = { x : f ( x ) >_ y V x >_ 0} a r e c o n v e x o v e r t h e n o n - n e g a t i v e o r t h a n t . d i f f e r e n t i a b l e w i t h r e s p e c t t o t h e p r i c e s v ^ , t h e n t h e c o n s u m e r ' s s y s t e m o f d e r i v e d demand e q u a t i o n s becomes ( p r o v i d e d t h e p a r t i a l d e r i v a t i v e s a r e n o t i d e n t i c a l l y z e r o ) : I f , f i n a l l y , h ( v ) ( the i n v e r s e i n d i r e c t u t i l i t y f u n c t i o n ) i s o n c e ah (v) 3v . -/ Z v. —(v) ; f o r a l l i . k - l k 9 V k ( I I -9) 17 19; p . 2 1 ] . 13 I f a l l t h e n e c e s s a r y c o n d i t i o n s a r e s a t i s f i e d , we have a r e a s o n a b l y compact way o f s o l v i n g f o r d e r i v e d demand e q u a t i o n s c o n s i s t e n t w i t h t h e c o n -s u m e r ' s u t i l i t y m a x i m i z a t i o n -One f u r t h e r s t e p i s n e c e s s a r y b e f o r e we may assume a f u n c t i o n a l f o r m . C o n s i d e r t h e f o l l o w i n g u t i l i t y m a x i m i z a t i o n p r o b l e m (where we assume the a l l o c a t i o n o f t i m e p r o b l e m h a s b e e n . s o l v e d ) : U ( X , L ) = F ( X , L ) MAX F ( X , . . . , X „ ; L ) w . r . t . x1 >_ 0,. . . ,xN >_ 0 L - 0 (11-10) s u b j e c t t o n ( i ) E p . X. - wL < V i = l 1 1 ( i i ) L <_ H where X . = number o f u n i t s o f t h e s e r v i c e s o f t h e i t h g o o d t h e c o n s u m e r - w o r k e r p u r c h a s e s d u r i n g t h e p e r i o d ; p . = t h e p r i c e (o r r e n t a l p r i c e f o r d u r a b l e goods) o f one u n i t o f good i ; w = t h e m a r k e t wage r a t e f o r o u r one t y p e o f l a b o u r s e r v i c e t h e c o n s u m e r - w o r k e r i s q u a l i f i e d t o s u p p l y ; L = t h e number o f h o u r s o f l a b o u r t h e c o n s u m e r - w o r k e r s u p p l i e s d u r i n g t h e p e r i o d ; V = n o n - l a b o u r income s p e n t d u r i n g the p e r i o d ; H = t o t a l number o f available h o u r s i n t h e p e r i o d . 14 In (11-10) t h e consumer h a s p r e f e r e n c e s d e f i n e d o v e r t h e s e r v i c e s o f c o n s u m p t i o n goods and l a b o u r s u p p l y . However , t h e method f o r o b t a i n i n g d e r i v e d demand f u n c t i o n s w i l l f a i l s i n c e we do n o t meet a l l o f t h e f o l l o w -i n g r e q u i r e m e n t s : ( i ) U = f v X ; L ) must be d e f i n e d o v e r t h e e n t i r e n o n - n e g a t i v e o r t h a n t ; ( i i ) a l l p r i c e s must be n o n - n e g a t i v e ( the wage r a t e e n t e r s n e g a t i v e l y ) ; ( i i i ) f u l l " i n c o m e " must be p o s i t i v e . A s i m p l e t r a n s f o r m a t i o n o f o u r v a r i a b l e s w i l l a c h i e v e t h e d e -s i r e d p r o p e r t i e s . We n e e d o n l y r e d e f i n e t h e u t i l i t y f u n c t i o n o v e r t h e d e -mand f o r " d i s w o r k " ( l e i s u r e ) r a t h e r t h a n t h e supply o f l a b o u r s e r v i c e s , a n d o u r new u t i l i t y f u n c t i o n i s a c c e p t a b l e : U ( X , H - L ) = f ( X , , . . . ,X :L) 1 N MAX U ( X , H - L ) w i r . t . X > 0,. . . , X „ > 0 1 — N — H-L> 0 (11-11) s u b j e c t t o : n ( i ) Z p . X. + w(H-L) < V + wH i-1 1 1 where t h e r e a r e n consumer goods and o n l y one t y p e o f l a b o u r s e r v i c e ; ( i i ) (H-L) < H 15 A s s u m i n g t h e t i m e c o n s t r a i n t i s s a t i s f i e d , t h e p r o b l e m b e c o m e s : MAX U(X) w . r . t . x 1 0 ( 1 1 - 1 2 ) s u b j e c t t o £ v . X . < 1 i 1 1 _ where X = (X- , . . . , X M ; H-L) 1 N V = V - h « ( P 1 P n ' * W ) F o r e s t i m a t i o n p u r p o s e s , the " g e n e r a l i z e d f u l l i n c o m e " v a r i a b l e V + wH i s t a k e n t o be t h e v a l u e o f t h e l e f t - h a n d s i d e o f [ I l - I K D I ; t h a t i s , we assume t h e b u d g e t c o n s t r a i n t i s f u l l y s a t i s f i e d . The f i n a l s t e p b e f o r e e m p i r i c a l work i s t o assume a f u n c t i o n a l f o r m f o r h ( v ) , t h e i n v e r s e i n d i r e c t u t i l i t y f u n c t i o n . CHAPTER I I I GENERALIZED LEONTIEF PREFERENCES AND THEIR ESTIMATION A . A GENERALIZED LEONTIEF U T I L I T Y FUNCTION The G e n e r a l i z e d L e o n t i e f f u n c t i o n a l f o r m (due t o D i e w e r t [7]) f i r s t a r o s e i n t h e c o n t e x t o f p r o d u c t i o n t h e o r y . T h i s p a r t i c u l a r f u n c t i o n f i r s t a p p e a r e d i n t h e h o m o t h e t i c 1 c a s e , b u t we w i l l work w i t h a n o n -h o m o t h e t i c v e r s i o n . C o n s i d e r t h e f o l l o w i n g f o r m f o r t h e i n v e r s e i n d i r e c t u t i l i t y f u n c t i o n h ( v ) : h ( V V 2 V N + K } where t h e r e a r e N consumer g o o d s a n d . K t y p e s o f l a b o u r s e r v i c e N+K N+K j v N+K = E E b . . v . ^ . 2 „ E , h / T T T _ n . , . , i j i D + 2 b . v . ( I I I - D i = 1 3 = 1 j = 1 os 3 where b . . = b , . V i / j ID" D i Remembering t h a t t h e c o n s u m e r ' s p r e f e r e n c e s e x t e n d o v e r g o o d s and l a b o u r s e r v i c e s , we may g e n e r a t e a s y s t e m o f d e r i v e d demand e q u a t i o n s (where x (v) = H - L „ i s a t y p i c a l l a b o u r s u p p l y f u n c t i o n ) : N+K K ^A u t i l i t y f u n c t i o n u (x ) i s h o m o t h e t i c i f t h e r e e x i s t s an i n c r e a s -i n g f u n c t i o n o f one r e a l v a r i a b l e g s u c h t h a t g ( u ( x ) ) i s homogeneous o f d e g r e e o n e . ( D i e w e r t [9; p . 9 8 ] ; o r i g i n a l l y d e f i n e d b y S h e p h a r d 1953 [ 3 3 a ] ) . 16 17 N + K h -h -h, { E b . . v . v . ^ + b . v . }^ j = l A 3 3 1 0 1 1 X 1 ( V ) = N+K N+K j . . N+K ^ ( I I I -2 ) { E i b, ,v, V + E b -v-2} k = l j = i k 3 k j j o l o_ 3 V. l The d e r i v e d demand f u n c t i o n s ( I I I -2 ) a r e homogeneous o f d e g r e e z e r o i n t h e unknown p a r a m e t e r s b and we a r e a l l o w e d one n o r m a l i z a t i o n : N+K N+K N+K E E b . . + r - £ b . = l ( I H - 3 ) i - 1 j - 1 1 3 k j = l 0 3 where k = v ^ ; v = v V i n 1961 . T h i s was done t o e n s u r e t h a t g ( i n d i r e c t x x 1 u t i l i t y ) w o u l d be p o s i t i v e i n 1961 . I n f a c t , o u r n o r m a l x z a t x o n s e t s g = — v i n 1961 . " I f b . = 0 f o r j = 1 , 2 , . . . , N + K , t h e n t h e [ c o r r e s p o n d i n g ] d i r e c t 03 u t i l i t y f u n c t i o n . . . r e d u c e s t o t h e ( h o m o t h e t i c ) g e n e r a l i z e d L e o n t i e f u t i l i t y f u n c t i o n ; i f i n a d d i t i o n , b . . = 0 f o r a l l i f j , t h e n t h e d i r e c t u t i l i t y f u n c -t i o n r e d u c e s t o t h e o r d i n a r y f i x e d p r o p o r t i o n s L e o n t i e f u t i l i t y f u n c t i o n . " [9 ; p . 2 3 ] . The d e r i v e d demand e q u a t i o n s ( I I I -2 ) may be e q u i v a l e n t l y r e p r e s e n t e d ( f o r e s t i m a t i o n p u r p o s e s ) by p e r f o r m i n g t h e f o l l o w i n g o p e r a t i o n s : ( i ) m u l t i p l y b o t h s i d e s o f e q u a t i o n i ( i =2 , . . . ,N+K) b y N+K N+K j, , N+K , \ ( E E b v.\* + E b o i v.*) v . k = l j-i Kj k ^ j = 1 ° 3 3 1 ( i i ) use r e l a t i o n ( I I I -3 ) ( i . e . , n o r m a l i z a t i o n ) t o s o l v e f o r b ^ i n te rms o f the o t h e r b . . and u s e t h i s r e s u l t t o e l i m i n a t e b ^ f r o m t h e N + K - l t r a n s f o r m e d e q u a t i o n s ; ( i i i ) impose t h e symmetry c o n d i t i o n s b ^ = b . . and c o l l e c t a l l terms i n t h e (unknown) b ^ on t h e r i g h t ha"ncl s i d e o f e q u a t i o n s 2 , . . . ,N+K . 18 We t h u s a r r i v e a t a s y s t e m o f consumer demand e q u a t i o n s ( I I I -4 ) w h i c h e x p r e s s e s ' m a r k e t ' s h a r e s ( i . e . , t h e s h a r e o f t o t a l e x p e n d i t u r e ) as a f u n c t i o n o f t h e unknown p a r a m e t e r s and t h e n o r m a l i z e d p r i c e s . V i X i * i = 2 ' - * • » N + K ) h N+K v . = E b { (v .x . - v h v . x . / v , ) + 6. — } , on i i n i I 1 m v , n= l 1 + E E bv^ ( 2 v . x . - 2v, 2 v . v . x . / v , l<k<j<N+K ^ 1 1 k D 1 1 1 +* ik v j i 5 / v 1 where + 6 i j v k * V i J s / v l ) N+K v . + E b .„ ( v . x . - v , v . x . / v , +6.„ — ) ( I I I -4 ) t = 2 A£ 1 i Jl- i i ' 1 i t v 6.. - {? " *h _j 1 l f 1 = 3 We may use l i n e a r r e g r e s s i o n t e c h n i q u e s t o e s t i m a t e t h e unknown b ^ j ' s i n ( I I I -4 ) " i f we assume t h a t t h e d i s t r i b u t i o n o f t h e e x p e n d i t u r e s h a r e s v . x . c o n d i t i o n a l on t h e v a l u e s o f t h e r i g h t hand s i d e v a r i a b l e s , i s m u l t i -1 1 2 v a r i a t e n o r m a l . " 2 D i e w e r t [9; p . 25] 19 The i n v e r s e i n d i r e c t u t i l i t y f u n c t i o n ( I I I - l ) h a s t h e same f i r s t and s e c o n d o r d e r p a r t i a l d e r i v a t i v e s ( e v a l u a t e d a t any p a r t i c u l a r p o i n t ) as t h e i n d i r e c t u t i l i t y f u n c t i o n ; t h e s e d e r i v a t i v e s a r e : 9h(v) NOTATION: l e t h . r e p r e s e n t TTJ 1 v i and h . . r e p r e s e n t 8v . v. i D N+K i . , b . . ( v . / v . P + b . v. 2=1 13 ] l 01 1 h . . = hh. .(v.v.) ID 1 ] h.. = -H ^ b . . (V.)~3/2{V.)H - . (V ) " V 2 (TTT-5) 11 . , i n 1 i 01 1 1111 =>J 3=1 We may u s e t h e s e p a r t i a l d e r i v a t i v e s t o e v a l u a t e p s e u d o e l a s t i c i t i e s s u b s t i t u t i o n be tween t h e u n n o r m a l i z e d demands i and j : [The u n n o r m a l i z e d demands a r e d e f i n e d as h^ ( v ) ] . a . . = h ( v ) h . . ( v ) / h . h . ( I I I -6 ) iD ID 1 D H e r e , a . . = 0 i f f b . . = 0 i ^ j ID !D I f we have a priori b e l i e f s t h a t t h e u n n o r m a l i z e d demand f o r g o o d i i s n o t r e s p o n s i v e t o c h a n g e s i n t h e p r i c e v , we may s e t b _ = 0 . T h i s w i l l add d e g r e e s o f f r e e d o m t o o u r model a n d r e d u c e m u l t i c o l l i n e a r i t y . A ' n o r m a l -i z e d ' demand s y s t e m i s o b t a i n e d by d i v i d i n g e a c h demand f u n c t i o n b y N+K E v h = m a r k e t demand. *=1 * * 20 The f o r m u l a f o r a ( H i c k s - A l l e n e l a s t i c i t i e s o f s u b s t i t u t i o n ) f o r (market ) demands i s : N+K k f i v k V v ) h i i ( v ) N+ K v k h i k ( v ) a i j h . ( v ) h . (v) h . (v) i n k = l "3 N * K v, h . , (v) N+K N+K £ k i k v h (v )v , , — r ~ r + I E k km m k = 1 h i ( v ) m = l k = l - T77 ( I I I _ 7 ) E v k h k ( v ) k = l K * A s D i e w e r t p o i n t s o u t , e v e n i f consumers do not o p t i m i z e a c c o r d i n g t o o u r mode l (see C h a p t e r I I ) , "we c a n s t i l l a s s e r t t h a t t h e r e a r e s e v e r a l a d ' v a n t a g e s t o f i t t i n g [ t h i s ] s y s t e m o f consumer demand a n d l a b o u r s u p p l y f u n c -t i o n s . . . F o r e x a m p l e , t h e demand f u n c t i o n s ( I I I -2 ) a r e homogeneous o f d e g r e e z e r o i n p r i c e s ( p . , . . . , p ) , wages ( w , , . . . , w ) , and n o n l a b o u r income V . 1 N 1 K A l s o t h e c o n s u m p t i o n demands and l a b o u r s u p p l i e s . . . a r e c o n s i s t e n t w i t h t h e c o n s u m e r ' s b u d g e t c o n s t r a i n t . F i n a l l y , t h e s y s t e m o f d e r i v e d demand e q u a -t i o n s . . . c a n p r o v i d e a good l o c a l a p p r o x i m a t i o n t o an a r b i t r a r y s y s t e m o f d e r i v e d demand f u n c t i o n s , c o n s i s t e n t w i t h u t i l i t y m a x i m i z i n g b e h a v i o u r . " 3 B . ECONOMETRICS IN BRIEF The unknown p a r a m e t e r s were e s t i m a t e d b y means o f a t w o - s t a g e p r o -c e d u r e due t o Z e l l n e r [ 4 1 ] . 3 D i e w e r t [ 9 ; p . 27] 21 Our m o d e l i s o f t h e f o r m : y f c = x t b + e t ; t = l T ( I I J _ 8 ) where y t i s a row v e c t o r o f e x p e n d i t u r e s h a r e s i n p e r i o d t ; i s a row v e c t o r o f t h e v a l u e s o f t h e i n d e p e n d e n t v a r i -a b l e s ( c a l c u l a t e d on t h e r i g h t - h a n d s i d e o f ( I I I - 4 ) ; b i s t h e m a t r i x o f unknown c o e f f i c i e n t s ; a n d e i s a row v e c t o r o f s t o c h a s t i c d i s t u r b a n c e t e r m s . Our s t o c h a s t i c s p e c i f i c a t i o n i s : ( i ) E ( £ t ' = 0 ; £ t ^ S n o r m a ^ - 1 y d i s t r i b u t e d ( i i ) E{e't e f c ) = E ( i i i ) E ( e e ) = 0 t s where e s i g n i f i e s t h e t r a n s p o s e o f e . . E i s assumed t o be a singular v a r i a n c e - c o v a r i a n c e m a t r i x s i n c e we a r e r e s t r i c t e d t o a lways be o n t h e b u d g e t c o n s t r a i n t . We a l s o assume z e r o i n t e r t e m p o r a l c o v a r i a n c e s . We t h e n " s t a c k " t h e demand e q u a t i o n s s o t h a t we have a s y s t e m w i t h (N+K-1)T o b s e r v a t i o n s . T h u s , we have d r o p p e d one e q u a t i o n , and we r u n an o r d i n a r y l e a s t s q u a r e s r e g r e s s i o n on t h e ' s t a c k e d ' s y s t e m and c a l -c u l a t e t h e r e s i d u a l s . F rom t h e r e s i d u a l s , we may o b t a i n an estimate o f E ( E ) ; we u s e E t o t r a n s f o r m ' * t h e d a t a ; and we s o l v e a g e n e r a l i z e d l e a s t s q u a r e s p r o b l e m w i t h t h e t r a n s f o r m e d d a t a . The GLS e s t i m a t e s o f t h e c o e f f i c i e n t s o f o u r consumer demand s y s t e m a r e , s u p p o s e d l y , more e f f i c i e n t . t h a n w o u l d be i n t h e s i n g l e -The r e a d e r i s r e f e r r e d t o A . S . G o l d b e r g e r , Econometric Theory ( W i l e y , 1964) p . 234 , f o r a c o n c i s e d e s c r i p t i o n o f t h e t r a n s f o r m a t i o n p r o c e s s . 22 e q u a t i o n e s t i m a t i o n c a s e . T h i s i s s u p p o r t e d by t h e t - s t a t i s t i c s , a l w a y s h i g h e r f o r t h e c o e f f i c i e n t s o f t h e " s e c o n d s t a g e " r e g r e s s i o n - t h a n f o r t h o s e o f t h e f i r s t s t a g e . The c o e f f i c i e n t s r e p o r t e d i n C h a p t e r s V and V I a r e t h o s e f r o m t h e (2nd s t a g e ) g e n e r a l i z e d l e a s t s q u a r e s m o d e l s . F o r a d e t a i l e d d e s -c r i p t i o n o f t h e p r o c e s s and i t s a s y m p t o t i c p r o p e r t i e s , see Z e l l n e r [41; p p . 3 4 9 - 3 5 2 ] . A comment on o u r s t o c h a s t i c s p e c i f i c a t i o n i s i n o r d e r : We may j u s t i f y the s p e c i f i c a t i o n o f z e r o i n t e r t e m p o r a l c o v a r i a n c e s by a s s u m i n g t h e e x i s t e n c e o f a s e p a r a b l e i n t e r t e m p o r a l u t i l i t y f u n c t i o n . In C h a p t e r IV , we d i s c u s s t h e d a t a m a n i p u l a t i o n s (and s o u r c e s ) n e c e s -s a r y f o r e s t i m a t i o n o f o u r consumer demand s y s t e m . CHAPTER IV DATA: CONCEPTS AND SOURCES A . THE TREATMENT OF DURABLE GOODS S i n c e we must decompose g r o s s e x p e n d i t u r e o n a d u r a b l e g o o d i n t o an i n v e s t m e n t component and a f l o w o f s e r v i c e s ( r e n t a l ) component , we must have d a t a ( i n s o f a r a s d u r a b l e s a r e c o n c e r n e d ) f o r t h e f o l l o w i n g : 1. The veal s t o c k o f e a c h t y p e o f d u r a b l e ( X D ! ) ; 2 . C u r r e n t d o l l a r g r o s s i n v e s t m e n t e x p e n d i t u r e o n e a c h d u r a b l e good $DE. ( t h i s s h o u l d i n c l u d e m a i n t e n a n c e e x p e n d i t u r e s i n c e t h i s p r e s u m a b l y r e p l e n i s h e s p a r t o f the e x i s t i n g s t o c k ) ; 3 . The o n e - p e r i o d d e p r e c i a t i o n r a t e (5 . ) assumed t o h o l d o v e r all vintages o f e a c h d u r a b l e g o o d , i . e . , we assume a p e r p e t u a l i n v e n t o r y m o d e l o f c a p i t a l s t o c k ; T h i s means t h a t i f we a r e l e f t w i t h 4% o f t h e s t o c k o f d u r a b l e i f r o m e i g h t y e a r s a g o , t h e u n i t s a r e i n d i s t i n g u i s h a b l e f r o m c u r r e n t p u r c h a s e s o f t h e g o o d ; we o n l y know t h a t some u n i t s h a v e d e t e r i o r -a t e d away; * 4 . A s t o c k - p r i c e d e f l a t o r PD. t o b r i n g (2) i n t o c o n s t a n t - d o l l a r t e r m s ; o r , i n p l a c e o f (2) and (4) a c o n s t a n t d o l l a r s e r i e s ; 5 . A s e r i e s o f " i n t e r e s t " r a t e s R b y w h i c h t o d i s c o u n t f u t u r e e x p e c t e d p r i c e s . The R w i l l be o p p o r t u n i t y c o s t s . 1 . S t o c k s The ( r e a l ) s t o c k o f d u r a b l e i (XD.) i s d e f i n e d a s : 23 24 * XD. = XD. (1-6 .) + $ D E . / P D . ; l 1 i t - 1 w h i c h i s t h e b a l a n c e o f l a s t p e r i o d ' s c a r r i e d - o v e r s t o c k (assumed t o d e p r e -c i a t e i n s t a n t a n e o u s l y i n t h e m i d d l e o f t h e c o n s u m e r ' s t i m e p e r i o d ) p l u s r e a l new i n v e s t m e n t i n t h e d u r a b l e g o o d ( a l s o assumed t o be made i n t h e m i d d l e o f t h e p e r i o d ) . T h i s u n d e p r e c i a t e d b a l a n c e c a r r i e s o v e r u n t i l t h e m i d d l e o f n e x t p e r i o d , a t w h i c h i n s t a n t t h e p r o c e s s r e p e a t s i t s e l f . T h i s i s s l i g h t l y d i f f e r e n t f rom t h e S t o n e and Rowe [35] method u s e d i n H e l l i w e l l et al [23] and Hamburger [ 2 1 ] , w h i c h d e p r e c i a t e s new i n v e s t m e n t by o n e - h a l f o f t h e p e r p e r i o d r a t e i m m e d i a t e l y u p o n p u r c h a s e . The p r o g r a m ' D E L T A ' (see A p p e n d i x ) c a l c u l a t e s t h e s t o c k f r o m a ( c o n s t a n t - d o l l a r ) s e r i e s o f e x p e n d i t u r e d a t a , an i n i t i a l s t o c k ( b e n c h m a r k ) , and a d e p r e c i a t i o n r a t e . 2 . I n i t i a l S t o c k s Save f o r t h e c a s e s o f h o u s i n g and l a n d , where t h e i n i t i a l s t o c k s a r e b a s e d on e a r l y s u r v e y s a n d e s t i m a t e s , t h e i n i t i a l s t o c k s f o r o u r b a s e y e a r (1946) h a v e b e e n c a l c u l a t e d i n t h e f o l l o w i n g manner:^" A r e a s o n a b l e a p p r o x i m a t i o n t o " t h e " d e p r e c i a t i o n r a t e ( f o r the p a r t i c u l a r d u r a b l e ) was u s e d t o d e t e r m i n e how many y e a r s i t w o u l d t a k e a p u r c h a s e c f D^ t o e s s e n t i a l l y ' d i s a p p e a r ' f r o m t h e s t o c k ( a g a i n a s s u m i n g e x p o n e n t i a l d e -cay) . F o r i n s t a n c e , i f 6 = .8 t h e n any i n v e s t m e n t i n t h i s g o o d f r o m one p e r i o d p a s t w o u l d c o n t r i b u t e .2 ( i . e . , = 1 - 6 J o f t h e o r i g i n a l e x p e n d i t u r e t o t h e c u r r e n t s t o c k ; e x p e n d i t u r e 2 two p e r i o d s ago w o u l d c o n t r i b u t e ( 1 - 6 . ) o r .04 o f D E . : t _ 2 ; See J . H e l l i w e l l and O t h e r s , " Q u a r t e r l y E s t i m a t e s o f P r i v a t e S e c t o r W e a l t h , " R e s e r v e Bank o f A u s t r a l i a , A u g u s t 1971 , p . 2 1 . The p u r p o s e o f t h e A u s t r a l i a n s t u d y (as i n t h e RDX2 model) i s t o measure t h e r e p l a c e m e n t v a l u e o f t h e n e t s t o c k o f a s s e t s . 25 and r e m a i n i n g f r o m t h r e e p e r i o d s b a c k w o u l d b e (1-6^) o r .008 o f t h a t p e r i o d ' s e x p e n d i t u r e . T h u s , an a p p r o x -i m a t i o n t o t h e ' i n i t i a l ' s t o c k f o r any g i v e n s t a r t i n g p o i n t t , w o u l d b e : D u r a b l e 3 E x p e n d i t u r e . ^ Z D E . ( 1 - 6 . ) U  x«*  1 w h i c h r e p r e s e n t s t h e sum o f t h e u n d e p r e c i a t e d p r o p o r t i o n o f p a s t i n v e s t m e n t e x p e n d i t u r e s . No te t h a t t h e l a r g e r t h e 6^ we c h o o s e , t h e l a r g e r looms i m m e d i a t e p a s t i n v e s t -ment i n f o r m i n g o u r c u r r e n t s t o c k . 3 . The D u r a b l e Goods a . C l o t h i n g A l t h o u g h no r e a s o n a b l e s e c o n d - h a n d m a r k e t e x i s t s , we s t i l l t r e a t c l o t h i n g as a d u r a b l e s i n c e o u r s i m p l e d e f i n i t i o n i n c l u d e s any g o o d w h i c h i s n o t c o m p l e t e l y consumed d u r i n g t h e e x p e n d i t u r e p e r i o d ( i . e . 0 <_ 6^ < 1 ) . By t h i s s t a n d a r d , an o l d p a i r o f s h o e s s t i l l c o n t r i b u t e some Va lue* t o t h e c o n -s u m e r ' s p e r s o n a l s t o c k o f c l o t h i n g , w h e t h e r he wears them o r l e a v e s them i n h i s c l o s e t . " T h e " d e p r e c i a t i o n r a t e f o r c l o t h i n g i s a d i f f i c u l t c o n c e p t , s i n c e a m a n ' s b r o g u e s may be k e p t f o r s i x y e a r s w h e r e a s h i s w i f e may r e p l a c e h e r e n t i r e w a r d r o b e on t h e s i m p l e p r e t e x t t h a t " f a s h i o n s h a v e c h a n g e d " o n l y s e v e n months a f t e r t h e i n i t i a l p u r c h a s e . However , a s s u m i n g some r a t i o n a l i t y , we h a v e d e -c i d e d upon an a n n u a l r a t e o f d e t e r i o r a t i o n o f . 5 w h i c h i m p l i e s a l i f e t i m e o f * a b o u t f i v e t o s i x y e a r s w i t h a u s e f u l l i f e t i m e o f two t o t h r e e y e a r s . T h i s seems r e a s o n a b l e when we c o n s i d e r t h e w i d e v a r i e t y o f e n t r i e s i n t h e c l o t h i n g c a t e g o r y . A f t e r t h e r e a l s t o c k s e r i e s was c a l c u l a t e d ( a s s u m i n g 6 = . 5 ) , i . e . , a s s u m i n g t h e r e i s ( a r b i t r a r i l y ) a t l e a s t 20-30% o f t h e i n i t i a l i n v e s t m e n t r e m a i n i n g . 26 d i f f e r e n t v a l u e s f o r 6 c were t r i e d , and t h e r e s u l t a n t 1969 s t o c k v a l u e s were t o o d i v e r g e n t f r o m t h e assumed l e v e l ; t h a t i s t o s a y , t h e v a l u e s e x -h i b i t e d e i t h e r t o o r a p i d a d e t e r i o r a t i o n (.6) o r t o o much a c c u m u l a t i o n t o seem c o r r e c t ( .3) and (.4) i f we b e l i e v e i n « c = . 5 ; o f c o u r s e , t h i s i s a l l a r b i t r a r y . ^ The e x p e n d i t u r e s e r i e s was e x t r a c t e d f r o m T a b l e s 53 a n d 54 o f C a n a d a ' s N a t i o n a l A c c o u n t s ( P e r s o n a l E x p e n d i t u r e on Consumer Goods a n d S e r v i c e s i n c u r r e n t and c o n s t a n t [1961] d o l l a r s r e s p e c t i v e l y ) a n d t h e i m p l i -c i t p u r c h a s e p r i c e i n d e x was o b t a i n e d by s i m p l e d i v i s i o n o f t h e c u r r e n t b y t h e c o n s t a n t d o l l a r v a l u e s . b . M o t o r V e h i c l e s Among consumer d u r a b l e s , motor v e h i c l e s command p e r h a p s t h e most agreement w i t h r e s p e c t t o d e p r e c i a t i o n r a t e s . I t i s a c c e p t e d b y most a u t h o r i t i e s t h a t an a u t o m o b i l e d e p r e c i a t e s anywhere f r o m 25 t o 30 p e r c e n t a n n u a l l y , and t h e " r e d b o o k " o f A u s t r a l i a a n d " b l u e b o o k " o f C a n a d a ( w h o l e -s a l e v a l u e s o f u s e d c a r s ) f o l l o w t h i s g u i d e l i n e i n v a l u a t i n g a u t o m o b i l e s . W h i l e i t i s a c k n o w l e d g e d t h a t c a r s o f d i f f e r e n t v i n t a g e s (as w o u l d b e e x -p e c t e d ) d e p r e c i a t e a t d i f f e r e n t r a t e s ; t h e p r e s e n t p a p e r assumes an " a v e r a g e " r a t e o f 28 p e r c e n t o v e r a l l v i n t a g e s . To s u p p o r t t h i s f i g u r e , we may l o o k t o s e v e r a l s o u r c e s : SOURCE ANNUAL 6 RATE [22] R e s e r v e Bank o f A u s t r a l i a .22 + o n e - h a l f o f q u a r t e r l y (August 1971) r a t e upon new i n v e s t -[23] Bank o f Canada ( S t r u c t u r e ment o f RDX2) .22 [25] H o u t h a k k e r and T a y l o r . 25 [21] Hamburger . 28 \ e h a v e n o t i n c l u d e d t h e c l o t h i n g s t o c k s e r i e s f o r a l t e r n a t i v e d e p r e -c i a t i o n r a t e s i n the A p p e n d i x . 27 Hamburger (above) s t a t e s t h a t t h i s r a t e " i s w i t h i n t h e r a n g e i m p l i e d by 3 t h e b e h a v i o u r o f p r i c e s i n t h e u s e d c a r m a r k e t , " and he s u g g e s t s t h a t Chow 4 and F r i e d m a n p r o v i d e v e r i f i c a t i o n . A n o t h e r v o t e o f s u p p o r t f o r t h i s r a t e i s t h e C a n a d i a n t a x a t i o n s y s t e m , u n d e r w h i c h a b u s i n e s s m a n may d e p r e c i a t e h i s c a r a t 30% t h e f i r s t y e a r and 25% t h e n e x t two y e a r s . The N a t i o n a l A c c o u n t s e n t r y i n c l u d e s motor v e h i c l e p a r t s as w e l l as n e t ( i . e . , l e s s t r a d e - i n v a l u e ) u s e d a u t o m o b i l e s . A c t u a l r e p a i r d a t a a r e i n c l u d e d i n " a u t o m o b i l e o p e r a t i n g e x p e n s e s and p u r c h a s e d t r a n s p o r a t i o n , " b u t a s e a r c h o f t h e s o u r c e s and n o t e s r e v e a l e d no way t o decompose t h e l a t t e r i n -t o " r e p a i r s t o a u t o m o b i l e s , " " o p e r a t i n g e x p e n s e s " ( g a s o l i n e , o i l , and p o s s i b -l y i n s u r a n c e ) , and " p u r c h a s e d t r a n s p o r t a t i o n . " T h e h i s t o r i c a l N a t i o n a l A c c o u n t s [ 13 -502 ; p p . 1 5 7 - 5 8 ] , d i s c u s s e s t h e p r o c e d u r e i n v o l v e d i n t h e i n c l u s i o n o f o n l y t h e p e r s o n a l u s e p o r t i o n o f c a r s a l e s i n t h e r e p o r t e d e x p e n d i t u r e d a t a . The same s o u r c e a l s o m e n t i o n s t h e c o v e r a g e o f " n e t " u s e d a u t o m o b i l e s : . . . t h e t r e a t m e n t o f p u r c h a s e s o f u s e d m o t o r v e h i c l e s by p e r s o n s f r o m businesses h a s b e e n c h a n g e d . The t o t a l amount p a i d by p e r s o n s l e s s t h e v a l u e o f t r a d e - i n s i s now i n c l u d e d i n p e r s o n a l e x p e n d i t u r e on consumer goods a n d s e r v i c e s . ^ G . Chow, " S t a t i s t i c a l Demand F u n c t i o n s f o r A u t o m o b i l e s a n d T h e i r U s e f o r F o r e c a s t i n g , " i n A . H a r b e r g e r ( E d . ) , The Demand for Durable Goods, C h i c a g o , 1960 [ 2 1 a ] . 4 C . F r i e d m a n , "The S t o c k o f A u t o m o b i l e s i n the U n i t e d S t a t e s , " Survey of Current Business ( O c t o b e r , 1 9 6 5 ) , p p . 2 1 - 2 8 . N a t i o n a l A c c o u n t s ( 1 3 - 5 0 2 ) , p . 1 0 3 . 28 The base stock was estimated in the manner discussed in section A, U S I N G 5 M V = * 2 8 a n d t h e constant dollar expenditure series from Table 5 4 of the National Accounts. It was necessary to accumulate depreciated investment from 1 1 years back ( 1 9 3 5 ) . c. Other Durables The concept of "other" durables arises as a residual category, name-ly, "durable goods" minus consumer expenditure on motor vehicles. This fact implies that the category encompasses a wide variety of goods. In fact, we see from the notes to Tables 5 3 and 5 4 (unpublished) that the category "dur-ables" includes house trailers, [AUTOMOBILES], furniture, household appliances, radio and television sets, and sporting and wheeled goods. By definition, then, the residual includes a l l but automobiles. Such items as watches, clocks, jewellery, silverware, tools, garden equipment, and toys are not considered 6 durables in the National Accounts. The most comprehensive discussion of "other durable goods" occurs in Helliwell et al [22], where the research went beyond regression equa-tions and statistical tests, since an actual survey of households was con-ducted in order to obtain estimates for the average lifetimes of the goods in question. [Another reason for the difficulty in treating the category is the obscurity of the 'base stock' concept]. Notwithstanding the dis-claimers, and recognizing the fact that the figures are s t i l l basically drawn from a hat," let us consider some results from the survey. The study 'These are, however, classified as "semi-durables." 29 c o n s i d e r e d s u c h f a c t o r s as t h e a v e r a g e age a t s c a r p p i n g and w e i g h t s f r o m a c o m p o s i t e consumer p r i c e i n d e x i n o r d e r t o a r r i v e a t an " a v e r a g e " q u a r t e r l y d e p r e c i a t i o n r a t e : (1) E l e c t r i c a l goods (wash ing m a c h i n e s , r e f r i g e r -a t o r s , c o o k e r s , t e l e v i s i o n s e t s , e t c . ) were f o u n d t o be t h e h i g h e s t d e p r e c i a t i n g goods i n t h e c a t e g o r y , w i t h a q u a r t e r l y r a t e o f 6.29%; (2) Hardware and o t h e r s u c h i t e m s were n e x t w i t h an e s t i m a t e d q u a r t e r l y r a t e o f 5.5%; and (3) F u r n i t u r e and f l o o r c o v e r i n g s ( k i t c h e n , l o u n g e , r e c r e a t i o n ) were e s t i m a t e d t o d e p r e c i a t e a t a r a t e o f 5.22% p e r q u a r t e r . 7 A p p l y i n g t h e w e i g h t s , we a r r i v e a t an a v e r a g e q u a r t e r l y r a t e o f 5.75% f o r 0 4 o t h e r d u r a b l e s . A c c u m u l a t i n g f o r f o u r q u a r t e r s [ i . e . , ( 1 - 1 y i e l d s an g a p p r o x i m a t e a n n u a l o f 21%. T h i s i s t h e f i g u r e we u s e i n t h i s s t u d y . In c a l c u l a t i n g a p r i c e i n d e x f o r t h i s r e s i d u a l c a t e g o r y we h a v e u s e d a w e i g h t e d i n d e x u n d e r t h e a s s u m p t i o n t h a t * * * P r i c e = W P + W P TOTAL MV MV OTH OTH DURABLES ( 1 " W M V ) * where W = a w e i g h t f o r motor v e h i c l e e x p e n d i t u r e ; p = motor v e h i c l e MV MV * p u r c h a s e p r i c e ; and P 0 T H = o t h e r d u r a b l e s p u r c h a s e p r i c e . E l e c t r i c a l ( . 4 3 ) ; F u r n i t u r e ( . 3 2 ) ; and Hardware ( . 2 5 ) . p T h i s seems r e a s o n a b l e r e l a t i v e t o 5 o f .28 s i n c e we w o u l d e x p e c t a c h a i r i n o n e ' s d e n t o l a s t somewhat l o n g e r t h a n a m o t o r v e h i c l e on t h e f r e e w a y . Hamburger e s t i m a t e s a r a t e o f . 5 b u t (a) a d m i t s t h a t i t i s p r o b a b l y t o o h i g h and (b) r e p o r t s t h a t a l i k e l i h o o d r a t i o t e s t y i e l d s a p r o b a b i l i t y t h a t t h e " t r u e " r a t e on o t h e r d u r a b l e s i s no g r e a t e r t h a n t h a t on a u t o m o b i l e s o f g r e a t e r t h a n 30 p e r c e n t [21 ; p . 1 1 3 7 ] . 30 and s o l v e d f o r * P * TOTAL r P MV MV OTH 1-W, MV u s i n g as w e i g h t s t h e e x p e n d i t u r e s h a r e ( i n c u r r e n t d o l l a r s ) $ e x p e n d i t u r e M . V . $ e x p e n d i t u r e d u r -a b l e s The r e s u l t a n t p r i c e i n d e x f o r o t h e r d u r a b l e s a p p e a r s a t t h e end o f * t h i s c h a p t e r . T h i s i s t h e P OTHDUR u s e d t o c a l c u l a t e t h e r e n t a l p r i c e PDO. P r o f e s s o r J . H e l l i w e l l h a s p o i n t e d o u t t h a t t h e n a t i o n a l a c c o u n t s e x p e n d i t u r e s e r i e s were n o t e s t i m a t e d c o n s i s t e n t l y , s i n c e motor v e h i c l e e x p e n d i t u r e d o e s n o t i n c l u d e s a l e s t a x w h i l e " o t h e r d u r a b l e g o o d s " c o e s a c c o u n t f o r t a x e s . We h a v e c h o s e n n o t t o a t t e m p t t o c o r r e c t f o r t h e t a x , s i n c e one a r b i t r a r y t a x r a t e ( f o r example 5.5%) i s i n a p p r o p r i a t e . In c a l c u l a t i n g , t h e b a s e s t o c k f o r O t h e r D u r a b l e s , we have a c c u m u l a t e d i n v e s t m e n t e x p e n d i t u r e ( d e p r e c i a t e d ) f o r 16 y e a r s p r i o r t o 1946 . d . H o u s i n g As m e n t i o n e d a b o v e , t h e N a t i o n a l A c c o u n t s t r e a t consumer e x p e n d i -t u r e on h o u s i n g as business c a p i t a l f o r m a t i o n , a n d t h e f i g u r e s r e p o r t e d i n g t h e consumer s e c t o r a r e i m p u t e d r e n t s , e t c . f rom t h e s t o c k o f h o u s i n g . R e c e n t l y , t h e H o u s i n g a n d B u i l d i n g P e r m i t s D i v i s i o n o f S t a t i s t i c s C a n a d a made a v a i l a b l e t o us some p r e l i m i n a r y r e s u l t s on t h e h o u s i n g s t o c k , and t h e s e d a t a w i l l be i n c o r p o r a t e d i n t o t h i s s t u d y . H o w e v e r , i t i s v a l u a b l e Consumer e x p e n d i t u r e s i n c l u d e a c t u a l r e n t s p a i d a n d r e n t s i m p u t e d t o v a r i o u s n o n - r e p o r t e d s o u r c e s . 31 t o f i r s t d i s c u s s o t h e r v a r i o u s s o u r c e s o f d a t a f o r t h i s v e r y i m p o r t a n t s e c t o r . One o f t h e f e a t u r e s o f t h i s s t u d y i s t h e i n c l u s i o n o f l a n d as a consumer d u r a b l e . S i n c e l a n d a n d s t r u c t u r e a r e c o m p l e m e n t a r y , i t i s s u r -p r i s i n g t h a t no o t h e r s t u d i e s h a v e made an a t t e m p t ( a l b e i t c r u d e ) t o t r e a t t h e demand f o r r e s i d e n t i a l l a n d . The C e n t r a l Mor tage a n d H o u s i n g C o r p o r a t i o n (CMHC) p u b l i s h e s an a n n u a l e n t i t l e d Canadian Housing Statistios3 w h i c h p r e s e n t s c o m p r e h e n s i v e i n f o r m a t i o n on new s t a r t s , c o m p l e t i o n s , method o f f i n a n c i n g and r e l a t e d d a t a f o r h o u s i n g . The main b o d y o f d a t a on c o s t s ( l a n d , c o n s t r u c t i o n , m o r t -g a g e , e t c . ) f o c u s e s on new s i n g l e - d e t a c h e d d w e l l i n g s f i n a n c e d u n d e r t h e N a t i o n a l H o u s i n g A c t (NHA). ( S i n c e t h e NHA f i n a n c e s a b o u t 60 p e r c e n t o f a l l s t a r t s i n C a n a d a , t h e s e d a t a a r e r e a s o n a b l y r e p r e s e n t a t i v e ) . L e s s f r e -q u e n t m e n t i o n i s made o f d u p l e x e s a n d m u l t i p l e d w e l l i n g s s i n c e t h e ma in c o n -c e r n o f t h i s p u b l i c a t i o n i s s i n g l e - d e t a c h e d d w e l l i n g s . T h e s e o t h e r c a t e -g o r i e s a r e , h o w e v e r , t r e a t e d . ( i ) R e s i d e n t i a l L a n d . W h i l e an i n d e x o f l a n d c o s t and i n d e x e s o f h o u s e s i z e a r e a v a i l a b l e f r o m t h e CMHC, no j u s t i f i c a t i o n e x i s t s f o r r e l a t i n g t h e cost o f l a n d t o a p a r t i c u l a r size o f l o t . M u n i c i p a l R e a l E s t a t e B o a r d s , o r a t l e a s t t h e V a n c o u v e r v e r s i o n , e s t i m a t e d a t a o n s i t e v a l u e s f o r a p a r t m e n t s , i n d u s t r i a l l a n d v a l u e s , and c o m m e r c i a l l a n d v a l u e s ^ S e e , f o r e x a m p l e , Real Estate Trends in Metropolitan Vancouver, 1971 , S t a t i s t i c a l and S u r v e y C o m m i t t e e , R e a l E s t a t e B o a r d o f G r e a t e r V a n -c o u v e r . 'Ibid., p . B 5 , C 7 , and C14 r e s p e c t i v e l y . 32 p e r s q u a r e f o o t . T h e s e d a t a , h o w e v e r , a r e n o t u s e f u l u n l e s s we h a v e r e l i a b l e e s t i m a t e s on t h e quantity o f s q u a r e f e e t . M u n i c i p a l S t a t i s t i c s ( p u b l i s h e d by most p r o v i n c i a l s t a t i s t i c a l b u r e a u s ) g i v e s p a r s e d a t a on t o t a l a c r e a g e and a s s e s s e d v a l u e o f l a n d s i t e s f o r t a x a t i o n p u r p o s e s ; b u t no b reakdown i s g i v e n f o r a s s e s s m e n t s f o r b u s i n e s s and p r i v a t e p u r p o s e s . T h u s , w h i l e we c a n c a l c u l a t e t h a t an " a c r e " o f l a n d i n B r i t i s h C o l u m b i a was a s s e s s e d on the average a t $2184 i n 1970 , and $39 ,608 i n G r e a t e r V a n c o u v e r , we c a n go no f u r t h e r . The o n l y c o m p r e h e n s i v e t r e a t m e n t o f l a n d i n i t s d i f f e r e n t u s e s i s i n G o l d s m i t h [ 1 9 ] ; b u t h i s work i s l i m i t e d t o w e a l t h e s t i m a t e s f o r t h e U.S.A. Our e a r l y e s t i m a t e s f o r t h e s t o c k o f r e s i d e n t i a l l a n d come f r o m F i r e s t o n e [ 1 4 ] . The F i r e s t o n e s e r i e s ( i n 1939 d o l l a r s ) i s a v a i l a b l e t o 1953 , and t h u s i t was n e c e s s a r y t o d e r i v e some e s t i m a t e s f o r l a t e r y e a r s . F i r e s t o n e ' s s e r i e s i s b a s e d on an i n t e r p o l a t i o n o f t h e r a t i o o f l a n d a c q u i -s i t i o n c o s t ( i n 1944) t o t o t a l c o s t o f t h e d w e l l i n g ( i n c l u d i n g l a n d ) . How-e v e r , s i n c e no o t h e r a t t e m p t s h a v e b e e n made, we h a v e c h o s e n t o u s e t h i s s e r i e s as a s t a r t i n g p o i n t . To e x t e n d t h e r e s i d e n t i a l l a n d s e r i e s , we h a v e assumed a s i m p l e r e l a t i o n s h i p b e t w e e n d i f f e r e n t t y p e s o f d w e l l i n g s and t h e s i z e o f l o t e a c h r e q u i r e s . T h u s , f o r e x a m p l e , i f an a p a r t m e n t b l o c k c o n -t a i n s 20 d w e l l i n g u n i t s and c o v e r s a l o t o f 10 ,000 s q u a r e f e e t , t h e n e a c h s u i t e " r e q u i r e s " 500 s q u a r e f e e t o f l a n d . S i m i l a r l y , i f a s i n g l e - d e t a c h e d d w e l l i n g i s e r e c t e d on a 3 ,000 s q u a r e f o o t l o t , t h e n we w o u l d s a y t h a t ( i f we l e t t h e 500 s q u a r e f e e t r e p r e s e n t one u n i t o f l a n d s t o c k ) t h e h o u s e u s e s s i x l a n d u n i t s . . S i n c e t h e 1944 r a t i o i s not r e p r e s e n t a t i v e o f a l l t ime p e r i o d s , t h i s i s c l e a r l y not a s a t i s f a c t o r y e s t i m a t e . 33 U s i n g t h e s e " l a n d u n i t s , " we may a p p r o x i m a t e a s e r i e s o f additions t o t h e l a n d s t o c k (which l i n k s t o F i r e s t o n e ' s ) i n t h e f o l l o w i n g manner : LAND. - LAND^ . = k{L • (N -D) + L_ • (N ) + L • (N )} t t - 1 1 1 2 2 3 3 where D = number o f d e m o l i t i o n s i n y e a r t ; L . = number o f ' l a n d u n i t s " r e q u i r e d b y d w e l l i n g s o f t y p e i ; l N^ = number o f new s t a r t s o f s i n g l e d e t a c h e d d w e l l i n g s i n y e a r t ; N 2 = number o f new row and d u p l e x s t a r t s ; N^ = number o f new a p a r t m e n t s s t a r t s . In o r d e r t o s o l v e f o r k , we must f i r s t e s t i m a t e L , L 2 , L 3 u s i n g F i r e s t o n e ' s 1952 and 1953 d a t a , and t h e n we may b u i l d up a s e r i e s o f a d d i -t i o n s ( i n 1939 d o l l a r s ) t o h i s l a n d s t o c k . The minimum l e g a l l o t s i z e r e q u i r e m e n t s ( to o b t a i n a C i t y o f V a n c o u v e r b u i l d i n g p e r m i t ) a r e : APARTMENTS ( P r i o r t o S e p t . 1, 1 9 6 5 ) : 5 ,400 s q . f t . ( S i n c e S e p t . 1, 1 9 6 5 ) : 6 ,000 s q . f t . LOW-DENSITY MULTIPLE HOUSING: 1 0 , 0 0 0 s q . f t . DUPLEX: 3 ,800 (- 4 , 8 0 0 ) s q . f t . S INGLE-DETACHED: 3 ,300 (- 4 , 8 0 0 ) s q . f t . ( T h e s e , o f c o u r s e , a r e o n l y b r o a d a p p r o x i m a t i o n s , a n d t h e e s t i m a t e s t o be d e r i v e d s h o u l d be c o n s i d e r e d t h e s a m e ) . U s i n g V a n c o u v e r l a n d r e q u i r e -ments and a s s u m i n g t h e " t y p i c a l " a p a r t m e n t b l o c k p r i o r t o t h e 1 9 6 0 ' s ( i n f a c t , we a r b i t r a r i l y s e t 1962 t o be " t h e " y e a r t h e a v e r a g e a p a r t m e n t b l o c k grew) c o n t a i n e d 24 d w e l l i n g s and t h e p o s t - 1 9 6 2 a p a r t m e n t c o n t a i n e d 48 d w e l l i n g s , 34 we make u s e o f t h e f o l l o w i n g i n f o r m a t i o n : SQUARE F E E T OF LAND DWELLING TYPE AVERAGE LOT ( s q . f t . ) PER DWELLING SINGLE-DETACHED 4 ,300 4 ,300 = 3 4 . 4 u n i t s DUPLEX OR ROW 4 ,300 2 ,150 = 1 7 . 2 u n i t s APARTMENT BLOCK: (24 d w e l l i n g s ) 1948-1962 5 ,400 s q . f t . 225 = 1 . 8 u n i t s (48 d w e l l i n g s ) 1963-1969 6 ,000 s q . f t . 125 = 1 u n i t D w e l l i n g s t a r t s o f d i f f e r e n t t y p e s come f r o m t h e C e n t r a l M o r t g a g e and H o u s i n g C o r p o r a t i o n and e s t i m a t e s o f d e m o l i t i o n s a r e f o u n d i n U r q u h a r t and B u c k l e y [DATA ( 2 2 ) ] . I t was n e c e s s a r y t o assume an a v e r a g e o f 9000 demo-l i t i o n s f r o m 1961 t o 1969 . T h u s , o u r " l a n d i n c r e m e n t s s e r i e s " i s b u i l t up b y s o l v i n g ALAND = k [ 3 4 . 4 ( N l - D ) + 17 .2 (N2 ) + 1 .8 (N3) ] 1952 t o 1953 f o r k and t h e n a p p l y i n g t h e v a l u e o b t a i n e d t o t h e d w e l l i n g s t a r t s s e r i e s ( i n 1963 t h e 1.8 i s r e p l a c e d b y 1 . 0 ) . We a d j u s t s i n g l e - d e t a c h e d o n l y ( f o r d i s -a p p e a r a n c e s ) s i n c e t h i s i s t h e most l i k e l y t o b e d e m o l i s h e d . Once t h i s s e r i e s (ALAND) was c o n s t r u c t e d , we l i n k e d F i r e s t o n e ' s ( i m p l i c i t ) p r i c e i n d e x w i t h a CMHC l a n d p r i c e i n d e x and t h u s c o n v e r t e d t h e 1939 d o l l a r l a n d s t o c k t o 1961 d o l l a r s . The r e s u l t a n t s e r i e s a p p e a r s a t t h e end o f t h i s c h a p t e r . 35 ( i i ) D w e l l i n g s . I n t a b u l a t i n g " t h e " s t o c k , we must r e c o g n i z e t h a t t h e r e a r e many methods o f t a k i n g a c c o u n t , and o u r p r o b l e m i s t h a t o f r e c o n c i l i n g t h e s e d i s p a r a t e m e a s u r e s i n t o a common y a r d s t i c k . The m a i n b a s e s (once we h a v e s o r t e d o u t s i n g l e - d e t a c h e d , row, d u p l e x , and a p a r t m e n t u n i t s ) a r e s q u a r e f e e t and r o o m s . I n s o f a r as r e n t e d q u a r t e r s a r e c o n c e r n e d , t h e 12 l a s t a l l - i n c l u s i v e s t u d y i n Canada was p u b l i s h e d i n 1959 a n d s t a t e d t h i s a b o u t a s t a n d a r d o f measurement : S i z e c a n be d e f i n e d i n s u c h te rms as number o f s q u a r e f e e t o f l i v i n g s p a c e , number o f r o o m s , o r number o f b e d r o o m s . The l a t t e r i s now w i d e l y a c c e p t e d as a m e a n i n g f u l d e s c r i p t i o n o f s i z e and has b e e n a d a p -t e d i n t h e s e r e n t t a b u l a t i o n s . M o s t d w e l l i n g u n i t s o f f e r e d f o r r e n t a r e d e s c r i b e d i n te rms o f b a c h e l o r a p a r t m e n t s o r 1 , 2 , 3 , o r more bedroom a p a r t m e n t s o r h o u s e s . T a b u l a t i o n by s i z e o f d w e l l i n g u n i t i s o n t h i s b a s i s . ^ 14 S i n c e 1953 , t h e r e h a s b e e n an a n n u a l p u b l i c a t i o n - w h i c h e s t i m a t e s t h e t o t a l . n u m b e r o f rooms (and d w e l l i n g u n i t s ) i n t h e C a n a d i a n h o u s i n g s e c -t o r . T h e s e d a t a a r e t a b u l a t e d i n U s h e r [36] where t h e t o t a l a n n u a l s t o c k o f rooms o f d w e l l i n g s p a c e i s r e p o r t e d f o r u n i t s f r o m 1 t o 9+ r o o m s . Some c o n -c e p t s f r o m t h e o r i g i n a l s o u r c e : D w e l l i n g — a d w e l l i n g i s d e f i n e d as a s t r u c t u r a l l y s e p -a r a t e s e t o f l i v i n g p r e m i s e s w i t h p r i v a t e e n -t r a n c e f r o m o u t s i d e t h e b u i l d i n g , o r f r o m a common h a l l w a y o r s t a i r w a y i n s i d e . C a n a d a , S t a t i s t i c s C a n a d a ( f o r m e r l y t h e D o m i n i o n B u r e a u o f S t a t i s t i c s , and h e n c e f o r t h r e f e r r e d t o as D B S ) , C a t a l o g u e N o . ( 6 2 - 5 1 9 ) . ^Ibid.j p . 1 0 . 1 4 D B S ( 6 4 - 2 0 2 ) . 36 H o u s e h o l d — a p e r s o n o r a g r o u p o f p e r s o n s o c c u p y i n g one d w e l l i n g u n i t i s d e f i n e d as a " h o u s e -h o l d . " The number o f h o u s e h o l d s w i l l t h e r e f o r e be e q u a l t o t h e number o f o c c u -p i e d d w e l l i n g s . A p a r t m e n t o r F l a t - i n c l u d e s : (a) d w e l l i n g u n i t s i n a p a r t m e n t b l o c k s o r a p a r t m e n t h o t e l s ; (b) s u i t e s i n d u p l e x e s o r t r i p l e x e s ( i . e . , where t h e d i v i s i o n b e t w e e n d w e l l i n g u n i t s i s h o r i z o n -t a l ) ; (c) s u i t e s i n s t r u c t u r a l l y c o n v e r t e d h o u s e s ; (d) l i v i n g q u a r t e r s l o c a t e d a b o v e , o r i n t h e r e a r o f s t o r e s , r e s t a u r a n t s , g a r a g e s , o r o t h e r b u s i n e s s p r e m i s e s ; (e) J a n i t o r s ' q u a r t e r s i n s c h o o l s , c h u r c h e s , w a r e -h o u s e s , e t c . ; and (f) p r i v a t e q u a r t e r s f o r employees^ j ,n h o s p i t a l s o r o t h e r t y p e s of i n s t i t u t i o n s . P i c k e t t [29] c a l c u l a t e d e a r l y e s t i m a t e s f o r t h e h o u s i n g s t o c k (1871-1921) u s i n g d e c e n n i a l c e n s u s i n f o r m a t i o n on o c c u p i e d , v a c a n t , a n d i n c o m p l e t e d w e l l i n g s . He b e g a n on t h e p r e m i s e t h a t " i t i s p o s s i b l e t o d e r i v e e s t i m a t e s o f d e c a d e c h a n g e s i n h o u s i n g s t o c k a n d , b y t h e a p p l i c a t i o n o f r e l a t e d e c o n o -16 mic i n d i c a t o r s , t o d i s t r i b u t e t h e s e c h a n g e s on an a n n u a l b a s i s . " Among h i s a s s u m p t i o n s were t h e f o l l o w i n g : (a) b e f o r e 1911 , a p a r t m e n t s were o f n e g l i g i b l e i m p o r t a n c e ; (b) i n t h e e a r l y y e a r s , s i n c e C a n a d a was an e x p a n d i n g f r o n t i e r s o c i e t y , t e m p o r a r y d w e l l i n g s were i m p o r t a n t ; (c) t h e 'economic i n d i c a t o r ' w h i c h h e u s e s t o d i s t r i b u t e d e c e n n i a l changes t o a n n u a l c h a n g e s i s a s e r i e s o n t h e consump-t i o n o f window g l a s s : 1 5 D B S ( 6 4 - 2 0 2 ) , 1971 , P p . 6 - 7 . 1 6 P i c k e t t , " R e s i d e n t i a l C a p i t a l F o r m a t i o n i n C a n a d a , 1 8 7 1 - 1 9 2 1 , " Canadian Journal of Economics and Political Science, V o l . 29 -1 ( F e b r u a r y , 1 9 6 3 ) , p. 4 1 . 37 T h u s , on a t h o u g h t no more p r o f o u n d t h a n t h a t h o u s e s h a v e w indows , i t was d e c i d e d t o s e c u r e i n f o r m a -t i o n on window g l a s s i m p o r t s and c o n s u m p t i o n ; make t h i s i n f o r m a t i o n c o n s i s t e n t w i t h c e r t a i n r e a s o n a b l e a s s u m p -t i o n s a b o u t b u i l d i n g a c t i v i t y , and t o a l l o c a t e t h e t o t a l number o f permanent h o u s e s c o m p l e t e d i n t h e s u c c e s s j ^ e d e c a d e s t o an a n n u a l b a s i s by means o f [ t h i s ] s e r i e s . . . P i c k e t t ' s v a l u e e s t i m a t e s a r e b a s e d on 1921 home v a l u e s i n F i r e -s t o n e (Residential Real Estate in Canada). I n t e r e s t i n g l y , P i c k e t t ' s e a r l y e s t i m a t e s a r e t o a s u r p r i s i n g e x t e n t s t a t i s t i c a l l y c o n s i s t e n t w i t h o f f i c i a l e s t i m a t e s f o r l a t e r y e a r s . 18 More r e c e n t l y , M a r i o n S t e e l e [ 3 4 ] , h a s t r e a t e d h o u s i n g s t a r t s as a consumer d e c i s i o n , and t h e s t o c k e s t i m a t e s she d e r i v e s a r e c o n s i s t e n t w i t h r e c e n t work b e i n g done a t S t a t i s t i c s C a n a d a . In f a c t , S t e e l e i s i n v o l v e d i n t h e g o v e r n m e n t ' s h o u s i n g s t o c k p r o j e c t , s o we may e x p e c t s i m i l a r i t i e s i n t h e r e s u l t s . The r e c e n t e s t i m a t e s b y S t a t i s t i c s C a n a d a o f h o u s i n g c a p i t a l s t o c k 19 a r e " e s t i m a t e s o f f i x e d r e p r o d u c i b l e r e s i d e n t i a l s t o c k a t m a r k e t v a l u e . " T h i s s t o c k i n c l u d e s a l l n o n - c o l l e c t i v e d w e l l i n g s i n t e n d e d f o r y e a r - r o u n d o c c u p a n c y , and n o t owned by t h e g o v e r n m e n t . I n c l u d e d a r e s u c h r e l a t e d i t e m s as p e r m a n e n t l y - f i x e d e q u i p m e n t and g a r a g e s . More i m p o r t a n t , " c a p i t a l f o r m a t i o n ' P i c k e t t , op. cit., p . 45 . 18 " D e t e r m i n a n t s o f O w n e r - O c c u p i e d D w e l l i n g S t a r t s , C a n a d a , 1 9 2 1 - 1 9 4 0 , " U n i v e r s i t y o f G u e l p h , M a r c h , 1972. 19 " E s t i m a t e s o f R e s i d e n t i a l C a p i t a l S t o c k and F l o w s , M e t h o d o l o g y , " H o u s i n g and B u i l d i n g P e r m i t s S e c t i o n , S t a t i s t i c s C a n a d a , 1972, p . 1 . 38 c o n t r i b u t i n g t o t h e s t o c k may t a k e t h e f o r m o f m a j o r a l t e r a t i o n s o r i m -20 p r o v e m e n t s t o e x i s t i n g d w e l l i n g s . " M a r k e t v a l u e s f r o m t h e 1941 C e n s u s a r e u s e d as a benchmark i n t h e s t o c k e s t i m a t e s , and d e p r e c i a t i o n o n t h e s t o c k was t a k e n a t two p e r c e n t a n n u a l l y i n a p e r p e t u a l i n v e n t o r y f r a m e w o r k , h u t a g a i n g r o s s c a p i t a l f o r -m a t i o n i s d e p r e c i a t e d a t o n e - h a l f t h e a n n u a l r a t e i n t h e c u r r e n t y e a r . T h u s , i t was n e c e s s a r y t o r e c a l c u l a t e t h e ( r e a l ) s t o c k f r o m t h e b e g i n n i n g o f t h e s e r i e s (1921) u s i n g o u r g e o m e t r i c d e p r e c i a t i o n w i t h no c u r r e n t p e r i o d d e p r e c i a t i o n on new c a p i t a l . A n o t h e r m i n o r change i n t h i s s t u d y i s t h e u s e o f 6 = . 0 3 , s i n c e t h i s w i l l mean t h a t 80 p e r c e n t o f t h e i n i t i a l v a l u e i s d e p r e c i a t e d i n 50 y e a r s as o p p o s e d t o 80 p e r c e n t i n 75 y e a r s a t an 21 a n n u a l r a t e o f . 0 2 . A f t e r h a l f a c e n t u r y , t h e r e i s g r e a t p r o b a b i l i t y t h a t a h o u s e w i l l e n d i n t h e d e m o l i s h e d g r o u p . The S t a t i s t i c s C a n a d a d a t a s e r i e s e x c l u d e s r e a l e s t a t e c o m m i s s i o n ( a l t h o u g h t h e N a t i o n a l A c c o u n t s i n c l u d e i t ) . I t i s c l e a r t h a t s u c h a compo-n e n t could b e c o n s i d e r e d p a r t o f c a p i t a l f o r m a t i o n , s i n c e c o m m i s s i o n i s p a i d t o f a c i l i t a t e t h e t r a n s f e r o f s t o c k . The f i g u r e s a r e a v a i l a b l e i n c u r r e n t and c o n s t a n t d o l l a r s , and t h u s t h e r e s u l t a n t i m p l i c i t s t o c k p r i c e i n d e x i s c o n s i s t e n t w i t h the o t h e r goods i n o u r m o d e l . 2 0 r . , Loc. cvt. 21 G o l d s m i t h [19] s u g g e s t s t h a t 50 y e a r s i s a good a p p r o x i m a t i o n t o " t h e " l i f e t i m e o f a h o u s e . 39 ( i i i ) P r o p e r t y T a x e s . S i n c e we w i l l b e c a l c u l a t i n g a u s e r c o s t f o r h o u s i n g and l a n d , we must a c c o u n t f o r p r o p e r t y t a x e s , w h i c h a r e a r e a l c o s t t o t h e c o n s u m e r . We w i l l assume t h e same p r o p e r t y t a x r a t e o n r e s i d e n t i a l l a n d a n d s t r u c t u r e s . In f a c t , what we b a s i c a l l y do i s ( i ) t o e s t i m a t e a s t o c k o f b u s i n e s s l a n d s e r i e s (LB) i n c u r r e n t d o l l a r s t o go w i t h o u r r e s i d e n t i a l l a n d ( L R ) , r e s i d e n t i a l s t r u c t u r e s ( S R ) , and a b u s i n e s s s t r u c t u r e s s e r i e s (SB) e s t i m a t e d by P r o f e s s o r A . D. W o o d l a n d ; ( i i ) t a k e t h e v a l u e o f p r o p e r t y t a x e s f r o m t h e N a t i o n a l A c c o u n t s as a r a t i o ( a n n u a l l y ) t o t h e t o t a l c u r r e n t d o l l a r v a l u e o f LR + SR + y ( L B + SB) where y i s a r e v a l u a t i o n f a c t o r o f b u s i n e s s p r o p e r t y f o r t a x a t i o n p u r p o s e s . A d e t a i l e d d e s c r i p t i o n a p p e a r s i n T a b l e I V - 4 i n t h e A p p e n d i x . B . THE RATE OF INTEREST RELEVANT TO CONSUMER EXPENDITURE DECISIONS In c h o o s i n g a d i s c o u n t r a t e f o r p u r c h a s e s o f consumer d u r a b l e s , we m u s t , o f c o u r s e , c o n f r o n t t h e e v e r - p r e s e n t p r o b l e m o f t h e d i s c r e p a n c y b e t w e e n b o r r o w i n g r a t e s and l e n d i n g r a t e s ; a p r o b l e m w h i c h o f t e n c o n f u s e s e m p i r i c a l a n a l y s e s . As a r o u g h a p p r o x i m a t i o n , t h e 1971 C a n a d i a n consumer w o u l d h a v e t o p a y a n y t h i n g f r o m 1%% ( f u l l y - s e c u r e d b a n k l o a n ) t o 12% (bank l o a n f o r consumer e x p e n d i t u r e s e c u r e d by t h e a s s e t i t s e l f ) t o 18% ( the maximum a l l o w -a b l e u n d e r most p r o v i n c i a l S m a l l L o a n s A c t s , and t h e a n n u a l r a t e c h a r g e d by a l l d e p a r t m e n t s t o r e s and c r e d i t c a r d o r g a n i z a t i o n s o n o u t s t a n d i n g b a l a n c e s ) T h i s i s p a r t o f P r o f e s s o r W o o d l a n d ' s c u r r e n t r e s e a r c h p r o j e c t o n p r o d u c t i o n f u n c t i o n s f o r C a n a d i a n i n d u s t r i e s . 40 i n o r d e r t o "bor row" f rom h i s f u t u r e l a b o u r income t o f i n a n c e c u r r e n t e x p e n d -i t u r e . The S m a l l L o a n s A c t r a t e i s non m a r k e t - d e t e r m i n e d ; r a t h e r , i t i s a l e g i s l a t e d " c e i l i n g " on consumer c r e d i t c h a r g e s . C l e a r l y , most o r g a n i z a -t i o n s a d h e r e v e r y c l o s e l y t o t h e " c e i l i n g " and r a r e l y w i l l an i n t e r e s t c h a r g e o f less than 16% b e i n e f f e c t u n d e r s u c h an a r r a n g e m e n t . D i e w e r t [ ( 1 0 , p . 26)] c a l c u l a t e s a r a t e o f r e t u r n a f t e r t a x e s o n c o r p o r a t e p r o f i t s and a f t e r income t a x e s on n o n - l a b o u r i n c o m e , i . e . , R = r - ( T c + T R ) / P R • K Before Taxes Corporate Personal Price Beginning Gross Private Taxes Taxes Index of Year Rate of Return Attributed for Real To Capital Capital Capital Income Stock Stock I f we assume t h a t R i s the n e t r a t e o f r e t u r n t h e consumer could have earned ( i . e . , t h e o p p o r t u n i t y c o s t ) had he n o t p u r c h a s e d t h e d u r a b l e , we a l s o assume t h a t t h e f u n d s were a v a i l a b l e f o r e i t h e r u s e . In s u c h a c a s e , a b o n d y i e l d s e r i e s ( s h o r t - t o - m e d i u m t e r m t o m a t u r i t y ) w o u l d s e r v e as a r e a s o n -a b l e p r o x y f o r t h e r a t e o f r e t u r n on a l t e r n a t i v e i n v e s t m e n t s ; f o r e x a m p l e , t h e y i e l d on Government o f C a n a d a b o n d s w i t h one t o t h r e e y e a r s l e f t t o m a t u r i t y may w e l l be t h e a p p r o p r i a t e r a t e f a c i n g t h e ' t y p i c a l ' consumer w i t h a s h o r t e r p l a n n i n g h o r i z o n . 22 The d i c h o t o m y i s w e l l - i l l u s t r a t e d i n two works b y t h e same a u t h o r ; h o w e v e r , t h e p r o b a b l e r e a s o n f o r t h i s i s t h a t t h e l a t t e r work i s more t h e o r e -t i c a l . W. E . D i e w e r t [10 , p . 8 ] . "One o f t h e m a i n s i m p l i f y i n g a s s u m p t i o n s i n o u r m o d e l i s t h a t t h e r e e x i s t s o n l y a s i n g l e f i n a n c i a l a s s e t , d e n o m i n a t e d 41 Hamburger [21] a r g u e s t h a t n o m i n a l b o n d and s a v i n g s a c c o u n t i n t e r -e s t r a t e s a r e v e r y r e l e v a n t i n e x p l a i n i n g e x p e n d i t u r e s on consumer d u r a b l e s , a l t h o u g h h i s r e s u l t s i n d i c a t e t h a t bond y i e l d s have t h e i r maximum e f f e c t on consumer e x p e n d i t u r e s a f t e r a f o u r - t o - s i x q u a r t e r l a g . In f a c t , Hamburger s u g g e s t s t h a t t h e ( r e l a t i v e ) l e n g t h o f t h e s e l a g s s u g g e s t s t h a t ( i n h i s c a s e , M o o d y ' s A a a r a t e on l o n g - t e r m c o r p o r a t e bonds) " i s a c t i n g p r i m a r i l y as a p r o x y f o r t h e r a t e s c h a r g e d on consumer c r e d i t , r a t h e r t h a n as a measure o f 2 3 t h e y i e l d s a v a i l a b l e on m a r k e t a b l e f i n a n c i a l a s s e t s . " He c o n c l u d e s : (a) m a r k e t a b l e f i n a n c i a l a s s e t s . a r e r e l a t i v e l y p o o r s u b s t i t u t e s f o r consumer d u r a b l e g o o d s ; and (b) t h e e s t i m a t e d l a g s may be more a p p r o p r i a t e -l y v i e w e d as e s t i m a t e s o f t h e r e a c t i o n t i m e s o f t h e s u p p l i e r s o f consumer c r e d i t t h a n t h o s e o f c o n s u m e r s . T h a t i s , t h e y s e r v e as i n d i c a t o r s o f t h e s p e e d w i t h w h i c h t h e r a t e s c h a r g e d on consumer c r e d i t a d j u s t t o changes i n o p e n - m a r k e t r a t e s . ^ 4 A n o t h e r w r i t e r (W. Weber) i n i n t e r t e m p o r a l consumer t h e o r y p r o p o s e t h a t r be an a v e r a g e e f f e c t i v e i n t e r e s t r a t e o r a n index o f i n t e r e s t rates 25 w h i c h t h e consumer f a c e s . What t h e above d i s c u s s i o n s u g g e s t s i s ( i ) t h a t t h e r e i s no s i n g l e u n -ambiguous " r a t e " w h i c h t h e consumer f a c e s ; a n d t h a t ( i i ) u n d e r d i f f e r e n t i n u n i t s o f t h e a g g r e g a t e c a p i t a l s t o c k , w h i c h i s e x p e c t e d t o y i e l d an own r a t e o f r e t u r n e q u a l t o R d u r i n g p e r i o d t . In [ 1 1 ; p . 63] r i s d e f i n e d as t h e o n e - p e r i o d i n t e r e s t r a t e a t w h i c h t h e consumer c a n b o r r o w . 23 Hamburger , op. ait., p . 1139 . 2 4 , . , Loc. ext. "The E f f e c t o f I n t e r e s t R a t e s on A g g r e g a t e C o n s u m p t i o n , " American Economic Review (Sep tember , 1 9 7 0 ) , p . 5 9 3 . 42 a s s u m p t i o n s , t h e o p p o r t u n i t y c o s t o f p u r c h a s i n g a consumer d u r a b l e may w e l l be e i t h e r a b o r r o w i n g r a t e (how much he must p a y f o r t h e f u n d s ) , a l e n d i n g r a t e (how much h e c o u l d c o n c e i v a b l y e a r n f r o m a d i f f e r e n t a l l o c a t i o n o f t h e f u n d s ) , o r some r a t e w h i c h l i e s be tween t h e t w o . One o f the e x i s t i n g r a t e o f r e t u r n s e r i e s i s a v a i l a b l e as ' R H O 1 f r o m t h e Bank o f C a n a d a RDX2 m o d e l . The s e r i e s r e p r e s e n t s (an e s t i m a t e f o r ) t h e n o m i n a l s u p p l y p r i c e o f c a p i t a l , and i s a v a i l a b l e f r o m 1952 q u a r t e r l y . T h i s s e r i e s , h o w e v e r , w o u l d be d i f f i c u l t t o e x t e n d b a c k t o 1946 . * The i n t e r e s t r a t e s a c t u a l l y u s e d were d i f f e r e n t f o r e a c h o f t h e d u r a b l e s . F o r c l o t h i n g , we u s e d an a v e r a g e y i e l d o n Government o f C a n a d a s e c u r i t i e s w i t h f i v e y e a r s t o m a t u r i t y ; f o r motor v e h i c l e s a n d o t h e r d u r -a b l e s , t h e r e s p e c t i v e r a t e s o f i n t e r e s t c h a r g e d t o f i n a n c e t h e i r p u r c h a s e s , and f o r h o u s i n g and l a n d t h e maximum ( a n n u a l a v e r a g e ) r a t e on N H A - i n s u r e d m o r t g a g e s . T h e s o u r c e s o f t h e s e s e r i e s a p p e a r i n T a b l e I V - 4 i n t h e A p p e n d i x . C . RENTAL PRICES The ' r e n t a l ' p r i c e i s e q u i v a l e n t t o t h e u s e r c o s t f o r one u n i t o f a d u r a b l e g o o d . ( I f t h e consumer p u r c h a s e s a u n i t o f good k , c a l l p^ t h e 26 p r i c e h e c h a r g e s h i m s e l f f o r t h e flow o f s e r v i c e s h e h a s u s e d ) . D i e w e r t , " I n t e r t e m p o r a l Consumer T h e o r y , " op. cit. 3 p . 9 : " T o f o r m t h e r e n t a l p r i c e (or u s e r c o s t ) f o r t h e s e r v i c e s o f one u n i t f o r t h e n t h good d u r i n g p e r i o d t , we i m a g i n e t h a t t h e consumer p u r c h a s e s t h e g o o d d u r i n g p e r -i o d t and t h e n s e l l s i t d u r i n g t h e f o l l o w i n g p e r i o d ( p o s s i b l y t o h i m s e l f ) . Then t h e d i s c o u n t e d e x p e c t e d r e n t a l p r i c e f o r t h e n t h consumer good d u r i n g p e r i o d t i s g i v e n by t h e d i s c o u n t e d c o s t o f t h e p u r c h a s e o f t h e n t h g o o d d u r i n g p e r i o d t m inus t h e d i s c o u n t e d r e s a l e v a l u e o f t h e d e p r e c i a t e d good d u r i n g p e r i o d t + 1 . . . * S i n c e i t i s u n l i k e l y one w o u l d b o r r o w t o f i n a n c e t h e p u r c h a s e o f c l o t h i n g t h e c h o s e n i n t e r e s t r a t e i s a l e n d i n g r a t e . F o r t h e o t h e r d u r a b l e s , where b o r r o w i n g i s more l i k e l y , we have c h o s e n t h e c o s t o f c r e d i t ( b o r r o w i n g r a t e s ) . 43 We w i l l make t h e s i m p l i f y i n g a s s u m p t i o n o f s t a t i c e x p e c t a t i o n s s o t h a t o u r consumer e x p e c t s c u r r e n t p r i c e s and i n t e r e s t r a t e s t o p r e v a i l . I n t h i s f ramework , t h e n ( < t " *kt> * ( 1 + V > - { 1 " V ^ k t + i where * p i s a s t o c k ( p u r c h a s e ) p r i c e ; and p t h e r e n t a l p r i c e . S i n c e we have assumed s t a t i c e x p e c t a t i o n s , P ^ t + ^ i - s e x p e c t e d t o be e q u a l t o P k t ? t h u s : ( * k t " p k t > • ( 1 + \ t > • ( 1 - V p i * k t T h i s r e d u c e s t o a f o r m u l a f o r p : * k t ( 1 + \t - 1 + V - p k t ( 1 + \ t } i - e - ' * * p k t ( 6 k + \ t } P k t " (1 + R^ t ) The r e n t a l p r i c e s f o r c l o t h i n g , a u t o m o b i l e s , and o t h e r d u r a b l e s a r e c a l c u l a t e d i n t h i s manner . T h o s e f o r h o u s i n g and l a n d , h o w e v e r , a r e s l i g h t l y m o d i f i e d , s i n c e i t i s i m p o r t a n t t o a c c o u n t f o r the e f f e c t s o f a p r o p e r t y t a x . T h u s , i f we l e t t r e p r e s e n t t h e r a t e o f p r o p e r t y t a x , t h e n t h e r e n t a l p r i c e f o r h o u s i n g b e c o m e s : 44 and t h a t o f l a n d (where t h e r e i s no d e p r e c i a t i o n ) : * * * P L t P L T - P L T ( 1 + t 5 " I + R ^ The R o l e o f E x p e c t a t i o n s C l e a r l y , t h e consumer h a s e x p e c t a t i o n s f o r f u t u r e p r i c e s , wage r a t e s , and i n t e r e s t r a t e s . S i n c e t h e r e n t a l p r i c e i s fo rmed f r o m a s t o c k p r i c e e x p e c t e d t o p r e v a i l , and s i n c e i t i s u n l i k e l y t h a t o u r consumer h a s p e r f e c t f o r e s i g h t , we h a v e assumed a m o d e l w i t h s t a t i c e x p e c t a t i o n s . T h e o r e t i -c a l l y , "we c o u l d make f u t u r e e x p e c t e d p r i c e s a d i s t r i b u t e d l a g o f p a s t p r i c e s and t h e n u s e t h e d e r i v e d demand e q u a t i o n s t o s i m u l t a n e o u s l y e s t i m a t e t h e p a r a -27 m e t e r s o f p r e f e r e n c e s as w e l l as t h e d i s t r i b u t e d l a g . " T h i s w o u l d l e a d t o v e r y c o m p l i c a t e d e s t i m a t i o n p r o c e d u r e s . D. NONDURABLES The s e r i e s f o r f o o d , a l c o h o l i c b e v e r a g e s , and t o b a c c o p r o d u c t s a r e d i r e c t l y f r o m t h e N a t i o n a l A c c o u n t s ( T a b l e s 53 and 54 , items* 2 , 3 , and 4 ) . T h e i m p l i c i t p r i c e i n d e x e s were c a l c u l a t e d b y d i v i d i n g t h e c u r r e n t d o l l a r e x p e n d i t u r e b y c o n s t a n t (1961) d o l l a r e x p e n d i t u r e . E . SERVICES We h a v e b r o k e n t h e N a t i o n a l A c c o u n t s " s e r v i c e s " i n t o (a) m e d i c a l c a r e and h e a l t h s e r v i c e s ; and (b) o t h e r s e r v i c e s . The ' o t h e r ' c a t e g o r y D i e w e r t , " I n t e r t e m p o r a l Consumer T h e o r y , " op. cit., p . 12 . 45 i n c l u d e s r e c r e a t i o n , t e l e p h o n e , c u l t u r a l s e r v i c e s , f i n a n c i a l , l e g a l , and s e v e r a l o t h e r s . A g a i n , s i n c e ' o t h e r ' i s a r e s i d u a l c a t e g o r y , i t was n e c e s -s a r y t o c a l c u l a t e a ' w e i g h t e d ' p r i c e i n d e x f o r ' o t h e r . ' The p r o c e d u r e was i d e n t i c a l t o t h a t u s e d i n c a l c u l a t i n g a p u r c h a s e p r i c e i n d e x f o r ' o t h e r d u r a b l e s . ' The p r i c e a n d q u a n t i t y s e r i e s a r e t a b u l a t e d a t t h e end o f t h e c h a p t e r . 1. M e d i c a l C a r e and H e a l t h S e r v i c e s B e g i n n i n g i n 1961 , t h e m a j o r p r o p o r t i o n o f e x p e n d i t u r e s on h o s p i t a l s a p p e a r s i n t h e government s e c t o r . To c o r r e c t f o r t h i s i n consumer e x p e n d i t u r e s , we h a v e added i n t h e g o v e r n m e n t ' s e x p e n d i t u r e o n h o s p i t a l s t o consumer h o s p i t a l e x p e n d i t u r e f o r t h e y e a r s 1961 t o 1969 . The c o n s t a n t d o l l a r s e r i e s was o b t a i n e d by d e f l a t i n g c u r r e n t d o l l a r v a l u e b y a p h y s i c i a n s e r v i c e s 28 p r i c e i n d e x . The d a t a were t a k e n f rom The National Finances 1970-71 [DATA (21 ) ; p . 10] and T a b l e 52 o f t h e N a t i o n a l A c c o u n t s (government t r a n s f e r s ) . The l a t t e r came i n f o r 1968 and 1969, where i t was n e c e s s a r y t o i n c l u d e f e d -e r a l [ t r a n s f e r ] e x p e n d i t u r e t o t h e p r o v i n c e s f o r m e d i c a r e i n " p h y s i c i a n s e r -29 v i c e s , " w h i c h i s one o f t h e components o f " m e d i c a l c a r e and h e a l t h s e r v i c e s . " T h u s , t h e m e d i c a l s e r i e s (and c o n s e q u e n t l y t h e o t h e r s e r v i c e s s e r i e s ) a r e not t h e same as t h o s e a p p e a r i n g i n t h e N a t i o n a l A c c o u n t s . l e m . I am i n d e b t e d t o P r o f e s s o r T . J . Wales f o r p o i n t i n g o u t t h i s p r o b -P r o f e s s o r D. U s h e r made t h i s i n f o r m a t i o n a v a i l a b l e . 4 6 F . THE SUPPLY OF LABOUR We t a k e t h e D i e w e r t - W o o d l a n d t o t a l wage b i l l (over a l l i n d u s t r i e s ) i n c u r r e n t d o l l a r s ( c a l l i t W) and c a l c u l a t e an " a v e r a g e " h o u r l y wage r a t e t h u s : 1 . S t a t i s t i c s C a n a d a — u n p u b l i s h e d d a t a o n a v e r a g e w e e k l y h o u r s worked ( c f . T a b l e IV -9 ) t i m e s 50 weeks = a v e r a g e a n n u a l h o u r s w o r k e d p e r p e r s o n . 2 . T o o b t a i n an a n n u a l h o u r s b i l l , we m u l t i p l y (1) by employment ( t a b u l a t e d i n [ 2 0 ] ) ; 3 . F i n a l l y , we d i v i d e W b y (2) t o o b t a i n an h o u r l y wage r a t e ( c f . T a b l e I V - 1 0 f o r t h i s and a l l s u b -s e q u e n t l a b o u r d a t a ) . I f we d i v i d e t h e t o t a l h o u r s b i l l b y o u r p o p u l a t i o n s e r i e s we a r r i v e a t p e r c a p i t a h o u r s w o r k e d ( L ) . In t h i s m a n n e r , we h a v e a consumer t h e o r y a p p r o a c h t o l a b o u r f o r c e p a r t i c i p a t i o n r a t e s . A s s u m i n g t h a t t h e average w o r k e r wou ld p r o b a b l y n o t work more t h a n 60 h o u r s p e r week f o r 52 weeks we may d e f i n e l e i s u r e h o u r s as £ = 3120 - L . We have assumed t h a t p h y s i o l o g i -c a l l y r e q u i r e d t i m e ( i . e . , s l e e p i n g ) i s not l e i s u r e . D i s c u s s i o n . A g a i n , w i t h the s u p p l y o f l a b o u r , we f a c e s e v e r a l p r o b l e m s . T h e r e i s , o f c o u r s e , t h e a g g r e g a t i o n p r o b l e m . More s e r i o u s l y , t h e r e i s t h e i n -s t i t u t i o n a l c o n s t r a i n t t h a t t h e c o n s u m e r - w o r k e r r e a l l y does n o t have a g r e a t d e a l o f c h o i c e i n s o f a r as choosing how many h o u r s he w i l l w o r k . T h i s i s n o t , i n t h e r e a l s e n s e , a d e c i s i o n v a r i a b l e . U n f o r t u n a t e l y , t h e r e i s no way t o c i r c u m v e n t t h i s d i f f i c u l t y . One f u r t h e r c o m p l i c a t i o n a r i s e s i n t h e t a x r a t e (see b e l o w ) , s i n c e i n h e r e n t i n t h e p r o g r e s s i v e t a x a t i o n s y s t e m i s a h i g h e r t a x b r a c k e t f o r more h o u r s worked ( i . e . , h i g h e r i n c o m e ) . A g a i n , we c a n n o t c a p t u r e t h e p r o g r e s s i v i t y o f t h e t a x s t r u c t u r e i n o u r m o d e l . 47 1. Tax on L a b o u r E a r n i n g s We make o n l y a c r u d e a d j u s t m e n t f o r income and o t h e r t a x e s on l a b o u r e a r n i n g s . O u r t a x r a t e (T) i s s i m p l y t h e r a t i o o f ( t o t a l d i r e c t t a x e s less s u c c e s s i o n d u t i e s and e s t a t e t a x e s ) = TD t o P e r s o n a l Income ( P I ) . The t a x e s a r e f o u n d i n T a b l e 44 o f t h e N a t i o n a l A c c o u n t s and P e r s o n a l Income i s f r o m T a b l e 4 o f t h e same s o u r c e . Thus T = T D / P I and W ( 1 - T ) i s t h e p r i c e o f t i m e . The s e r i e s TD and PI a p p e a r i n T a b l e I V - 1 1 o f t h e A p p e n d i x . T h u s , we h a v e d e v e l o p e d a r e a s o n a b l y b r o a d d a t a b a s e f o r c o n s u m p t i o n e x p e n d i t u r e i n p o s t - w a r C a n a d a . In C h a p t e r s V and VI we w i l l examine t h e r e -s u l t s o f o u r a n a l y s i s c a r r i e d o u t o n t h e s e d a t a . A P P E N D I X TO CHAPTER IV TABLE IV-1 AGGREGATE STOCK SERIES CONSTANT (1961) $MILLIONS BASE YEAR = 1946 YEAR CLOTHING 6 = .50 INITIAL STOCK= 1 4 23.92 PURCHASES X . = STOCK 1 MOTOR VEHICLES 6 = .28 INITIAL STOCK=237.92 PURCHASES X . = STOCK 1 OTHER DURABLES 6 = .21 INITIAL STOCX=l288.17 PURCHASES X. = STOCK ,1 HOUSING 6 = .03 INITIAL STOCK=11411.59 PURCHASES X . = STOCK l RESIDENTIAL LAND 6 = 0.0 INITIAL STOCK=3921.10 PURCHASES X . STOCK 1946 1676.00 2387.96 145.00 316.30 631.00 1648.65 678.39 11747.63 109.31 4030.41 1947 1653.00 2846.98 312.00 539.74 761.00 2063.43 668.89 12064.10 129.79 4160.21 1948 1511.00 2934.49 267.00 65.5.61 -747.00 2377.11 850.39 12552.57 129.91 4290.12 1949 1498.00 2965.24 461.00 933.04 831.00 2708.92 990.59 13166.59 148.92 4439.04 1950 1510.00 2992.62 753.00 1424.79 863.00 3003.04 1125.29 13896.89 272.00 4711.04 1951 1473.00 2969.31 663.00 1688.84 786.00 3158.40 839.20 14319.18 149.51 4860.55 1952 1606.00 3090.65 825.00 2040.97 904.00 3399.14 943.39 14833.00 155.60 5016.16 1953 1667.00 3212.32 939.00 2408.49 1115.00 3800.32 1250.50 15638.51 97.23 5113.39 1954 1682.00 3288.16 861.100 2595.11 1187.00 4189.25 1424.79 16594.15 107.58 5220.98 1955 1784.00 3428.08 1125.00 2993.48 1450.00 4759.50 1778.79 17875.12 138.91 5359.89 1956 1914.00 3628.04 1202.00 3357.30 1562.00 5322.00 1776.79 19115.66 125.29 5485.18 1957 1986.00 3800.02 1101.00 3518.26 1553.00 5757.38 1540.39 20082.59 114.49 5599.67 1958 2062.00 3962.01 1137.00 3670.14 1619,00 6167.33 1937.39 21417.51 ' 147.31 5746.98 1959 2155.00 4136.00 1192.00 3834.50 1736.00 6608.19 1867.39 22642.38 129.05 5876.04 1960 2242.00 4310.00 1184.00 3944.84 1723.00 6943.46 1521.20 23484.30 94.09 5970.13 1961 2276.00 4431.00 1227.00 4067.28 1856.00 7341.33 1488.00 24267.77 108.44 6078.57 1962 2352.00 4567.50 1416.00 4344.44 2063.00 7862.65 1549.59 25089.33 107.00 6185.58 1963 2393.00 4676.75 1621.00 4749.00 2123.00 8334.49 1613.70 25950.35 108.16 6293.74 1964 2477.00 4815.37 1871.00 5290.27 2301.00 8885.25 1870.79 27042.64 109.81 6V0-3.55 1965 2575.00 4982.68 2162.00 5970.99 2464.00 9483.34 1970.59 28201.96 107.44 6510.99 1966 2625.00 5116.34 2246.00 6545.11 2617.00 10108.84 1813.50 29169.40 98.86 6609.85 1967 2690.00 5248.17 2279.00 6991.48 2644.00 10629.98 1873.00 30167.32 106.04 6715.89 1968 2772.00 5396.08 2469.00 7502.86 2768.00 11165.68 2183.70 31446.00 111.94 6827.83 1969 2890.00 5588.04 2525.00 7927.06 3039.00 11859.89 2522.70 33025.31 118.66 6946.49 Note: In [40; p. 230], reference i s made t o a Department of Agriculture memo estimating the t o t a l area of r e s i d e n t i a l land i n Canada to be 2,160,000 acres i n 1963. This (using our r e a l stock i n 1961 dolla r s ) works out to be $2,913.77/acre i n constant d o l l a r s and $3,328.98/acre i n current d o l l a r s . vD 50 TABLE I V - 2 CANADA: POPULATION AND EMPLOYMENT (Thousands) YEAR * POPULATION 15+ EMPLOYMENT 1946 8 , 8 7 1 . 6 4 ,666 1947 9 , 0 1 2 . 6 4 ,832 1948 9 , 1 4 4 , 7 4 ,875 1949 9 , 5 0 8 . 9 4 ,916 1950 9 , 6 4 1 . 5 4 , 9 7 8 1951 9 , 7 5 8 . 7 5 ,098 1952 ." 1 0 , 0 0 6 . 3 5 ,161 1953 1 0 , 2 1 6 . 9 5 ,237 1954 1 0 , 4 5 2 . 3 5 ,244 1955 1 0 , 6 5 9 . 1 5 ,364 1956 1 0 , 8 5 5 . 5 5 ,586 1957 1 1 , 1 5 3 . 4 5 ,726 1958 1 1 , 3 9 4 . 8 5 ,694 1959 1 1 , 6 2 5 . 3 5 ,856. 1960 1 1 , 8 4 0 . 0 5 ,956 1961 1 2 , 0 4 6 . 4 6 , 0 5 0 1962 1 2 , 2 7 3 . 3 6 ,220 1963 1 2 , 5 1 3 . 1 6 ,366 1964 1 2 , 7 9 1 . 7 6 , 5 9 9 1965 1 3 , 0 8 7 . 7 6 , 8 4 8 1966 1 3 , 4 2 3 . 2 7 ,143 1967 1 3 , 8 1 1 . 5 7 ,364 1968 1 4 , 1 7 8 . 5 7 ,522 1969 1 4 , 5 4 2 . 4 7 ,764 15 y e a r s o f age and o l d e r . S o u r c e s : 1 . P o p u l a t i o n ~ DBS ( 9 1 - 2 0 1 ) ; ( 9 1 - 2 0 2 ) ; ( 9 1 - 5 1 1 ) . 2 . Employment — L a b o u r F o r c e S u r v e y , S p e c i a l T a b l e 3 c ; t a b u l a t e d i n [ 2 0 ] . 51 TABLE I V - 3 DURABLES: PURCHASE PRICE INDEXES MOTOR OTHER YEAR CLOTHING VEHICLES DURABLES HOUSING LAND 1946 0 .6122 0 .5586 0 .6534 0 .5410 0 .2497 1947 0 .6939 0 .6474 0 .8428 0 .6100 0 .2787 1948 0 .8432 0 .7715 0 .8263 0 .7150 0 .3188 1949 0 .8785 0 .8113 0 .8489 0 .7450 0 .3310 1950 0 .8821 0 .8207 0 .8852 0 . 7820 0 .3699 1951 0 .9830 0 .9366 1 .0018 0 .9020 0 .4027 1952 0 ,9875 0 .9527 1 .0177 VT. 0 .9179 0 .4542 1953 0 .9784 0 .9361 1.0032 0 .9260 0 .4600 1954 0 .9721 0 .9408 0 .9865 0 .9155 0 .6483 1955 0 .9608 0 .8684 0 .9632 0 .9360 0 .6990 1956 0 .9666 0 .8827 0 .9670 0 .9500 0 .7782 1957 0 .9668 0 .9655 0 .9825 0 .9770 0 .8685 1958 0 .9763 0 .9815 1.0036 0 .9740 0 .9496 1959 0 .9759 1 .0252 1.0062 0 .9730 0 .9734 1960 0 .9848 1 .0287 1 .0050 0 .9919 0 .9504 1961 1.0000 1.0000 1.0000 1.0000 1.0000 1962 1 .0098 0 .9859 0 .9990 0 .9970 1 .0695 1963 1 .0372 0 .9858 1 .0073 1 .0200 1.1425 1964 1 .0622 0 .9578 1 .0130 1 .0599 1 .1844 1965 1 .0796 0 .9500 1.0192 1.1209 1.1894 1966 1 .1188 0 .9328 1 .0401 1.1960 1 .3374 1967 1 .1729 0 .9491 1.0859 1 .2630 1 .3758 1968 1.2042 0 .9660 1 .1175 . 1 .2770 1 .4396 1969 1 .2384 0 .9711 1.1297 1 .3360 1.6145 S o u r c e : N a t i o n a l A c c o u n t s , Income and E x p e n d i t u r e , T a b l e s 53 and 54 ; L a n d — CMHC Index o f R e s i d e n t i a l L a n d C o s t s . 52 TABLE I V - 4 DURABLES: DISCOUNT RATES AND AVERAGE PROPERTY TAX RATE YEAR RSBY RMV RCFP RNHA PTAX 1946 .0169 .1300 .1560 .0450 .0638 1947 .0175 .1300 .1560 .0450 .0599 1948 .0227 .1300 .1560 .0450 .0564 1949 . 0 2 2 4 . .1300 .1560 .0450 .0566 1950 .0222 .1300 .1560 .0450 .0573 1951 .0258 .1300 .1560 .0500 .0618 1952 .0323 .1300 .1560 .0525 .0643 1953 .0344 .1500 .1690 .0525 .0653 1954 .0271 .1485 .1690 .0550 .0674 1955 .0275 .1530 .1860 .0525 .0678 1956 .0372 .1580 .2010 .0550 .0714 1957 .0460 .1580 .2010 .0600 .0746 1958 .0347 .1580 .1860 . 0600 .0752 1959 .0490 .1585 .1860 .0606 .0818 1960 .0455 .1585 .1860 .0675 .0848 1961 .0438 .1585 .1965 .0673 .0874 1962 .0456 .1585 .1985 .0650 .0898 1963 .0448 .1585 .1985 .0635 .0874 1964 .0471 .1490 .1985 .0625 .0871 1965 .0488 .1490 .1955 .0625 .0848 1966 .0555 .1395 .1995 .0692 .0822 1967 .0561 .1395 .2020 .0744 .0842 1968 .0668 .1390 .2010 .0884 .0894 1969 .0762 .1565 .2095 .0938 .0871 S o u r c e s : CLOTHING: RSBY — y i e l d o n Government o f C a n a d a bonds w i t h f i v e y e a r s t o m a t u r i t y . 1946 -1950 : U r q u h a r t a n d B u c k l e y (Data [ 2 2 J ) ; l i n k e d t o 1951 -1969 : RDX2 [23 — DATATAPE] SERIES RMS. 53 S o u r c e s ( c o n t i n u e d ) MOTOR V E H I C L E S : RMV — 1972 C a n a d i a n Consumer C r e d i t F a c t b o o k (DATA[17]) 1949 -1952 : 1953 -1969 : Low f r o m 1953 Mean o f h i g h and low r a t e s Taken f r o m F e d e r a t e d C o u n c i l o f S a l e s F i n a n c e Compan ies S u r v e y o f Ten L a r g e s t C o m p a n i e s . OTHER DURABLES: RCFP — as above f o r M o t o r V e h i c l e s . HOUSING AND LAND: (a) RNHA — ceiling on NHA mortgages (average of 12 months); Central Mortgage and Housing Corporation (DATA [19] and [ 2 0 ] ) . (b) PTAX — s e e N o t e s ( i ) Notes to Table IV-4 (i) Property Tax Rate (PTAX) The first step was to estimate a business land series (SB) in 1. F r o m [40; p . 230] we know t h a t i n 1963 t h e r e were a p p r o x i m a t e -l y 2 , 1 6 0 , 0 0 0 a c r e s o f r e s i d e n t i a l l a n d and t h a t c o m m e r c i a l a n d i n d u s t r i a l l a n d i s i n a 1:6 r a t i o t o r e s i d e n t i a l l a n d . T h i s y i e l d s an a p p r o x i m a t e 360 ,000 a c r e s o f b u s i n e s s l a n d i n 1963 . 2 . Assume b u s i n e s s l a n d = a r e a l s t o c k o f b u s i n e s s s t r u c t u r e s and e s t i m a t e a f o r 1963 . 3 . We t h u s may g e n e r a t e a b u s i n e s s l a n d s e r i e s ( i n a c r e s ) t h r o u g h -o u t o u r sample p e r i o d ; we v a l u e t h i s s e r i e s a t ( the 1961 d o l l a r v a l u e o f l a n d ) x ( l a n d p r i c e i n d e x ) t o a r r i v e a t a c u r r e n t d o l -l a r v a l u e o f b u s i n e s s l a n d . 4 . We t h e n r e v a l u e b u s i n e s s l a n d and s t r u c t u r e s i n t h e f o l l o w i n g manner : S t e e l e [34] r e p o r t s t h a t t h e 1940 t a x r a t e on LR + SR was 3.09%. T h i s i s c a l c u l a t e d f r o m t h e 1941 C e n s u s by t a k i n g t h e r a t i o o f p r o p e r t y t a x e s t o t h e v a l u e o f p r o p e r t y a s s e s s e d f o r t a x a t i o n . t h e f o l l o w i n g manner : 54 5. We may then calculate the residential property tax b i l l in 1940 as .0309 (SR + LR) = t . 6 . Assuming land and structures pay the same rate i n the business sector, we define a valuation factor Y in this way: TOTAL PROPERTY TAXES - T = .0309y (SB + LB) 7 . Then the annual tax rate on LR and SR, i.e., * TOTAL PROPERTY TAXES (Table 46 - NATIONAL ACCOUNTS)  t = {LR + SR + y (LB + SB)} (ii) Estimated Business Land Series = a SB (acres) 1940 142 ,287 1957 254 ,509 1946 144 ,988 1958 272 ,724 1947 149 ,799 1959 287 ,840 1948 156 ,138 1960 304 ,907 1949 163 ,733 1961 322 ,297 1950 171 ,646 1962 338 ,963 1951 180 ,190 1963 360 ,000 1952 190 ,204 1964 380 ,719 1953 199 ,909 1965 4 0 2 , 3 2 8 1954 212 ,084 1966 429 ,060 1955 224 ,251 1967 461 ,651 1956 237 ,554 1968 490 ,170 1969 515 ,479 TABLE I V - 5 DURABLES: RENTAL PRICES YEAR PCL PMV PDO PHOUS PL (1) (2) (3) (4) (5) 1946 0 .3112 0 .2027 0 .2069 0 .0733 0 .0267 1947 0 .3529 0 .2349 0 .2668 00 .0803 0 .0287 1948 0 .4310 0 .2799 0 .2616 0 .0916 0 .0317 1949 0 .4489 0 .2944 0 .2688 0 .0956 0 .0330 1950 0 .4506 0 .2978 0 .2803 0 .1009 0 .0371 1951 0 .5039 0 .3398 0 .3172 0 .1245 0 .0441 1952 0 .5092 0 .3457 0 .3222 0 .1310 0 .0519 1953 0 .5055 0 .3500 0 .3252 0 .1331 0 .0530 1954 0 .4989 0 .3510 0 .3198 0 .1355 0 .0775 1955 0 .4933 0 .3261 0 .3216 0 .1368 0 .0823 1956 0 .5006 0 .3339 0 .3309 0 .1444 0 .0961 1957 0 .5047 0 .3652 0 .3362 0 .1558 0 .1139 1958 0 .5045 0 .3712 0 .3351 0 .1559 0 .1252 1959 0 .5107 0 .3880 0 .3360 0 ,1627 0 .1352 1960 0 .5138 0 .3894 0 .3356 0 .1747 0 .1407 1961 0 .5210 0 .3785 0 .3397 0 .1786 0 .1505 1962 0 .5269 0 .3732 0 .3405 0 .1785 0 .1613 1963 0 .5408 0 .3731 0 .3433 0 .1788 0 .1681 1964 0 .5550 0 .3576 0 .3453 0 .1846 0 .1728 1965 0 .5649 0 .3547 0 .3457 0 .1926 0 . 1 7 0 8 1966 0 .5888 0 .3434 0 .3551 0 .2093 0 .1965 1967 0 .6176 0 .3494 0 .3722 0 .2291 0 .2111 1968 0 .6398 0 .3554 0 .3824 0 .2531 0 .2456 1969 0 .6630 0 .3665 0 .3918 0 .2676 0 .2791 (1) C l o t h i n g (2) M o t o r V e h i c l e s (3) O t h e r D u r a b l e s (4) H o u s i n g (5) L a n d TABLE I V - 6 NONDURABLES: PURCHASE PRICE INDEXES YEAR PFOOD PALC PTOB PMED POSERV (1) (2) (3) (4) (5) 1946 0 .5757 0 .8034 0 .8108 0 .5073 0 .5607 1947 0 .6517 0 .8079 0 .8484 0 .5296 0 .5961 1948 0 .7986 0 .8282 0 .8915 0 . 5 9 4 6 0 .6387 1949 0 .8132 0 .8265 0 .9074 0 . 6 2 2 6 0 .6699 1950 0 .8296 0 .8447 0 .9295 0 .6319 0 .7120 1951 0 .9534 0 .9169 1.0217 0 .6911 0 .7607 1952 0 .9463 0 .9165 1 .0508 0 .7495 0 .7934 1953 0 .9132 0 .9178 0 .9264 0 .7744 0 .8214 1954 0 .9094 0 .9198 0 .9147 0 .8107 0 .8492 1955 0 .9094 0 .9212 0 .9160 0 .8335 0 .8697 1956 0 .9201 0 . 9 2 3 6 0 .9165 0 .8633 0 .8930 1957 0 .9571 0 .9501 0 .9164 0 .9115 0 .9198 1958 0 .9954 0 .9638 0 .9167 0 .9463 0 .9493 1959 0 .9874 0 .9819 0 .9785 0 .9746 0 .9675 1960 0 .9903 0 .9923 0 . 9 9 5 7 0 .9926 0 .9842 1961 1.0000 1.0000 1.0000 1.0000 1 .0000 1962 1.0207 1.0205 1 .0038 1.0237 1 .0221 1963 1.0521 1 .0226 1 .0038 1 .0456 1 .0389 1964 1.0613 1.0508 1 .0124 1.0673 1.0629 1965 1 .0949 1.0602 1 .0463 1.0965 1 .0964 1966 1.1601 1 .0741 1.0897 1.1279 1.1382 1967 1 .1635 1 .0924 1.1333 1.1990 l . x « 6 8 1968 1.2051 1 .1718 1.2703 1 .2354 1.2460 1969 1.2376 1 .2121 1.3342 1.2872 1 .3331 P r i c e i n d e x s e r i e s f o r n o n d u r a b l e s and s e r v i c e s : (1) f o o d (2) a l c o h o l i c b e v e r a g e s (3) t o b a c c o p r o d u c t s (4) m e d i c a l c a r e and h e a l t h s e r v i c e s (5) o t h e r s e r v i c e s TABLE IV-7 PER CAPITA QUANTITY SERIES OTHER MOTOR OTHER YEAR FOOD ALCOHOL TOBACCO HEALTH SERVICES CLOTHING VEHICLES DURABLES HOUSING LAND 1946 373.773 53.315 45.877 77.102 453.531 269.169 35.654 185.835 1324.184 454.306 1947 374.052 58.918 45.382 •82.337 454.359 315.889 59.887 228.950 1338.582 461.599 1948 349.584 59.813 46.366 80.920 450.971 320.895 71.693 259.944 1372.661 469.137 1949 334.944 61.203 46.590 81.922 470.328 311.839 98.123 284.883 1384.659 466.830 1950 352.937 62.130 47.089 86.500 482.902 310.390 147.777 311.471 1441.362 488.621 1951 351.571 61.691 42.425 88.223 507.042 304.273 173.061 323.650 1467.324 498.074 1952 355.583 68.260 43.273 90.937 542.638 308.871 203.969 339.700 1482.366 501.300 1953 364.092 69.105 47.861 94.161 563.025 314.413 235.737 371.964 1530.650 500.484 1954 368.741 68.026 48.218 98.068 572.775 314.588 248.282 400.796 1587.607 499.505 1955 374.998 71.391 49.161 101.977 594.053 321.611 280.838 446.520 1676.982 502.846 1956 390.763 74.804 52.970 110.547 612.856 334.212 309.272 490.259 1760.919 505.290 1957 395.226 75.494 55.768 113.512 627.455 340.705 315.443 516.199 1800.580 502.059 1958 391.325 75.121 58.972 121.025 640.469 347.703 322.090 541.240 1879.586 504.352 1959 400.088 76.129 60.042 128.508 662.637 355.776 329.842 568.432 1947.681 505.453 1960 408.182 76.859 59.547 136.313 676.654 364.020 333.179 586.441 1983.472 504.234 1961 403.274 77.949 61.761 144.608 689.334 367.828 337.635 609.421 2014.524 504.597 1962 406.990 79.601 63.718 147.722 686.913 372.149 353.975 640.630 2044.221 503.987 1963 405.885 81.198 63.691 157.601 707.316 373.748 379.522 666.061 2073.855 502.972 1964 412.827 81.613 62.856 164.877 736.966 376.445 413.570 694.610 2114.077 500.602 1965 414.067 86.339 64.336 172.536 753.066 380.715 456.229 724.599 2154.844 497.489 1966 409.282 89.472 63.922 178.864 772.405 381.156 487.597 753.087 2173.059 492.420 1967 418.765 94.050 63.568 184.481 778.027 379.985 506.207 769.647 2184.217 486.253 1968 418.015 89.080 58.964 194.735 795.068 380.582 529.171 787.508 2217.865 481.562 1969 424.132 92.416 55.972 188.419 822.482 384.258 545.100 815.538 2270.967 477.672 ** Unadjusted: The durable series were adjusted by t h e i r respective r e n t a l p r i c e normalization factors: i . e . (* pl961) TABLE IV-8 CONSUMPTION MODEL: 'NORMALIZED' PRICES YEAR VF VA VT VMS VOS VCL VMV VDO VH VL 1946 0.6959 0.9712 0.9801 0.6132 0.6778 0.7220 0.6474 0.7363 0.4961 0.2145 1947 0.6848 0.8489 0.8915 0.5565 0.6264 0.7117 0.6521 0.8253 0.4724 0.2004 1948 0.7441 0.7717 0.8307 0.5541 0.5952 0.7708 0.6891 0.7176 0.4779 0.1963 1949 0.7231 0.7350 0.8069 0.5537 0.5957 0.7662 0.6917 0.7037 0.4760 0.1950 1950 0.6787 0.6911 0.7605 0.5170 0.5825 0.7076 0.6437 0.6751 0.4622 0.2017 1951 0.6804 0.6544 0.7292 0.4932 0.5429 0.6903 0.6407 0.6664 0.4975 0.2091 1952 0.6306 0.6107 0.7002 0.4995 0.5287 0.6513 0.6086 0.6320 0.4888 0.2298 1953 0.5823 0.5852 0.5907 0.4938 0.5238 0.6187 0.5896 0.6104 0.4752 0.2246 1954 0.5565 0.5629 0.5598 0.4961 0.5197 0.5860 0.5675 0.5761 0.4643 0.3151 1955 0.5293 0.5362 0.5331 0.4851 0.5062 0.5511 0.5015 0.5510 0.4458 0.3183 1956 0.4959 0.4978 0.4939 0.4653 0.4813 0.5178 0.4754 0.5250 0.4357 0.3441 1957 0.4834 0.4798 0.4628 0.4603 0.4645 0.4892 0.4873 0.4998 0.4406 0.3822 1958 0.4807 0.4654 0.4426 0.4569 0.4584 0.4676 0.4735 0.4763 0.4215 0.4017 1959 0.4528 0.4502 0.4487 0.4469 0.4436 0.4495 0.4701 0.4535 0.4177 0.4119 1960 0.4359 0.4367 0.4382 0.4369 0.4332 0.4340 0.4528 0.4348 0.4305 0.4115 1961 0.4275 0.4275 0.4275 0.4275 0.4257 0.4275 0.4275 0.4275 0.4275 0.4275 1962 0.4242 0.4241 0.4171 0.4254 0.4247 0.4203 0.4097 0.4165 0.4153 0.4454 1963 0.4206 0.4088 0.4013 0.4180 0.4153 0.4150 0.3941 0.4040 0.4002 0.4465 1964 0.4051 0.4010 0.3864 0.4073 0.4056 0.4065 0.3606 0.3879 0.3945 0.4382 1965 0.3975 0.3849 0.3799 0.3981 0.3980 0.3936 0.3402 0.3695 0.3915 0.4120 1966 0,3957 0.3663 0.3716 0.3846 0.3882 0.3854 0.3094 0.3565 0.3996 0.4453 1967 0.3744 0.3515 0.3647 0.3858 0.3819 0.3814 0.2970 0.3526 0.4128 0.4514 1968 0.3623 0.3523 0.3819 0.3714 0.3746 0.3692 0.2823 0.3384 0.4260 0.4906 1969 0.3471 0.3399 0.3742 0.3610 0.3739 0.3569 0.2716 0.3235 0.4202 0.5201 Note: Before these v. were c a l c u l a t e d the re n t a l prices were put into index form by d i v i d i n g each by i t s respective 1961 value. The per capita r e a l quantities for durable goods were adjusted accordingly, i . e . , each x. of a durable was m u l t i p l i e d by i t s 1961 re n t a l p r i c e so that the f i n a l p.x. would be unchanged. 59 TABLE I V - 9 ANNUAL WAGE B I L L S AND HOURS WORKED W ANNUAL WAGE B I L L S AVERAGE WEEKLY YEAR ($ M i l l i o n s ) HOURS 1946 6816 .72656 4 4 . 8 8 1947 7906 .87500 44 .06 1948 9081 .56641 4 3 . 8 6 1949 9772 .70703 4 3 . 8 5 1950 10552.85547 43 .00 1951 12278.62891 4 2 . 4 9 1952 13698.37109 4 2 . 1 4 1953 14872.83203 4 2 . 1 5 1954 15137.57031 4 1 . 9 7 1955 16264.78906 4 1 . 7 6 1956 18463.52344 41 .49 1957 20060.19531 4 1 . 0 2 1958 20583.25391 4 0 . 6 8 1959 22037.83984 40 .53 1960 22121.52734 4 0 . 2 1 1961 24197.37109 3 9 . 8 8 1962 25886.57812 3 9 . 5 7 1963 27600.56250 3 9 . 2 2 1964 30109 .81250 3 8 . 8 7 1965 33663.36328 3 8 . 6 5 1966 38040.68359 3 8 . 3 2 1967 41965 .41016 3 8 , 1 3 1968 45790 .33984 3 7 . 3 4 1969 50796 .35547 37 .00 N o t e s : 1 . T h i s wage s e r i e s i s e s t i m a t e d t o a c c o u n t f o r u n i n c o r p o r a t e d b u s i n e s s income and t h u s has more d e s i r a b l e p r o p e r t i e s t h a n the N a t i o n a l A c c o u n t s , w h i c h u n d e r e s t i m a t e s e l f - e m p l o y e d e a r n i n g s , e t c . The s e r i e s was made a v a i l a b l e by P r o f e s s o r s A . D. Woodland and W. E . D i e w e r t . 2 . The h o u r s were made a v a i l a b l e t h r o u g h t h e P r o d u c t i v i t y R e s e a r c h D i v i s i o n , S t a t i s t i c s C a n a d a . 60 TABLE I V - I O SOURCES USED TO CALCULATE THE RATE OF TAX ON LABOUR EARNINGS PI = PERSONAL INCOME ( T a b l e 4 - NAT. ACCTS) TABLE 44 - NAT. ACCTS) ($ m i l l i o n ) T O T . DIRECT TAX ($ m i l l i o n ) (1) (2) (3) (4) TD TD T = 57 1946 9 ,887 ^.06 — 20 - 34 = 852 .0861 1947 10 ,583 927 - 30 - 31 = 866 .0818 1948 12 ,161 986 - 29 - 29 = 928 .0763 1949 12 ,902 956 - 26 - 29 = 901 .0698 1950 13 ,681 915 - 35 - 31 = 849 .0620 1951 16 ,159 1279 - 35 - 34 = 1210 .0748 1952 17 ,900 1588 - 39 - 34 1515 .0846 1953 18 ,932 1748 - 40 - 33 = 1675 .0884 1954 19 ,006 1776 - 41 - 37 = 1698 .0893 1955 20 ,573 1855 - 55 - 72 = 1728 .0839 1956 22 ,817 2127 - 88 - 58 = 1981 .0869 1957 24 ,500 2350 - 69 - 57 = 2224 .0907 1958 25 ,893 2214 - 70 - 56 = 2088 .0806 1959 2 7 ,425 2444 - 76 - 54 = 2314 .0843 1960 28 ,921 2794 - 97 - 61 = 2636 .0911 1961 2 9 , 4 1 1 2844 - 80 - 66 = 2798 .0951 1962 3 1 , 9 6 6 3180 - 93 - 72 = 3015 .0943 1963 3 4 , 1 0 9 3387 - 89 - 82 = 3216 .0942 1964 3 6 , 6 1 8 3917 - 91 - 89 = 3737 .1020 1965 40 ,591 4433 - 101 - I l l = 4221 .1039 1966 45 ,702 5812 - 106 - 1.09 5597 .1224 1967 50 ,208 7011 - 96 - 119 = 6796 .1353 1968 55 ,213 8247 - 113 - 122 = 8012 .1451 1969 6 1 , 3 9 8 10 ,047 - 104 - 133 = 9810 .1597 (2) T o t a l D i r e c t T a x e s : T a b l e 44 , N a t i o n a l A c c o u n t s . (3) and (4) S u c c e s s i o n D u t i e s and E s t a t e T a x e s : F e d e r a l and P r o v i n c e s 61 TABLE I V - 1 1 LABOUR: HOURS, TAX AND WAGES YEAR L PER CAPITA £ = H - L w = WGRT T = TAU PTIME = W ( 1 -T) (Hours) (Hours) ( $ ) / h r ( $ ) / h r 1946 1180.226 1939 .774 0 . 6 5 0 .0861 0 .59 1947 1181 .111 1938 .888 0 .74 0 .0818 0 . 6 8 1948 1169 .078 1950.922 0 . 8 5 0 .0763 0 . 7 8 1949 1133.498 1986.502 0 . 9 1 0 .0698 0 . 8 4 1950 1110 .065 2009 .935 0 .99 0 .0620 0 . 9 2 1951 1109 .85Q 2010.150 1.13 0 . 0 7 4 8 1 .05 1952 1086 .738 2033 .262 1.26 0 .0846 1 .15 1953 1080 .266 2039 .734 1 .35 0 .0884 1 .23 1954 1052.832 2067 .167 1 .38 0 .0893 1 .25 1955 1050 .747 2069.253 1 .45 0 .0839 1 .33 1956 1067 .491 2052 .509 1.59 0 .0868 1.46 1957 1052.953 2067 .047 1.71 0 . 0 9 0 7 1 .55 1958 1016 .392 2103 .608 1 .78 0 .0806 1 .63 1959 1020 .807 2099 .193 1.86 0 .0843 1.70 1960 1011 .363 2108 .637 1 .85 0 . 0 9 1 1 1 .68 1961 1001.436 2118 .564 2 . 0 1 0 . 0 9 5 1 1.82 1962 1002 .686 2117 .314 2 . 1 0 0 .0943 1 .91 1963 997 .652 2122 .348 2 . 2 1 0 .0942 2 . 0 0 1964 1002 .615 2117 .385 2 . 3 5 0 .1020 2 . 1 1 1965 1011.159 2108 .841 2 .54 0 .1039 2 .28 1966 1019.577 2100.423 2 . 7 8 0 . 1 2 2 4 2 . 44 1967 1016 .505 2103 .495 2 . 9 9 0 .1353 2 .58 1968 990 .483 2129 .517 3 .26 0 .1451 2 .79 1969 987 .691 2132 .309 3 .54 0 .1597 2 .97 N o t e : I n a c t u a l p r o c e s s i n g , PTIME was p u t i n i n d e x f o r m PT IME f c ( ) and H - L was a d j u s t e d a c c o r d i n g l y , i . e . , (H-L) * PTIME 1 9 6 1 . P T I M E 1 9 6 1 Z TABLE IV-12 CONSUMPTION AND LEISURE: 'NORMALIZED' PRICES YEAR VF VA VT VMS vos VCL VMV VDO VH VL VTIME 1946 0. 2906 0. 4055 0.4092 0.2560 0. 2830 0.3015 0.2703 0.3074 0.2071 0.0895 0.1654 1947 0. 2866 0. 3553 0. 3731 0.2329 0.2621 0.2979 0.2729 0.3454 0.1977 0.08 39 0.1652 1948 0. 3067 0. 3181 0. 3424 0.2283 0. 2453 0.3177 0.2840 0.2957 0.1970 0.0809 0.1660 1949 0. 2904 0. 2952 0. 3241 0.2224 0. 2393 0.3077 0.2778 0.2826 0.1912 0.0783 0.1660 1950 0. 2692 0. 2741 0. 3017 0.2051 0. 2311 0.2807 0.2554 0.2678 0.1834 0.0800 0.1654 1951 Q.2717 0. 2613 0. 2911 0.1969 0. 2167 0.2756 0.2558 0.2661 0.1986 0.0835 0.1647 1952 0. 2461 0.2383 0. 2733 0.1949 0. 2063 0.2542 0.2375 0.2467 0.1907 0.0897 0.1652 1953 0. 2242 0. 2253 0.2274 0.1901 0. 2016 0.2382 0.2270 0.2350 0.1829 0.0864 0.1661 1954 0. 2153 0. 2178 0. 2166 0.1919 0. 2011 0.2267 0.2196 0.2229 0.1796 0.1219 0.1634 1955 0. 2034 0. 2060 0. 2049 0.1864 0. 1945 0.2118 0.1927 0.2117 0.1713 0.1223 0.1639 1956 0. 1900 0.1907 0. 1893 0.1783 0. 1844 0.19R4 0.1822 0.2012 0.1670 0.1319 0.1656 1957 0. 1844 0. 1830 0. 1765 0.1756 0. 1772 0.1866 0.1859 0.1907 0.1681 0.1458 0.1649 1958 0. 1807 0. 1750 0. 1664 0.1718 0. 1723 0.1758 0.1780 0.1791 0.1585 0.1510 0.1634 1959 0. 1717 0. 1708 0. 1702 0.1695 0. 1682 0.1705 0.1783 0.1720 0.1584 0.1562 0.1629 1960 0. 1704 0. 1707 0. 1713 0.1708 0.1693 0.1697 0.1770 0.1700 0.1683 0.1608 0.1592 1961 0. 1617 0. 1617 0. 1617 0.1617 0. 1617 0.1617 0.1617 0.1617 0.1617 0.1617 0.1617 1962 0. 1585 0. 1585 0. 1559 0.1590 0. 1587 0.1570 0.1531 0.1556 0.1552 0.1664 0.1630 1963 0. 1558 0. 1515 0. 1487 0.1549 0. 1539 0.1537 0.1460 0.1497 0.1483 0.1654 0.1634 1964 0. 1498 0. 1483 0. 1429 0.1507 0. 1500 0.1504 0.1334 0.1435 0.1459 0.1621 0.1640 1965 0.1448 0. 1402 0.1384 0.1450 0. 1450 0.1434 0.1239 0.1346 0.1426 0.1501 0.1661 1966 0. 1440 0. 1333 0. 1353 0.1400 0. 1413 0.1403 0.1126 0.1298 0.1455 0.1621 0.1668 1967 0. 1362 0. 1278 0. 1326 0.1403 0. 1389 0.1387 0.1080 0.1282 0.1501 0.1642 0.1667 1968 0. 1301 0. 1265 0. 1371 0.1334 0. 1345 0.1326 0.1014 0.1215 0.1530 0.1762 0.1658 1969 0. 1250 0. 1224 0. 1347 0.1300 0. 1346 0.1285 0.0978 0.1165 0.1513 0.1873 0.1653 to 63 C PROGRAM T C C A L C U L A T E A 0 E P R E C I A T E U STOCK S E R I E S C A S S U N E C A R R Y O V E R S T O C K C EPR EC I A T E S AT SAME I N S T A N T NEW I N V E S T -C K E N T C C C L ' R S . D I M E N S I O N S T O C K ( 3 0 ) , S P E N D ! 2 C > , I N D ! 3 C ) , I T I T L E ! 3 > 3 R E A C ( 5 , 1 , E N D = 9 9 ) N Y E A R » I f l A S E t I T I T L E 1 F C P M A T ( 2 1 5 , 3 A 4 ) R E A D ! 5 » 2 ) C E L T A . R I M T , ( S P E N D ! I ) , 1 = 1 , N Y E A P ) 2 F O R M A T < F 3 . 2 f F l C . C , / ( 8 F l C . O ) ) S T C C K ( l ) = ( R I M T * l l . - C E L T A ) ) • S P E N D ( l ) DC 1C I = 2 , N Y E A R S T O C K ( I ) = ( S T O C K ( 1 - 1 ) ) * ( 1 . - D E L T A ) +SPEND( I ) 10 C C N T I N U E V»R I TE (6 , 3 5 ) 25 F O R M A T ! / / / ) WRIT 6 ( 6 , 11 ) I T I T L E , C E L T A , I 8 A S E , R IN IT 11 F C R K A T ( 1 5 X , ' S T O C K S E R I E S F O P ' » l X f 3 A 4 / 15 X , ' D E P R E C I A T E C A T ' , 1 X , F 3 . 2 , 1 ' Y E A R L Y . ' / 1 5 X , « 8 A S E Y E A R I S " » 1 X , I 4 / 1 5 X , ' I N I T I A L S T O C K = ' , 2 X , F i : . 2 4 / 1 5 X , • {$MILL IONS ) ' / / ) W R I T E ( 6 , 8 0 ) 8C F O R K A T ( 1 8 X , ' Y E A R , , 4 X , « P U R C H 4 S E S , , l C X , , S T C C K « / 1 8 X t 3 2 ( , = » ) ) INC ! I )=I B A S E DO 23 L = 2 , N Y E A R 23 I N C H ) = I N D ( L - l ) +1 CO 50 K = 1 , N Y E A R 50 W R I T E ( 6 t l 2 ) I N 0 ( K ) , S P E N D ( K ) , S T O C K ! K ) 12 F O R M A T ! 1 8 X , 1 4 , 3 X , F 1 C . 4 , F 1 5 . 5 ) GC TC 3 9 9 S T O P ENC PROGRAM DELTA 64 C PROGRAM TO CALCULATE THE TERMS '."IF THE GE N. L FONT I E F . F UN CT I ON AL FORM C DENOTE SUM OVER INDEX ' I ' BY E / t = l , N / C AND THE KRONECKER DELT ^ 8Y D / I , J / C C UPON .MAKING THE NORMAL I 7 AT I ON C C 1 = (2. / S QR T(V * ) E / N = I,N/ BOM + E / I = 1» N/E/J =1 iN/ B ( I , J ) C AND SOLVING FOR fi(l,l) (WHERE V* IS THE COMMON PRICE IN 1961) C C B ( 1,1)= 1 - ( 2 / S Q R T ( V * ) : i / N = l , N / B0(N) - 2 * E E/1< I = I< J <I= N/ 8 U , J ) C - F/I= 2 » N/ 3 ( 1 , 1 ) C C WE FIND THAT THE SYSTEM OF CONSUMER DEMAND EQUATIONS IS GIVEN BY: C C V ( I ) X ( I ) / I = 2 » N / = C (1) E/N=1,N/ 00 ( N ) * ( V I I )X ( I ) - S 0RT ( V (N ) ) V ( I ) X ( I ) /V ( 1 ) C + D/I,M/ S O ( V I ) / V ( 1 ) ) C C (2 ) (A) + EE/K|=K<J<I =N/ B ( K , J ) * ( 2 V ( I ) X ( I ) - 2 S Q ( V ( K ) V ( J ) ) V ( I ) X ( I ) / V ( 1 ) C ( 3 ) + 0 / I , K / S Q R T ( V ( [ ) V l J ) ) / V ( l ) C (C) + D/ I»J/SQRT('V(K)V(I ) ) / V ( l ) C C (3) +E/L=2,N/ B ( L , L ) * ( V ( I ) X { I ) - V ( L ) V ( I ) X ( I ) / V ( 1 ) C + 0 / I , L / V ( I ) / V {1 ) ) C C NYE AR = NO. OF OBSERVATIONS C N=<? OF VARIABLES C A ( I , J , K , L ) = 8 ( I , J ) FOR THE KTH EQUATION AND THE LTH YEAR ( DBS.) C FOR K=2,N C A ( I , K , 1 , L ) = 3 0 ( 1 ) FCR THE KTH EQUATION AND THE LTH YEAR C DIMENSION A ( 2 0 ,20,20,25) , S V ( 2 0 ) , V ( 2 0 ) , X ( 2 0 ) EXTERNAL LE ONS COMMON S V 1 2 0 ) , V ( 2 0 ) ,X ( 20 ) ,NYEAR,N,BASE RE AD(5,1) NYEAR 1 FORMAT(15) RE AD(5,2) M 2 FORMAT(I 5) PEAC(5,163) BASE 163 F0R?-'AT(F7.0) WRITE!6,1C02) BASE 1002 F0RMAT(1X,F7.5) C DYNAMIC STORAGE ALLOCATION REPLACES DIMENSION C STATEMENT FOR ARRAY A IN MAIN PROGRAM IS = N-YEAR*N*N*N*4-CALL GSPACEI A, IS) C*LL CALLER!LE ONS,A) STOP END SUBROUTINE LEONS(A) DIMENSION A(N,N,N,NYEARI COMMON SV( 2 0 ) , V ( 2 0 ) , X ( 2 0 ) , N Y E A R , M , B A S E • DO 55 LY = 1,NYE AR REA0(3,3) ( V ( r ) , I = l , N ) 3 P 0 R M A T ( 5 X , 1 5 P 5 . 0) DO 5 1=1,N 5 S V ( I ) = S 0 R T ( V ( I ) ) RE AD ( 3 , 19) ( X! I ) , 1 = 1 , N) 19 FORMAT(12F9.6) N1=N-1 DO 50 I=2,N V X = V ( I ) * X ( I ) VF=VX/V(1) DG IG 1=2,N 65 C 10 **CALC (3) A ( L i I i I , L Y ) =VX-V!L )*VF A ( l , I , I , L Y ) = A ( I , l , I , L Y ) + V ( I ) / V ( 1 ) DG 20 K=1,N1 C **CALC ( 2 ) ( A ) THE UPPER TRIANGLE OF B ( I , J ) VFK=VF*SV(K) Kl=K+1 DO 21 J=K1,N 21 A ( K , J , I , L Y ) =2.*(VX - S V ( J ) * V F K ) 20 CONTINUE S V V = S V ( I ) / V ( 1 ) I F ( I . F O . N ) GO TO 51 C **CALC ( 2 K B ) FOR K=I 0/I,K/ K1=I+1 CO 21 J=K1,N 31 A! I , J , I,LY)=A( I , J , I,LY ) + S V ( J ) * S V V C **CALC ( 2 ) ( C ) FOR J=I 0 / I , J / 51 J 1 = I -1 DO 3 2 KK=1,J1 C **GALC (1) THE F.C ( I ) TERMS 32 A ( K K , I , I , L Y ) = A ( K K , I , I , L Y ) + S V ( K K ) * S V V 00 AO NN=1,N 40 A ( N N , I , 1 , L Y ) = I 2•/3A SE)*VX-SV INN)*VF A ( I , I , 1 , L Y ) = A ( I , I , 1 , L Y ) + S V ( I ) / V ( 1 ) 50 CONTINUE 55 CONTINUE C DATA ARE OUTPUTTFD UNFORMATTED ; MUST READ IN FREE FORMAT WRITE!7) (t (A! I , J , 1 , L ) ,L = l,NYE A R ) , J = 2 >N) , 1=1,N } DO 56 1=1,N 11 = 1 C CHECK FCR NO BB11 TERM I F ( I . E Q . l ) 11=2 WRITE!7) ( ( C A ( I , J , K , L ) , L = 1 , N Y E A R ) , K = 2 , N ) , J = I 1 , N ) 56 CONTINUE STOP ENO PROGRAM L F 66 C PRCGRAN TC CALCULATE E L A S T I C I T I E S OF SUBSTITUTION' FOR THE GENERALIZEC C LEON 7 I EF UT IL ITY FUNCTION (UNNCRMALIZEC C EN. ANOS ) C INPUT N= NUMBER OF GGCCS (B C O E F F I C I E N T S APE IN AN N BY N ARRAY C WHICH IS SYMMETRIC . I .E . B ( I , J ) = E ( J , I ) COMMON E . B l i S V t N DIMENSION V ( 3 0 ) , S V ( 3 C ) , B ( 3 0 , 3 0 ) , e i ( 3 C ) , H I A ( 3 0 ) R E A C l 5 , 8 ) N 8 FCRMATI I5 ) DC 6 I = 1,N 6 R E A D ( 5 , 4 ) (B ( I , J ) , J=1 ,N ) 4 F 0 R M A T ( F 1 1 . 8 ) R E A D ( 5 , A ) ( e 1 ( I ) , I = 1 , N ) 57 R E A D ( 5 , 3 , E N D = e 8 8 ) I Y E A R , ( V ( I ) , I = l , N ) 3 F O R M A T ( 1 4 , I X , ( 1 5 F 5 . C ) ) ViR I T E (6 ,718 ) IYEAR 718 FCRNATI 14X , I A / / / ) DC 1C 1=1,N IG SV( I ) = S CRT(V( I )) DC 16 1=1,N F IA ( I ) = H I ( I ) 16 CCNTINUE DC 993 1 = 1, N h R I T E ( 6 , U 3 ) I , H I A U ) 113 FORMAT! IX, • H • , 1 3 , 4 X , F 1 2 . 5 ) DO 993 J= I ,N I F ( J . E G . I ) GO TO 996 13 PCER = H I J ( I , J ) WR I T E ( 6 , 1 1 4 ) I , J . P D E R 114 FORMAT( I X , • H ' , 12, I 2 , 3 X , F 1 2 . 5 > GO TC 993 996 PCER = H I I (I ) 992 W R I T E ( 6 , 1 1 4 ) I , J , P C E R 993 CCNTINUE Y=C. UT IL = 0 . DC 54 1=1,N S = 0 . Y = Y + B 1 ( I ) * S V ( I ) DC 53 J=1,N 53 S = S + B ( I , J ) * S V ( J ) 54 UTIL = UTIL + S*SV( I ) UT IL=UT IL+2 . *Y CC111 1=1,N DC 111 J=I ,N I F ( I . E Q . J ) GO TO 49 S IGMA=UT IL*H. IJ ( I , J )/ (HI A ( I )*HIA (J ) ) GC TG 111 49 X=F IA ( I ) S IGMA=(UT I L *F I I( I ) ) / ( X *X ) 111 WR ITE (6 ,3C ) I ,J ,S IGMA 3C F C R M A T ( 1 0 X , , S I G . V A ' , I 2 , I 2 , 2 X , ' = , , F 1 2 . 6 ) GO TC 57 888 STCP END FUNCTION H I ( I ) COMMON B,81 , SV ,N CIMENSICN B ( 3 0 , 3 C ) , E l ( 3 0 ) , S V ( 3 0 ) X = 0 . CO 10 K=1,N X = X + E ( I , K ) * ( S V ( K )/ S V ( I ) ) HI = X + B H I ) / S V ( I ) RETURN ENC FUNCTION H I J ( I, J ) CGN'NCN 6 , B 1 , S V , N DIMENSION 8 ( 3 0 , 3 C ) , 8 1 ( 3 C ) , S V ( 3 0 ) H IJ= .5 * B( I ,J ) / ( S V ( I ) * S V ( J ) ) RETURN ENC FUNCTION HI I ( I ) CCfMCN E , B 1 , S V , N C IMENS ICN B ( 3 0 t 3 G ) . e i ( 3 C ) , S V ( 3 0 ) X = 0 . DG 10 J=1 ,N I F I J . E G . I ) GG TO 10 X = X + B ( I , J ) * ( S V ( J ) / S V ( I ) * * 3 ) CONTINUE H I I = - . 5 * ( X + B1( I ) / S V ( I ) ^ 3 ) RETURN END PROGRAM SIGUNN C PROGRAM TC CALCULATE E L A S T I C I T I E S OF SUBSTITUTION FOR THE GENERALIZED C LEONT IEF UT IL ITY FUNCTICN (NC R M A L IZEC CENANDS) C INPUT N= NUMBER OF GOODS (B C O E F F I C I E N T S ARE IN AN N BY N ARRAY C V-.HICH IS SYMMETRIC . I .E . E ( I , J ) = E ( J , I ) COMM.CN 8 , 3 1 , S V , N CIM ENS I ON V ( 3 0 ) , S V ( 3 C ) , 8 ( 3 C , 2 0 ) , B l ( 3 C ) , H I A ( 3 O ) , H I J A ( 3 0 , 3 O ) RE A D ( 5 , 8 ) N 8 FCRMATI I 5) DC 6 1=1,N 6 R E A D ( 5 , A ) ( B ( I , J ) , J = 1 , N ) 4 F C R M A T ( F l 1 . 8 ) RE AD { 5 , A ) { B H D , 1 = 1,N) 5 7 READ!5,3,ENO=8 8 8 ) I Y E A R , ( V ( I ) , 1 = 1 , N ) 3 FCRMAT(I A , I X , (15F5 .C ) ) K R I T E ( 6 , 7 1 8 ) I YEAR 718 F C R M A T ( 1 A X , I A / / / ) DC 10 1 = 1,N 1C SV{I ) = SCRT (V ( I ) ) DO 16 1 = 1,N F IA ( I ) = HI( I ) DC 16 J=1,N I F ( I . E C . J ) GG TO 705 H I J A ( I , J ) = H J ( I , J ) GC TG 16 705 H I J A ( I , J ) = H I I ( I ) 16 CONTINUE DO 993 1=1 ,N WR ITE (6 ,112 ) I ,H IA ( I ) 113 FORMAT! I X , ' H ' , I 3 , A X , F i 2 . 5 ) OG 9 93 J= I ,N I F U . E C . I ) GC TO 996 13 WRITE(6 ,11A) I , J , H I J A ( I , J ) 114 FORMAT( l X , l H l , I 2 t I 2 , 3 X , F 1 2 . 5 ) GO TO 993 996 PCER =H I I ( I ) 992 W R I T E ( 6 , 1 1 A ) I , J , P D E R 993 CCNTINUE SCN=G.O SCC=C.G CO 91 K=1,N S C C = S C C + ( V ( K ) * F I A ( K ) ) CC 91 M=1,N 91 SCN = S D N + ( V ( K ) * H I J A ( K , P ) * V ( K ) ) SC=SCN/SCD DC111 1=1, N VsRITE(6,393 ) I • V ( I ) 393 F G R M A T ( A X , ' V ( ' , 1 2 , ' ) = ' , A X , F 9 . 5 ) DC 111 J= I ,N SA=C.C SB=0.C SC=C.O CC = H I J A ( I , J ) / { F I A ( I ) - » F I A { J ) ) DO A8 K=1,N SA=SA+V(K ) *H IA (K ) SB = S B + ( V ( K ) * F I J A U , K ) ) S C = S C + { V ( K ) * F I J A l I , K ) ) A8 CCNTINUE SA=SA*CC SB=SB/H IA{J ) S C = S C / H I A ( I ) SIGMA=SA-S6-SC+SD 69 111 W R I T E ( 6 t 3 C ) I ,J ,S IGMA 30 F O R f A T l 1 0 X , • ( N C R M A L I Z E C CEMAND) S IGMA • , IX , I 2, I 2,2X , '= 1 ,F 1 2.6) V i R I T E ( 6 , 2 ) IVE AR 2 FORMAT! 1 2 X » / / 1 2 X , * E S T I M A T E D MARKET SHARES ' , 4 X , 14/ ) CO 24 1=1,N SHARE=C.O S L N - C . C DO 25 K=1,N 25 SUM=SUM *• V ( K )*HIA(K ) SHARE = VI I ) * I H I A( I )/SUM) 24 WR ITE (6 ,65 ) I,SHARE 65 FCRMAT ( 18X , • GOOD • , IX , 12 , IX, ' : ' , 4X, F 14 .6 ) GC TC 57 8 8 8 STOP ENC FUNCTION H I ( I ) COMMON B , 6 1 , S V , N DIMENSION B ( 3 0 , 3 0 , B 1 ( 3 C ) , S V ( 3 0 ) X = C . DC 1C K = l , N 1C X=X + B (I ,K) * S V ( K ) HI=(X + B K I ) ) /SV( I ) RETURN END FUNCTION H I J ( I » J ) COMMON B , B 1 , S V , N DI MENS ICN B ( 3 C , 3 C ) , E l ( 3 0 ) , SV (30 ) H IJ= .5 * B ( I , J ) / ( S V ( I ) * S V ( J ) ) RETURN ENC FUNCTION HI I ( I ) COMMON 8 , B 1 , S V , N DIMENSION B ( 3 0 , 3 0 ) , 8 1 ( 3 0 ) , S V ( 3 0 ) X = C . DC 1C J=1,N I F ( J . E Q . I ) GO TO 10 X=X+ e ( I , J ) * S V ( J ) 1C CONTINUE H I = - . 5 * ( X + B 1 ( I ) ) / ( S V ( I > * * 3 ) RETURN ENC PROGRAM SIGNORM C PROGRAM TC CALCULATE THE SHARES EACH GCCC IS ESTIMATED TO C HAVE OF THE MARKET ( I . E . THE ESTIMATED V ( I ) X U ) G IVEN THE C C O E F F I C I E N T S ESTIMATED BY THE GEN. LECNT IEF FUN'CTICN D I MEN SIGN V ( 3 0 ) , S V ( 3 C ) , B ! 3 0 , 3 C ) , E 1 ! 3 C ) , BNCT13C ) R E A D ( 5 , S ) N 8 FCRMATI I5 ) DC 6 1=1,N 6 R E A C ( 5 , 4 ) (B ( I , J ) • J = 1 » N ) 4 F C R M A T ( F l 1 . 3 ) R E A D ! 5 , 4 ) ( B l ( I ) ,1=1,N) 57 R E A C ( 5 , 3 , E N D = 6 8 8 ) I Y C A R , ( V ( I ) , I = 1 , N ) 3 FORMAT! 14, IX , ( 1 5 F 5 . C ) ) K R I T E ( 8 , 7 1 8 ) 1 YE AR 718 FCRMAT! 1 4 X , 1 4 / / / ) DO 10 1 = 1,N 10 SV( I ) = SCRT t V! I ) ) D E M = C . CEN2=0. DC 5 K=1,N DEN2=DEN2 + B l ( K ) * S V t K ) CO 5 J=1,N DEN1=CEN1+ B!K, J ) * S V I K ) * S V t J ) 5 CCNTINUE DEN = CEN 1 + DEN2 CO 11 L = l , N 11 B N C T ( L ) = B 1 ( L ) / S V ( L ) DC 2 1 = 2,N RN1=0. CO 9 J=1,N 9 RN1 = RN1 + B( I , J ) * S V ( J )/SV (!) SHARE=V( I ) * (RN1 + B N C T ( I ) ) / O E N WR ITE (6 ,7 ) I,SHARE 7 F C R M A T d X , ' M A R K E T SHARE, GOOD' , IX, 12, IX, • = , , 2 X , F I C « 4 ) 2 CCNTINUE GO TC 57 888 STCP ENC PROGRAM MS HA RE CHAPTER V REGRESSION RESULTS MODEL NO. 1 CONSUMPTION ONLY N o t e : To make n o t a t i o n more c o n c i s e , t h e goods w i l l b e r e f e r r e d t o b y t h e f o l l o w i n g s u b s c r i p t s : FOOD - 1 ALCOHOL - 2 TOBACCO - 3 MEDICAL SERVICES - 4 OTHER SERVICES - 5 CLOTHING - 6 MOTOR VEHICLES - 7 OTHER DURABLES - 8 HOUSING - 9 LAND - 10 71 72 TABLE V - l ESTIMATED (2nd s tage ) COEFFICIENTS FOR CONSUMER PREFERENCES: C o n s u m p t i o n O n l y COEFFICIENT ESTIMATE ( t - s t a t i s t i c ) STANDARD ERROR B12 - . 0 0 2 5 ( -0 .7823) .0035 B13 - . 0 0 6 3 ( -2 .9355) .0021 B14 - . 0 1 8 0 ( -4 .6343) . 0039. B15 - . 0 2 6 9 ( -3 .7712) .0071 B16 - . 0 1 1 9 ( -2 .3599) .0050 B22 - . 0 1 3 5 ( -3 .7758) .0036 B23 .0026 ( 1.3061) .0020 B24 .0136 ( 3 .3436) .0041 B25 - . 0 0 0 5 ( -0 .0949) .0054 B26 - . 0 0 5 1 ( -1 .6764) .0030 B27 - . 0 0 4 9 ( -3 .5594) .0014 B28 .0044 ( 3 .2139) .0014 B33 - . 0 0 2 6 ( -1 .5607) .0016 B34 .0084 ( 2 .9886) .0028 B35 - . 0 1 0 6 ( -3 .1528) .0034 B36 - . 0 0 0 7 ( -0 .3410) .0019 B44 - . 0 2 0 1 ( -2 .4041) .0083 B45 * - . 0 5 4 0 ( -6 .0065) .0090 B55 - . 0 0 7 8 ( -0 .5078) .0154 B56 - . 0 1 8 6 ( -3 .3756) .0055 B57 - . 0 1 6 1 ( -5 .3816) .0030 B58 - . 0 2 9 0 ( -7 .2237) .0040 B66 .0085 ( 1.7189) .0050 B67 .0035 ( 2 .4861) .0014 B68 - . 0 0 4 7 ( -2 .9154) .0016 B69 - . 0 2 8 2 ( -11 .1185) .0025 B77 - . 0 1 0 1 ( -7 .4168) .0014 B78 - . 0 0 9 4 ( -7 .7906) .0012 B79 - . 0 1 4 3 ( -6 .4622) .0022 B 7 , 1 0 - . 0 0 1 6 ( -2 .6079) .0006 B88 - . 0 1 6 1 ( -7 .9989) .0020 73 TABLE V - l ( C o n t i n u e d ) COEFFICIENT ESTIMATE ( t - s t a t i s t i c ) STANDARD ERROR B89 - . 0 3 4 5 ( -18 .1241) .0019 B 8 , 10 - . 0 0 4 6 ( - 5 . 7 5 0 5 ) .0008 B99 - . 0 0 0 5 (- 0 .0788) .0061 B 9 , 1 0 - . 0 0 6 2 (- 4 .9008) .0013 B I O , 1 0 .0070 ( 10 .8453) .0006 B o l .0716 ( 23 .5036) .0030 Bo2 .0080 ( 4 .3452) .0019 Bo3 .0091 ( 9 .1172) .0010 Bo4 .0538 ( 23 .8655) .0023 Bo5 .1439 ( 38 .8561) .0037 Bo6 .0473 ( 21 .9156) .0022 Bo7 .0417 ( 21.4250) .0019 Bo8 .0723 ( 42 .2632) .0017 Bo9 .0736 ( 20 .6606) .0036 B o l O .0075 ( 6 .8246) .0011 By s u b s t i t u t i n g , we s o l v e f o r b,, = -.01121 Summary S t a t i s t i c s ; C o n s u m p t i o n O n l y R 2 = 1.0000 S t a n d a r d E r r o r o f t h e R e g r e s s i o n = 0.99827 Number o f O b s e r v a t i o n s = 216 I f an e s t i m a t e d b . . i s p o s i t i v e , t h e goods i and j a r e , i n a s e n s e , p s e u d o -s u b s t i t u t e s . T r u e ^ s u b s t i t u t i o n and c o m p l e m e n t a r i t y a r e e s t i m a t e d and t a b l e d i n T a b l e V - 3 ( e l a s t i c i t i e s o f s u b s t i t u t i o n ) . 74 We may u s e t h e e s t i m a t e d c o e f f i c i e n t s t o c a l c u l a t e t h e p a r t i a l d e r i -v a t i v e s o f t h e i n d i r e c t u t i l i t y f u n c t i o n , and f r o m t h e s e p a r t i a l s and o u r ' n o r m a l i z e d ' p r i c e s , we may p r e d i c t m a r k e t s h a r e s . The p r e d i c t e d s h a r e s a r e r e p o r t e d and compared w i t h a c t u a l s h a r e s i n T a b l e V - 2 f o r t h e f i r s t and l a s t y e a r s i n o u r a n a l y s i s . TABLE V - 2 MODEL NO. 1 F ITTED MARKET SHARES (YEAR 1) " 1946 (1) FOOD GOOD ACTUAL = V.X. 1 1 F I T T E D = v h. / £ v . h where h . =^ ^ i i . k k i 9v . k i (2) ALCOHOL (3) TOBACCO (4) MEDICAL SERVICES (5) OTHER SERVICES (6) CLOTHING (7) MOTOR VEHICLES (8) OTHER DURABLES (9) HOUSING (10) LAND (YEAR 24) 1969 (1) FOOD (2) ALCOHOL (3) TOBACCO (4) MEDICAL SERVICES (5) OTHER SERVICES (6) CLOTHING (7) MOTOR VEHICLES (8) OTHER DURABLES (9) HOUSING (10) LAND .2601 .0518 .0449 .0473 .3074 .1013 .0090 .0465 .1173 .0146 .1474 .0314 .0210 .0680 .3075 .0714 .0560 .0896 .1703 .0374 .2697 .0471 .0547 .0144 .2989 .0995 - . 0 1 2 8 .0396 . 1657 .0232 .1547 .0310 .0226 .0700 . 3047 .0715 .0544 .0864 .1670 .0378 t h u s d w i l l n o t be d e f i n e d * i - e . , d e r i v e d demands. 75 Cor r e s r c c ^ i n g to each non-zero off-diagonal b^_. , we may ca l c u l a t e a Hick s - A l l e n ir..*rtial) e l a s t i c i t y of s u b s t i t u t i o n (a. .) between 13 the demands i and j , i n a p a r t i c u l a r time period ( i . e . , year) and evaluated at the p r e v a i l i n g p r i c e s . "While we have r e s t r i c t e d c e r t a i n b „ to be zero a priori, t h i s does net ianr-ly that o\.. = 0 (whereas d „ , the pseudo e l a s -t i c i t y , w i l l be = 0), s i - o s there are general s u b s t i t u t i o n e f f e c t s i n our normalized demand system O e e Chapter I I I , equation I I I - 7 ) . I f i s nega-t i v e we then know that the e l a s t i c i t i e s of demand are of the c o r r e c t sign. I f , however, we estimate a negative share f o r a good, the r e l a t e d a^. w i l l be meaningless. TABLE V-3 a. .: ELASTICITIES OF SUBSTITUTION ID MODEL NO. 1 CONSUMPTION ONLY (For Xormalized Market Demands) C. . > 0 -»• i . i SUBSTITUTES -j a. . < 0 ->• i . i COMPLEMENTS 1946 1961 1969 al 1 -3.925 -2.688 -2.892 al 2 -4.496 -0.628 -0.380 al 3 -8.738 -2.'748 -2.290 al 4 -6.675 -1.354 -0.876 al 5 -0.884 0.113 0 . 2 0 2 al 6 -2.608 -0.347 - 0 . 1 4 2 al 7 -62.702 2.475 1.840 al 8 30.344 2.845 2.235 al 9 2.356 1.505 1.249 al 10 -1.288 0.502 0.510 76 TABLE V - 3 ( C o n t i n u e d ) 1946 1961 1969 a 2 2 - 1 4 4 . 1 1 3 - 4 5 . 1 3 2 - 4 0 . 9 6 3 a 2 3 20 .161 8 .159 7 .392 a 2 4 404 .530 18 .377 12 .950 a 2 5 2 .378 0 .636 0 .538 a 2 6 - 16 .990 - 3 .664 - 2 .943 a 2 7 77 .774 - 4 .778 - 3 .333 a 2 8 73 .658 5 .952 4 .432 0\ 2 9 1 .168 0 .776 0 .621 a 2 10 - 2 .475 - 0 .226 - 0 . 117 a 3 3 - 30 .006 - 2 9 . 0 1 8 - 3 0 . 9 2 6 cr 3 4 242 .275 1 5 . 8 9 8 12 .086 0 3 5 - 8 .820 - 2 .405 - 1 .851 a"3 6 0 .897 0 . 8 4 3 0 .922 a 3 7 - 63 .952 2 . 2 3 3 1.709 a 3 8 29 .095 2 .603 2 .104 o 3 9 1 .107 1.262 1 .118 O 3 10 - 2 . 5 3 7 0 . 2 5 9 0 .379 a 4 4 - 1 2 3 1 . 8 0 2 - - 1 5 . 8 1 3 - 1 1 . 6 5 4 a 4 5 - 115 .493 - 4 .222 - 2 .569 a 4 6 6 4 . 5 7 9 3 .588 2 . 7 9 8 a 4 7 - 2 . 5 1 8 4 .145 2 .820 a 4 8 9 0 . 5 3 0 4 . 5 1 4 3 .215 o 4 9 6 2 . 5 4 1 3 .174 2 .229 o 4 10 5 8 . 8 9 7 2 .171 1 .490 a 5 5 5 .134 - 0 . 1 4 9 - 0 . 4 5 3 a 5 6 - 1 .473 0 .138 0 .284 a 5 7 2 .849 0 .265 0 .324 o 5 8 - 4 .411 0 .204 0 . 3 3 3 o~5 9 6 .260 1 .777 1.334 a 5 10 2 .616 0 .775 0 .595 a 6 6 17 .303 - 0 . 1 5 2 - 1 .456 O 6 7 - 1 0 0 . 7 6 7 5.196_ 3 .946 a 6 8 15 .199 1 . 8 1 0 ' 1.545 a 6 9 - 16.422:. - 3 . 9 1 4 - 2 .859 a 6 10 2 .787 1.196 1.146 77 TABLE V - 3 ( C o n t i n u e d ) 1946 1961 1969 a 7 7 - 9 6 9 . 4 3 2 - 1 3 . 1 5 9 - 1 1 . 5 2 3 d 7 8 250 .097 - 0 .780 - 0 .165 a 7 9 24 .175 - 1 .593 - 0 .853 a 7 10 - 1 8 .5 7 5 - 0 .634 - 0 .391 a 8 8 - 1 2 1 . 4 7 9 - 6 .678 - 6 .117 a 8 9 - 38 .431 - 3 .668 - 2 . 257 a 8 10 - 15 .213 - 2 .171 - 1 .403 a 9 9 1 .181 - 1 .582 - 1 .715 a 9 10 - 10 .930 - 2 .609 - 1 .794 a 10 10 37 .368 2 .234 - 0 .236 D i s c u s s i o n T h e s e c o n d - s t a g e e q u a t i o n f o r consumer e x p e n d i t u r e s a l o n e i s an e x c e l -l e n t f i t i n s o f a r as p r e d i c t i n g m a r k e t s h a r e s i s c o n c e r n e d , a n d an F t e s t r e -v e a l s t h a t we must r e j e c t t h e h y p o t h e s e s t h a t ( i ) b . = 0 V . ( i . e . , h o m o t h e t i c u t i l i t y f u n c t i o n ) ; and oj j ( i i ) b = 0 V i T< j ( i . e . , [ f i x e d p r o p o r t i o n ] L e o n t i e f p r e f e r e n c e s ) C o n s u m p t i o n M o d e l HYPOTHESES H : O ( i ) b . = 0 V . ( i . e . , h o m o t h e t i c u t i l i t y f u n c t i o n ) oj J F ( 1 0 , 170) = 3673 .107 T h u s , r e j e c t H . 78 ( i i ) H : o b . . = 0 V . f j ( i . e . , L e o n t i e f p r e f e r e n c e s ) F ( 2 7 , 170) = 162 .181 T h u s , r e j e c t H . J o In C h a p t e r V I we examine t h e r e s u l t s f o r t h e consumer demand s y s t e m when t h e demand f o r l e i s u r e i s s i m u l t a n e o u s l y d e t e r m i n e d . CHAPTER V I REGRESSION RESULTS MODEL NO. 2 CONSUMPTION AND LEISURE T h e n o t a t i o n i n t h i s c h a p t e r i s i d e n t i c a l t o t h a t o f C h a p t e r V , s a v e f o r t h e a d d i t i o n o f l e i s u r e , w h i c h w i l l be d e n o t e d b y s u b s c r i p t 11 ( e l e v e n ) . TABLE V I - 1 ESTIMATED (2nd s t a g e ) COEFFICIENTS FOR CONSUMER PREFERENCES: CONSUMPTION AND LEISURE COEFFICIENT ESTIMATE ( t - s t a t i s t i c ) STANDARD ERROR B12 - . 0 0 1 9 ( -3 .1237) .0006 B13 - . 0 0 0 5 ( -1 .6551) .0003 B14 - . 0 0 1 4 ( -4 .5962) .0003 B15 - . 0 0 2 7 ( -2 .6453) .0010 B16 - . 0 0 3 0 ( -3 .9616) .0008 B l , l l - . 0 2 6 9 ( -7 .8502) .0034 B22 - . 0 0 2 2 ( -3 .3116) .0007 B23 .0004 ( 1.3777) .0003 B24 .0009 ( 1.9234) .0004 B25 .0004 ( 0 .3838) .0010 B26 - . 0 0 1 1 ( -2 .1253) .0005 B27 .0012 ( 3 .8618) .0003 B28 .0007 ( 2 .6305) .0003 B 2 , l l . 0047 ( 2 .4284) .0019 B33 - . 0 0 0 5 ( -2 .5047) .0002 B34 . . 0 0 0 5 ( 2 .1353) .0002 B35 - . 0 0 2 0 ( -4 .7626) .0004 B36 - . 0 0 0 1 ( -0 .5266) .0003 B37 .0003 ( 1.2207) .0002 B 3 , l l - . 0 0 8 6 ( -7 .3576) .0012 79 TABLE V I - 1 ( C o n t i n u e d ) COEFFICIENT ESTIMATE ( t - s t a t i s t i c ) STANDARD ERROR B44 - . 0 0 0 8 ( -1 .4507) .0006 B 4 5 - . 0 0 4 7 ( -6 .6332) .0007 B 4 / 1 1 - . 0 0 2 8 ( -2 .3628) .0012 B 5 5 - . 0 0 6 3 ( -3 .0447) .0021 B 5 6 - . 0 0 0 7 ( -0 .7844) .0009 B 5 7 - . 0 0 2 6 ( -4 .8998) .0005 B 5 8 - . 0 0 1 8 ( -3 .2965) .0005 B 5 / 1 1 - . 0 4 6 5 ( -12 .3860) .0038 B 6 6 .0005 ( 0 .6035) .0008 B 6 7 .0010 ( 3 .1338) .0003 B 6 8 - . 0 0 0 9 ( -3 .0344) .0003 B 6 9 - . 0 0 3 1 ( -7 .4567) .0004 B 6 f l l - . 0 0 9 4 ( -3 .3364) .0028 B 7 7 - . 0 0 2 2 ( -7 .5456) .0003 B 7 8 - . 0 0 1 0 ( -4 .0444) .0002 B 7 9 - . 0 0 3 2 ( -10 .3469) .0003 B 7 1 Q - . 0 0 1 1 ( -6 .3310) .0002 B 7 ' f l l - . 0 1 7 6 ( -8 .3547) .0021 B 8 8 - . 0 0 1 8 ( -7 .7498) .0002 B 8 g - . 0 0 3 1 ( -10 .6450) .0003 B 8 1 0 - . 0 0 0 9 ( -6 .4149) .0001 g g ' ^ - . 0 0 8 9 ( -4 .6242) .0019 g g - . 0 0 2 8 ( -3 .5914) .0008 „ , 0 - . 0 0 2 8 ( -11 .7311) .0002 B 9 ' l ; L - . 0 4 3 8 ( -15 .4344) .0028 B l 0 1 Q - . 0 0 1 7 ( -9 .5607) .0002 B 1 0 ' 1 ; L - . 0 2 5 5 ( -16 .4287) .0016 B l l X 1 - . 4 8 7 4 ( -39 .1376) .0125 B o l ' .0164 ( 10 .4217) .0016 B o 2 - . 0 0 1 1 (- 1 .3065) .0008 .0044 ( 8 .8181) .0005 81 TABLE V I - 1 ( C o n t i n u e d ) COEFFICIENT ESTIMATE ( t - s t a t i s t i c ) STANDARD Bo4 .0036 (6 .2185) .0006 Bo5 .0281 (15.7032) .0018 Bo6 .0071 (5 .5029) .0013 Bo 7 .0103 (11 .3666) .0009 Bo 8 .0075 (8 .1338) .0009 Bo9 .0243 (17.6500) .0014 B o l O .0130 (18.4353) .0007 B o l l .2775 (82.0368) .0034 By s u b s t i t u t i n g / we s o l v e f o r b „ , = - . 0 0 2 2 5 7 Summary S t a t i s t i c s : C o n s u m p t i o n a n d L e i s u r e R 2 = 1 .000 S t a n d a r d E r r o r o f t h e R e g r e s s i o n - 0 .8422 Number o f O b s e r v a t i o n s = 240 The p r e d i c t e d m a r k e t s h a r e s a r e more a c c u r a t e ( i . e . , c l o s e t o a c t u a l v . x . ) t h a n t h o s e o f M o d e l N o . 1 , e s p e c i a l l y i n t h e l a t e r y e a r s . 82 TABLE V I - 2 MODEL NO. 2 CONSUMPTION AND LEISURE F ITTED MARKET SHARES (YEAR 1) 1946 GOOD ACTUAL = v . X . 1 1 F ITTED = v . h . / Z v h 1 1 k * k (1) FOOD (2) ALCOHOL (3) TOBACCO (4) MEDICAL SERVICES (5) OTHER SERVICES (6) CLOTHING (7) MOTOR VEHICLES (8) OTHER DURABLES (9) HOUSING (10) LAND (11) LEISURE .1092 .0216 .0187 .0197 .1283 .0422 .0036 .0194 .0489 .0061 .5823 .0920 .0248 .0172 .0222 .1244 .0455 .0116 .0266 .0436 .0082 .5838 (YEAR 24) 1969 (1) FOOD (2) ALCOHOL (3) TOBACCO (4) MEDICAL SERVICES (5) OTHER SERVICES (6) CLOTHING (7) MOTOR VEHICLES (8) OTHER DURABLES (9) HOUSING (10) LAND (11) LE ISURE .0534 .0113 .0075 .0245 .1107 .0257 .0201 .0323 .0614 .0134 .6397 .0598 .0108 .0079 .0248 .1113 .0272 .0185 .0304 .0598 .0120 .6374 83 TABLE V I - 3 a . . : E L A S T I C I T I E S OF SUBSTITUTION ID MODEL NO. 2 CONSUMPTION AND LEISURE (For N o r m a l i z e d M a r k e t Demands) -• -1946 1961 1969 a l l - 1 .070 - 1 3 . 9 0 3 - 1 2 . 2 9 1 a 1 2 25 .516 - 5 3 . 0 9 9 - 3 4 . 7 1 9 a 1 3 1.941 - 2 .356 - 0 .380 a 1 4 11 .770 - 1 6 . 3 0 4 - 9 .606 a 1 5 1.336 - 1 .418 - 1 .363 a 1 6 13 .234 - 2 4 . 4 9 3 - 1 5 . 1 1 9 a 1 7 - 2 6 . 0 6 3 17 .087 8 .994 a 1 8 - 5 .530 4 . 9 8 1 1.982 a 1 9 - 1 2 . 0 2 0 1 3 . 0 7 6 7 .669 a 1 10 - 2 6 . 7 5 8 36 .544 31 .802 a 1 11 - 0 .692 1 .668 1 .333 a 2 2 9 3 . 3 7 7 - 3 2 6 . 7 8 8 - 2 4 4 . 6 7 0 a 2 3 - 2 4 . 4 2 4 4 9 . 7 1 9 49 .018 a 2 4 - 2 5 . 8 8 8 39 .822 2 0 . 4 7 7 a 2 5 2 .219 - 4 . 8 0 6 - 4 . 256 a 2 6 29 .728 - 6 4 . 6 0 9 - 42 .821 a 2 7 - 1 0 7 . 9 0 4 8 5 . 5 2 5 4 8 . 3 6 1 a 2 8 - 2 2 . 9 2 8 23 .122 1 1 . 9 2 3 a 2 9 - 3 .727 - 2 . 6 7 5 - 2 .514 a 2 10 - 18 .464 20 .793 21 .619 a 2 11 - 5 .350 9 .199 6 . 4 2 6 a 3 3 4 . 2 9 5 - 9 4 . 0 1 3 - 1 2 0 . 9 0 5 a 3 4 - 34 .266 4 2 . 9 0 7 34 .122 a 3 5 13 .784 - 1 8 .1 6 4 - 1 2 . 8 2 4 a 3 6 - 0 . 8 9 3 2 .695 3 .919 a 3 7 - 58 .734 42 .842 32 .224 a 3 8 - 9 . 4 3 5 10 .648 9 .979 a 3 9 - 16 .43 5 18 .742 15 .666 a 3 10 - 31 .172 4 2 . 2 1 1 39 .799 a 3 11 2 . 3 2 7 - 2 .144 - 2 .161 84 TABLE V I - 3 ( C o n t i n u e d ) 1946 1961 1969 a 4 4 6 .682 - 53 .936 - 37 .497 a 4 5 28 .529 - 33 .141 - 18 .142 a 4 6 0 .024 0 .480 - 0 .666 a 4 7 - 2 5 . 2 0 6 12 .518 5 .632 o 4 8 - 4 .674 0 .412 - 1 .380 CT 4 9 - 1 1 . 1 6 4 8 .506 4 .306 a 4 10 - 2 5 . 9 0 1 31 .975 28 .439 a 4 11 - 4 . 166 5 .892 3 .749 o 5 5 - 1 .065 - 8 .636 - 7 . 4 3 3 o 5 6 0 . 0 8 7 0 .706 - 0 . 0 7 4 CT 5 7 5 .534 - 4 .157 - 2 .395 a 5 8 3 .309 - 4 .592 - 3 .326 CT 5 9 - 1 3 . 6 4 9 12 .951 7 .363 O 5 10 - 2 8 . 3 8 6 36 .419 31 .496 o 5 11 - 0 .411 1 .617 1 .314 o 6 6 - 1 5 . 8 5 0 - 2 .361 - 9 . 4 2 5 O 6 7 - 6 2 . 2 2 0 47 .795 26 .227 o 6 8 10 .384 - 14 .080 - 8 .579 o 6 9 14 .302 - 20 .716 - 1 2 . 6 8 5 o 6 10 - 2 6 . 0 5 9 35 .815 31 .536 o 6 11 - 2 . 0 4 3 3 .924 2 .784 0 7 7 195 .399 - 91 .349 - 5 9 . 6 1 5 CT 7 8 32 .976 - 13 .011 - 6 .762 CT 7 9 62 .871 - 2 5 . 1 0 8 - 1 3 . 3 0 1 CT 7 10 69 .956 - 24 .100 - 1 4 . 7 1 7 CT 7 11 4 .026 0 . 2 9 3 0 .584 CT 8 8 24 .478 - 4 6 . 6 9 0 - 3 3 . 1 1 6 a 8 9 29 .370 - 19 .635 - 1 0 . 8 7 7 CT 8 10 15 .817 - 3 .291 2 .057 o 8 11 - 3 .386 4 .880 3 .243 CT 9 9 - 1 3 . 9 1 8 - 3 .383 - 4 . 9 7 8 a 9 10 34 .234 - 20 .327 - 1 4 . 6 4 3 CT 9 11 2 .727 - 0 .672 - 0 .140 CT 10 10 39 .701 - 1 3 1 . 7 1 9 - 1 5 5 . 1 6 7 a 10 11 9 .759 - 8 .311 - 7 .191 a 11 11 0 .405 - 0 .995 - 0 .724 8 5 D i s c u s s i o n A g a i n t h e n u l l h y p o t h e s e s o f L e o n t i e f p r e f e r e n c e s and a h o m o t h e t i c ( g e n e r a l i z e d L e o n t i e f ) u t i l i t y f u n c t i o n a r e r e j e c t e d . I t i s i n t e r e s t i n g t o n o t e t h a t o n c e we a r e g i v e n t h e (average ) number o f h o u r s a member o f t h e l a b o u r f o r c e c h o o s e s t o work i n a g i v e n y e a r , o u r m o d e l w i l l e n d o g e n o u s l y d e t e r m i n e t h e ( a g g r e g a t e ) l a b o u r f o r c e p a r t i c i p a t i o n r a t e . C o n s u m p t i o n - L a b o u r S u p p l y M o d e l  H y p o t h e s e s : (i) H : o b . = 0 V. ( i . e . , h o m o t h e t i c u t i l i t y f u n c t i o n ) oj J . J F ( l l , 181) = 16718 .75 T h u s , r e j e c t H . J o ( i i ) H : o b ^ = 0 f1 j ( i . e . , L e o n t i e f p r e f e r e n c e s ) F ( 3 8 , 181) = 520 .857 T h u s , r e j e c t H . CHAPTER V I I CONCLUSIONS T h i s s t u d y , a t t h e v e r y l e a s t , h a s c o n t r i b u t e d some i n t e r e s t i n g d a t a t o t h e a r e a o f C a n a d i a n consumer e c o n o m i c s . On a s l i g h t l y h i g h e r l e v e l , t h e e m p i r i c a l r e s u l t s , r a n g i n g f r o m e x c e l l e n t f i t s i n p r e d i c t e d e x p e n d i t u r e * s h a r e s t o H i c k s - A l l e n e l a s t i c i t i e s o f s u b s t i t u t i o n , a r e i m p o r t a n t i n t h a t t h e y p r o v i d e a t e s t o f t h e r e v e a l e d p r e f e r e n c e a p p r o a c h t o t h e e s t i m a t i o n o f t h e u n d e r l y i n g u t i l i t y f u n c t i o n . A g o o d r e s u l t i s t h a t t h e p r e d i c t e d s h a r e s become more a c c u r a t e as we p r o g r e s s f u r t h e r i n t i m e , as t h u s i t i s l i k e l y t h a t t h e mode l may be u s e f u l f o r s h o r t - t e r m p r o j e c t i o n s o f consumer demand. The b a s i c d i f f i c u l t y , as m e n t i o n e d p r e v i o u s l y , i s t h e a g g r e g a t i o n p r o b l e m . A l t h o u g h we may be a b l e t o p r o v e t h e e x i s t e n c e o f individual u t i l i t y f u n c t i o n s and c a r r y o u t a n a l y s i s a t t h e m i c r o l e v e l , we h a v e no g u a r a n t e e t h a t when we a g g r e g a t e o v e r i n d i v i d u a l s ( o r , f o r t h a t m a t t e r , o v e r goods) t h e a g g r e g a t e u t i l i t y f u n c t i o n w i l l e x i s t . We o u g h t , t h e r e f o r e , t o r e c o g n i z e t h e e x i s t e n c e o f c e r t a i n b i a s e s . T h e r e i s a l s o t h e p o s s i b i l i t y t h a t c e r t a i n p o o r r e s u l t s ( e . g . , e l a s -t i c i t i e s o f s u b s t i t u t i o n f l u c t u a t i n g more t h a n w o u l d be e x p e c t e d ) c a n b e t r a c e d t o w e a k n e s s e s i n t h e o r i g i n a l d a t a . S i n c e some o f o u r s e r i e s a r e b a s e d on a r b i t r a r y assumpt i .ons ( f o r e x a m p l e , t h e ' s t o c k ' o f r e s i d e n t i a l l and ) The o n l y e x c e p t i o n b e i n g motor v e h i c l e s i n 1946 , where t h e s h a r e i s p r e d i c t e d t o be n e g a t i v e . The a c t u a l s h a r e was v e r y s m a l l , and t h u s i t i s e a s y enough t o s e e t h a t t h e model h a s n o t p r e d i c t e d w e l l a t t h e b e g i n n i n g . 86 87 t h e r e i s t h e e v e r - p r e s e n t p o s s i b i l i t y t h a t d a t a a n o m a l i e s have b i a s e d t h e e s t i m a t e d c o e f f i c i e n t s o r a t l e a s t d i s t o r t e d t h e o v e r a l l r e s u l t s ; n e v e r -t h e l e s s , we f e e l t h a t t h e s e s e r i e s a r e n e c e s s a r y and t h a t , h o p e f u l l y , c e r -t a i n o f them can be i m p r o v e d u p o n . The G e n e r a l i z e d L e o n t i e f F u n c t i o n a p p e a r s t o p r o v i d e an e x c e l l e n t f i t t o t h e d e r i v e d demand e q u a t i o n s , and we hope t o make u s e o f t h i s f u n c t i o n a l form i n t e s t i n g an e x t e n d e d m o d e l o f consumer d e m a n d - l a b o u r s u p p l y b e h a v i o u r . In f a c t , t h e n e x t a r e a t o be e x p l o r e d w i l l i n c l u d e human c a p i t a l ( i . e . , the demand f o r h i g h e r e d u c a t i o n i n an i n t e r t e m p o r a l choice f ramework) as w e l l as p h y s i c a l c a p i t a l ( d u r a b l e s ) and a more d i s a g g r e g a t e d t r e a t m e n t o f t h e l a b o u r s u p p l y d e c i s i o n , h o p e f u l l y e x t e n d i n g t o a g r o u p o f o c c u p a t i o n s . F u r t h e r , s i n c e one o f t h e s e r i o u s o m i s s i o n s o f t h i s s t u d y i s t h e endogenous d e t e r m i n a t i o n o f s a v i n g s , we hope t o i n c l u d e s u c h an e l e m e n t i n a f u t u r e m o d e l , p e r h a p s a c c o u n t i n g f o r t h e demand f o r f i n a n c i a l a s s e t s and r e a l b a l a n c e s . P e r h a p s , s i n c e we w i s h t o a v o i d c o l l i n e a r i t y , we w i l l a g g r e g a t e t h e n o n d u r a b l e s i n t o a s i n g l e c a t e -g o r y i n f u t u r e w o r k . I t s h o u l d be n o t e d t h a t e l a s t i c i t i e s o f demand c a n be c a l c u l a t e d d i r e c t l y f r o m t h e a.. and e s t i m a t e d s h a r e s . x i I t i s p e r h a p s o f i n t e r e s t t o examine a n o t h e r a p p r o a c h t o " l e i s u r e . " Nordhaus and T o b i n [ 2 8 ] , i n d e v e l o p i n g a new measure o f e c o n o m i c w e l f a r e , a t t e m p t t o q u a n t i f y some o f t h e i m p o r t a n t d i f f e r e n c e s b e t w e e n goods a n d s e r -v i c e s p r o d u c e d i n t h e m a r k e t p l a c e ( i . e . , what GNP measures ) and t h o s e a c t u a l l y a v a i l a b l e f o r u l t i m a t e consumer s a t i s f a c t i o n ( i . e . , c o n s u m p t i o n ) . T h e most i m p o r t a n t f a c t o r i n t h e d i f f e r e n c e b e t w e e n p r o d u c t i o n and w e l f a r e t u r n s o u t t o be the v a l u e o f l e i s u r e t i m e : 88 The o m i s s i o n o f l e i s u r e and o f nonmarke t p r o d u c t i v e a c t i v i t y f rom measures o f p r o d u c t i o n c o n -v e y s the i m p r e s s i o n t h a t e c o n o m i s t s a r e b l i n d l y m a t e r -i a l i s t i c . Economic t h e o r y t e a c h e s t h a t w e l f a r e c o u l d r i s e , even w h i l e NNP f a l l s , as the r e s u l t o f v o l u n t a r y c h o i c e s t o work f o r pay f ewer h o u r s p e r week , weeks p e r y e a r s , y e a r s p e r l i f e t i m e . 1 The wage r a t e , as i n t h e p r e s e n t s t u d y , i s c h o s e n t o be t h e p r i c e f o r l e i s u r e ; h o w e v e r , t h e y go one s t e p b e y o n d i n m a k i n g i m p u t a t i o n s f o r n o n m a r k e t a c t i v i t y as w e l l . I n t h e e n d , u s i n g - t h e i r i m p u t a t i o n s f o r t h e t i m e e l e m e n t s i n c o n s u m p t i o n , t h e a u t h o r s c a l c u l a t e a measure o f e c o n o m i c w e l f a r e (MEW), s e v e r a l v a r i a n t s o f w h i c h a r e compared w i t h NNP as t o g rowth o v e r t i m e . The b a s i c e f f e c t o f t h e i r i m p u t a t i o n s f o r l e i s u r e i s a r e d u c t i o n i n the g r o w t h r a t e i n s p i t e o f i n c r e a s i n g l e i s u r e c o n s u m p t i o n . In c l o s i n g , we w i l l examine t h e i n d i r e c t u t i l i t y f u n c t i o n . o b t a i n e d b y e v a l u a t i n g t h e i n v e r s e i n d i r e c t u t i l i t y f u n c t i o n h ( v ) and i n v e r t i n g i t . T h i s i s e v a l u a t e d a t t h e p r e v a i l i n g p r i c e s (v^) i n e a c h y e a r a n d w i t h t h e e s t i -mated b . . . ^•3 Nordhaus and T o b i n f 28; p . 9 ] . 89 TABLE V I I - 1 INDIRECT UT IL ITY FUNCTION g ( Y ; p) Y E A R C O N S U M P T I O N O N L Y C O N S U M P T I O N AND L E I S U R E 1946 2 .217888 6 .194567 1947 2 .223509 6 .189904 1948 2 .222746 6 .188863 1949 2 .224744 6 .185479 1950 2 .233116 6 .181176 1951 2 .237154 6 .180198 1952 2 .246631 6 .177883 1953 2 .257169 6 .176811 1954 2 .263582 6 .176455 1955 2 .276941 6 .176762 1956 2 .293592 6 .177373 1957 2 .301910 6 .178276 1958 2 .310517 6 .180124 1959 2 .323212 6 .181379 1960 2 .332206 6 .182951 1961 2 .339212 6 .184282 1962 2 .345377 6 .185060 1963 2 .356039 6 .186886 1964 2 .370543 6 .188728 1965 2 .383481 6 .190127 1966 2 .392507 6 .190932 1967 2 .399877 6 .192188 1968 2 .407138 6 .195193 1969 2 .417972 6 .197188 In t h e c o n s u m p t i o n m o d e l , t h e s t a n d a r d o f l i v i n g (a p r o x y f o r r e a l p e r - c a p i t a c o n s u m p t i o n ) , e x c e p t f o r a s l i g h t d i p i n 1948 , i s r i s i n g o v e r t i m e . When l e i s u r e i s i n c l u d e d , t h e v a l u e o f t h e i n d i r e c t u t i l i t y f u n c t i o n d e c l i n e s s l i g h t l y u n t i l 1954 and t h e n s t e a d i l y r i s e s . T h i s i s n o t u n -b e l i e v a b l e , s i n c e t h e e a r l y 1 9 5 0 ' s were a s s o c i a t e d w i t h l i t t l e e c o n o m i c g r o w t h . 90 A test of the accuracy of these indirect u t i l i t y functions is that the 1961 values, following our normalization (III-3) ought to be - i— or —— • Clearly, the following comparison indicates that our k v model has performed well: CONSUMPTION ONLY CONSUMPTION AND LEISURE V*1961 = .4275 V*1961 = .1617 = 2.33918 = 6.18429 g(Y;p) 1961 = 2.33921 g(Y;p) = 1961 6.18428 B I B L I O G R A P H Y A . REFERENCES [1] A l l e n , R. G . D. Mathematical Analysis for Economists. L o n d o n : M a c -M i l l a n and C o . L t d . , 1937 . [2] B e c k e r , G a r y S . 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" A n A p p l i c a t i o n o f t h e S h e p h a r d D u a l i t y T h e o r e m : A G e n e r a l i z e d L e o n t i e f P r o d u c t i o n F u n c t i o n , " Journal of P o l i t i c a l Economy, 79 ( M a y - J u n e , 1 9 7 1 ) , p p . 4 8 1 - 5 0 7 . [8] . " C a n a d i a n L a b o u r M a r k e t s : A N e o c l a s s i c a l E c o n o m e t r i c A p p r o a c h , " T e c h n i c a l R e p o r t N o . 2 0 , P r o j e c t f o r t h e E v a l u a t i o n and O p t i m i z a t i o n o f E c o n o m i c G r o w t h , U n i v e r s i t y o f C a l i f o r n i a , B e r k e l e y , 1969 . [9] . " C h o i c e on L a b o u r M a r k e t s and t h e T h e o r y o f t h e A l l o c a t i o n o f T i m e . " R e s e a r c h B r a n c h , P r o g r a m D e v e l o p m e n t S e r -v i c e , Depar tment o f Manpower and I m m i g r a t i o n , O t t a w a , 1 9 7 1 . [10] . " I n t e r t e m p o r a l Consumer T h e o r y and The Demand f o r D u r -a b l e s , " D i s c u s s i o n P a p e r N o . 5 3 , Depar tment o f E c o n o m i c s , U n i v e r -s i t y o f B r i t i s h C o l u m b i a , A p r i l , 1971 . [11] . "Wa l ras" T h e o r y o f C a p i t a l F o r m a t i o n and T h e E x i s t e n c e o f A Temporary E q u i l i b r i u m , " D i s c u s s i o n P a p e r N o . 7 6 , Depar tment o f E c o n o m i c s , U n i v e r s i t y o f B r i t i s h C o l u m b i a , 1972. [12] . U n p u b l i s h e d L e c t u r e N o t e s — M a t h e m a t i c a l E c o n o m i c s 5 1 5 , U n i v e r s i t y o f B r i t i s h C o l u m b i a , W i n t e r , 1970 . 91 92 [13] Evans, Michael K. Maaroeaononrio A c t i v i t y : Theory, Forecasting and Control. New York: Harper and Row, 1969 . [14] Firestone, 0 . J. Canada's Economic Development. London: Bowes and Bowes, 1958 . [15] . Residential Real Estate in Canada. Toronto: Univer-sity of Toronto Press, 1951 . [16] Friedman, Milton. A Theory of The Consumption Function. Princeton, N.J.: Princeton University Press, 1957 . [17] Friend, Irwin, and Robert Jones (Eds.). Study of Consumer Expenditures, Incomes, and Savings. Wharton School of Finance, University of Pennsylvania, 1960 . [18] Goldberger, Arthur S. "Functional Form and Utility: A Review of Con-sumer Demand Theory," Systems Formulation, Methodology, and Policy Workshop Paper 670Z, Social Systems Research Institute, University of Wisconsin, 1967 . [19] Goldsmith, Raymond W. The National Wealth of The United States in The Postwar Period. National Bureau of Economic Research, New York, 1962 . [20] G u s s m a n , T . K . "On O c c u p a t i o n a l Wages: A C o n v e r t e r f o r I n t e r c e n s i a l Y e a r s . " W o r k i n g P a p e r #13, P r o j e c t i o n s S t u d i e s U n i t , R e s e a r c h B r a n c h , P r o g r a m D e v e l o p m e n t S e r v i c e , Depar tment o f Manpower a n d I m m i g r a t i o n , O t t a w a , 1971. [21] Hamburger , M. " I n t e r e s t R a t e s and the Demand f o r Consumer D u r a b l e G o o d s , " American Economic Review, 57 (December , 1967) , p p . 1131-1153. [21aa ] H a n o c h , G i o r a . " G e n e r a t i o n o f New P r o d u c t i o n F u n c t i o n s T h r o u g h D u a l i t y , " mimeo, 1970. [21a] H a r b e r g e r , A r n o l d C . ( E d . ) . The Demand for Durable Goods. C h i c a g o : U n i v e r s i t y o f C h i c a g o P r e s s , 1960 . [22] H e l l i w e l l , J. F . et al. " Q u a r t e r l y E s t i m a t e s o f P r i v a t e S e c t o r W e a l t h , " R e s e a r c h D i s c u s s i o n P a p e r N o . 1 8 , R e s e r v e Bank o f A u s t r a l i a , 1971 . [23] . , H. T . S h a p i r o , G . R. S p a r k s , I. A . S t e w a r t , F . W. G o r b e t and D. R. S t e p h e n s o n . The Structure of RDX2. O t t a w a , Bank o f C a n a d a , 1971 . [24] H i c k s , J. R. Value and Capital. O x f o r d : A t t h e C l a r e n d o n P r e s s , 1946 . [25] H o u t h a k k e r , H . , and L e s t e r T a y l o r . Consumer Demand in The United States. (Second e d i t i o n ) . C a m b r i d g e , M a s s . : H a r v a r d U n i v e r s i t y P r e s s , 1970. 93 [26] J o h n s t o n , J . Econometric Methods. New Y o r k : M c G r a w - H i l l , 1963 . [27] L a n c a s t e r , K e l v i n . Mathematical Economics. New Y o r k : M a c M i l l a n , 1968 . [28] N o r d h a u s , W i l l i a m D., and James T o b i n . " Is Growth O b s o l e t e ? " i n Economic Growth, N a t i o n a l B u r e a u o f E c o n o m i c R e s e a r c h . ( F i f t i e t h A n n i v e r s a r y C o l l o q u i u m V ) , New Y o r k , 1972. [29] P i c k e t t , J a m e s . " R e s i d e n t i a l C a p i t a l F o r m a t i o n i n C a n a d a 1 8 7 1 - 1 9 2 1 , " Canadian Journal of Economics and P o l i t i c a l Science, V o l . 2 9 , N o . 1 ( F e b r u a r y , 1 9 6 3 ) , p p . 4 0 - 5 8 . [30] P o a p s t , J . V . , and W. R. W a t e r s . " I n d i v i d u a l I n v e s t m e n t : C a n a d i a n E x p e r i e n c e , " Journal of Finance, V o l . X V I I I , N o . 4 (December , 1 9 6 3 ) , p p . 6 4 7 - 6 6 5 . [31] . " R a t e s o f R e t u r n on Consumer D u r -a b l e s , " Journal of Finance, V o l . X I X , N o . 4 (December, 1 9 6 4 ) . [32] P o l l a k , R o b e r t . "The Demand f o r Consumer D u r a b l e s , " D e p a r t m e n t o f E c o n o m i c s S e m i n a r , U n i v e r s i t y o f B r i t i s h C o l u m b i a , March 1 4 , 1972. [33] S c h w e i t z e r , Thomas T . Personal Consumer Expenditures in Canada, 1926-75 ( P a r t s I and I I ) . S t a f f S t u d y N o . 2 6 , E c o n o m i c C o u n c i l o f C a n a d a . O t t a w a : Q u e e n ' s P r i n t e r , 1970 . [ 3 3 a ] - S h e p h a r d , R o n a l d W. Cost and Production Functions. P r i n c e t o n , N.J.-s P r i n c e t o n U n i v e r s i t y P r e s s , 1953 . [33b] . Theory of Cost and Production Functions. P r i n c e -t o n , N . J . : P r i n c e t o n U n i v e r s i t y P r e s s , 1970 . [34] S t e e l e , M a r i o n . " D e t e r m i n a n t s o f O w n e r - O c c u p i e d D w e l l i n g S t a r t s : C a n a d a , 1 9 2 1 - 1 9 4 0 . " Depar tment o f E c o n o m i c s , U n i v e r s i t y o f G u e l p h , 1972. [35] S t o n e , R i c h a r d and D. A . Rowe. "The M a r k e t Demand f o r D u r a b l e G o o d s , " Econometrica, V o l . XXV, N o . 3 (1957) , p p . 4 2 3 - 4 4 3 . [36] U s h e r , D a n . " M e a s u r i n g R e a l C o n s u m p t i o n From Q u a n t i t y D a t a , Canada 1935-1968 . (Mimeo) . T o be i n c l u d e d as a c h a p t e r i n a f o r t h c o m i n g b o o k . [37] W a l e s , T . J . "A G e n e r a l i z e d L i n e a r E x p e n d i t u r e M o d e l o f The Demand f o r N o n d u r a b l e Goods i n C a n a d a , " Canadian Journal of Economics (November, 1 9 7 1 ) , p p . 1471 -1484 . [38] Weber , Warren E . "The E f f e c t o f I n t e r e s t R a t e s on A g g r e g a t e C o n s u m p t i o n , " American Economic Review, 55 (Sep tember , 1 9 7 0 ) , p p . 5 9 1 - 6 0 0 . f 3 9 ' • " I n t e r e s t R a t e s , R e l a t i v e P r i c e s , a n d Consumer E x p e n d i t u r e f o r D u r a b l e s and N o n d u r a b l e s : A M u l t i - p e r i o d U t i l i t y M a x i m i z a t i o n A p p r o a c h . " Depar tment o f E c o n o m i c s , V i r g i n i a P o l y -t e c h n i c I n s t i t u t e and S t a t e U n i v e r s i t v . 1972. 94 [40] W i l s o n , G . W . , S c o t t G o r d o n , and S t a n i s l a w J u d e k . Canada: An Apprai-sal of Its Needs and Resources. T w e n t i e t h C e n t u r y F u n d , New Y o r k , 1965 . [41] Z e l l n e r , A . "An E f f i c i e n t Method o f E s t i m a t i n g S e e m i n g l y U n r e l a t e d R e g r e s s i o n s and T e s t s F o r A g g r e g a t i o n B i a s , " Journal of The American S t a t i s t i c a l Association, V o l . L V I I ( 1 9 6 2 ) , p p . 3 4 8 - 3 6 8 . B . DATA SOURCES C a n a d a , S t a t i s t i c s Canada ( f o r m e r l y t h e D o m i n i o n B u r e a u o f S t a t i s t i c s ) , O t t a w a : The Q u e e n ' s P r i n t e r . C a t a l o g u e Number [1] 11 -003 [2] 11 -206 [3] 13 -502 [4] 62 -002 [5] 62 -517 [6] 62 -519 [7] 62 -521 [8] 62 -525 [9] 62 -527 [10] 64-002 [11] 64-202 T i t l e Canadian S t a t i s t i c a l Review (monthly) S u p p l e m e n t t o Canadian S t a t i s t i c a l Review N a t i o n a l A c c o u n t s , Income and E x p e n d i -t u r e , , 1926-1956 N a t i o n a l Income and E x p e n d i t u r e A c c o u n t s "1926-1968 ( r e v i s e d s y s t e m ) , A u g u s t , 1969 P r i c e s a n d P r i c e I n d i c e s C i t y F a m i l y E x p e n d i t u r e , 1957 R e s i d e n t i a l R e n t s i n M a j o r C a n a d i a n C i t i e s , S e p t e m b e r , 1959 . P u b l i s h e d A p r i l , 1962 U r b a n F a m i l y E x p e n d i t u r e , 1959 U r b a n F a m i l y E x p e n d i t u r e , 1962 U r b a n F a m i l y E x p e n d i t u r e , 1964 New R e s i d e n t i a l C o n s t r u c t i o n H o u s e h o l d F a c i l i t i e s and E q u i p m e n t 95 Catalogue Number [12] 91-202 T i t l e Estimated Population by Age and £ex Groups, Canada and the Provinces [13] 91-511 Population by Sex and Age Uncatalogued Data [14] [15] National Accounts — Income and Expenditure Table 44: Table 46: Table 53; Table 54: Di r e c t Taxes - Persons, 1926-1969 In d i r e c t Taxes - 1926-1969 Personal Expenditures on Consumer Goods and Services i n Current D o l l a r s - 1926-1969 Personal Expenditure on Con-sumer Goods and Services i n Constant (1961) D o l l a r s , 1926-1969 Housing C a p i t a l Stock, 1921-1971, Housing and B u i l d i n g Permits Section, Business Finance D i v i s i o n , S t a t i s t i c s Canada, May, 1972 Other Sources [16] Bank of Canada, Statistical Summary (monthly). [17] Canadian Consumer Credit Factbook. Canadian Consumer Loan A s s o c i -ation, Toronto, 1972. [18] Economic Review. Ottawa, Mi n i s t r y of Finance, A p r i l , 1972. [19] Housing in Canada. Central Mortgage and Housing Corporation, Annual to 1965. [20] National Housing Statistics. Central Mortgage and Housing Corpora-t i o n , Annual from 1956. [21] The National Finances 1970-71. Canadian Tax Foundation, Toronto, 1970. [22] Urquhart, M. C. (Ed.), and K. A. H. Buckley (Asst. Ed.), Historical Statistics of Canada. Toronto: MacMillan, 1971. 

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