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The income elasticity of demand for cash balances in Canadian industry : an empirical investigation Scrivener, David Lionel 1968

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THE INCOME ELASTICITY OF DEMAND FOR CASH BALANCES IN CANADIAN INDUSTRY: AN EMPIRICAL INVESTIGATION  DAVID LIONEL SCRIVENER B.Sc,  U n i v e r s i t y o f B r i t i s h Columbia,  1965  A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF BUSINESS ADMINISTRATION i n the Department o f COMMERCE AND BUSINESS ADMINISTRATION  We accept t h i s t h e s i s as conforming to the r e q u i r e d  standard.  THE UNIVERSITY OF BRITISH COLUMBIA May,  1968.  In presenting this thesis in partial fulfilment of the requirements for an advanced degree at the University of British Columbia, I agree that the Library shall make it freely available for reference and Study.  I further agree that permission for extensive copying of this  thesis for scholarly purposes may be granted by the Head of my Department or by h.ils representatives.  It is understood that copying  or publication of this thesis for financial gain shall not be allowed without my written permission.  Department of  i^e/>*urizs^^'  The University of British Columbia Vancouver 8, Canada Date  ,ftf  i  ABSTRACT  T h i s study examines the t r a n s a c t i o n s  demand  f o r cash i n s e v e r a l s e c t o r s o f Canadian i n d u s t r y . In p a r t i c u l a r , the q u e s t i o n  of the e x i s t e n c e of  economies and diseconomies o f s c a l e i n the h o l d i n g of cash balances i s i n v e s t i g a t e d . In the e s t i m a t i o n procedure, s a l e s were used as an approximation of t r a n s a c t i o n s . balances were r e g r e s s e d  Average cash  on average annual s a l e s f i g u r e s  f o r f o u r t e e n i n d u s t r i a l groups i n the years 1957. and  i960.  Log. and o r d i n a r y l i n e a r f o r m u l a t i o n s  1958 were  used. R e g r e s s i o n c o e f f i c i e n t s i n d i c a t e d t h a t i n the m a j o r i t y o f cases,  e l a s t i c i t i e s o f cash w i t h r e s p e c t t o  s a l e s were approximately u n i t y , as t h e M e l t z e r model o f the demand f o r cash p r e d i c t s . two cases,  I n three out o f the f o r t y -  e l a s t i c i t i e s were s i g n i f i c a n t l y ( a t the .05  l e v e l ) l e s s than u n i t y , i n d i c a t i n g t h a t the Baumol-Tobin models might be r e l e v a n t i n some cases.  In f i v e  casesj  e l a s t i c i t i e s s i g n i f i c a n t l y g r e a t e r than u n i t y were found.  11  TABLE  OF  CONTENTS Page  CHAPTER I .  INTRODUCTION  Objectives  1.  The Relevance o f the Study  2.  Method  8.  L i m i t a t i o n s o f the Study CHAPTER I I  .....  9.  METHODOLOGY AND RESULTS  Source o f Data  12.  M a n i p u l a t i o n o f Data  1-3.  Results  15.  CHAPTER I I I  EVALUATION OF RESULTS  S i g n i f i c a n c e o f the R e g r e s s i o n E q u a t i o n s ..  22.  Sales E l a s t i c i t i e s  23.  E f f e c t o f Changes i n Economic  C o n d i t i o n s ..  31.  Comparison o f Cross S e c t i o n and Time series Results CHAPTER IV  CONCLUSIONS  Bibliography  32. 3.6. 37.  Appendix I A D e s c r i p t i o n o f the D e r i v a t i o n of Baumol's Cash I n v e n t o r y Model.  % Q .  Hi  LIST  OF  TABLES.  TABLE I .  C o e f f i c i e n t s Of D e t e r m i n a t i o n ( r ) F o r Log. And A r i t h m e t i c R e g r e s s i o n s .  TABLE I I .  E l a s t i c i t i e s Of Cash Balances With Respect To S a l e s F o r S e l e c t e d Indust r i a l S e c t o r s F o r Three T a x a t i o n Years.  TABLE I I I .  D i s t r i b u t i o n of E l a s t i c i t i e s ByT a x a t i o n Year.  TABLE IV.  Data From A l l Firms Grouped By Income C l a s s F o r i960.  TABLE V.  S t a t i s t i c s I l l u s t r a t i n g The P a t t e r n Of Payments And Degree Of C a p i t a l I n t e n s i t y Of The S u b c l a s s e s Of The Wood And Paper Products I n d u s t r i a l Group - 1958.  TABLE V I .  Comparison Of Cross S e c t i o n E l a s t i c i t i e s With Time S e r i e s Cash/Sales Ratios.  iv  ACKNOWLEDGMENT  The author wishes t o express h i s thanks t o Dr. W. W i n i a t a f o r proposing the t o p i c and s u p e r v i s i n g the w r i t i n g o f t h i s t h e s i s . Thanks go a l s o t o Mr. B i l l Amundson f o r h i s v a l u a b l e a s s i s t a n c e w i t h the computer programming.  - 1CHAPTER  I.  INTRODUCTION (A)  OBJECTIVES Recently,* many e m p i r i c a l and t h e o r e t i c a l  papers  have been p u b l i s h e d d e a l i n g w i t h the h o l d i n g s of cash and o t h e r l i q u i d a s s e t s by b u s i n e s s f i r m s . the purpose  1 .  It will  be  of t h i s t h e s i s t o examine the manner I n which  the aggregate  cash balances of Canadian b u s i n e s s f i r m s  v a r y K i t h income l e v e l s .  S p e c i f i c a l l y ; the q u e s t i o n of  the e x i s t e n c e of economies of s c a l e i n the use o f cash w i l l be i n v e s t i g a t e d .  The study i n v o l v e s the determin-  a t i o n of the Income e l a s t i c i t y of the demand f o r cash b a l a n c e s f o r t h r e e d i s t i n c t groupings of f i r m s . of average  The l o g s  cash balances are r e g r e s s e d on the l o g s o f  average annual s a l e s volumes f o r : (1)  1.  A number of Canadian i n d u s t r i e s u s i n g average  See R i c h a r d T. Selden, "The Postwar R i s e i n the V e l o c i t y of Money: A S e c t o r a l A n a l y s i s , " J o u r n a l of F i n a n c e , Dec., 1961; pp. 483 - 5^5; W i l l i a m J . Baumorj "The T r a n s a c t i o n s Demand f o r Cash: An Inventory T h e o r e t i c Approach;" Q u a r t e r l y J o u r n a l of Economicsy November;' 1952, pp. 5**5-556; James Tobin> "The I n t e r e s t E l a s t i c i t y of T r a n s a c t i o n s Demand f o r Cash*" Review of Economics and S t a t i s t i c s . August^; 1956 pp. 2*1-1 - 247; M i l t o n Friedman;' "The Demand f o r Money: Some T h e o r e t i c a l and E m p i r i c a l R e s u l t s ; o J o u r n a l of P o l i t i c a l Economy; August; 1959; PP. 327 - 351; A l l a n H. M e l t z e r , "The Demand f o r Money: "A C r o s s - S e c t i o n Study of Business Firmsy" Q u a r t e r l y J o u r n a l of Economics. August; 1963, pp. 405 - 422; R. C. Vogel and G. S. Maddala; "Cross S e c t i o n E s t i m a t e s of L i q u i d A s s e t Demand by Manufact u r i n g Corporations *" J o u r n a l o f F i n a n c e . December 1  1967? pp. 557 - 575.  - 2 cash and s a l e s f i g u r e s f o r i n d u s t r i a l c l a s s e s as o b s e r v a t i o n s . (2)  sub-  (2)  The manufacturing i n d u s t r y , which i s broken down by a s s e t s i z e c l a s s e s . Average cash and s a l e s f i g u r e s from each a s s e t s i z e c l a s s a r e used as o b s e r v a t i o n s .  (3)  A sample o f f i r m s c l a s s i f i e d by a s s e t groups and a sample o f f i r m s c l a s s i f i e d by income groups. Average cash and s a l e s f i g u r e s from each a s s e t and Income c l a s s r e s p e c t i v e l y a r e used as o b s e r v a t i o n s . The  above r e g r e s s i o n s a r e performed u s i n g the  o r d i n a r y l i n e a r f o r m u l a t i o n as w e l l as the l o g form. The  e f f e c t o f changes i n p r e v a i l i n g economic c o n d i t i o n s  on the income e l a s t i c i t y o f cash i s a l s o (B)  Investigated.  THE RELEVANCE OP THE STUDY The q u e s t i o n o f the e x i s t e n c e o f economies of  s c a l e I n h o l d i n g o f cash i s r e l a t e d t o the broader q u e s t i o n o f the motives f o r h o l d i n g cash balances. w i d e l y accepted  A  concept o f the f u n c t i o n s performed by  money i s based on the w r i t i n g s o f J . M. Keynes, Keynes' approach t o the r o l e of money d i f f e r s  (3)  from the  c l a s s i c a l a n a l y s i s p r i m a r i l y because i t focuses  attention  on the demand f o r money r a t h e r than on the supply  (2)  e.g. The E l a s t i c i t y f o r the Wood and Paper Products i n d u s t r y i s determined by u s i n g average cash and s a l e s f i g u r e s from the s u b c l a s s e s o f Plywood M i l l s , Sawmills, F u r n i t u r e , Paper Bags and Boxes, Pulp and Paper M i l l s , M i s c . Wood Products, and Misc. Paper Products as o b s e r v a t i o n s .  (3)  J.M. Keynes - The General Theory o f Employment. I n t e r e s t , and Money - New York, Harcourt, Brace,  19W.  of money.  The l i q u i d i t y preference  by Keynes p o s t u l a t e s  theory  three major motives why i n d i v i d u a l s  and b u s i n e s s f i r m s want t o h o l d money b a l a n c e s . motives a r e :  offered  These  the t r a n s a c t i o n s ' motive, the p r e c a u t i o n -  a r y motive, and the s p e c u l a t i v e motive.  The focus o f  t h i s t h e s i s w i l l be on the t r a n s a c t i o n s motive which r e l a t e s t o the need t o h o l d some q u a n t i t y o f money t o c a r r y on day-to-day economic d e a l i n g s . Almost a l l t r a n s a c t i o n s i n advanced economic systems i n v o l v e an exchange o f money, and s i n c e the cash r e c e i p t s of i n d i v i d u a l s and b u s i n e s s f i r m s a r e n o t p e r f e c t l y synchronized  w i t h t r a n s a c t i o n s i n v o l v i n g money o u t l a y s ,  i t I s necessary t h a t some money be h e l d I n order t o meet " d a i l y " f i n a n c i a l needs. In the Keynesian system the a c t u a l amount o f money h e l d t o s a t i s f y the t r a n s a c t i o n s motive (Lt) i s assumed to vary d i r e c t l y i n p r o p o r t i o n t o income (Y); so, we can d e s c r i b e the r e l a t i o n s h i p a s : The  =  a (Y).  b a s i s f o r t h i s statement i s t h a t I n a complex  s o c i e t y the volume o f economic t r a n s a c t i o n s v a r i e s d i r e c t l y w i t h income l e v e l . quantity  ^  Consequently, the a b s o l u t e  o f money balances needed t o c a r r y on these t r a n s  a c t i o n s a l s o v a r i e s d i r e c t l y i n p r o p o r t i o n t o the income level. More r e c e n t l y , s e v e r a l economists, notably W. Baumol (4)  A statement o f the c l a s s i c a l p o s i t i o n can be found i n : W.C.Peterson j^ Income, Employment, and Economic G r o w t h - N o r t o n and Co. New York, 1 9 6 2 . A  f  r  (5)  I b i d . -p. 3 4 4  - 4 and  J . T o b i n have presented  p r o p o s i t i o n s which q u e s t i o n  the t h e s i s t h a t cash balances vary i n d i r e c t t o income. act  Baumol ^  and T o b i n  ^)  proportion  argue t h a t i f f i r m s  i n a r a t i o n a l manner, cash balances w i l l tend to  l e s s than p r o p o r t i o n a l l y w i t h income, i m p l y i n g t h a t are economies of s c a l e i n the use  of cash.  vary there  In essence,  Baumol's c o n t e n t i o n i s t h a t the volume o f cash h e l d w i l l v a r y i n p r o p o r t i o n to the volume of t r a n s a c t i o n s i n v e r s e l y w i t h the c o s t s r e l a t e d to h o l d i n g  and  cash.^  S i m i l a r l y , T o b i n contends t h a t i n t e r e s t r a t e s w i l l i n f l u e n c e the amount of cash h e l d f o r t r a n s a c t i o n s purposes.  Both of these models, i f a s s o c i a t e d  var-  (9) i a b l e c o s t s are taken as zero c o l l a p s e , i n t o : C  =  /aY  J 2r  where C  =  Cash balance  (Average)  a  =  fixed costs  (pecuniary and  Y  =  income  r  =  interest rate  non-pecuniary)  where "non-pecuniary" means c o s t s which cannot be q u a n t i f i e d . The  square r o o t formula i m p l i e s t h a t i f a f i r m a c t s  to minimize the c o s t s a s s o c i a t e d w i t h the use of t r a n s (6) Baumol, op. c i t . (7) Tobin, op. c i t . (8) A d e s c r i p t i o n of the d e r i v a t i o n of Baumol's model i s g i v e n i n Appendix 1. 7  (9)  W i n i a t a , W. The Income E l a s t i c i t y o f the Demand f o r Money by Business Firms: An E m p i r i c a l T e s t . (Unpublished), 1966.  5 - a c t i o n s cash, i t s d o l l a r balance w i l l i n c r e a s e t h a n i n p r o p o r t i o n t o income.  less  I n o t h e r words, i f f i r m s  a c t i n accordance w i t h the theory then the income e l a s t i c i t y o f cash can be expected t o be about Another economist;" M. Friedman,  ^  1 0  0.5.  ^ has suggested  t h a t cash balances a r e permanent-income" e l a s t i c and n  t h a t i n the l o n g - r u n , r e a l money balances i n c r e a s e more than p r o p o r t i o n a l l y t o an i n c r e a s e i n r e a l permanent income.  Friedman's  e m p i r i c a l a n a l y s i s shows t h a t i n the  l o n g run, the e l a s t i c i t y o f money w i t h r e s p e c t  to i n -  come was 1.8  t o 1954.  over 20 b u s i n e s s c y c l e s from 1870  An a n a l y s i s o f the behaviour o f these v a r i a b l e s w i t h i n a c y c l e d i f f e r e d from the l o n g - r u n t r e n d i n t h a t the c a l c u l a t e d e l a s t i c i t i e s were about 0.2.  Interest rates  were found t o have l i t t l e e f f e c t on the demand f o r money. In a c r o s s s e c t i o n study o f American b u s i n e s s f i r m s A. H. M e l t z e r  proposes t h a t the demand f o r cash 1 s a  f u n c t i o n o f the f i r m ' s wealth  (non-human a s s e t s ) .  The  author begins w i t h the statement t h a t the s i z e o f a f i r m ' s money balance i s a f u n c t i o n o f a market r a t e o f i n t e r e s t and n e t wealth.  He then shows how s a l e s a r e  r e l a t e d t o w e a l t h by the i n t e r n a l r a t e o f r e t u r n on a s s e t s i n the i n d u s t r y and a v a r i a b l e r e p r e s e n t i n g i n the percentage o f the f i r m ' s a s s e t s i n use.  (10)  Friedman",  op. c i t . ?.3so  (11)  Meltzer,  op. c i t . -? 4oj  changes  - 6M e l t z e r performs a number o f c r o s s s e c t i o n cash s a l e s r e g r e s s i o n s and  on  f i n d s t h a t the demand f o r money  by f i r m s i s a f u n c t i o n of s a l e s t o a f i r s t  approxi-  mation, i s l i n e a r i n the l o g a r i t h m and u n i t e l a s t i c . M e l t z e r q u a l i f i e s h i s o v e r a l l c o n c l u s i o n s as b e i n g " f i r s t approximation"  a  s i n c e he does note t h a t economies  and diseconomies of s c a l e may  be found w i t h i n i n d i v i d u a l  industries.  (12) In a r e c e n t paper, K. Brunner and A. H.  Meltzer  have re-examined the q u e s t i o n of economies of s c a l e i n the use of cash i n a c r i t i q u e of the Baumol and models.  Tobin  Brunner and M e l t z e r r e j e c t these models on  e m p i r i c a l groundsf r e f e r r i n g t o the f i n d i n g s i n M e l t z e r ' s  (1963) The  c r o s s - s e c t i o n study. authors conclude t h a t : ".... the Baumol model p r o v i d e s l i t t l e reason f o r abandoning the e a r l i e r conc l u s i o n t h a t t o a f i r s t approximation the q u a n t i t y theory e x p l a i n s the observed cash h o l d i n g s of b u s i n e s s f i r m s when the o b s e r v a t i o n s are from c r o s s s e c t i o n s a t a p o i n t of time."  They s t a t e f u r t h e r t h a t economies and diseconomies of s c a l e o f the majgnitude p r e d i c t e d by the Baumol model become apparent o n l y when one  i s concerned w i t h  the  behaviour of s m a l l f i r m s or the d i s t r i b u t i o n s of b a i l e e s within Industrie,.  ( 1 3  cash  >  (12)  Brunner, K. and Meltzer,' A. "Economies of S c a l e i n Cash Balances Reconsidered." Q u a r t e r l y J o u r n a l of Economics.  (13)  I b i d . p. 427. M e l t z e r ' s 1963  The authors c i t e the f i n d i n g s o f Study as evidence f o r t h i s statement.  - 7 With r e g a r d Meltzer  t o Tobin's h y p o t h e s i s ,  Brunner and  s t a t e t h a t h i s p r i n c i p a l concern i s t o show-  t h a t i n t e r e s t r a t e s w i l l a f f e c t the amount o f t r a n s a c t i o n s balances h e l d i n the form o f money.  Tobin*s  a n a l y s i s does not n e c e s s a r i l y c o n t r a d i c t the q u a n t i t y theory  o f money because h i s a n a l y s i s i s not p r i m a r i l y  concerned w i t h the determinants o f t o t a l money  holdings  but r a t h e r w i t h computing the amount by which r e c e i p t s must change before  there i s a change i n the optimal  of t r a n s a c t i o n s between cash and l i q u i d  number  securities.  T o b i n i s n o t concerned w i t h economies of s c a l e i n the use  o f cash f o r i n d i v i d u a l f i r m s w i t h the p o s s i b l e ex-  c e p t i o n of those f i r m s who a r e c l o s e t o a p o i n t where a change i n the number o f t r a n s a c t i o n s between bonds and cash i s n e c e s s a r y .  Brunner and M e l t z e r  conclude t h a t  w h i l e the i s s u e o f economies o f s c a l e I n the demand f o r money i s p r i m a r i l y an e m p i r i c a l q u e s t i o n  i t i s possible  to s t a t e t h e o r e t i c a l l y t h a t r a t i o n a l behaviour o f the Baumol o r T o b i n type does not deny t h a t the q u a n t i t y theory  of money e x p l a i n s the c r o s s - s e c t i o n demand f o r  money by f i r m s t o a f i r s t  approximation.  I t would appear t h a t a c o n c l u s i v e t h e o r e t i c a l b a s i s f o r the e x i s t e n c e  o f economies o f s c a l e i n the demand f o r  money i s , as y e t ; u n d e f i n e d .  I t w i l l not be the purpose  of t h i s e x e r c i s e t o pursue the t h e o r e t i c a l argument any f u r t h e r , but r a t h e r t o d i s c o v e r whether o r not economies of s c a l e e x i s t e d a t s e l e c t e d p o i n t s i n time.  - 8 (C)  METHOD. The  a n a l y s i s employed i n t h i s c r o s s - s e c t i o n study  i s conceptually  s i m i l a r to t h a t of M e l t z e r  (1963).  Data  (ill) was  obtained  contains  from Canada t a x a t i o n s t a t i s t i c s  aggregate balance sheet and  ' which  x  income statement  d a t a f o r a l l Canadian business f i r m s s u b m i t t i n g tax r e t u r n s . were obtained  Cash and  income  s a l e s (or g r o s s revenue) f i g u r e s  f o r f i r m s i n s u b d i v i s i o n s of eleven  indus-  t r i a l c l a s s e s as w e l l as f o r the t o t a l of a l l manufact u r i n g f i r m s grouped i n t e n a s s e t c l a s s e s , a l l Canadian companies grouped i n a s s e t c l a s s e s , and  a l l Canadian  companies r e p o r t i n g a p r o f i t grouped i n Income c l a s s e s . To i n v e s t i g a t e the e f f e c t of p r e v a i l i n g economic cond i t i o n s on the demand f o r money? cash and were c o l l e c t e d f o r three t a x a t i o n y e a r s : representing  sales figures  1957  peaks i n the b u s i n e s s c y c l e and  p r e s e n t i n g a trough y e a r . ^ ^ 1  and 1958  i960 re-  Averages of the cash  and  s a l e s f i g u r e s were c a l c u l a t e d f o r each i n d u s t r i a l subd i v i s i o n and  each a s s e t and  income group.  The  logar-  (14)  Canada Dep*t of N a t i o n a l Revenue T a x a t i o n Statistics, Part II Tables 4-6.  (15)  T u r n i n g p o i n t s i n the business c y c l e are as April 1957 peak April 1958 trough January i960 peak March 1961 trough.  follows:  - 9ithms of these numbers were used i n a l i n e a r r e g r e s s i o n t o o b t a i n the e l a s t i c i t y of cash w i t h r e s p e c t t o sales.  Cash on s a l e s r e g r e s s i o n a n a l y s e s were done i n  a r i t h m e t i c as w e l l as i n l o g form.  S a l e s was  selected  as the independent v a r i a b l e whenever p o s s i b l e f o r two reasons.  S a l e s more c l o s e l y r e f l e c t s the s c a l e of oper-  a t i o n of most companies than does income.  I n the  approximations we are not concerned w i t h the increments t o the v a l u e of the f i r m a s s o c i a t e d w i t h net income but r a t h e r w i t h the major source of cash i n f l o w s y S a l e s ; which more c l o s e l y approximates  transactions.  Second?  u s i n g s a l e s f a c i l i t a t e s a comparison w i t h the r e s u l t s of o t h e r s t u d i e s . (D)  LIMITATIONS OF THE STUDY. Many of the r e s u l t s o f this- a n a l y s i s are not  s t r i c t l y comparable t o those o b t a i n e d i n o t h e r c r o s s s e c t i o n s t u d i e s such as those conducted by Meltzer'?  (1965)?  Frazer  (1964),  and Vogel and Maddala  (1967).  I t i s l i k e l y t h a t the f i n d i n g s w i l l d i f f e r because -the c l a s s i f i c a t i o n of the Canadian t a x a t i o n d a t a used here i s d i f f e r e n t from the American d a t a .  In Taxation  S t a t i s t i c s aggregate f i n a n c i a l f i g u r e s f o r f i r m s i n i n d u s t r i a l groups  (Mining, Quarrying and  Ollwells;  Petroleum Products," e t c . ) are not o r g a n i z e d i n t o a range of a s s e t c l a s s e s .  I n d u s t r i a l groups are s u b d i v i d e d as  t o v a r i o u s types of f i r m s r a t h e r than v a r i o u s a s s e t s i z e s . F o r example the group'of Wood and Paper Products i s sub-  - 10 -  d i v i d e d i n t o seven types of f i r m s :  Planer M i l l s ,  Saw  M i l l s ; F u r n i t u r e Manufacturing; Pulp, Paper Bags and Boxes, M i s c e l l a n e o u s Wood Products and M i s c e l l a n e o u s Paper Products.  A breakdown of f i r m s by a s s e t s i z e  i s a v a i l a b l e f o r o n l y two groups:  A l l firms submitting  tax r e t u r n s and a l l manufacturing expected t h a t because of the way  firms.  I t i s to be  i n which the d a t a i s  o r g a n i z e d , r e g r e s s i o n equations o b t a i n e d w i l l not  yield  c o e f f i c i e n t s of d e t e r m i n a t i o n as l a r g e as those of American s t u d i e s s i n c e cash and s a l e s f i g u r e s are p r o b a b l y d i s t r i b u t e d more randomly i n groups of f i r m s of heterogeneous  asset s i z e s .  In r e g a r d t o c r o s s s e c t i o n s t u d i e s i n g e n e r a l , s e v e r a l authors  ( n o t a b l y Kuh,  and Vogel and Maddala,  (1959)»  (1967) have  Grunfeld,  recently  (1961)  suggested  some l i m i t a t i o n s of a t h e o r e t i c a l nature i n h e r e n t i n t h i s type of a n a l y s i s .  I n g e n e r a l , these authors  state  t h a t one must be aware o f two sources of e r r o r : (1)  e r r o r s i n t r o d u c e d by the a r t i f i c i a l grouping of d i s s i m i l a r f i r m s .  (2)  e r r o r s i n t r o d u c e d by a g g r e g a t i o n over time; the problem i n d e a l i n g w i t h balance sheet f i g u r e s i s the s e l e c t i o n of a moment i n time which may not be r e p r e s e n t a t i v e . Balance sheet d a t a are not d e r i v e d from a s i n g l e p o i n t i n time because c o r p o r a t e year ends are d i s t r i b u t e d through the t a x a t i o n year.  Another problem w i t h the balance sheets of manu-  - 11 f a c t u r l n g companies i s the p r a c t i c e of 'window d r e s s ing. ' Vogel and Maddala conclude t h e i r a r t i c l e w i t h the warning  t h a t one must use c a u t i o n i n i n t e r p r e t i n g the  r e s u l t s of c r o s s s e c t i o n e s t i m a t e s and recommend t h a t r e g r e s s i o n v a l u e s o b t a i n e d from t h i s type of a n a l y s i s be compared w i t h time s e r i e s v a l u e s o b t a i n e d from the same group of f i r m s .  While t h i s l a t t e r p o i n t i s w e l l  taken i t i s not p o s s i b l e t o make t h i s type of comparison when u s i n g aggregate tax s t a t i s t i c s because  the pop-  u l a t i o n of f i r m s i n each c l a s s changes from year t o year. One must keep Vogel and Maddala's warning  i n mind,  however; and r e c o g n i z e t h a t the r e s u l t s of t h i s study must be regarded as a f i r s t approximation of the income e l a s t i c i t i e s of cash b a l a n c e s .  - 12 CHAPTER I I . METHODOLOGY (A)  AND  RESULTS.  SOURCE OP DATA The d a t a f o r t h i s t h e s i s was obtained from Canada  Department o f N a t i o n a l Revenue T a x a t i o n S t a t i s t i c s , P a r t Two,  T a b l e s 4 t o 6 f o r the t a x a t i o n years 1957, 1958 and  i960. T2  This publication c o l l e c t s selected s t a t i s t i c s  from  C o r p o r a t i o n Income Tax Returns f i l e d by companies i n  Canada d u r i n g a g i v e n t a x a t i o n year. above r e p r e s e n t an a g g r e g a t i o n  The t a b l e s mentioned  of f i n a n c i a l statement  data  from a sample o f f i r m s s u b m i t t i n g t a x r e t u r n s , and a r e entitled: Table 4  -  D i s t r i b u t i o n of F u l l y Tabulated Companies by I n d u s t r i a l C l a s s .  Table 5  -  D i s t r i b u t i o n of F u l l y T a b u l a t e d Companies by S i z e o f T o t a l A s s e t s .  Table 5A -  D i s t r i b u t i o n o f F u l l y T a b u l a t e d Manu f a c t u r i n g Companies by S i z e o f T o t a l Assets.  Table 6  D i s t r i b u t i o n o f F u l l y Tabulated Companies by Income C l a s s .  -  Profit  Tables 5 and 5A a r e broken down i n t o n i n e a s s e t s i z e c l a s s e s w h i l e Table 6 i s composed o f t e n income c l a s s e s . (1)  SAMPLE OF FIRMS:  Canada Tax S t a t i s t i c s aggregates  d a t a from a sample o f f i r m s s e l e c t e d i n t h e f o l l o w i n g manner:  A l l c o r p o r a t i o n s r e p o r t i n g w i t h t o t a l a s s e t s of  $1 m i l l i o n o r more, o r a c u r r e n t year p r o f i t o f a t l e a s t $50 thousand a r e i n c l u d e d .  C e r t a i n unnamed i n d u s t r i e s  c o n s i d e r e d s u b j e c t t o a b e r r a t i o n are a l s o sampled a t a 100$ r a t e .  The remaining  c o r p o r a t i o n s a r e s t r a t i f i e d by  - 13 i n d u s t r i a l c l a s s i f i c a t i o n and a 10% random sample s e l e c t e d i n each i n d u s t r i a l c l a s s .  20%  In the aggregate approximately  of c o r p o r a t i o n r e t u r n s submitted are a n a l y z e d . (2)  PERIOD COVERED:  S t a t i s t i c s are c o l l e c t e d d u r i n g the  t a x a t i o n y e a r which embraces a l l company r e t u r n s f o r f i s c a l p e r i o d s ending between January 1 and December 31 of a g i v e n c a l e n d a r year. 31.  Unless a company's f i s c a l y e a r ends on December  the d a t a submitted are l i k e l y to p e r t a i n t o p a r t s of  two  calendar years. (3)  SYSTEM OF CLASSIFICATION:  The system by which f i r m s  a r e c l a s s i f i e d I s based on the Standard I n d u s t r i a l  Classifi-  c a t i o n Manual i s s u e d by the Dominion Bureau o f S t a t i s t i c s . Where a company's a c t i v i t i e s a r e d i v e r s i f i e d , i t i s n o r m a l l y grouped  i n the I n d u s t r y where i t shows the g r e a t e s t volume  of s a l e s . (4)  DEFINITIONS: CASH:  In Canada T a x a t i o n S t a t i s t i c s , cash i s d e f i n e d  as cash on hand and i n bank d e p o s i t s a f t e r d e d u c t i n g o u t s t a n d i n g cheques or bank o v e r d r a f t s .  I t Is assumed that "bank  d e p o s i t s " r e f e r s t o both chequing and time d e p o s i t s . SALES:  In g e n e r a l ; t h i s term i n c l u d e s o n l y a c t u a l s a l e s  or revenue d e r i v e d from o p e r a t i o n s .  Capital profits,  inter-  branch or interdepartment s a l e s are excluded. (B)  MANIPULATION OF DATA. Cash and s a l e s f i g u r e s were c o l l e c t e d f o r each of the  s u b d i v i s i o n s of e l e v e n I n d u s t r i a l c l a s s e s .  To use the T r a n s -  p o r t a t i o n i n d u s t r i a l c l a s s as an example, cash and s a l e s t o t a l s were o b t a i n e d f o r the f o l l o w i n g e i g h t  subdivisions:  - 14 A i r Transport,  Water Transport,  1  Truck T r a n s p o r t ,  p o r t ; Urban T r a n s p o r t a t i o n and T a x i cabs'; other P i p e - l i n e s ; and Railways.  Average cash and  ^  The  same procedure was  Trans-  Transportation,  sales figures  were then c a l c u l a t e d f o r each of these e i g h t Subdivisions.  Bus  transportation  followed  for  s u b d i v i s i o n s of the other ten i n d u s t r i a l c l a s s e s and income or a s s e t c l a s s i n T a b l e s 5» 5A and The  6.  average f i g u r e s obtained were then used t o c a l c u l a t e a  r e g r e s s i o n equation; l i n e a r and  u s i n g the l e a s t - s q u a r e s  l i n e a r i n logarithms  between the average cash and To use  each  the T r a n s p o r t a t i o n  cash and  s a l e s f i g u r e s were computed.  group a g a i n as an example; average subdivisions  e t c . ; ) were used as o b s e r v a t i o n s  d e r i v i n g the r e g r e s s i o n equation. size classes  Ordinary  estimates of the r e l a t i o n s h i p  s a l e s f i g u r e s f o r each of the e i g h t  ( A i r ; Water T r a n s p o r t ;  method.  in  From the d a t a grouped  (the t o t a l Manufacturing I n d u s t r y ,  a l l Firms  grouped by A s s e t  c l a s s and  average cash and  s a l e s f i g u r e s were taken from each c l a s s  used as o b s e r v a t i o n s . were r e g r e s s e d  a l l Firms grouped by Income c l a s s )  When these f i g u r e s (cash and  the r e s u l t i n g r e g r e s s i o n e q u a t i o n i s our measure of e l a s t i c i t y of the demand f o r money w i t h r e s p e c t i n d u s t r y as a whole.  r e g r e s s i o n e q u a t i o n took the g e n e r a l l o g S where C =  and  sales)  i n l o g form, the r e g r e s s i o n c o e f f i c i e n t  the T r a n s p o r t a t i o n  by  of  the  to s a l e s f o r  In l o g a r i t h m s  the  form, l o g C = l o g a + b  the average cash balance, S =  the average  1. Each s u b d i v i s i o n i s d i v i d e d i n t o two f u r t h e r c a t e g o r i e s ; companies r e p o r t i n g a p r o f i t and companies r e p o r t i n g a l o s s . In t h i s study; s t a t i s t i c s f o r both p r o f i t and l o s s companies were added and an average was c a l c u l a t e d u s i n g t h i s t o t a l .  - 15 s a l e s volume and b = the e l a s t i c i t y o f cash w i t h to  sales.  Regression  respect  c o e f f i c i e n t s o f approximate u n i t y  i n d i c a t e t h a t there a r e n e i t h e r economies or diseconomies of s c a l e i n the use of cash i n a g i v e n i n d u s t r i a l  class.  To t e s t whether the e l a s t i c i t i e s obtained were s i g n i f i c a n t l y d i f f e r e n t from u n i t y , a t e s t o f the h y p o t h e s i s b = 1 was performed u s i n g the s t a t i s t i c b -  (2)  1  hT7  2  Where b i s the e l a s t i c i t y i n q u e s t i o n , r of d e t e r m i n a t i o n  that  i s the c o e f f i c i e n t  o f the r e g r e s s i o n e q u a t i o n and N i s the  number o f o b s e r v a t i o n s .  T h i s s t a t i s t i c has Student*s d i s -  t r i b u t i o n w i t h N - 2 degrees o f freedom. (C)  RESULTS The  f i n d i n g s o f the c r o s s s e c t i o n r e g r e s s i o n s a r e summar-  i z e d i n the t a b l e s a t the end of the chapter.  In general,  the r e s u l t s shown d e s c r i b e how w e l l the r e g r e s s i o n  equations  e x p l a i n the r e l a t i o n s h i p between the cash and s a l e s v a r i a b l e s and  the nature  o f the e l a s t i c i t i e s o f cash w i t h r e s p e c t t o  s a l e s which were obtained. TABLE I .  COEFFICIENTS OF DETERMINATION  ( r ) FOR 2  LOG. AND ARITHMETIC REGRESSIONS. The  c o e f f i c i e n t s of determination  g i v e an i n d i c a t i o n o f  how w e l l the c r o s s s e c t i o n e s t i m a t i o n s d e s c r i b e t h e r e l a t l o n (2)  M. R. S p i e g e l .  Schaum's O u t l i n e o f S t a t i s t i c s . Schaum P u b l i s h i n g Co. New York,  196l.  - 16 s h i p between the v a r i a b l e s i n that they i n d i c a t e how much of the v a r i a t i o n of o b s e r v a t i o n s from the r e g r e s s i o n l i n e i s e x p l a i n e d by the e q u a t i o n .  I t must be argued t h a t the  a r i t h m e t i c form of the approximation p r o v i d e s a b e t t e r exp l a n a t i o n , s i n c e r ' s f o r t h i s form were h i g h e r i n 26 out 2  o f the 31 s t a t i s t i c a l l y s i g n i f i c a n t equations. of d e t e r m i n a t i o n f o r the l o g equations ranged 0.98  w i t h a mean v a l u e o f  Coefficients from 0.37  to  o.S5 .  C o e f f i c i e n t s of d e t e r m i n a t i o n o b t a i n e d from the a r i t h metic equations ranged from 0.53  t o 0.99  w i t h a mean of  I t was found t h a t of the 42 r e g r e s s i o n s performed,  o.&b.  seven  of the l o g . and seven of the a r i t h m e t i c equations had coe f f i c i e n t s o f c o r r e l a t i o n ( r ) which d i d n o t d i f f e r c a n t l y from zero a t the .05  significance level.  signifi-  The S e r v i c e ;  Pood Products," and Finance and Investment c a t e g o r i e s account f o r most o f the n o n - s i g n i f i c a n t equations; although the c o e f f i c i e n t s f o r the Wholesale i n d u s t r y a r e f a i r l y low as well. 2 H i g h e s t r s were encountered  i n the d a t a c l a s s i f i e d by  s i z e c l a s s e s , the l a s t three c a t e g o r i e s i n Table I . TABLE I I .  ELASTICITIES OF CASH BALANCES WITH RESPECT TO SALES FOR SELECTED INDUSTRIAL SECTORS FOR THREE TAXATION YEARS.  E l a s t i c i t i e s of cash w i t h r e s p e c t t o s a l e s a r e equal t o the r e g r e s s i o n c o e f f i c i e n t s equations.  (b) o f the l o g . r e g r e s s i o n  The e l a s t i c i t i e s c a l c u l a t e d were a l l p o s i t i v e ;  w i t h a range of 0.54  t o 1.51  over a l l i n d u s t r i a l c l a s s e s  f o r a l l t h r e e y e a r s . W i t h i n some i n d u s t r i a l e l a s s e s , c o n s i d e r -  - 17 a b l e v a r i a t i o n was  noted over the t h r e e years s t u d i e d .  The Mining and Quarrying class-;* f o r example, went from an e l a s t i c i t y of about 1.0 than u n i t y i n  1958  and  i n 1957  i960.  to s i g n i f i c a n t l y greater The o v e r a l l mean e l a s t i c i t i e s ?  on the o t h e r hand; show l i t t l e v a r i a t i o n over the t h r e e y e a r s s t u d i e d and I n a l l cases are q u i t e c l o s e t o (See T a b l e  1.0  III).  (2) A f t e r a p p l y i n g the e f f i c i e n t s t i t was  ,  t ' test  ' t o the r e g r e s s i o n co-  found t h a t of the 34  statistically  s i g n i f i c a n t r e g r e s s i o n e q u a t i o n s , 26 had which c o u l d be c o n s i d e r e d t o be u n i t y .  elasticities Diseconomies  of  s c a l e were found i n t h r e e i n d u s t r i a l c l a s s e s ; C o n s t r u c t i o n  (1957? 1958)'? Wood ing  (1958, i960).  classes;  Products  (1958);  and M i n i n g and  Quarry-  Economies of s c a l e were found i n two  Petroleum Products  (i960)? and  Wholesale  (1957;  1958). TABLE  III.  DISTRIBUTION OF ELASTICITIES BY TAXATION YEAR.  The purpose o f t h i s Table i s t o show the e f f e c t o f changing economic c o n d i t i o n s i n the t h r e e years c o n s i d e r e d on the d i s t r i b u t i o n and average s i z e of the  elasticities.  The range of e l a s t i c i t i e s f o r each year i s as f o l l o w s :  1957 1958 i960 The (2)  0.76 0.54 0.67  -  1.38 1.47 1.51  o n l y d i f f e r e n c e noted between the peak years of  The »t' t e s t i s d e s c r i b e d i n p a r t (B) of t h i s Chapter.  1957  - 18 -  and  i960  and the trough year of  of e l a s t i c i t i e s i n the l a t t e r  1958  year.  was  a wider  dispersion  - 19 TABLE  I.  COEFFICIENTS OF DETERMINATION  ( r ) FOR LOG. AND 2  ARITHMETIC REGRESSIONS.  1957 Finance and I n v e s t ment Service  Log.  Arith.  0.79  (0.53)  1958 Log.  0.66  I960  Arith.  Log.  Arith.  (0.24)  (0.07)  (0.002)  (0.19) (0.37) (0.17)  (0.35)  (0.44)  0.43  T r a n s p o r t a t i on  0.77  0.98  0.77  0.98  0.74  0.97  Construction  0.94  0.98  0.96  0.99  (0.74)  (0.50)  Steel  0.82  0.97  0.75  0.85  0.61  0.85  0.94  0.98  0.94  0.99  0.76  0.98  0.93  0.98  0.97  0.99  0.98  0.99  0.41  0.15  (0.22)  Petroleum  Products  Wood Products Food Products  (0.015) 0.08  (0.156)  M i n i n g and Quarrying  0.67  0.58  0.86  0.64  0.85  0.68  Wholesale  0.37  0.66  0.43  0.62  (0.23)  (0.28)  Retail  0.86  0.97  0.82  0.97  0.88  0.98  T o t a l Manufacturing  0.98  0.99  0.98  0.98  0.98  0.99  A l l Firms (By I n come C l a s s )  0.99  0.98  0.98  0.99  0.98  0.99  A l l Firms (By A s s e t C l a s s )  0.98  0.99  0.97  0.98  0.98  0.99  1.  C o e f f i c i e n t s i n b r a c k e t s a r e from equations whose c o e f f i c i e n t of c o r r e l a t i o n d i d n o t d i f f e r s i g n i f i c a n t l y from zero a t the .05 s i g n i f i c a n c e l e v e l .  - 20 TABLE I I . ELASTICITIES OP CASH BALANCES WITH RESPECT TO INCOME FOR SELECTED INDUSTRIAL SECTORS FOR THREE TAXATION YEARS.  19$8  I960  1.32  1.23  (0.45)  (0.45)  (0.45)  0.94  Transportat1on  1.10  0.88  1.05  Construction  1.38*  1.45*  (1.25)  Steel  0.77  0.83  0.92  0.83  0.85  0.67**  Wood Products  1.24  1.27*  1.09  Food Products  (0.17)  (0.47)  (0.37)  Mining and Quarrying  0.98  1.47*  1.51*  Wholesale  0.76**  0.54**  Retail  0.83  0.81  0.88  T o t a l Manufacturing  1.04  1.05  0.92  A l l Firms  (By income c l a s s )  1.08  1.05  1.02  A l l Firms  (By a s s e t c l a s s )  1.09  1.06  1.04  Finance and  Investment  Service  Petroleum  1.  *  2.  **  3.  Products  (0.53)  Denotes e l a s t i c i t i e s s i g n i f i c a n t l y g r e a t e r than u n i t y at the .05 l e v e l . Denotes e l a s t i c i t i e s s i g n i f i c a n t l y at the .05 l e v e l .  l e s s than u n i t y  E l a s t i c i t i e s i n b r a c k e t s a r e from r e g r e s s i o n equations whose c o e f f i c i e n t of c o r r e l a t i o n d i d n o t d i f f e r s i g n i f i c a n t l y from zero a t the .05 l e v e l .  - 21 TABLE  III.  DISTRIBUTION OF ELASTICITIES  (b) BY TAXATION  YEAR.  i960 0.5 - 0.59 0.6 - 0.69 0.7 - 0.79  2  0.8  O.89  2  1  0.9 - 0.99  1  3  1.0 - 1.09  3  4  1.1 - 1.19  1  1.2 - 1.29  1  1.3 - 1.39  2  -  1.4 - 1.49 1.5 - 1.59 MEAN. STANDARD DEV.  1 1.03  1.04  1.00  0.2  0.33  0.2  - 22 CHAPTER  III  EVALUATION OF THE RESULTS (A)  SIGNIFICANCE OF THE REGRESSION EQUATIONS. One of the o u t s t a n d i n g d i f f e r e n c e s between the r e s u l t s  of  t h i s study and those found i n other s t u d i e s i s the r e l -  a t i v e l y h i g h number o f r e g r e s s i o n equations which a r e not s t a t i s t i c a l l y s i g n i f i c a n t , i . e . , equations whose r coe f f i c i e n t s do n o t d i f f e r s i g n i f i c a n t l y from zero a t the .05 level.  Almost 20$ of the r e g r e s s i o n estimates were found t o  be n o n - s i g n i f i c a n t , i n comparison w i t h o t h e r s t u d i e s where v i r t u a l l y a l l o f the r e g r e s s i o n s performed were claimed t o be significant.  T h i s r e s u l t can be e x p l a i n e d by the f a c t t h a t  t h e r e i s a b a s i c d i f f e r e n c e i n the manner i n which the c o r p o r a t i o n data i n Canada Tax S t a t i s t i c s and i t s American counterpart  ^  a r e organized.  As mentioned e a r l i e r  (Chapter I I , P a r t s A and B ) , the  d a t a f o r a g i v e n i n d u s t r i a l c l a s s i n Canada T a x a t i o n  Statistics  are grouped as t o type of business w h i l e the d a t a i n American S t a t i s t i c s of Income a r e grouped by a s s e t c l a s s .  The former  method r e s u l t s i n some cases I n a more random d i s t r i b u t i o n of o b s e r v a t i o n s when average cash and s a l e s f i g u r e s a r e r e g r e s s e d ,  2 which i n t u r n r e s u l t s i n r e l a t i v e l y lower r and r F u r t h e r , the grouping  figures.  of heterogeneous types of f i r m s  i n t o one i n d u s t r i a l c l a s s a l s o r e s u l t s i n a random d i s t r i b u t i o n of o b s e r v a t i o n s . under the Food Products (1)  Many d i s s i m i l a r f i r m s a r e aggregated and S e r v i c e groups i n Canada Tax  I n t e r n a l Revenue S e r v i c e , S t a t i s t i c s o f Income: C o r p o r a t i o n Income Tax Returns (Washington, U. S. Treasury)  - 23 2  S t a t i s t i c s and low r s r e s u l t when r e g r e s s i o n s are performed u s i n g s t a t i s t i c s from these c a t e g o r i e s .  Industrial classes  composed of more homogeneous types of f i r m s , Wood and Paper Products f o r example, y i e l d e d more s i g n i f i c a n t The h i g h r - squares  results.  obtained from r e g r e s s i o n s performed  on  d a t a c l a s s i f i e d by s i z e c l a s s can be a t t r i b u t e d to t h i s method of c l a s s i f i c a t i o n .  F u r t h e r , the s i m i l a r i t y i n the r e s u l t s f o r  a l l Firms grouped by A s s e t C l a s s and a l l Firms grouped by  In-  come C l a s s can be a t t r i b u t e d i n p a r t to the f a c t t h a t these d a t a are taken from approximately I n comparing the r  2  the same sample of f i r m s .  f i g u r e s of the l o g and the a r i t h m e t i c  equations f o r a g i v e n year, i t can be seen t h a t f o r most i n d u s t r i e s the a r i t h m e t i c form g i v e s a b e t t e r of the r e l a t i o n s h i p between cash and s a l e s .  approximation  The  relatively  h i g h e r lev:els of s i g n i f i c a n c e of the estimates of the o r d i n a r y l i n e a r equations i n d i c a t e t h a t hypotheses which suggest  a  roughly l i n e a r r e l a t i o n s h i p between cash and s a l e s should be g i v e n more a t t e n t i o n than the square-root (B)  hypothesis.  SALES ELASTICITIES I n the s i g n i f i c a n t r e g r e s s i o n equations, e l a s t i c i t i e s of  cash w i t h r e s p e c t t o s a l e s ranged from 0.54  to 1.51.  This  range i s c o n s i d e r a b l y g r e a t e r than those of o t h e r c r o s s s e c t i o n s t u d i e s , p a r t i c u l a r l y M e l t z e r ' s i n which a range of 0.88  to 1.2?  a range of  was  O.929  to  r e p o r t e d and Vogel and Maddala's where  1.077  was  given.  range of e l a s t i c i t i e s found here may the nature of the d a t a employed.  The r e l a t i v e l y wide a g a i n be e x p l a i n e d by  Sales e l a s t i c i t i e s  obtained  - 24 -  from the  'structured'  narrower range  (0.92  d a t a i n t h i s study had a much - 1.09)  than those obtained from  d a t a c l a s s i f i e d by i n d u s t r i a l t y p e s .  I t i s most l i k e l y  t h a t the e l a s t i c i t i e s i n o t h e r s t u d i e s (and from d a t a i n t h i s study) are very c l o s e t o 1.0 s t r u c t u r e d nature of the d a t a employed. Maddala  (1967) have n  the  certain  because of the As Vogel  and  observed.  .... although r e g r e s s i o n s r u n w i t h a s s e t s i z e o b s e r v a t i o n s f o r any i n d u s t r y or year y i e l d h i g h R - Squares and a s a l e s e l a s t i c i t y f o r cash c l o s e t o u n i t y , i t cannot be concluded t h a t l i q u i d a s s e t demand has been e x p l a i n e d or that there are no economies or diseconomies of s c a l e i n money h o l d i n g . These r e s u l t s can be a t t r i b u t e d t o the c l a s s i f i c a t i o n of the d a t a and miss p e c i f i c a t i o n from excluded v a r i a b l e s . n  To examine the e f f e c t d e s c r i b e d by Vogel and Maddala, average  cash and s a l e s f i g u r e s from each s i z e c l a s s were  p l o t t e d f o r s e v e r a l c l a s s e s o f d a t a grouped income c l a s s e s .  by a s s e t or  Average cash and s a l e s f i g u r e s f o r a l l  f i r m s grouped by Income c l a s s f o r example i n Table IV.  I t was  i960  are g i v e n as an -  found i n a l l cases t h a t  o b s e r v a t i o n s from the t h r e e l a r g e s t s i z e c l a s s e s are g i v e n much more weight  than o b s e r v a t i o n s from s m a l l e r  s i z e c l a s s e s when average  f i g u r e s are p l o t t e d , and i t was  thought a t f i r s t t h a t h i g h r - squares and u n i t i t i e s were caused by t h i s w e i g h t i n g . h y p o t h e s i s , r e g r e s s i o n s were performed  To t e s t  elastic-  this  f o r a l l data  grouped  by a s s e t or income c l a s s w i t h f i r s t the o b s e r v a t i o n s from the l a r g e s t s i z e c l a s s then the second l a r g e s t c l a s s omitted,  (2)  ' S t r u c t u r e d ' r e f e r s t o d a t a which are by a s s e t or income s i z e c l a s s e s .  classified  -  to  see I f t h i s would r e s u l t i n d i f f e r e n t r - squares o r  elasticities. two  -  2 5  I t was found, however, t h a t even w i t h the  l a r g e s t s i z e c l a s s o b s e r v a t i o n s removed, i n each case  the r - squares remained h i g h and the e l a s t i c i t i e s were  still  c l o s e t o u n i t y as i n the example below: STATISTICS PROM ALL FIRMS GROUPED BY ASSET CLASS -  i960 2 r  S t a t i s t i c s o b t a i n e d when o b s e r v a t i o n s from a l l 9 s i z e c l a s s e s were r e g r e s s e d  elasticity  O.98  1.04  0.98  1.04  O.98  1.03  S t a t i s t i c s obtained when l a r g e s t c l a s s was omitted S t a t i s t i c s w i t h two l a r g e s t s i z e c l a s s e s omitted S i n c e the s t a t i s t i c s  obtained from r e g r e s s i o n s performed  w i t h the two l a r g e s t s i z e c l a s s e s removed a r e n o t a p p r e c i a b l y d i f f e r e n t than those o b t a i n e d by r e g r e s s i n g a l l s i z e  class  o b s e r v a t i o n s the e f f e c t d e s c r i b e d by Vogel and Maddala can n o t be a t t r i b u t e d t o the g r e a t e r w e i g h t i n g g i v e n t o l a r g e s i z e c l a s s e s .  2 I t i s l i k e l y that high r  and u n i t e l a s t i c i t i e s a r e caused  by another e f f e c t which r e s u l t s when d a t a are grouped by s i z e class.  Table IV shows as an example the average cash, s a l e s  and a s s e t f i g u r e s f o r each s i z e c l a s s f o r Firms grouped by income c l a s s ,  i960.  I t can be seen t h a t the percent change  between s i z e c l a s s e s i n t h e average f i g u r e s a r e o f r o u g h l y the same order o f magnitude.  S i n c e the percent changes a r e  r o u g h l y the same; u n i t e l a s t i c i t i e s w i l l r e s u l t i f l o g s o f the average f i g u r e s a r e r e g r e s s e d .  - 26 TABLE DATA  FROM  ALL  IV  FIRMS  GROUPED  BY  INCOME  CLASS.  I960 Class (# thousand) Under 5  Average Cash 0.004  Average 0.12?  (50.0)  5 - 9.9  0.006  3,679  (184.0)  13,845 (149.2)  24,107 (266.0)  Over 5,000  4.874  9.671  1.005  (86.5)  (85/0)  (163.7) 1,000-4,999.9  2.613  5.277  0.381  (113.4)  (83.2)  (58.7)  500 - 999.9  1.224  2.852  0.240  (112.1)  (97.9)  (126.4)  250 - 499.9  0.577  1.441  0.106  (120.2)  (85.9)  (112.0) 100 - 249.9  0.262  0.775  0.050  46.3  (106.6)  (100.0) 50 - 99.9  0.179  0.375  0.025  (64.2)  (74.0)  (100)  25 - 49.9  0.109  0.215  0.012  Average Assets  (69.2)  (100) 10 - 24.9  Sales  (146.7) 34,157  (432.5)  (472.0) 137.91  181.90  Figures i n brackets are percent change between s t a t i s t i c s .  - 27 There does not appear to be any f a c t o r common to i n d u s t r i a l c l a s s e s which were shown t o have economies of s c a l e . While S a l e s e l a s t i c i t i e s s i g n i f i c a n t l y l e s s than 1.0  were  shown to e x i s t i n C o n s t r u c t i o n , Wood and Paper Products Mining,  no common p a t t e r n i s d i s c e r n i b l e i n such s t a t i s t i c s  as average Industry a s s e t s i z e , cash balances shown i n the f i g u r e s below:  Mining and Quarrying Wood and Paper Products.  Construction The  and  or s a l e s volumes,  ( F i g u r e s are i n $ M i l l i o n s )  Average Assets  Average Cash  4.598  0.138  0.703  0.017  0.282  0.015  Average Sales. 1.236  0.659 0.440  same l a c k of an o v e r a l l p a t t e r n i s seen i n the aggre-  gate s t a t i s t i c s of i n d u s t r i e s showing diseconomies of s c a l e . A d e t a i l e d examination of the p a t t e r n of payments, the c a p i t a l i n t e n s i t y and the a s s e t s i z e of the v a r i o u s subc l a s s e s of f i r m s i n each i n d u s t r y might r e v e a l some underlying relationships. While o n l y l i m i t e d i n f o r m a t i o n i s a v a i l a b l e from aggregate s t a t i s t i c s , some s i m i l a r i t i e s i n c a p i t a l i n t e n s i t y are found i n the s u b c l a s s e s  of the Wood and Paper Products I n d u s t r i a l  group shown i n Table V.  In 1958  this industry displayed  diseconomies of s c a l e i n cash h o l d i n g s . Having examined the r - squares and e l a s t i c i t i e s found i n our i n v e s t i g a t i o n , i t might be u s e f u l t o compare them w i t h the f i n d i n g s of two (1)  THE  other c r o s s s e c t i o n s t u d i e s .  MELTZER STUDY.  The  f o r m u l a t i o n of the r e g r e s s -  i o n estimates used i n t h i s t h e s i s i s e s s e n t i a l l y the same as M e l t z e r ' s s i n c e both are l o g . Cash = l o g a + b l o g s a l e s .  - 28 TABLE  V.  STATISTICS ILLUSTRATING THE PATTERN OF PAYMENTS AND DEGREE OF CAPITAL INTENSITY OF THE SUBCLASSES OF THE WOOD AND PAPER PRODUCTS INDUSTRIAL GROUP. Cash as % Total Assets  Receivables as % Total Assets  Building Payables as % and Equip- Total ment as % L i a b i l i t i e s . Total Assets  Plywood M i l l s  h  16  40  11  Sawmills  1  6  48  4  Furniture  3  21  38  13  5  11  48  5  2  3  58  3  Misc: Wood Products  2  18  41  10  Misc: Paper Products  4  12  52  8  Paper Bags and Boxes Pulp and Paper Mills  - 29 F o r h i s estimates M e l t z e r uses 126 i n d i v i d u a l r e g r e s s i o n s (14 i n d u s t r i e s i n 9 d i f f e r e n t years) w i t h a s s e t c l a s s  observ-  a t i o n s and f i n d s t h a t the demand f o r money i s a f u n c t i o n o f s a l e s , l i n e a r i n l o g a r i t h m s and u n i t e l a s t i c .  I n each of the  n i n e years and i n 12 o f the 14 i n d u s t r i e s the mean value o f the e l a s t i c i t i e s was g r e a t e r than 1.0.  E l a s t i c i t i e s of l e s s  than 1.0 were found i n 26 cases l a r g e l y concentrated i n particular industries.  M e l t z e r found some evidence t h a t  changes i n business c o n d i t i o n s r a i s e o r lower the estimates of the s a l e s e l a s t i c i t i e s of cash b a l a n c e s .  Years i n whloh  the business c y c l e reached a trough, 1938, 1946, and 1954, a l l had mean e l a s t i c i t i e s which were r e l a t i v e l y h i g h .  Conversely,  years i n which b u s i n e s s c o n d i t i o n s reached a peak had r e l a t i v e l y low mean e l a s t i c i t i e s . The r e s u l t s o f t h i s study do n o t e n t i r e l y agree w i t h M e l t z e r * s f i n d i n g s i n s p i t e o f the f a c t t h a t the average all  elasticities for  i n d u s t r i e s i n the years examined were approximately u n i t y  (see Table I I I ) .  The economies and diseconomies  of scale  found here a r e t o o s i g n i f i c a n t t o a l l o w us t o s t a t e , as M e l t z e r does, t h a t the " u n i t a r y " h y p o t h e s i s e x p l a i n s t h e demand f o r money. (2)  THE VOGEL AND MADDALA STUDY,.  These authors  contend  t h a t both the Baumol - T o b i n and the M e l t z e r models a r e e s s e n t i a l l y m o d i f i c a t i o n s o f the c e n t r a l t h e o r y t h a t m a r g i n a l r a t e s of r e t u r n , though c o n s t r a i n e d by wealth, d i s c o u n t e d by r i s k , and i n f l u e n c e d by payments p a t t e r n s and c o s t s o f f i n a n c i a l t r a n s a c t i o n s , a r e equated  f o r various assets.  Thus  attempts  - 30 to d i s t i n g u i s h u n e q u i v o c a l l y  between the two  on t h e o r e t i c a l grounds are somewhat beside Further, the use  models, even  the  point.  the authors r a i s e the e m p i r i c a l q u e s t i o n of only the s a l e s v a r i a b l e can a l l o w  d e s c r i m i n a t i o n among the v a r i o u s models.  s p e c i f i c e m p i r i c a l questions  statistical  section  on answering  of economies o f s c a l e i n cash  balances,' s u b s t i t u t i o n between money and government i t i e s ; and variables.  the i n f l u e n c e of i n t e r e s t r a t e s and  log Y  =  a  secur-  other  R e g r e s s i o n estimates were made f o r 14  s i z e c l a s s e s w i t h i n 16  how  (3)  In view of the above l i m i t a t i o n s of cross a n a l y s e s ? Vogel and Maddala concentrate  of  asset  i n d u s t r i e s u s i n g the form: +  l o g Sales  +  Dummy v a r i a b l e  where Y i s a l t e r n a t e l y cash and government s e c u r i t i e s and Dummies are i n t r o d u c e d  a l t e r n a t e l y f o r asset s i z e class  and  industrial class. The _nity  s a l e s e l a s t i c i t i e s of cash were found to be about  (0.995) when  g r e s s i o n equation," M e l t z e r and  i n d u s t r y dummies were used i n the r e about the same as those r e p o r t e d  obtained  from ' s t r u c t u r e d  1  by  d a t a i n t h i s study.  When dummies were i n t r o d u c e d which i n c r e a s e d i n s i z e w i t h i n c r e a s i n g a s s e t c l a s s e s ; the e l a s t i c i t i e s were s u b s t a n t i a l l y reduced to about  0.281.  From t h i s l a t t e r r e s u l t the authors  conclude t h a t i n some other s t u d i e s the i n f l u e n c e of a s s e t s i z e c l a s s d i f f e r e n c e s have been i n c o r r e c t l y a t t r i b u t e d to  (3)  The s a l e s v a r i a b l e i s used as an approximation f o r both t r a n s a c t i o n s and wealth i n v a r i o u s s t u d i e s .  - 31 the s a l e s v a r i a b l e ; and s t a t e f u r t h e r t h a t a s t r o n g argument can be made f o r economies of s c a l e i n money demand. The  empirical r e s u l t s of t h i s t h e s i s are not d i r e c t l y  comparable t o those obtained  by Vogel and Maddala because  of the d i f f e r e n t f o r m u l a t i o n s speculate?  employed.  I t i s possible to  however, t h a t i f s i z e c l a s s dummy v a r i a b l e s had  been used i n the r e g r e s s i o n s  performed u s i n g s t r u c t u r e d  the r e s u l t i n g e l a s t i c i t i e s may have been c o n s i d e r a b l y (C)  data,  lower.  EFFECT OF CHANGES IN ECONOMIC CONDITIONS.  Although i n t e r e s t r a t e s a r e assumed t o be constant  ina  c r o s s s e c t i o n estimate? changing economic c o n d i t i o n s between years c a n be expected t o a f f e c t an i n d u s t r y ' s  elasticities.  One might expect t h a t the s i z e o f the e l a s t i c i t i e s would  vary  I n v e r s e l y w i t h i n t e r e s t r a t e s s i n c e f i r m s would be encouraged t o s h i f t funds from cash balances i n t o short-term  securities  when y i e l d s a r e i n c r e a s i n g ? and t o add t o cash balances i f y i e l d s decrease. With regard  t o I n d i v i d u a l i n d u s t r i e s , the e l a s t i c i t i e s  tended t o vary c o n s i d e r a b l y  over the three sample years w i t h  no d i s t i n c t p a t t e r n emerging i n r e l a t i o n t o peak and trough years.  T h i s r e s u l t i s probably due i n p a r t t o the f a c t  that  although T a x a t i o n S t a t i s t i c s p u b l i s h e s d a t a f o r a g i v e n  cal-  endar y e a r ? there i s a d i s p e r s i o n o f corporate  year-ends  throughout the year? so t h a t the e f f e c t o f changes i n p r e v a i l i n g interest rates i s less noticeable.  F u r t h e r ; the  e f f e c t o f I n t e r e s t r a t e changes on a f i r m ' s mix o f cash and marketable s e c u r i t i e s v a r i e s w i t h the s i z e o f the f i r m .  - 32 Firms o f l a r g e a s s e t s i z e w i t h l a r g e h o l d i n g s o f cash can he expected t o r e a c t more n o t i c e a b l y t o changes i n the i n t e r e s t r a t e s on marketable  s e c u r i t i e s , while firms with  s m a l l cash balances may n o t f i n d i t economical t o i n v e s t i n cash s u b s t i t u t e s .  The d a t a f o r a g i v e n I n d u s t r i a l  c l a s s i s an average o f the cash and s a l e s f i g u r e s f o r f i r m s of many d i f f e r e n t a s s e t s i z e s , and changes i n these f i g u r e s caused by p r e v a i l i n g economic c o n d i t i o n s a r e hidden by t h e averaging process. (D)  COMPARISON OF CROSS SECTION AND TIME SERIES RESULTS  I t has been suggested by s e v e r a l authors ( G r u n f e l d , 1961, and Kuh, 1959) t h a t the f i n d i n g s o f a c r o s s s e c t i o n study should not be accepted a t f a c e v a l u e as an e x p l a n a t i o n o f behaviour.  Kuh suggests t h a t b i a s e s from v a r i a b l e s excluded  from the approximation procedure w i l l have s t r i k i n g l y  differ-  ent e f f e c t s on time s e r i e s and c r o s s s e c t i o n s , and t h a t as a r e s u l t , c r o s s s e c t i o n estimates cannot be taken as a v a l i d approximation without a comparison w i t h time s e r i e s r e s u l t s from a uniform group o f f i r m s .  While d a t a found i n Canada  T a x a t i o n S t a t i s t i c s i s taken from a sample o f f i r m s which changes from year t o year, i t i s i n t e r e s t i n g t o compare the time s e r i e s performance  o f the c a s h / s a l e s r a t i o s w i t h the  cross s e c t i o n e l a s t i c i t i e s .  This information i s given f o r  s t a t i s t i c a l l y s i g n i f i c a n t equations i n Table V I . I f the time s e r i e s r a t i o s a r e t o support c r o s s s e c t i o n e l a s t i c i t i e s which i n d i c a t e economies o f s c a l e one would expect t h a t i f an I n d u s t r y ' s s a l e s r i s e from one year t o  - 33 the next, the cash/sales  r a t i o should  decline.  If dis-  economies e x i s t ; an i n c r e a s e i n s a l e s should be by an i n c r e a s e i n the c a s h / s a l e s  figure.  accompanied  Third, i f e l a s t -  i c i t i e s are approximately u n i t y ? the cash/sales  ratio  should  remain unchanged. R e f e r r i n g t o T a b l e VI? i t can be seen t h a t i n s i x out ten cases cross s e c t i o n r e s u l t s are g e n e r a l l y w i t h the time s e r i e s r a t i o s .  In two  consistent  cases; Mining  and  Petroleum Products, time s e r i e s r a t i o s show a t r e n d to t h a t suggested by the e l a s t i c i t i e s and  of  i n two  opposite  other  S t e e l and Finance the comparison i s i n c o n c l u s i v e .  One  classes, ob-  v i o u s c o n t r a d i c t i o n , f o r example? i s seen i n the r e s u l t s f o r Mining i n 1958  where an e l a s t i c i t y of 1.4?  d i c a t i n g diseconomies. 1958,  the c a s h / s a l e s  economies of s c a l e .  was  While s a l e s i n c r e a s e d  found, i n from 1957  to  r a t i o a c t u a l l y decreased i n d i c a t i n g The  c o n f l i c t i n g r e s u l t s of the  two  e s t i m a t i o n methods can be a t t r i b u t e d t o the b i a s e s mentioned p r e v i o u s l y which a r i s e from the e x c l u s i o n o f dynamic v a r i a b l e s such as i n t e r e s t r a t e s .  The  main reason estimates  d i f f e r i s that time s e r i e s t y p i c a l l y r e f l e c t l o n g run ments whereas c r o s s s e c t i o n s r e f l e c t s h o r t e r run  adjust-  reactions  so t h a t dynamic s p e c i f i c a t i o n e r r o r s t h a t tend t o b i a s time s e r i e s r e s u l t s downwards are l e s s observable i n c r o s s  sections  (Kuh, 1959). The  e f f e c t of changes i n p r e v a i l i n g economic  conditions  i s more n o t i c e a b l e i n the time s e r i e s r a t i o s t h a n i n the cross s e c t i o n r e s u l t s .  The  cash/sales  r a t i o f o r a l l manu-  - 34 TABLE  VI.  COMPARISON OP CROSS SECTION ELASTICITIES WITH TIME SERIES CASH/SALES  RATIOS.  19^7  1218  Finance and Investment  Elasticities Cash/Sales % A Sales  1.32 0.292 +17.0  1.23 0.247 +8.7  T r a n s p o r t a t i on  Elasticities Cash/Sales % A Sales  1.10 0.067 +7.5  0.88 0.066 0  Construction  Elasticities Cash/Sales % A Sales  Steel  1?60 0.234 +10.3  (0.45) 0.29 -13.7  0.053 +12.0  1.05 0.056 +3.4  0.029 +15.3  1.45 1. 0.036 0.035 +5.3 +5.5  (1.25) 0.028 +4.3  Elasticities Cash/Sales % A Sales  0.77 0.029 +9.1  0.83 0.043 -7.6  0.92 0.035 -6.5  Petroleum  Elasticities Cash/Sales % A Sales  0.83 0.024 -33.0  0.85 0.024 -4.1  Wood and Paper  Elasticities Cash/Sales % A Sales  1.24 0.018 -0.3  Mining  Elasticities Cash/Sales % A Sales  0.98 0.133 -1.7  Wholesale  Elasticities Cash/Sales % A Sales  0.76 0.016 +3.0  1.27 1. 0.025 -4.8 1.47 1. 0.112 +1.7 0.54 20.016 0  Retail  Elasticities Cash/Sales % A Sales  0.83 0.017 +9.0  Total Manufacturing  Elasticities Cash/Sales % A Sales  1.04 0.028 -0.4  1.  Denotes  Diseconomy o f S c a l e  2.  Denotes  Economy o f S c a l e  3.  E l a s t i c i t i e s i n b r a c k e t s a r e from r e g r e s s i o n equations whose c o e f f i c i e n t s o f c o r r e l a t i o n d i d not d i f f e r s i g n i f i c a n t l y from Zero a t the .05 l e v e l .  1.381*  0.032 +12.8  0.020 +24.1  0.67 * 0.014 -6.0 1.09 0.024 -8.9  0.119 +7.4  1.51 0.105 +3.6  0.016 +6.0  (0.53) 0.015 +3.0  0.81 0.018 +5.0  0.017 +9.0  0.88 0.016 +1.0  1.05 0.034 -1.5  0.027 +8.5  0.92 0.025 +3.5  s  0.020 +15.0  - 35 -  -facturing firms rose from .028 to .034 from 1957 to 1958.  The increase i n t h i s r a t i o can be explained by  a decline i n the y i e l d s of marketable s e c u r i t i e s accompanying the decline i n economic a c t i v i t y i n the latel957 and 1958.  This e f f e c t i s more noticeable i n the time  series r e s u l t s since t h i s form of estimation better r e f l e c t s the influence of dynamic variables such as interest rates.  - 36 CHAPTER  IV.  C O N C L U S I O N S . The r e s u l t s of t h i s study have shown t h a t , t o a approximation, there are economies and diseconomies s c a l e i n the demand f o r cash i n some s e c t o r s of industry.  first of  Canadian  Although the o v e r a l l average e l a s t i c i t i e s f o r  a l l s e c t o r s i n the years t e s t e d were approximately u n i t y , c r o s s s e c t i o n and time s e r i e s r e s u l t s f o r i n d i v i d u a l i n d u s t r i a l c l a s s e s have shown t h a t i n s e v e r a l cases cash balances do not v a r y i n p r o p o r t i o n to s a l e s . Because of the wide range of the e l a s t i c i t i e s o b t a i n e d , the r e s u l t s d e s c r i b e d here cannot be s a i d t o support e i t h e r the Baumol - T o b i n or the M e l t z e r h y p o t h e s i s .  Few  economies of  s c a l e of the order p r e d i c t e d by the Baumol - T o b i n h y p o t h e s i s were found i n the c r o s s s e c t i o n e s t i m a t e s , although t h e r e i s some evidence i n the time s e r i e s r a t i o s that some e l a s t i c i t i e s may  be over estimated or hidden by the c r o s s s e c t i o n a p p r o x i -  mation.  Because of the d i f f i c u l t i e s i n a s s e s s i n g the e x t e n t  Ii, of the b i a s i n h e r e n t i n the approximation methods, the main c o n c l u s i o n s t a t e d above must be q u a l i f i e d as a f i r s t  approx-  imation. The e x i s t e n c e of economies and diseconomies suggests t h a t M e l t z e r s ' u n i t a r y f  1  of s c a l e  h y p o t h e s i s does not  ex-  p l a i n the demand f o r cash f o r the economy as a whole. The r e s u l t s of the study do not d i s c l o s e diseconomies s c a l e of the magnitude p r e d i c t e d by Friedman.  Further,  changes i n economic c o n d i t i o n s d i d not a f f e c t the o v e r a l l average  income e l a s t i c i t i e s of the demand f o r cash i n the  sectors studied.  of  - 37 B I B L I O G R A P H A l l e n , H. G. D.  Y. ^Mathmatloal A n a l y s i s f o r Economists. M a c M i l l a n & Co., London, 1953. 17  Baumol, W.,  "The T r a n s a c t i o n s Demand f o r Cash: An Inventory T h e o r e t i c Approach." Quarterly Journal of Economics. November 1952.  Brunner, K. and M e l t z e r , A.  "Economies o f S c a l e i n Cash Balances Reconsidered." Quarterly Journal of Economics. A»a • <°t ^ 7  De A l e s s i , L.  Department of N a t i o n a l Revenue  "The Demand f o r Money, a Cross S e c t i o n Study o f B r i t i s h Business Firms." Economica, August 1966. taxation Statistics P a r t Two. Queens P r i n t e r , Ottawa, 1959,  I960, 1962, 1966.  E z e k l e l , M. and Fox, K.  F r a z e r , W. J .  F r i e d l a n d , S.  Methods o f C o r r e l a t i o n and Regression A n a l y s i s . T h i r d Edit. John Wilkey & Son, New York, 1965. "The F i n a n c i a l S t r u c t u r e o f Manufacturing C o r p o r a t i o n s and the Demand f o r Money: Some E m p i r i c a l F i n d i n g s . " J o u r n a l o f P o l i t i c a l Economy. April 1964. The Economics o f Corporate Finance. Prentice H a l l Inc., New J e r s e y , 1966.  - 38 B I B L I P G B A P H Y Friedman,  M.  - Cont'd:  "The Demand f o r Money: Some T h e o r e t i c a l and E m p i r i c a l Results." J o u r n a l of P o l i t i c a l Economy, August 1959.  G r u n f e l d , Y.  "The I n t e r p r e t a t i o n o f Cross S e c t i o n E s t i m a t e s i n a Dynamic Model." Econometrlca. J u l y 1961.  Kuh, E.  "The V a l i d i t y o f Cross S e c t l o n a l l y Estimated Behavior Equations i n Time Series Applications." Econometrlca. A p r i l 1959.  L a i d l e r , D.  "Some Evidence o f the Demand f o r Money." J o u r n a l o f P o l i t i c a l Economy. February 1966.  M e l t z e r , A. H.  "The Demand f o r Money: A Cross S e c t i o n Study o f Business Firms." Q u a r t e r l y J o u r n a l o f Economics. August 1963.  M i l l e r , H. D. and Orr, D.  "A Model o f the Demand f o r Money by Firms." Q u a r t e r l y J o u r n a l o f Economics. August 1966.  Peterson, W. C.  Income, Employment and Economic Growth. Norton and Co. New York,  1962.  Selden, R. T.  "The Postwar R i s e i n the V e l o c i t y o f Money: A Sectoral Analysis." Journal of Finance. December 1961.  - 39 B I B  L I P G R A P H  Sprenkle, C. M.  Y  -  Cont"d.  "Large Economic U n i t s , Banks and t h e T r a n s a c t i o n s Demand f o r Money." Q u a r t e r l y J o u r n a l o f Economics August 1966.  Teigen, R. C.  "The Demand and Supply f o r Money." Eoonometrica 1964.  Tobin, J .  "The I n t e r e s t E l a s t i c i t y o f the T r a n s a c t i o n s Demand f o r Cash." Review o f Economics and S t a t i s t i c s . August 1956.  Vogel, R.C. and Maddala, G.S.  "Cross S e c t i o n E s t i m a t e s o f L i q u i d Asset Demand by Manufacturing C o r p o r a t i o n s . " December 1967.  Whalen, E. C.  "A Cross S e c t i o n Study o f Business Demand f o r Gash." J o u r n a l o f Finance, September 1965.  W i n i a t a , W.  "The Income E l a s t i c i t y o f the Demand f o r Money by Business Firms: An Empirical Test." Unpublished 1966.  t  APPENDIX AN  I.  OUTLINE OF THE DERIVATION OF BAUMOL S 1  CASH INVENTORY MODEL. By keeping p a r t of i t s a s s e t s i n the form of cash a f i r m i n c u r s c o s t s s i m i l a r t o those a s s o c i a t e d w i t h an i n v e n t o r y of any other a s s e t , i . e . h o l d i n g and o r d e r i n g costs.  Baumol a p p l i e s the f a m i l a r optimum l o t s i z e i n -  ventory model to minimize the c o s t s i n v o l v e d i n h o l d i n g cash. The focus of the author's a n a l y s i s i s on the t r a n s a c t i o n s demand f o r cash d i c t a t e d by r a t i o n a l  behaviour,  which means h o l d i n g the cash balance t h a t w i l l do the job a t minimum c o s t .  Baumol f i r s t assumes a s t a t e i n which  t r a n s a c t i o n s are p e r f e c t l y f o r e s e e n and occur i n a steady stream;" so t h a t i n the course of a g i v e n p e r i o d a f i r m w i l l pay out |T c o n t i n u o u s l y . Cash i s o b t a i n e d e i t h e r by borrowing  or s e l l i n g Investments;  i n e i t h e r case the  int-  e r e s t c o s t (or i n t e r e s t o p p o r t u n i t y c o s t ) i s $1 per d o l l a r per p e r i o d . throughout  Cash i s withdrawn i n l o t s of |C evenly  the y e a r and each time a withdrawal  spaced  i s made a  f i x e d "broker's f e e " of $b must be p a i d (b i n c l u d e s a l l noni n t e r e s t c o s t s of borrowing or making a cash w i t h d r a w a l ) . In t h i s s i t u a t i o n any value of C _ T w i l l enable the f i r m t o meet i t s payments e q u a l l y w e l l p r o v i d e d withdrawals are made o f t e n enough. withdrawals  Thus, the f i r m w i l l make T/C  over the course of the year a t a t o t a l c o s t  i n "broker's f e e s " of bT/C.  S i n c e cash i s spent i n a  steady stream between withdrawals, the average h o l d i n g s  - 41 are  $C/2. The annual i n t e r e s t c o s t o f h o l d i n g cash w i l l then be  iC/2.  Thus the t o t a l  c o s t of u s i n g cash f o r the year w i l l  be (1)  bT C  +  iC 2  To determine the optimum value o f C s e t the d e r i v a t i v e of  (1) w i t h r e s p e c t t o C equal t o zero t o o b t a i n -bT  A  or  (2)  +  Z  C  1  =  0  2  =  j  2bT  T h i s model a p p l i e s t o two cases:  Where cash i s o b t a i n e d  from i n v e s t e d c a p i t a l and where cash i s o b t a i n e d from borrowing  i n a n t i c i p a t i o n of f u t u r e r e c e i p t s .  One o t h e r case i s  p o s s i b l e where r e c e i p t s precede e x p e n d i t u r e s .  Here, the  f i r m has the o p t i o n of w i t h h o l d i n g some o r a l l o f i t s r e c e i p t s from i n v e s t i n g and simply keeping the cash u n t i l it  i s needed.  Baumol shows t h a t as i n the two p r e v i o u s  cases the optimum cash balance a f t e r t h e i n i t i a l ing of  cash h o l d -  i s used up w i l l vary w i t h the square r o o t o f the volume transactions.  Investment R=  The optimum amount t o be w i t h h e l d from  i s shown t o be C + T k  w  +  k d  i where k^. and k^ a r e constant terms a s s o c i a t e d w i t h the "broker's f e e s " f o r withdrawing and i n v e s t i n g cash r e s pectively.  The author s t a t e s t h a t even though R v a r i e s  more i n p r o p o r t i o n t o T than does C, the g e n e r a l nature o f  - hz the r e s u l t s I s u n a f f e c t e d . A f t e r o u t l i n i n g the model Baumol concedes t h a t  (2) i s  an o v e r s i m p l i f i c a t i o n and t h a t some of the u n d e r l y i n g assumptions, namely t h a t the f i r m ' s disbursements a r e constant  over time, t h a t there i s one r e l e v a n t i n t e r e s t  r a t e and that the "broker's f e e " i s constant  or varies  l i n e a r l y w i t h the sum i n v o l v e d , may be i n v a l i d . propose, however, t h a t (2) may be c o n c e p t u a l l y with respect  He does accurate  to the economy as a whole and t h a t the demand  f o r cash r i s e s l e s s than i n p r o p o r t i o n w i t h the volume of t r a n s a c t i o n s , so t h a t there a r e , i n e f f e c t , economies of l a r g e s c a l e i n the use o f cash.  E q u a t i o n (2) a l s o  confirms that the r a t i o n a l t r a n s a c t i o n s demand f o r cash w i l l be  >  0.  

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