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Aggregate production function and technological change in Canadian agriculture, 1935-65. McPherson, Allister John 1970

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THE  AGGREGATE PRODUCTION FUNCTION AND TECHNOLOGICAL CHANGE IN CANADIAN AGRICULTURE, 1935-65  by ALLISTER JOHN MCPHERSON B.Sc,  U n i v e r s i t y o f A l b e r t a , 1966  A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE i n the Department of A g r i c u l t u r a l Economics  We accept t h i s t h e s i s as conforming required  THE  t o the  standard  UNIVERSITY OF BRITISH COLUMBIA June, 1970  In p r e s e n t i n g t h i s t h e s i s  in p a r t i a l  f u l f i l m e n t of the  requirements  f o r an advanced degree at the U n i v e r s i t y of B r i t i s h Columbia,  I agree  t h a t the L i b r a r y s h a l l make i t f r e e l y , a v a i l a b l e f o r  and  Study.  I further  reference  agree that p e r m i s s i o n f o r e x t e n s i v e  c o p y i n g of  this  t h e s i s f o r s c h o l a r l y purposes may be granted by the Head of my Department or by nils r e p r e s e n t a t i v e s .  It  i s understood t h a t  copying  or p u b l i c a t i o n of t h i s t h e s i s f o r f i n a n c i a l g a i n s h a l l not be a l l o w e d w i t h o u t my w r i t t e n  Department of  permission.  Agricultural  The U n i v e r s i t y of B r i t i s h Vancouver 8, Canada Date June,  1970  Economics  Columbia  ABSTRACT A study was  undertaken  t o i n v e s t i g a t e the macro pro-  d u c t i o n r e l a t i o n s h i p s i n Canadian primary d u r i n g the 1935-65 p e r i o d .  agriculture  S p e c i f i c a l l y , the problem  t o measure s i m u l t a n e o u s l y the r a t e o f disembodied  was  techno-  l o g i c a l change and t e c h n o l o g i c a l change embodied i n machinery and implements, and m a t e r i a l  inputs.  To estimate t e c h n o l o g i c a l change, r e g r e s s i o n  esti-  mates were obtained f o r a l i n e a r homogeneous Cobb-Douglas p r o d u c t i o n f u n c t i o n , where r e a l gross a g r i c u l t u r a l output per person employed was  the dependent v a r i a b l e , and a time  index, weather index, and the annual f l o w o f r e a l c a p i t a l services  ( i n c l u d i n g m a t e r i a l i n p u t s ) per person  were the independent  variables.  The data, which  employed consisted  o f time s e r i e s o f t h i r t y - o n e annual o b s e r v a t i o n s , was  de-  r i v e d mainly from p u b l i c a t i o n s o f the Dominion Bureau o f Statistics. was  The r a t e o f disembodied  technological  change  estimated d i r e c t l y by s p e c i f y i n g a term which allowed  f o r s h i f t s i n the p r o d u c t i o n f u n c t i o n over time.  To mea-  sure the r a t e o f embodied t e c h n o l o g i c a l change, which assumed t o be capital-augmenting i n the v i n t a g e  was  sense,  s e v e r a l a l t e r n a t i v e v a l u e s f o r the improvement i n the productive  q u a l i t y o f machinery and implements, and  i n p u t s were imposed on the o r i g i n a l data s e r i e s .  material Based on  these a l t e r n a t i v e s , a m a t r i x of r e g r e s s i o n r e s u l t s was  ob-  t a i n e d , and the t r u e value o f the r a t e o f embodied technol o g i c a l change was sion.  i n f e r r e d by  choosing the " b e s t "  regres-  In a d d i t i o n , s e v e r a l a l t e r n a t i v e models were  investigated. When disembodied and  embodied t e c h n o l o g i c a l change  were s p e c i f i e d simultaneously,  the " b e s t " estimate o f  annual r a t e o f disembodied t e c h n o l o g i c a l change was  the 1.76  per cent, w h i l e embodied t e c h n o l o g i c a l change i n m a t e r i a l i n p u t s was was  estimated at 3*5  to 4»0  per cent  annually.  There  no evidence o f a p o s i t i v e r a t e o f embodied t e c h n o l o g i c a l  change i n machinery and However, i t was r e s u l t should be  implements i n any  o f the  regressions.  concluded t h a t t h i s a p r i o r i unexpected considered  s u b s t a n t i a l l y biased.  TABLE OF CONTENTS CHAPTER I.  PAGE 1  PRODUCTIVITY AND TECHNOLOGICAL CHANGE Purpose of the Study  1  Productivity  2  Technological Change  5  Productivity Change i n Canadian Agriculture  . .  12  The Problem II.  7  CONCEPTUAL FRAMEWORK FOR MEASURING TECHNOLOGICAL CHANGE  17  Neutrality of Technological Change . . . . . . .  17  Disembodied Technological Change . .  21  Embodied Technological Change  . .  23  Simultaneous Embodied and Disembodied 33  Technological Change  III.  Economies of Scale and Non-neutrality  36  Some Problems and Alternatives  40  METHOD OF ANALYSIS AND MEASUREMENT OF VARIABLES Model f o r Estimating Technological Change Measurement of the Variables  .  ...  46 46 52  Gross a g r i c u l t u r a l output (Q)  52  Weather index (w)  54  Labor (L)  56  Flow of c a p i t a l services (K)  59  V  CHAPTER IV.  PAGE 73  EMPIRICAL RESULTS Introduction  73  Results of the Basic Model  75  Model 1(a)  76  Model 1(b)  BO  Model 1(c)  61  Discussion of Model I  S3  Model with a l l Technological Change Embodied . .  67 66  Model II Model to Relax the Assumption of Constant Returns to Scale  69  Model I I I  90  Alternative Models to Relate Potential and Actual Output  . . . . . . .  91  Model IV(a)  91  Model IV (b)  92  Testing the Production Function f o r Stability-  V.  Over Time  93  Model V  94  SUMMARY AND CONCLUSIONS Summary Conclusions  9$ 96 101  Implications and Suggestions f o r Further Research  105  vi CHAPTER  PAGE  BIBLIOGRAPHY  10S  APPENDIX  115  LIST OF TABLES TABLE I.  PAGE Summary of Estimated Productivity Change i n Canadian Agriculture  II.  13  Gross Investment i n Machinery and Implements, Canadian Agriculture, 1921-65  III.  66  C o e f f i c i e n t s of Multiple Determination and Standard Errors of the Estimate f o r Model 1(a)  IV.  u t  e  f +  S^  2  1 L  - K e J , r S ^ = 0 . 0 , 1935-65 a  a  D  VII.  f +  1 _ a  a  f +  w f h w  X  a  a  129  Regression Estimates f o r Model 1 ( c ) :  2  Q=Ae e S^ L K , fWo.O, 1935-65 Regression Estimates f o r Model I I : f +  h w  1 _ a  a  130  2  Q=Ae S** f+  XI.  w f h w  Regression Estimates f o r Model 1(b): 2 Q=Ae e S L - K , iWo.O, 1935-65  u t  X.  119  Regression Estimates f o r Model 1 ( a ) : 2 Q=Ae e S L K , f t = - 0 . 0 1 - . 0 3 , 1935-65 . . 120  u t  IX.  95  116  Symbols Used i n the Models  u t  VIII.  ..  Time Series Data f o r Canadian Agriculture, 1935-65  VI.  7  Dummy Variables Specified f o r Model V i : Q=Ae  V.  7  hw  L  1 _ a  K , ^=0.0, 1935-65 a  Regression Estimates f o r Model I I I : 2 Q=Ae e ^ L K , rWO.O, 1935-65 u t  f +  h w  b  a  131  132  viii TABLE XII.  PAGE Regression Estimates f o r Model IV(a): Q » = A e L " K , /Uo.O, ut  XIII.  1  a  a  ut  f  w  1  a  a  rUo.O, 1935-65  134  Regression Estimates f o r Model V: Q ^ A e ^ e ^ ^ ^ L - ^ ^ , A^=0.0, 1  XV.  133  Regression Estimates f o r Model IV(b): Q=Ae e -s/ L - K ,  XIV.  1935-65  1935-65 . . 135  Regression Estimates f o r Model 1(a): Q ^ A e ^ e ^ S ^ ^ V - V ^ ^ O . O , f o r the  1935-49  and  1950-65 Subperiods  136  LIST OF FIGURES FIGURE  PAGE  1.  Factor  P r o p o r t i o n s and P r o d u c t i v i t y Change  2.  T e c h n i c a l l y E f f i c i e n t Combinations o f Labor and C a p i t a l Inputs a t Two L e v e l s  3.  P r o d u c t i v i t y Changes over Time  o f Technology  . . . .  . . .  4  5 13  ACKNOWLEDGEMENTS The author wishes t o g r a t e f u l l y  acknowledge the  generous assistance and guidance provided by h i s thesis supervisor, Dr. G. R. Winter.  In addition, the stimula-  t i n g i n t e l l e c t u a l environment provided by the s t a f f and fellow graduate students at the University of B r i t i s h Columbia was extremely motivating and enjoyable. Special appreciation i s extended to the author*s wife, Maria, whose assistance, patience and encouragement contributed immensely to the successful completion of t h i s study.  CHAPTER I PRODUCTIVITY AND I.  TECHNOLOGICAL CHANGE  PURPOSE OF THE STUDY  The purpose of t h i s study was to apply macroeconomic concepts to the measurement of technological change i n Canadian agriculture during the period 1 9 3 5 - 6 5 *  An  attempt was made to measure three separate kinds of techn o l o g i c a l change: technological change r e f l e c t e d i n the improved productive quality of machinery and implements, technological change r e f l e c t e d i n the improved productive quality of material inputs, and a l l other technological change derived as a r e s i d u a l . Technological change may  be regarded as an advance  i n technology which i s : ( l ) knowledge used by productive units (firms or farms i n t h i s case) regarding the p r i n c i p l e s of physical, b i o l o g i c a l and s o c i a l phenomena; (2)  knowledge regarding the a p p l i c a t i o n of these p r i n c i p l e s  to production such as the a p p l i c a t i o n of genetics to the development of better livestock or new v a r i e t i e s of crops; and  (3)  knowledge regarding the day-to-day operations of  production such as management techniques. Technological change i s an important and perhaps the most important factor responsible f o r economic growth.  2 Economists have made s i g n i f i c a n t attempts s i n c e the mid 1950*s t o measure t h e e f f e c t o f the r a t e o f  technological  change on a n a t i o n ' s r a t e o f economic growth. example, found t h a t almost n i n e t y increase  Solow, f o r  per cent o f the long-term  i n output p e r u n i t o f l a b o r i n p u t  S t a t e s was a t t r i b u t a b l e t o t e c h n o l o g i c a l  i n the United  change w i t h the  remaining t e n per cent a t t r i b u t a b l e to i n c r e a s e s quantity  o f c a p i t a l employed.  1  i n the  Although these r e s u l t s  were extremely rough, more r e c e n t s t u d i e s have confirmed t h a t the e f f e c t o f t e c h n o l o g i c a l  change on p r o d u c t i v i t y  over time has been s u b s t a n t i a l . II.  PRODUCTIVITY  S i n c e the e i g h t e e n t h century, economists and p o l i c y makers have been i n t e r e s t e d i n p r o d u c t i v i t y . productivity  Essentially,  i s a measure which expresses the r e l a t i o n s h i p  between output and the r e s o u r c e s u t i l i z e d i n i t s p r o d u c t i o n . More p r e c i s e l y , i t i s the r a t i o o f output t o a s i n g l e input  or t o a composite o f i n p u t s .  For example, the volume  o f output per man-year, and the number o f b u s h e l s per acre are e x p r e s s i o n s o f p r o d u c t i v i t y .  These r a t i o s are measures  o f performance r e l a t i n g the volume o f output produced t o  R.M. Solow, " T e c h n i c a l Change and t h e Aggregate P r o d u c t i o n Function," ''Review o f Economics and S t a t i s t i c s , 39:312-20, August, 1957. X  3 the volume of inputs used.  Productivity, however, i s not  synonymous with e f f i c i e n c y , since productivity simply expresses a physical r e l a t i o n s h i p between output and  input  while e f f i c i e n c y implies an optimum l e v e l of performance i n a productive s i t u a t i o n i n terms of the combination of inputs to produce a given l e v e l of output. As a description of a technical r e l a t i o n s h i p between output and inputs, productivity i s a c h a r a c t e r i s t i c of the i n d i v i d u a l economic unit, and i t s changes, therefore, indicate that the productive resources within the unit have been reorganized so as to a f f e c t output. productivity changes may  arise from a l l  Alternatively, sourcesincluding  s h i f t s i n production and employment of resources between units having d i f f e r e n t l e v e l s of productivity as well as productivity advances within i n d i v i d u a l u n i t s . concept i s more suitable for most economic and  This second policy  analysis at the macro l e v e l . For conceptual as well as p r a c t i c a l reasons, labor productivity, that i s , output per unit of labor input,  has  been the most commonly studied measure of productivity, since labor usually represents a major proportion  of value  added i n production, labor input i s r e l a t i v e l y easy to measure, and changes i n labor productivity are d i r e c t l y related to changes i n r e a l income per capita. years, there has been an increasing volume of  In recent empirical  4 work on productivity at a l l l e v e l s of aggregation which has contributed  to an extensive knowledge of the trends and  magnitudes of productivity change*  However, considerable  scope remains f o r further investigation of the causes and sources of productivity  increases.  In a broad sense, changes i n productivity may from three sources: (1) l o g i c a l change; (2)  the nature and rate of techno-  factor substitution i n response to  changes i n r e l a t i v e input prices; and or increases  result  (3)  economies of scale  i n the u t i l i z a t i o n of existing productive  capacity. The  e f f e c t s of changing factor proportions on pro-  d u c t i v i t y are e a s i l y shown i n Figure 1 where Capital input  .Q  2  •Ql Labor input Figure 1 .  Factor proportions and  productivity  change• Q]_ and Q2 represent the same l e v e l of output, but each i s produced by a d i f f e r e n t , although t e c h n i c a l l y e f f i c i e n t , combination of c a p i t a l and labor.  In response to a change  i n r e l a t i v e input prices, a s h i f t from Qi to Q2 would r e s u l t i n an increase  i n labor productivity as shown by  an  5  increase i n the output-labor r a t i o  and a decrease i n c a p i t a l  productivity. Economies o f scale exist when the percentage change i n required inputs i s l e s s than the percentage change i n the resultant output, when a l l inputs are increased i n the same proportion.  In t h i s s i t u a t i o n , i t i s obvious that pro-  d u c t i v i t y increases as output increases, since the outputinput r a t i o increases. III.  TECHNOLOGICAL CHANGE  A production function shows, f o r a given l e v e l of technology, the maximum output l e v e l which can be obtained from given amounts of inputs.  Technological change r e s u l t s  i n a s h i f t i n the production function over time.  In Figure 2,  Labor input Figure 2. Technically e f f i c i e n t combinations of labor and c a p i t a l inputs at two l e v e l s of technology. a s h i f t i n the production indifference curve from p o s i t i o n 1 to p o s i t i o n 2 indicates that an increase i n productivity  6 has occurred, since smaller amounts of c a p i t a l and labor 2 are now  required to produce the same l e v e l of output.  In  the usual case, and f o r purposes of t h i s study, t h i s increased productivity i s defined as the r e s u l t of disembodied technological change. The increase i n productivity shown i n Figure 2 i s not the r e s u l t of economies of scale, since the output l e v e l i s unchanged.  Factor (input) substitution i s also eliminated  as a possible source of increased productivity, since the l e v e l of output can always be produced at technology l e v e l 2 by a smaller combination of inputs employed i n the same proportion, as shown by a ray (R) through the o r i g i n , than at technology l e v e l 1. An i m p l i c i t assumption i n Figure 2 i s that the productive q u a l i t y of the inputs, labor and c a p i t a l , does not improve over time.  This homogeneity of inputs i s implied  because the production indifference curves for two instances i n time are drawn on the same indifference curve map.  Consequently, a second type of technological change,  namely embodied technological change, has been eliminated from Figure 2.  Embodied technological change i s defined  production indifference curve i s defined as a locus of t e c h n i c a l l y e f f i c i e n t input combinations a l l of which are capable of producing the same l e v e l of output.  7  as a change i n the productive quality of one or a l l o f the inputs used i n the production process.  For example, tech-  n o l o g i c a l change may be embodied i n labor as a r e s u l t o f improved health, higher educational attainments and t r a i n i n g programs.  S i m i l a r l y , technological change may be embodied  i n c a p i t a l i n the form of improved designs.-^  Embodied  technological change, therefore, gives r i s e to productivity increases as a r e s u l t of increased output l e v e l s corresponding to inputs measured i n " e f f i c i e n c y " u n i t s . Technological change may also be c l a s s i f i e d as neutral, labor-saving, or capital-saving. i n Chapter I I .  This topic i s discussed  Chapter I I also outlines techniques whereby  i t i s possible to estimate the rate of movement of the production function over time by a single number.  This i s  often used as a measure of disembodied technological change. IV.  PRODUCTIVITY CHANGE IN CANADIAN AGRICULTURE Several empirical studies have attempted to measure  productivity change i n Canadian agriculture over the past three or four decades.  In order to indicate the extent of  productivity change i n Canadian agriculture, and the attempts which have been made to i d e n t i f y the sources of  -^H.A.J. Green, "Embodied Progress, Investment, and Growth," American Economic Review, 56:138-51, March, 1966.  s productivity changes, a few of these studies are b r i e f l y discussed below. The f i r s t of the recent studies on productivity i n Canadian agriculture was 1950*s.^  -  completed by Lok i n the l a t e  Lok examined, f o r Canadian agriculture as a whole,  the r e l a t i o n s h i p between annual percentage changes i n t o t a l productivity and r e a l net return per farm over the years 1926-57•  Lok concentrated on the estimation of a t o t a l  productivity index.  He aggregated constant d o l l a r series  f o r i n d i v i d u a l inputs into a single constant d o l l a r index measuring t o t a l input, which was  then divided into a  constant d o l l a r index of t o t a l output. Lok devoted considerable attention to the discrepancies between productivity indexes when prices of d i f f e r e n t periods were used to weight the classes of outputs and inputs i n the construction series.^  of constant d o l l a r  As a r e s u l t of t h i s enquiry, he presented s i x  indexes showing t o t a l productivity change i n Canadian agriculture during 1 9 2 6 - 5 7 . ^  The  estimates ranged from  4-Siepko H. Lok, An Enquiry into the Relationships Between Changes i n Overall Productivity and Real Net Return per Farm, and Between Changes i n Total Output and Real Gross Return, Canadian Agriculture, 1 9 2 6 - 1 9 5 7 i Economics D i v i s i o n , Canada Department of Agriculture, Technical Publication 61/13 (Ottawa: 1 9 6 1 ) . 5  I b i d . , pp.  ^Lok,  10-11.  op_. c i t . , table 6 ,  p.  76.  9 a low i n c r e a s e o f 19.8 per cent over the p e r i o d 1926-57.  t o a h i g h o f 59.1 p e r cent  Although Lok made no attempt t o  q u a n t i f y the sources o f these estimated p r o d u c t i v i t y i n c r e a s e s , he d i d o f f e r some g e n e r a l reasons such as r e search  and education,  economies o f s c a l e f o r i n d i v i d u a l  f i r m s , and g r e a t e r adherence t o the p r i n c i p l e o f comparative 7 advantage. F u r n i s s has used s i m i l a r methods and b a s i c data sources as d i d Lok t o estimate p r o d u c t i v i t y change d u r i n g the p e r i o d 1935-60.  He estimated t h a t t o t a l a g r i c u l t u r a l  p r o d u c t i v i t y i n c r e a s e d by 60 per cent over t h i s p e r i o d , which i s e q u i v a l e n t t o an annual growth r a t e o f 1.9 per o cent. T h i s compared w i t h an annual growth r a t e o f 2.2 10 per cent d u r i n g t h e 1946-60 p e r i o d . F u r n i s s a l s o i n v e s t i g a t e d i n d i v i d u a l f a c t o r prod u c t i v i t i e s u s i n g t h e constant i n d i v i d u a l input r a t i o s .  d o l l a r method and output-  He found t h a t l a b o r p r o d u c t i v i t y  i n c r e a s e d by 183 p e r cent d u r i n g the 1935-60 p e r i o d . S i m i l a r l y , t h e p r o d u c t i v i t y o f l a n d and b u i l d i n g s  increased  ?Lok, op_. c i t . , pp. 20-21.  g I . F. F u r n i s s , " P r o d u c t i v i t y o f Canadian A g r i c u l t u r e , 1935-1960: a Quarter Century o f Change," Canadian J o u r n a l o f A g r i c u l t u r a l Economics, 12, No. 2: 41-53, 1964. 9lbid.» p. 42. 1 G  I b i d . , p. 51.  by 42 per cent over the 1935-60 period, but only 14 per cent over the 1946-60 period. output to c a p i t a l inputs  In I960, the r a t i o of t o t a l  ( a l l other inputs) was 36 per  cent l e s s than i n 1935, and s i m i l a r to the 1946 l e v e l . ^ Like Lok,  Furniss made no attempt t o quantitatively explain  these estimated productivity changes i n terms of technol o g i c a l change, economies of scale, and factor substitution. He did, however, indicate the nature of the changes i n input proportions  over the time period studied, and  suggested that s u b s t a n t i a l l y increased  inputs of purchased  feed, seed, f e r t i l i z e r s and pesticides had made an important contribution to increased t o t a l a g r i c u l t u r a l productivity. Mackenzie also has investigated productivity i n 12 Canadian a g r i c u l t u r e .  Unlike Lok and Furniss, who  investigated productivity change related to a gross measure of a g r i c u l t u r a l output, Mackenzie examined net labor xx  Ibid.,pp. 43-44.  W. Mackenzie, "The Terms of Trade, Productivity and Income of Canadian Agriculture," Canadian Journal of A g r i c u l t u r a l Economics, 9 , No. 2 : 1 - 1 3 , 1961; W. Mackenzie, "The Impact of Technological Change on the E f f i c i e n c y o f Production i n Canadian Agriculture," Canadian Journal of A g r i c u l t u r a l Economics, 1 0 , No. 1 : 4 1 - 5 3 , 1962; and W. Mackenzie, "Regional Changes i n Income, Terms of Trade and Productivity within Canadian Agriculture," Canadian Journal of A g r i c u l t u r a l Economics. 1 1 , No. 2 : 4 1 - 5 1 , 1963. 12  productivity change i n agriculture by deriving a measure of value added output i n r e a l terms (gross outputs l e s s 13 material inputs) per unit of labor input.  A comparison  of Mackenzie's estimates with those of Furniss, indicates that net labor productivity has increased much l e s s than gross labor productivity. inputs have contributed  This suggests that purchased  substantially to the phenomenal  labor productivity increases estimated by  Furniss.  Mackenzie ^" extended h i s estimates of net labor product1  i v i t y changes to a t o t a l net productivity index for Canadian agriculture by aggregating inputs into a measure  15 of t o t a l input i n a manner suggested by Kendrick.  On  t h i s basis, Mackenzie estimated that t o t a l net producti v i t y f o r Canadian agriculture increased by 37«0 to 43*6 per cent from the 1944-46 period to the 1954-56 period. explain Inthea recent increases i n labor n Canadian to Doctoral d i s productivity s e r t a t i o n , L ii attempted agriculture.  This i s the only study which has specif-  i c a l l y attempted to explain productivity changes i n terms  ^W.  Mackenzie, 1961,  p.  7.  Mackenzie, 1962,  p.  43.  15  J.W. Kendrick, "Productivity Trends i n Agriculture and Industry," Journal of Farm Economics, 40:1554-64* December, 1956. "^Lew-king L i , "Technological Change i n Canadian Agriculture" (unpublished Doctoral d i s s e r t a t i o n , University of Manitoba, Winnipeg, 1966).  of technological change, economies of scale, and factor substitution.  Using the Solow or geometric method, L i  estimated the rate of disembodied technological change on the basis of both net value added and gross measures of output.^  He estimated that disembodied technological  change has proceeded at an annual rate o f 3.1 per cent i n the a g r i c u l t u r a l sector as a whole f o r the period 1946-65.  •i ti-  Over the same period, net labor productivity increased by 176 per cent with 75.2 per cent of t h i s increase a t t r i b u table to technological change and the remainder, 24.8 per cent, attributable to increases i n the capital-labor r a t i o . Productivity increases have been well demonstrated f o r Canadian a g r i c u l t u r e .  The main r e s u l t s of the above  studies are summarized i n Table I . However, i n t e r p r e t i v e analysis i n the terms suggested i n t h i s chapter have only recently begun.  Important aspects of the problem of under-  standing productivity changes have not yet been investigated. V.  THE PROBLEM  In the r e a l world, i t i s d i f f i c u l t to i s o l a t e the e f f e c t s of technological change, factor substitution and economies of scale on changes i n productivity.  However,  M. Solow, "Technical Change and the Aggregate Production Function," Review of Economics and S t a t i s t i c s , 39:312-20, August, 1957. l 8  L i , op_. c i t . , p. 112.  13 TABLE I SUMMARY OF ESTIMATED PRODUCTIVITY CHANGE IN CANADIAN AGRICULTURE  Author  Productivity measure  Average annual percentage growth rate  Lok  t o t a l productivity, 1926-57  0.5-1.5  Furniss  t o t a l productivity, 1935-60 t o t a l productivity, 1946-60 labor productivity, 1935-60 land and buildings productivity, 1935-60 land and buildings productivity, 1946-60 c a p i t a l productivity, 1935-60 C a p i t a l productivity, 1946-60  Mackenzie  t o t a l net productivity, 1944-58  2.3  Li  disembodied technological change, 1946-65 net labor productivity, 1946-65  3.1 5*2  1.9 2.2 4.1 1.4 0.9 -2.6 0.0  one way to gain a better understanding of productivity changes over time i s to separate the productivity changes into the broad source components of technological change, factor substitution, and economies o f scale. i s shown i n Figure 3.  This concept  In time period t , 50 units of output  Capital input K =20  ;__  Ki=15  1 1 1  2  1 1 1  L =20 2  Figure 3»  t+l=100 t=50 L =25 1  Labor input  Productivity changes over time.  are produced with 25 units of labor and 15 units of c a p i t a l . In the subsequent time period, t+1, 100 units of output are produced with 20 units of c a p i t a l and 20 units of labor. Productivity has increased from time period t to time period t+1.  Both c a p i t a l and labor productivity r a t i o s  have increased and i t i s conceivable that t o t a l productivity has also increased, although t h i s cannot be ascertained from the l i m i t e d information.  Furthermore, i t i s impossible to  discuss why the increases i n productivity have occurred. Input substitution has occurred and may have contributed to the increase i n productivity, e s p e c i a l l y labor productivity.  However, disembodied technological change and/or  economies of scale may also have contributed to productivity change. The broad changes which have occurred i n Canadian agriculture are s i m i l a r to those portrayed i n the simple example above. t u r a l sector.  Productivity has increased i n the a g r i c u l There has been a substitution of c a p i t a l  f o r labor, and a g r i c u l t u r a l labor productivity has increased more r a p i d l y than i n any other major sector of the Canadian economy during the post war period."^  When the r e a l world  ^The Dominion Bureau of S t a t i s t i c s has estimated that output per person employed i n Canadian agriculture has increased by 5.5 per cent annually during 1946-67. This compares with 2.8 per cent f o r the commercial nonagricultural i n d u s t r i e s , and 4*3 per cent f o r the nonagricultural goodsproducing i n d u s t r i e s . See: Canada, Dominion Bureau o f S t a t i s t i c s . Aggregate.Productivity Trends, 1946-67. (Ottawa: Queen »s P r i n t e r , i y 6 t i ) .  a g r i c u l t u r a l sector i s considered,  the changing quality  of inputs over time further complicates  e f f o r t s to  attribute the sources o f productivity gains.  Embodied  technological change must also be considered,  and i t would  seem reasonable on a p r i o r i grounds t o postulate that the productive q u a l i t y of many a g r i c u l t u r a l inputs has increased over time. This study was designed to investigate technological change i n the aggregate primary a g r i c u l t u r a l sector i n Canada during the time period  1935-65.  S p e c i f i c a l l y , the  problem was: (1) to measure the rate of disembodied technological change; (2) to measure the rate of technological change which has been embodied i n a g r i c u l t u r a l machinery and implements; and (3) to measure the rate of technol o g i c a l change which has been embodied i n material inputs. This study did not investigate a l l of the possible sources of productivity change.  An assumption was made regarding  economies of scale, and the influences of the substitution of c a p i t a l f o r labor were not estimated.  Conceptually,  the measurement of embodied technological change should have been extended to include a l l inputs.  A priori, i t  would be reasonable to expect that the quality of the labor force has improved over time.  However, because of  data l i m i t a t i o n s and the lack o f suitable methods of analysis, t h i s study was l i m i t e d to the consideration of  16  embodied technological change i n two inputs  only.  Chapter II i s a review of the t h e o r e t i c a l framework and related empirical studies regarding the measurement of technological change. evaluated  Various models are interpreted and  i n terms of t h e i r contribution to t h i s study.  The model and data, including methods of derivation, manipul a t i o n and assumptions, used i n t h i s study are outlined i n Chapter I I I .  The r e s u l t s of the analysis and related d i s -  cussion are presented i n Chapter IV.  F i n a l l y , Chapter V  presents a summary and the main conclusions of the study.  and implications  CHAPTER I I CONCEPTUAL FRAMEWORK FOR MEASURING TECHNOLOGICAL CHANGE This chapter reviews the theory which i s pertinent to the measurement of technological change, and the methods and approaches which have been developed.  This review i s  not exhaustive, but rather i t concentrates on those methods and studies which have provided  the background f o r , and  contributed most to, the methods used i n t h i s study, which are outlined i n the following chapter. I.  NEUTRALITY OF TECHNOLOGICAL CHANGE  Economists d i s t i n g u i s h among three types of technol o g i c a l change as i t a f f e c t s the s h i f t i n the production function: neutral, labor-saving, and capital-saving technological change. In many methods, estimation o f the rate of technol o g i c a l change involves accurate s p e c i f i c a t i o n both of the aggregate production  function and of the form of  technological change.  In addition, i t has been customary,  for reasons of t h e o r e t i c a l and empirical convenience, to assume that technological change i s neutral.  When consider-  ing the question of n e u t r a l i t y , the usual procedure has been to make assumptions about the way i n which technological change a f f e c t s r e l a t i o n s h i p s between c e r t a i n variables  which are derived from the production function.  Techno-  l o g i c a l change i s then neutral i f i t s e f f e c t s do not a l t e r the r e l a t i o n s h i p between the chosen variables.  Because  there are several possible pairs of variables which may be chosen, alternative d e f i n i t i o n s or various forms of neutral technological change are possible.  The most widely used  and best known of these are the "Hicks" and "Harrod" d e f i n i t i o n s of neutral technological change. Technological  change i s neutral i n the Hicks sense  i f the r a t i o of the marginal product of labor to the marginal product of c a p i t a l i s unchanged when the capital-labor r a t i o i s unchanged.  When disembodied technological change i s  assumed to be an exogenous function of time ( t ) , the production function Y=f(K,L,t) i s implied.  I f technological change i s Hicks-neutral, the  function becomes Y=A(t)f(K,L) where A(t) i s any function o f time.  This i s the general  M.J. Beckmann and R. Sato, "Aggregate Production Functions and Types of Technical Progress: a S t a t i s t i c a l Analysis," American Economic Review. 59:88-101, March,1969. A more complete treatment, from which the following discussion i s drawn, of the implications of the two d e f i n i t i o n s i s found i n : F. Halm and R. Matthews, "The Theory of Economic Growth: a Survey," Economic Journal, 74: 779-901, December, 1964. 2  form of the production  function used to estimate disembodied  technological change i n t h i s study, and, therefore, neutral technological change was  Hicks-  i m p l i c i t l y assumed.  The Harrod d e f i n i t i o n i s based on the comparison of points on the two production  functions where the marginal  product of c a p i t a l i s constant.  Technological  change i s  neutral i n the Harrod sense i f the capital-labor r a t i o which r e s u l t s i n a constant marginal product of c a p i t a l a f t e r technological change, also causes the r a t i o to remain constant.  capital-output  With two inputs, Harrod-neutral  technological change i s shown a l g e b r a i c a l l y as Y=f(K,A(t)L) which indicates that Harrod-neutral technological change may  be described  as "labor-augmenting", since the labor  force i s measured i n e f f i c i e n c y units, A(t)L. change may  also be "capital-augmenting".  general form of the production  Technological  In t h i s case the  function i s  Y=f(A(t)K,L) which i s the mirror image of Harrod-neutral technological change with K and L reversed.  Capital-augmenting techno-  l o g i c a l change i s a useful concept i n the study of vintagec a p i t a l models, and i t i s equivalent to the concept of embodied technological change i n c a p i t a l which was t h i s study. I I I below.  used i n  The concept i s more f u l l y discussed i n Section  Technological  change i s neutral i n both the Hicks  and Harrod sense when the e l a s t i c i t y of substitution between labor and c a p i t a l i s unity.^ production  The Cobb-Douglas  function, which was used i n t h i s study, possesses  t h i s property  and, therefore, unequivocal n e u t r a l i t y was  i m p l i c i t l y assumed. Recently, Beckmann and Sato have generalized the concept of technological n e u t r a l i t y by extending the p r i n c i p l e that technological change i s neutral when the r e l a t i o n s h i p between a s p e c i f i c pair o f variables i s invariant through time, to relationships between variables other than those considered  i n the Hicks, Harrod, and  Solow d e f i n i t i o n s . ^ Under the Beckmann and Sato scheme technological change i s Hicks-neutral when the r e l a t i o n ship between the marginal rate of substitution and the c a p i t a l - l a b o r r a t i o i s constant, Harrod-neutral when the r e l a t i o n s h i p between the capital-output r a t i o and the i n t e r e s t rate does not change, and Solow-neutral when the r e l a t i o n s h i p between output per worker and the wage rate i s invariant.  After examining relationships between  output-capital r a t i o s , output-labor  r a t i o s , capital-labor  r a t i o s , i n t e r e s t rates, wage rates, marginal rates of  3Ibid., p. 6*29. ^Beckmann and Sato, op_. c i t . , p. 9 0 .  21 substitution, and labor's share, Beckmann and Sato suggested a number of i n t e r e s t i n g new  types of technological change.  They applied regression analysis to time series data f o r the U.S.,  Japanese, and German private non-farm economies  i n order to empirically investigate the implications of t h e i r formulations  of technological n e u t r a l i t y .  They con-  cluded that:^ (1) the t r a d i t i o n a l types of Hicks, Harrod, and Solow n e u t r a l i t y were for a l l countries at l e a s t as good as the unconvential  types of n e u t r a l i t y ; (2) Solow-  neutral technological change performed p a r t i c u l a r l y well; (3) general factor-augmenting technological change did not give a s u b s t a n t i a l l y improved explanation  of observed data  when compared with single-factor-augmenting change; and was  (4) i r r e s p e c t i v e of how  technological change  s p e c i f i e d , the estimated production  out to be close to a Cobb-Douglas or CES II.  technological  function turned function.^  DISEMBODIED TECHNOLOGICAL CHANGE  The rate of growth of t o t a l factor productivity i s conventionally defined as the difference between the rates  5Ibid., p.  95.  °The CES production function i s a more general function which allows the e l a s t i c i t y of substitution to be estimated. I t also contains e f f i c i e n c y and d i s t r i b u t i o n parameters so that both neutral and non-neutral technological change can be estimated. Although the CES function has been the most commonly applied i n recent work, i t was not employed i n t h i s study because, being a more general form, i t i s more d i f f i c u l t to estimate than the Cobb-Douglas form.  22  of growth of r e a l output and r e a l input, where the rates of growth of r e a l output and input are the weighted averages of the rates of growth of i n d i v i d u a l products and  inputs.  7  Under various assumptions (including n e u t r a l i t y , perfect competition, and constant returns to scale) a change i n t o t a l factor productivity may the production  be i d e n t i f i e d with a s h i f t i n  function, and changes i n r e a l output  and  input not accompanied by a change i n t o t a l factor productiv i t y may function.  be associated with movements along the Technological  i n the production  production  change i s also defined as a s h i f t  function, and the terms technological  change and t o t a l f a c t o r productivity have tended, i n practice, to be used interchangeably.  Much of the empirical work  during the 1950*s and early 1960 s concentrated on t h i s f  simple concept of deducting the contributions of increased c a p i t a l and labor inputs to increased  output, and a t t r i b u t -  ing the " r e s i d u a l " growth i n output to disembodied technol o g i c a l change or t o t a l factor productivity.  The  arithmetic index and the Solow model were the most common methods employed.  D.W. Jorgenson and Z. G r i l i c h e s , "The Explanation of Productivity Change," The Review of Economic Studies, 34:249-83, July, 1967. 7  This interchangeability depends upon the assumption of constant returns to scale, and i s v a l i d only i f economies or diseconomies of scale do not e x i s t .  The arithmetic index which has been used by Abramovitz^ and K e n d r i c k ^ may be defined as C=Y/(wL+iK) where Y i s output, w i s the r e a l wage rate i n the base period, L i s labor input (in physical units) i n a given year, i i s the r e a l return to c a p i t a l i n the base period, and K i s c a p i t a l input (in physical units) i n a given year.I- -  Perfectly competitive  1  equilibrium i s implied since  the weights, w and i , represent the marginal products of labor and c a p i t a l , respectively.  The c r i t i c a l assumption,  however, i s that the marginal products of the inputs are changed only by technological change and always i n the same proportion.  Therefore, the marginal products are  assumed to be independent of the r a t i o of the quantities of the inputs, which i s a very r e s t r i c t i v e assumption and not reasonable over a longer period where substantial changes may be expected i n the capital-labor r a t i o .  The  so c a l l e d constant d o l l a r method which, as noted i n Chapter I, has been used by Lok, Furniss, and Mackenzie to estimate productivity change i n Canadian agriculture  9 M . Abramovitz, "Resource and Output Trends i n the United States Since 1 8 7 0 , " American Economic Review,  4 6 : 5 - 2 3 , May, 1956.  J.W. Kendrick, Productivity Trends i n the United (Princeton: Princeton University Press, 1961TI  10  States  E.D. Domar, "On Total Productivity and A l l That," Journal of P o l i t i c a l Economy. 7 0 : 5 9 9 , December, 1962, 1:L  i s a s p e c i a l formulation of the arithmetic index. constant d o l l a r index may  be defined  The  as  C=y/(l+k) where y, 1 and k are the values of output, labor and respectively i n base year p r i c e s . assumption of competitive  capital,  Aside from the normal  equilibrium, the basic d i f f i c u l t y  with t h i s method (as well as with the arithmetic index) i s that i t i s not suited to either a l i n e a r or an expo12 n e n t i a l world.  For example, i f the values of output  and of inputs are l i n e a r with respect to time, C w i l l gradually approach a constant while i f they are  exponential,  the r e l a t i v e rate of growth of C w i l l approach the d i f ference between the rates of growth of output and of the fastest growing input. Solow derived, from very general assumptions, a somewhat better measure of the rate of movement of the production function than the arithmetic i n d e x . ^  Solow s 1  derivation was based on a l i n e a r homogeneous production function of the general form Y=A(t)f(K,L). Solow defined technological change as "any kind of s h i f t "  1 2  I b i d . , p.  607.  ^R. M. Solow, "Technical Change and the Aggregate Production Function," Review of Economics and S t a t i s t i c s . 39:312-20, August,. 1957.  i n the production function, and the term A(t) measures the cumulated e f f e c t of s h i f t s over t i m e . assumptions of perfect competition  1 4  With the further  and neutral technological  change, technological change between two periods i s given by A=Y-W K-W L k  1  where A, Y, L, and K are the percentage rates of change per unit of time of disembodied technological change, output, labor input and c a p i t a l input, r e s p e c t i v e l y .  W^ and W-L  are the shares of c a p i t a l and labor i n output which, under the assumptions of t h i s model, w i l l be equal to the elast i c i t y of output with respect to c a p i t a l and labor, respectively.  Given time series data on Y, L, K, Wj,. and  Wi, A can be estimated. The i n t e r p r e t a t i o n of the Solow model i s straightforward: disembodied technological change i s equal to the change i n the output which i s not accounted f o r by the changes i n c a p i t a l and labor.  Thus, as Domar has c l e a r l y  pointed out, disembodied technological change i s estimated i n t h i s method as a r e s i d u a l , and f o r t h i s reason he prefers to c a l l i t the " R e s i d u a l . "  1 4  15  I b i d . , p. 312.  E . D. Domar, "On the Measurement of Technological Change," Economic Journal, 71:712, December, 1961. 1 5  Upon applying the above model to the U.S. non-farm economy f o r the period 1909-49, Solow concluded that: (1) technological change was neutral on average; (2)  tech-  n o l o g i c a l change proceeded at an annual rate of about one per cent f o r the f i r s t h a l f of the period and two per cent f o r the l a s t h a l f ; and (3) 87.5 per cent of the increase i n gross output per man-hour could be attributed to technol o g i c a l change, and the remaining 12.5 per cent to increased use of capital." "^ 1  Lave has applied the Solow model to U.S. agriculture and concluded that: (1) technological change i n agriculture was twice as rapid as i n the private non-farm sector; and (2) technological change accounted f o r 60 to 73 per cent of the increase i n output per man-year during the 1850-1950 period with the remainder, 27 to 40 per cent, attributable to increases i n c a p i t a l . A s noted i n Chapter I, L i applied the Solow model to Canadian agriculture f o r the period 1946-65. Domar has provided  a more general i n t e r p r e t a t i o n of  the Solow model - the geometric index.  Since any l i n e a r  homogeneous production function with constant factor shares  ^Solow, op_. c i t . , p. 320. *^L. B. Lave, Technological Change: I t s Conception and Measurement. (New Jersey: Prentice-Hall, Inc., 1966),  pp. 4 7 - 5 7 . IS  Domar, op_. c i t .  w w i s of the Cobb-Douglas type, Domar i d e n t i f i e d L K x  weighted geometric mean.  k  as a  I t follows that, i f both L and K l k w  are index numbers with a common base, then L  w  K  is a  geometric index of inputs, each weighted by i t s share i n output i n the base period.  Disembodied  technological  change i s then the r a t i o between geometric indexes o f out19  puts and inputs.  7  The geometric index i s simply a geometric index number with constant factor shares as weights, and therefore d i f f e r s from the Solow model which uses current factor shares as weights.  However, with t h i s assumption, Domar  has derived an index which circumvents the underlying assumption of an aggregate production function with the accompanying implications.  Furthermore, since r e l a t i v e  factor shares appear to have been quite stable over time and r e l a t i v e prices have not, the geometric index seems to better approximate r e a l i t y than does the arithmetic index. The above models provide only i n d i r e c t measures of disembodied technological change.  They do not i s o l a t e the  e f f e c t s of "pure" technological change alone, but include i n the measures a l l increases i n output not accounted f o r by the growth of e x p l i c i t l y recognized inputs and, therefore, must be treated conceptually as r e s i d u a l s . 1 Q  I b i d . , p. 713  Moreover, these  methods are based on the notion that technological change i s disembodied, that i s , that a l l technological change consists of better methods and organization which improve the output performance of the inputs. assumed to be homogeneous over time.  The inputs are However, many changes  i n technology must be embodied i n new c a p i t a l i f they are to be u t i l i z e d .  In the above methods, c a p i t a l does not  change i n q u a l i t y , form, or composition, nor does i t act as a vehicle f o r the introduction of technological change into the productive process.  The methods reviewed i n the next  section were developed i n an attempt to e x p l i c i t l y recognize t h i s concept, and to provide estimates of the rate of embodied technological change. III.  EMBODIED TECHNOLOGICAL CHANGE  The concept of embodied technological change developed from the notion that c a p i t a l investment and technological advance influence each other i n such a way that t h e i r separation i s meaningless, i f not impossible.  I f techno-  l o g i c a l change cannot be implemented without introducing new kinds of c a p i t a l , then c a p i t a l investment may  be  regarded as the vehicle of technological advance, and c a p i t a l , therefore, cannot be considered homogeneous.  In  t h i s approach, technological change i s embodied i n new c a p i t a l , and may be regarded as a progressive reduction i n  29  the cost of producing c a p i t a l , or a l t e r n a t i v e l y , as a  20 progressive improvement of the quality of c a p i t a l . Therefore, c a p i t a l goods embody the technology of t h e i r date of construction, and those b u i l t at d i f f e r e n t dates ("vintages") are q u a l i t a t i v e l y d i s s i m i l a r .  A separate pro-  duction function i s required f o r each vintage and t o t a l  21 output i s the sum of output from a l l vintages i n use. In 1959, Solow reconstructed h i s e a r l i e r disembodied  22 model to make allowance f o r embodied technological change. Solow began by interpreting h i s disembodied model as a l i n e a r homogeneous Cobb-Douglas function Q=Be L K ~ ?i  a  1  a  where e^ i s an exogenous s h i f t function which measures the rate of neutral disembodied technological change. ^ 2  Solow's  embodied method i s based on a vintage model of production. Output at time t , Q ( t ) , from the surviving c a p i t a l equipv  ment of vintage v i s given by a l i n e a r homogeneous CobbF . Hahn and R. Matthews, "The Theory of Economic Growth: a Survey," Economic Journal, 74:343, December, 1964. 2 0  2 1  I b i d . , p. 837.  op  R. M. Solow, "Investment and Technical Progress," Mathematical Methods i n the S o c i a l Sciences, K. J . Arrow, editor (Stanford: Stanford University Press, I 9 6 0 ) , pp. 89-104. 23  ^This i s a more r e s t r i c t i v e formulation than the 1957 model, since disembodied technological change i s now assumed to advance at a constant rate,?\ , over time, and factor shares are also assumed constant over time.  )  Douglas production function Q (t)=Be L (t) K (t) - . A v  v  a  v  1  a  v  Embodied technological change, represented by 1\, i s assumed to be uniform, approximately capital-augmenting  exponential over time,  (Solow-neutral).  and  Therefore, a l l techno-  l o g i c a l progress appears as a steady improvement i n the quality of c a p i t a l goods at the rate ^ / ( 1 - a ) . emphasize obsolescence  To  2 4  rather than depreciation, c a p i t a l i s  assumed to be subject to a constant force of mortality, m, and the average length of l i f e of c a p i t a l i s l/m.-> 2  Labor  i s homogeneous and the a l l o c a t i o n of labor to c a p i t a l of various vintages i s assumed to equate the marginal product i v i t y of labor i n a l l uses.  As Solow demonstrated, i t  i s then possible to derive a measure of "equivalent c a p i t a l " at time t , J ( t ) , by summing the surviving c a p i t a l goods of past vintages i n c l u s i v e of time t , weighted according to t h e i r vintage.  Output at time t, Q(t), i s then given by Q(t)=Be-  m ( 1  - L(t) J(t) - . a )  a  1  a  Using exogenous estimates of a ( e l a s t i c i t y of output with respect to labor) and m, Solow estimated the value of  24  Solow, op_. c i t . , p. 9 1 .  25  The theory does not require an e x p l i c i t assumption about depreciation. However, the vintage composition of the stock of c a p i t a l i s required, and since such information i s not usually available, i t must be derived by employing an assumption about depreciation. See: Ibid., p. 93•  ft from time series of output, labor, and gross investment. For the U.S. private sector, 1919-53, he found that (S equalled about 0.025 which was s u b s t a n t i a l l y larger than the estimated value of 0.015 from his disembodied model.  However, the  difference i s i n the expected d i r e c t i o n , since i n the embodied model only new c a p i t a l benefits from technological advance rather than a l l c a p i t a l goods as i n the disembodied model. In 1962, Solow presented a s l i g h t l y d i f f e r e n t method f o r estimating c a p i t a l embodied technological change while drawing a d i s t i n c t i o n between actual and p o t e n t i a l output. In t h i s model a l l technological advance i s embodied i n new c a p i t a l goods, and the rate of embodied technological change i s , therefore, synonymous with the rate of improvement i n the productivity of c a p i t a l goods, ?\.  Assuming  that labor and c a p i t a l of various vintages are allocated so that output i s maximized, that i s , the marginal product i v i t y of labor i s equal i n a l l uses, the equivalent stock of c a p i t a l i n year t , J ( t ) , i s  where I(v) i s gross investment i n year v, and B(t-v) i s the amount surviving i n a l a t e r year t .  Potential output,  P ( t ) , i s then a function of the equivalent stock of c a p i t a l  R. M. Solow, "Technical Progress, Capital Formation, and Economic Growth," American Economic Review, 52:76-S6, May, 1962. <:D  and the available labor supply, L ( t ) , and i s given by P(t)=F(J(t), L ( t ) ) . No e x p l i c i t term representing technological change i s required because i t i s contained  in  J. ? 2  However, actual output, A ( t ) , i s l e s s than potent i a l output because of unemployment and i d l e c a p i t a l .  If  ii(t) i s the unemployment rate, then A(t)=f(u)F(J(t), L ( t ) ) . To derive empirical estimates of  and u, Solow used a  l i n e a r homogeneous Cobb-Douglas production  function  A^^BIO^^^J^ " . 1  3  Solow f i t t e d the function using various estimates of the equivalent stock of c a p i t a l which were derived by various values f o r the improvement factor ?\.  using  In an  e f f o r t to determine whether the rate of productivity improvement d i f f e r e d between plant and equipment, d i f f e r ent values of (\ were used f o r each component.  The  c r i t e r i a f o r determining the best estimate of r\ were the goodness of f i t and low standard  errors of the regression  coefficients. Solow* s above model provided two concepts used i n t h i s study: (1) the d i s t i n c t i o n between potential and  2 7  I b i d . . p. 77  33 actual output; and  (2) the p o s s i b i l i t y that d i f f e r e n t  kinds of c a p i t a l may  experience d i f f e r e n t rates of embodied  technological change. IV.  SIMULTANEOUS EMBODIED AND  DISEMBODIED  TECHNOLOGICAL CHANGE The methods outlined i n Section II depend on the assumption that technological advance increases the product i v i t y of old and new  c a p i t a l goods i n the same way  and i n  the same proportion.  On the other hand, methods described  i n Section III are based on the opposite assumption that technological advance can be introduced into the product i o n process only through new  c a p i t a l investment.  In the  r e a l world, the t r u t h most probably l i e s somewhere between these two extremes. The disembodied and embodied approaches to technol o g i c a l change were synthesized by Phelps i n a l i n e a r homogeneous Cobb-Douglas production  function  Q(t)=Ae J(t) L(t) u t  a  1  a  where u i s an estimate of neutral disembodied technological change, and J i s Solow*s equivalent c a p i t a l stock (which 28 embodies technological change at rate n ) . In t h i s model, E . S. Phelps, "The New View of Investment: a Neoc l a s s i c a l Analysis," Quarterly Journal of Economics, 76:549-67, November, 1962. 2 8  disembodied  t e c h n o l o g i c a l advance occurs i f u i O and 7^=0,  w h i l e embodied t e c h n o l o g i c a l advance occurs i f u=0 and ?\>0,  When b o t h u and A are p o s i t i v e , both kinds o f  t e c h n o l o g i c a l change occur j o i n t l y . I n t r i l i g a t o r extended  the Solow and Phelps models  e m p i r i c a l l y i n two ways: (1) embodied and  disembodied  t e c h n o l o g i c a l change were estimated j o i n t l y r a t h e r  than  s e p a r a t e l y as i n the Phelps method; and (2) t e c h n o l o g i c a l change embodied i n improved improved  q u a l i t y o f l a b o r as w e l l as  q u a l i t y o f c a p i t a l was e s t i m a t e d . ^  Intriligator  2  d e r i v e d h i s model by adding Solow*s unemployment  function  r e l a t i n g a c t u a l and p o t e n t i a l output to Phelps* embodied and disembodied  model.  H i s model, t h e r e f o r e , i s a l i n e a r  homogeneous Cobb-Douglas p r o d u c t i o n a c t u a l output, Q ( t ) , t o e q u i v a l e n t equivalent  function r e l a t i n g c a p i t a l , J ( t ) , and  labor, M(t), Q(t)=Ae  u t  e  b + c u + d u 2  J(t) M(tJ ' a  where u i s a measure o f n e u t r a l disembodied  1  3  technological  change, and J and M are c a p i t a l and l a b o r i n p u t s , respect i v e l y , weighted  f o r q u a l i t y change (embodied t e c h n o l o g i c a l  change). I n t r i l i g a t o r * s method o f e s t i m a t i o n was s i m i l a r to t h a t used by Solow i n h i s 1962 model, t h a t i s , the  D. I n t r i l i g a t o r , "Embodied T e c h n i c a l Change and P r o d u c t i v i t y i n the United S t a t e s , 1929-1958," Review o f Economics and S t a t i s t i c s . 47:65-70, February, 1965.  production function was estimated using the alternative c a p i t a l and labor input series based on various assumed l e v e l s of embodied technological change.  The r e s u l t s of  the various regressions were then compared i n order to choose among the assumed values f o r embodied technological change.  Using data f o r the U.S. private sector, 1929-58,  I n t r i l i g a t o r concluded that embodied and disembodied techn o l o g i c a l change must be treated simultaneously.^® Thus, I n t r i l i g a t o r provided a method, which was used i n t h i s study, f o r determining the rates of disembodied and embodied technological change simultaneously.  However,  many of the stringent assumptions of the previous Solow models were necessarily retained: (l) disembodied technol o g i c a l change i s Hicks-neutral and proceeds at a constant rate; (2) embodied technological change i s both c a p i t a l and labor-augmenting; (3) the production function i s l i n e a r homogeneous and Gobb-Douglas; (4) the economy i s i n a state of p e r f e c t l y competitive  equilibrium; and (5) the marginal  productivity of labor i s equated over a l l vintages of capital.  The v a l i d i t y and implications of two o f these  assumptions, n e u t r a l i t y and constant returns to scale, have been subject to considerable tigation.  scepticism and inves-  I f they are not v a l i d , biased estimates o f  Ibid., p. 6 9 .  disembodied technological change w i l l r e s u l t . discussed V.  This i s  i n the following section. ECONOMIES OF SCALE AND NON-NEUTRALITY  Walters has c l e a r l y pointed out that i f economies of scale are present i n the aggregate economy, i t s e f f e c t s w i l l be included i n the measure of disembodied technol o g i c a l change.3  1  In view of i t s importance, Walters  investigated the assumption of constant returns to scale by estimating the unrestricted Cobb-Douglas function Q=Ae K L ut  a  b  with s i m i l a r data to that used by Solow i n his 1957 paper. Walters found that the sum of a+b was s i g n i f i c a n t l y than one, thus i n d i c a t i n g economies of scale.  greater  According  to his estimates, 27 to 35 per cent of the increase i n output i n the U.S. private non-farm sector could be attributed to economies of scale with a consequent reduct i o n i n the proportion attributable to disembodied technological change.  However, as Walters indicated, the  implications of economies of scale i n the aggregate product i o n function are not clear, and his r e s u l t s cannot be regarded as overwhelming evidence against the hypothesis of constant returns to scale.  3lA. A. Walters, "A Note on Economies of Scale," Review of Economics and S t a t i s t i c s , 45:425-27, November,  1963.  37 Ferguson has expressed similar views.3  2  On the  basis of a study of the U.S. manufacturing sector, 1929-63 he concluded that i n aggregate studies covering long periods of time, a production function which i s homogeneous of degree one i s l i k e l y to provide economically more meaningful r e s u l t s even though these r e s u l t s may be s t a t i s t i c a l l y l e s s s i g n i f i c a n t than i n the case of homogeneity of degree greater than one (economies of scale).33 Ferguson also argued that homogeneity of degree greater than one should not be interpreted to mean that the aggregate economy i s subject to economies of scale.  In addition,  Kislev has suggested that many of the estimated aggregate production functions f o r U.S. agriculture, which have shown s i g n i f i c a n t economies of scale, are biased i n the d i r e c t i o n of overestimating economies of scale.34 The n e u t r a l i t y assumption most commonly questioned has been that of Hicks-neutral disembodied technological change.  For example, Resek questioned t h i s assumption i n  Solow*s 1957  paper, as well as the method which Solow used  3 2 C .E. Ferguson, "Substitution, Technical Progress, and Returns to Scale," American Economic Review, 5 5 : 2 9 6 - 3 0 5 , May, 1965. 33ibid.,  pp. 303-05.  34-Y. Kislev, "Overestimates of Returns to Scale i n Agriculture - A Case of Synchronized Aggregation," Journal of Farm Economics, 4 8 : 9 6 7 - 8 3 , November, 1966.  to test the n e u t r a l i t y assumption.-^  Resek suggested that  i f technological change i s non-neutral i n the Hicks sense, then some of the observed increases i n output per man could be attributed to the i n t e r a c t i o n of c a p i t a l or labor and technological change. One method of relaxing the assumption of Hicksn e u t r a l i t y i s to allow f o r other types of neutral technol o g i c a l change such as Harrod-neutral and Solow-neutral which are non-neutral or biased i n the Hicks sense.  To the  extent that other types of n e u t r a l i t y are also taken into account i n a method or model, the assumption of n e u t r a l i t y would l i k e l y lead to l e s s biased r e s u l t s than i n the case where only Hicks-neutral disembodied is a possibility.  technological progress  An example of t h i s approach i s a study  by David and van de Klundert of the private domestic sector of the U.S. economy, 1 8 9 9 - 1 9 6 0 . 3 °  They employed a homo-  geneous of degree one CES production function incorporating both labor and capital-augmenting technological change. The r e l a t i v e rates of labor and c a p i t a l augmentation can then be related to the usual concepts of neutral, laborsaving, and capital-saving technological advance i n the  3 5 R . W . Resek, "Neutrality of Technical Progress," Review of Economics and S t a t i s t i c s , 4 5 : 5 5 - 6 3 , February, 1963. 36p. A. David and T. van de Klundert, "Biased E f f i c i e n c y Growth and Capital-Labor Substitution i n the U.S., 1 8 9 9 - 1 9 6 0 . " American Economic Review. 55:357-94, June, 1965.  Hicks sense.  From the empirical application of t h e i r  model, they concluded that technological progress i n the private domestic sector of the U.S.  economy was  labor-  saving i n the Hicks sense. A quite d i f f e r e n t approach to non-neutrality  and  economies of scale has been suggested by Brown and Popkin.^^ They attempted to a t t r i b u t e changes i n output over any discrete time period to the weighted change i n inputs, economies of scale, and neutral and non-neutral technol o g i c a l change.  The method consisted of f i t t i n g a Cobb-  Douglas production function to various time periods i n order to i d e n t i f y time periods called "technological epochs," i n which there was  only neutral technological change.  Within each epoch, the influences on output of neutral technological change, economies of scale and  increased  inputs were estimated, and the changes i n the parameters of the estimated production function between epochs were then used to measure output change attributable to non-neutral technological change. However, the abrupt s h i f t from one epoch to another i s an approximation, since i t i s l i k e l y that a s h i f t i n  3 7  I b i d . . pp.  362-63.  38  M. Brown and J . Popkin, "A Measure of Technological Change and Returns to Scale," Review of Economics and Statistics. November, J  44:402-11,  1962.  technology occurs gradually over time.  Thus, the produc-  t i o n function i s misspecified at the ends and beginnings of a l l periods.  However, i f a study covers a long period  of time, the m i s s p e c i f i c a t i o n as a r e s u l t of using epochs compared with only one time period would be of a l e s s e r degree.  Using data for the U.S.  private non-farm sector,  1890-1958, Brown and Popkin found evidence of economies of scale, and showed that the e f f e c t s on output of non-neutral disembodied technological change were extremely small compared with the e f f e c t s of neutral technological change. In summary, the evidence against the assumption of constant returns to scale i s not conclusive.  The  question  of assuming n e u t r a l i t y i s r e a l l y a question of specifying the correct type of technological change.  However, i t must  be noted that i f the assumptions are not v a l i d , biased mates of technological change r e s u l t .  esti  The use of these  assumptions i n t h i s study i s discussed i n the following chapter. VI.  SOME PROBLEMS AND  ALTERNATIVES  The models and methods outlined i n the  previous  sections provided the basic concepts which were used i n t h i s study.  As an aid to i n t e r p r e t i n g the r e s u l t s of t h i s  study, i t i s useful to b r i e f l y outline the basic problems and objections to these methods, and some alternative  approaches. From an a n a l y t i c a l point of view, disembodied technol o g i c a l change has been treated as an exogenous variable which i s not explained by any economic phenomenon.  I t has  been c a l l e d the "Residual" and "a measure of our ignorance. "^^  The embodiment hypothesis (technological change  embodied i n factor inputs) was an attempt to r e l a t e part of t h i s residual to q u a l i t a t i v e change i n factor inputs. attempts have also been c r i t i c i s e d .  These  Although he conceded  that the embodiment hypothesis i s a p o t e n t i a l l y f r u i t f u l method of analysis, G r i l i c h e s has argued that i n practice i t turns out to be a mere "relabelling of an already empty box."  Moreover, i f the assumption that technological  40  change proceeds at constant exponential rates i s dropped, Jorgenson has shown that i t i s often impossible to d i s t i n guish capital-embodied from disembodied technological change on the basis of available d a t a .  4 1  However, David and  van de Klundert have defended the embodiment approach.  42  ^^Domar, op,, c i t . , p. 709. ^ Z . G r i l i c h e s , "Technological Change and Economic Theory: Discussion," American Economic Review, 55:344, May, 1965. D. W. Jorgenson, "The Embodiment Hypothesis," Journal of P o l i t i c a l Economy. 7 4 : 1 - 1 7 , February, i 9 6 0 . 41  42David and van de Klundert, op_. c i t . , pp. 357-59.  They argued that i t i s possible to i n f e r the rate of factor augmentation from conventional measures of inputs and outputs, and that t h i s may  be used to place p r i o r r e s t r i c t i o n s  on further attempts to empirically i d e n t i f y the sources of c a p i t a l and labor augmentation. The conception and estimation of an aggregate product i o n function r a i s e s numerous theoretical and p r a c t i c a l problems, although these are l e s s troublesome when the methods are applied to one sector such as agriculture rather than to the whole economy.43  There has been considerable  discussion i n the l i t e r a t u r e on the relevant concept of c a p i t a l as i t relates to the production  function.  has recently provided a useful review of the  Harcourt  controversies.44  In addition to the above conceptual problems, there are numerous d i f f i c u l t i e s i n obtaining accurate measurements of inputs and outputs which are required f o r any analysis.  empirical  The measurement of aggregate c a p i t a l i s particu-  l a r l y d i f f i c u l t because: ( l ) i t i s usually purchased not hired; (2)  i t i s durable; and  (3)  i t s cost i s ambiguous.45  43For a discussion see: L. B. Lave, Technological Change: Its Conception and Measurement (New Jersey: PrenticeH a l l , Inc., 1966), pp. 1 3 - 1 5 ; 3 7 - 3 8 ; 140-41. ^ G . C. Harcourt, "Some Cambridge Controversies i n the Theory of C a p i t a l , " Journal of Economic L i t e r a t u r e . 7 : 3 6 9 - 4 0 5 , June, 1969. ^ E . D. Domar, "On Total Productivity and A l l That," Journal of P o l i t i c a l Economy, 70:602, December, 1962.  Errors of measurement w i l l bias any estimate of g i c a l change.  time s e r i e s ; (2) and  (3)  arise from: (1)  Errors may  technolo-  errors i n the  non-homogeneity of the series over time;  errors stemming from the economy's not always being  i n long-run e q u i l i b r i u m .  40  The alternative approaches, l a r g e l y inspired by Denison, G r i l i c h e s and Jorgenson, are attempts to d i r e c t l y explain a large portion of the r e s i d u a l .  Denison attempted  to i d e n t i f y the important elements of quality change i n labor i n p u t s .  4 7  Increases i n output not accounted f o r by  increased amounts of inputs or quality changes of inputs were attributed to changes i n t o t a l factor productivity. Growth i n t o t a l factor productivity was  then ascribed to  p a r t i c u l a r sources that could be i d e n t i f i e d and quantified such as resource s h i f t s , economies of scale and the e f f e c t of demand pressures.  In t h i s way  Denison was  explain a large part of the r e s i d u a l .  able to  The Economic Council  has applied Denison*s methods to explain the growth of output i n the Canadian economy. ^ 4  ^ Lave, op_. ext., p.  Similar methods have  63.  Edward F. Denison, The Sources of Economic Growth i n the United States and the Alternatives Before Us, CED Supplementary Paper No. 13 (New York: Committee f o r Economic Development, 1962)• 47  ^Economic Council of Canada, The Challenge of Growth and Change, F i f t h Annual Review (Ottawa: Queen's Printer, T9o"8), pp. 7 - 6 1 . 4  been used by the Council to explain the growth i n labor productivity i n Canadian a g r i c u l t u r e . ^ G r i l i c h e s attempted to explain productivity change i n the U.S.  a g r i c u l t u r a l sector by estimating a cross-  sectional production function.-^ estimated was  The Cobb-Douglas function  homogeneous of degree greater than one with  s i x independent v a r i a b l e s : livestock expense, other  current  expense, machinery, land, buildings and man-years of labor. G r i l i c h e s then adjusted the time series data on inputs f o r changes i n quality, and combined these by using weights derived from the estimated production function. basis he was  On t h i s  able to account for a l l of the observed  increases i n t o t a l a g r i c u l t u r a l productivity, 1940-60. More recently, Jorgenson and G r i l i c h e s have examined the hypothesis that i f quantities of output and input are measured accurately, growth i n t o t a l output i s l a r g e l y explained by growth i n t o t a l i n p u t . ^ work of s o c i a l accounting,  Within the frame-  the hypothesis becomes that i f  r e a l output and r e a l input are accounted f o r accurately,  4 9 i b i d . , pp. 6 3 - 7 5 . -^Z. G r i l i c h e s , "The Sources of Measured Productivity Growth: United States Agriculture, 1 9 4 0 - 6 0 , " Journal of P o l i t i c a l Economy, 71:331-46, August, 1963. W. Jorgenson, and Z. G r i l i c h e s , "The Explanation of Productivity Change," Review of Economic Studies. 3 4 : 2 4 9 83, July, 1967.  the observed growth i n t o t a l factor productivity i s n e g l i gible. In summary, these alternative approaches attempt to make the r e s i d u a l disappear by constructing new measures of the growth of the various inputs which w i l l , when taken together, f u l l y account f o r the observed growth of output. This approach i s questionable to the extent that i t i s tantamount to tampering with the data.  Moreover, David and  van de Klundert have questioned whether t h i s represents an alternative approach.  They suggest that i t would be more  sensible to begin by t r y i n g to i d e n t i f y the form which factor augmentation  has taken, and then proceed to tackle  the i n t r i g u i n g , but quite d i s t i n c t question of the sources of such  augmentation.  52  The methods used i n t h i s study, which are presented i n the following chapter, draw heavily on the models f o r measuring embodied and disembodied  technological change  which are reviewed i n e a r l i e r sections of t h i s chapter.  52  D a v i d and van de Klundert, op_. c i t . , p. 358"  CHAPTER I I I METHOD OF ANALYSIS AND MEASUREMENT OF VARIABLES This chapter presents the basic model and data series which were used to estimate the rates of disembodied and embodied technological change i n Canadian agriculture, 193565.  The chapter consists of two parts: (1) Section I con-  tains a description of the basic model, a d e f i n i t i o n of variables, and a discussion of the implied assumptions; and (2) Section I I outlines the sources, methods, and assumptions which were employed i n the derivation of the time series data used to estimate the model's c o e f f i c i e n t s .  The actual  data series are presented i n Table V which i s found i n the Appendix.  Also found i n the Appendix i s Table VI which  presents a l i s t of symbols representing variables, parameters, and c o e f f i c i e n t s used i n t h i s study. I.  MODEL FOR ESTIMATING TECHNOLOGICAL CHANGE The basic model f o r t h i s study was a l i n e a r homoge-  neous Cobb-Douglas production function of the form <&«Ae e £ u t  f +  w + h w 2  L  1 _a  K  a  where: (1) Q represents annual gross output i n the primary a g r i c u l t u r a l sector at base period prices; (2) L represents the number of persons employed i n the a g r i c u l t u r a l sector;  47 (3)  K represents the equivalent annual flow of mate-  r i a l inputs (intermediate goods purchased from other sectors of the economy), and c a p i t a l services including livestock, land, buildings, and machinery and implements a l l measured at base period prices; (4)  t i s a time index, 1 , 2 ,  ...,31,  representing the  years during the time period 1935-65; (5)  w i s an annual index which was designed as a  proxy f o r environmental influences on output, and measures the observed deviations from the expected long-term trend of a weighted composite of crop y i e l d s ; (6)  e  u t  1  i s a s h i f t function designed to measure the  annual percentage rate (lOOu) of neutral disembodied techn o l o g i c a l change; and  2 (7)  e*  , + s w +  *  l w  i s a function designed to r e l a t e actual  output, Q, to p o t e n t i a l output through the weather index, w. The model was estimated i n natural l o g - l i n e a r form using the least-squares regression technique, which provided estimates of: the constant, InA*(=lnA+f); the disembodied  2 technological change c o e f f i c i e n t , u; the w and w c o e f f i c i e n t s , g and h; and the e l a s t i c i t y of output with respect to capital,a.  The time series data consisted of 31 obser-  vations on Q, t , w, L, and K f o r each of the years 1935-65. For purposes of t h i s study, the index i s called a "weather index".  The rates of technological  change embodied i n mate-  r i a l inputs, and i n machinery and implements,^ and ft respectively, were measured i n d i r e c t l y i n the manner suggested by Solow and I n t r i l i g a t o r , and reviewed above i n Chapter I I .  A p r i o r i values of ^ and /\ were used to 2  construct  alternative series f o r the K variable.  there was  an alternative time series f o r K f o r each possible  combination of £ and 7\ .  The model was  Thus,  estimated using each  of these alternatives which resulted i n a matrix of sion equations where each regression was.computed on basis of a d i f f e r e n t time series for K.  regresthe  The r e a l world  values of (3 and rl were then inferred by choosing the "best" regression  equation using the c r i t e r i a of goodness of f i t ,  significance l e v e l s of the estimated c o e f f i c i e n t s and  low  standard e r r o r s . The  above model i s based on several important assump-  t i o n s : (1) disembodied technological  change was  Hicks-neutral  and proceeded at a constant rate; (2) embodied technological constant rate and was  change proceeded at a  capital-augmenting i n the vintage  sense, which implies that the productive quality of mater i a l inputs improved at an annual rate of 100^ per cent, and that the productive quality of new  gross investment i n  ^Section II below outlines the detailed method used to derive the alternative K s e r i e s .  machinery and implements improved at an annual rate of 100 A per cent, that i s , machinery and implements purchased i n any year were 100?\ per cent more productive than those purchased i n the preceding year; (3) the Cobb-Douglas production function was l i n e a r homogeneous i n labor and c a p i t a l , which implies  constant  returns to scale and unitary e l a s t i c i t y of substitution between c a p i t a l and labor; (4) the a g r i c u l t u r a l sector was i n a state of perf e c t l y competitive  equilibrium;  (5) inputs of labor, l i v e s t o c k , land, and buildings were homogeneous over time; (6) c a p i t a l inputs were u t i l i z e d at a constant rate; and (7) labor was allocated so that i t s marginal product was equated over a l l vintages of machinery and implements. The construction of the data s e r i e s , p a r t i c u l a r l y f o r the flow of c a p i t a l services and the derivation of the equivalent stock of machinery and implements, required sever a l additional assumptions.  However, these are more  conveniently discussed i n the following section, which deals s p e c i f i c a l l y with measurement of the variables. The above assumptions are highly r e s t r i c t i v e . Assumptions (4),  (6) and (7) were necessary because of the  lack of f e a s i b l e operational a l t e r n a t i v e s .  Assumption  (5)  i s a serious deficiency i n t h i s study, since i t i s unreasonable to expect that the productive  quality o f these inputs  has remained unchanged over the entire period, 1935-65. However, within the context o f the general approach of t h i s study, alternative methods f o r measuring embodied technol o g i c a l change i n more than two factors are not a v a i l a b l e . In a recent study of technological change i n Canadian a g r i culture, 1946-65, L i empirically investigated the hypotheses of constant returns to scale, Hicks-neutral  disembodied  technological change and unitary e l a s t i c i t y of substitution between c a p i t a l and labor.  He did not f i n d any s t a t i s t i c a l  evidence which would r e j e c t any of these hypotheses.  3  How-  ever, since t h i s study covered a longer time period, a dummy variable was devised to investigate whether the parameters and c o e f f i c i e n t s of the production  function changed  s i g n i f i c a n t l y during the time period under study. The assumption of constant returns to scale was also relaxed i n an alternative model.  Therefore,  i t was possible to  compare the regression r e s u l t s under assumptions of economies or diseconomies of scale and constant returns to scale. The s p e c i f i c models used to investigate the s t a b i l i t y o f the production  function, and to relax the assumption of constant  •'Lew-king L i , "Technological Change i n Canadian Agriculture," (unpublished Doctoral d i s s e r t a t i o n , University of Manitoba, Winnipeg, 1968), pp. 7 6 - 8 7 .  returns to scale are outlined i n d e t a i l i n the following chapter. It i s well known that variations i n climatic conditions account f o r substantial year-to-year v a r i a t i o n i n a g r i c u l t u r a l production, especially i n the output of f i e l d crops.  One method of allowing f o r t h i s involves d i r e c t l y  adjusting the f i e l d crops component of output with a weather index.  This method has been used by L i , and was used as an  alternative i n t h i s study.  4  Such a procedure, however,  r e s u l t s i n the use of an independently calculated measure of potential output to estimate the production function. However, since the production function i t s e l f i s intended to provide an estimate of potential output, i t i s somewhat c i r c u l a r to impose an independently calculated measure of p o t e n t i a l output at the o u t s e t .  5  Therefore, i t i s more  l o g i c a l to introduce an expression into the production function which would r e l a t e potential and actual output.  (observed)  The basic functional form, ^ SW+hw , used i n t h i s +  e  study i s similar to the one used by Solow to relate potent i a l and actual output i n the U.S. economy through the unemployment r a t e .  This p a r t i c u l a r expression may  ^Ibid., pp. 4 3 - 4 4 . R. M. Solow, "Technical Progress, Capital Formation, and Economic Growth," American Economic Review, 52:77, May, 1962. 5  6  I b i d . , p. 78.  duplicate the l e f t h a l f of the normal curve, and, a p r i o r i , i t seemed to possess the r i g h t general shape.  However, as  outlined i n the following chapter an alternative functional form was also investigated. II.  MEASUREMENT OF THE VARIABLES  Annual time series data f o r gross output (Q), weather index (w), labor input (L), and the flow of c a p i t a l services (K),  were required to estimate technological!change. The  main data sources were publications of the Dominion Bureau of S t a t i s t i c s .  The series on output and c a p i t a l services  were measured at 1935-39 constant prices.  This base period  was chosen of necessity, since the o f f i c i a l price indexes, which were used as deflators, are constructed on the base period, 1935-39=100.  A description of the derivation of the  required time series follows. Gross A g r i c u l t u r a l Output (Q) Since the s p e c i f i c a t i o n of the production function included material inputs, the relevant concept of output was gross output rather than a measure of value-added production.  Gross a g r i c u l t u r a l output consists of three  components: (1) cash receipts from the sale of farm products (excluding inter-farm t r a n s f e r s ) ; (2) income i n kind; and (3) changes i n farm-held inventories of f i e l d crops and  5 3  livestock.  Each of these components was further subdivided  into f i e l d crops, l i v e s t o c k and livestock products, and forest and maple products which, i n turn, were deflated by the appropriate price index.  7  Total cash receipts, income  i n kind, and inventory changes f o r l i v e s t o c k and products, and f o r f i e l d crops were'deflated by the animal products and f i e l d products components, respectively, of the Canadian farm products price index.^  Total cash receipts and income  i n kind from forest and maple products were deflated by the lumber and timber component of the general wholesale price Q  index.  Gross output at base period prices was obtained as  the sum of the deflated l i v e s t o c k , f i e l d crops, and forest and maple products output. One variant of the gross output series was constructed by d i v i d i n g the t o t a l f i e l d crop component by the weather index described i n the following section.  This had the  e f f e c t of increasing gross output i n years of unfavorable 'For a detailed description of the various income components see data source: Canada, Dominion Bureau of S t a t i s t i c s , Handbook of A g r i c u l t u r a l S t a t i s t i c s . Fart I I : Farm Income - 1 9 2 6 - o " 5 [Ottawa: Queen's Printer, 1 9 6 7 ) Price index data source: Canada, Dominion Bureau of S t a t i s t i c s , Prices and Price Indexes (Ottawa: Queen's P r i n t e r , various issues)• 9 Price index data source: I b i d . This was not the most i d e a l price d e f l a t o r , but a more suitable alternative was not available.  weather conditions, and reducing the measure of output i n years of better than average weather conditions. The data series f o r gross output, Q, and gross output adjusted f o r weather influences, Q*, and 3 ,  are shown i n Table V, columns 2  respectively.  Weather Index (w) This variable was designed as a proxy f o r environmental e f f e c t s on a g r i c u l t u r a l output.  The concept used to  construct the index was suggested by S t a l l i n g s . ^  He  employed time series of crop y i e l d s from experimental plots where as many variables as possible were held constant. A trend was estimated to account f o r changing s o i l and seed quality over time.  fertility  The crop y i e l d v a r i a t i o n about  the estimated trend provided an i n d i c a t i o n of the year-toyear influence of weather on y i e l d s . volves two basic assumptions:  (1)  Such a method i n -  a l l variations i n y i e l d  due to non-weather influences not correlated with weather are randomly and normally d i s t r i b u t e d with an expected value of zero; and (2)  the trend of y i e l d s i s l i n e a r , and  can be removed by the simple regression of y i e l d on time. In view of the n o n a v a i l a b i l i t y of suitable experimental plot data, and the very aggregated nature of t h i s  James L. S t a l l i n g s , "A Measure of the Influence of Weather on Crop Production," Journal of Farm Economics. 43:1153-59, December, 1961. xu  study, average annual y i e l d s were used to construct the index. In t h i s respect the method used i n t h i s study d i f f e r e d from that suggested by S t a l l i n g s .  The significance of t h i s depar-  ture i n method i s that additional factors influencing y i e l d s , which could be held constant i n an experimental plot, were included i n the weather index developed f o r t h i s study. For example, the weather index may include such non-weather influences as annual variations i n seed and f e r t i l i z e r application, c u l t u r a l practices, and crop damage by pests. The weather index, therefore, i s an "ex post" measure of a l l influences on crop y i e l d s a f t e r removal o f the long-term l i n e a r trend.  However, t h i s did not seem to be a serious  l i m i t a t i o n f o r purposes of t h i s study.  Firstly, i t i s  reasonable to assume that the e f f e c t s of technological change on crop y i e l d s were accounted f o r by the estimated l i n e a r trend.  Therefore, the weather index would not remove the  e f f e c t of technological change which t h i s study to measure.  attempted  Secondly, since the c o r r e l a t i o n of the weather  index with the other explanatory variables, labor and c a p i t a l , was n e g l i g i b l e , the weather index would not exp l a i n any of the annual v a r i a t i o n i n output properly attributable to changes i n labor and c a p i t a l inputs. The actual weather index was constructed by estimating a simple regression o f the form y=a+bx  f o r each crop considered, where y i s the average y i e l d i n bushels per acre, and x i s a time index representing each of the years 1935-65.  The crops considered were a l l wheat,  oats, and barley i n each of the P r a i r i e Provinces.  A  weather index was computed f o r each crop i n each province from the regression r e s u l t s by dividing the observed y i e l d by the predicted y i e l d value.  The nine i n d i v i d u a l indexes  were then combined into a single aggregate weather index by weighting each according to t h e i r value of production as a proportion of the t o t a l value of production of a l l three crops i n the three p r o v i n c e s .  x±  The  aggregate  weather index i s shown i n Table V, column 4. Labor (L) Labor input was measured i n man-years on the basis of the number of persons employed annually i n agriculture as reported i n the Labour Force Survey.  The number of  persons employed includes those paid and unpaid, fourteen years of age and over.  Regular quarterly and monthly  surveys were not i n i t i a t e d u n t i l 1945•  Prior to t h i s ,  only annual estimates based on the number of persons employed at the beginning of June are available.  There-  S o u r c e of y i e l d and value of production data f o r 1 9 3 5 - 6 2 : Canada, Dominion Bureau of S t a t i s t i c s , Handbook of A g r i c u l t u r a l S t a t i s t i c s . Part I: F i e l d Crops (Ottawa: Queen's Printer, 1 9 6 4 J ; and for 1963-65: Canada, Dominion Bureau of S t a t i s t i c s . Quarterly B u l l e t i n of A g r i c u l t u r a l S t a t i s t i c s (Ottawa: Queen's Printer, various i s s u e s ) . xx  fore, to ensure a continuous and comparable series, the employment estimates used f o r the years 1946-65 were the June estimates rather than the annual averages.  This i s  a potential weakness i n that agriculture i s characterized by considerable seasonal f l u c t u a t i o n i n employment.  How-  ever, a comparison of the June estimates with the annual averages f o r the 1946-65 period shows that, while the June estimates were s l i g h t l y larger i n magnitude, the trend and year-to-year changes diverged very l i t t l e . Although the Labour Force Survey i s the only source of employment data f o r agriculture, the estimates have severe l i m i t a t i o n s which must be recognized.  In addition  to the sampling error of the survey i t s e l f , a simple measure such as the number of persons employed f a i l s to take into account the changing structure and quality of the a g r i c u l t u r a l labor force.  The average hours of work per  week have been d e c l i n i n g .  Therefore, other things being  equal, a simple measure of labor input such as the number of persons employed would be biased upwards i n the l a t e r years.  The age and sex composition of the labor force  i s ignored.  The proportion of people employed who  the younger age groups has been declining.  are i n  Therefore, to  the extent that older workers are.less productive because of t h e i r age, the labor input estimates could be biased upwards i n the l a t e r years.  On the other hand, however,  i t i s very l i k e l y that the q u a l i t y of the labor force has improved over time, as a r e s u l t of improved health standards and s k i l l s .  This would r e s u l t i n a downward bias i n  the measurement of labor input.  Ideally, the labor input  series should have been adjusted f o r these influences. However, f o r purposes of t h i s study such adjustments were not attempted because of the lack of appropriate information on the r e l a t i o n s h i p s involved.  Any adjustments made would  tend to be highly a r b i t r a r y and, therefore,  questionable.  Moreover, the e f f e c t s of the various influences are to some extent o f f s e t t i n g . L i attempted to account f o r the changing age and composition  of the a g r i c u l t u r a l labor force by  sex  developing  12  the concept of a man-equivalent.  However, a comparison  of L i s data with the labor input series used i n t h i s study f  f o r the 1946-65 period reveals that the average annual percentage decline i n the two series d i f f e r e d by l e s s than 0.2  per cent, and the year-to-year movements were very  similar.  This was  interpreted as an additional i n d i c a t i o n  that, given data l i m i t a t i o n s , detailed adjustments to the labor input series were not j u s t i f i e d . Thus, the measure of annual labor input used i n t h i s study was the June estimate of the t o t a l number of L i , op_. c i t . . p. 45*  59 persons employed i n a g r i c u l t u r e . ^ 1  Table V,  Measurement of the  (K) flow of c a p i t a l services  data s e r i e s at base p e r i o d  stock and  poultry  on farms;  prices:  (5) stock o f machinery and inputs.  The  (4) amount o f l a n d  implements; and  following  of  live-  (3) input;  (6) q u a n t i t y  of  method o f aggregating these compo-  nents i n t o a s i n g l e measure o f the i s outlined  (1) q u a n t i t y  required  (2) stock o f b u i l d i n g s ;  amount of b u i l d i n g d e p r e c i a t i o n ;  material  s e r i e s i s shown i n  column 5«  Flow o f C a p i t a l S e r v i c e s  six  The  flow of c a p i t a l  a b r i e f discussion  o f the  services  derivation  of each s e r i e s . Livestock poultry  and  poultry.  The  on farms at base p e r i o d  d i n g the  current  1 4  p r i c e s was  value of l i v e s t o c k and  animal products component o f the price index.  value o f l i v e s t o c k  The  derived  p o u l t r y by  by  and divi-  the  Canadian farm products  r e s u l t i n g s e r i e s i s shown i n Table  V,  •^Source f o r 1935-45: Canada, Dominion Bureau o f S t a t i s t i c s , Canadian Labour Force E s t i m a t e s , 1931-45. Reference Paper No. 23 (Ottawa: Queen's P r i n t e r , 1958); and f o r 1946-65: Canada, Dominion Bureau o f S t a t i s t i c s . The Labour Force (Ottawa: Queen's P r i n t e r , v a r i o u s i s s u e s ) . C u r r e n t v a l u e s o f l i v e s t o c k and p o u l t r y d a t a s o u r c e : Canada, Dominion Bureau o f S t a t i s t i c s , Q u a r t e r l y B u l l e t i n o f A g r i c u l t u r a l S t a t i s t i c s (Ottawa: Queen's P r i n t e r , v a r i o u s i s s u e s ) . P r i c e index d a t a s o u r c e : Canada, Dominion Bureau o f S t a t i s t i c s , P r i c e s and P r i c e Indexes (Ottawa: Queen's P r i n t e r , various issues). 1 4  60 column 7. Buildings.  Since the value of the stock of buildings  was not available separately, i t was necessary to derive the series from published estimates of gross investment and the depreciation figures which are discussed below. ^ x  The  net stock of a g r i c u l t u r a l buildings at base period prices i n year t+1 was defined as the net stock i n year t plus gross investment i n year t+1 minus depreciation i n year t, a l l at base period p r i c e s . prices was  Gross investment at base period  obtained by d e f l a t i n g the current d o l l a r e s t i -  mates of gross investment by the b u i l d i n g materials component of the price index numbers of commodities and services used by farmers.  The r e a l net stock of buildings  series i s shown i n Table V, column 8. Building depreciation.  The published estimates for  building depreciation do not include depreciation on  ''New construction (gross investment) data source f o r 1935-48: 0. J . Firestone, Private and Public Investment i n Canada 1926-1951, Department of Trade and Commerce Tottawa: King's Printer, 1951), p. 154; and f o r 1949-65: Canada, Dominion Bureau of S t a t i s t i c s , Private and Public Investment i n Canada. Outlook and Regional Estimates (Ottawa!! Queen's Printer, various i s s u e s ) . 16  Price index data source: Canada, Dominion Bureau of S t a t i s t i c s , Price Index Numbers of Commodities and Services Used by Farmers (Ottawa: Queen's Printer, various issues).  buildings located on rented farms.  Therefore, i t was  necessary to adjust the published e s t i m a t e s .  17  I t was  assumed that the average value of buildings on rented farms, part owner - part tenant farms, and owner operated farms was equal.  I t was further assumed that one-half of the  farms c l a s s i f i e d as part owner - part tenant had buildings on the rented portion. Using these assumptions, adjustment  an annual  factor was defined as the percentage of t o t a l  farms operated by tenants plus one-half of the percentage of part owner - part tenant farms.  The adjustment  factor  was calculated from Census of Agriculture data f o r census years, and values f o r intercensal years were interpolated. The building depreciation series adjusted to include rented farms was then obtained by dividing the published series by one minus the adjustment  factor, which increased  the published estimates by approximately f i f t e e n per cent. To arrive at depreciation at base period prices, the adjusted series was deflated by the building materials -I  price index.  d  The f i n a l series i s shown i n Table V,  column 9. 'Source of published estimates: Canada, Dominion Bureau of S t a t i s t i c s , Handbook of A g r i c u l t u r a l S t a t i s t i c s . Part I I : Farm Income - 1926-63 TTJttawa: Queen's Printer, 1967). 18 Source of price index data: Canada, Dominion Bureau of S t a t i s t i c s , Price Index Numbers of Commodities and Services Used by Farmers (Ottawa: Queen's Printer, various issues).  Land.  The t o t a l a g r i c u l t u r a l land area i n Canada  increased by l e s s than seven per cent from 1931 to In f a c t , between 1941 and 1961 there was i n t o t a l a g r i c u l t u r a l land area.  1966.  a s l i g h t decline  However, the r a t i o of  improved to unimproved land increased s u b s t a n t i a l l y from 1.1  i n 1935 to 1.6  i n 1965.  The land input series devel-  oped for t h i s study was an attempt to account f o r the s h i f t towards improved land.  For census years the acreage of  improved and unimproved land was  taken from the Census of  Agriculture, and estimates f o r the intercensal years were interpolated.  The value of t o t a l a g r i c u l t u r a l land at base  period prices was  then calculated by multiplying the  acreage estimates by the average value per acre during 1935-39 f o r improved and unimproved land, r e s p e c t i v e l y . ^ The r e s u l t i n g series i s shown i n Table V, column 10. Material inputs.  Material inputs r e f e r s to the goods  and services other than durable c a p i t a l which are purchased from the non-agricultural sector of the economy and consumed i n the process of production.  The material input  The average values per acre f o r 1935-39 were d e r i ved by d i v i d i n g the t o t a l value of land and buildings (less the value of buildings as derived for t h i s study) by the number of acres. This resulted i n a 1935-39 average value per acre of $19.60 and $4«20 for improved and unimproved land, r e s p e c t i v e l y . Source of t o t a l value of land and buildings data: Canada, Dominion Bureau of S t a t i s t i c s , Quarterly B u l l e t i n of A g r i c u l t u r a l S t a t i s t i c s (Ottawa: Queen's Printer, various issues)•  series at base period prices was derived as the sum of s i x items: (1) t o t a l machinery expenses (excluding machinery repairs) deflated by the price index f o r gasoline, o i l , and grease; (2) f e r t i l i z e r and lime expense deflated by the price index f o r f e r t i l i z e r ; the price index f o r feed;  (3) feed expense deflated by  (4) machinery repair expense  deflated by the price index for farm machinery; (5) b u i l d ing repairs (adjusted to include buildings on rented farms by employing the adjustment factor outlined above under building depreciation) deflated by the b u i l d i n g materials price index; and (6) the sum of other crop and l i v e s t o c k expense, e l e c t r i c i t y , telephone, and miscellaneous expense 70  deflated by the price index f o r hardware items.  This  procedure resulted i n a time series of material inputs at base period prices which embodies no technological change, that is,j2>s=0.  The basic series i s shown i n Table V,  column 12. Material input series embodying technological change at various rates were derived from the basic series by assuming that technological change occurred  at a constant  * Source of a l l material inputs expense data: Canada Dominion Bureau of S t a t i s t i c s , Handbook of A g r i c u l t u r a l S t a t i s t i c s , Part I I , Farm Income - 1926-55 (Ottawa: Queen's P r i n t e r , 1967). Source of a l l price index data: Canada, Dominion Bureau of S t a t i s t i c s , Price Index Numbers of Commodities and Services Used by Farmers (Ottawa: Queen's P r i n t e r , various issues)• u  64 annual rate of 100^ per cent.  Augmented material input  series f o r various values of ^ were e a s i l y derived by multiplying each observation, n, of the$=0 series by  (1+P)  n  where n=0,  1 , 2,  30.  To test the s e n s i t i v i t y of the method of estimating embodied technological change to the price indexes used to deflate the current d o l l a r value of material inputs, an alternative series for material inputs was derived by d e f l a t i n g the t o t a l current d o l l a r value of material input expenses by the general wholesale price i n d e x . wholesale price index was  21  The  general  chosen f o r t h i s purpose because  i t i s often used as a reference l e v e l against which to compare the movements of other price indexes.  The alternative  series f o r material inputs when^=0 i s shown i n Table V, column 13.  Based on t h i s a l t e r n a t i v e , material input series  embodying varying rates of technological change were constructed i n the manner outlined i n the preceding  para-  graph. Stock of machinery and implements.  Since a purpose  of t h i s study was to measure embodied technological change i n machinery and implements, knowledge about the vintage composition  of the stock of machinery and implements was  ^Source of wholesale price index data: Canada, Dominion Bureau of S t a t i s t i c s , Prices and Price Indexes (Ottawa: Queen's P r i n t e r , various issues)•  required.  Assuming that machinery and implements purchased  i n any year were 100 A per cent more productive than those purchased i n the preceding year, the equivalent stock of machinery and implements was defined as the sum of the surviving machinery and implements of d i f f e r e n t vintages, after weighting each vintage by the appropriate rate of embodied technological change.  Thus, derivation of the  equivalent stock of machinery and implements embodying technological change at an annual rate of 100 ?\ per cent required a time series of past gross investment measured i n volume terms, that i s , at base period prices, and knowledge about the service l i f e of machines and implements, that i s , knowledge about the rate of replacement of o l d investment goods. Gross investment at base period prices was obtained by d e f l a t i n g the current d o l l a r estimates of gross investment (Table I I , column 2) by the farm machinery component of the price index numbers of commodities and services used by farmers.  22  The r e s u l t i n g series of annual gross investment  at base period prices f o r 1921-65 i s shown i n Table I I , column 3.  To test the s e n s i t i v i t y of the method of measur-  ing embodied technological change to the price deflator, gross investment was also deflated by the USDA index of  Source of price index data: Canada, Dominion Bureau of S t a t i s t i c s , Price Index Numbers of Commodities and Services Used by Farmers (Ottawa: Queen's Printer, various i s s u e s ) .  66 TABLE I I GROSS INVESTMENT IN MACHINERY AND IMPLEMENTS, CANADIAN AGRICULTURE, 1921-65  Year (1) 1921 1922 1923 1924 1925 1926 1927 1928 1929 1930 1931 1932 1933 1934 1935 1936 1937 1938 1939 1940 1941 1942 1943 1944 1945 1946 1947 1948 1949 1950 1951 1952 1953 1954 1955 1956  Gross investment at 1935-39 prices Gross Deflated byDeflated by investment DBS price adj. USDA at current p r i c e s * index price index (2) (3) (4) of dollars thousands 53088 50590 59140 28725 30237 31952 45468 42240 42753 32105 31353 31261 33790 34515 33489 69200 70902 68719 88600 90872 87377 116200 115164 119057 100300 102872 99405 74227 72000 72217 26700 28135 26202 23400 24867 22180 15500 16830 15784 30600 32347 32797 34400 36021 35318 44200 45194 44964 62900 64712 62837 67400 64745 648O8 63000 60811 59886 82600 78072 74684 88400 81027 78929 71500 62500 60287 39400 33646 32059 72900 57949 61675 90400 78540 71069 131600 104527 110774 214900 170150 159067 280500 198093 178095 352395 222612 193517 197286 389640 236002 226480 206072 423065 227980 449805 230197 440255 223821 220017 296050 149596 148993 162850 160747 323745 176902 177409 371495  67 TABLE I I (continued)  Ye ax (1) 1957 1958 1959 I960 1961 1962 1963 1964 1965  Gross investment  Gross investment at 193?-39 prices Deflated by Deflated by DBS price a d j . USDA index price index  thousands 325655 347620 410650 423065 389640 456490 547215 612155 683780  (3)  (Jtl  ofdollars 145512 151750 146861 153339 165318 175867 166430 174532 149059 150266 170269 163969 200519 191401 216940 209499 240007 227547  *Source of gross investment data f o r 1921-25: Kenneth Buckley, C a p i t a l Formation i n Canada 1696-1930 (Toronto: University of Toronto Press, 1955), pp. 131-32; f o r 1926-46: 0. J . Firestone, Private and Public Investment i n Canada 1925-1951. Department of Trade and Commerce, TOttawa: King's Printer, 1951); and f o r 1949-65: Canada, Dominion Bureau of S t a t i s t i c s , Private and Public Investment i n Canada, Outlook and Regional Estimates (Ottawa: Queen's Printer, various i s s u e s ) . farm machinery prices paid by farmers. *  Before the USDA  index was used as a deflator, however, i t was converted to a 1935-39 base and adjusted f o r the changing value o f the U.S. d o l l a r i n Canadian funds.  Gross investment as deflated  by the adjusted USDA index i s shown i n Table I I , column 4.  •'Source of price index data: United States Department of Agriculture, A g r i c u l t u r a l S t a t i s t i c s (Washington: Government Printing O f f i c e , various i s s u e s ) .  Four basic hypotheses about the rate of replacement of old investment goods have been used i n t o t a l factor prod u c t i v i t y studies: (1) to replacement; (2)  accounting depreciation i s set equal  gross investment i n some e a r l i e r period  i s set equal to replacement; (3)  a weighted average of past  investment with weights derived from studies of the s u r v i v a l curves of i n d i v i d u a l pieces of equipment i s set equal to replacement; and (4)  each investment generates a series of  replacement investments over t i m e . study, hypothesis (2) ery  2 4  For purposes of t h i s  was adopted, and the stock of machin-  and implements was measured by assuming a service l i f e  of thirteen years a f t e r which the machine or implement i s discarded.  25  Thus, the stock of machinery and  implements  i s a thirteen-year moving sum of past gross investment at base period p r i c e s .  This method i s analogous to that used  by Hood and S c o t t ,  and to that suggested by G r i l i c h e s .  2 o  2 7  D. W. Jorgenson and Z. G r i l i c h e s , "The Explanation of Productivity Change," Review of Economic Studies.34:255, July, 1967. 24  25  service l i f e of thirteen years was also used by Hood and Scott. See: W.C. Hood and A. Scott, Output, Labour, and Capital i n the Canadian Economy, Royal Commission on Canada's Economic Prospects (Ottawa: Queen*s Printer, 1957), p. 473. I b i d . , pp. 234-37. 2 6  27  'Z. G r i l i c h e s , "Measuring Inputs i n Agriculture: a C r i t i c a l Survey," Journal of Farm Economics. 42:1417, December, I 9 6 0 .  The equivalent stock of machinery and implements i n year t , J(t),  was defined as  J(t)-  £  (i+^) Kv) v  v«=t-12 where I(v) i s the amount of gross investment i n year v at base period prices,  For<\*=0, the stocks o f machinery and  implements derived from gross investment deflated by the DBS price index and the USDA price index are shown i n Table V, columns 14 and 1 5 , respectively. Two assumptions are inherent i n t h i s method: (1) a l l machinery and implements have the same service l i f e which i s constant over time; and (2) gross investment at base period prices i s an unbiased measure of the quantity of machinery and implements actually brought into production during any given year.  Implicit i n the assumption of a  common service l i f e f o r a l l machinery and implements i s the condition that the service l i v e s of various kinds o f machinery and implements can be averaged into one representative figure, and that annual gross investments consist of constant proportions of the various kinds of machinery and implements.*  In order to provide an i n d i -  cation of the s e n s i t i v i t y of the method to assumptions about the service l i f e of machinery and implements, stocks of machinery and implements based on alternative assumpHood and Scott, 0 £ . c i t . , p. 239.  tions about the service l i f e and rate of replacement of old investment goods were also constructed. 9 2  However, the  r e s u l t s of the regression models using the various a l t e r natives followed the same pattern, and d i f f e r e d only s l i g h t l y i n degree from the r e s u l t s using the basic assumpt i o n of a thirteen-year service l i f e . 3 0  The issue involved  i n the assumption that gross investment at base period p r i ces i s a measure of the quantity of machinery and  imple-  ments a c t u a l l y brought into production, i s the separation of the values of transactions i n new a p r i c e and a quantity component.  investment goods into  This i s commonly  achieved by d e f l a t i n g current d o l l a r estimates by an appropriate price index.  However, an error i n t h i s separ-  ation w i l l a f f e c t the magnitude of the flow of c a p i t a l services, and r e s u l t i n a biased measure of technological  29 he a l t e r n a t i v e s were: (1) a fifteen-year sum of past gross investment; (2) a service l i f e function, l - ( t / 1 5 ) , which allows f o r a constant proportion of gross investment i n any year to be discarded i n each successive year; (3) a service l i f e function, l - ( t / l 5 ) , which allows for an increasing proportion of gross investment i n any year to be discarded; and (4) a service l i f e function, 1-(>/t/ -715), which allows f o r a decreasing proportion of gross investment i n any year to be discarded i n each successive year. T  2  30  2  ^ Since the regression r e s u l t s based on the a l t e r native assumptions did not a f f e c t the conclusions of the study, they are not reported.  change. Aggregation of the flow of c a p i t a l services.  The  annual flow of c a p i t a l services from the stocks of land, buildings and livestock was derived by assuming an annual rate of return on the investment  at base period prices.  The flow of c a p i t a l services from the stock of buildings also included depreciation. A method suggested  by  G r i l i c h e s was employed to convert the stock of machinery and implements into an annual flow of s e r v i c e s . ing  3 2  Assum-  that there i s no deterioration with age, and that the  flow of services i s constant over the l i f e span of a l l machines and implements, then the annual flow of services equals an annuity f o r the service l i f e at the rate of return.  As G r i l i c h e s points out, under these assumptions  the annuity equals the sum of annual interest and  depre-  c i a t i o n charges, with the interest charges f a l l i n g and the depreciation charges r i s i n g as the machine ages.33 Thus, the annual flow of c a p i t a l services derived for  t h i s study was the arithmetic sum of four components:  (l) the value of livestock, plus the value of land, plus 31  This also applies to a l l of the other variables i n t h i s study where the quantity has been measured by d e f l a t i n g current d o l l a r estimates by a price index. 3 Griliches, loc. c i t . 2  Ibid.  the stock of buildings, a l l at base period prices m u l t i p l i e d by the rate of r e t u r n ;  3 4  (2) b u i l d i n g depreciation at base  period prices; (3) material inputs at base period prices; and (4) the stock of machinery and implements at base period prices multiplied by the factor f o r a thirteen-year  annuity  at the rate of ret urn. 5 3  An annual rate of return of s i x per cent was assumed. An alternative rate of eight per cent was also employed. However, the regression r e s u l t s using an eight per cent return followed the same pattern and d i f f e r e d only s l i g h t l y i n degree from the r e s u l t s using the basic assumption of a s i x per cent return. The alternative r e s u l t s are not reported. 34  •^The factor f o r a thirteen-year, s i x per cent annuity i s 0.11296.  CHAPTER IV EMPIRICAL RESULTS I.  INTRODUCTION  The multiple regression routine of the "UBC  TRIP"  computer program was used to provide least-squares regression estimates.  The basic model was estimated i n natural  x  logarithmic form ln(Q/L)=lnA+ut+f+gw+hw +ln(K/L) +ln ^ 2  a  whereJJU i s a disturbance term about which the usual assumptions were made.  2  The output of the program included: (1)  the estimated regression c o e f f i c i e n t s ; (2) the standard errors of each regression c o e f f i c i e n t ; (3) the F-ratio and associated probability for each regression coefficient;3 (4) the standard error of the estimate, S;  (5) the c o e f f i -  J . H. Bjerring and R. H. H a l l , UBC TRIP (Triangular Regression Package) (Vancouver: University of B r i t i s h Columbia, Computing Centre, 1968). X  The usual assumptions are that/t-are random v a r i ables with zero expectation and constant variance, and are pairwise uncorrelated. See: J . Johnston, Econometric Methods (New York: McGraw-Hill Book Company, Inc., 1963), p. 107. 3  ^The F-ratio i s equivalent to the more common " t " t e s t . See: Ibid.. pp. 123-25. The associated probability i s the l e v e l at which the estimated regression c o e f f i c i e n t i s s i g n i f i c a n t l y d i f f e r e n t from zero. See: B j e r r i n g , op. c i t . . pp. 48-49.  74  cient of multiple determination, R ; 2  Watson d s t a t i s t i c , "d".  and (6) the Durbin-  There are two constant terms,  InA and f , i n the above model.  However, only one constant  term, lnA*=lnA+f, was estimated.  I f desired, InA* can be  separated by noting that actual output must equal potential output when the weather index equals one, which implies f+g(1.0)+h(1.0) =0. 2  Therefore, f can be determined, ates of g and h.  and thus InA, from estim-  A l l other c o e f f i c i e n t s are presented i n  the same units as they appeared i n the models. The method of determining the rate of embodied techn o l o g i c a l change i n machinery and implements and i n material inputs, ^ and  respectively, involved estimating a regres-  sion equation f o r each possible combination of the a p r i o r i imposed values f o r r\ andfb.  Thus, i f m alternative values  of A and n alternative values of ^ were imposed, there would be mxn possible combinations r e s u l t i n g i n a mxn of estimated equations.  matrix  The regression estimates f o r the  various models are presented i n the Appendix.  4  equation the estimated regression c o e f f i c i e n t s ,  For each R, 2  standard error of the estimate (S), and the Durbin-Watson  Each page of a p a r t i c u l a r table shows the regression estimates f o r several values of £ given a s p e c i f i c value of (\, that i s , the regression estimates for an i n d i v i d u a l equation are shown as a column with the column heading and table heading i d e n t i f y i n g the ^ and J\ value, respectively. 4  d statistic ficant  ("d") are shown.  A l l values o f "d" are i n s i g n i -  (that i s , r e j e c t the hypothesis of s e r i a l correlation)  at the one per cent l e v e l o f significance unless otherwise noted.  The standard errors of the regression c o e f f i c i e n t s  are shown i n parentheses.  The associated p r o b a b i l i t y of  the F-ratio f o r each c o e f f i c i e n t i s shown immediately below each standard error. The r e s u l t s of f i v e models are reported. the basic model outlined i n Chapter I I I .  Model I was  In Model I I a l l  technological change was assumed to be embodied i n machinery and implements and material inputs.  The assumption of  constant returns to scale was relaxed i n Model I I I , while two  alternatives for r e l a t i n g actual and potential output  were investigated i n Model IV.  F i n a l l y , Model V was an  attempt to assess the s t a b i l i t y o f the production function over time by introducing a dummy variable into the model. II.  RESULTS OF THE BASIC MODEL  Three alternative sets o f data were employed to e s t i mate the production function Q=Ae e S u t  f +  w + h w 2  L - K . 1  a  a  The regression r e s u l t s for each alternative set o f data are discussed  i n d i v i d u a l l y as Models 1(a),  (b) and (c).  Model 1(a)  (Table VII)  In t h i s model, material inputs were deflated by the i n d i v i d u a l price indexes (Table V, column 12), and gross investment  i n machinery and implements by the DBS  index (Table V, column 14). 0.08  price  ^ values ranging from 0.0 to  were used to construct alternative series f o r material  inputs, thus embodying technological change at the corresponding annual rates of 0.0 values ranging from -0.01  to 8,0 per cent.  to 0.03  Likewise, r\  were used to construct a l -  ternative stocks of machinery and implements embodying technological change at the corresponding annual rates of -1.0  to 3.0 per cent.  The matrix of regression r e s u l t s f o r  the various combinations  of j\ and ^ are shown i n Table VII.  (Table VII consists of nine pages; each page reports the results for a specific  Rvalue). 2  Table I I I shows the R  values and standard errors  of the estimate for a l l combinations  of ft and ^ .  It i s  evident from Table I I I that: (1) f o r a given A value, R  2  .  increased and then decreased as the value of ^ increased; and  (2) f o r a given ^ value, R  A increased.  2  decreased as the value of  Some i n d i v i d u a l numerical r e s u l t s are  summarized as follows: ft value Highest R Lowest R  2  2  (.9877) (.9847)  -0.01 0.03  ^ value 0.035  0.0  77 -co  o  o o CO  o o  O O  tO  to L A OO  •CO L A ONO  H CA OvO  O  to  OO  ^  OA t o O L A LA  ON  MD  o  O LA  -CO ONO  VO  O C A  o  o  vO vO O "CO L A ONO  H  vO L A vO O tO L A ONO  tO L A ONO  L A tO vO O tO L A ONQ  CVoA vQtO tO L A ONO  OACV  ON ON L A tO tO L A ONQ  ON ON  -CO L A ONO  tO L A ONO  OH vO O tO L A ONO  cv cv  cH - 4 OvO tO L A ONO  O O  to  vOvO tO L A  sOO tO L A ONO  H CA OvO tO L A ONO  O O vOvO tO L A ONO  O CV vO O  o  vOvO vO o tO L A ONO  L A - * O L A  0AO  ONO  -3-tO OA i - l vOtO O •CO LA o o tO L A ONO  o  •00 L A  o  o o  LA  voo  tO L A ONO  OvO tO L A ONO  LA  0\0  OvO tO L A ONO  tO  ocv  to o vO O tO L A ON O  ONO  -4-C0  CV CV  vO O tO L A ONO  NO  <r\0 to  H IA vOtO tO L A  tO  to  LA  o o  o o  Q LA  o CO  #  Q  OS  S .-3  o w M n EH  PQ  EH  «  §  O  Q  ONO  tO L A ONO  xO CV OLA tO LA ONO  OAO OvO tO LA ONQ  tO LA ONO  vO O tO L A ONO  C—.—I  OAO OvO tO L A ONQ  OM3 O^O tO L A ONO  OCV vO O tO L A ONO  to  LA  ovo  to  to  LA  ONO  \o-ca tO LA  ONQ  o o U N O tO L A  o o  vO  LA L A O LA  tO  LA CA  o  O L A •00 L A  -4-to  vO  O  tO L A OO  H LA \OtO tO L A ONQ  to  o t o  O-dLAO tO LA  H  LAOS tO L A ONO  D-. CO H fx)  CA  o  -00  » A  OO  CM CV  0\0  -00 LA  ONQ  ON tO \OvO tO L A ONQ  MD  tO  O LA  ONQ  C A rH vOtO tO L A ONQ  vOtO  to  LA  ONO  o o  EH  X! co  o o  CAr—I LAO tOvO OO  LA  cv o  vO CV O-LA tO L A  ONO  rH -3OvQ tO L A  o o  to  o  vO O tO L A OO  LAO vO O tO L A ONO  CV - 4 vOtO tO L A ONO  OO L A ON tO L A ONO  L A O L A O LA  tO  o o  CV  CA L A O  tO vO  o o  EH  LA-4"  cv o  OvO  O LA tO L A ONO  tO L A ONQ  H OA C-vO tO L A OO  LAO vO O tO L A ONO  0 0  OCA vO O tO L A OO  vOtO  H -4" vOtO  t o iH  -4-0  to  LA  OO  OvO vOtO tO L A OO  O C A L A ON tO L A  L A O L A ON tO L A  CVOA LAO  ONO  -*o  H\0  tOvO OO  lAO tOvO OO  o t o  O C A  LAO  M Cm  o  o  a>  % <D CO  s •H •p a> a>  £1 -p  CO  o  ft  a  CO  o o  B  a u  L A tO L A O tO L A  EH  S  d) •p  •H  EH  vO CV OLA  CO  o o  O  M  9 19  o  0\0  to  LA  ONO  LA  ON  tO L A ONO  ONO  t0\O  ONO  LAO tOvO OO  -4H  tOvO  o o  o CO  u o u u -a u T5  p CO  H O  o  I  LA O  o  LA  o  rH O  CV  o  LA  CV  o  CA  o  78 ft value Lowest S (.0551)  ^ value  -0.01  Most s i g n i f i c a n t u (0.35 per cent l e v e l )  0.03  Most s i g n i f i c a n t a (0.39 per cent l e v e l )  -0.01  0.035 0.0 0.035  Thus, the "best" regression based on the c r i t e r i a of goodness of f i t , low standard error of the estimate and significance l e v e l of the a c o e f f i c i e n t occurred when ^ = - 0 . 0 1 and ^ = 0 . 0 3 5 .  This implies embodied technological change i n  material inputs at the annual rate of 3»5 per cent, and i n machinery and implements at the negative annual rate of 1.0 per cent.  A negative rate of embodied technological change  i n machinery and implements was disturbing and contradicted a p r i o r i expectations.  This should most l i k e l y be considered  as a spurious r e s u l t f o r various reasons which are discussed below.  The s p e c i f i c negative value offtwhich would have  given the "best f i t " was not determined, since i n view of the questionable nature of the r e s u l t s , the model was not extended to include higher negative values f o r A . When fWO.O, that i s , no embodied technological change i n machinery and implements, the "best" regression (R =.9873) occurred when $=0,035 to 0 . 0 5 . The a c o e f f i c i e n t was most s i g n i f i c a n t when $ = 0 . 0 4 .  This indicates embodied technolo-  g i c a l change i n material inputs at an annual rate of approximately 4*0 per cent.  These r e s u l t s , therefore, sup-  port the hypothesis of substantial embodied technological  79 change i n material inputs. The u c o e f f i c i e n t , which i s an estimate of the annual rate of disembodied technological change (100 u), had the largest value and was most highly s i g n i f i c a n t i n the regressions when (*<=0.0. This was the expected r e s u l t , because i f embodied technological change i s not s p e c i f i e d , then a l l increases i n t o t a l factor productivity would show up as disembodied technological change.  However, with respect to  ft, the a p r i o r i expected r e s u l t s did not occur. and most s i g n i f i c a n t value of u occurred when  The largest  =0.03, rather  than when ft=0.0. This was further evidence which suggested that the r e s u l t s with respect to embodied technological change i n machinery and implements must be regarded as suspect. When no embodied technological change was s p e c i f i e d (ft=^=0.0), u=0.0246 i n d i c a t i n g an annual rate of disembodied technological change of 2.46 per cent.  In t h i s regression  the u c o e f f i c i e n t was highly s i g n i f i c a n t (1.44 per cent l e v e l ) with a r e l a t i v e l y low standard  error (.0095)*  (\=0.0 andf-0.04 (the "best" regression), u=0.0113.  When Thus,  when embodied technological change was s p e c i f i e d the e s t i mate of disembodied technological change declined, which supports the conclusion that a large portion of increases i n t o t a l factor productivity can be attributed t o technol o g i c a l change embodied i n material inputs.  I t should be  80 noted, however, that the estimates of u became increasingly imprecise and l e s s s i g n i f i c a n t as ^> increased. The a c o e f f i c i e n t was highly s i g n i f i c a n t with low standard errors i n a l l regressions.  The g c o e f f i c i e n t was  not s i g n i f i c a n t , while h was s i g n i f i c a n t at about the 15 per cent l e v e l .  Although the t e s t f o r s e r i a l c o r r e l a t i o n  was inconclusive f o r some regressions, s e r i a l correlation was not considered to be a problem. Model Kb)  (Table VIII)  This model was an attempt to assess the s e n s i t i v i t y of the method to an alternative deflator f o r gross investment i n machinery and implements.  In t h i s model gross  investment was deflated by the adjusted USDA price index (Table V, column 1 5 ) .  A matrix of regression r e s u l t s was  obtained f o r the various combinations of ^ and $ as outlined f o r Model 1(a) above.  The regression r e s u l t s when/l^O.O  are reported i n Table VIII. The regression r e s u l t s of Model 1(b) exhibited the same trends as Model 1(a) with only s l i g h t differences i n the magnitudes of the estimated c o e f f i c i e n t s and s t a t i s t i c a l measures.  The main r e s u l t s are summarized as follows: value  Highest R Lowest R  2  2  (.9879) (.9853)  Lowest S (.0547)  -0.01  ^ value 0.025-0.035  0.03 -0.01  0.0 0.02  -0.035  Rvalue  ft value Most s i g n i f i c a n t u (0.73  per cent l e v e l )  0.03  Most s i g n i f i c a n t a (0.31  per cent l e v e l ) - 0 . 0 1  0.0 0.025-Q.035  Thus, the general conclusions drawn from the r e s u l t s of Model 1(a) are applicable to t h i s model as w e l l .  In view of  the questionable nature of the r e s u l t s with respect to ft, only the regressions i n which ft=0.0 are reported. When ft=0.0, the "best" regression occurred when $=0,035, although R =.9875 i n a l l regressions when 2  to 0 . 0 5 .  =0.025  Thus, t h i s model gave a s l i g h t l y lower estimate  of embodied technological change i n material inputs  (approx-  imately 3«5 per cent compared with 4.0 per cent i n Model 1(a)).  The u c o e f f i c i e n t was almost i d e n t i c a l i n  Models 1(a) and  (b), (0.0113 compared with 0 . 0 1 1 5 ) .  The  a c o e f f i c i e n t , however, was s l i g h t l y more s i g n i f i c a n t i n Model 1(b) than i n Model 1(a). Thus, the r e s u l t s of Model 1(b) were very similar to those of Model 1(a), which suggests that the method was  not  p a r t i c u l a r l y sensitive to the alternative deflator f o r gross investment  i n machinery and implements.  cluded that the r e s u l t s of Model K b )  I t was  con-  did not provide  s i g n i f i c a n t evidence f o r preferring the adjusted USDA price index over the DBS index f o r purposes of t h i s study. Model 1(c)  (Table IX)  This model was an attempt to assess the s e n s i t i v i t y  82 of the method to an alternative d e f l a t o r f o r material inputs. In t h i s model, a l l material inputs were deflated by the general wholesale price index (Table V, column 1 3 ) .  A  matrix of regression r e s u l t s was obtained f o r the various combinations of ({ and ^ as outlined f o r Model 1(a) above. The r e s u l t s when ^=0.0 Like Model K b ) ,  are reported i n Table IX. the r e s u l t s of Model 1(c) showed the  same trends as Model 1(a).  The main r e s u l t s are summarized  as follows: ft value Highest R Lowest R  2  -0.01  (.9880)  2  (.9856)  $ value 0.025-0.035  0.02  Lowest S (.0543)  -0.01  Most s i g n i f i c a n t u (0.13 per cent l e v e l )  0.02  Most s i g n i f i c a n t a (0.26 per cent l e v e l )  -0.01  0.0 0.025-0.03 0.0 0.025-0.03  In view of the questionable nature of the r e s u l t s with respect to ^, only the regressions i n which ^=0.0  are reported.  When ^ = 0 . 0 , the "best" regression occurred when  f=0.035 to 0 . 0 4 , although R =.9877 i n a l l regressions when 2  $=0.03 to 0 . 0 4 .  Thus, t h i s model gave an estimate o f  embodied technological change i n material inputs which was i d e n t i c a l to the estimates of Models 1(a) and (b). However, the u c o e f f i c i e n t was considerably greater i n magnitude (0.0168 compared with 0 . 0 1 1 3 ) ,  and was more highly s i g n i f -  icant (10.72 per cent l e v e l compared with 3 8 . 5 3 ) , than i n Model 1 ( a ) .  83 Thus, the r e s u l t s of Model 1(c) were similar to those of Models 1(a) and  (b).  The most notable difference was  the  larger and more highly s i g n i f i c a n t estimate for disembodied technological pect to  change i n Model 1(c).  The r e s u l t s with res-  however, suggest that the method was  not  sensi-  t i v e to the alternative deflator f o r material inputs, i t was  and  concluded that the r e s u l t s of Model 1(c) did not  provide s i g n i f i c a n t evidence f o r preferring the general wholesale price index over the i n d i v i d u a l price indexes as a deflator for material inputs for purposes of t h i s study. Discussion  of Model I  On a p r i o r i grounds, the r e s u l t s of Models 1(a), (c) with respect to A were unexpected.  (b) and two  There are  possible i n t e r p r e t a t i o n s : (1) the rate of embodied tech-  nological change i n machinery and implements was,  i n fact,  negative during the 1935-65 period; or (2) the method f a i l e d to provide an unbiased estimate of embodied technol o g i c a l change.  Although t h i s study did not provide  s u f f i c i e n t evidence upon which to base a choice between these explanations, there are strong reasons to suspect that the l a t t e r interpretation i s the more plausible  and  realistic. Several factors could account for a biased or spurious estimate of embodied technological there was  the problem of obtaining  change.  First,  an accurate measurement  of the r e a l stock of machinery and implements.  Since  i n d i v i d u a l machines and implements are extremely heterogeneous, they must be aggregated i n value terms, and then deflated by a price index to arrive at a measure of the stock i n volume terms.  5  There are two alternatives f o r  measuring c a p i t a l goods i n value terms.  Capital goods may  be valued i n terms of input costs, or i n terms of their a b i l i t y :to produce (either on the basis of output or capacity).  The f i r s t alternative attributes a l l increases i n  output to changes i n the productivity of c a p i t a l i t s e l f , while the second alternative attributes a l l increases i n output to changes i n productivity i n the production of c a p i t a l goods.  Clearly, neither of these extreme altern-  atives was s a t i s f a c t o r y f o r purposes of t h i s study.  The  c r u c i a l problem was the separation of such elements as design improvements and s e r v i c e a b i l i t y (embodied technolog i c a l change) from changes i n the cost of production; that i s , the separation of increases i n the productivity of machines and implements from increases i n productivity i n the  production of machines and implements.  On the  assumptions that the suppliers of machinery and implements  The following discussion i s l a r g e l y drawn from: Richard Ruggles and Nancy Ruggles, "Concepts of Real Capital Stocks and Services," Output. Input and Productivity Measurement (Studies i n Income and Wealth, V o l . 25• Princeton: Princeton University Press, 1961), pp. 3#7-411. 5  do not have monopolistic power i n the product markets, and that the price charged continues to r e f l e c t c h i e f l y the price of inputs available to the a g r i c u l t u r a l machinery and implement industry, the appropriate measure of machinery  and implements f o r purposes of t h i s study was gross  investment deflated by a price index i n which quality changes of the machines and implements have been accounted for.  However, f o r purposes of constructing a price index,  quality changes are d i f f i c u l t to define and measure. Therefore, i t i s important to note that the price deflator used i n t h i s study may have been biased.  I f so, there  would be errors of measurement i n the data series f o r r e a l gross investment i n machinery and  implements.  However, even i f the estimate of r e a l gross investment was unbiased, the d i f f i c u l t problem of measuring the stock of machinery and implements and the flow of services would remain.  In t h i s regard, the r e s t r i c t i v e nature of  the assumptions used i n t h i s study i s outlined i n Chapter III. Secondly, there was the potential problem of changing rates of u t i l i z a t i o n of machinery and implements over time.  This may have been p a r t i c u l a r l y important i n t h i s  study i n view of the cycles i n gross investment.  As shown  i n Table I I , column 3, r e a l gross investment reached peaks i n 1928, 1952 and 1965, and troughs i n 1933 and  1958.  This resulted i n a stock of machinery and implements which actually declined during 1936-43 and 1959-65, but experienced very rapid growth during 1944-56.  Since a g r i c u l -  t u r a l output maintained a steady upward trend throughout the entire period, either other inputs were substituted f o r machinery and implements i n the short run, and/or the u t i l i z a t i o n rate of machinery and implements was  a variable.  The model could accommodate s u b s t i t u t a b i l i t y between c a p i t a l and labor, but i t did not take into account varying u t i l i z a t i o n rates for c a p i t a l . Thirdly, the assumption of a constant rate of embodied technological change i n machinery and implements may  have been inappropriate.  I t i s possible that a c y c l i c a l  pattern during the 1935-65 period may  have obscured a long-  term trend i n the rate of embodied technological change. Fourthly, i t was  possible that the time series data  did not provide enough independent v a r i a t i o n to allocate simultaneously  with a high degree of confidence  the i n -  creases i n t o t a l factor productivity to three sources disembodied technological change, and embodied  technolo-  g i c a l change i n both material inputs and machinery and implements.  In f a c t , there was  reason to suspect that the  model could not choose between alternative combinations of embodied technological change i n machinery and implements and material inputs.  For example, the c o r r e l a t i o n coef-  f i c i e n t between the flow of c a p i t a l services, K, when ft=0.0 and ^=0.02 on the one hand, and when ^=0.02 and P=0.0 on the other, was 0.9938 i n d i c a t i n g an almost exact l i n e a r r e l a t i o n s h i p between the two measures o f K.  There-  fore, the regression r e s u l t s f o r the two alternatives would not provide s u f f i c i e n t information to use as a basis f o r choice between the alternative combinations of the rates of embodied technological change.  This suggests that the model  may not have been capable o f estimating the rate of embodied technological change i n more than one f a c t o r . Thus, there were many reasons to suggest that the estimate of a negative rate of embodied technological change i n machinery and implements may have been s u b s t a n t i a l l y biased. III.  MODEL WITH ALL TECHNOLOGICAL CHANGE EMBODIED In Model I technological change, both embodied and  disembodied, was s p e c i f i e d to occur simultaneously.  Of  course, when /l=^=0.0 a l l technological change was assumed to be disembodied.  was estimated.  For Model I I a function o f the form  Therefore,  a l l technological change was  assumed to be embodied i n material inputs and machinery and implements.  A matrix o f regression r e s u l t s f o r the  various combinations offtand (3 was estimated using the  as same data series as i n Model 1(a).  The r e s u l t s whenft=0.0  are reported i n Table X. Model I I  (Table X)  The regression r e s u l t s of Model I I indicate a posit i v e rate o f embodied technological change i n material inputs. However, l i k e Model I, the "best" regression occurred when ft=-0.01, i n d i c a t i n g a negative rate o f embodied technologic a l change i n machinery and implements.  Therefore, f o r  reasons outlined above, only the r e s u l t s whenft=0.0are reported. A comparison of the r e s u l t s of the "best" regression when ft=0.0 i n Model I I , with those of Model 1(a), reveals the following points: (1) Model I I provided a higher estimate f o r the rate of embodied technological change i n material inputs (5.0 per cent compared with 4.0 per cent); (2) R and  2  was higher i n Model 1(a) (.9673 compared with .9870);  (3) the e l a s t i c i t y of output with respect to c a p i t a l ,  a, was larger (0.5416 compared with 0.4572), more highly s i g n i f i c a n t , and had a substantially lower standard  error  i n Model I I than i n Model 1(a). The higher estimate of embodied technological change i n Model I I was expected, since any technological change which was estimated i n Model 1(a) as disembodied  technolo-  g i c a l change was measured as embodied technological change i n Model I I .  The higher R  2  i n Model 1(a) provided some  evidence that embodied and disembodied technological change should be treated simultaneously, although t h i s evidence must be considered weak i n view of the lower standard error of the estimate, more highly s i g n i f i c a n t a, and lower standard error of a i n Model I I .  As expected, the e l a s t i -  c i t y of output with respect to c a p i t a l was higher i n Model I I , because a l l increases i n t o t a l factor productivity were assumed to be the r e s u l t of embodied technological change.  The r e l a t i v e l y greater indeterminancy  o f the e s t i -  mates of a i n Model 1(a) compared with Model I I was most l i k e l y due to the very high correlation between the flow of c a p i t a l services, K, and time, t , i n Model 1(a).  Of course,  t h i s problem of m u l t i c o l l i n e a r i t y did not arise i n Model I I , since t was not a specified variable. IV.  MODEL TO RELAX THE ASSUMPTION OF CONSTANT RETURNS TO SCALE  A l l other models reported i n t h i s study were homogeneous of degree one, that i s , constant returns to scale was assumed.  Model I I I was an attempt to assess the  s e n s i t i v i t y of the method to the assumption of constant returns to scale.  In Model I I I labor was introduced into  the production function as an independent variable. function Q=Ae  u t  e  f + g w f h w 2  L K b  a  The  was estimated using the same data series as i n Model 1(a). Estimates were obtained f o r ft=0.0 only, and are reported i n Table XI. Model I I I  (Table XI)  A comparison of the r e s u l t s of Model I I I with the r e s u l t s of Model 1(a) (whenA=0.0) shows the following: (1) Model I I I provided a s l i g h t l y higher estimate of the rate of embodied technological change i n material inputs (4.0 to 5«0 per cent compared with 4»0); (2) Model I I I gave a s u b s t a n t i a l l y higher estimate of the rate of disembodied technological change (1.99 to 1.88 per cent compared with 1.13); (3) the R  2  values were lower i n a l l regressions i n  Model I I I (.9513 compared with .9873 i n the "best" regression); (4) the a c o e f f i c i e n t was substantially lower i n Model I I I , had large standard errors and was not s i g n i f i cant; and (5) s e r i a l c o r r e l a t i o n i n the disturbance terra may have been a problem i n Model I I I , since the DurbinWatson test was inconclusive i n a l l regressions. The r e l a t i v e l y large standard errors f o r u and a were evidence of the problem of m u l t i c o l l i n e a r i t y i n Model III.  The three explanatory variables, t , K and L, were  highly correlated.  For example, the c o r r e l a t i o n c o e f f i c i e n t  between labor and the flow of c a p i t a l services when A=(*=0.0 was -0.9506. (5=0.08.  This increased to -0.9676 whenft=0.0 and  In Model I I I the sum of a+b was l e s s than one, which indicated the p o s s i b i l i t y o f diseconomies of scale i n the aggregate production  function.  However, t h i s r e s u l t was  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 . ^ In summary, the assumption of constant returns to scale resulted i n a s l i g h t l y lower estimate of the rate of embodied technological change i n material inputs, and a more s u b s t a n t i a l l y lower estimate of the rate o f disembodied technological change.  However, there was i n s u f f i c i e n t  s t a t i s t i c a l evidence t o r e j e c t the hypothesis of constant returns to scale, V.  ALTERNATIVE MODELS TO RELATE POTENTIAL AND ACTUAL OUTPUT  The p r i n c i p a l means f o r r e l a t i n g potential and actual output used i n t h i s study i s outlined i n Chapter I I I . alternative forms were investigated.  Two  These are discussed  i n d i v i d u a l l y as Models IV(a) and (b). Model IV(a)  (Table XII)  As described i n Chapter I I I , a measure o f p o t e n t i a l output, Q* (Table V, column 3), was derived from actual  The F - t e s t employed i s o u t l i n e d i n : Gerhard T i n t n e r , Econometrics (New Y o r k : John Wiley and Sons, I n c . , 1952), pp. 8 9 - 9 1 . S u b s t i t u t i o n of the appropriate values gave F=1.27. For one and t w e n t y - f i v e degrees of freedom, the c r i t i c a l values of the F d i s t r i b u t i o n are 7.77 and 4.24 f o r the one and f i v e per cent l e v e l s o f s i g n i f i c a n c e , r e s p e c t i v e l y .  gross output by dividing the f i e l d crops component by the weather index.  The production function Q =Ae L" "' K ,  ut  L  a  a  was then estimated using the same data series as i n Model 1(a) f o r t , L and K.  The r e s u l t s whenA=0.0 are reported  i n Table XII. A comparison of the r e s u l t s of Model IV(a) with the r e s u l t s of Model 1(a) (whenA«=0.0) reveals the following: (1) the "best" regression i n Model IV(a) occurred when f=0.G5 compared with f «=0.04 i n Model 1(a); (2) the R  2  values  were lower and the standard errors of the estimate were larger i n Model IV(a) (.9784 and .0675 compared with .9873 and .0560 i n the "best" regressions); and (3) the u and a c o e f f i c i e n t s were very similar i n magnitude and l e v e l of significance. Thus, d i r e c t l y adjusting gross output f o r weather influences resulted i n a s l i g h t l y larger estimate of the rate of embodied technological change i n material inputs. However, on the basis of goodness of f i t and low standard errors of the estimate, t h i s method was i n f e r i o r to the method of r e l a t i n g actual and potential output which was used i n Models I, I I , I I I and V. Model IV(b)  (Table XIII)  Another function which seemed a p r i o r i to have the r i g h t general shape f o r r e l a t i n g potential and actual out-  93 put i s the logarithmic, r e c i p r o c a l function y = e  f  - s /  w  .  Therefore, the production function  Q^Ae^e^V"^ was estimated using the same data series as i n Model 1(a). The r e s u l t s when ft=0.0 are reported i n Table XIII. Compared with Model 1(a), Model IV(b): (1) gave a lower estimate of the rate of embodied technological change i n material inputs (3»0 per cent compared with 4*0); and (2) provided estimates of the rate of disembodied  techno-  l o g i c a l change which were lower and also l e s s s i g n i f i c a n t . The R  fc  values were lower and the standard errors of the  estimate were higher i n Model IV(b) compared with Model 1(a). Thus, the use of the logarithmic, r e c i p r o c a l function to r e l a t e p o t e n t i a l and actual output resulted i n a lower estimate of both the rate of disembodied nological change.  and embodied tech-  However, on the basis of goodness of f i t  and low standard errors of the estimate, t h i s method was also i n f e r i o r to the p r i n c i p a l means f o r r e l a t i n g actual and potential output used i n Models I, I I , I I I and V. VI.  TESTING THE PRODUCTION FUNCTION FOR STABILITY OVER TIME Since agriculture experienced s i g n i f i c a n t s t r u c t u r a l  changes during the time period under study, i t was desirable to t e s t whether the estimated regression relationships were  stable over time.  The technique involved the use o f a dummy  variable, D, which took the value zero f o r a l l years prior, to a given date, and the value one f o r a l l subsequent years. On the basis of the most highly s i g n i f i c a n t dummy variable, the 1 9 3 5 - 6 5 period was divided into two sub-periods, and the hypothesis that the estimated regression c o e f f i c i e n t s were equal i n a l l three time periods was tested by computing the appropriate F - r a t i o . Model V  (Table XIV)  Using the same data as i n Model 1(a) whenA=(*=0.0, the production function  Q=AeuV+^  h w  V-aKV  D  was estimated f o r each o f the dummy variables, D]_ to D13, l i s t e d i n Table IV.  A s i g n i f i c a n t regression c o e f f i c i e n t  f o r D implies that a s i g n i f i c a n t change occurred i n at least part o f the r e l a t i o n s h i p from one period t o the other. The r e s u l t s of ten regressions with the most highly s i g n i f i c a n t D c o e f f i c i e n t s , j , are reported i n Table XIV.  In three  regressions, D2, D5 and D , j was s i g n i f i c a n t at the f i v e D  per cent l e v e l , and i n one regression, D , j was s i g n i f i D  cant at the one per cent l e v e l . with the dummy variable D  D  In addition, the regression  also had the highest R , lowest  standard error of the estimate, and the most highly s i g n i f i c a n t value f o r a.  Therefore, i t was concluded that a  s i g n i f i c a n t s h i f t occurred between the 1 9 3 5 - 4 9 and 1 9 5 0 - 6 5  TABLE IV DUMMY VARIABLES SPECIFIED FOR MODEL V i : Q=Ae  u t  e  f + g w f h w 2  Dummy variable  L - K e 1  a  a  j D  , M-O.O, 1935-65  Zeros  Ones  1935-40  1941-65  1935-45  1946-65  D3  1935-46  1947-65  4  1935-47  1948-65  5  1935-48  1949-65  D6  1935-49  1950-65  D  1935-50  1951-65  1935-51  1952-65  1935-52  1953-65  DlO  1935-53  1954-65  Dll  1935-54  1955-65  D  1 2  1935-55  1956-65  D  1 3  1935-60  1961-65  D  l  D  D  D  D  2  7  9  periods i n at least part o f the true production function relationship. In view of t h i s r e s u l t , the period under study was divided into two subperiods, 1935-49 and 1 9 5 0 - 6 5 .  Model  1(a) was estimated f o r each subperiod when f\=^=0.0.  The  96 regression r e s u l t s are shown i n Table XV. The regression r e s u l t s indicate that disembodied techn o l o g i c a l change occurred at a more rapid annual rate during the 1950-65 period than during the 1935-49 period (3.08 per cent compared with 1 . 0 9 ) .  In addition, the u c o e f f i c i e n t  was highly s i g n i f i c a n t i n the regression f o r the 1950-65 period, but not s i g n i f i c a n t i n the regression f o r the 193549 period.  However, the e l a s t i c i t y of output with respect  to c a p i t a l was more highly s i g n i f i c a n t i n the regression for the 1935-49 period than i n the regression f o r the 195065 period. To t e s t the hypothesis that the true set of regression c o e f f i c i e n t s was equal i n a l l three time periods, 1935-49, 1950-65 and 1935-65, that i s , that the observations for the 1950-65 period belonged to the same r e l a t i o n s h i p as those f o r the 1935-49 period, an F-test was performed.  7  On the basis of the test, there was i n s u f f i c i e n t s t a t i s t i c a l evidence to r e j e c t the hypothesis of equal sets of regression c o e f f i c i e n t s f o r a l l three time periods. This r e s u l t should not be interpreted as a contrad i c t i o n of the r e s u l t s obtained when the dummy variable was  'The t e s t i s outlined i n : Johnston, op_. c i t . , pp. 136-37. Substitution of the appropriate values gave F=2.47. For f i v e and twenty-one degrees of freedom, the c r i t i c a l values of the F d i s t r i b u t i o n are 4.04 and 2.68 f o r the one and f i v e per cent l e v e l s of s i g n i f i c a n c e , respectively.  introduced into the model.  The F-ratio tested the hypo-  thesis that the entire set of regression  coefficients  was  equal i n a l l three time periods, that i s , that the regression r e l a t i o n s h i p taken as a whole did not s h i f t cantly over time, while the s i g n i f i c a n t  signifi-  regression  c o e f f i c i e n t for D indicated that a l l or part of the regression r e l a t i o n s h i p shifted between the two  subperiods.  Therefore, interpreting the r e s u l t s of the F-test and dummy variable together, i t was  concluded that only part of the  r e l a t i o n s h i p shifted s i g n i f i c a n t l y over time. was  Although i t  not possible to determine precisely which part(s)  of  the r e l a t i o n s h i p underwent a s i g n i f i c a n t s h i f t , the regression r e s u l t s f o r the two  subperiods (Table XV)  suggest  that the constant term and u were s i g n i f i c a n t l y d i f f e r e n t i n the two  periods.  Both the constant term and u were almost  three times as large with r e l a t i v e l y much lower standard errors i n the 1950-65 period than i n the 1935-49 period.  CHAPTER V SUMMARY AND CONCLUSIONS I.  SUMMARY  Productivity increases i n Canadian agriculture over the past three or four decades have been well demonstrated. However, only recently have research e f f o r t s been directed s p e c i f i c a l l y towards i d e n t i f y i n g the sources o f the observed productivity gains.  The purpose of t h i s study was to  i d e n t i f y the kinds and magnitudes o f technological change which have contributed to t o t a l productivity gains i n Canadian agriculture. More s p e c i f i c a l l y , the problem was to measure: (1) the rate of disembodied technological change; (2) the rate of technological change embodied i n a g r i c u l t u r a l machinery and implements; and (3) the rate o f technological change embodied i n material inputs.  Disembodied technological  change was defined as a s h i f t i n the production Therefore,  function.  the rate o f disembodied technological change was  a measure of the e f f e c t on output of new technology which can be implemented with reliance on the e x i s t i n g resources or inputs.  General improvements i n farm management and  decision-making, adoption o f s o i l - t e s t i n g practices, and more e f f i c i e n t feed rations for l i v e s t o c k are obvious  examples of disembodied technological change.  Embodied  technological change, on the other hand, i s a measure of the e f f e c t on output of improved technology which must be implemented i n conjunction with improved or new inputs.  In p a r t i c u l a r , an attempt was  kinds of  made to measure the  rate of embodied technological change corresponding to changes i n the productive  quality of machines and implements.  I n t u i t i v e examples of technology which might be expected to be embodied i n machines and implements include: power options, e l e c t r i c s t a r t e r s , improved t i l l a g e implements, and e n t i r e l y new machines such as hay conditioners, side delivery rakes and machinery f o r handling  specialty crops.  S i m i l a r l y , the rate of embodied technological change i n material inputs was  an attempt to measure the corresponding  changes i n the productive  quality of material inputs.  I n t u i t i v e examples are improved seed v a r i e t i e s , more effect i v e herbicides and pesticides, improved f e r t i l i z e r s ,  and  feed additives. The analysis was  carried out f o r the aggregate p r i -  mary a g r i c u l t u r a l sector i n Canada for the 1935-65 period. To measure technological change, regression estimates were obtained f o r a l i n e a r homogeneous Cobb-Douglas  production  function where gross a g r i c u l t u r a l output per person employed was  the dependent variable, and a time index, weather  index, and the annual flow of c a p i t a l services (including  100 material inputs) per person employed were the independent variables.  The data required was  derived from publica-  tions of the Dominion Bureau of S t a t i s t i c s , and  consisted  of time series of thirty-one annual observations.  Gross  output and the flow of c a p i t a l services were measured at 1935-39 base period prices, while labor input was measured as the number of persons employed i n a g r i c u l t u r e . Hicks-neutral disembodied technological change measured by specifying an exponential i n the production was  function.  s h i f t function,  was e , u t  Embodied technological change  assumed to be capital-augmenting i n the vintage sense  so that machines and implements, and material inputs purchased i n any year were 100 ^ and 100$ t i v e l y , more productive ding year.  than those purchased i n the prece-  Alternative data series f o r the flow of c a p i t a l  services were constructed and $.  per cent, respec-  by imposing several values f o r A  A matrix of regression r e s u l t s was  the true values of r\ and  obtained, and  were i n f e r r e d by choosing the  "best" regression on the c r i t e r i a of goodness of f i t , ficance l e v e l s of the estimated c o e f f i c i e n t s and  signi-  low  standard errors. Several alternative models were investigated: (1) a l l technological change was  assumed to be embodied; (2) the  assumption of constant returns to scale was  relaxed;  (3)  alternative means of r e l a t i n g actual and potential output  101 were investigated; and (4) the s t a b i l i t y of the production function r e l a t i o n s h i p over time was tested.  Two hypotheses  were s t a t i s t i c a l l y tested: (1) constant returns to scale; and  (2) equal sets of regression c o e f f i c i e n t s i n the three  time periods, 1935-65, 1935-49 and 1950-65. II.  CONCLUSIONS  Many rigorous assumptions are implied i n the models as well as i n the derivation of the data s e r i e s , e s p e c i a l l y the stock of machinery and implements and the flow of c a p i t a l services.  Therefore,  the r e s u l t s obtained must be  interpreted c a r e f u l l y . I t i s p a r t i c u l a r l y important to note that the rate of technological change was assumed to be constant time.  over  Therefore, the estimated values must be interpreted  as long-term trends.  Also, there were undoubtedly errors  of measurement i n the v a r i a b l e s . from several sources:  These errors could arise  (1) the flow of c a p i t a l services and  gross output were measured i n constant d o l l a r s , and therefore, i t was i m p l i c i t l y  (and h e r o i c a l l y ) assumed that the  a g r i c u l t u r a l sector was i n long-run equilibrium; (2) problems of aggregation of economic units (farms) may have been present,  since the analysis and data employed were  f o r the aggregate a g r i c u l t u r a l sector taken as a whole; (3) the u t i l i z a t i o n rate of inputs was assumed constant  102 over time; and  (4) aggregation oyer products and inputs may  have introduced errors, since non-homogeneous products and inputs were aggregated into single measures of gross output, labor input, and c a p i t a l input.  In addition, there was the  problem of aggregating c a p i t a l inputs which have imputed rates of return and those which have market returns.  If  errors of measurement were present, and i t seems l i k e l y that they were, a dependence between the disturbance term and the observed values of the explanatory variables would e x i s t , which invalidates one of the basic assumptions of the l i n e a r regression model. would be b i a s e d .  Thus, the regression estimates  x  In addition, the r e s u l t s of the study are based on the assumption  that the model was correctly specified, that  i s , that the model was a true expression of the production relationships which actually existed i n the aggregate c u l t u r a l sector.  agri-  Of course, t h i s i s an untestable assump-  t i o n which can only be q u a l i t a t i v e l y judged on the basis of conformity with e x i s t i n g knowledge and theory, and whether the r e s u l t s are reasonable on such a p r i o r i grounds. With the preceding q u a l i f i c a t i o n s kept i n mind, the following main conclusions appear to be j u s t i f i e d .  J . Johnston, Econometric Methods (New York: McGraw-Hill Book Company, Inc., 1963), pp. 148-50.  103 1.  This study confirmed that there has been sub-  s t a n t i a l technological change i n Canadian a g r i c u l t u r e . When a l l technological change was assumed to be disembodied, i t was estimated to be about 2.46 to 2.70 per cent per year. On the c r i t e r i a of goodness o f f i t and most s i g n i f i c a n t u c o e f f i c i e n t , the "best" estimate of disembodied  technolo-  g i c a l advance (when embodied technological change was not specified) was 2.70 per cent annually during the period  1935-65. 2.  When a l l technological change was assumed to be  embodied, the "best" estimate was an annual rate of embodied technological change i n material inputs of about 5.0 to 6 . 0 per  cent. 3.  When both disembodied and embodied technological  change were specified simultaneously,  the estimates of the  annual rate of disembodied technological change ranged from 1.13 to 1.76 per cent, while embodied technological change i n material inputs was estimated at 3*5 to 4 . 0 per cent annually.  On the c r i t e r i a o f goodness of f i t and most  s i g n i f i c a n t u c o e f f i c i e n t , the "best" estimate o f the annual rate of disembodied technological change was 1.76 per cent.  I t should be noted, however, that i n these "best"  regressions the disembodied technological change c o e f f i c i e n t , u, had a r e l a t i v e l y large standard ficant .  error and was not s i g n i -  4.  There was no evidence of a p o s i t i v e rate of  embodied technological change i n machinery and implements i n any regressions.  I t was concluded that the disturbing  and a p r i o r i unexpected r e s u l t of a negative rate of embodied technological change i n machinery and implements should probably be considered  s u b s t a n t i a l l y biased, f o r  several reasons discussed. 5.  The r e s u l t s of t h i s study suggest that both d i s -  embodied and embodied technological change should be treated simultaneously.  This i s p a r t i c u l a r l y evident when a com-  parison i s made between regressions i n which a l l technolog i c a l change was s p e c i f i e d as disembodied (that i s , A«=p»0.0), and those where both disembodied and embodied technological change were s p e c i f i e d .  In a l l cases the R  2  values were  higher and standard errors o f the estimate lower when d i s embodied and embodied technological change were s p e c i f i e d simultaneously.  The evidence i s not as conclusive, however,  when the simultaneous case i s compared with the one i n which a l l technological change was s p e c i f i e d as embodied. Although the R  2  values were s l i g h t l y higher i n the simul-  taneous s p e c i f i c a t i o n , the standard error of the estimate was s l i g h t l y lower when a l l technological change was assumed to be embodied. 6.  There was i n s u f f i c i e n t s t a t i s t i c a l evidence to  r e j e c t the hypothesis of constant returns to scale.  How-  ever, the assumption of constant returns to scale did r e s u l t i n s l i g h t l y smaller estimates of the rate of both disembodied and embodied technological change. 7.  A comparison of the regression r e s u l t s f o r the  1935-49 and 1950-65 subperiods strongly suggests that d i s embodied technological change occurred at a more rapid rate during the 1950-65 period.  Moreover, t h i s r e s u l t i s  generally compatible with the r e s u l t s of previous  studies.  However, there was no s t a t i s t i c a l evidence which would res u l t i n the r e j e c t i o n of the hypothesis that the regression r e l a t i o n s h i p , when taken as a whole, was subperiods.  equal i n the  two  Therefore, the production function as a whole  appeared to be stable during the period under study. III.  IMPLICATIONS AND  SUGGESTIONS FOR FURTHER RESEARCH  The macro theory of production i s closely related to the theory of economic growth.  This study was  an i n v e s t i -  gation of the macro production r e l a t i o n s h i p s i n Canadian agriculture, and as such i t was  an attempt to contribute to  the e x i s t i n g knowledge about the sources of increased c u l t u r a l output per unit of input. single most i n t e r e s t i n g r e s u l t was  In t h i s regard,  agri-  the  the large role a t t r i b u -  ted to technological change embodied i n material inputs by a l l models investigated.  However, there are no d i r e c t  p o l i c y implications which can be drawn from t h i s study.  The following suggestions are offered f o r further research.  F i r s t l y , the present models could be refined i n  several ways. production  Alternative functional forms such as the CES  function could be investigated.  The measurement  of c a p i t a l was p a r t i c u l a r l y troublesome, and much additional research i s needed to improve these estimates.  Similarly,  the measurement of labor input was extremely rough and the p o s s i b i l i t y of technological change embodied i n labor should be investigated. recognize  In addition, i t would be desirable to  the regional differences i n Canadian agriculture  by disaggregating  the analysis on a geographical  basis.  Secondly, i t would be extremely i n t e r e s t i n g to bring such variables as the rate of research and development into the analysis.  L i t t l e i s known about the determinants of tech-  nological change, and any meaningful p o l i c y variables must focus on the factors which influence the rate of technolog i c a l change. on t h i s t o p i c .  Nelson has made some useful 2  observations  Thirdly, there i s the cost of technologi-  c a l change r e l a t i v e to i t s benefits.  In other words, there  i s the d i f f i c u l t and important question of the a l l o c a t i o n of resources to technology generating  a c t i v i t i e s from a  ''See: M. 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"Vintage Capital Models and Econometric Production Functions," Review of Economic Studies, 3 3 : 1-18, January, 1966.  A P P E N D I X  116 TABLE V TIME SERIES DATA FOR CANADIAN AGRICULTURE, 1935-65  Year (1)  1935 1936 1937 1938 1939 1940 1941 1942 1943 1944 1945 1946 1947 1948 1949 1950 1951 1952 1953 1954 1955 1956 1957 1958 1959 I960 1961 1962 1963 1964 1965  Gross output at 1935-39 prices Adj. f o r Weather Unadjusted index weather influence (2) (4) (3) - thousands 714692 678246 649721 750782 951000 953247 858138 1254375 960235 1181643 954172 1047257 1065622 1118516 1087086 1005254 1164233 1351133 1419083 1117393 1208839 1355879 1150249 1182370 1219542 1289950 1137814 1413262 1537396 1509317 I6O8468  of  dollars 742933 817834 857883 766809 853852 880568 897597 982733 930630 1109792 1023127 1052000 1182537 1162991 1277670 1016709 1079363 1092384 1240862 1342909 1152614 1202803 1224544 1238907 1282430 1294529 1509708 1404225 1432982 1563203 1523514  0.918 .631 .522 .954 1.251 1.191 .893 1.705 1.100 1.153 .838 .990 .804 .930 .740 .975 1.210 1.418 1.235 .719 1.107 1.258 .868 .872 .892 .993 .535 1.013 1.149 .934 1.107  Number of persons employed (5) thousands 1298 1319 1339 1359 1379 1344 1224 1139 1118 1136 1144 1271 1172 1186 1114 1066 991 927 911 906 880 808 777 746 739 690 712 694 695 679 649  117 TABLE V  Year (6) 1935 1936 1937 1938 1939 1940 1941 1942 1943 1944 1945 1946 1947 1948 1949 1950 1951 1952 1953 1954 1955 1956 1957 1958 1959 I960 1961 1962 1963 1964 1965  Livestock and poultry (7)  (continued)  Net stock of buildings (8)  thousands 574396 612201 569502 560188 634961 639664 499441 519636 678595 651395 612398 593449 573854 472120 516500 521528 595575 645360 590031 555845 596788 576233 586229 677764 720340 711098 737124 718105 769765 810433 726664  Depreciat i o n on buildings (9)  Land (10)  of d o l l a r s at 1935-39 prices 1351600 2061640 54064 2077880 47224 1306375 2093700 42502 1268903 1236533 45045 2107140 42166 1202311 2119180 37722 2131920 1171179 34060 1145869 2140159 2151800 31813 1122314 2159920 1101082 33240 2168040 31482 1080617 2176160 1064009 31559 2184280 1053283 33795 2191980 1041234 34325 31180 2199680 1029240 2207380 1029270 30034 1028256 28844 2214240 25888 1027105 2222534 1031220 2232720 26184 2244900 1036225 28551 1036990 2255400 28993 2266180 31040 1036171 IO364OI 32197 2275497 32858 2284940 1033005 2290960 1031552 35982 2296980 1029046 37854 2306920 39172 1023844 1036476 41700 2317120 1051472 42958 2331980 1065067 44270 2346680 1075297 45253 2361380 1086587 4836I 2376500  TABLE V  Year  (11) 1935 1936 1937 1938 1939 1940 1941 1942 1943 1944 1945 1946 1947 1948 1949 1950 1951 1952 1953 1954 1955 1956 1957 1958 1959 I960 1961 1962 1963 1964 1965  Material inputs, p«=0 Deflated Deflated by i n d i v i - by wholedual price sale price indexes index (12) (13)  (eoncluded)  Gross stock of machinery and implements,A=0 Deflated Deflated by adj. USDA by DBS price index price index (15) (14)  thousands o f d o l l a r s at 1935-39 prices 707466 682666 174961 1694H 174075 177669 707192 684877 182278 182353 740551 716453 199377 196460 770781 747772 225497 213413 760690 738939 225657 208516 747890 726246 246423 223922 709860 690011 286355 669488 650893 272181 336784 314609 628907 .610735 346837 662447 642482 324221 367195 340750 716120 691371 413327 371739 8IOO64 780114 454735 372595 947867 906384 411694 354737 1109939 1049161 413859 358113 1287357 1197714 411939 349656 1458647 1332163 434667 342790 I620382 1473427 376873 434064 1789768 1641521 445886 387063 1935517 1786854 457683 400376 2004086 1856918 471260 411014 2104436 1957378 513563 439299 2248199 2102221 497298 429753 2332036 2196022 536079 462155 2400357 2278292 556777 488396 2454901 2349632 559201 495272 2451181 2365097 2402147 56OOO4 499659 2344468 577179 2314920 519177 2349804 612057 546143 2314521 2309035 578178 2306781 2312462 644093 595164 2316591 2312029 664227  TABLE VI SYMBOLS USED IN THE MODELS  Symbol  Derivation  Q Q*  Variable Variable  L w K t D j\  Variable Variable Variable Variable Variable Parameter  ft e A f u  Parameter Number Estimated Estimated Estimated  g h j a b  Estimated Estimated Estimated Estimated Estimated  Meaning Gross a g r i c u l t u r a l output (thousands of 1935-39 dollars) Gross a g r i c u l t u r a l output adjusted for weather influences (thousands of 1935-39 dollars) Number of persons employed (thousands) Weather index (potential=actual output when w=1.0) Annual flow of c a p i t a l services (thousands of 1935-39 d o l l a r s ) Time index ( 1 , 2, 31) Dummy variable (ones and zeros f o r specified time periods) Rate of embodied technological change i n machinery and implements Rate of embodied technological change i n material inputs e = n i ^ o [ l + ( l / n ) ] and lne=l Constant c o e f f i c i e n t (lnA*=lnA+f) Constant c o e f f i c i e n t Regression c o e f f i c i e n t for rate of disembodied technological change Regression c o e f f i c i e n t for w Regression c o e f f i c i e n t for w Regression c o e f f i c i e n t for D E l a s t i c i t y of output with respect to c a p i t a l E l a s t i c i t y of output with respect to labor n  2  TABLE VII REGRESSION ESTIMATES FOR MODEL 1(a): Q = A e  0.0 lnA»  .025  .03  .035  e  f + s w + h w  .04  2 L  1 _ a  K , ft—O.Ol, 1935-65  .05  a  .06  .07  .08  3.0982 3.0320 3.0549, 3.1006 3.1616 3.2387 3.4251, 3.6303, 3.8337, 4.0210 (1.0002) (.9602) (.9441) (.9256) (.9408) (.8837) (.8383) (.7929) (.7495) (.7096) .0090 .0091 .0104 .0094 .0113 .0124 .0153, .0137 .0225 (.0092) (.0109) (.0113) (.0117) (.0120) (.0123) (.0129) (.0133) (.0137) .5206 .4092 .5125 .4794 .2336 .0208 .2975 .3577 .1695  u  .0094 (.0141)  .5171  .0988 .1038 .1006 .1052 .1024 .1049 .1052 .1053 .1054 .1055 (.2315) (.2250) (.2262) (.2296) (.2277) (.2252) (.2254) (.2251) (.2260) (.2299) .648O .6602 .6539 .6677 .6754 .6481 .6479 .6494 .6540 .6494  g  .1621 .1561 .1604 .1637 .1569 .1587 .1547 .1554 .1541 (.1053) (.1058) (.1073) (.1056) (.1082) (.1065) (.1054) (.1054) (.1078) (.1059) .1422 .1468 .1387 .1404 .1394 .1449 .1489 .1539 .1513 .1665 .1522  h  a  R  .02  u t  .4925  .5062  .5030  .4959  .4861  .4736  .4430  .4089  .3750  .3437  .9871  .9875  .9876  .9876  .9877  .9876  .9875  .9873  .9871  .9869  .0563  .0554  .0552  .0552  .0551  .0552  .0554  .0558  .0563  .0567  (.1682) (.1622) (.1597) (.1567) (.1533) (.1499) (.1424) (.1350) (.1277) (.1211) .0068 .0040 .0040 .0085 .0045 .0054 .0039 .0041 .0069 .0044 2  S "d"  1.540  1.589  1.601  1.611  1.619  1.624  1.630  1.629  1.626  1.621  TABLE VII (continued),A=-0.005 0.0 InA*  .02  .025  .03  .035  .04  .05  .06  .07  .08  3.2778, 3.4382 3.6290 3.8249 4.0105, (.9322) (.9134) (.8927) (.8486) (.8033) (.7591) (.7179) (.9933) (.9638) (.9493)  3.1479, 3.1736, 3.2166  3.2746,  u  .0108 .0092 .0118 .0146 .0089 .0162 .0236 .0095 .0089 .0131 (.0125) (.0122) (.0131) (.0135) (.0139) (.0142) (.0093) (.0111) (.0115) (.0118) .3992 .3430 .4809 .5213 .5331 .2789 .5295 .2135 .1511 .0173  g  .1012 .1052 .1051 .1051 .1043 .1029 .0993 .1053 (.2301) (.2319) (.2331) (.2286) (.2277) (.2272) (.2268) (.2268) (.2273) (.2285) .6510 .6668 .6598 .6522 .6503 .6539 .6745 .6511 .6543 .6614  h  .1048  .1528  .1543  .1547  .1553,  .1559  .1566  .1582  .1600  .1617  .1633  .1704  .1582  .1554  .1528  .1506  .1484  .1452  .1428  .1412  .1402  .4621  .4864  .4865  .4828  .4761  .4663  .4402  .4086  .3760  .3450  .9868  .9873  .9874  .9874  .9875  .9875  .9874  .9873  .9871  .9869  .0571  .0560  .0558  .0557  .0556  .0556  .0557  .0560  .0564  .0568  (.1039) (.1071) (.1067) (.1064) (.1062) (.1061) (.1063) (.1069) (.1076) (.1084)  a  R  .1044  (.1668) (.1626) (.1603) (.1576) (.1546) (.1512) (.1440) (.1366) (.1292) (.1224) .0048 .0088 .0048 .0072 .0050 .0051 .0059 .0054 .0059 .0099 2  S "d"  1.515  1.563  1.575  1.587  1.597  1.605  1.615  1.618  1.618  1.615  TABLE VII (continued), A=0.0 0.0 lnA»  .02  .025  .03  .035  .04  .05  .06  .07  3.4487 3.2685 3.2562 3.2602 3.2838 3.3282 3.4587 3.6305 3.8163 (.9824) (.9634) (.9514) (.9368) (.9198) (.9006) (.8583) ( . a i 3 5 ) (.7689)  .08 3.9983 (.7270)  .0090 .0096 .0113 .0089 .0087 (.0127) (.0133) (.0137) (.0141) (.0144) .5476 .4798 .5302 .5456 .3853  u  .0246 (.0095) .0144  .0125 .0139 .0155 .0173 (.0120) (.0124) (.0116) (.0112) .1910 .3246 .2574 .1323  g  .1030 (.2360) .6688  .1039 (.2312) .6603  h  .1630 .1596 .1558 .1579 .1613 .1536 .1546 .1565 .1549 .1553 (.1086) (.1071) (.1069) (.1079) (.1074) (.1069) (.1073) (.1078) (.1106) (.1083) .1481- .1452 .1566 .1542 .1592 .1519 .1431 .1417 .1619 .1735  a  .3468 .4572 .4362 .4676 .4642 .4079 .4322 .3771 .4675 .4649 (.1238) (.1524) (.1456) (.1308) (.1382) (.1605) (.1582) (.1555) (.1647) (.1623) .0076 .0060 .0058 .0092 .0080 .0065 .0138 .0059 .0065 .0071  R  2  S "d"  .1043 (.2302) .6577  .1048 (.2294) .6554  .1050 (.2288) .6538  .1050 (.2285) .6536  .1045 (.2285) .6548  .1033 (.2294) .6596  .1017 (.2307) .6661  .0998 (.2323) .6736  .9865  .9870  .9871  .9872  .9873  .9873  .9873  .9872  .9870  .9868  .0577-  .0566  .0564  .0562  .0560  .0560  .0560  .0562  .0565  .0569  1.495*  1.538  1.551  1.564  1.575  1.585  1.600  1.607  1.609  #Test f o r s e r i a l correlation i s inconclusive at one per cent l e v e l of significance.  1.608  TABLE VII (continued), A=0.005 0.0  .02  .025  .03  .035  .04  .05  .06  .07  .08  InA'  3.6323 3.4140 3.3827 3.3691" 3.3722 3.3968 3.4924 3.6415 3.8120 3.9862 (.9675) (.9598) (.9509) (.9389) (.9239) (.9070) (.8671) (.8237) (.7791) (.7366)  u  .0120 .0100 .0166 .0086 .0258 .0185 .0149 .0087 .0089 .0133 (.0096) (.0113) (.0118) (.0122) (.0125) (.0129) (.0135) (.0139) (.0143) (.0146) .1658 .5598 .3632 .2979 .4713 .0117 .1114 .2295 .5624 .5333  g  .1013 .1025 (.2389) (.2340) .6772 .6677  .1038 .1032 .1044 (.2328) (.2318) (.2310) .6587 .6613 .6643  h  .1546 (.1120) .1761  .1551 (.1096) .1655  .1553 (.1090) .1629  a  .4009 (.1620) .0193  .4398 .4456 (.1615) (.1602) .0110 .0096  .4485 (.1584) .0086  .4486 (.1560) .0078  R2  .9861  .9867  .9868  .9869  .9870  .9871  .9871  .9871  .9870  .9868  S  .0584  .0573  .0570  .0568  .0566  .0564  .0563  .0564  .0567  .0570  »!d"  1.478*  1.515  1.527  .1045 (.2304) .6574  .1556 .1559 .1564 (.1086) (.1081) (.1079) .1603 .1554 .1579  1.540  1.552  .1045 .1035 (.2299) (.2304) .6568 .6604  .1020 (.2314) .6659  .1003 (.2327) .6726  .1593 (.1078) .1478  .1609 (.1082) .1453  .1626 (.1088) .1435  .1577 (.1076) .1512  .4450 .4299 (.1533) (.1469) .0069 .0073  1.564  1.582  .4056 .3485 .3774 (.1398) (.1324) (.1254) .0082 .0097 .0073  1.593  1.599  *Test for s e r i a l correlation i s inconclusive at one per cent l e v e l of significance.  1.601  TABLE VII (continued), A=0.01 0.0 lnA»  .02  .025  .03  .035  .04  .05  .06  .07  .08  3.8218 3.5755 3.5298 3.4979 3.4821 3.4868 3.5456 3.6624~ 3.8161" 3.9781 (.9485) (.9523) (.9467) (.9371) (.9255) (.9109) (.8750) (.8337) (.7901) (.7470)  u  .0086 .0130 .0106 .0092 .0180 .0162 .0085 .0270 .0145 .0199 (.0130) (.0145) (.0137) (.0141) (.0148) (.0096) (.0115) (.0119) (.0123) (.0127) .3318 .5665 .5769 .5304 .4517 .2644 .1384 .0905 .1974 .0093  g  .1036 .1036 .1040 .1032 .1016 .1008 .1023 .1007 .0992 .1024 (.2316) (.2323) (.2333) (.2417) (.2369) (.2356) (.2344) (.2334) (.2327) (.2317) .6630 .6618 .6688 .6652 .6605 .6723 .6664 .6763 .6724 .6863  h  .1561 .1559 .1559 .1557 (.1133) (.1110) (.1104) (.1098) .1662 .1780 .1686 .1637  a  .3686 (.1586) .0269  .4120 (.1600) .0154  .9858  .9864  .9365  .9866  .9867  .9868  .9869  .9869  .9869  .9867  S  .0591  .0580  .0577  .0574  .0572  .0570  .0567  .0567  .0569  .0572  "d"  1.465*  1.494*  1.505*  R  2  .1562 (.1093) .1614  .4292 .4262 .4202 .4294 (.1593) (.1579) (.1561) (.1538) .0116 .0103 .0094 .0134  1.517  1.530  .1590 (.1083) .1507  .1606 .1622 (.1086) (.1091) .1477 .1454  .4204 .4015 (.1481) (.1413) .0085 .0084  .3763 .3495 (.1342) (.1270) .0103 .0091  .1566 .1576 (.1089) (.1084) .1545 .1589  1.542  1.563  1.578  1.587  .*Test f o r s e r i a l correlation i s inconclusive at one per cent l e v e l of significance. ;  1.592  TABLE VII (continued), 7\ =0.015  p lnA»  0.0  .02  .025  .03  .035  .04  .05  .06  .07  .08  4.0086 3.7466 3.6915 3.6453 3.6147 3.5980 3.6172 3.7002 3.8273 3.9767 (.9257) (.9403) (.9377) (.9322) (.9235) (.9120) (.8809) (.8427) (.8007) (.7581)  u  .0176 .0142 .0096 .0282 .0114 .0159 .0214 .0195 .0087 .0084 (.0097) (.0115) (.0120) (.0124) (.0128) (.0132) (.0139) (.0144) (.0148) (.0151) .4222 .2930 .5686 .5868 .1637 .1114 .5167 .0074 .0715 .2253  g  .0969 (.2444) .6957  h  .1568 .1568 .1570 .1588 .1568 .1568 .1577 .1603 .1619 .1569 (.1145) (.1123) (.1117) (.1111) (.1106) (.1101) (.1093) (.1091) (.1091) (.1094) .1668 .1690 .1578 .1502 .1623 .1711 .1645 .1537 .1793 .1475  a  .3826 .4098 .3368 .3946 .4007 .4065 .3924 .4077 .3739 .3493 (.1546) (.1578) (.1576) (.1568) (.1556) (.1538) (.1489) (.1427) (.1358) (.1238) .0186 .0161 .0126 .0106 .0142 .0100 .0103 .0215 .0113 .0367  R  2  S "d"  .0987 (.2397) .6856  .0996 (.2385) .6816  .1005 .1022 .1032 .1014 .1032 .1009 .1023 (.2372) (.2361) (.2351) (.2337) (.2332) (.2334) (.2341) .6736 .6656 .6701 .6774 .6649 .6677 .6727  .9855  .9860  .9862  .9863  .9864  .9866  .9867  .9868  .9867  .9867  .0597  .0586  .0584  .0581  .0578  .0576  .0572  .0571  .0571  .0573  1.455*  1.476*  1.485*  1.496*  1.508*  1.520  1.542  1.561  1.574  *Test f o r s e r i a l c o r r e l a t i o n i s inconclusive at one per cent l e v e l of significance.  1.581  TABLE VII (continued), f\=0.02 0.0 InA*  .02  .025  .03  .035  .04  .05  .06  .07  .08  4.1926 3.9287 3.8655 3.8109 3.7637 3.7311, 3.7108 3.7544 3.8506 3.9805 (.8998) (.9247) (.9252) (.9227) (.9176) (.9094) (.8844) (.8505) (.8106) (.7692)  u  .0126 .0090 .0103 .0084 .0157 .0194 .0175 .0231, .0212 .0294 (.0140) (.0146) (.0150) (.0153) (.0098) (.0116) (.0121) (.0125) (.0129) (.0133) .3820 .1298 .4930 .0866 .0058 .1851 .5625 .0546 .2483 .5933  g  .1001 .1020 .0980 .0960 .0992 .1017 .1009 .0970 .1024 .0943 (.2470) (.2426) (.2414) (.2402) (.2389) (.2378) (.2360) (.2349) (.2346) (.2350) .6700 .6736 .6920 .6962 .6879 .6725 .6694 .6833 .6793 .7055  h  .1580 .1579 .1583 (.1157) (.1137) (.1131) .1712 .1729 .1799  a  .3056 (.1500) .0495  .3514 (.1550) .0303  .9852  .9857  S  .0603  »d"  1.448*  R  2  .1578 .1577 .1577 (.1125) (.1119) (.1113) .1692 .1651 .1673  .1580 (.1104) .1609  .1601 .1616 .1589 (.1099) (.1097) (.1098) .1498 .1529 .1567  .3626 .3723 (.1552) (.1550) .0262 .0227  .3807 (.1544) .0196  .9859  .9860  .9861  .9863  .9865  .9866  .9866  .9866  .0593  .0590  .0588  .0585  .0582  .0578  .0575  .0574  .0575  1.462*  1.469*  1.478*  I.488*  1.499*  .3868 .3482 .3849 .3913 .3695 (.1532) (.1493) (.1439) (.1374) (.1306) .0119 .0125 .0139 .0123 .0173  1.522  1.542  1.558  *Test f o r s e r i a l correlation i s inconclusive at one per cent l e v e l of significance.  1.569  TABLE VII (continued),A=0.025 0.0 lnA«  .02  .025  .03  .035  .04  .05  .06  .07  .08  4.3683 4.1121 4.0460 3.9829 3.9277 3.8808 3.8241 3.8303 3.8912 3.9962 (.8715) (.9046) (.9081) (.9090) (.9073) (.9027) (.8846) (.8562) (.8199) (.7803)  u  .0230 .0140 .0306 .0211 .0086 .0248 .0113 .0193 .0174 .0095 (.0099) (.0116) (.0121) (.0125) (.0130) (.0134) (.0142) (.0148) (.0153) (.0156) .1460 .1002 .5446 .2025 .4563 .0653 .3341 .5911 .0045 .0407  g  .0941 .0915 .0931 (.2493) (.2454) (.2442) .7070 .7031 .7153  h  .1592 .1597 .1594 .1589 (.1168) (.1149) (.1144) (.1138) .1800 .1726 .1710 .1741  a  .2753 (.1451) .0655  .3201 (.1514) .0420  .3317 (.1521) .0366  .9850  .9854  .0608 1.444*  R  2  S "d»  .0976 .0998 .1010 .0952 .1013 .0964 (.2430) (.2418) (.2406) (.2385) (.2370) (.2362) .6810 .6896 .6758 .6987 .6739 .6941  .1006 (.2362) .6759  .1588 (.1132) .1694  .1586 (.1126) .1675  .1586 .1601 .1591 (.1116) (.1109) (.1104) .1558 .1637 .1597  .3428 (.1525) .0317  .3525 (.1524) .0275  .3609 (.1518) .0239  .3715 (.1491) .0186  .3715 (.1447) .0156  .9855  .9857  .9858  .9859  .9862  .9863  .9864  .9864  .0600  .0597  .0594  .0591  .0589  .0583  .O58O  .0578  .0578  1.451*  1.456*  1.463*  1.471*  1.480*  1.501*  1.523  .1614 (.1104) .1523  .3621 .3451 (.1388) (.1323) .0143 .0143  1.541  *Test f o r s e r i a l c o r r e l a t i o n i s inconclusive at one per cent l e v e l o f significance.  1.556  TABLE VII (continued), ft=0.03 0.0 lnA»  .02  .025  .03  .035  .04  .05  .06  .07  .08  4.5352 4.2911 4.2243 4.1612 4.0988" 4.0434 3.9587 3.9253~ 3.9496 4.0238 (.8410) (.8812) (.8873) (.8914) (.8928) (.8918) (.8807) (.8587) (.8273) (.7904)  u  .0318 (.0099) .0035  .0158 .0090 .0212 .0127 .0104 .0248 .0194 .0231 .0264 (.0116) (.0121) (.0126) (.0130) (.0135) (.0143) (.0150) (.0155) (.0159) .2796 .5803 .0300 .0748 .1589 .5149 .1117 .0483 .4095  g  .0884 (.2514) .7254  .1000 .1001 .0920 .0932 .0900 .0991 .0971 .0945 .0909 (.2380) (.2446) (.2393) (.2434) (.2458) (.2411) (.2375) (.2479) (.2469) .7058 .7012 .6840 .6796 .6792 .7180 .6915 .7105 .7144  h  .1600 .1598 .1606 .1608 .1603 .1595 .1613 (.1128) (.1139) (.1151) (.1156) (.1145) (.1178) (.1161) .1660 .1708 .1722 .1693 .1734 .1747 .1795  .1596 .1602 .1613 (.1119) (.1113) (.1110) .1585 .1623 .1549  a  .3330 .3482 .3232 .3012 .3123 .2897 .2475 (.1497) (.1483) (.1497) (.1398) (.1472) (.1484) (.1493) .0442 .0383 .0254 .0503 .0334 .0849 .0571  .3548 .3399 .3517 (.1449) (.1399) (.1339) .0204 .0167 .0177  R2  .9847  .9851  .9852  .9853  .9855  .9856  .9859  .9861  .9862  .9863  S  .0613  .0606  .0603  .0601  .0598  .0595  .0590  .0585  .0582  .0581  1.442*  1.443*  1.446*  1.451*  1.457*  I.464*  1.483*  1.503*  "d"  1.524  *Test f o r s e r i a l correlation i s inconclusive at one per cent l e v e l of significance.  1.540  TABLE VIII REGRESSION ESTIMATES FOR MODEL 1(b): Q = A e  ?  0.0  lnA»  .02  .025  .03  .035  u t  e  f + g w + h w  .04  L  1 _ a  .05  K , A=0.0, 1935-65 a  7O6  .07  " .08  3.2307, 3.1352 3.1461 3.1745, 3.2165, 3.2761 3.4326 3.6204 3.8125 3.9952 (.9738) (.9485) (.9355) (.9209) (.9034) (.8846) (.8431) (.8005) (.7580) (.7181) x  u  .0128 .0226 .0142 .0115 .0157 (.0094) (.0110) (.0114) (.0118) (.0122) .3536 .1630 .2242 .0221 .2894  g  .1028 .1100 .1083 .1089 .1069 .1049 .1007 .1097 .1123 .1093 (.2314) (.2276) (.2270) (.2266) (.2263) (.2263) (.2268) (.2282) (.2298) (.2315) .6406 .6700 .6368 .6376 .6617 .6389 .6534 .6363 .6375 .6457  h  .1610 .1498 .1522 .1571 .1591 .1529 .1553 .1627 .1537 .1544 (.1084) (.1066) (.1063) (.1061) (.1059) (.1059). (.1061) (.1067) (.1074) (.1082) .1588 .1510 .1412 .1758 .1471 .1559 .1444 .1424 .1619 .1534  a  .3780 .4866 .4878 .4664 .4409 .4759 .4099 .3475 .4824 .4693 (.1634) (.1599) (.1579) (.1556) (.1528) (.1498) (.1430) (.1360) (.1290) (.1224) .0056 .0068 .0048 .0048 .OO46 .0078 .0052 .0084 .0045 .0044  R  2  S »d"  .0086 .0092 .0105 .0087 .0089 (.0125) (.0130) (.0135) (.0139) (.0143) .5338 . 5461 .4103 .4927 .5477  .9870  .9874  .9875  .9875  .9875  .9875  .9875  .9873  .9871  .9869  .0566  .0557  .0556  .0555  .0554  .0554  .0556  .0559  .0563  .0567  1.532  1.572  1.583  1.593  1.602  1.609  1.618  1.620  1.619  1.617 H  TABLE IX REGRESSION ESTIMATES FOR MODEL 1(c):  0.0 lnA»  .025  .03  .035  Q=Ae e S u t  .04  f +  w + h w  2 L  .05  1-a  K ,A=0.0, 1935-65 a  .06  .07  .08  3.6030 3.4889 3.5180 3.5627 3.6228 3.8032 3.9636 4.1233 4.2673 (.8502) (.8064) (.7905) (.7732) (.7548) (.7071) (.6695) (.6347) (.6028) .0176 .0185 .0197 (.0094) (.0097) (.0100) .0860 .0450 .0645  .0168 .0165 (.0102) (.0104) .1232 .1072  .0158 .0157 .0159 (.0108) (.0111) (.0115) .1482 .1805 .1657  u  .0270 (.0079) .0021  S  .1318 .1401 .1416 .1436 .1357 .1440 .1429 .1441 .1399 (.2333) (.2271) (.2265) (.2261) (.2261) (.2270) (.2281) (.2295) (.2310) .5798 .5512 .5662 .5400 .5381 .5434 .5385 .5607 .5384  h  .1408 .1460 .1392 .1402 .1433 .1484 .1383 .1379 .1377 (.1092) (.1063) (.1060) (.1058) (.1057) (.1061) (.1065) (.1072) (.1078) .1932 .1936 .1872 .2006 .2040 .1817 .2158 .1971 .1774  a  .3722 .3458 .2956 .4128 .4030 .3194 .4199 .4244 .4037 (.1414) (.1345) (.1320) (.1291) (.1261) (.1178) (.1116) (.1058) (.1005) .0040 .OO56 .OO46 .0038 .0040 .0081 .0067 .0037 .0037  R2  .9870  .9876  .9877  .9877  .9877  .9376  .9875  .9373  .9872  S  .0567  .0552  .0551  .0550  .0550  .0552  .0555  .0559  .0562  "d»  1.612  1.690  1.703  1.712  1.720  1.721  1.722  1.719  1.715  TABLE X REGRESSION ESTIMATES FOR MODEL I I : Q = A e S f +  0.0  .02  .025  .03  .035  w + h w  2 L  .04  1 - a  K , A =0.0, 1935-65 a  .05  .06  .07  .08  InA'  .9269 1.8038 2.0018 2.1899 2.3679 2.5358 2.8419 3.1109 3.3464 3.5523 (.1821) (.1519) (.1468) (.1425) (.1389) (.1360) (.1316) (.1289) (.1271) (.1260)  g  .1218 .1201 .1498 .1436 .1283 .1385 .1343 .1244 .1571 .2024 (.2258) (.2274) (.2566) (.2343) (.2309) (.2283) (.2264) (.2252) (.2242) (.2246) .6000 .5628 .5150 .4426 .5416 .5907 .5785 .6075 .5527 .5291  h  a  .1073  .1305  .1346  .1382  .1412  .1439  .1481  .1511  .1534  .1552  .3842  .2437  .2224  .2051  .1916  .1811  .1671  .1593  .1553  .1534  (.1203) (.1098) (.1083) (.1070)~ (.1061) (.1056) (.1051) (.1053) (.1059) (.1066) .6806 .6201 .5416 .8578 .5923 .6495 .7133 (.0229) (.0173) (.0163) (.0154) (.0145) (.0138) (.0126) .0000 .0000 .0000 .0000 .0000 .0000 .0000  .4970 .4579 .4237 (.0116) (.0107) (.0100) .0000 .0000 .0000  R2  .9829  .9858  .9862  .9865  .9863  .9869  .9370  .9870  .9868  .9867  S  .0636  .0580  .0572  .0565  .0561  .0558  .0555  .0556  .0559  .0563  1.175*  1.383*  »d»  1.425  1.461  1.491  1.514  1.545  1.559  1.563  *Test f o r s e r i a l c o r r e l a t i o n i s inconclusive at one per cent l e v e l of significance.  1.562  TABLE XI REGRESSION ESTIMATES FOR MODEL I I I : Q = A e  p InA*  0.0  .02  .025  .03  .035  u t  e  f +  S  w + h w  2 L K , A=0.0, 1935-65 b  a  .04  .05  .06  .07  .08  7.9914  6.6457  6.3933  6.1298  6.0039  5.9191  6.0063  6.3616  6.7965  7.2655  .0574 1.565  .0570  .0569 1.567  .0568  .0567  .0567  .0567 1.590  .0568 1.593  .0569 1.594  .0570 1.593  (3.9918)(4.0902)(4.1326)(4.1479)(4.1294)(4.1144)(4.0219)(3.8433)(3.6421)(3.4580) .0210 .0188 .0226 .0320 .0240 u .0207 .0223 .0199 .0194 .0257 (.0113) (.0150) (.0160) (.0170) (.0177) (.0185) (.0196) (.0200) (.0202) (.0202) .2460 .3476 .2730 .1428 .3452 .0961 .0088 .2929 .3157 .1984 .1630 .1492 .1492 .1600 .1566 .1530 .1527 .1509 .1575 .1759 g (.2416) (.2414) (.2412) (.2411) (.2411) (.2413) (.2414) (.2417) (.2427) (.2418) .5388 .5132 .5442 .5270 .4816 .5484 .5484 .5209 .5394 .5297 .1301 .1316 .1272 .1302 .1258 h .1337 .1329 .1324 .1279 .1171 (.1143) (.1141) (.1141) (.1141) (.1141) (.1142) (.1144) (.1146) (.1147) (.1149) .2670 .2726 .2579 .2587 .2524 .2787 .2543 .2804 .2641 .3165 .5388 .4996 .4910 b .4892 .5119 .4947 .5241 .5333 .4895 .5014 (.1681) (.1672) (.1690) (.1692) (.1701) (.1712) (.1721) (.1677) (.1715) (.1734) .0052 .0070 .0042 .0086 .0082 .0064 .0077 .0045 .0043 .0077 .2820 .2688 .1968 .2506 .1578 .2701 .1212 a .2779 .2351, .2313 (.3113) (.3197) (.3217) (.3208) (.3166) (.3123) (.2977) (.2759) (.2527) (.2316) .5088 .4490 .3787 .3787 .7005 .3924 .4124 .4826 .4067 . .4492 R2 .9506 .9500 .9512 .9513 .9513 .9509 .9511 .9509 .9507 .9511 S  1.564  1.572  1.577  1.582  *Test f o r s e r i a l c o r r e l a t i o n i s i n c o n c l u s i v e a t one p e r cent l e v e l o f significance i n a l l regressions.  TABLE XII REGRESSION ESTIMATES FOR MODEL  r lnA»  0.0  .02  .025  .03  IV(a): Q » = A e .035  ut  .04  L ~ K , 1  a  a  .05  A =0.0, .06  1935-65 .07  .08  3.6856 3.5147 3.4985 3.5009 3.5218 3.5626 3.6865 3.8550 4.0384 4.2188 (1.1384)(1.1258)(1.1125)(1.0955)(1.0749)(1.0510) (.9966) (.9380) (.8794) (.8240) .0158 (.0134) .2460  .0140 .0123 (.0139) (.0143) .4040 .3245  .0108 (.0148) .4787  .0076 .0067 .0095 .0065 .0064 (.0151) (.0158) (.0163) (.0166) (.0169) .6856 .7048 .6373 .7039 .5427  u  .0232 (.0112) .0449  a  .4680 .4208 .4766 .4742 .4730 .4416 .4483 .3605 .4769 .3905 (.1953) (.1940) (.1920) (.1894) (.1862) (.1824) (.1737) (.1642) (.1546) (.1456) .0160 .0170 .0302 .0185 .0154 .0167 .0153 .0147 .0187 .0204  R2  .9774  .9780  .9781  .9782  .9783  .9784  .9784  .9784  .9783  .9781  S  .0691  .0682  .0680  .0678  .0677  .0676  .0675  .0676  .0678  .0681  »d"  1.850  1.890  1.901  1.912  1.921  1.928  1.936  1.937  1.934  1.928  TABLE XIII REGRESSION ESTIMATES FOR MODEL IV(b): Q » A e e - / L ~ K , A = 0 . 0 , 1935-65 u t  r .nA«  0.0  .02  .025  .03  .035  f  .04  e  w  1  a  .05  a  .06  .07  .08  3.5670 3.4818 3.4973 3.5303 3.5829 3.6566 3.8430 4.0645 4.2930 4.5091 (1.2718)(1.2668)(1.2551)(1.2392)(1.2193)(1.1956)(1.1403)(1.0786)(1.0155) (.9550)  u  .OO44 .0068 .0058 .0081 .0096 .0186 .0112 .0041 .0045 (.0168) (.0173) (.0188) (.0125) (.0151) (.0157) (.0163) (.0182) (.0194) .6301 .8106 .8046 .6921 .5542 .7379 .4685 .7935 .1449  g  -.3176 -.3197 -.3206 -.3216 -.3226 -.3237 -.3257, - . 3 2 7 4 - . 3 2 8 8 - . 3 2 9 9 (.0469) (.0467) (.0467) (.0467) (.0468) (.0468) (.0471) (.0475) (.0479) (.0483) .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000  a  .5300 .5220 .5188 .4804 .5346 .5104 .4441 .5363 (.2186) (.2188) (.2172) (.2149) (.2119) (.2083) (.1997) (.1899) .0222 .0201 .0201 .0196 .0238 .0257 .0194 .0195  R  2  S "d"  .0051 (.0198) .7869  .4063 (.1799) .0306  .3702 (.1702) .0366  .9749  .9752  .9752  .9752  .9752  .9752  .9750  .9748  .9745  .9742  .0772  .0767  .0767  .0767  .0767  .0767  .0770  .0774  .0778  .0783  1.874  1.898  1.905  1.910  1.914  1.917  1.918  1.913  1.906  1.899  TABLE XIV  2 REGRESSION ESTIMATES FOR MODEL V: Q=Ae e SW+kw L ~ K e , A =P=0.0, 1935-65 ut  D InA* u g h a j R2 S "d»  Dl  D  2  3.8387 (.9437) .0320 (.0096) .0027 .1258 (.2225) .5833 .1376 (.1044) .1969 .3635 .5037 (.1705) (.1536) .0066 .0291 .0541 -.0787 (.0399) (.0378) .1840 .0455 .9885 .9874 .0568 .0544 1.551* 1.683  3.0299 (1.0150) .0192 (.0101) .0673 .0813 (.2328) .7272 .1549 (.1089) .1638  D  D  3  4  D  1  f+  5  3.0012 (.9461) .0244 (.0089) .0105 .0814 (.2218) .7152 .1642 (.1040) .1230  D6  a  D  a  7  jD  DlO  1 X  D13  2.1505 2.5205 3.0274 2.8945 3.0478 (.9038)(1.1566)(1.1064)(1.1095)(1.0178) .0190 .0196 .0193 .0224 .0215 (.0081) (.0100) (.0099) (.0099) (.0101) .0610 .0257 .0309 .0377 .0615 -.1100 .1752 .0851 .1349 .0973 (.1979) (.2312) (.2382) (.2355) (.2395) .6796 .7218 .5084 .6485 .4775 .1478 .1229 .1619 .1564 .1469 (.0927) (.1085) (.1113) (.1105) (.1117) .1930 .2816 .1446 .1689 .1195  3.4769 (.9667) .0274 (.0095) .0079 .0983 (.2322) .6779 .1525 (.1088) .1702  3.4531 (.9444) .0280 (.0093) .0057 .0990 (.2269) .6690 .1545 (.1063) .1552  .4273 (.1621) .0137 -.0538 (.0394) .1811 .9874 .0568 1.736  .5076 .6443 .5874 .5047 .4299 (.1587) (.1509) (.1938) (.1865) (.1584) .0038 .0003 .0055 .0117 .0114 - . 0 6 9 0 -.0844 - . 1 3 3 5 - . 0 7 1 9 - . 0 3 9 9 (.0390) (.0398) (.0384) (.0497) (.0472) .0020 .0418 .1569 .4104 .0854 .9868 .9880 .9909 .9885 .9875 .0484 .0566 .0581 .0542 .0555 1.692 1.659 1.444* 1.895 1.717  %  D  .5246 .4967 (.1858) (.1700) .0089 .0071 .0501 -.0471 (.0442) (.0386) .2038 .2976 .9871 .9873 .0576 .0570 1.434* 1.620  *Test f o r s e r i a l correlation i s inconclusive at one per cent l e v e l of significance.  136 TABLE XV REGRESSION ESTIMATES FOR MODEL 1(a): Q=Ae e e L "K , ^=0.0, FOR THE 1935-49 AND 1950-65 SUBPERIODS ut  f +  w + h w 2  1  a  a  1935-49 subperiod  1950-65 subperiod  1.1424 (1.4696)  3.2510 (1.3939)  u  .0109 (.0120) .3872  .0308 (.0134) .0406  g  .1925 (.2775) .5096  -.0701 (.3930) .3395  h  .1179 (.1243) .3680  .2608 (.2023)  .8119 (.2449)  .0077  .4461 (.2340) .0804  R2  .9706  .9738  S  .0539  .0481  InA'  a  »d"  2.122  .2222  1.513*  *Test f o r s e r i a l correlation i s inconclusive at one per cent l e v e l of s i g n i f i c a n c e .  

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