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The contribution of schooling to Canadian farm income Labadan, Eloisa Marcos 1979

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THE CONTRIBUTION OF SCHOOLING TO CANADIAN FARM INCOME by ELOISA MARCOS LABADAN B . S c , U n i v e r s i t y o f t h e P h i l i p p i n e s , 1970 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE i n THE FACULTY OF GRADUATE STUDIES Department o f A g r i c u l t u r a l Economics We a c c e p t t h i s t h e s i s as c o n f o r m i n g t o t h e r e q u i r e d s t a n d a r d THE UNIVERSITY OF BRITISH COLUMBIA A p r i l , 1979 © E l o i s a Marcos Labadan In presenting this thesis in partial fulfilment of the requirements for an advanced degree at the University of British Columbia, I agree that the Library shall make it freely available for reference and study. I further agree that permission for extensive copying of this thesis for scholarly purposes may be granted by the Head of my Department or by his representatives. It is understood that copying or publication of this thesis for financial gain shall not be allowed without my written permission. Department of Agricultural Economics The University of British Columbia 2075 Wesbrook Place Vancouver, Canada V6T 1W5 Date April 27,1979 ABSTRACT The b a s i c o b j e c t i v e s o f t h i s t h e s i s are t o b u i l d an e a r n i n g s f u n c t i o n f o r farm incomes o f Canadian farm o p e r a t o r s , and e s t i m a t e the r a t e o f r e t u r n t o s c h o o l i n g . I t i s h y p o t h e s i z e d t h a t the low l e v e l s o f farm income a r e r e l a t e d t o t h e low i n v e s t m e n t i n e d u c a t i o n by farm o p e r a t o r s . I f r e a s o n a b l e e s t i m a t e s o f p o s i t i v e r e t u r n s t o s c h o o l i n g a r e found, they w i l l be u s e f u l f o r p o l i c y makers i n c o n s i d e r i n g the improvement o f t h e q u a l i t y o f farm o p e r a t o r l a b o u r v i a s c h o o l i n g , as an a l t e r n a t i v e measure t o i n c r e a s e farm income. To a c h i e v e t h e g o a l s o f t h i s s t u d y , an e a r n i n g s f u n c t i o n i s b u i l t f o r t h e group o f e n t r e p r e n e u r s , i n p a r t i c u l a r the farm o p e r a t o r s . As a t e s t o f f u n c t i o n a l form a d i g r e s s i o n i s made and a v a l u e added approach d i s c u s s e d and u t i l i z e d as an a l t e r -n a t i v e way o f computing th e c o n t r i b u t i o n o f s c h o o l i n g t o farm income. A l t h o u g h b o t h methods y i e l d e d s i g n i f i c a n t e s t i m a t e s o f the r e t u r n t o s c h o o l i n g comparable t o p r e v i o u s s t u d i e s , the v a l u e added approach was found t o be a b e t t e r s p e c i f i e d formu-l a t i o n w i t h r e s p e c t t o e s t i m a t i n g the p r o d u c t i v i t y o f s c h o o l i n g i n farm p r o d u c t i o n . The e s t i m a t e o f t h e m a r g i n a l p r o d u c t o f s c h o o l i n g u s i n g t h e e a r n i n g s f u n c t i o n approach was found t o be h i g h e r as we c o n c e n t r a t e d on t h e f u l l - t i m e f a r m e r s . F o r t h e v a l u e added approach, t h e e s t i m a t e s d i f f e r e d as we v a r i e d t h e i n p u t s p e c i f i c a t i o n , b e i n g h i g h e r as we d e c r e a s e t h e number o f d e c i s i o n v a r i a b l e s i n the e s t i m a t i n g e q u a t i o n . E s t i m a t e s f o r b o t h models however have t h e i r r e s p e c t i v e b i a s e s and sho r t c o m i n g s a t t r i b u t a b l e m a i n l y t o the v a r i a b l e s o m i t t e d i n both s p e c i f i c a t i o n s . These e s t i m a t e s c o u l d be improved w i t h the a v a i l a b i l i t y o f b e t t e r s p e c i f i e d v a r i a b l e s and use o f an a l t e r n a t i v e a n a l y t i c a l p r o c e d u r e . I n a d d i t i o n t o p r o v i d i n g s t r o n g e v i d e n c e t h a t s c h o o l i n g i s a s i g n i f i c a n t d e t e r m i n a n t o f farm incomes, t h i s s t u d y a l s o l e d t o a n o t h e r i m p o r t a n t c o n c l u s i o n . U s i n g a t r a n s f o r m e d l a b o u r v a r i a b l e i n t h e v a l u e added f u n c t i o n a t the census d i v i s i o n l e v e l l e d t o an i m p o r t a n t f i n d i n g t h a t a s i m i l a r o u t p u t - i n p u t r e l a t i o n s h i p e x i s t s i n the a g r i c u l t u r a l s e c t o r s o f b o t h the U.S. and Canada. S p e c i f i c a l l y t h e r e l a t i o n s h i p was i d e n t i c a l f o r the e l a s t i c i t i e s o f o u t p u t w i t h r e s p e c t t o l a b o u r , w i t h r e s p e c t t o e d u c a t i o n ( s c h o o l i n g ) , and w i t h r e s p e c t t o t h e w e i g h t e d l a b o u r v a r i a b l e ( p r o d u c t o f l a b o u r and s c h o o l i n g ) v a l u e s o f s e l e c t e d y e a r s . i v TABLE OF CONTENTS CHAPTER Page I. INTRODUCTION 1 1.1 Problem S e t t i n g 2 1.2 O b j e c t i v e s o f t h e Study 5 1.3 Importance o f t h e Study 6 1.4 Guide t o T h e s i s 7 I I THEORETICAL FRAMEWORK 9 2.1 The Human C a p i t a l Approach t o . . . - -Income D i s t r i b u t i o n 9 2.2 Development o f t h e Model 11 2.3 E v a l u a t i o n o f the E a r n i n g s F u n c t i o n 17 I I I APPLICATION OF THE MODEL TO THE AGRICULTURAL SECTOR 23 3.1 M o d i f i e d E a r n i n g s F u n c t i o n f o r Farm O p e r a t o r s 23 3.2 D i g r e s s i o n : V a l u e Added Approach 25 3.3 P r o d u c t i v e V a l u e o f E d u c a t i o n 26 IV METHODOLOGICAL FRAMEWORK AND DATA CONSIDERATIONS 31 4.1 Data Sources 31 4.2 E a r n i n g s F u n c t i o n 3 2 4.2.1. Data Requirements 32 4.2.2. E m p i r i c a l Model 39 4.3 V a l u e Added F u n c t i o n 41 4.3.1. Data Requirements 41 4.3.2. E m p i r i c a l Model 41 4.4 Census D i v i s i o n 4 5 V V RESULTS AND DISCUSSION 4 8 5.1 M i c r o Data L e v e l 4 8 5.1.1. E a r n i n g s F u n c t i o n 48 5.1.2. V a l u e Added F u n c t i o n 5 2 5.2 Census D i v i s i o n L e v e l 55 5.2.1. E a r n i n g s F u n c t i o n . 55 5.2.2. V a l u e Added F u n c t i o n 58 5.3 Summary o f R e s u l t s 61 VI SUMMARY AND CONCLUSIONS 64 BIBLIOGRAPHY 70 APPENDIX A. T a b l e s on t h e Comparison o f Urban-R u r a l E d u c a t i o n l e v e l s and Income L e v e l s 7 3 APPENDIX B. G l o s s a r y o f Terms 76 APPENDIX C. T a b l e s on R e c e i p t s f o r Wheat S a l e s (1961-71) and Comparison o f D e c l a r e d Farm Income w i t h Computed Farm Income V a l u e s (1971) 82 APPENDIX D. Income Q u e s t i o n From The Long Form 1971 Census P o p u l a t i o n Q u e s t i o n n a i r e 85 v i LIST OF TABLES TABLE Page R e g r e s s i o n e s t i m a t e s o f t h e m o d i f i e d e a r n i n g s f u n c t i o n f o r farm o p e r a t o r s w i t h S a l e s o f a t l e a s t $2500, farm employment income (FEI)>0, and days worked on farm (DAYSON)>1.0 by o c c u p a t i o n s t a t e d . Canada. 19 71 49 R e g r e s s i o n e s t i m a t e s o f t h e m o d i f i e d e a r n i n g s f u n c t i o n f o r farm o p e r a t o r s w i t h S a l e s o f a t l e a s t $2500, farm employment income (FEI)>0, by days worked o f f - f a r m (DAYSOFF) gr o u p s . Canada. 1971 51 R e g r e s s i o n e s t i m a t e s 3 o f the v a l u e added f u n c t i o n f o r farm o p e r a t o r s w i t h S a l e s o f a t l e a s t $2500, and days worked on farm (DAYSON)>1.0 f o r d i f f e r e n t s p e c i f i c a t i o n s , (n=88,473). Canada. 1971 54 R e g r e s s i o n e s t i m a t e s o f t h e m o d i f i e d e a r n i n g s f u n c t i o n f o r farm o p e r a t o r s w i t h S a l e s o f a t l e a s t $2500, u s i n g r e p o r t e d days worked on farm (DAYSON) and p r e d i c t e d DAYSON*, and u s i n g census d i v i s i o n averages (n=24 2 ) . Canada. 1971. . 57 R e g r e s s i o n e s t i m a t e s o f the v a l u e added f u n c t i o n f o r farm o p e r a t o r s w i t h S a l e s o f a t l e a s t $2500, u s i n g d i f f e r e n t s p e c i f i c a t i o n s and u s i n g census d i v i s i o n a verages (n=242). Canada. 1971 60 v i i TABLE Page A . l P e r c e n t a g e D i s t r i b u t i o n o f t h e Urban and R u r a l P o p u l a t i o n 15 y e a r s and o v e r Showing E d u c a t i o n a l Achievement a t the Academic L e v e l s , Canada. 1961 and 1971 74 A.2 R a t i o s o f Census Farm F a m i l y Income t o Urban F a m i l y Income, Canada. S e l e c t e d y e a r s 75 C l T o t a l Cash R e c e i p t s from S a l e s o f Wheat, Canada and t h e P r a i r i e P r o v i n c e s , 1961-1971 83 C.2 Comparison o f D e c l a r e d Net Farm Income w i t h Computed V a l u e s , S e l e c t e d P r o v i n c e s and Census D i v i s i o n s , Canada. 1971 84 v i i i L IST OF.FIGURES FIGURE Page 1 How E d u c a t i o n (E) A f f e c t s Income (Y) 10 i x ACKNOWLEDGEMENTS I w i s h t o e x p r e s s my s i n c e r e a p p r e c i a t i o n t o Dr. R i c k B a r i c h e l l o , my t h e s i s a d v i s o r f o r h i s guidance i n the under-t a k i n g o f t h i s r e s e a r c h . The o r g a n i z a t i o n and p r e s e n t a t i o n o f t h e f i n a l m a n u s c r i p t has been g r e a t l y improved by h i s s u g g e s t i o n s . I would a l s o l i k e t o thank t h e members o f my t h e s i s committee, Dr. George Kennedy, Dr. P e t e r C h i n l o y and Dr. J . M a c M i l l a n f o r t h e i r h e l p f u l s u g g e s t i o n s and comments which l e d t o s u b s t a n t i a l improvements i n t h i s t h e s i s . Thanks a r e extended t o the Department o f A g r i c u l t u r a l Economics a t U.B.C. f o r p r o v i s i o n o f f i n a n c i a l s u p p o r t and S t a t i s t i c s Canada f o r p r o v i d i n g the d a t a used i n t h i s s t u d y . 1 CHAPTER I INTRODUCTION The r o l e o f e d u c a t i o n i n p r o d u c t i v i t y has been the s u b j e c t o f r e s e a r c h f o r the p a s t two decades. S t u d i e s concerned w i t h growth a c c o u n t i n g i n d i c a t e d t h a t a l a r g e p o r t i o n o f growth remains unaccounted f o r a f t e r c o n v e n t i o n a l economic f a c t o r s a r e c o n s i d e r e d . G r i l i c h e s (1963) and Welch (1966) t r i e d t o e x p l a i n t h i s r e s i d u a l t h r o u g h a human c a p i t a l framework o f wh i c h e d u c a t i o n i s a major component. These s t u d i e s i n d i c a t e t h a t the economic growth was accompanied by a s u b s t a n t i a l i n c r e a s e i n t h e e d u c a t i o n a l l e v e l o f the l a b o u r f o r c e . T h i s s t u d y i s i n t e r e s t e d i n e s t a b l i s h i n g the c o n t r i b u t i o n o f e d u c a t i o n on the l a b o u r e a r n i n g s o f a p a r t i c u l a r s e c t o r o f the Canadian farm p o p u l a t i o n , the farm o p e r a t o r s . E a r l y i n v e s t i g a t i o n o f education-Income r e l a t i o n s h i p s based the a n a l y s i s on a s k i l l c r e a t i o n framework. E d u c a t i o n i s an i n v e s t m e n t w h i c h p r o v i d e s knowledge, improves s k i l l s and i s u n d e r t a k e n by i n d i v i d u a l s w i t h the e x p e c t a t i o n o f i n c r e a s e d e a r n i n g s i n t h e f u t u r e . As w i t h any o t h e r i n v e s t m e n t , i t i s i m p o r t a n t t o measure the r a t e o f r e t u r n from such an i n v e s t -ment . An i m p o r t a n t s t u d y by M i n c e r (195 8) was one o f the f i r s t t o a p p l y human c a p i t a l c o n c e p t s d i r e c t l y t o the p e r s o n a l d i s t r i b u t i o n o f e a r n i n g s . S e v e r a l s t u d i e s have d e a l t w i t h computations o f t h e r e t u r n t o e d u c a t i o n u s i n g e i t h e r - w a g e d i f f e r e n t i a l methods (comparison o f e a r n i n g s o f two groups w i t h d i f f e r e n t s c h o o l c o m p l e t i o n l e v e l s ) and the use o f r e g r e s s i o n a n a l y s i s t o d i r e c t l y compute the r a t e o f r e t u r n t o 2 e d u c a t i o n ( v i a f o r m a l s c h o o l i n g ) . The l a t t e r , r e f e r r e d t o i n the l i t e r a t u r e as an e a r n i n g s f u n c t i o n i s an e q u a t i o n w i t h e a r n i n g s as the dependent v a r i a b l e , r e g r e s s e d on s c h o o l i n g and o t h e r v a r i a b l e s . A l l o f t h e s e were o r g a n i z e d by Becker (1964) i n t o a c o h e r e n t t h e o r e t i c a l model wh i c h s i n g l e o ut i n d i v i d u a l i n v e s t m e n t b e h a v i o r as t h e b a s i c f a c t o r i n t h e h e t e r o g e n e i t y o f l a b o r incomes. T h i s s t u d y w i l l f o c u s on t h e r o l e o f s c h o o l i n g on the farm income o f Canadian farm o p e r a t o r s . Two methods have thus f a r been u t i l i z e d t o measure r a t e o f r e t u r n t o e d u c a t i o n i n a g r i c u l t u r e . One approach c o n s i d e r s e d u c a t i o n as one o f s e v e r a l i n p u t s i n an aggr e g a t e a g r i c u l t u r a l p r o d u c t i o n f u n c t i o n , w i t h the o b j e c t i v e o f t e s t i n g i f the i n p u t e d u c a t i o n has a s i g n i f i c a n t l y p o s i t i v e m a r g i n a l p r o d u c t . An a l t e r n a t i v e method i s t o c o n s t r u c t an e a r n i n g s f u n c t i o n f o r farm o p e r a t o r s supplemented by f a c t o r s i m p o r t a n t i n p r o d u c t i o n t h e o r y . A l t h o u g h t h e p r o d u c t i o n f u n c t i o n approach has, been more e x t e n s i v e l y used G r i l i c h e s (1964), K h a l d i (1975), Huffman / (1974) and Fane (1975) , t h i s s t u d y w i l l u t i l i z e t he e a r n i n g s f u n c t i o n approach. 1.1 Problem S e t t i n g The most s t r i k i n g d i s c r e p a n c y i n income l e v e l s i n t h e Canadian economy i s not so much between p r o v i n c e s as between the a g r i c u l t u r a l s e c t o r and non a g r i c u l t u r a l s e c t o r i n a l l p a r t s o f t h e c o u n t r y . A r e c e n t study by Shaw (1977) showed t h a t i n 1970, p e r c a p i t a cash income i n Canada's farm s e c t o r 3 was o n l y about one h a l f t h a t o f Canada's urban s e c t o r , and w i t h an a d justment f o r income i n k i n d , t h e per c a p i t a farm: non farm income r a t i o i n c r e a s e s t o about 0.62. The r e l a t i v e l y lower l e v e l s o f farm income have been the c o n c e r n o f p o l i c y makers f o r a l o n g t i m e . Due t o l a r g e farm o u t m i g r a t i o n , p o l i c y makers have been concerned w i t h i m p r o v i n g the economic w e l l - b e i n g o f the r e m a i n i n g farm p o p u l a t i o n and i n s u r i n g the e f f i c i e n t u t i l i z a t i o n o f a g r i c u l t u r a l r e s o u r c e s . Government p o l i c i e s t o i n c r e a s e farm income a r e i n the form of s u b s i d i e s f o r farm o u t p u t and some s e l e c t e d i n p u t s . These measures ( w h o l l y concerned w i t h the p h y s i c a l i n p u t and o u t p u t components o f t h e p r o d u c t i o n p r o c e s s ) a r e e f f e c t i v e i n t r a n s -f e r r i n g r e s o u r c e s from the urban s e c t o r t o t h e r u r a l farm s e c t o r . However such w e a l t h r e d i s t r i b u t i o n may n o t be t h e most e f f i c i e n t method o f n a r r o w i n g the income gap between t h e s e two groups and i n most cases such measures b e n e f i t t h e w e l l to-do f a r m e r s a t t h e expense o f s m a l l t ime f a r m e r s . I t can be argued t h a t t h e low incomes from f a r m i n g a r e i n f l u e n c e d by t h e low i n v e s t m e n t i n e d u c a t i o n by f a r m e r s . Indeed, a l o o k a t t h e r u r a l farm - urban p e r c e n t a g e s o f s c h o o l i n g completed shows t h a t urban r e s i d e n t s a r e more s c h o o l e d (Appendix T a b l e A . l ) . I t i s a l s o a p p arent from the f i g u r e s t h a t t h e r e has been s u b s t a n t i a l improvement i n s c h o o l i n g achievement f o r b o t h t h e urban and r u r a l farm p o p u l a t i o n f o r the t e n y e a r p e r i o d (1961-1971). C l o s e r exami-n a t i o n r e v e a l s t h a t the r u r a l farm p o p u l a t i o n has made g r e a t e r r e l a t i v e p r o g r e s s so t h a t the gap i n achievement r a t e s between 4 the two groups has narrowed. I n 1961, p r o p o r t i o n s w i t h a secondary o r h i g h e r e d u c a t i o n i n urban and r u r a l farm a r e a s were 58.7% and 36.5% r e s p e c t i v e l y , a d i f f e r e n c e o f 22.2 pe r c e n t a g e p o i n t s . I n 1971 t h e r e s p e c t i v e p r o p o r t i o n s have r i s e n t o 66.3% and 49.7%, a r e d u c t i o n o f the d i f f e r e n c e t o 16.6 pe r c e n t a g e p o i n t s . L o o k i n g a t the r a t i o s o f farm f a m i l y c a s h income t o urban f a m i l y cash income (Appendix T a b l e A . 2 ) , we note an i n c r e a s i n g t r e n d between the 1958 and 1970 f i g u r e s . T h i s i m p l i e s t h a t t h e d i f f e r e n t i a l between farm f a m i l y incomes and urban f a m i l y incomes has a l s o narrowed d u r i n g the 12 y e a r p e r i o d . T h i s r a i s e s the q u e s t i o n o f how s c h o o l i n g as an i n v e s t m e n t c o n t r i b u t e s t o farm income, the i s s u e w h i c h i s t h e main c o n c e r n o f t h i s s t u d y . I f we a r e t o a r r i v e a t a r e a s o n a b l e e s t i m a t e o f t h e c o n t r i b u t i o n o f s c h o o l i n g t o farm income, t h e n we might be a b l e t o recommend p o l i c y a l t e r n a t i v e s t o r a i s e farm incomes. T h i s p o s s i b l e r e l a t i o n between low e d u c a t i o n a l a t t a i n -ment and r e l a t i v e p o v e r t y has been d i s c u s s e d i n a r e p o r t by the Canadian C o u n c i l on R u r a l Development ( R u r a l Canada, 1970;  P r o s p e c t s and P r o b l e m s ) . They s t a t e d t h a t the cha n g i n g n a t u r e o f the l a b o r f o r c e demand r e q u i r e s a major change i n t h e Canadian economy, s p e c i f i c a l l y t o r a i s e the l e v e l o f e d u c a t i o n a l a t t a i n m e n t i n r u r a l a r e a s . I f r u r a l Canadians a r e t o move towards p a r i t y w i t h urban C a n a d i a n s , the r e p o r t c o n t i n u e d , improvements i n t h e o v e r a l l q u a l i t y o f e d u c a t i o n a v a i l a b l e t o them i s e s s e n t i a l . The same o b s e r v a t i o n was made by the F e d e r a l Task F o r c e on A g r i c u l t u r e (Canadian A g r i c u l t u r e i n t h e 5 S e v e n t i e s , 1969), which recommended s h o r t term measures t o s o l v e t h e problem (mobile manpower c l i n i c s i n r u r a l a r e a s ) . 1.2 O b j e c t i v e s o f t h e Study The p r i m a r y o b j e c t i v e o f t h i s s t u d y i s t o d e t e r m i n e the c o n t r i b u t i o n o f s c h o o l i n g t o Canadian farm o p e r a t o r s . There has been o n l y one o t h e r s t u d y u n d e r t a k e n w i t h Canadian d a t a on t h i s t o p i c , a l t h o u g h t h e r e s e a r c h d e a l t more on the l e v e l and d i s t r i b u t i o n o f farm income and how i t compares w i t h non-farm income (Shaw, 1977). T h i s s t u d y w i l l f o c u s on the e a r n i n g s o f one p a r t i c u l a r f a c t o r o f p r o d u c t i o n , l a b o u r , and w i l l b u i l d a model t o e x p l a i n the d e t e r m i n a n t s o f l a b o u r e a r n i n g s a l o n g the l i n e s o f human c a p i t a l t h e o r y and p r o d u c t i o n f u n c t i o n t h e o r y . The model s t a r t s w i t h t h e e a r n i n g s f u n c t i o n adapted t o t h e n o n - a g r i c u l t u r a l s e c t o r , w h i c h w i l l be d e v e l o p e d i n t o a w o r k i n g model t a k i n g i n t o account t h e c h a r a c t e r i s t i c s o f the farm s e c t o r . As a d i g r e s s i o n and t e s t o f f u n c t i o n a l form, a v a l u e added f u n c t i o n w i l l be u t i l i z e d and e s t i m a t e s o f r e t u r n t o e d u c a t i o n ( v i a y e a r s o f s c h o o l i n g ) w i l l be computed f o r b o t h models. The s p e c i f i c o b j e c t i v e s o f t h i s s t u d y a r e : 1. t o b u i l d an e a r n i n g s f u n c t i o n f o r farm incomes o f Canadian farm o p e r a t o r s 2. t o e s t i m a t e , u s i n g the above model the r a t e o f r e t u r n t o s c h o o l i n g . To a t t a i n t h e above o b j e c t i v e s , t h e r e w i l l be two approaches t a k e n , one u s i n g an e a r n i n g s f u n c t i o n and as a t e s t o f 6 f u n c t i o n a l form, a value added f u n c t i o n . The l a t t e r approach was i n i t i a t e d by Welch (1970) and l a t e r a p p l i e d by H a l l e r (1972) i n :his study on r u r a l development i n Columbia. A d i s c u s s i o n of the r e l a t i o n of the earnings f u n c t i o n and value added f u n c t i o n w i l l be made and consequent t r a n s f o r m a t i o n s of the a v a i l a b l e data to f i t both models w i l l be d i s c u s s e d i n d e t a i l i n the f o l l o w i n g c h a p t e r s . 1.3 Importance of the Study The i s s u e of the c o n t r i b u t i o n of s c h o o l i n g to farm income i s an important one f o r v a r i o u s reasons. F i r s t l y , i f reasonable estimates o f p o s i t i v e r e t u r n s t o s c h o o l i n g are found, they w i l l be u s e f u l f o r p o l i c y makers i n c o n s i d e r i n g the improvement of the q u a l i t y of farm operator labour v i a s c h o o l i n g , as an a l t e r n a t i v e measure to i n c r e a s e farm income. Secondly, a re c e n t study by Shaw (1977) suggests t h a t s c h o o l i n g has an ambiguous e f f e c t on farm income, an i s s u e which t h i s study w i l l attempt t o c l a r i f y . T h i s study i s a l s o important i n t h a t i t a p p l i e s r e c e n t developments i n human c a p i t a l theory (Welch (1970) and Mincer (1974)) to the study of a g r i c u l t u r a l incomes and i t u t i l i z e s more d e t a i l e d data than p r e v i o u s l y used. S p e c i f i c a l l y i t w i l l embody developments i n the Mincer (1974) work and i n c l u d e the v a r i a b l e s "weeks worked" and "labour market'experience". As w i t h o t h e r forms of investment, i t i s important to measure the monetary p a y - o f f from e d u c a t i o n . I f we can have a s a t i s f a c t o r y measure of the r a t e of r e t u r n to ed u c a t i o n , we 7 can compare t h i s w i t h r a t e s o f r e t u r n t o o t h e r i n v e s t m e n t s l i k e p h y s i c a l c a p i t a l . These e s t i m a t e s can a l s o be compared w i t h the r e s u l t s o f p r e v i o u s s t u d i e s , p a r t i c u l a r l y t h o s e w h i c h u t i l i z e d U.S. d a t a t o f i n d o u t i f t h e same e a r n i n g s - s c h o o l i n g r e l a t i o n s h i p e x i s t s i n the farm s e c t o r o f t h e two c o u n t r i e s . 1.4 Guide t o T h e s i s The t h e o r e t i c a l model i s d i s c u s s e d i n Chapter I I . I t s t a r t s w i t h a d i s c u s s i o n o f the human c a p i t a l approach t o income d i s t r i b u t i o n and the e a r l y l i t e r a t u r e p e r t a i n i n g t o the development o f the e a r n i n g s f u n c t i o n . The development o f the model based on an e a r l i e r s t u d y f o l l o w s ' . The e a r n i n g s f u n c t i o n i s t h e n e v a l u a t e d i n the l i g h t o f p r e v i o u s e m p i r i c a l e v i d e n c e and a number o f t h e o r e t i c a l c o n s i d e r a t i o n s . Chapter I I I d e a l s w i t h a d i s c u s s i o n o f the a p p l i c a t i o n o f the e a r n i n g s f u n c t i o n t o e n t r e p r e n e u r s , i n p a r t i c u l a r , farm o p e r a t o r s . The d i s c u s s i o n l e a d s t o a w o r k i n g e q u a t i o n w h i c h i s s i m i l a r t o a v a l u e added f u n c t i o n . F o r c o m p a r a t i v e purposes and as a t e s t o f f u n c t i o n a l form, the v a l u e added approach as an a l t e r n a t i v e method o f e s t i m a t i n g the c o n t r i b u t i o n o f s c h o o l i n g t o farm income i s pursue d . The n e x t c h a p t e r c o n s i d e r s the w o r k i n g models f o r b o t h the e a r n i n g s f u n c t i o n and the v a l u e added f u n c t i o n , and the d a t a t r a n s f o r m a t i o n s t o v a r i o u s v a r i a b l e s w h i c h a r e a v a i l a b l e f o r t h i s s t u d y . Both the e a r n i n g s f u n c t i o n and the v a l u e added f u n c t i o n a r e a p p l i e d t o d i f f e r e n t d a t a s e t s t o t e s t t h e e f f e c t on t h e e s t i m a t e d c o n t r i b u t i o n o f s c h o o l i n g t o farm 8 income, and the r e s u l t s a r e p r e s e n t e d i n Chapter V. Reasonable e s t i m a t e s o f r e t u r n t o s c h o o l i n g u s i n g b o t h models, a r e found. I n C h a p t e r VI the main f i n d i n g s o f the s t u d y a r e summarized and the b i a s e s o f t h e e s t i m a t e s a r e d i s c u s s e d . I m p l i c a t i o n s of the i m p o r t a n c e o f t h e r e s u l t s a r e s t r e s s e d as w e l l as s u g g e s t i o n s f o r f u r t h e r s t u d y . 9 CHAPTER I I THEORETICAL MODEL 2.1 The Human C a p i t a l Approach t o Income D i s t r i b u t i o n E d u c a t i o n i s among the f a c t o r s o f t e n c i t e d i n e f f o r t s t o e x p l a i n c u r r e n t wage and income l e v e l s . T h i s s t u d y w i l l f o c u s on e d u c a t i o n ( s p e c i f i c a l l y f o r m a l s c h o o l i n g ) and i t s e f f e c t on farm income o f Canadian farm o p e r a t o r s . I n g e n e r a l as p e o p l e a c q u i r e more s c h o o l i n g o r t r a i n i n g , t h e i r incomes t e n d t o i n c r e a s e as p r o d u c t i v i t y r i s e s and they become more aware o f and q u a l i f i e d f o r b e t t e r p a y i n g j o b s . E d u c a t i o n can. a l s o e f f e c t income t h r o u g h i n c r e a s e d m o b i l i t y and through an i n c r e a s e d a b i l i t y o f the more h i g h l y educated p e r s o n s t o adopt new t e c h n o l o g i c a l i n n o v a t i o n s (Nelson and P h e l p s , 1966). To e x p l a i n t h e i n c o m e - e d u c a t i o n r e l a t i o n s h i p , t a k e t h e case o f an i n d i v i d u a l . The b a s i c assumption i s t h a t t h e i n d i v i d u a l i n v e s t s i n e d u c a t i o n w i t h t h e b a s i c e x p e c t a t i o n o f an i n c r e a s e i n income i n h i s l a b o u r income i n the f u t u r e . An i n c r e a s e i n h i s income i s e x p e c t e d as t h e i n c r e a s e i n educa-t i o n l e a d s t o a g r e a t e r human c a p i t a l s t o c k . R e a l i z a t i o n o f the i n c r e a s e i n income may l e a d t o i n c r e a s e d o p p o r t u n i t y t o p a r t i c i p a t e i n f u r t h e r i n v e s t m e n t s i n e d u c a t i o n . T h i s r e l a t i o n s h i p i s shown i n F i g u r e 1, where the f l o w o f an i n d i v i d u a l ' s income i n time t i s r e l a t e d t o h i s s t o c k o f e d u c a t i o n i n time t - 1 . Time p e r i o d s are p r e s e n t e d t o show the n o n - s i m u l t a n e o u s n a t u r e o f the system and the f a c t t h a t a t i m e frame e x i s t s . 10 AE t - 1 A O P , AE t+m A H C t - 1 AY. A H C t+m t - 1 t t+m Time S c a l e AE = change i n s t o c k o f e d u c a t i o n A H C = change i n human c a p i t a l s t o c k A Y = change i n l a b o u r income A O P = change i n o p p o r t u n i t y f o r e d u c a t i o n a l e x p e r i e n c e s t = time p e r i o d m = 1, 2 .. . k »> i m p l i e s ^ may l e a d t o F i g u r e 1. How E d u c a t i o n (E) A f f e c t s Income ( Y ) 11 Human c a p i t a l models s i n g l e o u t i n d i v i d u a l i n v e s t m e n t b e h a v i o r as t h e b a s i c f a c t o r i n t h e h e t e r o g e n e i t y o f l a b o u r incomes. The model i s f o r m u l a t e d i n terms o f t r a i n i n g p e r i o d s w h i c h a r e completed b e f o r e e a r n i n g s b e g i n and a p p l i e s s t r i c t l y t o s c h o o l i n g , r a t h e r than t o a l l o c c u p a t i o n a l t r a i n i n g . A l t h o u g h i t i s r e c o g n i z e d t h a t f a c t o r s l i k e a b i l i t y and f a m i l y background are e s s e n t i a l v a r i a b l e s t o c o n s i d e r as d e t e r m i n a n t s of income, t h i s s t u d y w i l l f o c u s on a s i n g l e d e t e r m i n i s t i c model wh i c h f o c u s e s on i n v e s t m e n t , i n p a r t i c u l a r , s c h o o l i n g . I n d i v i d u a l s a r e assumed t o be i n t e r e s t e d i n m a x i m i z i n g the p r e s e n t v a l u e o f t h e i r incomes, and e a r n i n g s per u n i t o f time over the w o r k i n g l i f e a r e assumed t o be c o n s t a n t . I l l u s t r a t e d i n t h e n e x t s e c t i o n i s the development o f the model ( a f t e r C h i s w i c k and M i n c e r , 1972) whi c h w i l l be the b a s i s o f the e a r n i n g s f u n c t i o n we w i l l m o d i f y l a t e r t o r e l a t e s c h o o l i n g t o farm income. 2.2 Development o f t h e Model The t h e o r e t i c a l b a s i s o f t h e e a r n i n g s f u n c t i o n i s the human c a p i t a l model f o r m u l a t e d by Beck e r (1964) and m o d i f i e d l a t e r by C h i s w i c k and M i n c e r (1972). The s t a r t i n g p o i n t i s the b a s i c r e l a t i o n between g r o s s e a r n i n g s and i n v e s t m e n t i n human c a p i t a l w h i c h c o u l d be w r i t t e n f o r an i n d i v i d u a l i i n year j a s : where: E_.^ - g r o s s e a r n i n g s = " o r i g i n a l " endowment ( e a r n i n g s i n t h e absence o f inve s t m e n t ) = p r e v i o u s i n v e s t m e n t r . = r a t e o r r e t u r n t o i n v e s t m e n t i n th e t y e a r A l t e r n a t i v e l y , we can e x p r e s s C t^ as a f r a c t i o n o f e a r n i n g s ( i . e . C . = k .E . ) . I f the o r i g i n a l endowment (E .) i s assumed c o n s t a n t a c r o s s y e a r s and i n d i v i d u a l s , we can w r i t e j - l (2) E.. = E + E r ^ . k . E . . 31 o t i t i t i o r : j - l (3) E . . = E TT (1 + r . . k. . ) l i o t = 1 t l t l By t a k i n g t h e n a t u r a l l o g a r i t h m o f b o t h s i d e s o f e q u a t i o n (3) we o b t a i n : j - l (4) I n ( E j ± ) = l n ( E Q ) + E l n ( l + r t ± k t i ) U s i n g the r e l a t i o n t h a t the n a t u r a l l o g o f one p l u s a s m a l l number i s a p p r o x i m a t e l y e q u a l t o t h a t s m a l l number { l n ( l + r . . k . . ) « r . . k . . } : t i t i t i t i (5) l n ( E . . ) = l n ( E 0 ) + V k f c i 13 The number of p e r i o d s of investment i n t r a i n i n g ( j - l ) can be decomposed i n t o S years of s c h o o l i n g and (j-S-1) years of labour market experience. We f u r t h e r assume t h a t the d i r e c t c o s t s of s c h o o l i n g are equal to the p o t e n t i a l earnings of students a t t h a t l e v e l , i m p l y i n g t h a t k ^ = 1 f o r the s c h o o l i n g y e a r s . T h i s assumption was used and defended by Hanoch (1967). I n c o r p o r a t i n g these assumptions, equation (5) reduces t o : j - l (6) l n E.. = l n E + r.S. + £ r..k.. Hi o i i t = s + 1 t i t i At t h i s p o i n t the model assumes f u l l employment of the worker d u r i n g the year. A c t u a l "net e a r n i n g s " are lower than "net f u l l employment e a r n i n g s " by the amount he l o s e s when he i s unemployed, or f o r t h a t matter, underemployed. Mincer has suggested t h a t weeks worked was an a p p r o p r i a t e s t a n d a r d i z i n g v a r i a b l e to c o n t r o l f o r t r a n s i t o r y f l u c t u a t i o n i n unemployment, I f we assume t h a t E^' = weekly earnings and E^ = annual earnings, E. = E . 1 . (W.) l l l Y where W^  = number of weeks worked, and y i s the e l a s t i c i t y of earnings w.r.t. weeks worked. With these m o d i f i c a t i o n s , the earnings f u n c t i o n becomes: j - l (7) l n E.. = l n E + r.S. + Z r. .k. . + yln W. D i o i i t = s + 1 t i t i To e v a l u a t e r . k , . , c e r t a i n assumptions are needed, t i t i Rate of r e t u r n on investment, r ^ . , i s assumed constant ( r . . = r . * ) , t i t i i 14 and t h e f r a c t i o n o f g r o s s e a r n i n g s i n v e s t e d , k f c, i s assumed t o d e c l i n e o v e r t i m e . The assumption o f t h i s c o n s t a n t r a t e o f r e t u r n t o i n v e s t m e n t , i s s u p p o r t e d e m p i r i c a l l y by M i n c e r (1974). The second assumption i s s u p p o r t e d by t h e c o n t e n t i o n t h a t s i n c e o p p o r t u n i t y c o s t o f time i n v e s t e d i n e x p e r i e n c e r i s e s w i t h a d d i t i o n a l e x p e r i e n c e , t h e p r o f i t a b i l i t y o f a d d i -t i o n a l i n v e s t m e n t d e c r e a s e s . A l s o , a d d i t i o n a l e x p e r i e n c e reduces t h e l e n g t h o f t h e r e m a i n i n g w o r k i n g l i f e , and conse-q u e n t l y , t h e p r o f i t a b i l i t y o f i n v e s t m e n t . We assume t h a t k d e c r e a s e s l i n e a r l y w . r . t . t i m e and t h e r e f o r e E r i * k t i s a p a r a b o l i c f u n c t i o n o f e x p e r i e n c e (T) The p r e c e d i n g f u n c t i o n s u t i l i z e g r o s s e a r n i n g s as t h e dependent v a r i a b l e s . However, n e t o r o b s e r v e d e a r n i n g s a r e more r e a d i l y a v a i l a b l e and hence i f E_. = g r o s s e a r n i n g s , n e t e a r n i n g s o f Y_. = E_. (1 - k_.) . T a k i n g the l o g a r i t h m o f b o t h s i d e s , l n Y. = l n E. + l n (1 - k.) 3 3 3 E v a l u a t i n g l n ( l - k_.) by u s i n g a T a y l o r e x p a n s i o n around T* t a k e n t o the 3 r d term, l n (1 - k.) = -k (1 - k /2) + (k /T*) (1 - k ) T y o o o' o 2 2 2 + (-k /2T ) T o ' I n c o r p o r a t i n g t h e n e t e a r n i n g s r e l a t i o n and t h e l i n e a r d e c l i n e i n t h e e x p e r i e n c e term, e q u a t i o n (7) reduces t o : 1 I f k,. = k (1 - T./T*) f o r j > s + 1 , where T* i s t h e number t i o l J = o f y e a r s o f p o s i t i v e n e t p o s t s c h o o l i n v e s t m e n t , c o n v e r t i n g t o c o n t i n u o u s t i m e : _ / T i r . * k^.dT = r . * k T. - (r.*k„/2T*) T. 2 0 I t i l o l l 0 l (8) l n Y.. = { I n E - k (1 + k /2)} + r.S. +{r.* k 31 o o o 1 1 1 0 + k / T * ( l + k )} T. - { ( r . k T* + k 2 ) / 2 ( T * ) 2 } T. 2 o 0 1 1 0 o 1 + l n (Wi) + The r e s i d u a l u. r e f l e c t s i n d i v i d u a l d i f f e r e n c e s i n e a r n i n g s f o r 1 g i v e n l e v e l s o f s c h o o l i n g and age and employment. I t a l s o i n c l u d e s e f f e c t s o f d i s c r i m i n a t i o n , d i f f e r e n c e s i n n o n p e c u n i a r y a s p e c t s o f j o b s , n o n l a b o u r income ( i f t h i s i s i n c l u d e d i n t h e income c o n c e p t ) , and e r r o r s o f measurement. The assumption t h a t an i n d i v i d u a l i s c o n t i n u o u s l y a c q u i r i n g e x p e r i e n c e i n t h e l a b o u r market a f t e r l e a v i n g s c h o o l , means t h a t t h i s f o r m u l a t i o n o f t h e model i s more r e l e v a n t f o r a n a l y s i n g incomes o f males than incomes o f f e m a l e s . T h i s i s so because a number o f t h e l a t t e r group f r e q u e n t l y have l o n g p e r i o d s o f absence from t h e l a b o u r f o r c e . F i n a l l y , i t w i l l be assumed t h a t a c r o s s i n d i v i d u a l s t h e c o e f f i c i e n t s o f s c h o o l i n g and e x p e r i e n c e i n e q u a t i o n (8) a r e random v a r i a b l e s independent o f s c h o o l i n g (S) and e x p e r i e n c e ( T ) . There a r e t h e o r e t i c a l r e a s o n s t o s u p p o r t t h i s a s s u m p t i o n . U t i l i z i n g t he model f o r t h e s u p p l y and demand f o r funds f o r i n v e s t m e n t i n human c a p i t a l (developed by Bec k e r ( 1 9 6 7 ) ) , t h o s e w i t h h i g h e r m a r g i n a l r a t e s o f r e t u r n f o r a g i v e n l e v e l o f s c h o o l i n g ( w i t h w e a l t h h e l d c o n s t a n t ) , have a g r e a t e r i n c e n t i v e t o i n v e s t . I n t h i s c a s e , t h e r e i s a p o s i t i v e c o r r e l a t i o n between s c h o o l i n g l e v e l and r a t e o f r e t u r n . F o r a g i v e n l e v e l o f a b i l i t y , however, th o s e w i t h g r e a t e r w e a l t h have a lower d i s c o u n t r a t e and t h e r e f o r e i n v e s t more and r e c e i v e a lower r a t e 16 o f r e t u r n . T h i s i m p l i e s a . n e g a t i v e c o r r e l a t i o n between s c h o o l i n g and r a t e o f r e t u r n . Hence, t h e s i g n o f the c o r r e l a t i o n between t h e r e t u r n t o s c h o o l i n g r a t e t o an i n d i v i d u a l , and h i s s c h o o l i n g l e v e l , i s ambiguous. T h i s a m b i g u i t y has been e m p i r i c a l l y s u p p o r t e d by M i n c e r (1974), when he showed t h a t t h e r a t e o f r e t u r n from s c h o o l i n g i s u n c o r r e l a t e d w i t h t h e i n d i v i d u a l ' s l e v e l o f s c h o o l i n g ( h o l d i n g e x p e r i e n c e and weeks worked i n t h e y e a r , c o n s t a n t ) . W i t h t h e s e assumptions and m o d i f i c a t i o n s , e q u a t i o n (8) reduces t o : (9) I n Y. = x + r . S. + r ± ' T +6T2 + Y ( l n W±) + VK where: I n Y. = n a t u r a l l o g a r i t h m o f a n n u a l n e t 1 e a r n i n g s o f i n d i v i d u a l i x = c o n s t a n t i n t e r c e p t r . = r a t e o f r e t u r n t o s c h o o l i n g l = y e a r s o f s c h o o l i n g T = y e a r s o f l a b o u r market e x p e r i e n c e W_^  = weeks worked d u r i n g the y e a r u. = r e s i d u a l term assumed t o be a random v a r i a b l e Heckman and P o l a c h e k (19 74) p r e s e n t e d e m p i r i c a l e v i d e n c e on the c o r r e c t f u n c t i o n a l form o f the r e g r e s s i o n r e l a t i o n s h i p between e a r n i n g s as the r e g r e s s a n d and s c h o o l i n g and e x p e r i e n c e as t h e r e g r e s s o r s . They found t h a t among s i m p l e t r a n s f o r m a -t i o n s , t h e n a t u r a l l o g a r i t h m o f the dependent v a r i a b l e e x h i b i t e d the b e s t f i t , u s i n g the Box and T i d w e l l method. 17 They a l s o showed, somewhat l e s s c l e a r l y , t h a t t h e above s c h o o l i n g and e x p e r i e n c e model i s g e n e r a l l y p r e f e r a b l e t o o t h e r f o r m u l a t i o n s w i t h t h e o n l y p o t e n t i a l q u i b b l e s b e i n g on the use o f weeks worked r a t h e r t h a n t h e l o g a r i t h m o f weeks worked as t h e r e g r e s s o r . There i s a l s o some a m b i g u i t y a c r o s s t h e d a t a s e t s i n p r e f e r r i n g a l i n e a r and q u a d r a t i c e x p e r i e n c e v a r i a b l e t o t h e n a t u r a l l o g a r i t h m o f t h e e x p e r i e n c e term. 2.3 E v a l u a t i o n o f t h e E a r n i n g s F u n c t i o n T r e a t e d i n a s i n g l e r e g r e s s i o n c o n t e x t a c r o s s t h e p o p u l a t i o n s t u d i e d , e s t i m a t e d v a l u e s o f t h e r e g r e s s i o n c o e f f i c i e n t s a r e i n t e r p r e t e d as i n t e r p e r s o n a l averages i n t h e r e s i d u a l term. T h i s i s an i m p o r t a n t assumption o f t h e model, f o r i f we r e c o g n i z e t h a t d i f f e r e n c e s among pe r s o n s e x i s t , we a r e s a y i n g t h a t t h e e a r n i n g s f u n c t i o n i s n o t a s t r u c t u r a l r e l a t i o n , because i t i s m a r g i n a l v a l u e s t h a t d e t e r m i n e b e h a v i o r , n ot a v e r a g e s , and t h e f i t t e d f u n c t i o n o n l y summarizes o b s e r v e d e q u i l i b r i u m p o i n t s . A l s o t h e average r a t e of r e t u r n f o r each p e r s o n i s a f f e c t e d by h i s own a b i l i t y and f i n a n c i a l c o n s t r a i n t s , w h i c h i n t u r n a f f e c t i n v e s t m e n t . I n o t h e r words, b o t h r . and S. i n t h e above e q u a t i o n a r e not d i s -1 1 t r i b u t e d i n d e p e n d e n t l y , o f each o t h e r . C o n s e q u e n t l y , i s not d i s t r i b u t e d i n d e p e n d e n t l y o f t h e e r r o r term i n a c r o s s s e c -t i o n a l r e g r e s s i o n , b i a s i n g t h e e s t i m a t e o f t h e p o p u l a t i o n 18 average r a t e o f r e t u r n . ,Unbiased e s t i m a t e s o f t h e r a t e o f r e t u r n a r e o b t a i n e d when and y^ from e q u a t i o n (9) a r e u n c o r r e l a t e d , t h a t i s , when s c h o o l i n g and t h e o m i t t e d v a r i a b l e s a r e u n c o r r e l a t e d and t h e r e a r e no e r r o r s o f measurement. There i s e v i d e n c e t o b e l i e v e , however, t h a t o t h e r v a r i a b l e s whose e f f e c t s a r e impounded i n t h e r e s i d u a l , may be c o r r e l a t e d w i t h t h e s c h o o l i n g v a r i a b l e . A p e r s o n ' s i n v e s t m e n t s i n h e a l t h and m i g r a t i o n has been found t o be p o s i t i v e l y c o r r e l a t e d w i t h h i s l e v e l o f s c h o o l i n g (Grossman, 1972 and F e i n , 1965). T h i s i m p l i e s t h a t a p o s i t i v e c o r r e l a t i o n between s c h o o l i n g and t h e component o f t h e e r r o r term r e f l e c t i n g the r e t u r n from t h e s e i n v e s t m e n t s e x i s t s , s i n c e i t i s n o t l i k e l y t h a t t h e i r r a t e o f r e t u r n a r e s u f f i c i e n t l y n e g a t i v e l y c o r r e l a t e d w i t h the l e v e l o f s c h o o l i n g ( C h i s w i c k , 19 7 4 ) . We a l s o c o u l d e x p e c t t h a t f a m i l y w e a l t h may be p o s i t i v e l y c o r r e l a t e d w i t h s c h o o l i n g . A n o t h e r component i n t h e e r r o r term i s d i f f e r e n t i a l a b i l i t y . C h i s w i c k (1974) d i s c u s s e s t h i s r e s i d u a l component, as r e f l e c t e d i n d i f f e r e n c e s i n t h e r a t e o f r e t u r n from i n v e s t m e n t s i n s c h o o l i n g . Assuming t h a t y^ i n e q u a t i o n (9) i s e q u a l t o (d S. + y' .) where d = (r. - r ) i s t h e d i f f e r e n c e S I o / 1 S 3 _ between t h e r a t e o f r e t u r n r e c e i v e d by t h e i * " * 1 p e r s o n and t h e average r a t e o f r e t u r n r . S i n c e t h e e x p e c t e d v a l u e o f d g i s z e r o , S and d sS would be u n c o r r e l a t e d and t h e r e would be no b i a s from t h i s s o u r c e , i f S and d were independent of each o t h e r . " The b i a s o f t h e r a t e o f r e t u r n t o s c h o o l i n g when a b i l i t y i s o m i t t e d i n t h e e a r n i n g s f u n c t i o n has been the s u b j e c t o f many s t u d i e s . G i n t i s (1971), i n r e v i e w i n g n i n e d i f f e r e n t s t u d i e s found t h a t w i t h an a b i l i t y c o r r e c t i o n , t h e s c h o o l i n g c o e f f i c i e n t was reduced by 4% t o 35% (or an average o f 1 0 % ) . Hanuschek (1973) u s i n g an AFQT (Armed F o r c e s Q u a l i f i c a t i o n T est) s c o r e as an a b i l i t y measure f o r a sample o f U.S. Armed F o r c e s w o r k e r s , found an o v e r a l l r e d u c t i o n o f 14%, when t h i s t e s t s c o r e was i n c l u d e d i n t h e e a r n i n g s f u n c t i o n . I n a l m o s t a l l o f t h e s e s t u d i e s , d i r e c t measures o f a b i l i t y i n the e a r n i n g s f u n c t i o n i n d i c a t e d a r e l a t i v e l y s m a l l d i r e c t c o n t r i -b u t i o n o f t h e a b i l i t y v a r i a b l e t o t h e e x p l a n a t i o n o f e a r n i n g s . A t t h e same t i m e the r e d u c t i o n i n t h e s c h o o l i n g c o e f f i c i e n t (due t o an a b i l i t y c o r r e c t i o n ) was l i k e w i s e s m a l l . G r i l i c h e s (1977) however found t h a t i f s c h o o l i n g i s t e s t e d s y m m e t r i c a l l y w i t h a b i l i t y measures ( t h a t i s , a l l o w i n g s c h o o l i n g t o be s u b j e c t t o e r r o r s o f measurement and t o be c o r r e l a t e d t o t h e d i s t u r b a n c e i n t h e e a r n i n g s f u n c t i o n ) , the i m p l i e d n e t a b i l i t y C h i s w i c k (1974, p. 44) argues t h a t i t i s not s u f f i c i e n t f o r S and dS t o be u n c o r r e l a t e d - i . e . i f f . i s u n c o r r e l a t e d w i t h l S ±, Cov(d s,S) = 0 . We know t h a t E ( d g ) = 0. Then Cov(d g,S) = E {d (S - S)} = E ( d ,S) = 0. Thus, Cov(S, d S) = E{(S - S) s s s (d S)} = E ( d S 2) - S E (d S) = E ( d S 2 ) . Hence, Cov (S, d S) s s s s s 2 = 0 i f Cov ( d g S ) = 0, wh i c h n e c e s s a r i l y h o l d s when d g and S are independent. b i a s i s e i t h e r n i l o r n e g a t i v e , i n s t e a d o f p o s i t i v e . These r e s u l t s r a i s e t h e q u e s t i o n o f what a b i l i t y r e a l l y measures and what k i n d o f measurements would be d e s i r a b l e t o g e t c l o s e r t o a human c a p i t a l c o n c e p t . T h i s has l e d r e c e n t i n v e s t i g a t i o n t o abandon d i r e c t measurement o f a b i l i t y a l t o g e t h e r and adapt s t a t i s t i c a l methods s u i t a b l e f o r the purpose: unobserved v a r i a n c e components and f a c t o r a n a l y s i s ( G r i l i c h e s , 1974). Another problem w i t h s i m p l e l e a s t squares e s t i m a t e s o f e a r n i n g s f u n c t i o n s i s t h e case o f s i m u l t a n e o u s e q u a t i o n b i a s . Some o f the independent v a r i a b l e s may be p a r t o f a s i m u l t a n e o u s system o f e q u a t i o n s and a r e t h e r e f o r e endogeneous ( l i k e s c h o o l i n g and weeks worked). The amount o f time s p e n t w o r k i n g (W^) i s a d e c i s i o n made by t h e farm o p e r a t o r and as such, i s an endogeneous v a r i a b l e . One way t o overcome t h i s b i a s i s t o r e t a i n weeks worked as an e x p l a n a t o r y v a r i a b l e , b u t use a p r e d i c t e d v a l u e i n i t s p l a c e (two-stage l e a s t squares p r o c e d u r e w i t h weeks worked as an i n s t r u m e n t ) . S c h o o l i n g i s t h e r e s u l t , a t l e a s t i n p a r t o f the o p t i m i z i n g b e h a v i o u r by t h e i n d i v i d u a l s and t h e i r f a m i l i e s . T h i s b e h a v i o u r i s based on some a n t i c i p a t e d e a r n i n g s f u n c t i o n . The s e r i o u s n e s s o f t h e b i a s r e s u l t i n g from t h i s depends on how c l o s e i n d i v i d u a l s a r e t o p r e d i c t i n g t h e i r own f u t u r e and t o what e x t e n t t h e i r a c t i o n s c o u l d be i n t e r p r e t e d as o p t i m i -z i n g . The b i a s may not be so s e r i o u s because o f the e f f e c t o f u n a n t i c i p a t e d e v e n t s on e a r n i n g s and t h e i n f l u e n c e o f t h e f a m i l y background and s o c i o - e c o n o m i c f a c t o r s on the e d u c a t i o n a l l e v e l o f t h e i n d i v i d u a l . I n t h i s case o n l y a s m a l l p a r t o f 21 the school achievement can be a t t r i b u t e d to the i n d i v i d u a l 1 s own o p t i m i z i n g behaviour. In c r o s s s e c t i o n data, b i a s due to v i n t a g e e f f e c t s o ccurs because i n d i v i d u a l s w i t h d i f f e r e n t l e v e l s o f experience must a l s o , when observed a t a p o i n t of time, d i f f e r i n the date of en t r y i n t o the labour f o r c e . Due to accumulation of knowledge i t i s l i k e l y t h a t d i f f e r e n t o p p o r t u n i t i e s and thus investment d e c i s i o n s are a s s o c i a t e d w i t h i n d i v i d u a l s of d i f f e r e n t v i n t a g e s . A r e g r e s s i o n of the l o g of earnings on years o f s c h o o l i n g i n which a l l age groups are pooled, t h e r e -f o r e r e s u l t s i n a downward b i a s e d estimate of the slope c o e f f i c i e n t of s c h o o l i n g . The downward b i a s would not be f u l l y e l i m i n a t e d by r e s t r i c t i n g the r e g r e s s i o n to s p e c i f i e d age groups. For a giv e n age, an a d d i t i o n a l year o f s c h o o l i n g i m p l i e s one year l e s s o f experience. Since years o f s c h o o l i n g and experience are n e g a t i v e l y c o r r e l a t e d i n the c r o s s s e c t i o n , the omission o f experience from the earnings f u n c t i o n r e s u l t s i n a downward b i a s i n the s c h o o l i n g c o e f f i c i e n t . To summarize, i t appears t h a t wealth, m i g r a t i o n and h e a l t h are p o s i t i v e l y c o r r e l a t e d w i t h earnings (with s c h o o l i n g h e l d constant) and p o s i t i v e l y c o r r e l a t e d with s c h o o l i n g . Omission of these v a r i a b l e s t h e r e f o r e b i a s e s the estimate o f the r e t u r n to s c h o o l i n g upwards. The e f f e c t , however, of o m i t t i n g the a b i l i t y v a r i a b l e and e r r o r s o f measurement i s not c l e a r . In a c r o s s - s e c t i o n a l earnings f u n c t i o n , some simultaneous equation b i a s i s i m p l i e d because some of the independent v a r i a b l e s ( l i k e weeks worked and s c h o o l i n g l e v e l ) may be p a r t o f a s i m u l t a n e o u s system o f e q u a t i o n s . A two s t a g e l e a s t squares p r o c e d u r e c o u l d be used t o c o r r e c t f o r t h e e n d o g e n e i t y o f weeks worked. The b i a s a r i s i n g from the e n d o g e n e i t y o f t h e s c h o o l i n g l e v e l , however i s assumed n o t t o be so s e r i o u s because o f t h e l a r g e i n f l u e n c e o f o t h e r f a c t o r s ( f a m i l y back-> ground and s o c i o - e c o n o m i c v a r i a b l e s ) on the i n d i v i d u a l ' s s c h o o l i n g l e v e l . E m p i r i c a l l y , t h e r e i s no v a r i a b l e w h i c h would s t r i c t l y s a t i s f y a l l the r e q u i r e m e n t s imposed by t h e t h e o r y . No v a r i a b l e i s t r u l y exogenous, i s u n c o r r e l a t e d w i t h t h e r e s i d u a l s o f t h e e a r n i n g s , and i s n o t s u b j e c t t o any degree o f c h o i c e by t h e i n d i v i d u a l . T h i s i m p l i e s t h a t i n a c r o s s -s e c t i o n a l e a r n i n g s f u n c t i o n , one must be aware o f t h e b e n e f i t s and s h o r t c o m i n g s o f i n c l u d i n g each s e t o f v a r i a b l e s and keep t h e s e i n mind i n i n t e r p r e t i n g t h e r e s u l t i n g c o e f f i c i e n t s o f such an e q u a t i o n . 23 CHAPTER I I I APPLICATION OF THE MODEL TO  THE AGRICULTURAL SECTOR 3.1 M o d i f i e d E a r n i n g s F u n c t i o n f o r Farm O p e r a t o r s The e a r n i n g s f u n c t i o n , which i s based on a permanent income h y p o t h e s i s , i s n o t d i r e c t l y a p p l i c a b l e t o farm income. C r o s s - s e c t i o n a l d a t a on farm income c o n t a i n s many t r a n s i t o r y f a c t o r s p r o v i d i n g a wide d i v e r g e n c e from permanent income. An e a r n i n g s f u n c t i o n cannot a c c o u n t f o r t h i s due t o t h e unknown e x t e n t and d i s t r i b u t i o n o f t r a n s i t o r y f a c t o r s . I n p a r t i c u l a r , v a r i a t i o n i n weather c o n d i t i o n s has an i m p o r t a n t i n f l u e n c e on n e t self-employment income from f a r m i n g , and depending on the t i m i n g o f a p a r t i c u l a r census o r s u r v e y , t h e r e s u l t i n g d a t a f o r any r e g i o n o r farm may be h i g h l y u n r e p r e s e n t a t i v e o f t h e l o n g term s i t u a t i o n . Net farm income i s t h e r e t u r n t o u n p a i d f a m i l y ( i n c l u d i n g o p e r a t o r ) l a b o u r and farm-owned c a p i t a l . S i n c e t h e e a r n i n g s f u n c t i o n i s d e f i n e d f o r l a b o u r e a r n i n g s , we a r e i n t e r e s t e d i n the r e t u r n t o t h e o p e r a t o r s ' l a b o u r o r t h e shadow p r i c e o f h i s farm employment. T h i s i s n o t d i r e c t l y o b s e r v a b l e , because the r e t u r n t o owned c a p i t a l i s a l s o i n c l u d e d i n t h e r e p o r t e d farm income v a r i a b l e . An a d d i t i o n a l s o u r c e o f b i a s i s a p o s s i b l e u n d e r r e p o r t i n g due e i t h e r t o c a p i t a l r e i n v e s t m e n t d e c i s i o n s o r t o t a x - r e l a t e d m a t t e r s . I f we were t o i g n o r e the t r a n s i t o r y n a t u r e o f farm income, we c o u l d attempt t o e s t i m a t e an e a r n i n g s f u n c t i o n f o r farm income as l o n g as a c o r r e c t i o n c o u l d be made t o s e p a r a t e 24 the r e t u r n t o n o n - o p e r a t o r l a b o u r i n p u t s . By u s i n g net farm income as t h e " e a r n i n g s " v a r i a b l e and a d d i n g r i g h t - h a n d s i d e v a r i a b l e s t o a c c o u n t f o r o t h e r ( n o n - o p e r a t o r l a b o u r ) farm i n p u t s , we a r r i v e a t a type o f e a r n i n g s f u n c t i o n f o r e n t r e p r e n e u r s , s p e c i f i c a l l y , farm o p e r a t o r s . I n t h e f o r m u l a t i o n o f t h e e a r n i n g s f u n c t i o n i n Chapter I I (eq. 9) a l l t h e o t h e r f a c t o r s not p r e s e n t l y i n c l u d e d i n the model were a l l impounded i n t h e r e s i d u a l term y^. One o f t h e s e r e s i d u a l components i s n o n l a b o u r income ( i f i n c l u d e d i n the income c o n c e p t , as i n t h i s c a s e ) . F o r an e n t r e p r e n e u r t h e r e f o r e a b e t t e r s p e c i f i e d e a r n i n g s f u n c t i o n s h o u l d i n c l u d e f a c t o r s t o measure t h e e f f e c t o f t h e s e o m i t t e d n o n - o p e r a t o r l a b o u r f a c t o r s , on h i s income. S p e c i f i c a l l y , t h e s e f a c t o r s a r e farm c a p i t a l and u n p a i d f a m i l y l a b o u r i n the case o f farm o p e r a t o r s . E q u a t i o n (9) i s t h e r e f o r e m o d i f i e d a c c o r d i n g l y t o f i t t h e group under s t u d y , t h e e n t r e p r e n e u r s , s p e c i f i c a l l y , the farm o p e r a t o r s . (10) I n Y. = x + r i S i + r ± ' T + BT 2 + y ( I n W±) + a ( I n FC/i + oa (lnUFI^) + y where: I n Y. l n a t u r a l l o g o f farm e a r n i n g s o f farm o p e r a t o r i x c o n s t a n t term r . l r e t u r n t o s c h o o l i n g S . I y e a r s o f s c h o o l i n g T y e a r s o f e x p e r i e n c e 25 W. l = weeks worked d u r i n g t h e y e a r FC. 1 = farm c a p i t a l UFL. l = u n p a i d f a m i l y l a b o u r - r e s i d u a l term 3.2 D i g r e s s i o n : V a l u e Added Approach I t w i l l be noted t h a t i f s c h o o l i n g (S) were i n l o g i n s t e a d o f l i n e a r form and t h e e x p e r i e n c e term (T) were o m i t t e d from e q u a t i o n ( 1 0 ) , we have a s p e c i a l form o f v a l u e added f u n c t i o n o r p r o f i t f u n c t i o n . I n the s t u d y o f the c o n t r i b u t i o n of s c h o o l i n g t o farm income we c o u l d e i t h e r use t h e e a r n i n g s f u n c t i o n ( t r a n s f o r m e d t o f i t e n t r e p r e n e u r s as d i s c u s s e d above) o r a p r o d u c t i o n f u n c t i o n approach ( G i s s e r (1965), Huffman ( 1 9 7 4 ) ) . For c o m p a r a t i v e purposes and as a t e s t o f f u n c t i o n a l form, we w i l l d i s c u s s t h e v a l u e added f o r m u l a t i o n . I n e s t i m a t i n g r a t e s o f r e t u r n t o s c h o o l i n g u s i n g a p r o d u c t i o n f u n c t i o n framework, we need f i r s t o f a l l t o d i s c u s s how s c h o o l i n g a f f e c t s p r o d u c t i v i t y o r o u t p u t . T h i s q u e s t i o n o f how e d u c a t i o n i n f l u e n c e s p r o d u c t i v i t y has been the s u b j e c t o f many s t u d i e s . N e l s o n and P h e l p s (1966) s u g g e s t e d a way i n whic h e d u c a t i o n might a f f e c t p r o d u c t i v i t y and d i f f u s i o n o f t e c h n o l o g y , when they p o i n t e d t o t h e l i k e l i h o o d t h a t a t any g i v e n t i m e , t h e r e w i l l e x i s t a gap between the t e c h n o l o g y a v a i l a b l e and the t e c h n o l o g y a l r e a d y i n use. They suggested t h a t i f e d u c a t i o n changes t h e a b i l i t y o f an i n d i v i d u a l t o a d j u s t t o ch a n g i n g c o n d i t i o n s , t h e n the c o n t r i b u t i o n o f 26 e d u c a t i o n t o p r o d u c t i v i t y w i l l be r e l a t e d t o t h e r a t e o f t e c h n o l o g i c a l change and t o t h e s i z e o f the d i s c r e p a n c y between a c t u a l and optimum use o f i n p u t s . There a r e a number o f s t u d i e s f o c u s i n g on the i n f l u e n c e o f e d u c a t i o n on farm p r o d u c t i v i t y . G i s s e r (196 5) found t h a t a d d i t i o n a l s c h o o l i n g encouraged farm o u t m i g r a t i o n b u t a t t h e same time i n c r e a s e d t h e p r o d u c t i v i t y o f t h o s e who s t a y e d on the farms. Welch (19 70) worked w i t h t h e d e t e r m i n a n t s o f the p r o d u c t i v i t y (measured by wage r a t i o s ) o f more r e l a t i v e t o l e s s s c h o o l e d i n d i v i d u a l s i n t h e U.S. farm p o p u l a t i o n . Huffman (1974) f o c u s e d on a s i n g l e d i m e n s i o n o f a l l o c a t i v e e f f i c i e n c y : t h e adjustment o f f a r m e r s t o t h e change i n the optimum q u a n t i t y o f a s i n g l e i n p u t , n i t r o g e n f e r t i l i z e r i n c o r n p r o d u c t i o n . The r a t e o f adjustment t o d i s e q u i l i b r i u m i n n i t r o g e n usage was found t o be p o s i t i v e l y r e l a t e d t o the l e v e l o f e d u c a t i o n o f f a r m e r s , the a v a i l a b i l i t y o f i n f o r m a t i o n ( e x t e n s i o n ) and t h e s c a l e i n c e n t i v e t o be i n f o r m e d ( a c r e s o f corn) . 3.3 The P r o d u c t i v e V a l u e o f E d u c a t i o n The p a s t s t u d i e s s t r e s s e d t h e importance o f e d u c a t i o n as a f a c t o r o f p r o d u c t i o n and have been i n c l u d e d o f t e n as an adjustment f o r q u a l i t y o f l a b o u r . Welch d i s t i n g u i s h e d two d i s t i n c t c o n t r i b u t i o n s o f e d u c a t i o n on p r o d u c t i v i t y . The s t a r t i n g p o i n t o f h i s a n a l y s i s i s t o q u e s t i o n whether e d u c a t i o n ' s c o n t r i b u t i o n t o p r o d u c t i v i t y i s t o t a l l y d i r e c t i n n a t u r e . I t may be i n d i r e c t s i n c e p a r t o f i t s v a l u e c o u l d be 27 d e r i v e d from e f f e c t s on t h e use o f o t h e r i n p u t s . I f t h i s i s the c a s e , the m a r g i n a l p r o d u c t o f e d u c a t i o n s h o u l d be measured t o i n c l u d e such i n d i r e c t p r o d u c t i v i t y e f f e c t s . Welch d e s i g n a t e s the d i r e c t e f f e c t o f e d u c a t i o n on p r o d u c t i v i t y as t h e "worker e f f e c t " and t h e i n d i r e c t e f f e c t t h a t e d u c a t i o n has on p r o d u c t i v i t y o p e r a t i n g t h r o u g h t h e use o f o t h e r f a c t o r s o f p r o d u c t i o n , as the " a l l o c a t i v e e f f e c t " . A l l o c a t i v e s k i l l s r e f l e c t a c a p a b i l i t y t o economize under c o n d i t i o n s o f u n c e r t a i n and i m p e r f e c t knowledge o f b o t h t e c h n i c a l and economic parameters o f t h e p r o d u c t i o n p r o c e s s e s . The i s o l a t i o n o f t h e s e e f f e c t s can be seen, u s i n g t h e f o l l o w i n g v a l u e added p r o d u c t i o n f u n c t i o n ( t a k e n d i r e c t l y from Welch (1970) pp. 44-45) : Q = ( x x z x E x) + p 2 q 2 ( x 2 z 2 E 2) - P x X where: q ^ q 2 = two d i f f e r e n t p r o d u c t s p ^ P 2 = t h e p r i c e s o f t h e s e two p r o d u c t s X = p u r c h a s e d i n p u t s w i t h p r i c e p Z = o t h e r f a r m - s u p p l i e d i n p u t s E = e d u c a t i o n and where: E = + E 2 Z° = z 1 + z 2 x = x^ j^  + x 2 1 = dE 1/dE + dE 2/dE 0 = d z ^ d E + d z 2 / d E dX/dE = dx 1/dE + dx 2/dE 28 I f v a l u e added i s t a k e n as a f u n c t i o n o f t h e t o t a l q u a n t i t i e s o f e d u c a t i o n and s u p p l i e d i n p u t s , Q = f ( E , Z ^ ) , t h e m a r g i n a l p r o d u c t o f e d u c a t i o n i s ; 3f/3E = p 2 ( 3 q 2 3 E ) + { p ^ B q ^ E ) - P 2 ( 3 q 2 / 3 E ) } clE^/dE + { p 1 ( 3 q 1 / 3 z ) - ppq2/dz)} d z ^ d E + {Pj^id^/d^-) ~ P 2 ( 3 q 2 / 8 x ) } d x x d E + { P 2 ( 3 ( 3 2 ' / 9 x ) " P x> d x/dE. I n th e p r e c e d i n g e q u a t i o n , the f i r s t term i s t h e pure worker e f f e c t and t h e n e x t t h r e e terms r e f e r t o g a i n s from a l l o c a t i n g the r e s p e c t i v e f a c t o r s o f e d u c a t i o n , s u p p l i e d i n p u t s and p urchased i n p u t s e f f e c t i v e l y between competing u s e s . The l a s t term r e f e r s t o the a l l o c a t i v e g a i n from s e l e c t i n g t h e " r i g h t " q u a n t i t y o f p urchased i n p u t s . The c o n c e p t o f t h e v a l u e added f u n c t i o n i s s i m i l a r t o the v a r i a b l e p r o f i t f u n c t i o n s u g g e s t e d by Y o t o p o u l o s and Nugent (19 76) f o r t h e a n a l y s i s o f p r o d u c t i o n t o overcome the s i m u l t a n e o u s e q u a t i o n b i a s i n the p r o d u c t i o n f u n c t i o n . V a r i a b l e p r o f i t i s d e f i n e d as g r o s s r e t u r n s l e s s e x p e n d i t u r e on v a r i a b l e (purchased) i n p u t s and i s a f u n c t i o n o f owned i n p u t s (farm c a p i t a l and f a m i l y l a b o u r i n the case o f a g r i c u l t u r e ) . S i n c e we a r e i n t e r e s t e d i n measuring th e p r o d u c t i v i t y o f s c h o o l i n g , we would want t o h o l d c o n s t a n t as few r i g h t hand s i d e v a r i a b l e s as p o s s i b l e . T h i s w i l l a l l o w fewer c o n s t r a i n t s on t h e avenues by which s c h o o l i n g can o p e r a t e t o improve 29 p r o d u c t i v i t y . Use o f t h e v a l u e added f u n c t i o n no l o n g e r i n c l u d e s t h e l e v e l o f v a r i a b l e (purchased) i n p u t s on the r i g h t hand s i d e and hence the r e s u l t i n g r e t u r n s t o s c h o o l i n g i n c l u d e s t h e g a i n s from c h o o s i n g t h e optimum l e v e l s o f pu r c h a s e d i n p u t s and h i r e d l a b o u r . A n o t h e r way o f r e d u c i n g the number o f r i g h t hand s i d e v a r i a b l e s i s t o ag g r e g a t e i n p u t s and t h i s i s p o s s i b l e w i t h the c a p i t a l v a r i a b l e components. By u t i l i z i n g an a g g r e g a t e d c a p i t a l v a r i a b l e we a r e a l l o w i n g t h e s c h o o l i n g c o e f f i c i e n t t o p i c k up any r e t u r n s t o t h e farm o p e r a t o r from r e - a l l o c a t i n g among t h e s e c a p i t a l components. The m a r g i n a l p r o d u c t o f s c h o o l i n g s h o u l d r e f l e c t t h i s when th e c a p i t a l components a r e agg r e g a t e d i n t o one v a r i a b l e . I n t h e f o r m u l a t i o n o f the v a l u e added f u n c t i o n we a r e l e f t w i t h t h e q u a n t i t i e s o f "owned" i n p u t s ( f a m i l y l a b o u r and c a p i t a l ) as the d e t e r m i n a n t s o f v a l u e added o r v a r i a b l e p r o f i t . S i n c e t h e l e v e l o f v a l u e added i s dependent on the l d v e l o f purchased i n p u t s , p r o f i t m a x i m i z i n g b e h a v i o r i n the i n p u t market s u g g e s t s the importance o f t h e p r i c e s o f t h e v a r i a b l e i n p u t s t o t h e v a l u e added f u n c t i o n . I d e a l l y t h e v a l u e added f u n c t i o n s h o u l d be f o r m u l a t e d w i t h t h e f o l l o w i n g r i g h t hand s i d e v a r i a b l e s : s c h o o l i n g o f t h e farm o p e r a t o r , the q u a n t i t y o f farm f a m i l y l a b o u r , t h e q u a n t i t y o f c a p i t a l , t h e p r i c e o f purchased v a r i a b l e i n p u t s and t h e p r i c e o f h i r e d l a b o u r . The Cobb-Douglas form w i l l be used i n the v a l u e - a d d e d f u n c t i o n , because w i t h i t s s i m p l e f u n c t i o n a l form, i t y i e l d s s t a t i s t i c a l l y s i g n i f i c a n t e s t i m a t e s o f the c o e f f i c i e n t s w i t h o u t 30 i m p o s i n g e x c e s s i v e d a t a r e q u i r e m e n t s . Some p r o p e r t i e s o f the Cobb-Douglas f u n c t i o n a r e c o n s i s t e n t w i t h some a p r i o r i n o t i o n s o f economic t h e o r y , l i k e t h e p o s i t i v e b u t d e c l i n i n g m a r g i n a l p r o d u c t s , v a r i a b l e r e t u r n s t o s c a l e , the i n v e r s e r e l a t i o n between t h e m a r g i n a l r a t e o f s u b s t i t u t i o n and f a c t o r p r o p o r t i o n s . The p r o p e r t y which would seem u n r e a l i s t i c , however, i s the u n i t a r y e l a s t i c i t y o f s u b s t i t u t i o n among f a c t o r s , w h i c h becomes l i m i t i n g when t h e r e a r e more tha n two f a c t o r s o f p r o d u c t i o n , because the p r o p e r t y o f u n i t a r y e l a s t i c i t y o f s u b s t i t u t i o n must h o l d f o r each and e v e r y p a i r o f f a c t o r s . The problem o f a g g r e g a t i n g i n p u t s has been d i s c u s s e d by G r i l i c h e s (1957) who s t a t e d t h a t i n u s i n g the Cobb-Douglas framework, use o f g e o m e t r i c sums (summation o f the l o g v a l u e s o f t h e c a p i t a l f l o w components) i n s t e a d o f a r i t h m e t i c sum ( l o g a r i t h m o f t h e sum o f t h e c a p i t a l f l o w v a r i a b l e s ) i n aggre-g a t i n g i n p u t s w i l l m i n i m i z e b i a s . 31 CHAPTER IV METHODOLOGICAL MODELS AND  DATA CONSIDERATIONS 4.1 Data Sources I n the c o m p u t a t i o n o f b o t h the e a r n i n g s f u n c t i o n and t h e v a l u e added f u n c t i o n , we w i l l u t i l i z e t he 1971 A g r i c u l t u r e -P o p u l a t i o n L i n k a g e Data which i s the c o m p u t e r i z e d l i n k a g e o f the i n d e p e n d e n t l y enumerated 19 71 Census o f P o p u l a t i o n and Census o f A g r i c u l t u r e ( f o r a d e f i n i t i o n o f terms used, p l e a s e r e f e r t o Appendix B ) . The d a t a a l s o a l l o w s us t o u t i l i z e m i c r o - d a t a (9 0,000 i n d i v i d u a l farm r e c o r d s ) f o r b o t h the e a r n i n g s f u n c t i o n and t h e v a l u e added f u n c t i o n . We w i l l a l s o use census d i v i s i o n averages (24 2 census d i v i s i o n s f o r Canada) i n o r d e r t o c o r r e c t f o r the e n d o g e n e i t y o f one o f t h e v a r i a b l e s i n our e q u a t i o n (by u s i n g a two s t a g e l e a s t squares p r o c e d u r e , a s t a t i s t i c a l package n o t a v a i l a b l e a t the m i c r o l e v e l ) . The r e s u l t s a t t h e census d i v i s i o n l e v e l a r e a l s o i m p o r t a n t f o r comparison w i t h e a r l i e r r e s e a r c h . We have o b s e r v a t i o n s o n l y f o r one y e a r , 1970, and we cannot say t h a t i t was a " t y p i c a l " and normal y e a r f o r a g r i c u l t u r e , p a r t i c u l a r l y f o r wheat f a r m i n g . I t was the y e a r when wheat f a r m e r s , due t o a c c u m u l a t i o n o f u n s o l d s t o c k s o f wheat, were engaged i n a f e d e r a l scheme o f r e d u c t i o n o f wheat p l a n t i n g s by about 15% (22 m i l l i o n a c r e s ) . T h e i r t o t a l r e c e i p t s from wheat s a l e s t h a t y e a r was c o n s i d e r a b l y lower (38% l o w e r t h a n the 1961-71 average f o r Canada) t h a n o t h e r y e a r s ( r e f e r t o Appendix T a b l e C . l ) . Wheat fa r m e r s i n 1971 comprised 10% o f t h e t o t a l farm o p e r a t o r s and c o n t r i b u t e d 14% o f t o t a l farm c a s h r e c e i p t s from s a l e o f p r o d u c t s i n Canada. S i n c e t h i s s t u d y w i l l use c r o s s - s e c t i o n a l d a t a f o r a l l farms, r e g a r d l e s s o f farm commodity produced, t h e e f f e c t ( i f any) o f t h i s wheat acreage r e d u c t i o n and d r a m a t i c f a l l i n g r o s s r e c e i p t s i n our a n a l y s i s cannot be measured. 4 . 2 E a r n i n g s F u n c t i o n 4.2.1. Data Requirements The t h e o r e t i c a l model f o r the e a r n i n g s f u n c t i o n w i l l be u t i l i z e d f o r farm o p e r a t o r s and t h e r o l e o f s c h o o l i n g w i l l be a n a l y z e d . The model r e g r e s s e s l o g o f farm income on s c h o o l i n g 2 l e v e l ( S ) , e x p e r i e n c e ( T ) , (T ) , l o g o f days worked (DAYSON), l o g o f u n p a i d f a m i l y l a b o u r (UFL), and l o g o f farm c a p i t a l (FC) A d e s c r i p t i o n o f the d a t a a v a i l a b l e and t h e t r a n s f o r m a t i o n o f some v a r i a b l e s a r e d i s c u s s e d below: a. "Farm employment income" (FEI) There i s a r e a s o n t o b e l i e v e t h a t t h e r e i s some measure-ment e r r o r from some u n d e r r e p o r t i n g b i a s on t h e p r o c e s s o f c o l l e c t i n g t h e d a t a . The n e t farm income f i g u r e s were t a k e n from t h e income q u e s t i o n o f t h e P o p u l a t i o n Census ( r e f e r t o Appendix D f o r t h e a c t u a l q u e s t i o n ) o f the same y e a r , b u t not c o u n t e r c h e c k e d w i t h t h e o p e r a t o r s ' s a l e s and expenses f i g u r e s (both d e c l a r e d i n the A g r i c u l t u r e C e n s u s ) . I n the P o p u l a t i o n Census income q u e s t i o n , no s p e c i f i c i n s t r u c t i o n s were g i v e n to t h e farm o p e r a t o r , as t o what expenses t o c o n s i d e r and what d e p r e c i a t i o n r a t e t o use i n the c o m p u t a t i o n o f h i s n e t farm income ( d e f i n e d i n t h e q u e s t i o n n a i r e as v a l u e o f a g r i c u l t u r a l p r o d u c t s s o l d minus o p e r a t i n g expenses minus d e p r e c i a t i o n ) . Hence, u n l e s s t h e farmer r e f e r r e d t o h i s r e c o r d s (e.g. h i s t a x a b l e income r e p o r t e d i n A p r i l o f t h e same y e a r ; the census was t a k e n June 1) w h i c h may be u n d e r r e p o r t e d i n any c a s e , the d i f f e r e n c e between t h i s census measure and the " t r u e " n e t farm income v a l u e m i g h t be s u b s t a n t i a l . To t e s t t h i s p o s s i b l e b i a s from u n d e r r e p o r t i n g , the d e c l a r e d v a l u e s ( r e p o r t e d . f a r m income) were compared w i t h "computed" n e t farm income ( u s i n g the census d e f i n i t i o n above) t h a t i s p o s s i b l e from r e p o r t e d census d a t a . U s i n g a d e p r e c i a t i o n r a t e o f 15% o f t h e v a l u e o f machinery and e q u i p -ment ( a c c o r d i n g t o t h e Farmer's and Fisherman's Income Tax Guide (19 77) t h i s r a t e i s more o f an upper l i m i t , b u t used i n t h i s c a s e t o compensate f o r any c o s t u n d e r e s t i m a t i o n , i f our e x p e n d i t u r e d a t a i s i n c o m p l e t e ) comparison o f the d e c l a r e d and computed farm income f i g u r e s showed t h a t the d e c l a r e d v a l u e s were c o n s i d e r a b l y l o w e r t h a n the computed v a l u e s ( r e f e r t o Appendix T a b l e C.2). The farm o p e r a t o r may n o t d e l i b e r a t e l y u n d e r r e p o r t h i s income, but unknowingly o v e r s t a t e h i s o p e r a t i n g expenses ( i . e . c o v e r i n g l e g i t i m a t e o p e r a t i n g c o s t s and d e p r e c i a t i o n c o s t s as w e l l as c o s t s o f c a p i t a l d e e p e n i n g ) . T h i s f i n d i n g l e a d s us t o p r e f e r c o n s t r u c t i o n o f a n e t farm income v a r i a b l e from t h e census s a l e s and expenses d a t a , a measure t h a t i s l e s s s u b j e c t t o the measurement e r r o r s d i s c u s s e d above compared t o t h e d e c l a r e d farm income v a l u e s . 34 To d i s t i n g u i s h t h i s measure from t h e census ( d e c l a r e d ) n e t farm income v a l u e , we s h a l l c a l l i t n e t farm employment income ( F E I ) . b. S c h o o l i n g (S) Y e a r s o f s c h o o l i n g o f t h e farm o p e r a t o r (S) i s a v a i l a b l e from t h e l i n k a g e d a t a . The v a r i a b l e y e a r s o f s c h o o l i n g i s e q u i v a l e n t t o a c t u a l y e a r s spent i n s c h o o l , o r t h e h i g h e s t grade a t t a i n e d p l u s y e a r s s p e n t i n p o s t secondary s c h o o l ( i f a p p l i c a b l e ) . S i n c e t h e i n t e r e s t o f t h i s s t u d y i s t o measure the management a b i l i t y o f the farm o p e r a t o r v i a h i s e d u c a t i o n , and t h e a v a i l a b l e d a t a i s y e a r s spent i n s c h o o l , a n o t h e r measure, s c h o o l i n g u n i t (SU) w i l l be used t o r e p r e s e n t t h e " e d u c a t i o n " t h a t a farm o p e r a t o r p o s s e s s e s . The v a r i a b l e s c h o o l i n g u n i t (SU) was f o r m u l a t e d by Welch (1966) and r e p r e s e n t s t h e y e a r s o f s c h o o l i n g w e i g h t e d by average income. T h i s measure was a l s o u t i l i z e d by Huffman (1974) . c. E x p e r i e n c e (T) A c t u a l y e a r s s p e n t i n f a r m i n g ( e x p e r i e n c e ) i s not a v a i l a b l e from t h e Census d a t a . T h i s poses a problem e s p e c i a l l y because the farm o p e r a t o r may be engaged i n b o t h farm and non-farm a c t i v i t i e s , and farm e x p e r i e n c e i s l i k e l y t o be q u i t e d i f f e r e n t from non-farm e x p e r i e n c e . I n t h i s case we have the a l t e r n a t i v e o f c o n s i d e r i n g a p r o x y measure f o r t h e e x p e r i e n c e v a r i a b l e . By assuming t h a t the i n d i v i d u a l i n v e s t s i n e x p e r i e n c e each y e a r a f t e r l e a v i n g school., e x p e r i e n c e c o u l d be measured as age minus s c h o o l i n g y e a r s minus 5 (T = Age -S - 5 ) . T h i s d e f i n i t i o n f o r e x p e r i e n c e has a l s o been u t i l i z e d by C h i s w i c k 35 and Mincer (1972) and Mincer (1974). By the d e f i n i t i o n of the sample we are i n t e r e s t e d i n , we are, by v i r t u e of the experience v a r i a b l e a t t r i b u t i n g a l l the years spent a f t e r s c h o o l i n g , to work experience, r e g a r d l e s s o f whether i t was farm or non-farm work. We are i n e f f e c t , u s i n g a v a r i a b l e which i s not s p e c i f i e d p r o p e r l y , but we are l e f t w ith the c h o i c e of i n c l u d i n g i t , w i t h the knowledge of i t s l i m i t a t i o n s , or o m i t t i n g an experience v a r i a b l e a l t o g e t h e r . The b i a s r e s u l t i n g from e x c l u d i n g a measure of experience was d i s c u s s e d i n the preceding chapter. However, the assumption (t h a t an i n d i v i d u a l i s c o n t i n u -o u s l y engaged i n a c q u i r i n g experience i n the labour market a f t e r f i n i s h i n g school) made i n Chapter I I t h a t the model i s more r e l e v a n t to males than to females i s e s p e c i a l l y f i t t i n g f o r our sample because female farm o p e r a t o r s comprise o n l y 3% of the t o t a l sample. d. Days worked on Farm (DAYSON) The time spent working i s a v a i l a b l e i n days i n s t e a d of weeks worked, and i s on the o p e r a t o r ' s o f f farm employment. By assuming a f i x e d l e i s u r e demand of 6 5 days, or e q u i v a l e n t l y a f i x e d t o t a l work time of 6 days per week f o r 50 weeks i n a year, the number of days worked on the farm (DAYSON) i s p r o x i e d by (300 - DAYSOFF; where DAYSOFF i s the number of days worked o f f - f a r m ) . A s i m i l a r approximation f o r the labour days worked ( f a m i l y and hired) was u t i l i z e d by G r i l i c h e s (1964) . 36 e. Farm C a p i t a l (FC) For the c a p i t a l v a r i a b l e , we have stock v a l u e s of l a n d and b u i l d i n g s , the v a l u e of machinery and equipment, and the value of l i v e s t o c k . C a p i t a l i n p u t s are measured by s e r v i c e flow u n i t s , t h a t i s , by d e p r e c i a t i o n and i n t e r e s t computed as percentages of the value of v a r i o u s stocks of i n p u t s . The s e r v i c e flow of c a p i t a l stock v a l u e s are computed u s i n g a r e a l i n t e r e s t r a t e of 6%."^  On the b a s i s of assumed d e p r e c i a t i o n r a t e s , the s e r v i c e flow from machinery and equipment was computed a t 17% of i t s stock value and the s e r v i c e flow from l i v e s t o c k was c a l c u l a t e d as 10% of i t s stock v a l u e ( K h a l d i , 1975). The v a l u e of l a n d and b u i l d i n g s was converted i n t o a s e r v i c e flow v a r i a b l e , by computing 3% of i t s stock value ( r e f e r s t o a c o m p e t i t i v e r a t e of r e t u r n of 6% and 3% r a t e o f a p p r e c i a t i o n o f r e a l e s t a t e v a l u e s ) . I t i s r e c o g n i z e d however t h a t there are r e g i o n a l d i f f e r e n c e s i n the r a t e of a p p r e c i a -t i o n values but we do not have the data f o r each r e g i o n . Rather we are l i m i t e d to an average value c a l c u l a t e d f o r Canada. Hence we may be o v e r e s t i m a t i n g the l a n d i n p u t f o r farms n e a r e s t to urban areas and underestimating i t f o r those i n the r u r a l areas. To best capture the r e t u r n s to s c h o o l i n g we c o u l d aggregate the components of the farm c a p i t a l stock i n t o one c a p i t a l v a r i a b l e . A problem a r i s i n g from t h i s procedure i s t h a t i n r e s t r i c t i n g a l l the components of the c a p i t a l stock '''Jenkins, Glen, C a p i t a l i n Canada: I t s S o c i a l and P r i v a t e  Performance 1965-1974. D i s c u s s i o n Paper no. 98. Economic C o u n c i l of Canada. Ottawa. Oct. 1977. pp. 57-62. 37 to carry the same c o e f f i c i e n t , a misspecification of the model r e s u l t s . However, t h i s also allows the schooling c o e f f i c i e n t to pick up any returns to the operator from r e - a l l o c a t i n g among these c a p i t a l components. The return to schooling i s estimated holding constant the l e v e l of t o t a l c a p i t a l , allowing the c a p i t a l components to vary. Since agriculture i s a t e c h n i c a l l y dynamic industry, the new developments i n c a p i t a l inputs l i k e machinery and equipment could be expected to r e s u l t i n a considerable degree of disequilibrium i n these input markets. The c o e f f i c i e n t of schooling should r e f l e c t t h i s by being larger when the c a p i t a l components are aggre-gated to one variable. Use of geometric sums (summation of the log values of the c a p i t a l flow components) instead of arithmetic sums (logarithm of the sum of the c a p i t a l flow components) i n aggregating inputs w i l l minimize bias ( G r i l i c h e s , 1957) . f. Unpaid Family Labour (UFL) The Census data unfortunately does not have any d i r e c t measure of the time spent working on the farm by the unpaid family members. We are therefore l e f t with the alternative of using measures of p o t e n t i a l l y available farm labour, l i k e spouse's l e v e l of schooling (SSYOS) and number of children (NUMCH). However, a preliminary c o r r e l a t i o n analysis (at the census d i v i s i o n level) showed a high degree of c o r r e l a t i o n between operator's l e v e l of schooling and the spouse's l e v e l of schooling (SSYOS). Since we are b a s i c a l l y interested i n 38 a measure of unpaid f a m i l y labour we are then l e f t w i t h the proxy v a r i a b l e , number of c h i l d r e n (NUMCH). L i m i t i n g the proxy v a r i a b l e f o r unpaid f a m i l y labour to one v a r i a b l e a l s o reduces the number o f r i g h t - h a n d - s i d e determinants i n the equation. Another p o i n t to c o n s i d e r i s the q u e s t i o n of the r e l e v a n t s e c t o r of the farm p o p u l a t i o n to analyze. S t a t i s t i c s Canada's d e f i n i t i o n o f a census farm i s an a g r i c u l t u r a l h o l d i n g o f a t l e a s t an a c r e , and s a l e s of $50 or more d u r i n g the preceding 12 months. The r e s u l t i n g p o p u l a t i o n of farm o p e r a t o r s then i n c l u d e d both the f u l l - t i m e or commercial farmers and those who are simply backyard gardeners. Since t h i s study i s i n t e r e s t e d i n the c o n t r i b u t i o n of s c h o o l i n g to farm income, we w i l l focus our a t t e n t i o n to the sample who are engaged i n farming on a f u l l - t i m e b a s i s . E x c l u s i o n of hobby farmers (e.g. backyard gardeners) i s p r e f e r r a b l e and one way to do t h i s i s to c o n s i d e r the sample of farm o p e r a t o r s w i t h s a l e s of a t l e a s t $2500. In a d d i t i o n to t h i s , s e p a r a t i o n of f u l l - t i m e farmers from the hobby farmers c o u l d be done by u s i n g the "occupation s t a t e d " (during census week) c r i t e r i a ( i . e . "farmer" and "other than f a r m e r " ) . Another method i s to segregate farm o p e r a t o r s by days worked o f f - f a r m (DAYSOFF) wi t h the assump-t i o n t h a t those who spend l e s s time working o f f - f a r m (and con-sequently spend more time i n farming), are the more f u l l - t i m e , commercial farmers. There are many f a c t o r s l e f t out i n our model, l i k e a b i l i t y and school q u a l i t y , f o r example, to make i t a s a t i s f a c t o r y 39 micro-data model. I t i s n o t un r e a s o n a b l e t o assume t h a t as a f i r s t a p p r o x i m a t i o n many o f t h e f a c t o r s wash o u t w i t h a g g r e g a t i o n . G r o u p i n g o f fa r m e r s a c c o r d i n g t o o c c u p a t i o n o r days worked, f o r example i s o l a t e s any d i f f e r e n c e between them. W i t h i n group v a r i a n c e o f c o e f f i c i e n t s i s nonzero b u t may be e x p e c t e d t o be s m a l l e r t h a n the v a r i a n c e o f the whole p o p u l a -t i o n . 4.2.2. E m p i r i c a l Model Based on the d a t a r e q u i r e m e n t s o f t h e t h e o r e t i c a l model, the d a t a a v a i l a b l e and d a t a t r a n s f o r m a t i o n s needed, we come up w i t h a w o r k i n g e q u a t i o n f o r t h e commercial farm o p e r a t o r s (those w i t h s a l e s o f a t l e a s t $2500) u s i n g i n d i v i d u a l farm o p e r a t o r s as t h e u n i t o f o b s e r v a t i o n : (10) l n FEI = a + b S + c T + d ( T ) 2 + e l n DAYSON + f l n FC + g InNUMCH where: l n FEI S T l n DAYSON l n FC = n a t u r a l l o g o f farm employment income ( S a l e s - VIN - HLP - f u e l and o i l expenses -r e n t p a i d ) ; VIN = c o s t o f p u r c h a s e d c h e m i c a l s , f e e d , f e r t i l i z e r s and custom machine r e n t a l ; HLP = c o s t o f h i r e d l a b o u r = y e a r s o f s c h o o l i n g o f. farm o p e r a t o r = y e a r s o f e x p e r i e n c e (T = Age - S - 5) = n a t u r a l l o g o f days worked on farm (DAYSON = 300 - DAYSOFF); where DAYSOFF = number o f days worked o f f farm = n a t u r a l l o g o f t h e aggr e g a t e d f l o w o f c a p i t a l s e r v i c e s ( l o g (3% VLB) + l o g (10% VL) + l o g (17% VME)) where VLB = v a l u e o f l a n d and b u i l d i n g s ; VL = v a l u e o f l i v e s t o c k ; and VME = v a l u e o f machinery and equipment 40 I n NUMCH = n a t u r a l l o g o f t h e number o f c h i l d r e n , aged 13-18. In o r d e r t o s e p a r a t e t h e commercial f a r m e r s from the r e s t o f the p o p u l a t i o n , s e p a r a t e r e g r e s s i o n runs o f e q u a t i o n (10) s h o u l d be done ( i n a d d i t i o n t o t h e s a l e s r e s t r i c t i o n c r i t e r i a ) f o r t h e f o l l o w i n g d a t a s e t s : 1. o c c u p a t i o n c r i t e r i a ; f o r c o m p a r a t i v e purposes e a r n i n g s f u n c t i o n w i l l be computed s e p a r a t e l y f o r : a. a l l farm o p e r a t o r s b. farm o p e r a t o r s who s t a t e d t h e i r o c c u p a t i o n 0 ( d u r i n g census week) as "farmer" o r "farm manager" c. farm o p e r a t o r s who s t a t e d t h e i r o c c u p a t i o n ( d u r i n g census week) as " o t h e r t h a n farmer o r farm manager" 2. days worked o f f - f a r m (DAYSOFF) c r i t e r i a ; f o r c o m p a r a t i v e purposes e a r n i n g s f u n c t i o n w i l l be computed s e p a r a t e l y f o r : a. farm o p e r a t o r s who do not work o f f the farm (DAYSOFF = 0 ) ; t h i s i m p l i e s t h a t farm o p e r a t o r works f u l l t i m e on h i s farm and c o u l d be c o n s i d e r e d as a commercial f a r m e r . b. farm o p e r a t o r s who work o f f the farm, b u t not more th a n 50 days (1< DAYSOFF< 50) c. farm o p e r a t o r s who work o f f the farm a t l e a s t 150 days (DAYSOFF >149) . 41 4.3 V a l u e Added F u n c t i o n 4.3.1. Data Requirements I n t h e f o r m u l a t i o n o f the v a l u e added f u n c t i o n d i s c u s s e d i n the p r e v i o u s c h a p t e r , v a l u e added i s r e g r e s s e d on owned i n p u t s , p r i c e o f p u r c h a s e d i n p u t s and p r i c e o f h i r e d l a b o u r . The d e f i n i t i o n o f v a l u e added i n t h i s case i s s i m i l a r t o our d e f i n i t i o n o f farm employment income (FEI) i n our e a r n i n g s f u n c t i o n . Owned i n p u t s namely, t h e s c h o o l i n g l e v e l o f the farm o p e r a t o r , q u a n t i t y o f f a m i l y l a b o u r and amount o f farm c a p i t a l a r e t h e same v a r i a b l e s a p p e a r i n g i n the r i g h t hand s i d e o f t h e t r a n s f o r m e d e a r n i n g s f u n c t i o n f o r e n t r e p r e n e u r s ( e q u a t i o n 1 0 ) . The e x p e r i e n c e (T) term however w i l l n o t be i n c l u d e d i n t h e v a l u e added f o r m u l a t i o n . A l t h o u g h e x p e r i e n c e c o u l d be c o n s i d e r e d an "owned" i n p u t o r a l a b o u r q u a l i t y i n d e x , t h e a v a i l a b l e measure f o r i t i s n o t a good p r o x y v a r i a b l e . U n f o r t u n a t e l y even i f we have a r i c h d a t a s o u r c e , no d a t a i s a v a i l a b l e f o r p r i c e o f p u r c h a s e d i n p u t s . Our v a l u e added f u n c t i o n t h e r e f o r e t a k e s a form s i m i l a r t o t h e w o r k i n g e q u a t i o n f o r t h e e a r n i n g s f u n c t i o n , w i t h e x p e r i e n c e e x c l u d e d and a l l v a r i a b l e s i n l o g s because we a r e u s i n g the Cobb-Douglas form. 4.3.2. E m p i r i c a l Model Wi t h t h e d a t a c o n s i d e r a t i o n s d i s c u s s e d i n the p r e c e d i n g s e c t i o n t h e w o r k i n g e q u a t i o n f o r the v a l u e added f u n c t i o n i s as f o l l o w s : 42 (11) I n VA = a + b I n S + c I n DAYSON + d I n FC + e I n NUMCH where: I n VA I n S In DAYSON I n FC I n NUMCH = n a t u r a l l o g o f v a l u e added ( S a l e s - VIN -HLP - f u e l & o i l expenses - r e n t p a i d ) ; VIN = c o s t o f purchased c h e m i c a l s , f e e d , f e r t i l i z e r s and custom machine r e n t a l ; HLP = c o s t o f h i r e d l a b o u r . = n a t u r a l l o g o f s c h o o l i n g o f farm o p e r a t o r . = n a t u r a l l o g o f days.worked on farm (DAYSON^ 300 - DAYSOFF) where DAYSOFF = number o f days worked o f f - f a r m . = n a t u r a l l o g o f the agg r e g a t e d f l o w o f c a p i t a l s e r v i c e s <log (3% VLB) + l o g (10% VL) + l o g (17% VME)) where VLB = v a l u e o f l a n d and b u i l d i n g s ; VL = v a l u e o f l i v e s t o c k ; and VME = v a l u e o f machinery and equipment. = n a t u r a l l o g o f t h e number o f c h i l d r e n , aged 13-18. I t w i l l be no t e d t h a t t h e d e f i n i t i o n o f v a l u e added i s i d e n t i c a l t o how we d e f i n e d farm employment income (FEI) i n e q u a t i o n ( 1 0 ) . T h i s i s done f o r ease o f comparison o f t h e r e s u l t s o f t h e two e q u a t i o n s i n the n e x t c h a p t e r . S i n c e we a r e i n t e r e s t e d i n measuring the p r o d u c t i v i t y o f s c h o o l i n g we s h a l l a g a i n f o c u s on the f u l l - t i m e f a r m e r , u s i n g t h e s a l e s r e s t r i c t i o n ( S a l e s o f a t l e a s t $2500). We d i s c u s s e d e a r l i e r t h e r a t i o n a l e f o r a g g r e g a t i n g the c a p i t a l components i n t o one v a r i a b l e and we s h a l l t r y t o prove t h i s e m p i r i c a l l y by m o d i f y i n g e q u a t i o n ( 1 1 ) . We s h a l l compute, f o r t h e same sample a v a l u e added f u n c t i o n w i t h the t h r e e c a p i t a l v a r i a b l e components e n t e r i n g t h e e q u a t i o n as s e p a r a t e v a r i a b l e s : (11a) l n VA = a + b l n S + c l n DAYSON + d l n FLB + e l n FL + f l n FME + g l n NUMCH where a l l the v a r i a b l e s a r e d e f i n e d as i n e q u a t i o n (11) w i t h the a d d i t i o n o f : l n FLB = l o g (3% VLB) where VLB = v a l u e o f l a n d and b u i l d i n g s l n FL = l o g (10% VL) where VL = v a l u e o f l i v e s t o c k l n FME = l o g (17% VME) where VME = v a l u e o f machinery and equipment R e s u l t s o f e q u a t i o n (11a) w i l l be compared w i t h t h o s e o f e q u a t i o n (11) f o r t h e same sample o f farm o p e r a t o r s . We e x p e c t t h a t the r e t u r n s t o s c h o o l i n g from e q u a t i o n (11) w i l l be h i g h e r r e l a t i v e t o t h e c o r r e s p o n d i n g measure from e q u a t i o n ( 1 1 a ) . T h i s i s because t h e s c h o o l i n g c o e f f i c i e n t i n e q u a t i o n (11) p i c k s up t h e g a i n s from r e - a l l o c a t i n g among t h e t h r e e components o f c a p i t a l ( v a l u e o f l a n d and b u i l d i n g s ; v a l u e o f l i v e s t o c k and v a l u e o f machinery and equipment) w i t h i n the aggregate measure o f farm c a p i t a l ( l n F C ) . Another method we c o u l d use t o show the a l l o c a t i v e g a i n s p i c k e d up by t h e s c h o o l i n g v a r i a b l e v i a i n p u t s p e c i f i c a t i o n , i s t o compare e q u a t i o n (11) w i t h an e q u a t i o n where h i r e d l a b o u r c o s t i s a d e t e r m i n a n t o f v a l u e added and appears on the r i g h t hand s i d e o f t h e e q u a t i o n : ( l i b ) l n VA1 = a + b l n S + c l n DAYSON + d l n FC + e l n NUMCH + f l n HLP where t h e dependent v a r i a b l e , as a r e s u l t o f t h e l a b o u r c o s t i n p u t a p p e a r i n g on t h e r i g h t hand s i d e , i s r e d e f i n e d a s : I n VA1 = n a t u r a l l o g o f V A l where V A l = ( S a l e s - VIN -f u e l and o i l expenses - r e n t p a i d ) ; and VIN = c o s t o f purchased c h e m i c a l s , f e e d , f e r t i l i z e r s and custom machine r e n t a l . and where a l l t h e v a r i a b l e s a r e d e f i n e d as i n e q u a t i o n (11) w i t h t h e a d d i t i o n o f : I n HLP = n a t u r a l l o g o f h i r e d l a b o u r c o s t (HLP) The V A l f o r m u l a t i o n measures the e f f e c t o f s c h o o l i n g , g i v e n the l e v e l o f h i r e d l a b o u r e x p e n d i t u r e . The s c h o o l i n g c o e f f i c i e n t i s e x p e c t e d t o be lo w e r (compared t o the s c h o o l i n g c o e f f i c i e n t i n e q u a t i o n (11)) because i t e x c l u d e s t h e g a i n s from c h o o s i n g t h e optimum l e v e l o f h i r e d l a b o u r . A l l t he above f o r m u l a t i o n s have the i m p l i c i t a s s u m p t i o n t h a t l a b o u r (measured by days worked) i s homogeneous t h r o u g h o u t th e p o p u l a t i o n . One farmer o p e r a t o r ' s l a b o u r i n p u t i s assumed to be as p r o d u c t i v e as h i s n e i g h b o r ' s l a b o u r i n p u t . Labour q u a l i t y i n t h i s c a s e i s measured by human c a p i t a l i n v e s t m e n t i n t h e form o f s c h o o l a t t a i n m e n t o f t h e farm o p e r a t o r , s c h o o l -i n g b e i n g t r e a t e d as a s e p a r a t e i n p u t o f p r o d u c t i o n . A n o t h e r method t o i n c o r p o r a t e l a b o u r q u a l i t y i n the v a l u e added f u n c t i o n i s t o use i t as a w e i g h t i n g f a c t o r f o r the l a b o u r i n p u t - t h a t i s , t o c o n s i d e r a s c h o o l i n g - l a b o u r p r o d u c t as the l a b o u r i n p u t ( c o r r e c t e d f o r l a b o u r q u a l i t y i n t h i s c a s e ) . T h i s p r o c e d u r e ( a l s o t e s t e d by G r i l i c h e s ( 1 9 6 4 ) ) , c o u l d be t e s t e d by r e d e f i n i n g o ur l a b o u r i n p u t as ( S c h o o l i n g x DAYSON) o r SDAYS (11c) I n VA = a + b I n SDAYS + c I n FC + d I n NUMCH R e s u l t s o f e q u a t i o n (11c) w i l l be compared t o thos e o f e q u a t i o n (11) t o see i f t h i s f o r m u l a t i o n i s a b e t t e r f o r m u l a t i o n o f t h e v a l u e added f u n c t i o n . F o r c o m p a r a t i v e p u r p o s e s , e q u a t i o n (11c) w i l l a l s o be r u n u t i l i z i n g census d i v i s i o n averages and t h e r e s u l t s compared w i t h G r i l i c h e s (19 64) work which was based on aggregate d a t a ( s t a t e a v e r a g e s ) . 4.4 Census D i v i s i o n I n o r d e r t o c o r r e c t f o r the e n d o g e n e i t y o f the v a r i a b l e weeks worked, a two-stage l e a s t squares p r o c e d u r e w i l l be used w i t h weeks worked as an i n s t r u m e n t . I n o t h e r words, weeks worked (or i n t h i s p a r t i c u l a r p o p u l a t i o n , days worked) w i l l be r e g r e s s e d on a number o f v a r i a b l e s and t h e r e s u l t i n g p r e d i c t e d v a l u e o f days worked w i l l i n t u r n be u t i l i z e d i n the e a r n i n g s f u n c t i o n . U n f o r t u n a t e l y , t h i s method i s not f e a s i b l e w i t h t h e m i c r o d a t a because the e x i s t i n g S t a t i s t i c s Canada r e g r e s s i o n packages do n o t p e r m i t such two-step procedures. We can, however, use t h e census d i v i s i o n averages and p r o c e e d t o c o r r e c t f o r t h e e n d o g e n e i t y o f days worked. We w i l l do t h i s u s i n g t h e f o l l o w i n g e q u a t i o n s : (10a) l n FEI = a + b S + c T + d ( T ) 2 + e l n DAYSON* + f l n FC + g l n NUMCH where a l l t h e v a r i a b l e s a r e d e f i n e d as i n e q u a t i o n (10) u s i n g DAYSON* i n s t e a d o f DAYSON, and where DAYSON* = (300 - DAYSOFF*) w i t h DAYSON* d e f i n e d a s : DAYSOFF* = a + b S + c F C + d NUMCH + e WWAGE + f UER + g URBY + h DUER + i DURBY 46 where DAYSOFF* i s t h e p r e d i c t e d v a l u e o f days worked o f f farm r e g r e s s e d on v a r i a b l e s most o f which were d e f i n e d b e f o r e w i t h the a d d i t i o n o f : WWAGE = p r o x y measure f o r h i r e d l a b o u r (weekly wage r a t e ) . UER = unemployment r a t e f o r males aged 24-44 y e a r s , w i t h s c h o o l i n g l e v e l n ot g r e a t e r t h a n h i g h s c h o o l g r a d u a t i o n and g r e a t e r t h a n o r e q u a l t o grade 8. URBY = average l a b o u r e a r n i n g s f o r males aged 24-44 y e a r s , w i t h s c h o o l i n g l e v e l n ot g r e a t e r t h a n h i g h s c h o o l g r a d u a t i o n and g r e a t e r t h a n o r e q u a l t o grade 8 ( v a l u e s f o r 65 c i t i e s u t i l i z e d , w i t h t h e v a l u e o f urban e a r n i n g s o f t h e n e a r e s t c i t y chosen f o r a p a r t i c u l a r census d i v i s i o n ) . DUER = UER x DCITY where DCITY i s t h e d i s t a n c e from t h e n e a r e s t c i t y . DURBY = URBY x DCITY. A l l o f t h e above v a r i a b l e s a r e assumed t o a f f e c t t h e amount o f time a farm o p e r a t o r spends w o r k i n g o f f - f a r m . The l a s t two v a r i a b l e s (DUER and DURBY) were added t o c o r r e c t f o r t h e degree o f u r b a n i z a t i o n o f t h e census d i v i s i o n concerned w h i c h may i n f l u e n c e t h e demand f o r t h e o f f - f a r m l a b o u r o f farm o p e r a t o r s . We e x p e c t t h e r e g r e s s i o n c o e f f i c i e n t s t o d i f f e r , u s i n g t h e two d a t a s e t s (micro d a t a v s . census d i v i s i o n averages) because o f the d i f f e r e n c e i n t h e l e v e l o f a g g r e g a t i o n . U s i n g census d i v i s i o n a v e r a g e s , we a l l o w s c h o o l i n g t o c a p t u r e the g a i n s from a l l o c a t i n g r e s o u r c e s between competing uses and i t i s c l e a r t h a t a g r i c u l t u r e a t t h e census d i v i s i o n l e v e l i s much more d i v e r s i f i e d t h a n a t t h e m i c r o o r i n d i v i d u a l farm l e v e l , v i a the commodities produced. Hence the census d i v i s i o n a g g r e g a t i o n a l l o w s more room f o r a l l o c a t i v e a b i l i t y t h a n the m i c r o l e v e l , a n d t h e s c h o o l i n g c o e f f i c i e n t s h o u l d c a p t u r e t h i s by b e i n g l a r g e r . 48 CHAPTER V RESULTS AND DISCUSSION 5.1 M i c r o d a t a l e v e l 5.1.1. E a r n i n g s f u n c t i o n We w i l l d i s c u s s t h e r e s u l t s o f the m o d i f i e d e a r n i n g s f u n c t i o n u s i n g m i c r o d a t a , f o r t h e farm o p e r a t o r s . T a b l e 1 shows the r e g r e s s i o n e s t i m a t e s 1 o f the m o d i f i e d e a r n i n g s f u n c t i o n f o r a l l farm o p e r a t o r s ( d a t a s e t A ) . The r a t e o f 2 r e t u r n t o s c h o o l i n g i s p o s i t i v e and s i g n i f i c a n t , w i t h a m a r g i n a l p r o d u c t o f $132. We c o u l d t e s t t h e t y p e o f farm p o p u l a t i o n w i t h r e s p e c t t o f u l l t i me f a r m i n g by u s i n g an " o c c u p a t i o n s t a t e d " ( d u r i n g census week) c r i t e r i a . The "farmer and farm manager" group (data s e t B) shows the h i g h e s t r a t e o f r e t u r n t o s c h o o l i n g and t h e c o r r e s p o n d i n g m a r g i n a l p r o d u c t o f s c h o o l i n g (MP g = r a t e o f r e t u r n t o s c h o o l i n g x average e a r n i n g s (FEI)) i s $173 (vs. $132 f o r a l l farms and $50 f o r t h e " o t h e r t h a n f a r m e r " group ( C ) ) . I n o t h e r words the r e t u r n s t o s c h o o l i n g i n farm p r o d u c t i o n i n c r e a s e s as t h e i n d i v i d u a l s p e c i a l i z e s i n f a r m i n g o r i s engaged i n i t on a f u l l - t i m e b a s i s . The c o r r e s p o n d i n g average farm employment income 3 f i g u r e s a l s o f o l l o w t h i s p a t t e r n . 1 2 the squared e x p e r i e n c e term (T ) was dropped from e s t i m a t i n g e q u a t i o n (10) because o f m u l t i c o l l i n e a r i t y problems (between T and T 2) i n v a l i d a t i n g t h e r e s u l t i n g c o e f f i c i e n t s . 2 use o f s c h o o l i n g u n i t s (SU) i n s t e a d o f s c h o o l i n g y e a r s (S) i n b o t h the e a r n i n g s f u n c t i o n and v a l u e added f u n c t i o n d i d not e x h i b i t any s i g n i f i c a n t d i f f e r e n c e i n t h e r e s u l t i n g r e g r e s s i o n c o e f f i c i e n t s . 3$6470, $7229 and $4379 f o r a l l farms ( A ) , farmer and farm managers (B) and the non-farmer group ( C ) , r e s p e c t i v e l y . 49 T a b l e 1. R e g r e s s i o n e s t i m a t e s o f the m o d i f i e d e a r n i n g s f u n c t i o n f o r farm o p e r a t o r s w i t h S a l e s o f a t l e a s t $2500, farm employment income (FEI)>0, and days worked on farm (DAYSON)>1.0 by o c c u p a t i o n s t a t e d . Canada. 1971. Data S et A l l Farm O p e r a t o r s Farmers and Other t h a n (A) Farm Managers (B) (B) Sample s i z e 88 ,472 68,709 19,763 S .020 .023 .011 (36.46) (37.45) (10.04) T -.002 -.002 -.004 (14 .34) (16.04) (1.64) I n DAYSON .166 .123 .100 (43.64) (16 .83) (18.89) l n FC .112 .113 .085 (119.05) (105.41) (42.53) I n NUMCH .031 .043 -.012 (15.45) (20.09) (2.58) -2 R .20 .21 .11 Reg. F 4490 3609 481 MP >> $132 $173 $50 Data Source: A g r i c u l t u r e - P o p u l a t i o n L i n k a g e Data. 1971. U n p u b l i s h e d . S t a t i s t i c s Canada. r e g r e s s i o n c o e f f i c i e n t ( t - s t a t i s t i c ) k-MP = m a r g i n a l p r o d u c t o f s c h o o l i n g 50 The c o e f f i c i e n t o f farm c a p i t a l (FC) i s h i g h l y s i g n i f i c a n t f o r a l l d a t a s e t s and i s h i g h e s t f o r t h e f u l l - t i m e f a r m e r s ( B ) . F o r t h e days worked (DAYSON), and u n p a i d f a m i l y l a b o u r v a r i a b l e (NUMCH), the c o r r e s p o n d i n g c o e f f i c i e n t s f o r the farmer group (B) a r e c o n s i s t e n t l y h i g h e r t h a n the o t h e r than farmer group, group ( C ) , i m p l y i n g t h a t the f u n c t i o n i s -2 b e t t e r f i t t e d (as t h e R a l s o i n d i c a t e s ) and b e t t e r s p e c i f i e d f o r t h e group o f farm o p e r a t o r s who a r e more s e r i o u s l y engaged i n f a r m i n g t h a n t h o s e who a r e n o t . A n o t h e r means o f i l l u s t r a t i n g t h i s p a t t e r n i t t o use t h e days worked c r i t e r i a t o s e p a r a t e d i f f e r e n t f a rm o p e r a t o r s and compare th e r e s u l t i n g c o e f f i c i e n t s . U s i n g e q u a t i o n ( 1 0 ) , T a b l e (2) shows the r e s u l t s by c o n s i d e r i n g t h r e e groups and t h e more s p e c i a l i z e d commercial farmers a r e r e p r e s e n t e d by those who worked f u l l - t i m e on t h e i r farms, o r d i d not work o f f - f a r m (DAYSOFF = 0 ) . The r e s u l t i n g m a r g i n a l p r o d u c t o f s c h o o l i n g i s a g a i n h i g h e s t f o r the f u l l - t i m e commercial f a r m e r s ($166 v s . $154 and $24 f o r t h o s e who worked (1-50) days and t h o s e who worked a t l e a s t 150 days o f f the farm, r e s p e c t i v e l y ) . As the r e s u l t s o f e q u a t i o n s i n T a b l e s 1 and 2 show, g r o u p i n g o f farm o p e r a t o r s a c c o r d i n g t o t h e " o c c u p a t i o n s t a t e d " o r the "days worked" c r i t e r i a i s an e f f e c t i v e means o f f o c u s i n g on the f u l l - t i m e f a r m e r s f o r whom the e a r n i n g s f u n c -t i o n model was s p e c i f i e d f o r . I n b o th t a b l e s (1 and 2 ) , we note t h a t t h e e x p e r i e n c e (T) term was s i g n i f i c a n t i n a l l d a t a s e t s b u t n e g a t i v e i n s i g n . The e x p e r i e n c e v a r i a b l e we a r e u s i n g i s not w e l l 51 g T a b l e 2. R e g r e s s i o n e s t i m a t e s o f the m o d i f i e d e a r n i n g s f u n c t i o n f o r farm o p e r a t o r s w i t h S a l e s o f a t l e a s t $2500, farm employment income (FEI)>0, by days worked o f f - f a r m (DAYSOFF) groups. Canada. 1971 Data S et DAYSOFF = 0 l£DAYSOFF£50 DAYSOFF>150 Sample s i z e 64,079 8,169 9 , 702 S .023 .023 .007 (35.60) (13.25) (3.75 T -.002 -.001 -.001 (18.84) (2.96) (2.35 I n DAYSON 1.27 -.014 (7.25) (2.08 l n FC .112 .120 .069 (103.02) (39.62) (22.84 l n NUMCH .042 .026 -.005 (13.31) (4.28) (0.69 -2 R .21 .22 .05 Reg. F 4322 449 112 H P * $166 $154 $24 Data Source: A g r i c u l t u r e - P o p u l a t i o n L i n k a g e Data. 19 71. U n p u b l i s h e d . S t a t i s t i c s Canada. a r e g r e s s i o n c o e f f i c i e n t ( t - s t a t i s t i c ) M^P^ , = m a r g i n a l p r o d u c t o f s c h o o l i n g s p e c i f i e d , as d i s c u s s e d e a r l i e r . I n i n t e r p r e t i n g the e x p e r i e n c e c o e f f i c i e n t , we h o l d c o n s t a n t a l l o t h e r v a r i a b l e s , i n c l u d i n g t h e s c h o o l i n g v a r i a b l e . Due t o t h e d e f i n i t i o n o f e x p e r i e n c e (T = Age - S c h o o l i n g - 5 ) , we may be m e a s u r i n g , i n s t e a d , an age v a r i a b l e o r v i n t a g e e f f e c t . The younger farm o p e r a t o r s t e n d t o be more s c h o o l e d t h a n the o l d e r o p e r a t o r s (as e v i d e n c e d by t h e r e l a t i v e i n c r e a s e i n t h e e d u c a t i o n a l l e v e l o f t h e farm p o p u l a t i o n d u r i n g the 1961-71 p e r i o d , r e f e r e n c e d on page 3, and a l s o due t o the n e g a t i v e c o r r e l a t i o n between s c h o o l i n g and e x p e r i e n c e (-0.48) o f t h i s d a t a s e t ) . T h i s n e g a t i v e c o r r e l a t i o n between s c h o o l i n g and e x p e r i e n c e , and the n e g a t i v e r e l a t i o n ( c o r r e l a t i o n o f -0.2 2) between e x p e r i e n c e and t h e dependent v a r i a b l e farm employment income (FEI) makes i n t e r p r e t a t i o n o f t h e c o e f f i c i e n t o f e x p e r i e n c e d i f f i c u l t . Even i f we had a r e a s o n a b l e measure o f t h e e x p e r i e n c e v a r i a b l e t o s t a r t w i t h , i n t e r p r e t a t i o n o f t h e e x p e r i e n c e c o e f f i c i e n t n e c e s s i t a t e s c e r t a i n v a l u e s f o r k Q and T* (see page 15 a b o v e ) . 5.2.2. V a l u e added f u n c t i o n We now d i s c u s s t h e r e s u l t s o f e s t i m a t i n g r a t e s o f r e t u r n t o s c h o o l i n g u s i n g the v a l u e added f u n c t i o n a t t h e m i c r o d a t a l e v e l . S p e c i f i c a t i o n A i n T a b l e 3 shows the r e g r e s s i o n c o e f f i c i e n t s u s i n g our e s t i m a t i n g v a l u e added e q u a t i o n ( 1 1 ) . We note t h a t a l l t h e c o e f f i c i e n t s a r e s i g n i f i c a n t and the m a r g i n a l p r o d u c t o f s c h o o l i n g i s $260, a r e t u r n h i g h e r than our m o d i f i e d e a r n i n g s f u n c t i o n r e s u l t o f $173. We h y p o t h e s i z e d e a r l i e r t h a t t h e r e t u r n t o s c h o o l i n g from a s p e c i f i c a t i o n w i t h an aggr e g a t e d farm c a p i t a l v a l u e w i l l be h i g h e r r e l a t i v e t o the s c h o o l i n g c o e f f i c i e n t o f a s p e c i f i c a t i o n u s i n g d i s a g g r e g a t e d c a p i t a l v a l u e s ( v a l u e o f l a n d and b u i l d i n g s , v a l u e o f l i v e s t o c k and v a l u e o f machinery and equipment e n t e r -i n g the e q u a t i o n s e p a r a t e l y ) . T h i s i s s u p p o r t e d by d a t a on T a b l e 3 when we compare t h e c o e f f i c i e n t o f s c h o o l i n g i n s p e c i f i c a t i o n A w i t h the c o r r e s p o n d i n g c o e f f i c i e n t o f s p e c i f i c a t i o n B. The d i f f e r e n c e (.366 v s . .123, o r c o r r e s p o n d i n g l y , m a r g i n a l p r o d u c t s o f $260 and $87 r e s p e c t i v e l y ) i s a t t r i b u t a b l e t o the g a i n s t h a t t h e s c h o o l i n g c o e f f i c i e n t p i c k s up from r e - a l l o c a t i n g among t h e t h r e e components o f c a p i t a l w i t h i n the aggregate measure farm c a p i t a l ( F C ) . S p e c i f i c a t i o n C i n T a b l e 3 shows a n o t h e r method t o i l l u s t r a t e the a l l o c a t i v e g a i n s p i c k e d up by t h e s c h o o l i n g v a r i a b l e v i a i n p u t s p e c i f i c a t i o n . S i n c e s p e c i f i c a t i o n C i n c l u d e s HLP ( h i r e d l a b o u r c o s t ) as an i n p u t c o s t i n the r i g h t hand s i d e o f t h e v a l u e added f u n c t i o n , t h e s c h o o l i n g c o e f f i c i e n t o f t h i s s p e c i f i c a t i o n i s as e x p e c t e d , lower compared t o t h e s p e c i f i c a t i o n A c o e f f i c i e n t ( w i t h a m a r g i n a l p r o d u c t o f $212 v s . $260) because i t l o s e s the g a i n s from b e t t e r d e c i s i o n making i n c h o o s i n g optimum l e v e l s o f h i r e d l a b o u r . T a b l e 3 a l s o compares t h e r e g r e s s i o n e s t i m a t e s o f e q u a t i o n (11) i n s p e c i f i c a t i o n A w i t h the r e s u l t s o f e q u a t i o n (11c) u s i n g t h e same d a t a s e t . I n s p e c i f i c a t i o n D, t h e wei g h t e d l a b o u r v a r i a b l e (SDAYS) e x h i b i t e d a s i g n i f i c a n t c o e f f i c i e n t (.18 3) w i t h a v a l u e between the s e p a r a t e s c h o o l i n g Table 3. Regression estimates of the value added function for farm operators with Sales of at least $2500, and days worked on farm (DAYSON)>1.0 for different specifications, (n=88,473). Canada. 1971. Specification A b B b C C Db ln Schooling .366 .123 .279 (42.21 (15.06) (36.15) ln DAYSON .154 .141 .141 (40.68) (40.34) (42.08) ln'NUMCH .029 .035 .026 .029 (14.98) (19.16) (15.28) (14.74) In FC .113 ln FLB .478 (128 .77) ln FME .139 (52.90) ln FL .053 (50.21) ln HLP .169 (138.48) .114 (120.75) (121.20) ln SDAYSd - 1 8 3 (50.68) -20 .32 .34 .19 Reg- F 5369 6954 9148 6936 M P s e $260 $87 $212 Data Source: Agriculture-Population Linkage Data. 1971. Unpublish-ed. Statistics Canada. aregression coefficient (t-statistic) ^dependent variable = VA = (Sales - VIN - rent paid - fuel and o i l expenses - HLP); where VIN = cost of purchased chemicals, feed, f e r t i l i z e r and custom machine rental; HLP = cost of hired labour. cdependent variable = VA1 = (Sales - VIN - rent paid - fuel and o i l expenses). d l n SDAYS = log (Schooling x DAYSON). eMPg = marginal product of schooling c o e f f i c i e n t (.366) and l a b o u r c o e f f i c i e n t (.154) o f s p e c i f i c a t i o n ( A ) . The o t h e r v a r i a b l e s changed o n l y s l i g h t l y and i n s i g n i f i c a n t l y , w i t h the change i n the l a b o u r v a r i a b l e s p e c i f i c a t i o n . But s i n c e our main i n t e r e s t i n t h i s s t u d y i s t o e s t i m a t e t h e r e t u r n s t o s c h o o l i n g , the r e s u l t s o f s p e c i f i -c a t i o n D, which l a c k s a s e p a r a t e measure f o r r e t u r n t o s c h o o l i n g ( s i n c e i t i s r e s t r i c t e d t o t h e same c o e f f i c i e n t as DAYSON) c o u l d not be r e a l l y compared w i t h t h e r e s u l t s o f t h e f i r s t d a t a s e t , f o r purposes o f f u n c t i o n a l form. Comparison w i t h the r e s u l t s o f t h e G r i l i c h e s (1964) s t u d y w i l l be more r e l e v a n t i n the census d i v i s i o n l e v e l r e g r e s s i o n r e s u l t s i n the n e x t s e c t i o n , because t h e a g g r e g a t i o n l e v e l used i s more comparable (census d i v i s i o n and s t a t e a v e r a g e s ) . 5.2 Census D i v i s i o n L e v e l 5.2.1. E a r n i n g s f u n c t i o n A n a l y s i s o f t h e d a t a u t i l i z i n g t h e census d i v i s i o n a verages i s u n d e r t a k e n f o r c o m p a r a t i v e purposes and t o use a two-stage l e a s t squares p r o c e d u r e (not f e a s i b l e a t t h e m i c r o l e v e l ) i n d e a l i n g w i t h the e n d o g e n e i t y o f t h e v a r i a b l e days worked. T a b l e 4 shows the r e g r e s s i o n e s t i m a t e s o f a m o d i f i e d e a r n i n g s f u n c t i o n u s i n g t h e days worked v a r i a b l e i n s p e c i f i c a -t i o n (1) and t h e p r e d i c t e d days worked v a l u e i n s p e c i f i c a t i o n ( 2 ) . The p r e d i c t i n g e q u a t i o n f o r days worked i s shown i n the t a b l e ( f o o t n o t e b ) . A l l t h e d e t e r m i n a n t s e x h i b i t e d s i g n i f i c a n t c o e f f i c i e n t s w i t h t h e e x p e c t e d s i g n s . The wage r a t e (WWAGE) v a r i a b l e i s o f t h e o p p o s i t e s i g n as we would e x p e c t , b u t i n s i g n i f i c a n t . The two v a r i a b l e s DUER ( d i s t a n c e from c i t y (DCITY x unemployment r a t e (UER)) and DURBY ((DCITY) x urban e a r n i n g s (URBY)), as c o r r e c t i o n s f o r t h e degree o f u r b a n i z a -t i o n , behaved as p r e d i c t e d and s u p p o r t s the v i e w t h a t demand f o r l a b o u r o f f - f a r m i s i n f l u e n c e d not o n l y by the unemployment r a t e and the urban e a r n i n g s ( i n a d d i t i o n t o a l l t h e o t h e r v a r i a b l e s ) b ut the l o c a t i o n w i t h r e s p e c t t o the c i t y , o f t h e farm o p e r a t o r . Comparing r e s u l t s o f s p e c i f i c a t i o n s (1) and ( 2 ), we note an i n c r e a s e i n the s c h o o l i n g c o e f f i c i e n t ( . 056 t o .080) as we go from a days worked t o a p r e d i c t e d days worked (DAYSON*) v a r i a b l e s p e c i f i c a t i o n ( w i t h a c o r r e s p o n d i n g i n c r e a s e i n t h e m a r g i n a l p r o d u c t o f s c h o o l i n g , $440 t o $ 6 2 9 ). The e x p e r i e n c e v a r i a b l e i s i n s i g n i f i c a n t i n b o t h c a s e s and the l a b o u r v a r i a b l e i n c r e a s e d s i g n i f i c a n t l y ( 0 .544 t o 1 . 5 0 ) . Use o f the p r e d i c t e d l a b o u r i n p u t v a r i a b l e (DAYSON*) c o n t r i b u t e s t o a b e t t e r s p e c i f i e d e a r n i n g s f u n c t i o n because i t c o r r e c t s f o r t he en d o g e n e i t y i n h e r e n t i n the v a r i a b l e . There were no s i g n i f i -c a n t d i f f e r e n c e s , however, f o r t h e c a p i t a l v a r i a b l e ( . 260 t o . 259) o r the f a m i l y l a b o u r v a r i a b l e ( . 102 t o .112) . Comparing r e s u l t s o f d a t a s e t (1) i n T a b l e 4 w i t h t h e c o r r e s p o n d i n g e a r n i n g s f u n c t i o n r e s u l t s o f d a t a s e t ( A ) , a l l farms (Table 1 ), we note t h a t a l l v a r i a b l e s e x h i b i t e d r e l a t i v e l y h i g h e r c o e f f i c i e n t s a t th e census d i v i s i o n l e v e l . The e x p e r i e n c e term a l s o becomes p o s i t i v e and i n s i g n i f i c a n t . The s c h o o l i n g c o e f f i c i e n t i n p a r t i c u l a r , i n c r e a s e d 180% (from .0 20 t o . 056) o r a c o r r e s p o n d i n g $308 d i f f e r e n c e ($132 t o $440) i n 57 Table 4. Regression estimates of the modified earnings function for farm operators with Sales of at least $2500, using reported days worked on farm (DAYSON) and predicted DAYSON*, and using census division averages (n=242). Canada. 1971 Specification 1 2 Schooling(S) .056 .080 (2.14) (2.56) Experience(T) .003 -.002 (0.25) (0.16) ln DAYSON .544 (1.69) ln DAYSON*'3 1.50 (2.06) ln FC .260 .259 (10.62) (10.61) ln NUMCH .102 .112 (0.90) (0.98) -2 R .53 .53 Reg. F 52.53 53 .11 MP C s $440 $627 Data Source: Agriculture-Population Linkage Data. 19 71. Unpublished. S t a t i s t i c s Canada. aregression coefficient (t-statistic) In DAYSON* = log (300 - DAYSOFF*) where• DAYSOFF* = 6.08 S - .005 FC + .087 WWAGE - 1.96 UER (5.40) (2.31) (1.49) (2.40) + .008 URBY + .014 DUER - .000007 DURBY (5.74) (3.29) (2.49) + 3.73 NUMCH (2.24) , R = .37 where DAYSOFF* i s the predicted value of DAYSOFF when regressed on schooling (S); farm capital (FC); hired wage rate (WWAGE); unemployment of males (24-44 years old) whose schooling level i s not greater than high school graduation but greater than or equal to grade 8 (UER); urban earnings of males (24-44 years old) whose schooling level i s not greater than high school graduation but greater than or equal to grade 8 (URBY); DUER = (UER x DCITY), where DCITY i s distance from nearest city; and DURBY = (URBY x DCITY). CMP = marginal product of schooling. 58 the m a r g i n a l p r o d u c t v a l u e . These r e s u l t s were e x p e c t e d s i n c e t h e a g g r e g a t e d l e v e l (census d i v i s i o n ) a l l o w s more room f o r a l l o c a t i v e a b i l i t y ( v i a commodities produced) and the s c h o o l i n g c o e f f i c i e n t c a p t u r e d t h i s . 5.2.2. V a l u e added f u n c t i o n U t i l i z i n g the v a l u e added f u n c t i o n , we c o r r e c t f o r the e n d o g e n e i t y o f days worked i n a s i m i l a r two s t a g e l e a s t squares p r o c e d u r e as d i s c u s s e d above f o r t h e m o d i f i e d e a r n i n g s f u n c t i o n . T a b l e 5 shows the r e g r e s s i o n e s t i m a t e s o f a v a l u e added f u n c t i o n u s i n g t h e days worked v a r i a b l e i n s p e c i f i c a t i o n (1) and t h e p r e d i c t e d days worked v a l u e (DAYSON*) i n s p e c i f i c a -t i o n ( 2 ) . The p r e d i c t i n g e q u a t i o n f o r days worked i s shown i n t h e t a b l e ( f o o t n o t e b) and i s the same e q u a t i o n used i n t h e p r e c e d i n g t a b l e , f o r c o r r e c t i n g the e n d o g e n e i t y o f days worked i n t h e e a r n i n g s f u n c t i o n f o r m u l a t i o n . Comparing r e s u l t s o f t h e two s p e c i f i c a t i o n s we note a s u b s t a n t i a l l y h i g h e r e s t i m a t e o f t h e r e t u r n t o s c h o o l i n g f o r the p r e d i c t e d days worked s p e c i f i c a t i o n ( w i t h a c o r r e s p o n d i n g i n c r e a s e i n the m a r g i n a l p r o d u c t o f s c h o o l i n g , from $4 38 t o $639). T h i s f o r m u l a t i o n i s c l e a r l y a b e t t e r s p e c i f i e d e q u a t i o n because t h e use o f t h e p r e d i c t e d l a b o u r i n p u t v a r i a b l e (DAYSON*) c o r r e c t s f o r t h e s i m u l t a n e o u s e q u a t i o n b i a s a r i s i n g from t h e r e p o r t e d days worked v a r i a b l e (DAYSON). The same t a b l e shows the r e g r e s s i o n e s t i m a t e s o f a v a l u e added f u n c t i o n u s i n g d i s a g g r e g a t e d c a p i t a l v a r i a b l e s ( s p e c i f i -c a t i o n 3.) . As i n a s i m i l a r t e s t o f f u n c t i o n a l form (Table 3 f o r t h e m i c r o data) performed e a r l i e r , T a b l e 5 r e v e a l s t h a t t h e f o r m u l a t i o n w i t h the a g g r e g a t e d c a p i t a l s p e c i f i c a t i o n ( 1 ) , a l l o w s t h e s c h o o l i n g c o e f f i c i e n t t o p i c k up the g a i n s from r e - a l l o c a t i n g among t h e d i f f e r e n t c a p i t a l components. A g a i n , the e s t i m a t e d c o e f f i c i e n t s and m a r g i n a l p r o d u c t s o f v a l u e added f u n c t i o n s a t the census d i v i s i o n l e v e l a r e h i g h e r compared t o the c o r r e s p o n d i n g e s t i m a t e s o f f u n c t i o n s computed a t t h e m i c r o l e v e l ( r e f e r t o T a b l e 3) . T a b l e 5 a l s o i l l u s t r a t e s t h e census d i v i s i o n l e v e l t r e a t m e n t o f t h e v a l u e added s p e c i f i c a t i o n u s i n g the t r a n s f o r m e d l a b o u r v a r i a b l e (SDAYS, w e i g h t e d by s c h o o l i n g , as the l a b o u r q u a l i t y i n d e x ) . I n s p e c i f i c a t i o n ( 1 ) , we note t h a t the o u t p u t e l a s t i c i t y w i t h r e s p e c t t o l a b o u r o r DAYSON (0.527) a r e not s i g n i f i c a n t l y d i f f e r e n t from each o t h e r . 1 That t h e o u t p u t e l a s t i c i t i e s f o r b o t h l a b o u r q u a n t i t y (DAYSON) and the l a b o u r q u a l i t y ( s c h o o l i n g ) a r e not s i g n i f i c a n t l y d i f f e r e n t i m p l i e s t h a t we can combine the two v a r i a b l e s i n t o one measure o f l a b o u r , as i n s p e c i f i c a t i o n (4) o f T a b l e 5. The p r o d u c t (SDAYS) o f the l a b o u r and s c h o o l i n g v a r i a b l e s , e x h i b i t e d a more s i g n i f i c a n t c o e f f i c i e n t (.44 7 w i t h t - v a l u e o f 2.26) t h a n the two v a r i a b l e s (DAYSON and s c h o o l i n g ) e x h i b i t e d when they e n t e r e d t h e e q u a t i o n s e p a r a t e l y i n s p e c i f i c a t i o n (1) o f t h e same t a b l e . More i m p o r t a n t i s the f i n d i n g t h a t t h e s e r e s u l t s the computed t - s t a t i s t i c f o r t h e t e s t o f e q u a l i t y o f t h e two c o e f f i c i e n t s i s 0.34; t h e " c r i t i c a l " v a l u e o f t w i t h 241 degrees o f freedom i s a t l e a s t 1.96. Table 5 Regression estimates of the value added function for farm operators with Sales of at least $2500, using d i f f e r e n t s p e c i f i c a t i o n s and using census d i v i s i o n averages (n=242). Canada. 1971 l n S .428 (2.07) .624 (2.50) .239 (1.26) l n DAYSON .527 (1.65) .730 (2.48) l n DAYSON* 1.42 (1.99) l n FC .259 (11.41) .262 (11.57 .260 (11.65) l n NUMCH .086 (0.87) .118 (1.17) .195 (2.16) .093 (0.99) l n FLB .560 (11.29) ln FL .089 (2.43) ln FVME -.005 (0.51) l n SDAYS R2 Reg. F .61 62.46 $438 .53 66 .44 $639 .61 62.46 $244 .447 (2.26) .53 87.99 Data Source: Agriculture-Population Linkage Data. 1971. Unpublished. S t a t i s t i c s Canada. regression c o e f f i c i e n t ( t - s t a t i s t i c ) l n DAYSON* where: log (300 - DAYSOFF*) DAYSOFF* = 6.08 S (5.40) + .008 URBY (5.74) .005 FC + .087 WWAGE - 1.96 UER (2.31) (1.49) (2.40) .014 DUER - .000007 DURBY (3.29) (2.49) +3.73 NUMCH (2.24) R 2 = .37 where DAYSOFF* i s the predicted value of DAYSOFF when regressed on schooling (S); farm c a p i t a l (FC); hired wage rate (WWAGE); unemployment of males (24-44 years old) whose schooling l e v e l i s not greater than high school, but greater than grade 8 (UER); urban earnings of males (24-44 years old) whose schooling l e v e l i s not greater than high school but greater than grade 8 (URBY); DUER = (UER x DCITY), where DCITY i s distance from nearest c i t y ; and DURBY = (URBY x DCITY). °SDAYS = log (schooling x DAYSON) MPg = marginal product of schooling. a r e a l m o s t i d e n t i c a l t o t h e c o e f f i c i e n t s found by G r i l i c h e s (1964, page 966) when he r a n an aggregate p r o d u c t i o n f u n c t i o n u t i l i z i n g p o o l e d 1954-59 d a t a f o r t h e U.S. The c o e f f i c i e n t s he found were as f o l l o w s : 0.511 f o r l a b o u r ; 0.405 f o r e d u c a t i o n and 0.44 8 f o r ( l a b o u r x e d u c a t i o n ) . A l t h o u g h o ur d a t a i s f o r 1971, t h e t w e l v e - y e a r d i f f e r e n c e c o u l d a p p r o x i m a t e l y compensate f o r t h e l a g t h a t Canadian a g r i c u l t u r e has, b e h i n d t h e l e v e l o f American a g r i c u l t u r a l t e c h n o l o g y and e x t e n s i o n s e r v i c e s . T h i s p r o v i d e s us w i t h a.comparable b a s i s f o r t h e b e h a v i o u r o f the a g r i c u l t u r a l s e c t o r s o f b o t h c o u n t r i e s . I t a l s o p r o v e s t h a t i n b o t h c o u n t r i e s e d u c a t i o n i s a s i g n i f i c a n t d e t e r m i n a n t o f o u t p u t ( e a r n i n g s ) , as a l a b o u r q u a l i t y i n d e x o r as an independent i n p u t o f p r o d u c t i o n i t s e l f . 5.3 Summary o f R e s u l t s I n summary, t h i s s t u d y has e s t i m a t e d r e a s o n a b l e measures o f t h e r e t u r n t o s c h o o l i n g whether u s i n g m o d i f i e d e a r n i n g s f u n c t i o n approach o r a v a l u e added f u n c t i o n a p p r o a c h . We note however t h a t h i g h e r e s t i m a t e s o f t h e c o n t r i b u t i o n t o s c h o o l i n g t o farm income a r e a r r i v e d a t , u t i l i z i n g t he v a l u e added approach. As both f u n c t i o n s u t i l i z e d t h e same v a r i a b l e s ( w i t h the e x c l u s i o n o f t h e e x p e r i e n c e term i n the v a l u e added f u n c t i o n ) , we a r e i n c l i n e d t o c o n c l u d e t h a t the v a l u e added f o r m u l a t i o n , w i t h r e s p e c t t o e s t i m a t i n g r e t u r n s t o farm employment income (or synonymously, v a l u e added) i s a b e t t e r s p e c i f i e d f u n c t i o n . The e s t i m a t e d m a r g i n a l r e t u r n (annual) t o s c h o o l i n g , 62 u s i n g t h e v a l u e a d d e d ' s p e c i f i c a t i o n a t the m i c r o l e v e l ( s p e c i -f i c a t i o n (A) i n T a b l e 3) i s $260 per y e a r o f s c h o o l i n g . T h i s v a l u e i s based on t h e assumption o f a 30 0-day work y e a r . Our sample r e p o r t s an average o f 2 30 days t h a t t h e farm o p e r a t o r works on t h e farm. By e x t r a p o l a t i n g t h i s r e t u r n t o a f u l l (300 day) y e a r o f farm work, the r e t u r n t o s c h o o l i n g i n c r e a s e s t o $375 per y e a r o f s c h o o l i n g . T h i s i s comparable t o Fane's e s t i m a t e o f $321 (Fane, 1972) u s i n g 1961 d a t a from U.S. Corn B e l t S t a t e s . The e q u a t i o n s u s i n g census d i v i s i o n a v e r a g e s , when compared t o t h e r e s u l t s o f e q u a t i o n s u s i n g m i c r o d a t a , a l l gave h i g h e r e s t i m a t e s due l a r g e l y t o t h e a g g r e g a t i o n d i f f e r e n c e . Our models however a r e based on m i c r o d a t a and t h e census d i v i s i o n approach was u n d e r t a k e n p r i m a r i l y t o c o r r e c t f o r t h e e n d o g e n e i t y o f one o f t h e independent v a r i a b l e s . A t t h e census d i v i s i o n l e v e l t h e e s t i m a t e d r e t u r n t o s c h o o l i n g was $639, a f t e r a two s t a g e l e a s t s quares p r o c e d u r e was u t i l i z e d , w i t h days worked as t h e i n s t r u m e n t . T h i s i s c l e a r l y t h e b e s t s p e c i f i e d v a l u e added f u n c t i o n s p e c i f i c a t i o n i n t h i s s t u d y because th e s i m u l t a n e o u s e q u a t i o n b i a s a r i s i n g from t h e endogenous v a r i a b l e (days worked) has been c o r r e c t e d f o r . U s i n g a t r a n s f o r m e d l a b o u r v a r i a b l e i n t h e v a l u e added f u n c t i o n a t t h e census d i v i s i o n l e v e l l e d t o an i m p o r t a n t f i n d i n g t h a t a s i m i l a r o u t p u t - i n p u t r e l a t i o n s h i p e x i s t s i n the a g r i c u l t u r a l s e c t o r s o f t h e U.S. and Canada. I n p a r t i c u l a r , the r e l a t i o n s h i p was i d e n t i c a l f o r t h e e l a s t i c i t i e s o f o u t p u t with respect to the weighted labour variable (or product of these two factors) values of selected years. It i s recognized that the estimates for the earnings function can be improved with additional information (like actual years of experience) and other measures to enable us to treat the endogeneity of schooling and i t s rate of return, which we assumed i n t h i s study both to be exogenous. For the value added function, the s p e c i f i c a t i o n of the model could be improved with measures for prices of inputs. 64 VI SUMMARY AND CONCLUSIONS A p p l i c a t i o n o f the e a r n i n g s f u n c t i o n t o t h e a g r i c u l t u r a l s e c t o r has been done by i n c o r p o r a t i n g the unique c h a r a c t e r i s t i c s o f t h e s e c t o r i n t o t he human c a p i t a l model w i t h n e t farm employment income as t h e dependent v a r i a b l e . W i t h t h e main o b j e c t i v e o f e s t i m a t i n g the r e t u r n s t o s c h o o l i n g , an e a r n i n g s f u n c t i o n f o r Canadian farm o p e r a t o r s was f o r m u l a t e d , t a k i n g i n t o a c c o u n t a l l the v a r i o u s d a t a t r a n s f o r m a t i o n s needed by the model t o be a p p l i c a b l e t o t h e a v a i l a b l e d a t a . W i t h t h i s c ompleted, a d i g r e s s i o n on the v a l u e added f u n c t i o n f o l l o w e d because o f t h e s i m i l a r i t y i n f u n c t i o n a l form o f the two models. As a t e s t o f f u n c t i o n a l form, t h e v a l u e added approach was pursued, w i t h t h e s i m i l a r o b j e c t i v e o f e s t i m a t i n g t h e c o n t r i -b u t i o n o f s c h o o l i n g t o farm income. U s i n g m i c r o d a t a , r a t e s o f r e t u r n t o s c h o o l i n g were computed and i n a l l c a s e s the c o r r e s p o n d i n g m a r g i n a l p r o d u c t s o f s c h o o l i n g u s i n g b o t h t h e m o d i f i e d e a r n i n g s f u n c t i o n and v a l u e added approach, were s u b s t a n t i a l . The e s t i m a t e s u s i n g t h e m o d i f i e d e a r n i n g s f u n c t i o n approach, were however l o w e r t h a n the c o r r e s p o n d i n g measures when v a l u e added was used, r a i s i n g t h e q u e s t i o n o f t h e c o r r e c t f u n c t i o n a l form t o use. I n t h e m o d i f i e d e a r n i n g s f u n c t i o n approach, use o f two c r i t e r i a ( o c c u p a t i o n s t a t e d and days worked) t o s e p a r a t e t h e commercial f a r m e r s ( f o r whom t h e model was s p e c i f i e d ) proved t o be u s e f u l i n a r r i v i n g a t r e a s o n a b l e e s t i m a t e s o f t h e c o n t r i b u t i o n o f s c h o o l i n g t o farm o p e r a t o r income. I n b o t h 65 c a s e s , the f i t was b e t t e r and t h e r e t u r n t o s c h o o l i n g h i g h e r , when the group i s more s p e c i a l i z e d i n f a r m i n g . The v a l u e added f u n c t i o n approach l i k e w i s e gave e s t i m a t e s o f t h e r e t u r n t o s c h o o l i n g which d i f f e r e d as d i f f e r e n t i n p u t s p e c i f i c a t i o n s were used. The a g g r e g a t e d c a p i t a l v a r i a b l e f o r m u l a t i o n y i e l d e d a h i g h e r r e t u r n t o s c h o o l i n g t h a n t h e d i s a g g r e g a t e d c a p i t a l s p e c i f i c a t i o n . S c h o o l i n g was found t o be an i m p o r t a n t d e t e r m i n a n t o f v a l u e added and i t s r o l e i n c r e a s e s as we d e c r e a s e t h e number o f d e c i s i o n v a r i a b l e s i n the e s t i m a t i n g e q u a t i o n . E s t i m a t e s o f the a n n u a l c o n t r i b u t i o n o f s c h o o l i n g found i n t h i s s t u d y a r e $172 per y e a r o f s c h o o l i n g ( u s i n g a m o d i f i e d e a r n i n g s f u n c t i o n ) and $375 per s c h o o l i n g y e a r ; ( u s i n g a v a l u e added f u n c t i o n ) both o f t h e s e v a l u e s were a d j u s t e d f o r a f u l l 300-day work y e a r . The l a t t e r e s t i m a t e i s comparable t o the e s t i m a t e found i n the U.S. Corn B e l t S t a t e s , a r e t u r n o f $321 (Fane, 1972). F o r t h e e a r n i n g s f u n c t i o n , t h e problem of s i m u l t a n e o u s e q u a t i o n b i a s a r i s i n g from t h e e n d o g e n e i t y o f days worked was remedied a t t h e census d i v i s i o n l e v e l w i t h the use o f a two-stage l e a s t squares p r o c e d u r e (which was not f e a s i b l e a t t h e m i c r o l e v e l ) . I t i s r e c o g n i z e d , however, t h a t even w i t h t h i s c o r r e c t i o n , e s t i m a t e s o f t h e r e t u r n t o s c h o o l i n g a r e n o t w i t h o u t b i a s e s . The b i a s a r i s e s from the s c h o o l i n g v a r i a b l e , which we assumed t o be exogenous i n t h i s s t u d y . Added t o t h i s i s the measure o f farm e a r n i n g s which i n c l u d e s r e t u r n t o o p e r a t o r ' s l a b o u r and o t h e r owned i n p u t s . A l t h o u g h c o r r e c t i o n s f o r t h e s e f a c t o r s were made t o e n a b l e us t o b u i l d a m o d i f i e d 66 e a r n i n g s f u n c t i o n f o r e n t r e p r e n e u r s , p a r t i c u l a r l y farm o p e r a t o r s , t h e p r o c e d u r e was no t p a r t i c u l a r l y c o n v e n t i o n a l and th e t h e o r e t i c a l j u s t i f i c a t i o n f o r d o i n g so i s not too s t r o n g . T h i s however does n o t weaken the r e s u l t s o f t h i s s t u d y . As we d i s c u s s e d i n t h e p r e v i o u s c h a p t e r , the r e s u l t s i n d i c a t e t h a t t h e v a l u e added f u n c t i o n i s a b e t t e r s p e c i f i e d f o r m u l a t i o n w i t h r e s p e c t t o e s t i m a t i n g the c o n t r i b u t i o n o f s c h o o l i n g t o farm income. The e s t i m a t e s o f t h e r e t u r n t o s c h o o l i n g u s i n g the v a l u e added approach a l s o has i t s s h o r t c o m i n g s . The o m i s s i o n o f the p r i c e s o f the i n p u t s p u r c h a s e d and t h e h i r e d l a b o u r wage r a t e has b i a s e d t h e s c h o o l i n g c o e f f i c i e n t . A p r i o r i e x p e c t a t i o n s l e a d us t o assume a n e g a t i v e c o r r e l a t i o n between p r i c e s o f i n p u t s p u r c h a s e d and s c h o o l i n g , so o m i s s i o n o f the p r i c e o f i n p u t s b i a s e s t h e s c h o o l i n g c o e f f i c i e n t upwards. On the o t h e r hand, i f we assume a p o s i t i v e c o r r e l a t i o n between s c h o o l i n g and the h i r e d l a b o u r wage r a t e , t h e s c h o o l i n g c o e f f i c i e n t w i l l be b i a s e d downwards when the h i r e d wage r a t e i s e x c l u d e d from t h e e q u a t i o n . The n e t e f f e c t on s c h o o l i n g w i l l depend on which b i a s w i l l dominate. A n o t h e r b i a s a r i s i n g from our e s t i m a t e o f t h e r e t u r n t o s c h o o l i n g i n farm p r o d u c t i o n , i s t h a t i t i s an i n c o m p l e t e measure o f i t s p r o d u c t i v i t y . The l e v e l o f aggregate c a p i t a l s e r v i c e s and days worked on the farm a r e h e l d c o n s t a n t . Any g a i n s from o p t i m i z i n g t h e l e v e l o f t o t a l c a p i t a l and f a m i l y l a b o u r a r e n o t c a p t u r e d by our s c h o o l i n g c o e f f i c i e n t and as a r e s u l t our measure o f t h e p r o d u c t i v i t y o f s c h o o l i n g i s a lower bound e s t i m a t e . However the s c h o o l i n g p r o d u c t i v i t y measures behave as p r e d i c t e d and we have shown t h i s t h r o u g h the d i f f e r e n t s p e c i f i c a t i o n s we have t e s t e d . U s i n g t h e v a l u e added approach on t h e census d i v i s i o n l e v e l , and c o r r e c t i n g f o r t h e e n d o g e n e i t y o f days worked y i e l d e d a m a r g i n a l p r o d u c t of s c h o o l i n g o f $639 per y e a r o f s c h o o l i n g . A d j u s t i n g f o r a f u l l (300-day) work y e a r , t h i s i n c r e a s e s t o an a n n u a l i n c r e m e n t i n v a l u e added o f $831 per y e a r o f s c h o o l i n g . C l e a r l y t h e s e r e s u l t s , b e i n g i n the lower bound o f t h e complete measure o f t h e p r o d u c t i v i t y o f s c h o o l i n g , s t r o n g l y i n d i c a t e t h a t s c h o o l i n g as an i n v e s t m e n t i s an i m p o r t a n t d e t e r m i n a n t o f farm incomes. I n a n o t h e r t e s t o f f u n c t i o n a l form t h e l a b o u r v a r i a b l e was w e i g h t e d by t h e l a b o u r q u a l i t y i n d e x , e d u c a t i o n ( s c h o o l i n g i n t h i s c a s e ) . A t t h e census d i v i s i o n l e v e l t h i s l e d t o an i m p o r t a n t f i n d i n g about th e s i m i l a r i t y o f t h e r e s u l t s w i t h t h o s e o f a U.S. s t u d y by G r i l i c h e s (1964). S p e c i f i c a l l y , t h e r e l a t i o n s h i p was i d e n t i c a l f o r t h e e s t i m a t e d o u t p u t e l a s t i c i -t i e s w i t h r e s p e c t t o l a b o u r , w i t h r e s p e c t t o e d u c a t i o n ( s c h o o l i n g ) and w i t h r e s p e c t t o t h e ( l a b o u r x e d u c a t i o n ) v a r i a b l e . I n summary, t h i s s t u d y has succeeded i n b u i l d i n g a m o d i f i e d e a r n i n g s f u n c t i o n f o r t h e Canadian farm o p e r a t o r s , and i n e s t i m a t i n g t h e c o n t r i b u t i o n o f s c h o o l i n g t o farm income, u s i n g t h i s model. As a d i g r e s s i o n and t e s t o f f u n c t i o n a l form, a v a l u e added f u n c t i o n approach was u t i l i z e d t o augment the a n a l y s i s . A l t h o u g h b o t h methods y i e l d e d r e a s o n a b l e e s t i m a t e s 68 o f t h e m a r g i n a l p r o d u c t o f s c h o o l i n g , t h e v a l u e added approach was found t o be a b e t t e r s p e c i f i e d e q u a t i o n , f o r purposes o f e s t i m a t i n g the p r o d u c t i v i t y o f s c h o o l i n g . The r e s u l t s o f t h i s s t u d y a l s o d i s p r o v e an e a r l i e r c o n t e n t i o n about the ambiguous e f f e c t t h a t s c h o o l i n g has on farm income, w h i c h a n o t h e r s t u d y (Shaw, 1977) s u g g e s t s . T h i s s t u d y p r o v i d e s s t r o n g e v i d e n c e t h a t s c h o o l i n g i s an i m p o r t a n t d e t e r m i n a n t o f farm incomes. P o l i c y makers c o u l d a l s o u t i l i z e the f i n d i n g s o f t h i s s t u d y as g u i d e l i n e s i n p o l i c i e s t o improve t h e w e l l - b e i n g o f f a r m e r s ( l i k e i n c r e a s i n g farm i n c o m e s ) . T h i s c o u l d be done by up-g r a d i n g t h e farm l a b o u r q u a l i t y t h r o u g h p o l i c i e s w hich w i l l l e a d t o i n c r e a s e d i n v e s t m e n t i n f a r m e r s ' e d u c a t i o n a l a t t a i n -ment. Improvements i n t h e s e e s t i m a t e s a r e however, s t i l l p o s s i b l e w i t h t h e a v a i l a b i l i t y o f new d a t a and t h e use o f an improved a n a l y t i c a l p r o c e d u r e (system o f s i m u l t a n e o u s e q u a t i o n s p r o c e d u r e , a t the m i c r o l e v e l ) . 69 B I B L I O G R A P H Y 70 BIBLIOGRAPHY B e c k e r , G.S. "Human C a p i t a l and t h e P e r s o n a l D i s t r i b u t i o n o f Income: An A n a l y t i c a l Approach." W.S. Woytinsky L e c t u r e no. 1. Ann A r b o r : U n i v . o f M i c h i g a n . 1967. . Human C a p i t a l . Second e d i t i o n . New Yo r k . Columbia U n i v e r s i t y P r e s s . (1964). 1975. Be c k e r , G.S. and C h i s w i c k , B.R. 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" A merican J o u r n a l o f A g r i c u l t u r a l Economics. v o l . 56. Fe b r u a r y 1974. pp. 84-97. J e n k i n s , G.P. C a p i t a l i n Canada: I t s S o c i a l and P r i v a t e  Performance 1965-1974. D i s c u s s i o n Paper no. 98. Economic C o u n c i l o f Canada. October 19 77. K h a l d i , N. " E d u c a t i o n and A l l o c a t i v e E f f i c i e n c y . " American  J o u r n a l o f A g r i c u l t u r a l Economics, v o l . 5 7(4) . November 1975. pp. 650-656. M i n c e r , J . "Investment i n Human C a p i t a l and P e r s o n a l Income D i s t r i b u t i o n . " J o u r n a l o f P o l i t i c a l Economy, v o l . 66. August 1958. pp. 281-302. 72 M i n c e r , J . S c h o o l i n g , E x p e r i e n c e and E a r n i n g s . N a t i o n a l Bureau o f Economic R e s e a r c h . New York. 1974. N e l s o n , R. and P h e l p s , E. "Investment i n Humans, T e c h n o l o g i c a l D i f f u s i o n and Economic Growth." American Economic Review, v o l . 6 1 ( 2 ) . May 1966. pp. 69-75. Rosen, S. "Human C a p i t a l : A Survey o f E m p i r i c a l R e s e a r c h . " Paper p r e s e n t e d a t the T h i r d World Congress o f t h e E c o n o m e t r i c S o c i e t y . T o r o n t o . 197 5. Shaw, P.R. Canada's Farm P o p u l a t i o n : A n a l y s i s o f Income and R e l a t e d C h a r a c t e r i s t i c s . P r e p a r e d f o r t h e S t a t i s t i c s Canada's 1971 Census Monograph Program. Ottawa. 1977. Welch, F. " E d u c a t i o n i n P r o d u c t i o n . " J o u r n a l o f P o l i t i c a l  Economy, v o l . 78. 1970. pp. 35-59. Weiss, Y. and L i l l i a r d , L.A. " E x p e r i e n c e , V i n t a g e , and Time E f f e c t s i n t h e Growth o f E a r n i n g s : American S c i e n t i s t s , 1960-1970." J o u r n a l o f P o l i t i c a l Economy. 1978. v o l . 86. pp. 427-448. Y o t o p o u l o s , P.A. and Nugent, J.B. Economics o f Development: E m p i r i c a l I n v e s t i g a t i o n s . Harper and Row, New Y o r k . 1976. A P P E N D I X A T a b l e s on the Comparison o f U r b a n - R u r a l E d u c a t i o n a l A t t a i n m e n t and F a m i l y Income L e v e l s 74 T a b l e A . l P e r c e n t a g e D i s t r i b u t i o n o f t h e Urban and R u r a l P o p u l a t i o n 15 Ye a r s and ov e r Showing E d u c a t i o n a l Achievement a t t h e Academic L e v e l s , Canada. 1961 and 1971. 1 9 6 1 A r e a E l e m e n t a r y Secondary Some U n i v . U n i v . Degree Canada 46.8 47.1 3.1 3.0 Urban 41.3 51.4 3.6 3.7 R u r a l 60.6 36 .4 2.0 1.0 Non-farm 58 .3 38.2 2.2 1.3 Farm 64 .5 33.5 1.5 0.5 1971 E l e m e n t a r y Secondary Some U n i v . U n i v . Degree Canada 37.2 53 .0 5.2 4.0 Urban 33.7 55.1 5.7 5.0 R u r a l 49 .3 45.6 3.3 1.8 Non-farm 48.9 45.6 3.4 2.0 Farm 50.3 45.5 3.2 1.0 Source: 1971 Census o f Canada. P r o f i l e S t u d i e s . E d u c a t i o n a l A t t a i n m e n t i n Canada. C a t a l o g u e 99-708. v o l . V - P a r t : 1. March 1977. (Table 6, p. 2 1 ) . 75: T a b l e A.2 R a t i o s o f Census Farm F a m i l y Income t o Urban F a m i l y Income, Canada, S e l e c t e d Y e a r s . R a t i o Cash Income Cash Income Non-farm f a m i l y a d j u s t e d f o r u n i t used as income i n k i n d denominator Year Source 1941 Census o f A g r i -c u l t u r e .40 1958 Sample Farm Survey . 5 4 1970 A g r i -c u l t u r e p o p u l a -t i o n l i n k a g e d a t a .67 (.72) 57 Urban f a m i l i e s headed by wage e a r n e r s .62 Urban f a m i l i e s .80 (.85) Urban f a m i l i e s ( a l l f a m i l i e s ) S o urce: Adapted from P. Shaw Farm Incomes: A Look a t L e v e l s ,  O r i g i n s , D i s t r i b u t i o n and Farm: Non-Farm Comparisons. 1977. (p. 2 7 ) . The r e l e v a n t s o u r c e s a r e : a) DBS, Economic D i f f e r e n t i a l s i n F a m i l y S i z e , Canada, 1941, B u l l . no. F-S, (which s u p p l i e d average f a m i l y income o f f a m i l i e s headed by wage e a r n e r s ) and 1941 Census o f A g r i c u l t u r e (which s u p p l i e d average t o t a l farm f a m i l y income); b) J.M. F i t z p a t r i c k , " D i s t r i b u t i o n o f Income i n Canadian A g r i c u l t u r e . " Paper p r e s e n t e d t o t h e 35th Annual M e e t i n g , Canadian A g r i c u l t u r a l Economics S o c i e t y , 1965 (which s u p p l i e d average t o t a l farm f a m i l y income a c c o r d i n g t o t h e 19 58 Sample Farm S u r v e y ) , and DBS (which s u p p l i e d e s t i m a t e s o f 1958 urban t o t a l f a m i l y income; and c) 1971 A g r i c u l t u r e - P o p u l a t i o n L i n k a g e and 1971 Census o f Canada. 7 6 A P P E N D I X B G l o s s a r y o f Terms 77 GLOSSARY OF TERMS 1. Census-farm: T h i s term i s d e f i n e d i n the 1971 Census as a farm, r a n c h o r o t h e r a g r i c u l t u r a l h o l d i n g o f one a c r e o r more w i t h s a l e s o f a g r i c u l t u r a l p r o d u c t s , d u r i n g the 12-month p e r i o d p r i o r t o the c e n s u s , o f $50 o r more. 2. O p e r a t o r : T h i s term i s used i n the Census o f A g r i c u l t u r e t o d e s i g n a t e t h e p e r s o n who i s d i r e c t l y r e s p o n s i b l e f o r the a g r i c u l t u r a l o p e r a t i o n o f t h e h o l d i n g , whether as owner, t e n a n t o r h i r e d manager. As o n l y one o p e r a t o r i s l i s t e d f o r each c e n s u s - f a r m , t h e number o f census farms i s t h e same as t h e number o f o p e r a t o r s . I f , f o r example, the h o l d i n g was o p e r a t e d as a p a r t n e r s h i p , o n l y one p a r t n e r was c o n s i d e r e d t o be t h e o p e r a t o r . 3. Farm Income (net s e l f - e m p l o y m e n t o r income from farming) -R e f e r s t o t o t a l r e c e i p t s from farm s a l e s l e s s d e p r e c i a t i o n and o p e r a t i n g expenses d u r i n g 19 70, r e g a r d l e s s o f whether the farm was o p e r a t e d by t h e respondent a l o n e o r i n p a r t n e r s h i p , o r f o r t h e re s p o n d e n t by a p a i d manager. I n the case o f a p a r t n e r s h i p , o n l y the share o f income a c t u a l l y r e c e i v e d was r e p o r t e d . Cash advances and supplementary and a s s i s t a n c e payments from governments as w e l l as acreage r e d u c t i o n payments were c o n s i d e r e d as farm income. P r o v i s i o n was made f o r r e p o r t i n g a l o s s o r no income. 78 4. C a p i t a l v a l u e s : T h i s i s the v a l u e o f c e n s u s - f a r m c a p i t a l : l a n d and b u i l d i n g s , machinery and equipment ( i n c l u d i n g a u t o m o b i l e s ) , l i v e s t o c k and p o u l t r y . Census-farm o p e r a t o r s were asked t o g i v e a v a l u e f o r l a n d and b u i l d i n g s , farm machinery and equipment on t h e i r h o l d i n g r e g a r d l e s s o f t e n u r e . The v a l u e r e p o r t e d was t o be an e s t i m a t e o f t h e market v a l u e , n o t t h e o r i g i n a l , r e p l a c e m e n t o r a s s e s s e d v a l u e . The v a l u e o f l a n d and b u i l d i n g s was t o be the v a l u e o f t h e p r o p e r t y when used f o r a g r i c u l t u r a l p u r p o s e s . F o r a r e a s s u r r o u n d i n g c i t i e s o r towns, t h e r e a l e s t a t e v a l u e f o r n o n - a g r i c u l t u r a l purposes o f t h e c e n s u s - f a r m p r o p e r t y was n o t t o be r e p o r t e d . The v a l u e t o be r e p o r t e d f o r farm machinery was t h e p r e s e n t market v a l u e - t h a t i s , t h e amount f o r which the machinery and equipment would s e l l i f t h e r e was a w i l l i n g buyer and a w i l l i n g s e l l e r , and not a f o r c e d s a l e . The number and v a l u e was t o be r e p o r t e d f o r a g r i c u l t u r a l machines on t h e h o l d i n g a t the census d a t e , r e g a r d l e s s o f whether t h e machines were owned by the o p e r a t o r o r someone e l s e . O l d machines no l o n g e r b e i n g used were not t o be r e p o r t e d . Equipment owned i n p a r t n e r s h i p was t o be r e p o r t e d on t h e c e n s u s - f a r m where i t was l o c a t e d . V a l u e s f o r the l i v e s t o c k and p o u l t r y r e p o r t e d i n the census were c o m p i l e d from d a t a on average farm v a l u e s f o r v a r i o u s t y p e s o f l i v e s t o c k and p o u l t r y o b t a i n e d by the A g r i c u l t u r a l D i v i s i o n o f S t a t i s t i c s Canada. 79 5. H i r e d a g r i c u l t u r a l l a b o u r : T o t a l weeks o f p a i d a g r i c u l t u r a l l a b o u r (15 y e a r s and over) h i r e d d u r i n g 197 0 were r e c o r d e d . The number o f p a i d a g r i c u l t u r a l w o r k ers employed on a y e a r - r o u n d b a s i s as o f June 1, 1971 was a l s o t o be enumerated. (Housework was not i n c l u d e d as a g r i c u l -t u r a l l a b o u r ) . Any p e r s o n d o i n g a g r i c u l t u r a l work on t h e c e n s u s - f a r m f o r wages, s a l a r y , commission o r on a p i e c e -r a t e l a b o u r c o n t r a c t b a s i s was r e p o r t e d as p a i d l a b o u r . T h i s i n c l u d e d p a i d managers and members o f the o p e r a t o r ' s f a m i l y r e c e i v i n g r e g u l a r o r s p e c i f i e d c a s h wages. T o t a l weeks o f a g r i c u l t u r a l work done by members o f a H u t t e r i t e C olony were i n c l u d e d as a g r i c u l t u r a l l a b o u r and f u l l - t i m e l a b o u r o f t h e c o l o n y was i n c l u d e d as p a i d y e a r round a g r i c u l t u r a l w o r k e r s . 6. S e l e c t e d e x p e n d i t u r e s : These e x p e n d i t u r e s , whether p a i d i n c a s h o r o b t a i n e d on c r e d i t , were r e p o r t e d f o r each c e n s u s - f a r m f o r the y e a r 1970. Cash wages p a i d t o h i r e d a g r i c u l t u r a l l a b o u r d i d not i n c l u d e amount p a i d f o r house-work, custom work and c o n s t r u c t i o n l a b o u r . Custom work was t o be i n c l u d e d i n the i t e m "machine r e n t a l , custom work, o r c o n t r a c t work". Taxes were the amount l e v i e d on a l l a g r i c u l t u r a l p r o p e r t y owned and o p e r a t e d by t h e r e s p o n d e n t on June 1, 1971 whether p a i d o r n o t . Rent was on a l l r e n t e d o r l e a s e d a g r i c u l t u r a l p r o p e r t y o p e r a t e d by the r e s p o n d e n t on t h a t same d a t e . F u e l and o i l used d i d not i n c l u d e t h a t used i n a u t o m o b i l e s . F i n a l l y , l i m e was n o t i n c l u d e d i n commercial f e r t i l i z e r s p u r c h a s e d . 7. V a l u e o f a g r i c u l t u r a l p r o d u c t s s o l d ( s a l e s ) : Respondents were asked t o r e p o r t the v a l u e o f a l l a g r i c u l t u r a l p r o d u c t s s o l d d u r i n g 1970 (whether r e c e i v e d by the o p e r a t o r o r some o t h e r p e r s o n ) . They were t o i n c l u d e c a s h advances f o r s t o r e d g r a i n , d e f i c i e n c y payments and patronage d i v i d e n d s f o r t h e p a r t i c u l a r p r o d u c t s i n v o l v e d . F o r t e n a n t - o p e r a t e d farms, t h e l a n d l o r d ' s share o f p r o d u c t s s o l d was t o be i n c l u d e d . P r o d u c t s o f an i n s t i t u t i o n a l farm o r H u t t e r i t e C o lony used by t h e same were c o n s i d e r e d s o l d and an e s t i m a t e o f t h e i r v a l u e i n the a p p r o p r i a t e q u e s t i o n . 8. Census d i v i s i o n : I n c l u d e s a v a r i e t y o f t i t l e s such as the a d m i n i s t r a t i v e u n i t s o f t h e p r o v i n c e s o f P r i n c e Edward I s l a n d , Nova S c o t i a , New B r u n s w i c k , Quebec, and O n t a r i o c a l l e d " c o u n t i e s " ; B r i t i s h Columbia's r e g i o n a l d i s t r i c t s ; O n t a r i o ' s r e g i o n a l m u n i c i p a l i t i e s , t e r r i t o r i a l d i s t r i c t s , d i s t r i c t m u n i c i p a l i t y and m e t r o p o l i t a n m u n i c i p a l i t y ; and f i n a l l y t h e use o f t h e t i t l e "census d i v i s i o n " i t s e l f , c r e a t e d by S t a t i s t i c s Canada i n c o l l a b o r a t i o n w i t h the p r o v i n c i a l governments o f Newfoundland, M a n i t o b a , Saskatchewan and A l b e r t a , s i n c e t h e s e p r o v i n c e s do n o t pos s e s s a d m i n i s t r a t i v e u n i t s comparable t o the c o u n t i e s o f t h e o t h e r p r o v i n c e s . 9. O f f - f a r m work d u r i n g 1970: Two q u e s t i o n s r e l a t i n g t o a l l o f f - f a r m work performed d u r i n g 19 70 by the c e n s u s - f a r m o p e r a t o r were asked . F i r s t , "How many days d i d you (the o p e r a t o r ) work o f f t h i s h o l d i n g a t p a i d a g r i c u l t u r a l and 81 n o n - a g r i c u l t u r a l work d u r i n g 1970?" Exchange work was n o t t o be i n c l u d e d . The second asked f o r t h e " k i n d o f p a i d o f f - f a r m work done d u r i n g 19 70 and number of days worked a t each." F o r a g r i c u l t u r a l work o f f the h o l d i n g , custom work was n o t t o be i n c l u d e d . O c c u p a t i o n : R e f e r s t o t h e s p e c i f i c t y p e o f work th e p e r s o n d i d on t h e j o b , as d e t e r m i n e d by t h e r e p o r t i n g o f t h e k i n d o f work, the d e s c r i p t i o n o f t h e most i m p o r t a n t d u t i e s and the j o b t i t l e . Data r e l a t e t o the r e s p o n d e n t ' s j o b i n t h e week p r i o r t o e n u meration i f he o r she had a j o b d u r i n g t h a t week o r t o t h e j o b o f l o n g e s t d u r a t i o n s i n c e J a n u a r y 1, 19 70 i f n o t employed i n t h a t week. P e r s o n s w i t h two o r more j o b s d u r i n g the r e f e r e n c e week were asked t o g i v e t h e i n f o r m a t i o n f o r the one a t w h i c h they worked t h e most h o u r s . A P P E N D I X C T a b l e s on R e c e i p t s from Wheat S a l e s (1961-71) and Comparison o f D e c l a r e d Farm Income V a l u e s w i t h Computed Farm Income V a l u e s (19 7 1 ) . 83 APPENDIX T a b l e C l T o t a l Cash R e c e i p t s from S a l e o f Wheat , Canada and t h e P r a i r i e P r o v i n c e s , 1961-71. Year Canada M a n i t o b a Saskatchewan A l b e r t a P r a i r i e P r o v i n c e s ( m i l l i o n d o l l a r s ) 1961 572 74 343 136 553 1966 999 114 627 234 975 1967 1043 123 645 246 1014 1968 973 123 579 244 946 1969 895 92 410 168 670 1970 471 52 298 93 443 1971 673 68 413 129 610 % change o f 1970 r e c e i p t s compared w i t h 1961-71 ave. -38% -43% -37% -47% -40% I n c l u d e s Canadian Wheat Board payments and net cash advance made under t h e p r o v i s i o n s o f t h e P r a i r i e G r a i n Advance Payments A c t i n 1957. Source: S e l e c t e d A g r i c u l t u r a l S t a t i s t i c s f o r Canada. Economics Branch P u b l i c a t i o n 75/10. June 1975. T a b l e 40. 84 T a b l e C.2 Comparison o f D e c l a r e d Net Farm Income w i t h Computed V a l u e s , S e l e c t e d P r o v i n c e s and Census D i v i s i o n s , Canada, 19 71. Net Farm Income P r o v i n c e / C e n s u s 2 D i v i s i o n Computed D e c l a r e d % D i f f e r e n c e Nova S c o t i a 3328 935 -256 Quebec 3577 1922 - 86 O n t a r i o 7201 1708 -322 Man i t o b a 4399 1440 -205 Saskatchewan 4550 1831 -148 B r i t i s h Columbia 4604 1026 -349 A r t h a b a s k a , Quebec 4964 2489 - 99 D i v . 1 5 , M a n i t o b a 3144 1298 -142 computed as ( g r o s s farm s a l e s - s e l e c t e d e x p e n d i t u r e s -d e p r e c i a t i o n c o s t ) . D e p r e c i a t i o n c o s t was assumed t o be 15% o f t h e v a l u e o f machinery and equipment. V a l u e o f s a l e s and e x p e n d i t u r e s and v a l u e o f machinery & equipment were t a k e n from S t a t i s t i c s Canada. 1971 Advance B u l l e t i n . Census o f Canada. C a t . no. 96-729; 96-730; 96-731 and 96-732. computed as ((B-A)/B) 100. A P P E N D I X D Income Q u e s t i o n From The Long Form 19 Census P o p u l a t i o n Q u e s t i o n n a i r e 86 INCOME QUESTION FROM THE LONG FORM 1971 CENSUS POPULATION QUESTIONNAIRE QUESTION SUR LE REVENU TIREE DU QUESTIONNAIRE COMPLET DU RECENSEMENT DE LA POPULATION DE 1971 40. INCOME FOR 1970 (State in dollars only) (a) During 1970 what were your total wages and salaries, commissions, bonuses, tips, etc.? (before any deductions) Amount * /OO C N o n . (b) During 1970 what was your nel income from self-employment or operating your own non-farm business or professional practice? State total business income less expenses of operation. If lost money, give amount and write "Loss". Amount 5 / ° ° - None (c) During 1970 what was your net income from operating a farm on your own account or in partnership? State total farm income less expenses of operation. If lost money, give amount and write "Loss". Amount * / ° ° : N o n e (d) During 1970 how much income did you receive from: 1. Family and youth allowances? Amount * t _ _ _ / ° ° - N o n e 2. Government old age pensions, Canada pensions, and Quebec pensions? Amount * /OO 1 None 3. Other government income? {e.g., unemployment insurance, veterans' pensions and allowances, welfare) Amount * / ° ° ~ N o n e 4. Retirement pensions from previous employment? Amount * /OO Z None 5. Bond and deposit interest and dividends? Amount S /OO Z None 6. Other investment income? {e.g., net rents) Amount 5 /OO C None 7. Other income? {e.g., alimony) Amount * / ° ° G None (e) During 1970 what was your total income? {a+b + c+d) J Amount * /OO C None 40. REVENU DE 1970 (Montant en dollars seulement) a) Quelaete", en 1970, le montant total de votre salaire ou traitement, de vos commissions, gratifications, pourboires, etc.{avant les deductions) Montant $ /OO O Aucun b) Quelaete\ en 1970, votre revenu net provenant d'un travail a votre compte, de I'exploitation d'une entreprise non agricole ou de I'exerci ce d'une profession? Indiquez le revenu total moms les frais d'exploitation. En cas de perte, donnez le montant et ecrivez "Perte ", Montant * /OO - A u c u n c) Quel a e'te*, en 1970, votre revenu net provenant d'une exploitation agricole a votre compte ou en association? Indiquez le revenu total mains les frais d'exploitation. En cas de perte. donnez le montant et ecrivez "Perte". Montant * / ° ° c A u c u n d) Quel a ete. en 1970 , votre revenu provenant des sources suivantes; 1. Allocations lamiiiales et allocations scolaires? Montant * / ° ° - A u c u n 2. Pensions de vieillesse de l'E*tat. du Regime de pensions du Canada et du Regime des rentes du Quebec? Montant * /OO c A u c u n 3. Autres sources publiques {par ex.. prestationsd'asiuratice-chOmag. pensions aux anciens combatlants, bien-etre social) ? Montant * / ° ° A u c u n 4. Pensions de retraite relatives a un emploi anteVieur? Montant * /OO C Aucun 5. InteVets d'obligations et de d^p6ts et dividendes? Montant * /OO 3 Aucun 6. Autre revenu de placements (par ex. • loyers nets)? Montant * /OO Aucun 7. Autre revenu (par ex., pension altmenlaire) ? Montant * /OO C Aucun e) Quel a e'te" votre revenu total en 1970 ? (a + b + c-rd) | | Montant * / ° ° 0 A u c u n 

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