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The effect of education on farm profit and productivity in Canada Cunningham-Dunlop, Catherine 1986

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THE EFFECT OF EDUCATION ON FARM PROFIT AND PRODUCTIVITY IN CANADA V by CATHERINE CUNNINGHAM-DUNLOP A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE i n THE FACULTY OF GRADUATE STUDIES Department of 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 the r e q u i r e d s t a n d a r d THE UNIVERSITY OF BRITISH COLUMBIA June, 1986 © C a t h e r i n e Cunningham-Dunlop, 1986 3 In presenting t h i s thesis i n p a r t i a l f u l f i l m e n t of the requirements for an advanced degree at the University of B r i t i s h Columbia, I agree that the Library s h a l l make i t f r e e l y a v a i l a b l e f o r reference and study. I further agree that permission for extensive copying of t h i s thesis for scholarly purposes may be granted by the head of my department or by h i s or her representatives. I t i s understood that copying or p u b l i c a t i o n of t h i s thesis for f i n a n c i a l gain s h a l l not be allowed without my written permission. Department of A& C* £M\h*fak EC(fY\0^£S> The University of B r i t i s h Columbia 2075 Wesbrook Place Vancouver, Canada V6T 1W5 Date ~3WvC |< l^ A b s t r a c t T h i s r e s e a r c h was u n d e r t a k e n t o a d d r e s s the problem of s c a r c e and c o n f l i c t i n g e v i d e n c e c o n c e r n i n g t h e e f f e c t of e d u c a t i o n on farm p r o f i t and p r o d u c t i v i t y i n Canada. The g o a l s of t h i s t h e s i s were t w o - f o l d : t o measure the r e t u r n s a c c r u i n g t o Canadian f a r m - o p e r a t o r s who have g e n e r a t e d human c a p i t a l t h r o u g h the s c h o o l i n g p r o c e s s ; and second, t o c o n s i d e r t h e i m p l i c a t i o n s of such measurements. A model r e f l e c t i n g the r o l e of e d u c a t i o n i n the d e c i s i o n - m a k i n g p r o c e s s of Canadian f a r m - o p e r a t o r s was d e v e l o p e d . Both the p r o d u c t i o n f u n c t i o n approach and the p r o f i t f u n c t i o n approach were d i s c u s s e d . The v a r i a b l e p r o f i t f u n c t i o n approach was found t o be the most a p p r o p r i a t e model f o r r e p r e s e n t i n g the r o l e of s c h o o l i n g i n the d e c i s i o n - m a k i n g p r o c e s s of the Canadian f a r m - o p e r a t o r . An e x t e n s i o n of the v a r i a b l e p r o f i t f u n c t i o n model was a l s o p r e s e n t e d , wherein o p e r a t o r on-farm l a b o u r s u p p l y and a g g r e g a t e d p h y s i c a l c a p i t a l were endogenized i n a s i m u l t a n e o u s e q u a t i o n s framework. The main s o u r c e of d a t a used i n the t h e s i s was the 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 base c o m p i l e d from i n f o r m a t i o n g a t h e r e d i n the 1971 Census and the 1981 Census. The s c h o o l i n g c o e f f i c i e n t g e n e r a l l y i n c r e a s e d as a d j u s t m e n t s were made i n the model so t h a t more c h a n n e l s of d e c i s i o n - m a k i n g were open t o the f a r m - o p e r a t o r . These a d j u s t m e n t s i n c l u d e d the a d d i t i o n of an a g r i c u l t u r a l r e s e a r c h v a r i a b l e , the a g g r e g a t i o n of c a p i t a l i n t o one i i v a r i a b l e and the movement from a g r o s s s a l e s p r o d u c t i o n f u n c t i o n t o a v a r i a b l e p r o f i t f u n c t i o n . Based on e s t i m a t i o n s of a v a r i a b l e p r o f i t f u n c t i o n , t h e m a r g i n a l p r o f i t e f f e c t of an a d d i t i o n a l y e a r of s c h o o l i n g f o r a Canadian f a r m - o p e r a t o r was computed t o be $1003 (1970 $) u s i n g d a t a from th e 1971 Census and $3161 (1980 $) u s i n g d a t a from the 1981 Census. E s t i m a t i o n s of the v a r i a b l e p r o f i t f u n c t i o n w i t h i n s t r u m e n t a l v a r i a b l e s were found t o be s u c c e s s f u l i n d e s c r i b i n g the r o l e of s c h o o l i n g i n the f a r m - o p e r a t o r ' s d e c i s i o n - m a k i n g p r o c e s s . I t was c o n c l u d e d t h a t the net r e t u r n s t o s c h o o l i n g i n Canadian a g r i c u l t u r e a r e h i g h l y p o s i t i v e . T a b l e of C o n t e n t s 1 . INTRODUCTION 1 1.1 Problem Statement 2 1.2 O b j e c t i v e s 3 1.3 T h e s i s O u t l i n e 4 2. THEORETICAL FRAMEWORK 5 2.1 G e n e r a l Approach 5 2.2 The V a l u e of E n t r e p r e n e u r i a l A b i l i t y 7 2.3 The E f f e c t s of S c h o o l i n g i n P r o d u c t i o n .10 3. MODEL SPECIFICATION 14 3.1 The P r o d u c t i o n F u n c t i o n Approach 15 3.2 The P r o f i t F u n c t i o n Approach 18 3.3 E x t e n s i o n of the Model 21 4. EMPIRICAL IMPLEMENTATION 25 4.1 Data Requirements 25 4.2 Data Sources 26 4.3 D e f i n i t i o n s of V a r i a b l e s 29 4.4 F u n c t i o n a l Form 38 5. RESULTS 42 5.1 R e s u l t s Based on 1971 Census Data 43 5.2 R e s u l t s Based on 1981 Census Data 48 5.3 E x t e n s i o n of the V a r i a b l e P r o f i t F u n c t i o n 53 5.4 Relevance of the V a l u e of S c h o o l i n g i n Canadian A g r i c u l t u r e .....64 6. SUMMARY AND CONCLUSIONS 68 7. BIBLIOGRAPHY 74 8. APPENDIX 78 8.1 Census Labour Q u e s t i o n s 79 i v L i s t o f T a b l e s T a b l e Page 1. Summary S t a t i s t i c s , 1971 C e n s u s D a t a 40 2. Summary S t a t i s t i c s , 1981 C e n s u s D a t a 41 3. E s t i m a t i o n s o f A l t e r n a t e S p e c i f i c a t i o n s o f G r o s s S a l e s P r o d u c t i o n F u n c t i o n s , WLS 1971 C e n s u s D a t a 44 4. E s t i m a t i o n s o f A l t e r n a t e S p e c i f i c a t i o n s o f V a l u e - A d d e d P r o d u c t i o n F u n c t i o n s a n d V a r i a b l e P r o f i t F u n c t i o n s , WLS, 1971 C e n s u s D a t a 47 5. E s t i m a t i o n s o f A l t e r n a t e S p e c i f i c a t i o n s o f G r o s s S a l e s P r o d u c t i o n F u n c t i o n s , WLS, 1931 C e n s u s D a t a . 4 9 6. E s t i m a t i o n s o f A l t e r n a t e S p e c i f i c a t i o n s o f V a l u e - A d d e d P r o d u c t i o n F u n c t i o n s , WLS, 1981 C e n s u s D a t a 51 7. E s t i m a t i o n o f a V a r i a b l e P r o f i t F u n c t i o n w i t h I n s t r u m e n t a l V a r i a b l e s f o r C a p i t a l a n d L a b o u r , WLS, 1971 C e n s u s D a t a .55 8. E s t i m a t i o n o f a V a r i a b l e P r o f i t F u n c t i o n w i t h I n s t r u m e n t a l V a r i a b l e s f o r C a p i t a l a n d L a b o u r , WLS, 1981 C e n s u s D a t a 56 9. Net P r e s e n t V a l u e o f an A d d i t i o n a l Y e a r o f S c h o o l i n g i n F a r m i n g , 1971 C e n s u s D a t a 65 10. Net P r e s e n t V a l u e o f an A d d i t i o n a l Y e a r o f S c h o o l i n g i n F a r m i n g , 1981 C e n s u s D a t a . . . . . . 6 6 v Acknowledgements I would l i k e t o thank my a d v i s o r , R i c k B a r i c h e l l o , f o r c o n t r i b u t i n g so much t i m e , e n t h u s i a s m , and thought t o t h i s t h e s i s . He was a s o u r c e of encouragement and guidance throughout the e n t i r e c o u r s e of the r e s e a r c h . I have b e n e f i t t e d g r e a t l y from w o r k i n g w i t h him. I would a l s o l i k e t o thank Tim H a z l e d i n e and Ashok K o t w a l f o r b e i n g on my t h e s i s committee. They both p r o v i d e d many s u g g e s t i o n s t h a t improved the q u a l i t y of t h i s t h e s i s . T h i s t h e s i s i s d e d i c a t e d t o my grandmother, M a r i c a H o r v a t , and t o my aun t , K a t i a D a v i d o v i t c h , f o r t h e i r many c o n t r i b u t i o n s t o my e d u c a t i o n . T h e i r wisdom and g e n e r o s i t y w i l l always be remembered. v i 1. INTRODUCTION A main p o l i c y g o a l i n the Canadian a g r i c u l t u r a l s e c t o r c o n t i n u e s t o be the improvement of farm incomes and p r o d u c t i v i t y . T r a d i t i o n a l l y , t h i s g o a l has been a d d r e s s e d t h r o u g h the i m p l e m e n t a t i o n of m a r k e t i n g boards and government s u b s i d y programs. In s t u d i e s c o n c e r n i n g the n o n - a g r i c u l t u r a l s e c t o r , however, t h e r e i s e v i d e n c e t h a t i n c r e a s e s i n incomes and p r o d u c t i v i t y can be a c h i e v e d t h r o u g h i n c r e a s e s i n an i n d i v i d u a l ' s e d u c a t i o n a l l e v e l . G i v e n t h i s e v i d e n c e , i t would seem t h a t i n c r e a s i n g the a v a i l a b i l i t y and q u a l i t y of r u r a l e d u c a t i o n c o u l d p o t e n t i a l l y q u a l i f y as an a l t e r n a t i v e p o l i c y t o o l f o r i m p r o v i n g farm incomes and p r o d u c t i v i t y . However, s t u d i e s s p e c i f i c a l l y r e l a t e d t o the Canadian a g r i c u l t u r a l s e c t o r a f f o r d l i t t l e c o n f i r m a t i o n of t h i s h y p o t h e s i s . In c o n t r a s t , t h e r e has been s c a r c e and c o n f l i c t i n g e v i d e n c e i n the Canadian a g r i c u l t u r a l s e c t o r c o n c e r n i n g the e f f e c t of e d u c a t i o n on incomes and p r o d u c t i v i t y . W i t h the e x c e p t i o n of B a r i c h e l l o ' s work, 1 the o n l y o t h e r major study t o g i v e a t t e n t i o n t o the v a l u e of e d u c a t i o n i n Canadian a g r i c u l t u r e i s Shaw's Canada's Farm  P o p u l a t i o n . 2 Whereas B a r i c h e l l o ' s r e s u l t s show t h a t the r e t u r n s t o s c h o o l i n g i n Canadian a g r i c u l t u r e a r e ' B a r i c h e l l o , R., "The S c h o o l i n g of Farm Youth i n Canada," Ph.D. d i s s e r t a t i o n , U n i v e r s i t y of C h i c a g o , 1979; "The P r o d u c t i v e V a l u e of S c h o o l i n g i n Canadian A g r i c u l t u r e , " D i s c u s s i o n Paper, Y a l e U n i v e r s i t y and U n i v e r s i t y of B r i t i s h C o l u m b i a , F e b r u a r y , 1984. 2Shaw, P. Canada's Farm P o p u l a t i o n , Ottawa, S t a t i s t i c s Canada, 1979. 1 2 s i g n i f i c a n t l y p o s i t i v e , Shaw's c o n c l u s i o n s i n d i c a t e t h a t the r e t u r n s t o s c h o o l i n g c o u l d a c t u a l l y be n e g a t i v e . Shaw has w r i t t e n t h a t " h i g h e r e d u c a t i o n does not produce commensurate b e n e f i t s i n f a r m i n g . That i s , a c e r t a i n l e v e l of e d u c a t i o n ( e . g . h i g h s c h o o l g r a d u a t i o n ) i s not n e c e s s a r y t o q u a l i f y f o r a farm o c c u p a t i o n , nor a r e t h e r e o b v i o u s r e t u r n s a c c r u i n g from a l a r g e l y f o r m a l or c l a s s i c a l e d u c a t i o n . I n o t h e r words, p u r s u i t of e d u c a t i o n may mean d e l a y e d e a r n i n g s f o r t h o s e who have d e c i d e d on a f a r m i n g c a r e e r , w i t h o u t any compensating i n c r e a s e i n income." 3 G i v e n t h e s e two oppposing s e t s of r e s u l t s and the f a c t t h a t no s t u d i e s have been done making use of d a t a from the 1981 c e n s u s , i t i s c l e a r t h a t a d d i t i o n a l r e s e a r c h i s w o r t h w h i l e t o measure the e f f e c t of e d u c a t i o n on farm incomes and p r o d u c t i v i t y i n Canada. T h i s i n f o r m a t i o n would be u s e f u l t o a g r i c u l t u r a l p o l i c y - m a k e r s i f e v i d e n c e showed t h a t i n c r e a s e d q u a l i t y and a v a i l a b i l i t y of r u r a l e d u c a t i o n i s a c o s t - e f f e c t i v e a l t e r n a t i v e t o the c u r r e n t p o l i c y t o o l s of m a r k e t i n g boards and government s u b s i d i e s f o r i m p r o v i n g farm incomes and p r o d u c t i v i t y . 1.1 PROBLEM STATEMENT In l i g h t of the ov e r v i e w g i v e n above, t h i s t h e s i s w i l l a d d r e s s the f o l l o w i n g problems: 1. In the few s t u d i e s t h a t have been done t o i n v e s t i g a t e the r e l a t i o n s h i p between e d u c a t i o n " and farm p r o f i t and p r o d u c t i v i t y i n Canada, c o n f l i c t i n g r e s u l t s have 3Shaw, Canada's Farm P o p u l a t i o n , p. 38-9. " E d u c a t i o n and s c h o o l i n g a r e c o n s i d e r e d synonymous. 3 c r e a t e d the demand f o r a d d i t i o n a l r e s e a r c h . 2. At p r e s e n t , t h e r e a r e no s t u d i e s i n Canada which e s t i m a t e the v a l u e of e d u c a t i o n i n a g r i c u l t u r e u s i n g d a t a from the 1981 Census. 3. As a r e s u l t of t h i s i n f o r m a t i o n gap, c u r r e n t f a r m - o p e r a t o r s , p r o s p e c t i v e e n t r a n t s , and a g r i c u l t u r a l p o l i c y - m a k e r s i n Canada a r e a l l not f u l l y i n f o r m e d as t o the e f f e c t of a d d i t i o n a l e d u c a t i o n on farm p r o f i t and p r o d u c t i v i t y . 1.2 OBJECTIVES The o v e r a l l g o a l s of t h i s t h e s i s a r e t w o - f o l d : f i r s t , t o measure the r e t u r n s a c c r u i n g t o Canadian f a r m - o p e r a t o r s who have g e n e r a t e d human c a p i t a l t h r o u g h the s c h o o l i n g p r o c e s s ; and, second, t o c o n s i d e r the i m p l i c a t i o n s of such measurements. In o r d e r t o a c h i e v e t h e s e g o a l s , s e v e r a l s p e c i f i c o b j e c t i v e s must be met. These o b j e c t i v e s a r e : t o b u i l d a model which r e f l e c t s the r o l e of e d u c a t i o n i n t h e d e c i s i o n - m a k i n g p r o c e s s of Canadian f a r m - o p e r a t o r s ; t o i d e n t i f y the r e l e v a n t v a r i a b l e s i n the model; t o c o l l e c t the d a t a needed f o r e s t i m a t i o n of the model; t o e s t i m a t e , u s i n g the above model, the e f f e c t of f a r m - o p e r a t o r s c h o o l i n g on farm p r o f i t and p r o d u c t i v i t y ; and, f i n a l l y , t o i n t e r p r e t t h i s measurement of the v a l u e of s c h o o l i n g and t o a p p l y i t t o the c o n t e x t of 4 d e c i s i o n s made by c u r r e n t f a r m - o p e r a t o r s , p r o s p e c t i v e e n t r a n t s , and a g r i c u l t u r a l p o l i c y - m a k e r s . 1.3 THESIS OUTLINE T h i s t h e s i s i s composed of s i x c h a p t e r s . In Chapter Two, the t h e o r e t i c a l framework f o r the model i s p r e s e n t e d . A t t e n t i o n i s f o c u s s e d on the human c a p i t a l approach t o the r e t u r n s t o e n t r e p r e n e u r i a l a b i l i t y and the v a l u e of e d u c a t i o n i n p r o d u c t i o n . The model i s then d e v e l o p e d i n Chapter Three w i t h d i s c u s s i o n of b o t h the p r o d u c t i o n f u n c t i o n approach and the p r o f i t f u n c t i o n a pproach. In Chapter F o u r , the d a t a s o u r c e s , d e f i n i t i o n s of v a r i a b l e s , and the c h o i c e of f u n c t i o n a l form a r e a l l d i s c u s s e d . The e m p i r i c a l r e s u l t s a r e p r e s e n t e d i n Chapter F i v e . These r e s u l t s i n c l u d e measurements of the v a l u e of s c h o o l i n g i n Canadian a g r i c u l t u r e d e r i v e d by e s t i m a t i n g a s a l e s p r o d u c t i o n f u n c t i o n and a v a r i a b l e p r o f i t f u n c t i o n u s i n g d a t a from b o t h the 1971 Census and the 1981 Census. F i n a l l y , a summary and c o n c l u s i o n s w i t h s u g g e s t i o n s f o r f u t u r e r e s e a r c h a r e g i v e n i n Chapter S i x . 2. THEORETICAL FRAMEWORK 2.1 GENERAL APPROACH N e o - c l a s s i c a l p r o d u c t i o n t h e o r y and the human c a p i t a l a p p r o a c h t o g e t h e r p r o v i d e the t h e o r e t i c a l framework f o r the model. W h i l e b o t h approaches c o n t r i b u t e t o the model -s p e c i f i c a l l y , n e o - c l a s s i c a l p r o d u c t i o n t h e o r y a l l o w s us t o make c e r t a i n a s s u m p t i o n s about the b e h a v i o r of the f a r m - o p e r a t o r , and the human c a p i t a l approach a l l o w s us t o d e t e r m i n e the economic v a l u e of human a b i l i t i e s such as s k i l l s g e n e r a t e d t h r o u g h s c h o o l i n g - they a r e a l s o i n c o n f l i c t . The two i s s u e s c a u s i n g c o n f l i c t between the approaches a r e t h e e q u i l i b r i u m a s s u m p t i o n s of p e r f e c t i n f o r m a t i o n and the methods of a g g r e g a t i n g a c r o s s i n d i v i d u a l farms, c o m m o d i t i e s , and i n p u t s . C o n s i d e r i n g the l a t t e r i s s u e f i r s t , a c c o r d i n g t o the human c a p i t a l a p p r o a c h , a g g r e g a t i o n a c r o s s d i f f e r e n t t e c h n o l o g i e s i s d e s i r a b l e so t h a t the d a t a c o n t a i n a l l t h e v a r i o u s a l t e r n a t i v e s open t o the farme r . For example, i f the d a t a s e t i s " c e n s o r e d " t o i n c l u d e o n l y homogeneous farms p r o d u c i n g t h e same commodity, the g a i n s t o management d e c i s i o n - m a k i n g from c h o o s i n g an e f f i c i e n t o u tput mix w i l l not be c a p t u r e d . On the o t h e r hand, n e o - c l a s s i c a l p r o d u c t i o n t h e o r y makes c l e a r the d i s a d v a n t a g e s of a g g r e g a t i n g a c r o s s d i f f e r e n t c o m m o d i t i e s . U n l e s s i t can be assumed t h a t a l l i n d i v i d u a l p r o d u c t i o n f u n c t i o n s a r e i d e n t i c a l and l i n e a r , t he use of a g g r e g a t e d a t a i n the 5 6 e m p i r i c a l a n a l y s i s of p r o d u c t i o n f u n c t i o n s w i l l r e s u l t i n m i s - s p e c i f i c a t i o n . The r e q u i r e d assumptions of l i n e a r i t y and i d e n t i c a l i n d i v i d u a l f u n c t i o n s a r e t o o r e s t r i c t i v e , making the c o s t s of a g g r e g a t i o n w i t h o u t m i s - s p e c i f i c a t i o n v e r y h i g h . The assumption of p e r f e c t i n f o r m a t i o n i n n e o - c l a s s i c a l p r o d u c t i o n t h e o r y a l s o imposes a c o s t l y r e s t r i c t i o n on the r e s e a r c h . I f a l l the f a r m - o p e r a t o r s d i d inde e d have p e r f e c t i n f o r m a t i o n about new i n p u t s , new p r o d u c t i o n t e c h n i q u e s , and new market o p p o r t u n i t i e s , everyone would base m a n a g e r i a l d e c i s i o n s on the same body of knowledge. There would be no r e t u r n s a c c r u i n g t o a f a r m - o p e r a t o r who t r i e d t o i n c r e a s e h i s / h e r own body of knowledge because i t i s assumed t h a t everyone a l r e a d y has a c c e s s t o the o p t i m a l l e v e l of knowledge. In t h i s sense, t h e r e would be no economic v a l u e a t t a c h e d t o e n t r e p r e n e u r i a l a b i l i t y . The human c a p i t a l a p p r o a c h , however, a l l o w s us t o h y p o t h e s i z e t h a t , i n the c o n t e x t of new i n f o r m a t i o n which i s c o s t l y t o a c q u i r e and which d e p r e c i a t e s over t i m e , d i s e q u i l i b r i a a r i s e . When t h i s o c c u r s , t h e r e a r e measurable r e t u r n s a c c r u i n g t o e n t r e p r e n e u r s h i p . T h i s approach i s c o n s i s t e n t w i t h the r e a l w o r l d g i v e n t h a t most, i f not a l l , f a r m - o p e r a t o r s base m a n a g e r i a l d e c i s i o n s on u n c e r t a i n f o r e c a s t s of p r i c e s and i m p e r f e c t l y u n d e r s t o o d p r o d u c t i o n t e c h n o l o g y . T h e r e f o r e , the assum p t i o n of p e r f e c t i n f o r m a t i o n s h a l l be r e l a x e d i n t h i s r e s e a r c h . 7 N e o - c l a s s i c a l p r o d u c t i o n t h e o r y p r o v i d e s the g e n e r a l framework f o r t h i s r e s e a r c h . W i t h i n t h i s framework, the human c a p i t a l approach goes beyond the n e o - c l a s s i c a l p r o d u c t i o n t h e o r y a ssumption t h a t d e c i s i o n - m a k i n g i s t r i v i a l . The 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 u n d e r l y i n g the model used i n t h i s r e s e a r c h a r e s e t m a i n l y i n the c o n t e x t of the human c a p i t a l approach and draw h e a v i l y from the i m p o r t a n t r e s e a r c h of S c h u l t z 5 and W e l c h 6 whose c o n t r i b u t i o n s a r e summarized i n the next two s e c t i o n s . 2.2 THE VALUE OF ENTREPRENEURIAL ABILITY The main c o n t r i b u t i o n of S c h u l t z i s the n o t i o n t h a t the v a l u e of e n t r e p r e n e u r i a l a b i l i t y i n a g r i c u l t u r e depends on the p r e v a l e n t r a t e of change of p r o d u c t i o n t e c h n o l o g y and, more g e n e r a l l y , on the d i s e q u i l i b r i a i n any a s p e c t of economic a c t i v i t y . E n t r e p r e n e u r i a l a b i l i t y , i n t u r n , i s h y p o t h e s i z e d t o be c o r r e l a t e d w i t h and best c u l t i v a t e d t h r o u g h f o r m a l s c h o o l i n g . When the s t o c k of a v a i l a b l e p r o d u c t i o n t e c h n o l o g y remains unchanged ( i . e . , i n t r a d i t i o n a l a g r i c u l t u r e ) f a r mers need o n l y t o f o l l o w the same p r o d u c t i o n t e c h n i q u e s t h a t have been used f o r g e n e r a t i o n s by t h e i r f o r e b e a r s . P r o d u c t i o n a c t i v i t i e s a r e r o u t i n e and r e p e t i t i v e r e q u i r i n g no a d j u s t m e n t s . C o n s e q u e n t l y , i n p u t t a r g e t s a r e b o t h known and unchanging 5 S c h u l t z , T.W. "The V a l u e of the A b i l i t y t o D e a l w i t h D i s e q u i l i b r i a , " J o u r n a l of Economic L i t e r a t u r e 13 (September 1975): 827-846. 6 W e l c h , 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 of P o l i t i c a l  Economy 78 (Januar y 1970): 35-59. 8 which e n a b l e s the f a r m - o p e r a t o r t o a p p l y the a v a i l a b l e r e s o u r c e s a t the o p t i m a l l e v e l and mix. Farmers i n a t r a d i t i o n a l a g r i c u l t u r e a r e thus r e l i e v e d of the n e c e s s i t y t o r e l y on e n t r e p r e n e u r i a l a b i l i t i e s such as r e s p o n d i n g e f f i c i e n t l y t o new p r o d u c t i o n o p p o r t u n i t i e s by a c c e s s i n g , p r o c e s s i n g , and a p p l y i n g the new i n f o r m a t i o n . Because t h e r e i s no need f o r the t r a d i t i o n a l f a r m - o p e r a t o r t o a c q u i r e e n t r e p r e n e u r i a l a b i l i t y , t h i s a b i l i t y has no economic v a l u e i n the c o n t e x t of t r a d i t i o n a l a g r i c u l t u r e . On the o t h e r hand, the dynamic s t a t e of a m o d e r n i z i n g a g r i c u l t u r e p r e c l u d e s t h e a s s u m p t i o n s t h a t the a v a i l a b l e r e s o u r c e s a r e b e i n g o p t i m a l l y used and t h a t e n t r e p r e n e u r i a l a b i l i t y has no economic v a l u e . An environment i s d e f i n e d as m o d e r n i z i n g i f i t i n c l u d e s "the a v a i l a b i l i t y of new c r o p v a r i e t i e s , i n n o v a t i v e p l a n t i n g methods, e r o s i o n c o n t r o l , and the a v a i l a b i l i t y of modern i n p u t s such as i n s e c t i c i d e s , f e r t i l i z e r s , and t r a c t o r s or m a c h i n e s . " 7 A f a r m - o p e r a t o r i n a m o d e r n i z i n g a g r i c u l t u r e , by d e f i n i t i o n , must t r y t o be aware of the e x i s t e n c e and i m p l i c a t i o n s of new r e s o u r c e s and p r o d u c t i o n o p p o r t u n i t i e s . New i n f o r m a t i o n i s c o n t i n u a l l y d e p r e c i a t i n g the v a l u e of o l d i n f o r m a t i o n . Even knowledge g a i n e d t h r o u g h e x p e r i e n c e becomes l e s s and l e s s u s e f u l as new knowledge r e q u i r e s t h a t the f a r m - o p e r a t o r r e v i e w and p o s s i b l y a d j u s t former d e c i s i o n s . D i s e q u i l i b r i a a r e i n e v i t a b l e i n such an environment because i t t a k e s time f o r 7 J a m i s o n , D.T. and Lau, L . J . Farmer E d u c a t i o n and Farm  E f f i c i e n c y , B a l t i m o r e : The Johns Hopkins U n i v e r s i t y P r e s s , 1982, p. 38. 9 the f a r m - o p e r a t o r t o r e a l l o c a t e r e s o u r c e s i n response t o the new p r o d u c t i o n p o s s i b i l i t i e s . Once the s e changes have been c o m p l e t e d , new o p p o r t u n i t i e s s t i l l a r i s e t h a t might change the o p t i m a l use of r e s o u r c e s and n e c e s s i t a t e a r e a l l o c a t i o n . In b o t h t r a d i t i o n a l and m o d e r n i z i n g a g r i c u l t u r e s , t h e r e a r e t a r g e t s t h a t r e p r e s e n t the o p t i m a l l e v e l and mix of i n p u t s t o be used i n the p r o d u c t i o n p r o c e s s . W h i l e t h e s e t a r g e t s a r e r e l a t i v e l y easy t o h i t by a l l f a r m - o p e r a t o r s i n a t r a d i t i o n a l a g r i c u l t u r e , t h e i r achievement i n a m o d e r n i z i n g a g r i c u l t u r e cannot be taken f o r g r a n t e d and i s d i r e c t l y r e l a t e d t o the l e v e l of e n t r e p r e n e u r i a l a b i l i t y of each f a r m - o p e r a t o r . In o r d e r t h a t the v a l u e of e n t r e p r e n e u r i a l a b i l i t y i n a m o d e r n i z i n g a g r i c u l t u r e may be c l e a r l y d e p i c t e d , I w i l l use the a n a l o g y of a comparison between t a r g e t p r a c t i c e a t a s h o o t i n g range and h u n t i n g . In a t r a d i t i o n a l a g r i c u l t u r e , as mentioned above, t a r g e t s a r e b o t h s t a t i o n a r y and easy t o d i s c e r n which i s much l i k e h i t t i n g p o s t e d t a r g e t s a t a s h o o t i n g range. By r e p e a t i n g and p r a c t i c i n g the same a c t i o n s over and o v e r , i t i s p o s s i b l e t o c o n s i s t e n t l y h i t the t a r g e t . I n c o n t r a s t , t h e t a r g e t s i n a m o d e r n i z i n g a g r i c u l t u r e a r e d i f f i c u l t t o d i s c e r n and are c o n t i n u a l l y moving and c h a n g i n g . T h i s s h o u l d b r i n g t o mind a h u n t i n g scene where the prey i s d i f f i c u l t t o see by b e i n g a l t e r n a t e l y exposed and hidden from view and i s i n motion. E n t r e p r e n e u r i a l a b i l i t y s e r v e s t h e f a r m - o p e r a t o r i n a m o d e r n i z i n g a g r i c u l t u r e the same way t h a t t r a c k i n g s k i l l s 10 a n d t h e a b i l i t y t o c o n s i s t e n t l y h i t a m o v i n g t a r g e t w o u l d s e r v e t h e h u n t e r . I n o t h e r w o r d s , e n t r e p r e n e u r i a l a b i l i t y h e l p s t h e f a r m - o p e r a t o r t o f i n d t h e t a r g e t - t h r o u g h a c c e s s i n g a n d p r o c e s s i n g new i n f o r m a t i o n - a n d t h e n t o h i t t h e t a r g e t - t h r o u g h v a r i a t i o n s i n t h e l e v e l a n d m i x o f t h e i n p u t s a n d t h e o u t p u t s . T h e s e same s k i l l s w o u l d n o t be v a l u a b l e i n a t r a d i t i o n a l a g r i c u l t u r e j u s t a s t h e h u n t i n g s k i l l s m e n t i o n e d a b o v e w o u l d n o t be u s e f u l a t a s h o o t i n g r a n g e w i t h s t a t i o n a r y t a r g e t s . T h i s i m p l i e s t h a t e n t r e p r e n e u r i a l a b i l i t y o n l y h a s e c o n o m i c v a l u e i n t h e c o n t e x t o f new i n f o r m a t i o n and d i s e q u i l i b r i a . 2.3 THE EFFECTS OF SCHOOLING IN PRODUCTION The n o t i o n t h a t t h e d i s e q u i l i b r i a c r e a t e d i n a m o d e r n i z i n g e n v i r o n m e n t g e n e r a t e t h e r e t u r n s t o s c h o o l i n g i s a l s o p r e v a l e n t i n t h e work o f W e l c h . W e l c h w r i t e s t h a t "much o f t h e ' l e v e r a g e ' a s s o c i a t e d w i t h a d d e d s c h o o l i n g i s d rawn f r o m t h e d y n a m i c a l i m p l i c a t i o n s o f c h a n g i n g t e c h n o l o g y . " 8 Of g r e a t e r c o n s e q u e n c e , h o w e v e r , i s h i s s e p a r a t i o n o f t h e r e t u r n s t o s c h o o l i n g i n p r o d u c t i o n i n t o two e f f e c t s : t h e " w o r k e r e f f e c t " a n d t h e " a l l o c a t i v e e f f e c t " . 9 The " w o r k e r e f f e c t c o r r e s p o n d s t o an i n c r e a s e i n o u t p u t w h i c h i s p o s s i b l e t h r o u g h t h e s c h o o l i n g - o h a n c e d a b i l i t y o f t h e w o r k e r t o a c c o m p l i s h more w i t h t h e g i v e n r e s o u r c e s . The w o r k e r s i m p l y becomes a " b e t t e r w o r k e r " a s a r e s u l t o f a h i g h e r s k i l l l e v e l a c q u i r e d t h r o u g h s c h o o l i n g . S p e c i f i c a l l y , t h e 8 W e l c h , " E d u c a t i o n i n P r o d u c t i o n " , p. 55. 9 W e l c h , " E d u c a t i o n i n P r o d u c t i o n " , p. 42. 11 "worker e f f e c t " i s d e f i n e d by Welch as the m a r g i n a l p r o d u c t of e d u c a t i o n which i s the " i n c r e a s e d output per u n i t change i n e d u c a t i o n h o l d i n g o t h e r f a c t o r q u a n t i t i e s c o n s t a n t . " 1 0 The key d i f f e r e n c e between the "worker e f f e c t " and the " a l l o c a t i v e e f f e c t " l i e s i n the p hrase " h o l d i n g o t h e r f a c t o r q u a n t i t i e s c o n s t a n t " . The " a l l o c a t i v e e f f e c t " c a p t u r e s the r e t u r n s t o s c h o o l i n g when t h i s r e s t r i c t i o n i s r e l a x e d and the f a c t o r q u a n t i t i e s a r e a l l o w e d t o v a r y . Whereas the "worker e f f e c t " c o r r e s p o n d s t o a more e f f i c i e n t performance of c e r t a i n p r o d u c t i o n t a s k s , the " a l l o c a t i v e e f f e c t " r e f e r s t o the e n t r e p r e n e u r i a l a b i l i t y d i s c u s s e d above i n the c o n t e x t of S c h u l t z ' s r e s e a r c h - t h a t i s , the a b i l i t y t o a c c e s s , p r o c e s s and a p p l y p r i c e and t e c h n i c a l i n f o r m a t i o n c o n c e r n i n g new p r o d u c t i o n p o s s i b i l i t i e s . T h e r e f o r e , the a l l o c a t i v e e f f e c t of a change i n e d u c a t i o n may r e s u l t i n the change of o t h e r i n p u t s and/or the i n t r o d u c t i o n of a new i n p u t t h a t would have not o t h e r w i s e been used. The d i f f e r e n c e between the "worker e f f e c t " and the " a l l o c a t i v e e f f e c t " can be demonstrated by t a k i n g the d e r i v a t i v e of a s i m p l e v a l u e - a d d e d f u n c t i o n t o f i n d the m a r g i n a l p r o d u c t of e d u c a t i o n . 1 1 G i v e n the value-added f u n c t i o n Q = P i Q i ( x , , z 1 f E,) + p 2 q 2 ( x 2 , z 2 r E 2 ) ~ PoX where the two p r o d u c t s produced, q, and q 2 , a r e each a f u n c t i o n o f : e d u c a t i o n , E; f a r m - s u p p l i e d i n p u t s , Z; and 1 0 W e l c h , " E d u c a t i o n i n P r o d u c t i o n " , p. 42. 1 1 T h i s example i s from Welch's " E d u c a t i o n i n P r o d u c t i o n " , p. 44-45. 12 p u r c h a s e d i n p u t s , X. A l s o , i t i s assumed t h a t E = E, + E 2 , Z = z, + z 2 , X = + x 2 . T o t a l l y d i f f e r e n t i a t i n g t h e s e t h r e e e q u a t i o n s g i v e s : 1 2 1= dET/dE + dE 2/dE, 0 = dz,/dE + d z 2 / d E , dX/dE = dx,/dE + d x 2 / d E . F i n a l l y , t o t a l l y d i f f e r e n t i a t i n g the value-added f u n c t i o n w i t h r e s p e c t t o E and s u b s t i t u t i n g the above t h r e e e q u a t i o n s g i v e s t h e m a r g i n a l p r o d u c t of e d u c a t i o n : 9Q/9E = p 2 ( 9 q 2 / 9 E ) + { p ^ q ^ E ) - p 2 O q 2 /9E)} dE,/dE + { p , O q ,/3z) - p 2 ( 9 q 2 / 9 z ) } dz,/dE + {p,(dq,/dx) -p 2 ( 9 q 2 / 9 x ) } d x ^ d E + { p 2 ( 3 q 2 / 9 x ) - p 0} dX/dE. The f i r s t term i n the above e q u a t i o n i s the "worker e f f e c t " of e d u c a t i o n . The next t h r e e terms r e p r e s e n t the " i n p u t a l l o c a t i o n e f f e c t " or the g a i n s from e f f i c i e n t l y a l l o c a t i n g e d u c a t i o n , f a r m - s u p p l i e d i n p u t s , and purchased i n p u t s among competing uses. The l a s t term r e p r e s e n t s the " i n p u t s e l e c t i o n e f f e c t " or the g a i n from s e l e c t i n g the " r i g h t " q u a n t i t y of purc h a s e d i n p u t s . These l a s t f o u r terms t o g e t h e r r e p r e s e n t the " a l l o c a t i v e e f f e c t " of e d u c a t i o n . 1 2 I t i s assumed t h a t s e l e c t i o n and a l l o c a t i o n of v a r i a b l e i n p u t s among competing uses i s a f u n c t i o n of e d u c a t i o n because a l l farmers do not p o s s e s s the same a b i l i t y t o d e c i d e upon o p t i m a l l e v e l s (X = f ( E ) ) . F u r t h e r m o r e , i t i s assumed t h a t the q u a n t i t y of f a r m - s u p p l i e d i n p u t s i s f i x e d i n t h e s h o r t run and the a l l o c a t i o n of the f i x e d i n p u t s among competing uses a l s o depends on e d u c a t i o n (Z^ = g ( E ) ) . P u d a s a i n i (1983), p. 510. 13 Welch emphasizes t h a t the r o l e of e d u c a t i o n i n p r o d u c t i o n i s t w o - f o l d : v a r i a t i o n s i n the l e v e l of s c h o o l i n g may l e a d t o v a r i a t i o n s i n the l e v e l of o u t p u t ( t h e "worker e f f e c t " ) ; and v a r i a t i o n s i n the l e v e l of s c h o o l i n g may l e a d t o v a r i a t i o n s i n the use of o t h e r i n p u t s which i n t u r n may l e a d t o a v a r i a t i o n i n o u t p u t ( t h e " a l l o c a t i v e e f f e c t " ) . G i v e n t h a t the "worker e f f e c t " and the " a l l o c a t i v e e f f e c t " t o g e t h e r c a p t u r e the e n t i r e r e t u r n s t o s c h o o l i n g , i t i s i m p o r t a n t t h a t the model chosen f o r t h i s r e s e a r c h a l l o w s f o r b o t h of t h e s e e f f e c t s t o be d e t e r m i n e d . 3. MODEL SPECIFICATION Faced w i t h the q u e s t i o n of what k i n d of methodology would be a p p r o p r i a t e f o r d e t e r m i n i n g the economic v a l u e of e d u c a t i o n i n a g r i c u l t u r e , i t i s f i r s t u s e f u l t o l o o k toward the n o n - a g r i c u l t u r a l s e c t o r f o r p o t e n t i a l examples. In the n o n - a g r i c u l t u r a l s e c t o r , the economic b e n e f i t s of e d u c a t i o n a r e a s s e s s e d by a n a l y z i n g a g e - e a r n i n g s p r o f i l e s or e s t i m a t i n g e a r n i n g s f u n c t i o n s . However, t h e s e same methods cannot be a p p l i e d as r e a d i l y t o the a g r i c u l t u r a l s e c t o r g i v e n t h a t f a r m e r s a r e t y p i c a l l y s e l f - e m p l o y e d . The r e t u r n t o f a r m - o p e r a t o r s ' l a b o u r i s not d i r e c t l y o b s e r v a b l e because r e p o r t e d net farm income a l s o i n c l u d e s the r e t u r n t o owned c a p i t a l . As a r e s u l t , i t would be d i f f i c u l t t o i s o l a t e f a r m - o p e r a t o r e a r n i n g s d a t a . A r e v i e w of the l i t e r a t u r e c o n c e r n i n g the e f f e c t of e d u c a t i o n i n a g r i c u l t u r e shows t h a t e d u c a t i o n has been found t o have a p o s i t i v e e f f e c t i n the f o l l o w i n g ways: 1. more s c h o o l i n g i n c r e a s e s r u r a l farm incomes and s t i m u l a t e s o u t m i g r a t i o n from the farm t o h i g h e r - e a r n i n g non-farm jo b s ( G i s s e r 1965); 2. more s c h o o l i n g of f a r m - o p e r a t o r s i n c r e a s e s the r a t e of a djustment t o c h a n g i n g optimum q u a n t i t i e s of i n p u t s and o u t p u t (Huffman 1974; P e t z e l 1978); 3. more s c h o o l i n g of f a r m - o p e r a t o r s i n c r e a s e s farm p r o f i t s (Jamison and Lau 1984); 4. more s c h o o l i n g of f a r m - o p e r a t o r s i n c r e a s e s p r o d u c t i v i t y ( G r i l i c h e s 1963 and 1964; K h a l d i 1975; Fane 1975; 1 4 15 B a r i c h e l l o 1979 and 1984; P u d a s a i n i 1983). 3.1 THE PRODUCTION FUNCTION APPROACH In s t u d i e s c o n c e r n i n g the a g r i c u l t u r a l s e c t o r , the methodology most commonly used t o a s s e s s the economic b e n e f i t s of e d u c a t i o n i s t h e e s t i m a t i o n of a g r o s s s a l e s p r o d u c t i o n f u n c t i o n w i t h e d u c a t i o n as an i n p u t . The g r o s s s a l e s p r o d u c t i o n f u n c t i o n i s e m p i r i c a l l y p r e f e r a b l e t o an e n g i n e e r i n g p r o d u c t i o n f u n c t i o n because o u t p u t e x p r e s s e d i n v a l u e terms a l l o w s us t o a g g r e g a t e a c r o s s heterogeneous p r o d u c t s . F o l l o w i n g t h i s a p p r o a c h , our g r o s s s a l e s p r o d u c t i o n f u n c t i o n has the g e n e r a l form o f : Q = q(FT, FD, CH, RL, RM, HL, LS, LB, M, L, W, E, A, R) where Q = S a l e s FT = F e r t i l i z e r and l i m e FD = Feed CH = C h e m i c a l s RL = Rented Land RM = Rented M a c h i n e r y HL = H i r e d Labour LS = L i v e s t o c k and p o u l t r y LB = Land and b u i l d i n g s M = Machinery and equipment L = Farm f a m i l y and o p e r a t o r l a b o u r time W = Weather E = E d u c a t i o n of f a r m - o p e r a t o r 16 A = " A b i l i t y " of f a r m - o p e r a t o r R = A g r i c u l t u r a l r e s e a r c h The f i r s t e l e v e n independent v a r i a b l e s ( f e r t i l i z e r and l i m e t h r o u g h weather) a r e c o n v e n t i o n a l f a c t o r i n p u t s used i n the e s t i m a t i o n of an 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 beyond the p u r e l y b i o l o g i c a l l e v e l . The l a s t t h r e e v a r i a b l e s ( e d u c a t i o n t h r o u g h a g r i c u l t u r a l r e s e a r c h ) do not q u a l i f y as c o n v e n t i o n a l and as such need some e x p l a i n i n g . C o n s i d e r i n g the arguments of S c h u l t z and Welch g i v e n i n the p r e v i o u s c h a p t e r and the numerous s t u d i e s p r e s e n t e d above, i t i s c l e a r t h a t e d u c a t i o n b e l o n g s i n an 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 . I t i s not e n t i r e l y c l e a r , however, what r o l e an " a b i l i t y " v a r i a b l e woul.d p l a y i n the p r o d u c t i o n f u n c t i o n . The main p o i n t of c o n f u s i o n i s the q u e s t i o n of j u s t e x a c t l y what i s meant by " a b i l i t y " i n t h e sense of making a farm more p r o d u c t i v e . Does a b i l i t y r e f e r t o a p erson's IQ? A l t e r n a t i v e l y , does a b i l i t y r e f e r t o a p e r s o n ' s d r i v e or energy? Even i f i t were c l e a r which d e f i n i t i o n was more a p p r o p r i a t e , we would s t i l l have the problem of how t o measure " a b i l i t y " . Measures of IQ a r e s u b j e c t t o p o s s i b l y l a r g e ( t e s t - r e t e s t ) e r r o r s 1 3 and measures of an unobserved l a t e n t v a r i a b l e such as energy a r e d i f f i c u l t , i f not i m p o s s i b l e , t o f i n d . F u r t h e r m o r e , the r o l e of " a b i l i t y " i n the p r o d u c t i o n f u n c t i o n i s ambiguous. Does " a b i l i t y " have an independent e f f e c t on p r o d u c t i v i t y beyond i t s i n d i r e c t 1 3 G r i l i c h e s , " 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 : Some Ec o n o m e t r i c Problems", p. 6. 17 e f f e c t on the number of y e a r s of s c h o o l i n g completed? A l t h o u g h t h e r e a r e no immediate answers t o t h e s e q u e s t i o n s , an " a b i l i t y " v a r i a b l e , i f a v a i l a b l e , s h o u l d s t i l l be t e s t e d f o r s i g n i f i c a n c e i n a p r o d u c t i o n f u n c t i o n . R e t u r n i n g once a g a i n t o the r e s e a r c h of S c h u l t z and Welch, we a r e reminded t h a t the v a l u e of e n t r e p r e n e u r i a l a b i l i t y g e n e r a t e d t h r o u g h t h e s c h o o l i n g p r o c e s s i s i n a l a r g e p a r t d e t e r m i n e d by t h e r a t e of f l o w of new i n p u t s i n t o a g r i c u l t u r e . Taken a s t e p f u r t h e r , the s i t u a t i o n s of d i s e q u i l i b r i a c r e a t e d by a g r i c u l t u r a l r e s e a r c h c o n t r i b u t e t o the o v e r a l l e f f e c t of s c h o o l i n g on p r o d u c t i v i t y . G r i l i c h e s (1964) and K h a l d i (1975) a r e among those who i n c l u d e d a g r i c u l t u r a l r e s e a r c h as a v a r i a b l e i n the p r o d u c t i o n f u n c t i o n . G r i l i c h e s combined p u b l i c e x p e n d i t u r e s on r e s e a r c h w i t h e x p e n d i t u r e s on e x t e n s i o n , w h i l e K h a l d i o n l y i n c l u d e d e x p e n d i t u r e s on r e s e a r c h . A l t h o u g h the g r o s s s a l e s p r o d u c t i o n f u n c t i o n i s the most common approach t a k e n i n the l i t e r a t u r e f o r e s t i m a t i n g the economic v a l u e of s c h o o l i n g i n a g r i c u l t u r e , i t i s not the most a p p r o p r i a t e approach f o r t h i s r e s e a r c h . T h i s becomes c l e a r by comparing the 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 i n a v a l u e - a d d e d f u n c t i o n 1 " t o the 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 i n a g r o s s s a l e s p r o d u c t i o n f u n c t i o n . The main d i f f e r e n c e between a v a l u e - a d d e d and a g r o s s s a l e s f u n c t i o n i s t h a t the q u a n t i t y of purchased i n p u t s ij> i n c l u d e d as an independent v a r i a b l e i n a g r o s s s a l e s f u n c t i o n and i s not 1 " R e f e r t o page 12 f o r an example of the 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 i n a value-added f u n c t i o n . 18 i n c l u d e d as an independent v a r i a b l e i n a val u e - a d d e d f u n c t i o n . C o n s e q u e n t l y , dX/dE e q u a l s z e r o i n a g r o s s s a l e s f u n c t i o n . The m a r g i n a l p r o d u c t of e d u c a t i o n i n a g r o s s s a l e s f u n c t i o n o n l y i n c l u d e s the "worker e f f e c t " and t h e " i n p u t - a l l o c a t i o n e f f e c t " , but not the " i n p u t - s e l e c t i o n e f f e c t " . The l a s t term i n the m a r g i n a l p r o d u c t e x p r e s s i o n f o r s c h o o l i n g i n a val u e - a d d e d f u n c t i o n goes t o z e r o when the f u n c t i o n becomes a g r o s s s a l e s f u n c t i o n because dX/dE e q u a l s z e r o . 3.2 THE PROFIT FUNCTION APPROACH Whereas e s t i m a t i o n of a p r o d u c t i o n f u n c t i o n w i t h an e d u c a t i o n v a r i a b l e o n l y a l l o w s f o r the "worker e f f e c t " and the " i n p u t - s e l e c t i o n e f f e c t " t o be d e t e r m i n e d , e s t i m a t i o n of a v a l u e - a d d e d or a p r o f i t f u n c t i o n b r i n g s us c l o s e r t o the g o a l of c h o o s i n g a model which a l l o w s f o r the "worker e f f e c t " , the " i n p u t - s e l e c t i o n e f f e c t " and the " i n p u t - a l l o c a t i o n e f f e c t " t o a l l be i n c l u d e d i n the measurement of s c h o o l i n g ' s m a r g i n a l p r o d u c t . The e s s e n t i a l d i f f e r e n c e between the p r o d u c t i o n f u n c t i o n approach and the p r o f i t f u n c t i o n approach i s t h a t the l a t t e r assumes p r o f i t - m a x i m i z i n g b e h a v i o r . These b e h a v i o r a l r e s t r i c t i o n s a l s o p l a y an i m p o r t a n t r o l e i n d e t e r m i n i n g which type of p r o f i t f u n c t i o n would be be s t s u i t e d f o r the model: a r e s t r i c t e d p r o f i t f u n c t i o n or an u n r e s t r i c t e d p r o f i t f u n c t i o n . Because of the extended time frame a l l o w e d f o r making and a d j u s t i n g d e c i s i o n s , the 19 u n r e s t r i c t e d p r o f i t f u n c t i o n r e q u i r e s t h a t the f i r s t o r d e r c o n d i t i o n s f o r a l l i n p u t c h o i c e s must be s a t i s f i e d . In o t h e r words, i n a maximized u n r e s t r i c t e d p r o f i t f u n c t i o n , b o t h the amount and a l l o c a t i o n of a l l the i n p u t s a r e assumed t o be a t the o p t i m a l l e v e l . T a k i n g i n t o c o n s i d e r a t i o n adjustment c o s t s , i t o f t e n i s c o n s i d e r e d u n r e a l i s t i c t o assume t h a t a l l the i n p u t s a r e a t t a r g e t l e v e l s . But more i m p o r t a n t l y h e r e , we a r e i n t e r e s t e d i n how each f a r m - o p e r a t o r a r r i v e s a t d e c i s i o n s c o n c e r n i n g t a r g e t l e v e l s and how s u c c e s s f u l he/she i s a t c a r r y i n g them o u t . T h i s i n f o r m a t i o n would be l o s t , however, i f an u n r e s t r i c t e d p r o f i t f u n c t i o n was chosen f o r the model. An u n r e s t r i c t e d p r o f i t f u n c t i o n would not a l l o w us t o d i s t i n g u i s h between the d e c i s i o n s of those f a r m - o p e r a t o r s w i t h more e d u c a t i o n and t h o s e f a r m - o p e r a t o r s w i t h l e s s because a l l d e c i s i o n s a r e assumed t o be made a t the o p t i m a l l e v e l . A r e s t r i c t e d or v a r i a b l e p r o f i t f u n c t i o n , on the o t h e r hand, does not impose the a ssumption t h a t a l l i n p u t c h o i c e s a r e a t the o p t i m a l l e v e l . W h i l e the v a r i a b l e or purchased i n p u t s a r e assumed t o be a t the p r o f i t - m a x i m i z i n g l e v e l , the f i x e d i n p u t s , b e i n g more c o s t l y t o v a r y i n the s h o r t - r u n , would not n e c e s s a r i l y be a t the p r o f i t - m a x i m i z i n g l e v e l a t a p a r t i c u l a r p o i n t i n t i m e . The d i s c r e p a n c y between the t a r g e t l e v e l f o r the f i x e d i n p u t s and the a c t u a l l e v e l of f i x e d i n p u t s i s i n v e r s e l y r e l a t e d t o the e n t r e p r e n e u r i a l a b i l i t y or e d u c a t i o n a l l e v e l of the f a r m - o p e r a t o r . In a d d i t i o n t o the advantage of i n c l u d i n g e d u c a t i o n i n the d e c i s i o n - m a k i n g 20 p r o c e s s of c h o o s i n g the l e v e l and mix of f i x e d i n p u t s , a r e s t r i c t e d p r o f i t f u n c t i o n a l s o a l l o w s the p u r c h a s e d i n p u t s t o be endogenous and d e t e r m i n e d i n p a r t by the e n t r e p r e n e u r i a l a b i l i t y of the f a r m - o p e r a t o r . The v a r i a b l e p r o f i t f u n c t i o n has the g e n e r a l form o f : 7r = 7r(Pq, Px, LS, LB, M, L, W, E, A, R) where 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 revenues l e s s e x p e n d i t u r e s on v a r i a b l e i n p u t s ( f e r t i l i z e r and l i m e , f e e d , c h e m i c a l s , r e n t e d l a n d , r e n t e d machinery, and h i r e d l a b o u r ) and where: Pq = Output p r i c e index Px = Input p r i c e s LS = L i v e s t o c k and p o u l t r y LB = Land and b u i l d i n g s M = M a c h i n e r y and equipment L = Farm f a m i l y and o p e r a t o r l a b o u r time W = Weather E = E d u c a t i o n of f a r m - o p e r a t o r A = " A b i l i t y " of f a r m - o p e r a t o r R = A g r i c u l t u r a l r e s e a r c h The l e v e l of v a r i a b l e i n p u t s i s not i n c l u d e d on the r i g h t - h a n d s i d e and can t h e r e f o r e be c o n s i d e r e d endogenous. T h i s means t h a t one l e s s i n p u t group i s h e l d c o n s t a n t , hence l e a v i n g open a n o t h e r c h a n n e l f o r e d u c a t i o n t o i n f l u e n c e the d e c i s i o n - m a k i n g p r o c e s s of the f a r m - o p e r a t o r . I t s h o u l d be 21 noted t h a t farm f a m i l y l a b o u r time i s not c o n s i d e r e d t o be a v a r i a b l e i n p u t . I f i t i s assumed t o be a v a r i a b l e i n p u t , then we a l s o have t o assume t h a t the f a r m - o p e r a t o r and a l l the members of the farm f a m i l y who a r e o l d enough t o work a r e a l l o c a t i n g t h e i r l a b o u r time o p t i m a l l y between the on-farm and o f f - f a r m l a b o u r m a r k e t s . A l t h o u g h not i m p l a u s i b l e , such an assumption may be u n r e a l i s t i c c o n s i d e r i n g adjustment c o s t s and i n f o r m a t i o n c o s t s . The c o s t s would be h i g h e s t i n a s i t u a t i o n where the f a r m - o p e r a t o r or farm f a m i l y member had never worked o f f t h e farm b e f o r e . In a d d i t i o n t o c h o o s i n g the a p p r o p r i a t e f u n c t i o n a l approach f o r e s t i m a t i o n — a v a r i a b l e p r o f i t f u n c t i o n — t h e r e a r e two o t h e r p r o c e d u r e s t h a t can be added t o the model t h a t s h o u l d a l s o h e l p us t o a c h i e v e the g o a l of h o l d i n g as l i t t l e c o n s t a n t as p o s s i b l e so t h a t the complete e f f e c t s of s c h o o l i n g on p r o d u c t i v i t y and p r o f i t can be d e t e r m i n e d . 3.3 EXTENSION OF THE MODEL The f i r s t e x t e n s i o n of the model i s t o e s t i m a t e the v a r i a b l e p r o f i t f u n c t i o n i n a s i m u l t a n e o u s e q u a t i o n s framework. Because the l e v e l and mix of the f i x e d i n p u t s , such as c a p i t a l and o p e r a t o r l a b o u r , a r e d e t e r m i n e d i n p a r t by the s c h o o l i n g l e v e l of the f a r m - o p e r a t o r , t h e s e i n p u t s s h o u l d r e a l l y be c o n s i d e r e d as endogenous. T h e r e f o r e , a systems method of e s t i m a t i o n i s n e c e s s a r y t o e l i m i n a t e the 22 s i m u l t a n e o u s e q u a t i o n b i a s which would o c c u r i f t h e s e "endogenous" f i x e d f a c t o r s were i n c l u d e d i n t h e s e t of e x p l a n a t o r y v a r i a b l e s . The second e x t e n s i o n of the model i s t o ag g r e g a t e the t h r e e main components of p h y s i c a l c a p i t a l — v a l u e of l i v e s t o c k and p o u l t r y , v a l u e of l a n d and b u i l d i n g s , and v a l u e of machinery and equipment -- i n t o one c a p i t a l v a r i a b l e . The a g g r e g a t i o n of p h y s i c a l c a p i t a l i n t o one v a r i a b l e l e a v e s room f o r the f a r m - o p e r a t o r t o use the s c h o o l i n g - e n h a n c e d e n t r e p r e n e u r i a l a b i l i t y t o a l t e r the l e v e l and mix of t h e s e c a p i t a l components. Because the a g g r e g a t i o n e q u a t i o n would be i n the same form as the f u n c t i o n b e i n g e s t i m a t e d , t h i s method r e f l e c t s t h e o p t i o n s open t o a f a r m - o p e r a t o r when c h o o s i n g the o p t i m a l l e v e l s and mix of the v a r i o u s components of p h y s i c a l c a p i t a l . However, t h e r e i s a t r a d e o f f i n v o l v e d i n c h o o s i n g the method of a g g r e g a t i o n as a way t o reduce the number of exogenous v a r i a b l e s . A l t h o u g h a g g r e g a t i o n i s d e s i r a b l e i n the c o n t e x t of the human c a p i t a l approach, i t may l e a d t o m i s - s p e c i f i c a t i o n of the f u n c t i o n when the r e s t r i c t i o n s of n e o - c l a s s i c a l p r o d u c t i o n t h e o r y a r e a l s o c o n s i d e r e d . T a k i n g t h e s e two p o i n t s i n t o c o n s i d e r a t i o n , the s t r u c t u r a l and reduced form e q u a t i o n s of the extended model a r e : if = J r ( P q , Px, K°, L°, W, E, A, R) K° = k ( E , Pq, Px, OFFI, HLWR) 23 L° = M E , Pq, Px, OFFW, HLWR, K°) where K° = P r e d i c t e d a g g r e g a t e d p h y s i c a l c a p i t a l L° = P r e d i c t e d farm f a m i l y and o p e r a t o r l a b o u r time Pq = Output p r i c e i n d e x Px = Input p r i c e s W = Weather E = E d u c a t i o n of f a r m - o p e r a t o r A = " A b i l i t y " of f a r m - o p e r a t o r R = A g r i c u l t u r a l r e s e a r c h OFFI = O f f - f a r m income HLWR = H i r e d l a b o u r wage r a t e OFFW = O f f - f a r m wage r a t e The s p e c i f i c a t i o n of the f i x e d f a c t o r e q u a t i o n s i s guid e d by f a c t o r demand t h e o r y . S p e c i f i c a l l y , by H o t e l l i n g ' s Lemma we know t h a t a f i r m ' s demand f u n c t i o n f o r a f a c t o r depends on the p r i c e of out p u t and the p r i c e s of a l l the i n p u t s . 1 5 T h e r e f o r e , the e q u a t i o n s f o r p r e d i c t e d c a p i t a l and p r e d i c t e d farm f a m i l y and o p e r a t o r l a b o u r time i n c l u d e Pq, Px and HLWR among the s e t of e x p l a n a t o r y v a r i a b l e s . O f f - f a r m income i s i n c l u d e d i n the c a p i t a l e q u a t i o n t o r e p r e s e n t c r e d i t - w o r t h i n e s s of the f a r m - o p e r a t o r . The v a r i a b l e s i n c l u d e d i n the l a b o u r e q u a t i o n a r e s i m i l a r t o those i n c l u d e d i n a farm f a m i l y l a b o u r s u p p l y f u n c t i o n i n a study done by Huffman (1980) except t h a t 1 5 V a r i a n , Microeconomic A n a l y s i s , p. 52-54. 24 p r e d i c t e d c a p i t a l i s a l s o i n c l u d e d and p r i c e s of v a r i a b l e i n p u t s a r e used i n s t e a d of e x p e n d i t u r e s on v a r i a b l e i n p u t s . The p r e d i c t e d c a p i t a l v a r i a b l e i s i n c l u d e d i n the l a b o u r e q u a t i o n t o r e f l e c t the v a l u e of f a m i l y and o p e r a t o r l a b o u r time on the farm. The h i g h e r the l e v e l of c a p i t a l on the farm, the more v a l u a b l e l a b o u r time on the farm becomes. As a r e s u l t , more time w i l l be a l l o c a t e d t o on-farm l a b o u r . A c c o r d i n g t o Huffman, the l e v e l of e d u c a t i o n a l s o a f f e c t s b o th on farm and o f f - f a r m work d e c i s i o n s . W h i l e i n c r e a s e d e d u c a t i o n l e a d s t o i n c r e a s e d farm e f f i c i e n c y , the net e f f e c t on both on-farm and o f f - f a r m l a b o u r s u p p l y i s ambiguous. I f i n c r e a s e d s c h o o l i n g c a u s e s the v a l u e of the f a r m - o p e r a t o r ' s time t o go up even more o f f the farm than on the farm, the r e s u l t w i l l be a d e c i s i o n t o work l e s s on the farm. S i m i l a r l y , i f the v a l u e of the f a r m - o p e r a t o r ' s time i s h i g h e r on the farm (as a r e s u l t of an i n c r e a s e i n farm e f f i c i e n c y ) , then more time w i l l be a l l o c a t e d t o on-farm work. 4. EMPIRICAL IMPLEMENTATION 4.1 DATA REQUIREMENTS In the p r e c e d i n g c h a p t e r , t h r e e models were p r e s e n t e d : a g r o s s s a l e s p r o d u c t i o n f u n c t i o n , a v a r i a b l e p r o f i t f u n c t i o n , and an extended v e r s i o n of the v a r i a b l e p r o f i t f u n c t i o n . T h i s t h e s i s i n c l u d e s e m p i r i c a l a n a l y s i s of a l l t h r e e models based on d a t a from t h e 1971 Census and the 1981 Census. The f o l l o w i n g v a r i a b l e s were i d e n t i f i e d as r e l e v a n t and ar e r e q u i r e d f o r t h e e s t i m a t i o n of the e f f e c t s of s c h o o l i n g i n a g r o s s s a l e s p r o d u c t i o n f u n c t i o n and i n a v a r i a b l e p r o f i t f u n c t i o n : 1. S a l e s of a g r i c u l t u r a l p r o d u c t s (Q) 2. F e r t i l i z e r and l i m e (FT) 3. Feed (FD) 4. C h e m i c a l s (CH) 5. Rented Land (RL) 6. Rented machinery (RM) 7. H i r e d Labour (HL) 8. V a r i a b l e p r o f i t (TT) 9. Output p r i c e i n d e x (Pq) 10. I n p u t p r i c e s (Px) 11. L i v e s t o c k and p o u l t r y (LS) 12. Land and b u i l d i n g s (LB) 13. M a c h i n e r y and equipment (M) 14. Farm f a m i l y and o p e r a t o r l a b o u r time (L) 25 26 15. Weather and random d i s t u r b a n c e s (W) 16. E d u c a t i o n of f a r m - o p e r a t o r (E) 17. " A b i l i t y " of f a r m - o p e r a t o r (A) 18. A g r i c u l t u r a l r e s e a r c h (R) 19. O f f - f a r m income (OFFI) 20. O f f - f a r m wage r a t e (OFFW) B e f o r e p r e s e n t i n g the e m p i r i c a l r e s u l t s , i t i s n e c e s s a r y t o d e s c r i b e the d a t a s o u r c e s used and t o d i s c u s s the a p p r o p r i a t e forms of measurement f o r each v a r i a b l e . A l s o , the a p p r o p r i a t e form of the f u n c t i o n s b e i n g e s t i m a t e d must be c o n s i d e r e d . 4.2 DATA SOURCES The main sou r c e of d a t a used i n the t h e s i s i s t h e 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 . T h i s d a t a base was c r e a t e d i n 1971 by S t a t i s t i c s Canada i n an e f f o r t t o combine t h e i n f o r m a t i o n r e t r i e v e d i n bo t h the Census of A g r i c u l t u r e and the Census of P o p u l a t i o n . W h i l e the Census of A g r i c u l t u r e was c a r r i e d out i n 1971 and 1981 w i t h a 100% sample coverage of a l l farms, the Census of P o p u l a t i o n randomly sampled one i n t h r e e i n 1971 and one i n f i v e i n 1981. T h e r e f o r e , t h e r e i s a one i n f i f t e e n chance t h a t the same person f i l l e d out the Census of P o p u l a t i o n q u e s t i o n a i r e i n both census y e a r s . C o n s e q u e n t l y , the d a t a i s p r e d i s p o s e d towards use i n c r o s s s e c t i o n a l models r a t h e r than t i m e - s e r i e s models. 27 In a d d i t i o n t o i n c o m p a t i b i l i t y w i t h t i m e - s e r i e s models, o t h e r l i m i t a t i o n s of the Ag-Pop d a t a base must a l s o be c o n s i d e r e d . Because a c c e s s t o t h e i n f o r m a t i o n g a t h e r e d i n a census i s s u b j e c t t o c e r t a i n c o n f i d e n t i a l i t y r u l e s , v a r i a b l e s i n the Ag-Pop d a t a base a r e not a v a i l a b l e a t the i n d i v i d u a l farm l e v e l f o r each census d i v i s i o n ( c a l l e d w e i g h t i n g a r e a s i n the 1981 c e n s u s ) . O b s e r v a t i o n s a r e o n l y a v a i l a b l e a t the census d i v i s i o n l e v e l i n the form of randomly rounded a v e r a g e s . S i n c e t h e r e i s no gu a r a n t e e t h a t the census d i v i s i o n s have been d e f i n e d t o i n c l u d e o n l y a s e t of farms f a c i n g s i m i l a r p r o d u c t i o n p o s s i b i l i t i e s , t h e ag g r e g a t e census d i v i s i o n a verages c o u l d h i d e or " b l u r " a c t u a l i n f o r m a t i o n from i n d i v i d u a l farms c o n t a i n e d i n the raw d a t a . F u r t h e r m o r e , even i f t h e i n d i v i d u a l farm r e s p o n s e s t o census q u e s t i o n s were a v a i l a b l e , t h e r e i s no way t o v e r i f y t h a t t h e s e r e p l i e s a r e a c c u r a t e . An a d d i t i o n a l d i s a d v a n t a g e of u s i n g census d a t a i s the f a c t t h a t any one y e a r i s r e a l l y j u s t a "snapshot" of the o v e r a l l moving p i c t u r e of a g r i c u l t u r e . A census y e a r may not be t y p i c a l of the g e n e r a l l o n g e r term s t a t e of the a g r i c u l t u r a l s e c t o r . A l t h o u g h 1980 can be c o n s i d e r e d a t y p i c a l year f o r Canadian a g r i c u l t u r e , 1970 was u n u s u a l . In 1970, Canadian wheat f a r m e r s were i n v o l v e d i n a f e d e r a l scheme c a l l e d Lower I n v e n t o r i e s f o r Tommorrow (LIFT) d e s i g n e d t o reduce the a c c u m u l a t i o n of u n s o l d wheat s t o c k s by l i m i t i n g a c reage f o r wheat p l a n t i n g s . As a r e s u l t , Canadian wheat f a r m e r s r e c e i v e d 38% l e s s i n wheat s a l e s 28 d u r i n g 1970 than the 1961-1971 average (Labadan 1979). T h e r e f o r e , g e n e r a l i z a t i o n s based on r e s u l t s from a n a l y s i s u s i n g 1971 census d a t a must be made w i t h caution.. W h i l e the Ag-Pop d a t a base cannot p r o v i d e the i d e a l d a t a s e t f o r t h i s s t u d y - which would be c r o s s - s e c t i o n a l o b s e r v a t i o n s a t the i n d i v i d u a l farm l e v e l f o r a s e r i e s of y e a r s - i t i s s t i l l t h e b e s t d a t a source of which I am aware f o r the i n f o r m a t i o n r e q u i r e d i n the t h e s i s . The f o l l o w i n g t y p e s of farms have been e x c l u d e d from the d a t a s e t a l r e a d y o b t a i n e d from the Ag-Pop d a t a base: 1. A l l census-farms t h a t f a l l i n t o the c a t e g o r y of i n s t i t u t i o n , community p a s t u r e , H u t t e r i t e c o l o n y , or " o t h e r " ; 2. A l l "hobby farms" 1 6 w i t h t o t a l s a l e s of a g r i c u l t u r a l p r o d u c t s l e s s than $2,500 i n 1970 and $6850 i n 1980 ($6850 i s the 1980$ e q u i v a l e n t of $2500 i n 1970); 3. A l l census farms f o r which v a r i a b l e p r o f i t ( g r o s s v a l u e of 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 e x p e n d i t u r e on f e e d , c h e m i c a l s , f e r t i l i z e r , c a s h wages, l a n d r e n t , and machine r e n t a l s ) i s n e g a t i v e or z e r o . A l l the v a r i a b l e s used i n the e m p i r i c a l a n a l y s i s , e x cept f o r a g r i c u l t u r a l r e s e a r c h and the ouput p r i c e i n d e x , a r e from the Ag-Pop L i n k a g e and a r e i n the form of census 1 6 C e n s u s farms were d e f i n e d as a farm, r a n c h or o t h e r a g r i c u l t u r a l h o l d i n g w i t h s a l e s of 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 t h e p a s t t w e l v e months of $250 or more i n the 1981 Census of A g r i c u l t u r e and $50 or more i n 'the 1971 Census of A g r i c u l t u r e . 29 d i v i s i o n a v e r a g e s per farm. The s o u r c e s f o r the a g r i c u l t u r a l r e s e a r c h v a r i a b l e and the o u t p u t p r i c e index a r e g i v e n w i t h the v a r i a b l e d e f i n i t i o n s below. 4.3 DEFINITIONS OF VARIABLES 1. S a l e s of A g r i c u l t u r a l P r o d u c t s (Q) T h i s v a r i a b l e i s d e f i n e d t o i n c l u d e o n l y t h o s e o b s e r v a t i o n s of t o t a l g r o s s v a l u e of a g r i c u l t u r a l p r o d u c t s s o l d t h a t were g r e a t e r than $2500 i n 1970 and g r e a t e r than $6850 i n 1980. A l s o i n c l u d e d i n the v a r i a b l e a r e l a n d l o r d ' s share of p r o d u c t s s o l d , M a r k e t i n g Board, Canadian Wheat Board, and o t h e r agency payments r e c e i v e d i n 1980 ( 1 9 7 0 ) , d i r e c t s a l e s ( e . g . from r o a d s i d e s t a n d s ) , c a s h .advances, s t a b i l i z a t i o n and d e f i c i e n c y payments. 2. F e r t i l i z e r and l i m e (FT) T h i s i n p u t i s measured i n v a l u e terms r a t h e r than p h y s i c a l q u a n t i t y terms. E x p e n d i t u r e on l i m e i s not a v a i l a b l e f o r 1970 i n the Ag-Pop L i n k a g e , so o n l y e x p e n d i t u r e on f e r t i l i z e r i s i n c l u d e d f o r 1970. The 1980 v a r i a b l e i n c l u d e s e x p e n d i t u r e on both f e r t i l i z e r and l i m e . 3. Feed (FD) A l s o measured i n v a l u e terms, t h i s v a r i a b l e i s d e f i n e d as e x p e n d i t u r e on f e e d i n 1980 (1970). Feed i n c l u d e s hay, g r a i n , mixed f e e d s , c o n c e n t r a t e s , and supplements. 4. C h e m i c a l s (CH) 30 E x p e n d i t u r e s on i n s e c t i c i d e s , h e r b i c i d e s , f u n g i c i d e s , p e s t i c i d e s a r e a l l i n t h i s v a r i a b l e which i s e x p e n d i t u r e s on a g r i c u l t u r a l c h e m i c a l s i n 1980 (1970). Rented Land (RL) T h i s v a r i a b l e i s d e f i n e d as r e n t p a i d i n 1980 (1970) f o r a g r i c u l t u r a l l a n d and b u i l d i n g s r e n t e d or l e a s e d from o t h e r s . A l s o i n c l u d e d i n t h i s v a r i a b l e a r e t a x e s p a i d by the f a r m - o p e r a t o r on the r e n t e d l a n d and b u i l d i n g s . Rent i n c l u d e s b oth r e n t p a i d on a c a s h b a s i s and on a share b a s i s . Rented Machinery (RM) T h i s v a r i a b l e i s d e f i n e d as e x p e n d i t u r e s i n 1980 (1970) on machine r e n t a l and custom work (and c o n t r a c t work i n 1970). H i r e d Labour (HL) The h i r e d l a b o u r v a r i a b l e i n c l u d e s e x p e n d i t u r e s i n 1980 (1970) on 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 . T h i s v a r i a b l e does not i n c l u d e amount p a i d f o r housework or custom work, (or c o n s t r u c t i o n l a b o u r i n 1970). V a r i a b l e P r o f i t (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 t o t a l g r o s s v a l u e of 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 , Q) minus e x p e n d i t u r e s on v a r i a b l e i n p u t s ( f e e d , c h e m i c a l s , f e r t i l i z e r , h i r e d l a b o u r , l a n d and machine r e n t a l ) . O nly o b s e r v a t i o n s w i t h p o s i t i v e v a r i a b l e p r o f i t a r e i n c l u d e d . 31 9. Output P r i c e Index (Pq) T h i s i s one of the few v a r i a b l e s t h a t does not come from the Ag-Pop L i n k a g e . P r o v i n c i a l farm p r i c e s f o r 1980 and 1970 were s u p p l i e d by S t a t i s t i c s Canada f o r the f o l l o w i n g c o mmodities: p o t a t o e s , hogs, c a t t l e , c a l v e s , a p p l e s , s m a l l f r u i t s , s o f t f r u i t s , v e g e t a b l e s , g r a i n s , and o i l s e e d s . Farm p r i c e s f o r d a i r y ( i n d u s t r i a l and f l u i d m i l k ) and f o r p o u l t r y (eggs and b r o i l e r s ) were found i n the D a i r y Review and the P o u l t r y Market  Review, r e s p e c t i v e l y . Because the e m p i r i c a l a n a l y s i s i n v l o v e s a l l of a g r i c u l t u r e and not j u s t one i n d u s t r y w i t h i n a g r i c u l t u r e ( e . g . d a i r y ) , an index was c o n s t r u c t e d f o r the ou t p u t p r i c e s . P r o v i n c i a l farm p r i c e s were n o r m a l i z e d by the c o r r e s p o n d i n g p r i c e s i n the numeraire r e g i o n . The r e s u l t i n g p r i c e r a t i o s were then w e i g h t e d by the farm c a s h r e c e i p t s f o r each commodity w i t h i n each p r o v i n c e f o r the 1970 i n d e x , and by farm s a l e s f o r a broader commodity g r o u p i n g (e.g. f r u i t s and v e g e t a b l e s , r e d meats, p o u l t r y , e t c . ) w i t h i n each census d i v i s i o n f o r the 1980 i n d e x . 10. Input P r i c e s (Px) (Pf and P I ) I d e a l l y , we would l i k e i n p u t p r i c e s f o r the f o l l o w i n g f a c t o r s : f e e d , c h e m i c a l s , f e r t i l i z e r , h i r e d a g r i c u l t u r a l l a b o u r , r e n t e d l a n d , and r e n t e d machines f o r each census d i v i s i o n or a t l e a s t f o r each p r o v i n c e . However, o n l y d a t a on f e r t i l i z e r p r i c e s ( f o r 1980 o n l y ) and h i r e d l a b o u r wage r a t e s a r e a v a i l a b l e . The 32 f e r t i l i z e r p r i c e (1980) i s a c t u a l l y a proxy d e r i v e d by d i v i d i n g e x p e n d i t u r e on f e r t i l i z e r (and l i m e ) by the t o t a l amount (tonnes) used on c r o p l a n d , tame hay, and improved p a s t u r e . The h i r e d l a b o u r wage r a t e i s a l s o a p r o x y d e r i v e d i n much the same way: e x p e n d i t u r e on cash wages f o r h i r e d a g r i c u l t u r a l l a b o u r (HL) i s d i v i d e d by t o t a l weeks of p a i d h i r e d a g r i c u l t u r a l l a b o u r ( i n c l u d i n g b o t h y e a r - r o u n d and s e a s o n a l l a b o u r ) f o r 1980 and f o r 1970. The c o e f f i c i e n t of these, i n p u t p r i c e p r o x i e s i n the e s t i m a t e d p r o f i t f u n c t i o n c o u l d be e i t h e r p o s i t i v e or n e g a t i v e depending on whether q u a l i t y v a r i a t i o n s or r e g i o n a l v a r i a t i o n s dominate. 11. L i v e s t o c k and P o u l t r y (LS) In o r d e r t o r e f l e c t the s e r v i c e f l o w from the c a p i t a l component of l i v e s t o c k and p o u l t r y , the s t o c k of l i v e s t o c k and p o u l t r y ( e x p r e s s e d i n v a l u e terms) was m u l t i p l i e d by 0.08 i n both 1980 and 1970. T h i s c o e f f i c i e n t was a r r i v e d a t by assuming the i n t e r e s t r a t e t o be 0.06 and the d e p r e c i a t i o n r a t e of l i v e s t o c k and p o u l t r y t o be 0.02. T h i s d e p r e c i a t i o n r a t e i s somewhat a r b i t r a r y however, g i v e n t h a t l i v e s t o c k c o u l d a c t u a l l y a p p r e c i a t e over a c e r t a i n p e r i o d of t i m e . 12. Land and B u i l d i n g s (LB) T h i s v a r i a b l e was a l s o d e f i n e d by m u l t i p l y i n g the s t o c k of r e n t e d and owned l a n d and b u i l d i n g s ( e x p r e s s e d i n v a l u e terms) by the annual c o s t of l a n d and b u i l d i n g s , 0.03 i n 1970 and 0.01 i n 1980. The an n u a l c o s t was 33 d e r i v e d by assuming i n t e r e s t r a t e s f o r b o t h y e a r s t o be 0.06 and an a p p r e c i a t i o n r a t e of 0.03 i n 1970 and 0.05 i n 1980. A l t h o u g h measurements of l a n d i n v a l u e terms c o u l d be s u b j e c t t o s i t e - b i a s , measurements of l a n d i n a c r e s c o u l d a l s o i n v o l v e e r r o r s due t o d i v e r s i t y of l a n d f e r t i l i t y and s o i l q u a l i t y ( K h a l d i 1975, p.651) Measurement i n terms of v a l u e i s e m p i r i c a l l y p r e f e r a b l e so t h a t the t h r e e components of p h y s i c a l c a p i t a l can be a g g r e g a t e d i n t o one c a p i t a l v a r i a b l e e x p r e s s e d i n v a l u e terms. 13. M a c h i n e r y and Equipment (M) T h i s v a r i a b l e i s d e f i n e d i n the same way as the o t h e r two p h y s i c a l c a p i t a l v a r i a b l e s : the s t o c k of r e n t e d and owned machinery and equipment ( i n v a l u e terms) i s m u l t i p l i e d by a n n u a l c o s t which i s 0.17 i n 1970 and 0.21 i n 1980. The a n n u a l c o s t i s based on an i n t e r e s t r a t e of 0.06 i n b o t h y e a r s and a d e p r e c i a t i o n r a t e of 0.11 i n 1970 and 0.15 i n 1980. The d e p r e c i a t i o n r a t e s a r e a compromise between the t r u e economic d e p r e c i a t i o n r a t e and the a l l o w a b l e c a p i t a l c o s t a l l o w a n c e . 14. Farm F a m i l y and O p e r a t o r Labour Time (L) (LHR, LDY, and OCC) (CH) The i d e a l s p e c i f i c a t i o n of t h i s v a r i a b l e would be a measure of the time spent w o r k i n g on t h e farm by a l l the u n p a i d farm f a m i l y members, i n c l u d i n g the f a r m - o p e r a t o r . U n f o r t u n a t e l y , such d a t a a r e not a v a i l a b l e and we must s e t t l e f o r a v a r i a b l e t h a t o n l y 34 measures the f a r m - o p e r a t o r ' s time w o r k i n g on t h e farm. There a r e t h r e e d i f f e r e n t v a r i a b l e s , a l l from the Ag-Pop L i n k a g e , t h a t c o u l d be used t o measure the f a r m - o p e r a t o r ' s time w o r k i n g on the farm. The f i r s t v a r i a b l e (LHR) i s d e r i v e d by s u b t r a c t i n g t o t a l hours worked o f f the farm by the o p e r a t o r from t o t a l hours worked (both on and o f f the farm) by the o p e r a t o r . The v a r i a b l e i s d e f i n e d d i f f e r e n t l y f o r 1970 and 1 9 8 0 . 1 7 The main d i f f e r e n c e between the census q u e s t i o n s i n the two y e a r s i s t h a t i n 1970, t o t a l hours worked by the o p e r a t o r was found by m u l t i p l y i n g hours u s u a l l y worked each week by t o t a l number of weeks worked, w h i l e i n 1980, number of hours worked l a s t week was m u l t i p l i e d by t o t a l number of weeks worked. The q u a l i t y of t h i s v a r i a b l e i n each year depends on whether " l a s t week" was a u s u a l week or not ( i n 1980) and on whether the f a r m - o p e r a t o r a c c u r a t e l y remembered the " u s u a l " number of hours worked per week thr o u g h o u t the year ( i n 1970). G i v e n t h a t " l a s t week" i s not l i k e l y t o always be a t y p i c a l week, i t would seem t h a t the 1970 d e f i n i t i o n of the v a r i a b l e i s p r e f e r a b l e t o the 1980 d e f i n i t i o n . An a l t e r n a t e v a r i a b l e (LDY) was d e r i v e d t o a v o i d u s i n g the s u s p e c t " t o t a l number of hours worked by the o p e r a t o r " i n e i t h e r y e a r . I n s t e a d , t o t a l time worked by the o p e r a t o r (both on and o f f the farm) was assumed t o be c o n s t a n t a t 300 days per y e a r . O p e r a t o r on-farm l a b o u r 1 7 R e f e r t o the appendix f o r examples of the census q u e s t i o n s used f o r each year t o d e r i v e t h i s v a r i a b l e . 35 time was found by s u b t r a c t i n g t o t a l number of o f f - f a r m days from 300. T h i s same measure of on-farm l a b o u r time was used by G r i l i c h e s (1964). A t h i r d measure of o p e r a t o r on-farm l a b o u r time was a l s o found i n the Ag-Pop L i n k a g e . T h i s v a r i a b l e (OCC) i s d e f i n e d as the p e r c e n t of f a r m - o p e r a t o r s who d e c l a r e f a r m i n g t o be t h e i r main o c c u p a t i o n . F i n a l l y , i n o r d e r t o r e f l e c t younger f a m i l y members' u n p a i d c o n t r i b u t i o n t o farm l a b o u r , a v a r i a b l e d e f i n e d as the number of c h i l d r e n aged between t h i r t e e n and e i g h t e e n y e a r s o l d (CH) was a l s o o b t a i n e d from the Ag-Pop L i n k a g e . 15. Weather and Random D i s t u r b a n c e s (W) I d e a l l y , we would l i k e a weather inde x t h a t v a r i e d a c r o s s census d i v i s i o n s or p r o v i n c e s t o be i n c l u d e d as an exogenous v a r i a b l e a f f e c t i n g b o t h p r o d u c t i v i t y and p r o f i t s . However, t h i s i n f o r m a t i o n i s u n a v a i l a b l e i n the Ag-Pop L i n k a g e and has not been o b t a i n e d e l s e w h e r e . Weather i s one of the o m i t t e d v a r i a b l e s . 16. E d u c a t i o n of Farm-Operator (E) T h i s v a r i a b l e i s d e f i n e d as the t o t a l number of y e a r s c o m p l e t e d by the f a r m - o p e r a t o r i n s c h o o l . Y e a r s spent i n e l e m e n t a r y , s e c o n d a r y , p o s t - s e c o n d a r y , and u n i v e r s i t y a r e a l l i n c l u d e d . A l t h o u g h t h e r e might be d i f f e r e n c e s i n q u a l i t y of s c h o o l i n g between d i f f e r e n t a r e a s , s c h o o l i n g i s s t i l l c o n s i d e r e d t o be a s t a n d a r d i z e d p r o d u c t i v e i n p u t t h a t is^ comparable between a r e a s (Welch 1966, p.380) W h i l e time spent i n 36 s c h o o l i s the b e s t measure of how much s c h o o l i n g a p e r s o n has had, i t i s s t i l l not c l e a r what i s the best u n i t of measurement t o be used. For example, i f the Cobb-Douglas f u n c t i o n a l form i s chosen f o r t h e e m p i r i c a l a n a l y s i s , s h o u l d the s c h o o l i n g v a r i a b l e be i n c l u d e d i n n a t u r a l l o g a r i t h m form i n the same manner as a l l the o t h e r v a r i a b l e s , or s h o u l d the s c h o o l i n g v a r i a b l e be i n c l u d e d i n a d i f f e r e n t form? The d a t a was s u b j e c t e d t o a t e s t t o compare the method of measuring s c h o o l i n g i n n a t u r a l l o g a r i t h m form t o the a l t e r n a t i v e method of measuring s c h o o l i n g i n a q u a d r a t i c form. The t e s t r e s u l t s i n d i c a t e d t h a t the n a t u r a l l o g a r i t h m form of measurement i s a p p r o p r i a t e f o r the s c h o o l i n g v a r i a b l e . 17. " A b i l i t y " of Farm-Operator (A) As mentioned i n Chapter Three, an " a b i l i t y " v a r i a b l e s h o u l d be i n c l u d e d on t h e o r e t i c a l grounds but i t i s v e r y d i f f i c u l t t o f i n d a s a t i s f a c t o r y measure of such a v a r i a b l e . T h e r e f o r e , i n a d d i t i o n t o weather, " a b i l i t y " w i l l a l s o be o m i t t e d i n the e m p i r i c a l model. What a r e the consequences of o m i t t i n g an " a b i l i t y " v a r i a b l e ? Or, more t o the p o i n t , what w i l l be the e f f e c t on t h e s c h o o l i n g c o e f f i c i e n t i f " a b i l i t y " i s o m i t t e d ? Fane (1975) s t a t e s t h a t i f the d a t a a r e grouped by county (or census d i v i s i o n ) , the s p u r i o u s b i a s t o 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 o m i t t i n g " a b i l i t y " would most l i k e l y be even s m a l l e r than the b i a s t h a t would 37 o c c u r i f the d a t a were grouped by e d u c a t i o n . Fane's i n t e r p r e t a t i o n i s t h a t the use of d a t a grouped by r e l a t i v e l y l a r g e r e g i o n s keeps " a b i l i t y " c o n s t a n t . F u r t h e r m o r e , G r i l i c h e s (1977) found the b i a s t o the s c h o o l i n g c o e f f i c i e n t by o m i t t i n g an " a b i l i t y " v a r i a b l e t o be r e l a t i v e l y minor i n a s t u d y a n a l y z i n g the r e l a t i o n s h i p between income and s c h o o l i n g . Presumably, t h i s r e s u l t s t i l l h o l d s when income i s r e p l a c e d by farm p r o f i t or p r o d u c t i o n . 18. A g r i c u l t u r a l R e s e a r c h (R) T h i s v a r i a b l e i s d e f i n e d as the s t o c k of p r o v i n c i a l and f e d e r a l e x p e n d i t u r e s on a g r i c u l t u r a l r e s e a r c h f o r a p e r i o d of t h i r t e e n y e a r s e n d i n g two y e a r s p r e v i o u s t o the census y e a r . In o t h e r words, f o r t h e 1971 Census d a t a s e t , p u b l i c e x p e n d i t u r e s on a g r i c u l t u r a l r e s e a r c h was summed over a p e r i o d of t h i r t e e n y e a r s s t a r t i n g i n 1957 and ending i n 1969. A l l e x p e n d i t u r e s were put i n t o c u r r e n t 1970 or 1980 d o l l a r s u s i n g the GNE i n f l a t o r . T h i s t h i r t e e n y e a r timeframe f o r measuring the s t o c k of e x p e n d i t u r e s i s a l l o w i n g f o r any l o n g - t e r m e f f e c t s of r e s e a r c h t o be i n c o r p o r a t e d i n the model. Because f e d e r a l e x p e n d i t u r e s on a g r i c u l t u r a l r e s e a r c h f o r t h e y e a r s mentioned above was o n l y a v a i l a b l e a g g r e g a t e d a t the l e v e l of E a s t e r n Canada and Western Canada, p r o v i n c i a l w e i g h t s were c a l c u l a t e d based on the 1983-1984 d i s t r i b u t i o n a c r o s s p r o v i n c e s of f e d e r a l e x p e n d i t u r e s on a g r i c u l t u r a l r e s e a r c h programs. These 38 w e i g h t s were found i n the A g r i c u l t u r e Canada p u b l i c a t i o n F e d e r a l A g r i - F o o d E x p e n d i t u r e s , 1982-1983  and 1983-1984 by Monique R o d i e r . The d a t a on the a c t u a l l e v e l s of p r o v i n c i a l and f e d e r a l e x p e n d i t u r e s f o r 1957-1969 and 1967-1979 were found i n a n o t h e r A g r i c u l t u r e Canada p u b l i c a t i o n An A n a l y s i s of Sources  of M u l t i f a c t o r P r o d u c t i v i t y growth i n Canadian  A g r i c u l t u r e , 1961 and 1980, w i t h P r o j e c t i o n s t o 2000 by George Brinkman. 19. O f f - f a r m Income (OFFI) O f f - f a r m income i s d e f i n e d as t h e t o t a l o f f - f a r m e a r n i n g s by the f a r m - o p e r a t o r i n 1980 (1970) i n c l u d i n g wages, s a l a r i e s and non-farm self-employment income. 20. O f f - f a r m Wage Rate (OFFW) T h i s v a r i a b l e was d e r i v e d by d i v i d i n g o f f - f a r m income by the t o t a l h ours of o f f - f a r m work by the f a r m - o p e r a t o r . The summary s t a t i s t i c s , a r i t h m e t i c mean and s t a n d a r d d e v i a t i o n , f o r a l l the v a r i a b l e s d i s c u s s e d above a r e g i v e n i n T a b l e 1 and i n T a b l e 2. 4.4 FUNCTIONAL FORM The Cobb-Douglas f u n c t i o n a l form was chosen f o r the e s t i m a t i o n of the g r o s s s a l e s p r o d u c t i o n f u n c t i o n and the v a r i a b l e p r o f i t f u n c t i o n . As the p r o d u c t i o n f u n c t i o n u n d e r l y i n g the Cobb-Douglas p r o f i t f u n c t i o n i s a Cobb-Douglas p r o d u c t i o n f u n c t i o n , t h e r e i s a d i r e c t r e l a t i o n 39 between b o t h f u n c t i o n s . Fane (1975), K h a l d i (1973), G r i l i c h e s (1964), and B a r i c h e l l o (1979 and 1984) a r e among those who have a l s o used the Cobb-Douglas f u n c t i o n a l form when e s t i m a t i n g the economic v a l u e of s c h o o l i n g i n a g r i c u l t u r e . The Cobb-Douglas i s the most common f u n c t i o n a l form used i n such e s t i m a t i o n s because i t i s s i m p l e and t h e r e a r e no s t r o n g reasons a g a i n s t u s i n g i t . A l t h o u g h the assumption of a u n i t a r y e l a s t i c i t y of s u b s t i t u t i o n between i n p u t s may impose a r e s t r i c t i o n on the t e c h n o l o g y , G r i l i c h e s (1964, p.964) s t a t e s t h a t a t h i g h e r l e v e l s of a g g r e g a t i o n (e.g. census d i v i s i o n s ) t h e r e does not seem t o be any s t r o n g prima f a c i e e v i d e n c e a g a i n s t u s i n g the Cobb-Douglas f u n c t i o n a l form. TABLE I Summary S t a t i s t i c s , 1971 Census Data Mean (S tandard D e v i a t i o n ) Whole P r a i r i e s Sample Only Va r i ab les (n -168) (n -49) Sales of A g r i c u l t u r a l Products (1970 S) 1S925 (7479 .5 ) 13942 (5543.2) V a r i a b l e P r o f i t (1970 $) 10818 (4675 .9 ) 8357.3 (2771.7) School ing of Farm-Operator ( y r s ) 8.455 (1 .0577) 7.541 (0 .9954) A g r i c u l t u r a l Research ( M i l l i o n s of 1970 S) 97 .90 (48 .586) 83.860 (47 .357) Value - Added (1970 S) 12048 (5858 .2 ) 9395.5 (3636 .5 ) Value of Land and B u i l d i n g s (1970 $) 52578 (32827 . ) 27126 (10152 . ) Value of L i v e s t o c k and P o u l t r y O 9 7 0 S) 1 1462 (6517 .4 ) 9443.8 (2294 .4 ) Value of Machinery (1970 s) 12140 (3343 .7 ) 9525.1 (2316.4) H i r e d Labour Wages (1970 $) 1229.6 (1684 .7 ) 1038.3 (1025 .8 ) Non-Labour Expenses (1970 S) 3877.7 (2434 .4 ) 4546.4 (2282.8) H i r e d Labour Wage Rate (1970 S/wk) 66.176 (14 .860 ) 58.317 (9 .8590) On-farm Operator Labour (days) 263.50 (13 .077 ) 269.43 (8 .3506) On-farm Operator Labour (hours) 2071.5 (165 .46 ) 2128.6 (121 .73) No. o f Farm Fami ly C h i l d r e n 13-18 y r s o l d 0.8355 (0 .2361) 1.0316 (0 .2395) Age of Farm-Operator 47 .896 ( 1 . 7 5 7 0 ) 47.145 (2 .1502) O f f - f a r m Wage Rate (1970 S /h r ) 8.2873 (3 .0974 ) 8.9165 (3 .1493) O f f - f a r m Income (1970 $ / y r ) 2317.6 (899 .50 ) 2077.5 (630 .16) Output P r i ce Index 0.9943 (0 .2215 ) 0.9679 (0 .1611) % of Farm-Operators Who Declare Farming as Main Occupat ion 75.086 (8 .4044 ) 74.190 (6 .8772) TABLE 2 Summary S t a t i s t i c s , 1981 Census Data Mean (Standard D e v i a t i o n ) V a r i a b l e s Whole Sample (n-263) P r a i r i e s O n l y (n-119) Sales of A g r i c u l t u r a l Products (1980 5) Va r iab le P r o f i t (1980 S) School ing of Farm-Operator ( y r s ) A g r i c u l t u r a l Research ( M i l l i o n s of 1930 $) Value - Added (1980 s) Value of Land and B u i l d i n g s (1980 5) Value of L i v e s t o c k and P o u l t r y (1980 ; ) Value of Machinery (1980 5) H i red Labour Wages (1980 $) Non-Labour Expenses (1980 S) H i red Labour Wage Rate (1980 $ / v k ) On-farm Operator Labour (days) On-farm Operator Labour (hours ) No. of Farm Fami l y C h i l d r e n 13-18 y r s o l d Age of F a c -Operator O f f - f a r * Wage Rate (1980 S / h r ) O f f - f a r m Income (1980 5 / y r ) Output P r i c e Index P r i c e of F e r t i l i z e r (1980 $ / t o n ) % of Farm-Operators Who Declare Farming as Main Occupat ion 6907 3 74921 (30430. ) (27832. ) 463)9 47328 (19910. ) (18703. ) 9.951 9.657 (0 .8695) (0 .9059) 333.35 418.57 (142 .42) (156.10) 50596 52973 (22649. ) (21448. ) 376020 274140 (244160) (194090) 40587 42194 (21459. ) (15067. ) 66101 51796 (20863. ) (11630. ) 4279.5 5649.4 (5164.4) (5628.4) 18477. 21948 (10405. ) (10195. ) 189.48 177.00 (35 .268) (32 .792) 253.18 254.00 (18 .937) (21 .543) 1810.2 1871.3 (209 .86) (217 .05) 0.6374 0.7039 (0 .1530) (0 .1627) 46.473 46.161 (1 .8385) (2 .1669) 17.076 18.983 (6 .9673) (8 .7149) 5966.7 6041.6 (2539 .0 ) (2207.9) 1.0151 0.9829 (0 .0859) (0 .0627) 279.94 254.27 (68 .569) (52.232) 78.254 77.715 (8 .5589) (8 .2132) 5. RESULTS A g r o s s s a l e s p r o d u c t i o n f u n c t i o n , a v a r i a b l e p r o f i t f u n c t i o n , and an extended v e r s i o n of the v a r i a b l e p r o f i t f u n c t i o n were e s t i m a t e d s e p a r a t e l y f o r both census y e a r s . Weighted l e a s t squares method of r e g r e s s i o n a n a l y s i s was n e c e s s a r y t o c o r r e c t f o r the h e t e r o s e d a s t i c i t y p r e s e n t i n b o t h d a t a s e t s . 1 8 The e s t i m a t e d Cobb-Douglas g r o s s s a l e s p r o d u c t i o n f u n c t i o n f o r both census y e a r s u s i n g w e i g h t e d l e a s t squares i s as f o l l o w s : InS = a 0 + a , l n E + a 2 l n N L X + a 3 l n H L + a„lnR + a 5 l n K + a 6 l n L where S = S a l e s of a g r i c u l t u r a l p r o d u c t s s o l d a = E s t i m a t e d c o e f f i c i e n t s E = E d u c a t i o n of f a r m - o p e r a t o r NLX = Non-labour v a r i a b l e e x p e n s e s 1 9 HL = E x p e n d i t u r e on h i r e d l a b o u r wages R = A g r i c u l t u r a l r e s e a r c h K = P h y s i c a l c a p i t a l , i n v a r i o u s forms L = O p e r a t o r on-farm l a b o u r t i m e ; LHR, LDY, or OCC The e s t i m a t e d Cobb-Douglas v a r i a b l e p r o f i t f u n c t i o n f o r both census y e a r s u s i n g weighted l e a s t squares i s as f o l l o w s : 1 8 H e t e r o s c e d a s t i c i t y became apparent a f t e r s u b j e c t i n g the d a t a t o the Park T e s t . The weight used i s 1/the number of farms i n each census d i v i s i o n squared f o r b o t h 1970 and 1980. 1 9 F e e d , c h e m i c a l s , f e r t i l i z e r , l a n d r e n t , and machine r e n t a r e i n c l u d e d . 42 43 l r i 7 r = b 0 + b , l n E + b 2 l n P q + b 3 l n P x + b„lnL + b s l n K + b 6 l n R where 7r = V a r i a b l e P r o f i t b = E s t i m a t e d c o e f f i c i e n t s E = E d u c a t i o n of f a r m - o p e r a t o r Pq = Output p r i c e i n d e x Px = Input p r i c e s ; P i and Pf L = O p e r a t o r on-farm l a b o u r t i m e ; LDY or OCC K = P h y s i c a l c a p i t a l , i n v a r i o u s forms R = A g r i c u l t u r a l r e s e a r c h B e f o r e d i s c u s s i n g the extended v e r s i o n of the v a r i a b l e p r o f i t f u n c t i o n , the r e s u l t s from t h e e s t i m a t i o n s of the g r o s s s a l e s p r o d u c t i o n f u n c t i o n and the v a r i a b l e p r o f i t f u n c t i o n a r e p r e s e n t e d i n the f o l l o w i n g two s e c t i o n s . 5.1 RESULTS BASED ON 1971 CENSUS DATA T u r n i n g f i r s t t o the 1971 Census g r o s s s a l e s p r o d u c t i o n f u n c t i o n r e s u l t s p r e s e n t e d i n T a b l e 3, i t can be seen t h a t a l l the v a r i a b l e s i n r e g r e s s i o n s 1.2 th r o u g h 1.5 behave as p r e d i c t e d w i t h p o s i t i v e c o e f f i c i e n t s and h i g h t - r a t i o ' s . The l i v e s t o c k v a r i a b l e s i n r e g r e s s i o n s 1.2 and 1.3 a r e an e x c e p t i o n . The n e g a t i v e c o e f f i c i e n t s can be e x p l a i n e d , however, i f a d e c i s i o n has been made t o augment the b r e e d i n g h e r d . In t h i s s i t u a t i o n , as the v a l u e of the l i v e s t o c k goes up, t h e s a l e s w i l l d e c r e a s e i f h i g h e r p r i c e s a r e e x p e c t e d i n the f u t u r e . TABLE 3 E s t i m a t i o n s of A l t e r n a t e S p e c i f i c a t i o n s of Gross Sales P r o d u c t i o n F u n c t i o n s , WLS, 1971 Census d a t a , ( t - r a t i o s ) 1.1 1.2 1.3 1.4 1.5 SALES SALES SALES SALES SALES SCHOOLING OF OPERATOR (E) -0 .125 ( - 1 . 4 6 ) 0.158 ( 2 . 2 4 ) 0.153-( 2 . 1 7 ) 0. ( 2 . 183 10) 0. ( 3 . 266 55) NON-LABOUR EXPENSES (NLX) 0.372 (15 .47) 0.417 (21 .86 ) 0.408 (25 .15 ) 0. ( 1 8 . 384 50) 0. ( 2 2 . 399 38) HIRED LABOUR WAGES (HL) 0.234 (9 .78 ) 0.127 ( 6 . 4 4 ) 0.134 ( 7 . 4 6 ) 0. ( 8 . 161 96) 0. (12 . 197 34) ON-FARM OPERATOR LABOUR (LHR) 0.949 (15 .21) ON-FARM OPERATOR LABOUR (LDY) 2.934 (21 .43 ) 2.881 (23 .86 ) 2 . ( 17 . 792 95) 2 . ( 2 1 . 877 59) LAND & 0.086 0.182 BUILDINGS (LB) (2 .63 ) ( 7 . 4 1 ) MACHINERY & 0.239 0.247 EQUIPMENT (M) ( 2 . 8 1 ) ( 3 . 7 5 ) LIVESTOCK & - 0 . 0 8 9 - 0 . 0 5 0 - 0 . 0 4 1 POULTRY (LS) ( - 2 . 6 2 ) ( - 1 . 8 8 ) ( - 1 . 6 9 ) CAPITAL 0 '95 (LB + M) (10 115) CAPITAL 0.135 0.093 (LB + M • LS) ( 1 3 . 6 9 ) (9 .34 ) RESEARCH (R) 0.082 0.059 0.060 0.066 ( 8 . 2 9 ) ( 7 . 5 3 ) ( 7 . 8 9 ) ( 7 . 8 2 ) R X .9412 .9629 .9629 .9381 .9549 MARGINAL SALES EFFECT OF - $ 235 $ 298 $ 288 $ 345 $ 501 SCHOOLING (70 $) 45 The e s t i m a t i n g s t r a t e g y was t o b e g i n w i t h the f a m i l i a r p r o d u c t i o n f u n c t i o n and t o proceed making changes i n acc o r d a n c e w i t h the t h e o r y , so t h a t the 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 i n c r e a s e s w i t h each s t e p . R e g r e s s i o n s 1.1 and 1.2 d i f f e r o n l y i n the s p e c i f i c a t i o n of the o p e r a t o r l a b o u r v a r i a b l e . A comparison of th e s e two r e g r e s s i o n s l e a d s t o the c o n c l u s i o n t h a t the o p e r a t o r l a b o u r v a r i a b l e LHR i s i n f e r i o r . The p o t e n t i a l reasons f o r the low q u a l i t y of t h i s v a r i a b l e a r e d i s c u s s e d i n Chapter F o u r . T h e r e f o r e , a t t h i s s t a g e i n the e s t i m a t i o n p r o c e s s , a d e c i s i o n was made t o drop LHR i n f a v o r of LDY which i s d e f i n e d as 300 days minus t o t a l days of o f f - f a r m l a b o u r t h a t y e a r . The d i f f e r e n c e between r e g r e s s i o n s 1.2 and 1.3 i s the a g g r e g a t i o n of two u n i t s of p h y s i c a l c a p i t a l , l a n d and b u i l d i n g s and machinery, i n t o one v a r i a b l e . I n or d e r t o m i n i m i z e the b i a s , the a g g r e g a t i o n i s c o n s i s t e n t w i t h the Cobb-Douglas f u n c t i o n a l form. In o t h e r words, the v a r i a b l e s a r e a g g r e g a t e d so t h a t the l o g a r i t h m of each v a r i a b l e i s summed t o g e t h e r r a t h e r than t a k i n g the l o g a r i t h m of the sum of the v a r i a b l e s . A l l of the c a p i t a l components a r e a g g r e g a t e d i n t o one v a r i a b l e i n r e g r e s s i o n 1.4. As p r e d i c t e d , summation of t h e c a p i t a l components i n t o one v a r i a b l e i n c r e a s e s the m a r g i n a l s a l e s e f f e c t of s c h o o l i n g . T h i s i n c r e a s e s h o u l d r e f l e c t the a d d i t i o n a l o p t i o n s made a v a i l a b l e t o the f a r m - o p e r a t o r by b e i n g a b l e t o a l l o c a t e among a l l t h r e e components of c a p i t a l . R e g r e s s i o n s 1.4 and 1.5 are the same except f o r the i n c l u s i o n of the r e s e a r c h v a r i a b l e i n r e g r e s s i o n 1.5. A g a i n , as would be 46 e x p e c t e d a c c o r d i n g t o the t h e o r i e s of S c h u l t z and Welch, the v a l u e of s c h o o l i n g i s h i g h e r when r e s e a r c h i s i n c l u d e d . As the p r o d u c t i o n f u n c t i o n becomes a p r o f i t f u n c t i o n , we would a l s o e xpect the measurement of the v a l u e of s c h o o l i n g t o i n c r e a s e . The r e s u l t s i n T a b l e 4 c o n f i r m t h i s h y p o t h e s i s . R e g r e s s i o n 1.6, an e s t i m a t i o n of a value-added p r o d u c t i o n f u n c t i o n 2 0 i l l u s t r a t e s t h e 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 as the g r o s s s a l e s p r o d u c t i o n f u n c t i o n becomes c l o s e r t o a v a r i a b l e p r o f i t f u n c t i o n . The c o e f f i c i e n t i n r e g r e s s i o n 1.6 i s 0.427 which i s over 130 % h i g h e r than the c o e f f i c i e n t i n t h e c o r r e s p o n d i n g g r o s s s a l e s p r o d u c t i o n f u n c t i o n ( r e g r e s s i o n 1.4). T h i s i n c r e a s e 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 i s the r e s u l t of o p t i m i z i n g w i t h r e s p e c t t o non-labour v a r i a b l e expenses. As the dependent v a r i a b l e changes t o v a r i a b l e p r o f i t i n r e g r e s s i o n 1.7, the s c h o o l i n g c o e f f i c i e n t i n c r e a s e s once a g a i n . The m a r g i n a l p r o f i t e f f e c t of s c h o o l i n g i n r e g r e s s i o n 1.7 ($1003 i n c r e a s e i n v a r i a b l e p r o f i t s per y e a r of a d d i t i o n a l s c h o o l i n g ) i s over 100% l a r g e r than the h i g h e s t m a r g i n a l s a l e s e f f e c t measured w i t h the e s t i m a t i o n of a p r o d u c t i o n f u n c t i o n ($501 i n c r e a s e i n s a l e s per y e a r of a d d i t i o n a l s c h o o l i n g ) . A comparison of the r e g r e s s i o n 1.7 and 1.8 i n T a b l e 4 a l s o l e n d s s u p p o r t t o the h y p o t h e s i s t h a t the e f f e c t of s c h o o l i n g i s p o s i t i v e l y r e l a t e d t o the f l o w of new i n p u t s and i n f o r m a t i o n i n t o a g r i c u l t u r e . The m a r g i n a l p r o f i t e f f e c t i s lower i n r e g r e s s i o n 1.6 when r e s e a r c h i s not i n c l u d e d . The 2°Value-added i s d e f i n e d as s a l e s minus n o n - l a b o u r v a r i a b l e expenses. TABLE 4 Est i m a t i o n s of A l t e r n a t e S p e c i f i c a t i o n s of Value-Added Production Functions and V a r i a b l e P r o f i t Functions WLS, 1971 Census data ( t - r a t i o s ) 1.6 1.7 1.8 _ VAR P VAR P SCHOOLING 0.427 0.760 0.784 OF OPERATOR (E) ( 3 . 5 6 ) ( 5 . 4 6 ) (5 .50 ) PRICE 0 .049 0.066 INDEX (Pq) ( 0 . 7 2 ) (0 .92 ) HIRED LABOUR 0.600 0.583 WAGE RATE (PI) ( 6 . 5 8 ) ( 6 . 2 4 ) ON-FARM OPERATOR LABOUR (LHR) ON-FARM 4 .069 5.509 5.566 OPERATOR (19 .64 ) ( 2 4 . 0 2 ) (23 .19) LABOUR (LDY) LAND & BUILDINGS (LB) MACHINERY £, EQUIPMENT (M) LIVESTOCK & POULTRY (LS) CAPITAL (LB + M) CAPITAL 0.176 0.190 0.184 (LB • M • LS) ( 12 .79 ) ( 1 0 . 2 8 ) ( 9 . 1 6 ) RESEARCH (R) 0.013 ( 0 . 8 1 ) R V .8843 .8311 .8308 MARGINAL PROFIT a EFFECT OF $ 608 $ 972 $ 1003 SCHOOLING (70 S) a Marginal value-added e f f e c t of s c h o o l i n g 48 p o s i t i v e c o e f f i c i e n t f o r the h i r e d l a b o u r wage r a t e i s unexpected but s t i l l p l a u s i b l e i f t h i s v a r i a b l e i s p i c k i n g up v a r i a t i o n s , i n q u a l i t y more than v a r i a t i o n s a c r o s s r e g i o n s . 5.2 RESULTS BASED ON 1981 CENSUS DATA The r e s u l t s from the 1971 census d a t a l e n d s t r o n g support t o our hypotheses c o n c e r n i n g the e f f e c t of s c h o o l i n g on farm p r o f i t and p r o d u c t i v i t y . The r e s u l t s from the 1981 census d a t a a r e a l s o s u p p o r t i v e but not as c o n s i s t e n t . The r e s u l t s from e s t i m a t i o n s of a g r o s s s a l e s p r o d u c t i o n f u n c t i o n u s i n g 1981 census d a t a a r e p r e s e n t e d i n T a b l e 5. A l t h o u g h the same g e n e r a l e s t i m a t i n g s t r a t e g y was f o l l o w e d f o r e s t i m a t i o n s of the 1981 d a t a as w i t h e s t i m a t i o n s of the 1971 d a t a , the measurement of the v a l u e of s c h o o l i n g d i d not i n c r e a s e w i t h each s t e p as i t d i d i n the 1971 e s t i m a t i o n s . The f i r s t t h r e e r e g r e s s i o n s i n T a b l e 5 show a comparison between the t h r e e p o s s i b l e l a b o u r v a r i a b l e s . As can be seen i n r e g r e s s i o n 2.1, the v a r i a b l e LHR i s a l s o i n f e r i o r i n 1981. The v a r i a b l e LDY i n r e g r e s s i o n 2.2 appears t o be more a c c u r a t e and the s c h o o l i n g c o e f f i c i e n t i n c r e a s e s , though i t i s i n s i g n i f i c a n t . I n r e g r e s s i o n 2.3, a new o p e r a t o r l a b o r v a r i a b l e i s i n t r o d u c e d which i s d e f i n e d as the p e r c e n t of f a r m - o p e r a t o r s who d e c l a r e d f a r m i n g t o be t h e i r main o c c u p a t i o n (OCC). T h i s v a r i a b l e seems t o be an improvement over the LDY v a r i a b l e and the s c h o o l i n g c o e f f i c i e n t r e f l e c t s t h i s by i n c r e a s i n g and becoming s i g n i f i c a n t a t the 10% 4 9 TABLE 5 E s t i m a t i o n s of A l t e r n a t e S p e c i f i c a t i o n s of Gross Sales Production Functions, WLS, 1981 Census data ( t - r a t i o s ) 2. 1 2.2 2.3 2.4 2.5 SALES SALES SALES SALES SALES SCHOOLING OF OPERATOR (E) -0.598 (-4.37) 0.158 (1.15) 0.311 (1.85) 0. 173 (1.04) 0.234 (1.39) NON-LABOUR EXPENSES (NLX) 0.412 (14.21) 0.491 (20.02) 0.607 (22.92) 0.619 (23.14) 0.643 (24.78) HIRED LABOUR WAGES (HL) 0.167 (8.03) 0.171 (8.83) 0.083 (3.65) 0.068 (3.00) 0.059 (2.59) ON-FARM OPERATOR LABOUR (LHR) 1.070 (21.31) ON-FARM OPERATOR LABOUR (LDY) 1 .475 (23.66) ON-FARM OPERATOR LABOUR (OCC) 0.933 (18.28) 0.893 (17.65) 0.866 (17.10) LAND & BUILDINGS (LB) 0.289 (12.68) 0.142 (6.96) 0.048 (1.95) MACHINERY £. EQUIPMENT (M) 0.034 (1.07) 0.185 (6.32) 0.207 (5.97) LIVESTOCK & POULTRY (LS) 0.138 (4.66) 0.087 (3.12) 0.185 (5.66) 0.216 (6.78) CAPITAL (LB + M) 0.106 (5.95) CAPITAL (LB + M + LS) 0.131 (8.10) RESEARCH (R) -0.043 (-2.86) 0.011 (0.86) 0.025 (1.69) 0.014 (0.93) 0.023 (1.60) R* .9748 .9781 .9696 .9684 .9674 MARGINAL SALES EFFECT OF SCHOOLING (80 $) - $ 4151 $ 1097 $ 2159 $ 1201 $ 1624 50 l e v e l . The next s t e p , shown i n r e g r e s s i o n 2.4, i s t o agg r e g a t e two components of c a p i t a l , l a n d and b u i l d i n g s and machi n e r y , i n t o one v a r i a b l e . L i v e s t o c k i s i n c l u d e d as a s e p a r a t e v a r i a b l e . The m a r g i n a l s a l e s e f f e c t of s c h o o l i n g d e c r e a s e s s l i g h t l y when t h i s s p e c i f i c a t i o n of p h y s i c a l c a p i t a l i s used. In r e g r e s s i o n 2.5, a l l t h r e e components of p h y s i c a l c a p i t a l a r e a g g r e g a t e d i n t o one v a r i a b l e . The m a r g i n a l s a l e s e f f e c t of s c h o o l i n g i n r e g r e s s i o n 2.5 i s h i g h e r than i n the p r e v i o u s r e g r e s s i o n b u t , c o n t r a r y t o our h y p o t h e s i s , i t i s s t i l l lower than the e f f e c t found i n r e g r e s s i o n 2.3 where none of the c a p i t a l components have been a g g r e g a t e d . In T a b l e 6, the r e s u l t s from e s t i m a t i o n s of the v a r i a b l e p r o f i t f u n c t i o n and the v a l u e - a d d e d p r o d u c t i o n f u n c t i o n a r e p r e s e n t e d . A l l the v a r i a b l e s a r e s i g n i f i c a n t a t the 5% l e v e l and have t h e p r e d i c t e d s i g n s . In r e g r e s s i o n 2.6, an e s t i m a t i o n of t h e value-added p r o d u c t i o n f u n c t i o n , the s c h o o l i n g c o e f f i c i e n t i s between the c o e f f i c i e n t s i n r e g r e s s i o n s 2.5 and 2.7 as would be e x p e c t e d . The l a s t two r e g r e s s i o n s d i f f e r o n l y i n the i n c l u s i o n of the r e s e a r c h v a r i a b l e i n r e g r e s s i o n 2.8 and not i n r e g r e s s i o n 2.7. C o n t r a r y t o the h y p o t h e s i s t h a t the s c h o o l i n g c o e f f i c i e n t w i l l i n c r e a s e i f the l e v e l of t e c h n o l o g y i s i n c l u d e d i n the model, the s c h o o l i n g c o e f f i c i e n t i s lower i n r e g r e s s i o n 2.8 when the r e s e a r c h v a r i a b l e i s added. There a r e s e v e r a l p o s s i b l e e x p l a n a t i o n s f o r t h i s b e h a v i o r . The r e s e a r c h v a r i a b l e i s d e f i n e d as the s t o c k of p u b l i c e x p e n d i t u r e s on TABLE 6 E s t i m a t i o n s of A l t e r n a t e S p e c i f i c a t i o n s o f Value-Added P r o d u c t i o n Func t i ons and V a r i a b l e P r o f i t Func t ions WLS, 1981 Census d a t a ( t - r a t i o s ) 2 .6 2 .7 2.8 V^A VAR P VAR P SCHOOLING 1.158 OF OPERATOR (E) ( 3 . 8 6 ) PRICE INDEX (Pq) HIRED LABOUR WAGE RATE ( P I ) PRICE OF FERTILIZER ( P f ) ON-FARM OPERATOR LABOUR (OCC) 1 .562 ( 1 9 . 5 9 ) LAND & BUILDINGS (LB) MACHINERY 6 EQUIPMENT (M) LIVESTOCK t POULTRY (LS) CAPITAL (LB «• M) CAPITAL (LB • M + LS) RESEARCH (R) 0.256 ( 8 . 8 4 ) R* .8783 MARGINAL PROFIT EFFECT OF SCHOOLING (80 $) $ 5888 2.633 ( 7 . 2 5 ) 1 .069 ( 3 . 8 2 ) - 0 . 7 2 4 ( - 7 . 4 1 ) - 0 . 5 7 2 ( - 7 . 9 7 ) 2 .169 ( 2 7 . 0 6 ) 0.679 (2 .33 ) 1.378 (6 .78 ) -1 .052 ( -14 .28 ) -0 .174 ( - 3 . 0 0 ) 2.339 (32.13) 0.312 ( 9 . 0 2 ) .8482 $ 12,256 0.440 (16.72) -0 .248 ( -15 .39) .9210 $ 3161 a Marg ina l v a l u e - a d d e d e f f e c t o f s c h o o l i n g 52 a g r i c u l t u r a l r e s e a r c h over a p e r i o d of t h i r t e e n y e a r s (1967-1979) f o r each p r o v i n c e . T h i s v a r i a b l e may not be a c c u r a t e l y r e f l e c t i n g the l e v e l of t e c h n o l o g y f a c i n g the f a r m - o p e r a t o r i n 1980 f o r two r e a s o n s : f i r s t l y , the t h i r t e e n y e a r time p e r i o d may not a l l o w f o r s i g n i f i c a n t d i f f e r e n c e s i n r e s e a r c h a c t i v i t y d u r i n g the most r e c e n t and t h e r e f o r e most r e l e v a n t y e a r s ( e . g . , 1975-1979) a c r o s s the p r o v i n c e s t o be a p p a r e n t ; s e c o n d l y , t h i s v a r i a b l e does not i n c l u d e o t h e r i m p o r t a n t i n d i c a t i o n s of t h e l e v e l of t e c h n o l o g y or of the o c c u r r e n c e of economic d i s e q u i l i b r i a and as such i s an i n a d e q u a t e measure of the environment d e s c r i b e d by S c h u l t z as n e c e s s a r y f o r g e n e r 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 example of a n o t h e r i n d i c a t i o n of t h e p r e v a l e n t l e v e l of t e c h n o l o g y a c r o s s r e g i o n s would be a measure of i n c r e a s e d l e v e l s of c a p i t a l i n p u t s such as p e r s o n a l computers. The d e c i s i o n s of some f a r m - o p e r a t o r s t o use computers would have the e f f e c t of r a i s i n g the o v e r a l l l e v e l of s k i l l s n e c e s s a r y f o r e f f e c t i v e farm management. For example, the i n c r e a s e d a v a i l a b i l i t y of p e r s o n a l computers would have the e f f e c t of r a i s i n g t h e l e v e l of s k i l l s n e c e s s a r y i n f i n a n c i a l farm management. Fa r m - o p e r a t o r s w i t h h i g h e r l e v e l s of e d u c a t i o n would f i n d i t e a s i e r t o a c q u i r e t h e s e new s k i l l s . C o n s e q u e n t l y , the v a l u e of s c h o o l i n g would i n c r e a s e i n a g r i c u l t u r e . D i s e q u i l i b r i a i n the i n p u t m a r k e t s , such as r i s i n g c a p i t a l v a l u e s and i n t e r e s t r a t e s , would a l s o n e c e s s i t a t e improved f i n a n c i a l management s k i l l s and i n c r e a s e the v a l u e of s c h o o l i n g i n a g r i c u l t u r e . 53 I f the above hypotheses a r e c o r r e c t , the m a r g i n a l p r o f i t e f f e c t of s c h o o l i n g s h o u l d be h i g h e r i n 1980 than i n 1970 g i v e n t h a t the l e v e l of t e c h n o l o g y was not as h i g h nor were i n p u t markets as u n s t a b l e i n 1970. A f t e r c o n v e r t i n g 2 1 t h e 1970 m a r g i n a l p r o f i t e f f e c t found i n r e g r e s s i o n 1.8 i n t o 1980 d o l l a r s , a comparison of the two f i g u r e s p r o v i d e s s u p p o r t f o r the argument above. The m a r g i n a l p r o f i t e f f e c t found w i t h 1971 Census d a t a i s $ 2487 ( i n 1980 $ ) . The m a r g i n a l p r o f i t e f f e c t found w i t h 1981 Census d a t a i s $ 3161 ( i n 1980 $ ) . The f a c t t h a t the measurement of the v a l u e of s c h o o l i n g i s twenty-seven p e r c e n t h i g h e r i n 1980 i s most l i k e l y due t o d i s e q u i l i b r i a i n i n p u t markets and t o the i n c r e a s e d l e v e l and a v a i l a b i l i t y of new t e c h n o l o g y i n 1980. 5.3 EXTENSION OF THE VARIABLE PROFIT FUNCTION In Chapter Three, an e x t e n s i o n of the v a r i a b l e p r o f i t f u n c t i o n was p r e s e n t e d wherein on-farm o p e r a t o r l a b o u r s u p p l y and a g g r e g a t e d p h y s i c a l c a p i t a l a r e e n d o genized i n a s i m u l t a n e o u s e q u a t i o n s framework. A l t h o u g h t h e r e a r e s e v e r a l e c o n o m e t r i c methods t h a t can be a p p l i e d t o a c h i e v e t h i s r e s u l t , o n l y one o p t i o n i s f e a s i b l e u s i n g w e i g h t e d l e a s t s q u a r e s . 2 2 As a r e s u l t , o p e r a t o r l a b o u r and farm c a p i t a l were endogenized u s i n g i n s t r u m e n t a l v a r i a b l e s . The i n s t r u m e n t a l v a r i a b l e s were c r e a t e d by e s t i m a t i n g c a p i t a l and o p e r a t o r l a b o u r time and s a v i n g the p r e d i c t e d v a l u e s i n 2 1 T h e GNE i n f l a t o r (2.48) was used. 2 2 I t i s not p o s s i b l e t o use w e i g h t e d l e a s t s q u a r e s w i t h two s t a g e l e a s t squares or a systems method. 54 new v a r i a b l e s . 2 3 Weighted l e a s t s q u a r e s was used f o r e s t i m a t i o n of a l l t h r e e e q u a t i o n s , t h u s c o r r e c t i n g f o r the problem of h e t e r o s c e d a s t i c i t y a p p a r e n t i n the d a t a . The r e s u l t s from e s t i m a t i o n s of t h i s extended v a r i a b l e p r o f i t f u n c t i o n a r e p r e s e n t e d i n T a b l e 7 and Ta b l e 8. T u r n i n g f i r s t t o the e s t i m a t i o n of the c a p i t a l e q u a t i o n u s i n g 1971 Census d a t a ( r e g r e s s i o n 3.1), i t can be seen t h a t the v a r i a b l e s a r e a l l of the c o r r e c t s i g n and a r e h i g h l y s i g n i f i c a n t . F u r t h e r m o r e , the a d j u s t e d R square i n d i c a t e s t h a t over 78 % of the v a r i a t i o n i n c a p i t a l i s e x p l a i n e d . A r e s e a r c h v a r i a b l e i s i n c l u d e d i n t h e c a p i t a l e q u a t i o n i n s t e a d of i n the v a r i a b l e p r o f i t f u n c t i o n because t e c h n o l o g i c a l change i s most l i k e l y t o be embodied i n the v a l u e of p h y s i c a l c a p i t a l . F u r t h e r m o r e , the s i g n i f i c a n t c o e f f i c i e n t of the s c h o o l i n g v a r i a b l e i n d i c a t e s t h a t the l e v e l of c a p i t a l on a farm i s s t r o n g l y i n f l u e n c e d by the l e v e l of s c h o o l i n g of the f a r m - o p e r a t o r . T h i s s u p p o r t s the h y p o t h e s i s t h a t t h e l e v e l of s c h o o l i n g a t t a i n e d by the f a r m - o p e r a t o r p l a y s an i m p o r t a n t r o l e i n the d e c i s i o n - m a k i n g p r o c e s s of c h o o s i n g the l e v e l and mix of f i x e d i n p u t s . The e s t i m a t i o n of the on-farm o p e r a t o r l a b o u r e q u a t i o n i n r e g r e s s i o n 3.2 r e v e a l s a weak l i n k i n the model. The s i g n s of t h e output p r i c e index v a r i a b l e , the p r e d i c t e d c a p i t a l v a r i a b l e , and the o f f - f a r m wage r a t e v a r i a b l e a r e a l l c o n t r a r y t o e x p e c t a t i o n . As o u t p u t p r i c e s i n c r e a s e , the v a l u e of the o p e r a t o r ' s time on t h e farm a l s o i n c r e a s e s . 2 3 R e f e r t o page 22 f o r a p r e s e n t a t i o n of the e q u a t i o n s i n the model. TABLE 7 E s t i m a t i o n of a V a r i a b l e P r o f i t F u n c t i o n w i t h I n s t r u m e n t a l V a r i a b l e s f o r C a p i t a l and Labour WLS, 1971 Census d a t a ( t - r a t i o s ) 3.1 3.2 3.3 CAPITAL LABOUR VAR P SCHOOLING OF OPERATOR (E) 2.277 (4 .72 ) - 0 . 1 4 0 ( - 3 . 2 7 ) 0.576 (4 .06 ) PRICE INDEX (Pq) 1 .254 (5 .02 ) - 0 . 1 0 0 ( - 4 . 1 0 ) 0.531 (7 .31 ) HIRED LABOUR WAGE RATE ( P I ) 1.032 ( 3 . 0 4 ) 0.008 ( 0 . 2 9 ) 1 .251 (12 .46) ON-FARM OPERATOR LABOUR (PRED LDY) - 1 . 7 1 2 ( - 1 7 . 7 3 ) CAPITAL (PRED K) - 0 . 0 0 5 ( - 1 . 2 6 ) - 0 . 1 7 9 ( - 1 5 . 3 5 ) RESEARCH (R) 0.328 ( 6 . 5 5 ) OFF-FARM INCOME (OFI) 0.798 ( 4 . 5 6 ) OFF-FARM WAGE RATE (OFW) 0.094 ( 5 . 4 3 ) CHILDREN (CH) . 0.001 ( 0 . 0 5 ) .7858 .5101 .7906 MARGINAL PROFIT a EFFECT OF $ 546 SCHOOLING (70 $) a The o f f - f a r m g a i n s ( S 2 8 7 / y r ) f rom spending l e s s t i m e on the farm have not been i n c l u d e d i n t h i s c a l c u l a t i o n of the m a r g i n a l p r o f i t e f f e c t o f s c h o o l i n g . 56 E s t i m a t i o n of a V a r i a b l e P r o f i t F u n c t i o n w i t h I n s t r u m e n t a l V a r i a b l e s f o r C a p i t a l and Labour WLS, 1981 Census d a t a ( t - r a t i o s ) «•> 4-2 4 .3 CAPITAL LABOUR VAR P SCHOOLING OF OPERATOR (E) 5.497 (10 .90) - 1 . 2 8 4 ( - 9 . 9 6 ) 3.781 ( 5 . 8 9 ) PRICE INDEX (Pq) -0 .501 ( - 1 . 3 4 ) - 0 . 6 4 6 ( - 6 . 3 1 ) - 0 . 7 6 3 ( - 1 . 4 9 ) HIRED LABOUR WAGE RATE ( P I ) 1 .736 (10 .41) 0.418 ( 8 . 2 4 ) - 0 . 5 9 8 ( - 3 . 1 5 ) PRICE OF FERTILIZER ( P f ) 0.094 (0 .72 ) 0.141 ( 4 . 9 9 ) - 0 . 6 0 1 ( - 4 . 7 0 ) ON-FARM OPERATOR LABOUR (PRED OCC) 0.860 ( 3 . 8 3 ) CAPITAL (PRED K) 0 .040 ( 2 . 2 9 ) 0.262 ( 3 . 6 4 ) RESEARCH (R) 0.257 (8 .16 ) OFF-FARM INCOME (OFI) 0.704 (9 .27 ) OFF-FARM WAGE RATE (OFW) 0.052 ( 2 . 5 3 ) CHILDREN (CH) - 0 . 3 3 1 ( - 8 . 1 5 ) R* .7456 .7521 .5180 MARGINAL PROFIT EFFECT OF SCHOOLING (80 $) $ 18,465 a a The o f f - f a r m ga in3 ($ 1666 /y r ) f rom spend ing l e s s t ime on the farm nave not been i n c l u d e d i n t h i s c a l c u l a t i o n o f t h e m a r g i n a l p r o f i t e f f e c t o f s c h o o l i n g . 57 C o n s e q u e n t l y , more time s h o u l d be a l l o c a t e d t o on-farm l a b o u r which would be i l l u s t r a t e d by a p o s i t i v e c o e f f i c i e n t f o r the o u t p u t p r i c e v a r i a b l e . However, the o u t p u t p r i c e index c o e f f i c i e n t i s n e g a t i v e and s i g n i f i c a n t . The o f f - f a r m wage r a t e r e f l e c t s the f a r m - o p e r a t o r ' s o p p o r t u n i t y c o s t and as such s h o u l d have a n e g a t i v e e f f e c t on on-farm l a b o u r t i m e . T h i s c o e f f i c i e n t i s a l s o of the wrong s i g n and i s s i g n i f i c a n t . As the l e v e l of c a p i t a l i n c r e a s e s , the v a l u e of t h e o p e r a t o r ' s time on the farm s h o u l d a l s o i n c r e a s e . The p r e d i c t e d c a p i t a l c o e f f i c i e n t s h o u l d be p o s i t i v e . However, i t i s n e g a t i v e though i n s i g n i f i c a n t . A v a r i a b l e i n d i c a t i n g the number of c h i l d r e n aged between 13 and 18 y e a r s o l d was i n c l u d e d as a measure of t h e l a b o u r c o n t r i b u t i o n by f a m i l y members s t i l l l i v i n g a t home. T h i s v a r i a b l e i s a l s o i n s i g n i f i c a n t . A l t h o u g h t h e l a b o u r e q u a t i o n appears t o be i n a p p r o p r i a t e l y s p e c i f i e d i n t h a t most of the v a r i a b l e s a r e e i t h e r of t h e wrong s i g n or a r e i n s i g n i f i c a n t , the s c h o o l i n g v a r i a b l e remains s i g n i f i c a n t and s t a b l e . The s i g n i f i c a n t c o e f f i c i e n t of the s c h o o l i n g v a r i a b l e i s s u p p o r t i v e of the h y p o t h e s i s t h a t the l e v e l of s c h o o l i n g a f f e c t s the a l l o c a t i o n of time between the on-farm and o f f - f a r m l a b o u r m a r k e t s . The n e g a t i v e s i g n of t h e c o e f f i c i e n t can be e x p l a i n e d i f i n c r e a s e d s c h o o l i n g caused the v a l u e of the f a r m - o p e r a t o r ' s time t o go up even more o f f the farm than on the farm. G i v e n the weak r e s u l t s i n the l a b o u r e q u a t i o n , e s t i m a t i o n of the v a r i a b l e p r o f i t f u n c t i o n w i t h the l a b o u r 58 and c a p i t a l i n s t r u m e n t a l v a r i a b l e s cannot be e x p e c t e d t o p r o v i d e s t r o n g r e s u l t s c o n s i s t e n t w i t h t h e o r y . As can be seen i n r e g r e s s i o n 3.3, both i n s t r u m e n t a l v a r i a b l e s are h i g h l y s i g n i f i c a n t w i t h the wrong s i g n . C o n s i d e r i n g the r e s u l t s o b t a i n e d w i t h o u t i n s t r u m e n t a l v a r i a b l e s where both th e c a p i t a l and l a b o u r v a r i a b l e s a r e p o s i t i v e and h i g h l y s i g n i f i c a n t ( T a ble 4 ) , i t would seem t h a t the p u z z l i n g r e s u l t s i n r e g r e s s i o n 3.3 a r e due t o problems w i t h the model not t o unexpected r e l a t i o n s h i p s i n t h e r e a l w o r l d . As such, more complete d a t a f o r the l a b o u r e q u a t i o n s h o u l d improve the model. The r e s u l t s of t h e e s t i m a t i o n of the v a r i a b l e p r o f i t f u n c t i o n w i t h i n s t r u m e n t a l v a r i a b l e s based on 1981 Census d a t a a r e p r e s e n t e d i n T a b l e 8. A l t h o u g h not w i t h o u t some problems of i n s i g n i f i c a n t v a r i a b l e s and v a r i a b l e s w i t h unexpected s i g n s , the 1981 r e s u l t s a r e more c o n s i s t e n t w i t h t h e o r y than the 1971 r e s u l t s . The e s t i m a t i o n of t h e c a p i t a l e q u a t i o n i n r e g r e s s i o n 4.1 i s s i m i l a r t o the c a p i t a l e q u a t i o n e s t i m a t e d u s i n g 1971 Census d a t a e xcept t h a t the p r i c e of f e r t i l i z e r i s a l s o i n c l u d e d . With the e x c e p t i o n of t h e output p r i c e v a r i a b l e and the f e r t i l i z e r v a r i a b l e , the r e s u l t s a r e s t r o n g . The s c h o o l i n g c o e f f i c i e n t i s p o s i t i v e and h i g h l y s i g n i f i c a n t g i v i n g f u r t h e r e v i d e n c e t o the i m p o r t a n c e of the r o l e s c h o o l i n g p l a y s i n the c h o i c e of the l e v e l and mix of c a p i t a l . The o u t p u t p r i c e i n d e x and the f e r t i l i z e r p r i c e a r e b oth i n s i g n i f i c a n t . However, the r e s e a r c h v a r i a b l e and the o f f - f a r m income v a r i a b l e a r e both 59 of the e x p e c t e d s i g n and a r e h i g h l y s i g n i f i c a n t . The l a b o u r e q u a t i o n seems t o be i n a p p r o p r i a t e l y s p e c i f i e d w i t h the o u t p u t p r i c e index and the o f f - f a r m wage r a t e c o e f f i c i e n t s b e i n g of the wrong s i g n and s i g n i f i c a n t . The o t h e r v a r i a b l e s , however, a r e a l l s i g n i f i c a n t and c a r r y s i g n s c o n s i s t e n t w i t h t h e o r y . The h i r e d l a b o u r wage r a t e and the p r i c e of f e r t i l i z e r a r e both p o s i t i v e , as i s e x p e c t e d of the p r i c e s of s u b s t i t u t e s i n a f a c t o r demand e q u a t i o n . The p r e d i c t e d c a p i t a l v a r i a b l e i s a l s o p o s i t i v e i n d i c a t i n g t h a t i n c r e a s e d c a p i t a l r a i s e s the v a l u e of the o p e r a t o r ' s l a b o u r time on t h e farm. The n e g a t i v e c o e f f i c i e n t of the c h i l d r e n v a r i a b l e can be e x p l a i n e d i f the c h i l d r e n aged between 13 and 18 y e a r s o l d p r o v i d e l a b o u r t h a t can be s u b s t i t u t e d f o r p a r t of t h e f a r m - o p e r a t o r ' s l a b o u r . T h i s i s r e a l i s t i c c o n s i d e r i n g t h a t a t y p i c a l f a r m - o p e r a t o r p e r f o r m s many t a s k s , some of which i n v o l v e l e s s management s k i l l s than o t h e r s . F i n a l l y , the c o e f f i c i e n t of the s c h o o l i n g v a r i a b l e g i v e s e v i d e n c e t o s u p p o r t the h y p o t h e s i s t h a t the l e v e l of s c h o o l i n g of the f a r m - o p e r a t o r does i n f l u e n c e d e c i s i o n s t o a l l o c a t e l a b o u r time between the on-farm and o f f - f a r m l a b o u r m a r k e t s . In t h i s c a s e , the n e g a t i v e c o e f f i c i e n t of the s c h o o l i n g v a r i a b l e i n d i c a t e s t h a t the f a r m - o p e r a t o r ' s time has i n c r e a s e d more o f f the farm than on the farm. The r e s u l t s from the e s t i m a t i o n s of the c a p i t a l and l a b o u r e q u a t i o n s u s i n g 1981 Census d a t a were, on the whole, s t r o n g e r than those r e s u l t s o b t a i n e d w i t h the 1971 Census d a t a so i t i s not s u r p r i s i n g t h a t e s t i m a t i o n of the 1981 60 v a r i a b l e p r o f i t f u n c t i o n a l s o p r o v i d e s more r o b u s t r e s u l t s t han e s t i m a t i o n of the 1971 p r o f i t f u n c t i o n . R e g r e s s i o n 4.3 shows t h a t a l l the v a r i a b l e s e x c e p t the ou t p u t p r i c e index a r e s i g n i f i c a n t and of the c o r r e c t s i g n . The r e l a t i v e l y low a d j u s t e d R square of .5180 i n d i c a t e s , however, t h a t almost h a l f of the v a r i a t i o n i n v a r i a b l e p r o f i t remains u n e x p l a i n e d w i t h t h i s model. T h i s would suggest t h a t a l t h o u g h the 1981 r e s u l t s a r e an improvement over t h e 1971 r e s u l t s , b o t h the 1981 and the 1971 models of the v a r i a b l e p r o f i t f u n c t i o n w i t h i n s t r u m e n t a l v a r i a b l e s c o u l d b e n e f i t from d i f f e r e n t s p e c i f i c a t i o n and b e t t e r q u a l i t y v a r i a b l e s i n the l a b o u r e q u a t i o n . For i n s t a n c e , an improved measurement of the f a r m - o p e r a t o r ' s o p p o r t u n i t y c o s t would be d e s i r a b l e , g i v e n t h a t the v a r i a b l e used (OFFW) t o r e f l e c t t h e o f f - f a r m wage r a t e i s d e r i v e d u s i n g census d a t a based on p o t e n t i a l l y i n a c c u r a t e r e s p o n s e s . A l s o , v a r i a b l e s which measured o f f - f a r m unemployment r a t e s or d i s t a n c e t o the n e a r e s t l a r g e urban c e n t e r s s h o u l d h e l p t o b e t t e r e x p l a i n the f a r m - o p e r a t o r ' s on-farm l a b o u r s u p p l y . A l t h o u g h e s t i m a t i o n s of the v a r i a b l e p r o f i t f u n c t i o n w i t h i n s t r u m e n t a l v a r i a b l e s were not w i t h o u t problems f o r b o t h the 1971 and the 1981 Census d a t a s e t s , t h e s e e s t i m a t i o n s can s t i l l p r o v i d e c o n s i d e r a b l e i n s i g h t i n t o the r o l e of s c h o o l i n g i n Canadian a g r i c u l t u r e . S p e c i f i c a l l y , the r e s u l t s from t h i s model s u p p o r t the h y p o t h e s i s t h a t the l e v e l of s c h o o l i n g of the f a r m - o p e r a t o r a f f e c t s the l e v e l and mix of p h y s i c a l c a p i t a l and o p e r a t o r on-farm l a b o u r . I n 61 b o t h t h e 1971 and the 1981 r e s u l t s , t he s c h o o l i n g c o e f f i c i e n t i s h i g h l y s i g n i f i c a n t i n a l l t h r e e e q u a t i o n s of the model. F u r t h e r m o r e , the s i g n s of the s c h o o l i n g c o e f f i c i e n t s i n t h e s e r e s u l t s a r e a l s o i n accordance w i t h the p r e d i c t i o n s made i n the c o n t e x t of t h e human c a p i t a l t h e o r i e s of S c h u l t z and Welch. T h e r e f o r e , i n the sense of d e s c r i b i n g the r o l e of s c h o o l i n g i n the d e c i s i o n - m a k i n g p r o c e s s of the f a r m - o p e r a t o r , the model of t h e extended v a r i a b l e p r o f i t f u n c t i o n w i t h i n s t r u m e n t a l v a r i a b l e s i s s u c c e s s f u l . Up t o t h i s p o i n t , no mention has been made of the m a r g i n a l p r o f i t e f f e c t s of s c h o o l i n g found w i t h t h i s model ( T a b l e s 7 and 8 ) . I t s h o u l d be noted t h a t t h e s e measurements of $546 (1970 $) and $18,465 (1980 $) a r e r a d i c a l l y d i f f e r e n t from the measurements o b t a i n e d from e s t i m a t i o n s of a v a r i a b l e p r o f i t f u n c t i o n w i t h o u t i n s t r u m e n t a l v a r i a b l e s which a r e $1003 (1970 $) and $3161 (1980 $ ) . 2 " Given the d i s c r e p a n c y between t h e two s e t s of measurements, the q u e s t i o n a r i s e s as t o which s e t of measurements i s more r e l i a b l e . I n o r d e r t o compare the d i f f e r e n t measurements, i t i s f i r s t n e c e s s a r y t o e x p l a i n how the m a r g i n a l p r o f i t e f f e c t s i n T a b l e s 7 and 8 were d e r i v e d . The m a r g i n a l p r o f i t e f f e c t s were computed by t r a n s l a t i n g t he i n f o r m a t i o n g i v e n i n a l l t h r e e e q u a t i o n s of the model about the r o l e of s c h o o l i n g i n a f f e c t i n g farm p r o f i t i n t o a s i m p l e e q u a t i o n . As s h o u l d be 2 " R e f e r t o T a b l e s 4 and 6. 62 r e c a l l e d from the d i s c u s s i o n of Welch's r e s e a r c h i n Chapter Two, the r o l e of e d u c a t i o n i n the d e c i s i o n - m a k i n g p r o c e s s of the f a r m - o p e r a t o r i s t w o - f o l d : v a r i a t i o n s i n the l e v e l of s c h o o l i n g may l e a d t o v a r i a t i o n s i n the l e v e l of p r o f i t ("the worker e f f e c t " ) ; and v a r i a t i o n s i n the l e v e l of s c h o o l i n g may l e a d t o v a r i a t i o n s i n the use of o t h e r i n p u t s which i n t u r n may l e a d t o a v a r i a t i o n i n p r o f i t ("the a l l o c a t i v e e f f e c t " ) . The e q u a t i o n used f o r computing the m a r g i n a l p r o f i t e f f e c t of s c h o o l i n g a l l o w s f o r b o t h of th e s e e f f e c t s t o be d e t e r m i n e d . The e q u a t i o n i s as f o l l o w s : drr/dE = 5i(/dE + (3w/3K)*(3K/3E) + ( 3TT/3L) * ( 3L/3E) where ir r e f e r s t o v a r i a b l e p r o f i t , E r e f e r s t o s c h o o l i n g of the f a r m - o p e r a t o r , K r e f e r s t o p h y s i c a l farm c a p i t a l , and L r e f e r s Jto the o p e r a t o r ' s l a b o u r s u p p l y t o the farm. The f i r s t term i n the e q u a t i o n r e p r e s e n t s the "worker e f f e c t " of s c h o o l i n g w h i l e the l a s t two terms r e p r e s e n t the " a l l o c a t i v e e f f e c t " of s c h o o l i n g . U s i n g the c o e f f i c i e n t s found i n the e s t i m a t i o n s ( T a b l e s 7 and 8) and t h e a r i t h m e t i c means of the v a r i a b l e s , the a c t u a l numbers c o r r e s p o n d i n g t o the above e q u a t i o n a r e as f o l l o w s : 1971 Census d a t a s e t $546 = $737 - $498 + $307 1981 Census d a t a s e t $18,465 = $17,599 + $6005 - $5139 The s i g n s of the l a s t two terms a r e d i f f e r e n t i n the 63 e q u a t i o n s because th e s i g n s of the p r e d i c t e d l a b o u r and c a p i t a l v a r i a b l e s i n t h e v a r i a b l e p r o f i t f u n c t i o n were n e g a t i v e u s i n g the 1971 Census d a t a s e t and p o s i t i v e u s i n g the 1981 Census d a t a s e t ( T a b l e 7 and 8 ). These measurements of the m a r g i n a l p r o f i t e f f e c t s of s c h o o l i n g s h o u l d be i n t e r p r e t e d w i t h c a u t i o n f o r two r e a s o n s : f i r s t , the s p e c i f i c a t i o n of the model w i t h i n s t r u m e n t a l v a r i a b l e s based on the 1971 Census d a t a e s p e c i a l l y needs t o be improved; and second, a comparison of the e s t i m a t e d on-farm l o s s e s due t o s c h o o l i n g w i t h the e s t i m a t e d o f f - f a r m g a i n s due t o s c h o o l i n g based on the 1981 Census r e v e a l s t h a t i t i s d i f f i c u l t t o t r a n s l a t e the l a b o u r v a r i a b l e (OCC) ( d e f i n e d as the p e r c e n t a g e of f a r m - o p e r a t o r s who d e c l a r e f a r m i n g t o be t h e i r main o c c u p a t i o n ) i n t o an a c t u a l measurement of l a b o u r days s u p p l i e d by the f a r m - o p e r a t o r on the farm. The o f f - f a r m g a i n s s h o u l d be a t l e a s t comparable i f not g r e a t e r than the on-farm l o s s e s . However, the o f f - f a r m g a i n s found w i t h 1981 d a t a were o n l y $1666 compared w i t h the on-farm l o s s e s which were $5139. T h i s would mean t h a t t h e f a r m - o p e r a t o r was c h o o s i n g t o a l l o c a t e h i s / h e r l a b o u r time between the on-farm and o f f - f a r m markets i n such a way t h a t would r e s u l t i n t h e l o s s of $3473. T h i s i s not c o n s i s t e n t w i t h the assumption of r a t i o n a l i t y i m p l i c i t i n t h e o r i e s of p r o f i t m a x i m i z a t i o n . T h e r e f o r e , i t must be c o n c l u d e d t h a t the a c t u a l l e v e l s s u p p l i e d by the e s t i m a t i o n s of the v a r i a b l e p r o f i t f u n c t i o n w i t h i n s t r u m e n t a l v a r i a b l e s a r e i n a c c u r a t e . The i n a c c u r a c y 64 i s most l i k e l y due t o s p e c i f i c a t i o n problems and the d i f f i c u l t y i n t r a n s l a t i n g the 1981 l a b o u r v a r i a b l e (OCC) i n t o a c t u a l day u n i t s . G i v e n t h e s e d i f f i c u l t i e s , the most r e l i a b l e measurements o b t a i n e d i n t h i s t h e s i s of the m a r g i n a l p r o f i t e f f e c t s of s c h o o l i n g would be tho s e presented i n T a b l e s 4 and 6 which were $1003 (based on 1971 Census d a t a , i n 1970 $) and $3161 (based on 1981 Census d a t a i n 1980 $ ) . 5.4 RELEVANCE OF THE VALUE OF SCHOOLING IN CANADIAN  AGRICULTURE The g o a l s of t h i s r e s e a r c h a r e t w o - f o l d : f i r s t , t o measure the r e t u r n s a c c r u i n g t o f a r m - o p e r a t o r s who have g e n e r a t e d human c a p i t a l t h r o u g h the s c h o o l i n g p r o c e s s ; and, second, t o a p p l y t h i s measurement t o the c o n t e x t of d e c i s i o n s made by f a r m - o p e r a t o r s , p r o s p e c t i v e e n t r a n t s , and a g r i c u l t u r a l p o l i c y m a k e r s . The f i r s t of t h e s e g o a l s has been a c c o m p l i s h e d . I t now remains t o c o n s i d e r how the i n f o r m a t i o n g e n e r a t e d i n t h i s t h e s i s c o u l d be r e l e v a n t t o d e c i s i o n - m a k i n g . T a b l e s 9 and 10 a r e p r e s e n t e d t o i l l u s t r a t e t h a t t h e r e a r e h i g h l y 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 i n a g r i c u l t u r e even a f t e r the i n i t i a l c o s t s have been i n c l u d e d . The measurements of the v a l u e of s c h o o l i n g i n a g r i c u l t u r e ($1003 i n 1970 $ and $3161 i n 1980 $) have been t r a n s l a t e d i n t o i n v e s t m e n t s by s u b t r a c t i n g the c o s t s and d i s c o u n t i n g w i t h r e a l d i s c o u n t r a t e s . The r e s u l t i n g net p r e s e n t v a l u e s of an a d d i t i o n a l TABLE 9 Net Present Value of an A d d i t i o n a l Tear o f Schoo l i ng i n Farming, 1971 Census d a t a (1980 S) Years Real D iscoun t Rates Remaining i n Farming 2% 4% 6% 30 S 39,516 $ 27,131 $ 18,657 40 $ 51,852 $ 33,351 $ 21,844 50 $ 61,970 $ 37,555 $ 23,624 Net Present Va lue - (MPS - C) / (1 + r ) where: MP m M a r g i n a l p r o f i t e f f e c t o f s c h o o l i n g C " e d u c a t i o n a l c o s t s o f $ 3 2 1 9 / y r + o p p o r t u n i t y c o s t s o f 5 3441 /y r r - r e a l d i s c o u n t r a t e n - number o f y e a r s rema in ing i n f a r m i n g TABLE 10 Net Present Value of an A d d i t i o n a l Year of Schoo l ing i n Farming , 1981 Census da ta (1980 S) 66 Years Remaining i n Farming Real D i s c o u n t Rates 2% 4% 6% 30 $ 53,782 $ 37,975 $ 27,140 40 $ 69,458 $ 45,879 $ 31,191 50 $ 82,317 $ 51,220 $ 33,452 n Net Present Va lue - (MP $ - C) / (1 + r ) where: MP- » M a r g i n a l p r o f i t e f f e c t o f s c h o o l i n g C - e d u c a t i o n a l c o s t s o f $ 7500/yr • o p p o r t u n i t y c o s t s o f $ 9853/yr r - r e a l d i s c o u n t r a t e n - number o f y e a r s r e m a i n i n g i n f a r m i n g 67 year of s c h o o l i n g r e v e a l t h a t even w i t h c o n s e r v a t i v e e s t i m a t e s of the c o s t s and of t h e r e t u r n s , s c h o o l i n g i s a good in v e s t m e n t i f a c a r e e r as a f a r m - o p e r a t o r i s c o n s i d e r e d . The i n f o r m a t i o n i n the t a b l e s would be u s e f u l t o farm f a m i l i e s w i t h c h i l d r e n who a r e d e c i d i n g whether t o c o n t i n u e w i t h s c h o o l , or t o q u i t s c h o o l and s t a r t f a r m i n g f u l l - t i m e . These p r o s p e c t i v e e n t r a n t s s h o u l d be a b l e t o make t h e i r d e c i s i o n w i t h knowledge t h a t a d d i t i o n a l s c h o o l i n g a c t u a l l y does pay i n f a r m i n g . In a d d i t i o n t o p r o s p e c t i v e e n t r a n t s , young c u r r e n t f a r m - o p e r a t o r s would a l s o be i n t e r e s t e d t o l e a r n t h a t a d d i t i o n a l s c h o o l i n g would h e l p i n c r e a s e farm p r o f i t s . T a b l e 10, f o r i n s t a n c e , i n d i c a t e s t h a t a f a r m - o p e r a t o r w i t h f o r t y y e a r s r e m a i n i n g i n f a r m i n g w i t h a r e a l d i s c o u n t r a t e of 4 % can e x p e c t the t o t a l r e t u r n s a c c r u i n g from an a d d i t i o n a l y e a r of s c h o o l i n g t o be $ 45,879 (1980 $ ) . F i n a l l y , a g r i c u l t u r a l p o l i c y - m a k e r s would a l s o be i n t e r e s t e d i n the i n f o r m a t i o n c o n t a i n e d i n T a b l e s 9 and 10. I f the p u b l i c c o s t s of i n c r e a s i n g the a v a i l a b i l i t y and q u a l i t y of r u r a l s c h o o l i n g a r e l o w e r than the r e t u r n s t o the a g r i c u l t u r a l s e c t o r from i n c r e a s e d p r o f i t s and t h e r e t u r n s t o s o c i e t y on the whole, then t h i s a l t e r n a t i v e t o the p o l i c y t o p i s of m a r k e t i n g boards and government s u b s i d y programs f o r i n c r e a s i n g farm incomes and p r o d u c t i v i t y can be c o n s i d e r e d . 6. SUMMARY AND CONCLUSIONS T h i s r e s e a r c h was un d e r t a k e n t o ad d r e s s the problem of s c a r c e and c o n f l i c t i n g e v i d e n c e c o n c e r n i n g t h e e f f e c t of e d u c a t i o n on farm p r o f i t and p r o d u c t i v i t y i n Canada. F u r t h e r m o r e , u n t i l now, t h e r e have been no s t u d i e s i n Canada which e s t i m a t e the v a l u e of e d u c a t i o n i n a g r i c u l t u r e u s i n g d a t a from t h e 1981 Census. T h i s t h e s i s a t t e m p t e d t o f i l l the i n f o r m a t i o n gap f a c i n g c u r r e n t f a r m - o p e r a t o r s , p r o s p e c t i v e e n t r a n t s , and a g r i c u l t u r a l p o l i c y - m a k e r s c o n c e r n i n g the e f f e c t of a d d i t i o n a l e d u c a t i o n on farm p r o f i t and p r o d u c t i v i t y . The g o a l s of t h i s t h e s i s were t w o - f o l d : t o measure the r e t u r n s a c c r u i n g t o Canadian f a r m - o p e r a t o r s who have g e n e r a t e d human c a p i t a l t h r o u g h the s c h o o l i n g p r o c e s s ; and second, t o c o n s i d e r the i m p l i c a t i o n s of such measurements. In o r d e r t o a c h i e v e t h e s e g o a l s , s e v e r a l s p e c i f i c o b j e c t i v e s were met. The f i r s t o b j e c t i v e was t o b u i l d a model which r e f l e c t s the r o l e of e d u c a t i o n i n the d e c i s i o n - m a k i n g p r o c e s s of Canadian f a r m - o p e r a t o r s . The t h e o r e t i c a l f o u n d a t i o n s were l a i d f o r t h i s model i n Chapter Two w i t h a d i s c u s s i o n of the human c a p i t a l t h e o r i e s of S c h u l t z and Welch. The main c o n t r i b u t i o n of S c h u l t z t o the model i s the n o t i o n t h a t the v a l u e of s c h o o l i n g i n a g r i c u l t u r e depends on the p r e v a l e n t r a t e of change of p r o d u c t i o n t e c h n o l o g y o r , more g e n e r a l l y , on d i s e q u i l i b r i a i n any a s p e c t of economic a c t i v i t y . The main c o n t r i b u t i o n of Welch t o t h e model i s h i s s e p a r a t i o n of 68 69 t h e r e t u r n s t o s c h o o l i n g i n p r o d u c t i o n i n t o two e f f e c t s : the "worker e f f e c t " and the " a l l o c a t i v e e f f e c t " . Based on the c o n t r i b u t i o n s of S c h u l t z and Welch, the s p e c i f i c a t i o n of the model was d e v e l o p e d i n Chapter Three. A f t e r c o n s i d e r i n g b o t h the p r o d u c t i o n f u n c t i o n approach and the p r o f i t f u n c t i o n a pproach, i t was c o n c l u d e d t h a t e s t i m a t i o n of a v a r i a b l e p r o f i t f u n c t i o n would b e s t r e p r e s e n t the r o l e of s c h o o l i n g i n the d e c i s i o n - m a k i n g p r o c e s s of the f a r m - o p e r a t o r . An e x t e n s i o n of the v a r i a b l e p r o f i t model was a l s o p r e s e n t e d , wherein o p e r a t o r on-farm l a b o u r s u p p l y and a g g r e g a t e d p h y s i c a l c a p i t a l were endogenized i n a s i m u l t a n e o u s e q u a t i o n s framework. The next two o b j e c t i v e s of t h i s t h e s i s , t o i d e n t i f y the r e l e v a n t v a r i a b l e s and t o c o l l e c t the d a t a needed f o r e s t i m a t i o n of the model were a c h i e v e d i n Chapter F o u r . In t h i s c h a p t e r , the main source of d a t a used i n the t h e s i s , the 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 base, was a l s o d e s c r i b e d w i t h a t t e n t i o n g i v e n t o b oth the advantages and d i s a d v a n t a g e s of u s i n g such a d a t a base. A f t e r p r e s e n t i n g t h e d e f i n i t i o n s of a l l the v a r i a b l e s used i n t h e e s t i m a t i o n s , the c h o i c e of Cobb-Douglas as the f u n c t i o n a l form was a l s o d i s c u s s e d . In Chapter F i v e , the f i n a l two o b j e c t i v e s were met. These were t o e s t i m a t e the e f f e c t of f a r m - o p e r a t o r s c h o o l i n g on farm p r o f i t and p r o d u c t i v i t y i n Canada and t o i n t e r p r e t t h e measurements. R e s u l t s from e s t i m a t i o n s of a g r o s s s a l e s p r o d u c t i o n f u n c t i o n and a v a r i a b l e p r o f i t f u n c t i o n u s i n g 70 d a t a from b o t h the 1971 Census and the 1981 Census were p r e s e n t e d . Based on t h e s e r e s u l t s , the m a r g i n a l p r o f i t e f f e c t of s c h o o l i n g was computed t o be $1003 ( i n 1970 $) and $3161 ( i n 1980 $ ) . The net p r e s e n t v a l u e of an a d d i t i o n a l y e a r of s c h o o l i n g i n f a r m i n g was c a l c u l a t e d u s i n g the above measurements of the r e t u r n s t o s c h o o l i n g , e s t i m a t e s of c o s t s ( e d u c a t i o n a l and o p p o r t u n i t y c o s t s ) , a s p r e a d of r e a l d i s c o u n t r a t e s , and d i f f e r e n t age groups. The r e s u l t i n g t a b l e s were p r e s e n t e d t o i l l u s t r a t e t h a t the net r e t u r n s t o s c h o o l i n g i n a g r i c u l t u r e a r e h i g h l y p o s i t i v e . I t was h y p o t h e s i z e d t h a t t h i s i n f o r m a t i o n would be u s e f u l t o c u r r e n t f a r m - o p e r a t o r s , p r o s p e c t i v e e n t r a n t s , and a g r i c u l t u r a l p o l i c y - m a k e r s . The c o n c l u s i o n s t h a t can be drawn from the r e s e a r c h r e p o r t e d i n t h i s t h e s i s f a l l i n t o t h r e e c a t e g o r i e s . The f i r s t c a t e g o r y c o n c e r n s the o b j e c t i v e of b u i l d i n g a model which r e f l e c t s the r o l e of e d u c a t i o n i n the d e c i s i o n - m a k i n g p r o c e s s of Canadian f a r m - o p e r a t o r s . G i v e n the r e s u l t s p r e s e n t e d i n T a b l e s 3, 4, 5, and 6, i t i s p o s s i b l e t o c o n c l u d e t h a t the models of the g r o s s s a l e s p r o d u c t i o n f u n c t i o n and the s i n g l e e q u a t i o n v a r i a b l e p r o f i t f u n c t i o n were a p p r o p r i a t e l y s p e c i f i e d t o r e f l e c t the r o l e of s c h o o l i n g . E v i d e n c e s u p p o r t i n g t h i s c o n c l u s i o n i s g i v e n by the changes i n the s c h o o l i n g c o e f f i c i e n t t h a t o c c u r r e d when a d j u s t m e n t s were made i n the models so t h a t more c h a n n e l s of d e c i s i o n - m a k i n g were open t o the f a r m - o p e r a t o r . These a d j u s t m e n t s i n c l u d e the a d d i t i o n of an a g r i c u l t u r a l r e s e a r c h 71 v a r i a b l e , t h e a g g r e g a t i o n of c a p i t a l i n t o one v a r i a b l e 2 5 and the movement from a g r o s s s a l e s p r o d u c t i o n f u n c t i o n t o a v a l u e - a d d e d p r o d u c t i o n f u n c t i o n t o a v a r i a b l e p r o f i t f u n c t i o n . The s c h o o l i n g c o e f f i c i e n t changed as a r e s u l t of t h e s e a d j u s t m e n t s from 0.158 ( r e g r e s s i o n 1.2) t o 0.784 ( r e g r e s s i o n 1.8) u s i n g 1971 Census d a t a and from 0.234 ( r e g r e s s i o n 2.5) t o 0.679 ( r e g r e s s i o n 2.8) u s i n g 1981 Census d a t a . E s t i m a t i o n s of the v a r i a b l e p r o f i t f u n c t i o n w i t h i n s t r u m e n t a l v a r i a b l e s were a l s o s u c c e s s f u l i n d e s c r i b i n g the r o l e of s c h o o l i n g i n the f a r m - o p e r a t o r ' s d e c i s i o n - m a k i n g p r o c e s s . I t was shown t h a t v a r i a t i o n s i n the l e v e l of s c h o o l i n g l e a d t o v a r i a t i o n s i n the l e v e l s of c a p i t a l and the on-farm o p e r a t o r l a b o u r s u p p l y . E v i d e n c e i s g i v e n by the s t a b l e and s i g n i f i c a n t s c h o o l i n g c o e f f i c i e n t i n each of the t h r e e e q u a t i o n s of the model ( T a b l e s 7 and 8 ) . The second c a t e g o r y of c o n c l u s i o n s t h a t can be drawn from the r e s u l t s p r e s e n t e d i n t h i s t h e s i s c o n c e r n s t h e s p e c i f i c a t i o n of the r e l e v a n t v a r i a b l e s and the c h o i c e of a f u n c t i o n a l form. The c h o i c e of a Cobb-Douglas f u n c t i o n a l form appears t o have been a p p r o p r i a t e g i v e n the c o n s i s t e n t l y h i g h a d j u s t e d R squares and the h i g h l e v e l of s i g n i f i c a n c e of most of the v a r i a b l e s . O v e r a l l , the s p e c i f i c a t i o n of the v a r i a b l e s a l s o seems t o have been a p p r o p r i a t e . The v a r i a b l e s t h a t c o u l d b e n e f i t from d i f f e r e n t s p e c i f i c a t i o n a r e the 2 5 W h i l e the 1971 r e s u l t s seemed t o s u p p o r t the h y p o t h e s i s t h a t t h i s would a l l o w g r e a t e r " l e v e r a g e " t o the s c h o o l i n g v a r i a b l e i n a l l o c a t i n g between t h e v a r i o u s components of c a p i t a l , the 1981 r e s u l t s were not as c l e a r . 72 o f f - f a r m wage r a t e , t h e on-farm o p e r a t o r l a b o u r s u p p l y and the r e s e a r c h v a r i a b l e . F u r t h e r m o r e , i t can be h y p o t h e s i z e d t h a t the u n u s u a l l y h i g h c o e f f i c i e n t s of the l a b o u r v a r i a b l e s (LDY and OCC) are due t o a p o s i t i v e b i a s from o m i t t e d v a r i a b l e s such as " a b i l i t y " of the f a r m - o p e r a t o r . The t h i r d and f i n a l c a t e g o r y of c o n c l u s i o n s t h a t can be drawn from t h e r e s u l t s c o n c e r n s the measurements of the v a l u e of s c h o o l i n g i n Canadian a g r i c u l t u r e . The most r e l i a b l e e s t i m a t e s of the r e t u r n s t o an a d d i t i o n a l y e a r of s c h o o l i n g found i n t h i s t h e s i s were $1003 (1970 $) based on 1970 d a t a and $3161 (1980 $) based on 1980 d a t a . The v a l u e of t h e s e e s t i m a t e s l i e s not i n t h e i r a c t u a l l e v e l s , but i n the f a c t t h a t they a r e h i g h l y p o s i t i v e and comparable t o average urban l a b o u r market r e t u r n s . 2 6 Futhermore, a comparison of the two e s t i m a t e s a f t e r a c c o u n t i n g f o r i n f l a t i o n r e v e a l s t h a t the r e t u r n s t o s c h o o l i n g were 27 % h i g h e r i n 1980 than i n 1970. I t i s p o s s i b l e t o c o n c l u d e t h a t t h i s i n c r e a s e i s due t o the g r e a t e r degree of d i s e q u i l i b r i a i n i n p u t markets i n 1980. F i n a l l y , the measurements of the m a r g i n a l p r o f i t e f f e c t s of s c h o o l i n g can a l s o be used t o compute the net p r e s e n t v a l u e of s c h o o l i n g i n a g r i c u l t u r e . Even w i t h r e l a t i v e l y h i g h e s t i m a t e s of c o s t s , i t was found t h a t the net r e t u r n s t o s c h o o l i n g a r e h i g h l y p o s i t i v e ( T a b l e s 7 and 2 6 T h e average e a r n i n g s d i f f e r e n t i a l i n 1970 between h i g h s c h o o l g r a d u a t i o n and u n i v e r s i t y i s $1150. The e a r n i n g s d i f f e r e n t i a l between h i g h s c h o o l g r a d u a t e s and tho s e w i t h "some h i g h s c h o o l " i s a p p r o x i m a t e l y $500 per y e a r . B a r i c h e l l o 1984, p. 20. 73 8) i n Canadian a g r i c u l t u r e . These r e s u l t s p r o v i d e s t r o n g e v i d e n c e t o c o u n t e r Shaw's c o n c l u s i o n t h a t " p u r s u i t of e d u c a t i o n may mean d e l a y e d e a r n i n g s f o r t h o s e who have d e c i d e d on a f a r m i n g c a r e e r , w i t h o u t any compensating i n c r e a s e i n income." 2 7 The h i g h l y 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 found i n t h i s t h e s i s i n d i c a t e a t y p e of market f a i l u r e and g i v e r i s e t o the q u e s t i o n of why p e o p l e a re not g e t t i n g more e d u c a t i o n . Even more a c c u r a t e measurements of the e f f e c t of s c h o o l i n g on farm p r o f i t and p r o d u c t i v i t y i n Canada c o u l d be o b t a i n e d w i t h an improved d a t a s e t . The s i n g l e l a r g e s t c o n s t r a i n t e n c o u n t e r e d i n t h i s r e s e a r c h was the l a c k of a p p r o p r i a t e o p e r a t o r on-farm and o f f - f a r m l a b o u r d a t a . T h e r e f o r e , s u g g e s t i o n s f o r f u t u r e r e s e a r c h i n c l u d e the use of b e t t e r s p e c i f i e d v a r i a b l e s f o r the o f f - f a r m wage r a t e and the on-farm o p e r a t o r l a b o u r s u p p l y . A f i n a l s u g g e s t i o n would be t o p o o l the two d a t a s e t s used i n t h i s s t u d y , so t h a t even more i n f o r m a t i o n c o n c e r n i n g the v a l u e of s c h o o l i n g i n Canadian a g r i c u l t u r e c o u l d be e x t r a c t e d . 2 7Shaw 1979, p. 38-9. 7. BIBLIOGRAPHY B a r i c h e l l o , R. "The S c h o o l i n g of Farm Youth i n Canada." U n p u b l i s h e d Ph.D. d i s s e r t a t i o n , U n i v e r s i t y of C h i c a g o , (December 1979) . "The P r o d u c t i v e V a l u e of S c h o o l i n g i n Canadian A g r i c u l t u r e . " D i s c u s s i o n Paper, Y a l e U n i v e r s i t y and U n i v e r s i t y of B r i t i s h C o lumbia, ( F e b r u a r y 1984). B e c k e r , G.S. and C h i s w i c k , B.R. " E d u c a t i o n and the D i s t r i b u t i o n of E a r n i n g s . " A m e r i c a n Economic Review. V o l . 61, No. 2 (May 1966): 358-369. Brinkman, G.L. An A n a l y s i s of So u r c e s of M u l t i f a c t o r P r o d u c t i v i t y Growth i n Canadian A g r i c u l t u r e , 1961 t o  1980, w i t h P r o i e c t i o n s t o 2000. R e g i o n a l Development Branch, A g r i c u l t u r e Canada (December 1984), Appendix T a b l e 2, p. 72, Appendix T a b l e 3, p. 73. Fane, G. "The P r o d u c t i v e V a l u e of E d u c a t i o n i n A g r i c u l t u r e i n the U.S. Corn B e l t , 1964." U n p u b l i s h e d Ph.D. d i s s e r t a t i o n , H a r v a r d U n i v e r s i t y (May 1972). . " E d u c a t i o n and the M a n a g e r i a l E f f i c i e n c y of Farmers." Review of Economics and S t a t i s t i c s . V o l . 57, No. 4 (November 1975): 452-461. G i n t i s , H. " E d u c a t i o n , Technology, and t h e C h a r a c t e r i s t i c s of Worker P r o d u c t i v i t y . " American Economic Review,  Papers and P r o c e e d i n g s . V o l . 61, No. 2, Supplement (May 1971): 266-279. . " S c h o o l i n g and the A g r i c u l t u r a l Labor F o r c e . " U n p u b l i s h e d Ph.D. d i s s e r t a t i o n , U n i v e r s i t y of Chic a g o (December 1962). G i s s e r , M. " S c h o o l i n g and the Farm Problem." E c o n o m e t r i c a . V o l . 33, No. 3 ( J u l y 1965): 582-592. 74 75 G r i l i c h e s , Z. " S p e c i f i c a t i o n B i a s i n E s t i m a t e s of P r o d u c t i o n F u n c t i o n s . " J o u r n a l of Farm Economics. V o l . 39, No. 1 (F e b r u a r y 1957): 8-20. . " E s t i m a t e s of the Aggregate 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 from C r o s s - S e c t i o n a l Data." J o u r n a l of Farm Economics. V o l . 45, No. 2 (May 1963): 419-428. . "Research E x p e n d i t u r e s , E d u c a t i o n , and the Aggregate 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 . " American  Economic Review. V o l . 54, No. 6 (December 1964): 961-974. . " E r r o r s i n V a r i a b l e s and Other U n o b s e r v a b l e s . " E c o n o m e t r i c a . V o l . 42, No. 6 (November 1974): 971-998. . " 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 : Some Eco n o m e t r i c Problems." E c o n o m e t r i c a . V o l . 45, No. 1 (Ja n u a r y 1977): 1-22. Huffman, W. " D e c i s i o n Making: The Rol e of E d u c a t i o n . " American J o u r n a l of A g r i c u l t u r a l Economics. V o l . 56 (F e b r u a r y 1974): 84-97. . " A l l o c a t i v e E f f i c i e n c y : The R o l e of Human C a p i t a l . " Q u a r t e r l y J o u r n a l of Economics. V o l . 91 (F e b r u a r y 1977): 59-79. . "Farm and Off-Farm Work D e c i s i o n s : The R o l e of Human C a p i t a l . " Review of Economics and  S t a t i s t i c s . V o l . 62, No. 1 (F e b r u a r y 1980): 14-23. J a m i s o n , D.T. and Lau, L . J . Farmer E d u c a t i o n and Farm E f f i c i e n c y . B a l t i m o r e : The Johns Hopkins U n i v e r s i t y P r e s s , 1982. K h a l d i , N. "The P r o d u c t i v e V a l u e of E d u c a t i o n i n the U.S. A g r i c u l t u r e , 1964." U n p u b l i s h e d Ph.D. d i s s e r t a t i o n , S o u t h e r n M e t h o d i s t U n i v e r s i t y ( J a n u a r y 1973). . " 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 i n U.S. A g r i c u l t u r e . " American J o u r n a l of A g r i c u l t u r a l  Economics. V o l . 57 (November 1975): 650-657. 76 Labadan, E.M. "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 Canadian Farm Income." U n p u b l i s h e d M.Sc. t h e s i s U n i v e r s i t y of B r i t i s h Columbia ( A p r i l 1979). 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, Papers and P r o c e e d i n g s . V o l . 56, No. 2 (May 1966): 69-75. P e t z e l , T.E. " E d u c a t i o n and the Dynamics of S u p p l y . " U n p u b l i s h e d Ph.D. d i s s e r t a t i o n , U n i v e r s i t y of Chic a g o (December 1976). . "The R o l e of E d u c a t i o n i n the Dynamics of Su p p l y . " American J o u r n a l of A g r i c u l t u r a l Economics. V o l . 60 (August 1978): 445-451. P u d a s a i n i , S.P. "The E f f e c t s of E d u c a t i o n i n A g r i c u l t u r e : E v i d e n c e from N e p a l . " American J o u r n a l of A g r i c u l t u r a l  Economics . V o l . 65 (August 1983): 509-515. R o d i e r , M. F e d e r a l A g r i - F o o d E x p e n d i t u r e s , 1982-1983  and 1983-1984. R e g i o n a l Development Branch, A g r i c u l t u r e Canada (September 1985), S e c t i o n 2, p. 25. S c h u l t z , T.W. "The V a l u e of the A b i l i t y t o D e a l w i t h D i s e q u i l i b r i a . " J o u r n a l of Economic L i t e r a t u r e . V o l . 13 (September 1975): 827-846. . "Investment i n E n t r e p r e n e u r i a l A b i l i t y . " S c a n d i n a v i a n J o u r n a l of Economics. V o l . 82, No. 4 (1980): 437-448. Shaw, P. Canada's Farm P o p u l a t i o n . Ottawa: S t a t i s t i c s Canada, 1979. Sumner, D.A. "Labor Supply and E a r n i n g s of Farm F a m i l i e s w i t h Emphasis on Off-Farm Work." U n p u b l i s h e d Ph.D. d i s s e r t a t i o n , U n i v e r s i t y of C h i c a g o (March 1978). Welch, F. "Measurement of the Q u a l i t y of S c h o o l i n g . " , American Economic Review, Papers and P r o c e e d i n g s . V o l . 56 (May 1966): 379-392. 77 . "The D e t e r m i n a n t s of the R e t u r n t o S c h o o l i n g i n R u r a l Farm A r e a s , 1959." U n p u b l i s h e d Ph.D. d i s s e r t a t i o n , ? U n i v e r s i t y of Chicago (June 1966). . " 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 of P o l i t i c a l Economy. V o l . 78, No. 1 ( J a n u a r y / F e b r u a r y 1970): 35-59. . "The R o l e of Investment i n Human C a p i t a l i n A g r i c u l t u r e . " In D i s t o r t i o n s of A g r i c u l t u r a l  I n c e n t i v e s . E d i t e d by T.W. S c h u l t z . B l o o m i n g t o n : I n d i a n a U n i v e r s i t y P r e s s , 1978. Y o t o p o u l o s , P.A. and Nugent, J.B. Economics of Development:  E m p i r i c a l I n v e s t i g a t i o n s . New York: Harper and Row, 1976. 78 8. APPENDIX 79 8 . 1 CENSUS LABOUR QUESTIONS S o u r c e : C e n s u s o f P o p u l a t i o n , 1971 3 3 . How many h o u r s d o y o u u s u a l l y w o r k e a c h week? 0 1 - 1 9 0 2 0 - 2 9 0 3 0 - 3 4 0 3 5 - 3 9 0 4 0 - 4 4 0 4 5 - 4 9 0 50 o r m o r e 3 9 . ( a ) I n how many w e e k s d i d y o u w o r k d u r i n g 1970? Include weeks worked part-time, leave with pay and weeks of self-employment. O D i d n o t w o r k d u r i n g 1970 0 1 - 1 3 O 1 4 - 2 6 O 2 7 - 3 9 0 4 0 - 4 8 O 4 9 - 5 2 ( b ) Was t h i s w o r k m a i n l y f u l l - t i m e o r p a r t - t i m e ? O O F u l l - t i m e P a r t - t ime S o u r c e : C e n s u s o f A g r i c u l t u r e , 1971 1 9 5 . How many d a y s d i d y o u ( t h e o p e r a t o r ) w o r k 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 a n d n o n - a g r i c u l t u r a l w o r k d u r i n g 1970? (Do n o t i n c l u d e e x c h a n g e w o r k ) 0 N o n e . 81 S o u r c e : C e n s u s o f C a n a d a , 1981 3 9 . ( a ) L a s t w e e k , how many h o u r s d i d y o u w o r k ( n o t i n c l u d i n g h o u s e w o r k o r o t h e r w o r k a r o u n d y o u r home)? Incl ude: working for wages, salary, tips or commission, working in your own business, farm or professional practice, working without pay i n a family farm or business. H o u r s ( t o t h e n e a r e s t h o u r ) 4 5 . ( a ) I n how many w e e k s d i d y o u w o r k d u r i n g 1980 ( n o t i n c l u d i n g h o u s e w o r k o r o t h e r w o r k a r o u n d y o u r h o m e ) ? Include those weeks in which you: * worked full-time or part-time; * were on vacation or sick leave with pay; * were self-employed. ( b ) D u r i n g m o s t o f t h o s e w e e k s , d i d y o u w o r k f u l l - t i m e o r p a r t - t i m e ? Mark one box only 0 N o n e . Weeks 0 N o n e . 0 0 F u l l - t i m e P a r t - t i m e S o u r c e : C e n s u s o f A g r i c u l t u r e , 1981 1 3 4 . How many d a y s d i d y o u ( t h e o p e r a t o r ) w o r k o f f t h i s h o l d i n g i n 1980 a t : (Do n o t i n c l u d e e x c h a n g e w o r k . C o n v e r t p a r t d a y s t o f u l l d a y s on t h e b a s i s o f an 8 h o u r d a y . ) ( a ) p a i d a g r i c u l t u r a l w o r k ? ; None ( b ) p a i d n o n - a g r i c u l t u r a l w o r k ? ; None 

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