Hayami Wang Allen Morishima Allen

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1 * Allen Morishima 6 DOI: /j.cnki.jae de Brauw 2002 Wang 2016 Binswanger 1978 Hayami 1985 Hicks 1932 Huang 2009 Lin 1991 Wang 2017 Wang 2016 Yang % 52% 53% % 26% 17% *

2 Hayami Wang Allen Morishima Allen Wang 2016 Morishima Wang 2016 Morishima

2018 4 10 Wang 2016 15 1 ~ 3 19902015 3. 8% 5.

2 8700 72% 52% 53% 19812015 2016 1 19802015

3 Wang ~ % 5. 8% 8. 7% % 52% 53% Battese 1995 Kumbhakar

19812015 2016 3 19802015 i t Q it Q it = f( X it T β ) + v it - u it 1 μ it = γ 0 + γ 1 ln( S it ) + ε it 2 1 X it X 1 X 2 X 3 T β f( X it T β ) v it N 0 σ v u it u it ~ N + μ it σ u 2 S it γ 0 γ 1 ε

4 i t Q it Q it = f( X it T β ) + v it - u it 1 μ it = γ 0 + γ 1 ln( S it ) + ε it 2 1 X it X 1 X 2 X 3 T β f( X it T β ) v it N 0 σ v u it u it ~ N + μ it σ u 2 S it γ 0 γ 1 ε it 1 β Q it X it X it Q it Gujarati and Porter 2005 Hicks 1932 Robinson 1933 Hicks 1932 Robinson Allen 1938 Blackorby 1989 Chambers 1988 del Valle 2000 Hoff 2004 Koizumi 1976 Kuga 1972 McFadden 1963 Sajadifar 2010 Sato 1973 Wang DES DES Hicks x i x j 7

5 σ DES ij = x i f i + x j f j x i x j * f i f j 2 f ij f i f j - f ii f 2 j - f jj f 2 i i j f i = lnq Q f ln x i x ii = f i f ij = f i DES i x i x j Blackorby and Russell 1989 DES DES Chambers Allen AES Allen Allen AES σ AES ij = n k = 1 x k f k x i x j * H ij H 0 f 1 f n f 1 f 11 f 1n H = f n f n1 f nn i j n n k = 1 n k H Hessian Matrix 5 H H H ij H i j DES AES DES AES Blackorby and Russell 1989 Allen DES Hicks AES 3. Morishima MES Morishima Morishima 1967 MES Hicks Blackorby 1981 and 1989 Koetse 2008 Sharma 2002 Wang MES Kuga 1972 MES σ MES ij = f j x i * H ij H f j x j * H jj H i j H Hessian Matrix H ij H i j DES Allen AES Morishima MES DES AES MES DES AES MES MES AES DES Blackorby 1981 and Shadow McFadden 1963 AES DES DES AES MES

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8 DES AES MES DES Allen AES Morishima MES 3 DES AES MES 3 DES AES DES AES DES Morishima MES DES AES DES Allen AES Morishima MES 6 11

9 DES AES MES 1. Allen R. G. D. Mathematical Analysis for Economists. London Macmillan press ltd Battese G. E. T. J. Coelli. A Model for Technical Inefficiency Effects in a Stochastic Frontier Production Function for Panel Data. Empirical Economics ~ Binswanger H. P. V. W. Ruttan. Induced Innovation Technology Institutions and Development. Baltimore Johns Hopkins University Press Blackorby C. R. R. Russell. The Morishima Elasticity of Substitution Symmetry Constancy Separability and its Relationship to the Hicks and Allen Elasticities. Review of Economic Studies ~ Blackorby C. R. R. Russell. Will the Real Elasticity of Substitution Please Stand Up A Comparison of the Allen /Uzawa and Morishima Elasticities. The American Economic Review ~ Chambers R. G. Applied Production Analysis A Dual Approach. Cambridge Cambridge University Press de Brauw A. J. Huang S. Rozelle L. Zhang Y. Zhang. The Evolution of China s Rural Labor Markets During the Reforms. Journal of Comparative Economics ~ del Valle I. I. Astorkiza K. Astorkiza. Estimating the Elasticity of Substitution among Inputs Making up Fishing Effort An Application to the VIII Division European Anchovy Fishery. 10th International Institute of Fisheries Economics and Trade IIFET Conference Corvallis Oregon U. S. A Gujarati D. N. D. C. Porter. Basic Econometrics. New York McGraw-Hill /Irwin Hayami Y. Sources of Agricultural Productivity Gap Among Selected Countries. American Journal of Agricultural Economics ~ Hayami Y. V. W. Ruttan. Agricultural Development An International Perspective. Baltimore The Johns Hopkins University Press Hicks J. R. The Theory of Wages. London Macmillan press ltd Hoff A. The Linear Approximation of the CES Function with n Input Variables. Marine Resource Economics ~ Huang J. Y. Wu S. Rozelle. Moving off the Farm and Intensifying Agricultural Production in Shandong A Case Study of Rural Labor Market Linkages in China. Agricultural Economics ~

10 15. Koetse M. J. H. L. F. de Groot R. J. G. M. Florax. Capital-energy Substitution and Shifts in Factor Demand A Meta-analysis. Energy Economics ~ Koizumi T. A Further Note on Definition of Elasticity of Substitution in Many Input Case. Metroeconomica ~ Kuga K. T. Murota. A Note on Definitions of Elasticity of Substitution in Many Input Case. Metroeconomica ~ Kumbhakar S. C. M. Denny M. Fuss. Estimation and Decomposition of Productivity Change When Production is not Efficient A Paneldata Approach. Econometric Reviews ~ Lin J. Y. Prohibition of Factor Market Exchanges and Technological Choice in Chinese Agriculture. The Journal of Development Studies ~ McFadden D. Constant Elasticity of Substitution Production Functions. The Review of Economic Studies ~ Morishima M. A Few Suggestions on the Theory of Elasticity. Economic Review ~ Robinson J. V. The Economics of Imperfect Competition. London Macmillan Sajadifar S. A. Arakelyan N. khiabani. The Linear Approximation of the CES Function to Parameter Estimation in CGE Modeling. International Conference on Business and Economics Research ICBER Kuala Lumpur Malaysia Sato R. T. Koizumi. On the Elasticities of Substitution and Complementarity. Oxford Economic Papers ~ Sharma S. C. The Morishima Elasticity of Substitution for the Variable Profit Function and the Demand for Imports in the United States. International Economic Review ~ Wang X. J. Huang S. Rozelle. Off - farm Employment and Agricultural Specialization in China. China Economic Review ~ Wang X. F. Yamauchi J. Huang. Rising Wages Mechanization and the Substitution between Capital and Labor Evidence from Small Scale Farm System in China. Agricultural Economics ~ Yang J. Z. Huang X. Zhang T. Reardon. The Rapid Rise of Cross-Regional Agricultural Mechanization Services in China. American Journal of Agricultural Economics ~ ~ ~ ~ ~ ~ ~ ~ ALLEN ~ ~ ~ Morishima ~ ~ ~ ~ ~ ~

11 ~ ~ 62 Elasticity of Substitution between Machines and Labor in China s Agricultural Production A Comparison Based on Various Elasticity Estimations MIN Shi XIANG Cheng WANG Xiaobing Abstract It s important for decision makers to study the elasticity of substitution between machines and labor not only for understanding the intensity of machine - labor substitution but also for improving the resource allocation based on the price changes of factors of production.this article used commodity-wise province-level panel data from 1984 to 2012 to investigate the substitution between machines and labor through estimating frontier production functions.the results showed that both the direct elasticity of substitution and Allen elasticity of substitution underestimated machine-labor substitution and that the Morishima elasticity of substitution could better reflect the substitution elasticity.the analysis also demonstrated that the substitution elasticity of machine-labor was statistically significant in the production of the six major crops of which wheat faced the fastest substitution of labor by machines cotton and japonica rice had large development potential for mechanization. The results could provide theoretical implications for the related research and empirical basis for policymakers to further promote the agricultural mechanization. Keywords Agricultural products Mechanization Labor Elasticity of substitution 14

Feder Chapple 2002 Barslund Stiglitz Klychova Pal

Feder Chapple 2002 Barslund Stiglitz Klychova Pal 2018 4 * 400716 DOI:10.13246/j.cnki.jae.2018.04.005 20142017 2009 2. 16 2014 5. 4 3. 43% 6. 22% 2. 79 2009 1. 46 2014 3. 4 5. 08% 3. 81% 1. 27 GDP 9. 17% ** * ** 11&ZD047 14AZ034 13CFX080 CYB16057 2010