A Chance–Constrained Data Envelopment Analysis Approach to Problem Provincial Productivity Growth in Vietnamese Agriculture from 1995 to 2007

ABSTRACT

This study employs a chance-constrained data envelopment analysis (CDEA) approach with two models (model A and model B) to decompose provincial productivity growth in Vietnamese agriculture from 1995 to 2007 into technological progress and efficiency change. The differences between the chance - constrained programming model A and model B are assumptions imposed on the covariance matrix. The decomposition allows us to identify the contributions of technical change and the improvement in technical efficiency to productivity growth in Vietnamese production. Sixty-one provinces in Vietnam are classified into Mekong - technology and other -technology categories. We conduct a Mann-Whitney test to verify whether the two samples, the Mekong technology province sample and the other technology sample, are drawn from the same productivity change populations. The result of the Mann-Whitney test indicates that the differences between the Mekong technology category and the other technology category from two models are more significant. Two important questions are whether some provinces in the samples could maintain their relative efficiency rank positions in comparison with the others over the study period and how to further examine the agreements between the two models. The Kruskal - Wallis test statistic shows that technical efficiency from both models for some provinces are higher than those of them in the study period. The Malmquist results show that production frontier has contracted by around 1.3 percent and 0.31 percent from chance-constrained model A and model B, respectively, a year on average over the sample period. To examine the agreements or disagreements in the total factor productivity indexes we compute the correlation between Malmquist indexes, which is positive and not very high. Thus there is a little discrepancy between the two Malmquist indexes, estimated from the chance - constrained models A and B.

This study employs a chance-constrained data envelopment analysis (CDEA) approach with two models (model A and model B) to decompose provincial productivity growth in Vietnamese agriculture from 1995 to 2007 into technological progress and efficiency change. The differences between the chance - constrained programming model A and model B are assumptions imposed on the covariance matrix. The decomposition allows us to identify the contributions of technical change and the improvement in technical efficiency to productivity growth in Vietnamese production. Sixty-one provinces in Vietnam are classified into Mekong - technology and other -technology categories. We conduct a Mann-Whitney test to verify whether the two samples, the Mekong technology province sample and the other technology sample, are drawn from the same productivity change populations. The result of the Mann-Whitney test indicates that the differences between the Mekong technology category and the other technology category from two models are more significant. Two important questions are whether some provinces in the samples could maintain their relative efficiency rank positions in comparison with the others over the study period and how to further examine the agreements between the two models. The Kruskal - Wallis test statistic shows that technical efficiency from both models for some provinces are higher than those of them in the study period. The Malmquist results show that production frontier has contracted by around 1.3 percent and 0.31 percent from chance-constrained model A and model B, respectively, a year on average over the sample period. To examine the agreements or disagreements in the total factor productivity indexes we compute the correlation between Malmquist indexes, which is positive and not very high. Thus there is a little discrepancy between the two Malmquist indexes, estimated from the chance - constrained models A and B.

KEYWORDS

Total Factor Productivity, Technical Efficiency Change, Technological Progress, Chance-Constrained Programming

Total Factor Productivity, Technical Efficiency Change, Technological Progress, Chance-Constrained Programming

Cite this paper

nullN. Minh and P. Khanh, "A Chance–Constrained Data Envelopment Analysis Approach to Problem Provincial Productivity Growth in Vietnamese Agriculture from 1995 to 2007,"*Open Journal of Statistics*, Vol. 1 No. 3, 2011, pp. 217-235. doi: 10.4236/ojs.2011.13026.

nullN. Minh and P. Khanh, "A Chance–Constrained Data Envelopment Analysis Approach to Problem Provincial Productivity Growth in Vietnamese Agriculture from 1995 to 2007,"

References

[1] W. Mao and W.W. Koo, “Productivity Growth, Technological Progress, and Efficiency Change in Chinese Agriculture after Rural Economic Reforms: A DEA Approach,” China Economic Review, Vol. 8. No. 2, 1997, pp. 157-174. doi:10.1016/S1043-951X(97)90004-3

[2] M. Nishimizu and J. M. Page, “Total Factor Productivity Growth, Technological Progress and Technical Efficiency Change: Dimensions of Productivity Change in Yugoslavia, 1965-1978,” The Economic Journal, Vol. 92, No. 368. 1982, pp. 920-936. doi:10.2307/2232675

[3] N. K. Minh and G. T. Long, “Factor Productivity and Efficiency of the Vietnamese Economy in Transition,” Asia-Pacific Development Journal, Vol. 15, No.1, 2008, pp. 93-117.

[4] A. Charnes and W. W. Cooper, “Chance-Constrained Programming,” Management Science, Vol. 6, No.1, 1959, pp. 73-79. doi:10.1287/mnsc.6.1.73

[5] W. W. Copper, H. Deng, Z. Huang and S. X. Li., “Chance Constrained Programming Approaches to Congestion in Stochastis Data Envelopment Analysis,” Euro- pean Journal of Operation Research, Vol. 155, No. 2, 2004, pp. 487-501. doi:10.1016/S0377-2217(02)00901-3

[6] W. W. Copper, Z. Huang., V. Lelas, S. X. Li and O. Olesen, “Chance Constrained Programming Formulations for Stochastic Characterizations of Efficiency and Dominance in DEA,” Journal of Productivity Analysis, Vol. 9, No.1, 1998, pp. 53-79. doi:10.1023/A:1018320430249

[7] T. Chen, “A Measurement of Taiwan’s Bank Efficiency and Productivity Change during the Asian Financial Crisis,” International Journal of. Services Technology and Management, Vol. 6, No. 6, 2005, pp. 525-543. doi:10.1504/IJSTM.2005.007510

[8] T. Chen, “A Comparison of Chance-Constrained DEA and Stochastic Frontier Analysis: Bank Efficiency in Taiwan,” The Journal of the Operational Research Society, Vol. 53, No. 5, 2002, pp. 492-500. doi:10.1057/palgrave.jors.2601318

[9] V. J. Gali and C. G. Brown, “Assisting Decision- Making in Queensland Barley Production through Chance Constrained Programming,” The Australian Journal of Agricultural and Resource Economics, Vol. 44, No. 2, pp. 269-287. doi:10.1111/1467-8489.00111

[10] M. Zhu, D. B. Taylor, S. C. Sarin and R. A. Kramer, “Chance Constrained Programming Models for Risk Based Economic and Policy Analysis of Soil Conservation,” Agricultural and Resource Economics Review, Vol. 23, No. 1, 1994, 58-65.

[11] J. Zheng and A. Hu, “An Empirical Analysis of Productivity in China (1997-2001),” Journal of Chinese Economic and Business Studies, Vol. 4, No. 3, 2006, pp. 221-239. doi:10.1080/14765280600991917

[12] D. W. Caves, L. R. Christensen and W. E. Diewert, “Multilateral Comparisons of Output, Input and Productivity using Superlative Index Numbers,” The Economic Journal , Vol. 92, No. 365, 1982, pp. 73-86. doi:10.2307/2232257

[13] R F?re, S. Grosskopf, M. Norris and Z. Zhang, “Productivity Growth, Technical Progress and Efficiency Change in Industrialized Countries,” The American Economic Re- view, Vol. 84, No. 1, 1994, pp. 66-83.

[14] K. C. Land, C. A. Knox Lovell and S. Thore “Chance- Constrained Data Envelopment Analysis,” Managerial and Decision Economics, Vol. 14, No. 6, 1993, pp. 541- 554. doi:10.1002/mde.4090140607

[15] M. J. Farrell, “The Measurement of Productive Efficiency,” Journal of the Royal Statistical Society, Vol. 120, No. 3, 1957, pp. 253-290. doi:10.2307/2343100

[16] J. Felipe, “Total Factor Productivity Growth in East Asia: A Critical Survey,” The Journal of Development Studies, Vol. 35, No.4, pp. 1-41. doi:10.1080/00220389908422579

[17] K. P. Kalirajan, M. B. Obwona and S. Zhao, “A Decomposition of Total Factor Productivity Growth: The Case of Chinese Agricultural Growth before and after Reforms,” American Journal of Agricultural Economics, Vol. 78, No.2, 1996, pp. 331-338. doi:10.2307/1243706

[18] S. Kim and G. Han, “A Decomposition of Total Factor Productivity Growth in Korean Manufacturing Industries: A Stochastic Frontier Approach,” Journal of Productivity Analysis, Vol. 16, No 3, 2001, pp. 269-281. doi:10.1023/A:1012566812232

[19] J. Kim and L. J. Lau, “The Source of Economic Growth of the East Asian Newly Industrialized Countries,” Journal of the Japanese and International Economies, Vol. 8, No.3, September 1994, pp. 235-271. doi:10.1006/jjie.1994.1013

[20] J. Kim and L. J. Lau, “The Source of Asian Pacific Economic Growth,” The Canadian Journal of Economics, Vol. 29, Apr 1996, pp. 5116-5154.

[21] B. L. Miller and H. M. Wagner, “Chance-Constrained Programming with Joint Constraints,” Operations Research, Vol. 13, No. 6, 1965, pp. 930-945. doi:10.1287/opre.13.6.930

[22] O. B. Olesen and N. C. Petersen, “Chance Constrained Efficiency Evaluation,” Management Science, Vol. 41, No. 3, 1995, pp. 442-457. doi:10.1287/mnsc.41.3.442

[1] W. Mao and W.W. Koo, “Productivity Growth, Technological Progress, and Efficiency Change in Chinese Agriculture after Rural Economic Reforms: A DEA Approach,” China Economic Review, Vol. 8. No. 2, 1997, pp. 157-174. doi:10.1016/S1043-951X(97)90004-3

[2] M. Nishimizu and J. M. Page, “Total Factor Productivity Growth, Technological Progress and Technical Efficiency Change: Dimensions of Productivity Change in Yugoslavia, 1965-1978,” The Economic Journal, Vol. 92, No. 368. 1982, pp. 920-936. doi:10.2307/2232675

[3] N. K. Minh and G. T. Long, “Factor Productivity and Efficiency of the Vietnamese Economy in Transition,” Asia-Pacific Development Journal, Vol. 15, No.1, 2008, pp. 93-117.

[4] A. Charnes and W. W. Cooper, “Chance-Constrained Programming,” Management Science, Vol. 6, No.1, 1959, pp. 73-79. doi:10.1287/mnsc.6.1.73

[5] W. W. Copper, H. Deng, Z. Huang and S. X. Li., “Chance Constrained Programming Approaches to Congestion in Stochastis Data Envelopment Analysis,” Euro- pean Journal of Operation Research, Vol. 155, No. 2, 2004, pp. 487-501. doi:10.1016/S0377-2217(02)00901-3

[6] W. W. Copper, Z. Huang., V. Lelas, S. X. Li and O. Olesen, “Chance Constrained Programming Formulations for Stochastic Characterizations of Efficiency and Dominance in DEA,” Journal of Productivity Analysis, Vol. 9, No.1, 1998, pp. 53-79. doi:10.1023/A:1018320430249

[7] T. Chen, “A Measurement of Taiwan’s Bank Efficiency and Productivity Change during the Asian Financial Crisis,” International Journal of. Services Technology and Management, Vol. 6, No. 6, 2005, pp. 525-543. doi:10.1504/IJSTM.2005.007510

[8] T. Chen, “A Comparison of Chance-Constrained DEA and Stochastic Frontier Analysis: Bank Efficiency in Taiwan,” The Journal of the Operational Research Society, Vol. 53, No. 5, 2002, pp. 492-500. doi:10.1057/palgrave.jors.2601318

[9] V. J. Gali and C. G. Brown, “Assisting Decision- Making in Queensland Barley Production through Chance Constrained Programming,” The Australian Journal of Agricultural and Resource Economics, Vol. 44, No. 2, pp. 269-287. doi:10.1111/1467-8489.00111

[10] M. Zhu, D. B. Taylor, S. C. Sarin and R. A. Kramer, “Chance Constrained Programming Models for Risk Based Economic and Policy Analysis of Soil Conservation,” Agricultural and Resource Economics Review, Vol. 23, No. 1, 1994, 58-65.

[11] J. Zheng and A. Hu, “An Empirical Analysis of Productivity in China (1997-2001),” Journal of Chinese Economic and Business Studies, Vol. 4, No. 3, 2006, pp. 221-239. doi:10.1080/14765280600991917

[12] D. W. Caves, L. R. Christensen and W. E. Diewert, “Multilateral Comparisons of Output, Input and Productivity using Superlative Index Numbers,” The Economic Journal , Vol. 92, No. 365, 1982, pp. 73-86. doi:10.2307/2232257

[13] R F?re, S. Grosskopf, M. Norris and Z. Zhang, “Productivity Growth, Technical Progress and Efficiency Change in Industrialized Countries,” The American Economic Re- view, Vol. 84, No. 1, 1994, pp. 66-83.

[14] K. C. Land, C. A. Knox Lovell and S. Thore “Chance- Constrained Data Envelopment Analysis,” Managerial and Decision Economics, Vol. 14, No. 6, 1993, pp. 541- 554. doi:10.1002/mde.4090140607

[15] M. J. Farrell, “The Measurement of Productive Efficiency,” Journal of the Royal Statistical Society, Vol. 120, No. 3, 1957, pp. 253-290. doi:10.2307/2343100

[16] J. Felipe, “Total Factor Productivity Growth in East Asia: A Critical Survey,” The Journal of Development Studies, Vol. 35, No.4, pp. 1-41. doi:10.1080/00220389908422579

[17] K. P. Kalirajan, M. B. Obwona and S. Zhao, “A Decomposition of Total Factor Productivity Growth: The Case of Chinese Agricultural Growth before and after Reforms,” American Journal of Agricultural Economics, Vol. 78, No.2, 1996, pp. 331-338. doi:10.2307/1243706

[18] S. Kim and G. Han, “A Decomposition of Total Factor Productivity Growth in Korean Manufacturing Industries: A Stochastic Frontier Approach,” Journal of Productivity Analysis, Vol. 16, No 3, 2001, pp. 269-281. doi:10.1023/A:1012566812232

[19] J. Kim and L. J. Lau, “The Source of Economic Growth of the East Asian Newly Industrialized Countries,” Journal of the Japanese and International Economies, Vol. 8, No.3, September 1994, pp. 235-271. doi:10.1006/jjie.1994.1013

[20] J. Kim and L. J. Lau, “The Source of Asian Pacific Economic Growth,” The Canadian Journal of Economics, Vol. 29, Apr 1996, pp. 5116-5154.

[21] B. L. Miller and H. M. Wagner, “Chance-Constrained Programming with Joint Constraints,” Operations Research, Vol. 13, No. 6, 1965, pp. 930-945. doi:10.1287/opre.13.6.930

[22] O. B. Olesen and N. C. Petersen, “Chance Constrained Efficiency Evaluation,” Management Science, Vol. 41, No. 3, 1995, pp. 442-457. doi:10.1287/mnsc.41.3.442