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Getting Implicit Shadow Prices Right for the Estimation of the Malmquist Index: The Case of Agricultural Total Factor Productivity in Developing Countries


  • Nin Pratt, Alejandro
  • Yu, Bingxin


The Malmquist index has become extensively used in international comparisons of agricultural productivity since it does not require prices for its estimation, which are normally not available. However, the DEA approach used to estimate this index still uses implicit price information. This entails potential problems because these methods are susceptible to the effect of data noise, and shadow prices can prove to be inconsistent with prior knowledge on cost shares. In this paper we analyze implicit input shadow shares used in the DEA approach to estimate agricultural productivity using the Malmquist index for 72 developing countries. We then set bounds to the implicit input shares introducing information on their likely value and compare constrained and unconstrained input shares. We conclude that the incidence of zero shadow prices justifies the introduction of constraints in the estimation of the Malmquist index. The paper also presents detailed results of TFP growth in developing countries using constrained shadow shares for their estimation. We find that agricultural TFP has been growing steadily in the past 20 years even if countries like China, Brazil and India are not considered. Remarkably, we find a clear improvement in the performance of Sub-Saharan Africa since the mid 1980s.

Suggested Citation

  • Nin Pratt, Alejandro & Yu, Bingxin, 2009. "Getting Implicit Shadow Prices Right for the Estimation of the Malmquist Index: The Case of Agricultural Total Factor Productivity in Developing Countries," 2009 Conference, August 16-22, 2009, Beijing, China 51797, International Association of Agricultural Economists.
  • Handle: RePEc:ags:iaae09:51797

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    References listed on IDEAS

    1. Kuosmanen, Timo & Cherchye, Laurens & Sipilainen, Timo, 2006. "The law of one price in data envelopment analysis: Restricting weight flexibility across firms," European Journal of Operational Research, Elsevier, vol. 170(3), pages 735-757, May.
    2. Timo Kuosmanen & Thierry Post & Timo Sipiläinen, 2004. "Shadow Price Approach to Total Factor Productivity Measurement: With an Application to Finnish Grass-Silage Production," Journal of Productivity Analysis, Springer, vol. 22(1), pages 95-121, July.
    3. Francisco Pedraja-Chaparro & Javier Salinas-Jimenez & Peter Smith, 1997. "On the Role of Weight Restrictions in Data Envelopment Analysis," Journal of Productivity Analysis, Springer, vol. 8(2), pages 215-230, May.
    4. Tim J. Coelli & D. S. Prasada Rao, 2005. "Total factor productivity growth in agriculture: a Malmquist index analysis of 93 countries, 1980-2000," Agricultural Economics, International Association of Agricultural Economists, vol. 32(s1), pages 115-134, January.
    5. E. Thanassoulis & R. Allen, 1998. "Simulating Weights Restrictions in Data Envelopment Analysis by Means of Unobserved DMUs," Management Science, INFORMS, vol. 44(4), pages 586-594, April.
    6. Allen, R. & Thanassoulis, E., 2004. "Improving envelopment in data envelopment analysis," European Journal of Operational Research, Elsevier, vol. 154(2), pages 363-379, April.
    7. Maria Portela & Emmanuel Thanassoulis, 2006. "Zero weights and non-zero slacks: Different solutions to the same problem," Annals of Operations Research, Springer, vol. 145(1), pages 129-147, July.
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    Cited by:

    1. Breisinger, Clemens & van Rheenen, Teunis & Ringler, Claudia & Nin Pratt, Alejandro & Minot, Nicholas & Aragon, Catherine & Yu, Bingxin & Ecker, Olivier & Zhu, Tingju, 2010. "Food security and economic development in the Middle East and North Africa," IFPRI discussion papers 985, International Food Policy Research Institute (IFPRI).
    2. Jackeline Velazco & Vicente Pinilla, 2017. "Development models, agricultural policies, and agricultural growth: Peru, 1950-2010," Documentos de Trabajo de la Sociedad Española de Historia Agraria 1704, Sociedad Española de Historia Agraria.
    3. Biagia De Devitiis & Ornella Wanda Maietta, 2015. "Shadow Prices of Human Capital in Agriculture. Evidence from European FADN Regions," CSEF Working Papers 415, Centre for Studies in Economics and Finance (CSEF), University of Naples, Italy.
    4. Yu, Bingxin & Nin Pratt, Alejandro, 2011. "Agricultural Productivity and Policies in Sub-Saharan Africa," 2011 Annual Meeting, July 24-26, 2011, Pittsburgh, Pennsylvania 105400, Agricultural and Applied Economics Association.
    5. Md Ali & K. Klein, 2014. "Water Use Efficiency and Productivity of the Irrigation Districts in Southern Alberta," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 28(10), pages 2751-2766, August.
    6. Lachaud, Michee & Bravo-Ureta, Boris & Ludena, Carlos, 2015. "Agricultural Productivity Growth in Latin America and the Caribbean (LAC): An analysis of Climatic Effects, Convergence, and Catch-up," 2015 Conference, August 9-14, 2015, Milan, Italy 211721, International Association of Agricultural Economists.
    7. Butzer, Rita & Mundlak, Yair & Larson, Donald F., 2010. "Measures of fixed capital in agriculture," Policy Research Working Paper Series 5472, The World Bank.
    8. Lachaud, Michee Arnold & Bravo-Ureta, Boris E. & Ludena, Carlos E., 2015. "Agricultural productivity growth in Latin America and the Caribbean and other world regions: An analysis of climatic effects, convergence and catch-up," Working Papers 40, University of Connecticut, Department of Agricultural and Resource Economics, Charles J. Zwick Center for Food and Resource Policy.

    More about this item


    Malmquist; shadow prices; total factor productivity; Production Economics; Productivity Analysis; Research Methods/ Statistical Methods; D2;

    JEL classification:

    • D2 - Microeconomics - - Production and Organizations


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