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Estimating Disaggregate Production Functions: An Application to Northern Mexico

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  • Msangi, Siwa
  • Howitt, Richard E.

Abstract

This paper demonstrates a robust method for achieving disaggregation in the estimation of flexible-form farm-level multi-input production functions using minimally-specified data sets. Since our ultimate goal is to address important questions related to the distributional effects of policy changes, we place emphasis on the ability of the model to reproduce the characteristics of the existing production system and to predict the outcomes of these changes at a high level of disaggregation. Achieving this requires the use of farm-level models that are estimated across a wide spectrum of sizes and types, which is often difficult to do with traditional econometric methods, due to limitations of data. The approach to estimating flexible-form production functions used in this paper overcomes these limitations, and also avoids the problems that frequently hinder the application of budget-based representative farm models to these type of analyses – namely, that of poor calibration to observed behavior. In our estimation procedure, we use a two-stage approach that first generates a set of observation-specific shadow values for incompletely priced inputs, such as irrigation water or family labor, which are used in the second stage, along with the nominal input prices, to produce estimates of crop-specific production functions using Generalized Maximum Entropy (GME) methods. These functions are able to capture the individual heterogeneity of the local production environment, while still allowing the production function to replicate the input usage and outputs produced in the sample data. Since we are able to generate demand, supply, and substitution elasticities, a wide range of policy responses can be modeled. Our paper demonstrates this methodology through an empirical application to Mexico, drawing from a small set of cross-section data collected in the northern Rio Bravo regions. The estimates show that there is considerable heterogeneity in the behavioral response of farmer households of different sizes, both in terms of the returns to scale, as well as in the elasticities of substitution and derived demands for water. Compared to the aggregate-level estimation, we obtain much more accurate and informative policy response behavior, when shocks are imposed on the model.

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Bibliographic Info

Paper provided by American Agricultural Economics Association (New Name 2008: Agricultural and Applied Economics Association) in its series 2006 Annual meeting, July 23-26, Long Beach, CA with number 21080.

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Date of creation: 2006
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Handle: RePEc:ags:aaea06:21080

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Keywords: Research Methods/ Statistical Methods;

References

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  1. Antle, John M. & Capalbo, Susan M., 2000. "Econometric-Process Models For Integrated Assessment Of Agricultural Production Systems," Trade Research Center Research Discussion Papers 29234, Montana State University, Department of Agricultural Economics and Economics.
  2. Golan, Amos & Judge, George G. & Miller, Douglas, 1996. "Maximum Entropy Econometrics," Staff General Research Papers 1488, Iowa State University, Department of Economics.
  3. Paris, Quirino & Caputo, Michael R., 2001. "Sensitivity Of The Gme Estimates To Support Bounds," Working Papers 11966, University of California, Davis, Department of Agricultural and Resource Economics.
  4. Golan, Amos & Judge, George & Robinson, Sherman, 1994. "Recovering Information from Incomplete or Partial Multisectoral Economic Data," The Review of Economics and Statistics, MIT Press, vol. 76(3), pages 541-49, August.
  5. H. Alan Love, 1999. "Conflicts between Theory and Practice in Production Economics," American Journal of Agricultural Economics, Agricultural and Applied Economics Association, vol. 81(3), pages 696-702.
  6. Alig, Ralph J. & Adams, Darius M. & McCarl, Bruce A., 1998. "Impacts Of Incorporating Land Exchanges Between Forestry And Agriculture In Sector Models," Journal of Agricultural and Applied Economics, Southern Agricultural Economics Association, vol. 30(02), December.
  7. Sergio H. Lence & Douglas J. Miller, 1998. "Recovering Output-Specific Inputs from Aggregate Input Data: A Generalized Cross-Entropy Approach," American Journal of Agricultural Economics, Agricultural and Applied Economics Association, vol. 80(4), pages 852-867.
  8. Quirino Paris & Richard E. Howitt, 1998. "An Analysis of Ill-Posed Production Problems Using Maximum Entropy," American Journal of Agricultural Economics, Agricultural and Applied Economics Association, vol. 80(1), pages 124-138.
  9. Golan, Amos & Judge, George & Perloff, Jeffrey M, 1996. "Estimating the Size Distribution of Firms Using Government Summary Statistics," Journal of Industrial Economics, Wiley Blackwell, vol. 44(1), pages 69-80, March.
  10. Miller, Douglas & Lence, Sergio H., 1998. "Estimation of Multi-Output Production Functions with Incomplete Data: A Generalized Maximum Entropy Approach," Staff General Research Papers 1219, Iowa State University, Department of Economics.
  11. Thomas Heckelei & Hendrik Wolff, 2003. "Estimation of constrained optimisation models for agricultural supply analysis based on generalised maximum entropy," European Review of Agricultural Economics, Foundation for the European Review of Agricultural Economics, vol. 30(1), pages 27-50, March.
  12. Just, Richard E & Antle, John M, 1990. "Interactions between Agricultural and Environmental Policies: A Conceptual Framework," American Economic Review, American Economic Association, vol. 80(2), pages 197-202, May.
  13. Mendelsohn, Robert & Nordhaus, William D & Shaw, Daigee, 1994. "The Impact of Global Warming on Agriculture: A Ricardian Analysis," American Economic Review, American Economic Association, vol. 84(4), pages 753-71, September.
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Cited by:
  1. Akpalu, Wisdom & Hassan, Rashid M. & Ringler, Claudia, 2008. "Climate variability and maize yield in South Africa: Results from GME and MELE methods," IFPRI discussion papers 843, International Food Policy Research Institute (IFPRI).

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