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Estimation of Coherent Demand Systems with Many Binding Non-Negativity Constraints

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Abstract

Two econometric issues arise in the estimation of complete systems of producer or consumer demands when many non-negativity constraints are binding for a large share of observations, as frequently occurs with micro-level data. The first is computational. The econometric model is essentially an endogenous switching regimes model which requires the evaluation of multivariate probability integrals. The second is the relationship between demand theory and statistical coherency. If the indirect utility or cost function underlying the demand system does not satisfy the regularity conditions at each observation, the likelihood is incoherent in that the sum of the probabilities for all demand regimes is not unity and maximum likelihood estimates are inconsistent. The solution presented is to use the Gibbs Sampling technique and data augmentation algorithm and rejection sampling, to solve both the dimensionality and coherency problem. With rejection sampling one can straightforwardly impose only the necessary conditions for coherency, coherency at each data point rather than global coherency. The method is illustrated with a series of simulated demand systems derived from the translog indirect random utility function. The results highlight the importance of imposing regularity when there are many non-consumed goods and the gains from imposing such conditions locally rather than globally.

Suggested Citation

  • Mark M. Pitt & Daniel L. Millimet, 1999. "Estimation of Coherent Demand Systems with Many Binding Non-Negativity Constraints," Working Papers 99-4, Brown University, Department of Economics.
  • Handle: RePEc:bro:econwp:99-4
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    Cited by:

    1. Koji Miyawaki & Yasuhiro Omori & Akira Hibiki, 2016. "Exact Estimation of Demand Functions under Block-Rate Pricing," Econometric Reviews, Taylor & Francis Journals, vol. 35(3), pages 311-343, March.
    2. von Haefen, Roger H., 2002. "A Complete Characterization Of The Linear, Log-Linear, And Semi-Log Incomplete Demand System Models," Journal of Agricultural and Resource Economics, Western Agricultural Economics Association, vol. 27(2), pages 1-39, December.
    3. Gould, Brian W. & Yen, Steven T., 2002. "Food Demand In Mexico: A Quasi-Maximum Likelihood Approach," 2002 Annual meeting, July 28-31, Long Beach, CA 19667, American Agricultural Economics Association (New Name 2008: Agricultural and Applied Economics Association).
    4. Daniel J. Phaneuf & Catherine L. Kling & Joseph A. Herriges, 2000. "Estimation and Welfare Calculations in a Generalized Corner Solution Model with an Application to Recreation Demand," The Review of Economics and Statistics, MIT Press, vol. 82(1), pages 83-92, February.
    5. Raja Chakir & Alban Thomas, 2003. "Simulated maximum likelihood estimation of demand systems with corner solutions and panel data application to industrial energy demand," Revue d'économie politique, Dalloz, vol. 113(6), pages 773-799.
    6. Solon, Gary, 2010. "A simple microeconomic foundation for a Tobit model of consumer demand," Economics Letters, Elsevier, vol. 106(2), pages 131-132, February.
    7. Alain Bousquet & Raja Chakir & Norbert Ladoux, 2002. "Modeling Corner Solutions with Panel Data: Application to Industrial Energy Demand in France," 10th International Conference on Panel Data, Berlin, July 5-6, 2002 C3-2, International Conferences on Panel Data.
    8. Prinz, Aloys & Bünger, Björn, 2012. "Balancing ‘full life’: An economic approach to the route to happiness," Journal of Economic Psychology, Elsevier, vol. 33(1), pages 58-70.
    9. Malaga, Jaime E. & Pan, Suwen & Duch-Carvallo, Teresa, 2009. "Did Mexican Meat Demand Change under NAFTA?," 2009 Conference, August 16-22, 2009, Beijing, China 51430, International Association of Agricultural Economists.
    10. Gould, Brian W. & Lee, Yoonjung & Dong, Diansheng & Villarreal, Hector J., 2002. "Household Size And Composition Impacts On Meat Demand In Mexico: A Censored Demand System Approach," 2002 Annual meeting, July 28-31, Long Beach, CA 19722, American Agricultural Economics Association (New Name 2008: Agricultural and Applied Economics Association).
    11. Qian, Hang, 2009. "Estimating SUR Tobit Model while errors are gaussian scale mixtures: with an application to high frequency financial data," MPRA Paper 31509, University Library of Munich, Germany.
    12. Millimet, Daniel L. & Tchernis, Rusty, 2008. "Estimating high-dimensional demand systems in the presence of many binding non-negativity constraints," Journal of Econometrics, Elsevier, vol. 147(2), pages 384-395, December.

    More about this item

    Keywords

    Coherency; Gibbs Sampling; demand systems; translog; data augmentation; Markov Chain Monte Carlo;

    JEL classification:

    • C3 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables
    • C4 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics
    • D0 - Microeconomics - - General

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