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Simulated Maximum Likelihood Estimation of the Linear Expenditure System with Binding Non-Negativity Constraints

Author

Listed:
  • Chihwa Kao

    (Department of Economics and Center for Policy Research, Syracuse University)

  • Lung-fei Lee

    () (Department of Economics, The Ohio State University)

  • Mark M. Pitt

    (Department of Economics, Brown University)

Abstract

This paper discusses issues on the estimation of consumer demand equations subject to binding non-negative constraints. We propose computationally feasible specifications and a simulated maximum likelihood (SML) method for demand systems. Our study shows that the econometric implementation of the SML estimates can avoid high-dimensional integration problems. As contrary to the simulation method of moments and simulated pseudo-likelihood methods that require the simulation of demand quantities subject to nonnegativity constraints for consumers in the sample, the SML approach requires only simulation of the likelihood function. The SML approach avoids solving for simulated demand quantities because the likelihood function is conditional on observed demand quantities. We have applied SML approach for the linear expenditure system (LES) with non-negativity constraints. The results of a seven-goods demand system are presented. The results provide empirical evidence on the importance of taking into account possible cross equation correlations in disturbances.

Suggested Citation

  • Chihwa Kao & Lung-fei Lee & Mark M. Pitt, 2000. "Simulated Maximum Likelihood Estimation of the Linear Expenditure System with Binding Non-Negativity Constraints," CEMA Working Papers 50, China Economics and Management Academy, Central University of Finance and Economics, revised Apr 2001.
  • Handle: RePEc:cuf:wpaper:50
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    References listed on IDEAS

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    Cited by:

    1. Solon, Gary, 2010. "A simple microeconomic foundation for a Tobit model of consumer demand," Economics Letters, Elsevier, vol. 106(2), pages 131-132, February.
    2. repec:spr:joptap:v:141:y:2009:i:1:d:10.1007_s10957-008-9489-9 is not listed on IDEAS
    3. 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.
    4. José M. Labeaga & Xavier Labandeira & Xiral López-Otero, 2018. "Energy Tax Reform and Poverty Alleviation in Mexico," Working Papers 1801, Universidade de Vigo, Departamento de Economía Aplicada.
    5. 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.
    6. Pofahl, Geoffrey M. & Capps, Oral, Jr. & Clauson, Annette L., 2005. "Demand for Non-Alcoholic Beverages: Evidence From The ACNielsen Home Scan Panel," 2005 Annual meeting, July 24-27, Providence, RI 19441, American Agricultural Economics Association (New Name 2008: Agricultural and Applied Economics Association).
    7. 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.
    8. Golan, Amos & LaFrance, Jeffrey T & Perloff, Jeffrey M. & Seabold, Skipper, 2017. "Estimating a Demand System with Choke Prices," Department of Agricultural & Resource Economics, UC Berkeley, Working Paper Series qt4qt9q8vr, Department of Agricultural & Resource Economics, UC Berkeley.
    9. Cassioli, A. & Di Lorenzo, D. & Sciandrone, M., 2013. "On the convergence of inexact block coordinate descent methods for constrained optimization," European Journal of Operational Research, Elsevier, vol. 231(2), pages 274-281.
    10. Cristian Ricardo Nogales Carvajal, 2009. "Un sistema lineal de gasto: identificando patrones de consumo de alimentos en Bolivia," Investigación & Desarrollo 0109, Universidad Privada Boliviana, revised Jan 2009.
    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.

    More about this item

    Keywords

    Simulated likelihood; Linear expenditure system; Non-negativity constraints; Multivariate censored variables; Nonlinear simultaneous equations;

    JEL classification:

    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
    • C34 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Truncated and Censored Models; Switching Regression Models
    • D12 - Microeconomics - - Household Behavior - - - Consumer Economics: Empirical Analysis

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