IDEAS home Printed from https://ideas.repec.org/a/cuf/journl/y2001v2i1p215-235.html
   My bibliography  Save this article

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, 2001. "Simulated Maximum Likelihood Estimation of the Linear Expenditure System with Binding Non-Negativity Constraints," Annals of Economics and Finance, Society for AEF, vol. 2(1), pages 215-235, May.
  • Handle: RePEc:cuf:journl:y:2001:v:2:i:1:p:215-235
    as

    Download full text from publisher

    File URL: http://www.aeconf.net/Articles/May2001/aef020110.pdf
    Download Restriction: no

    File URL: http://down.aefweb.net/AefArticles/aef020110.pdf
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Borsch-Supan, Axel & Hajivassiliou, Vassilis A., 1993. "Smooth unbiased multivariate probability simulators for maximum likelihood estimation of limited dependent variable models," Journal of Econometrics, Elsevier, vol. 58(3), pages 347-368, August.
    2. Soest, Arthur van & Kapteyn, Arie & Kooreman, Peter, 1993. "Coherency and regularity of demand systems with equality and inequality constraints," Journal of Econometrics, Elsevier, vol. 57(1-3), pages 161-188.
    3. Van Soest, Arthur & Kooreman, Peter, 1990. "Coherency of the indirect translog demand system with binding nonnegativity constraints," Journal of Econometrics, Elsevier, vol. 44(3), pages 391-400, June.
    4. Jeongwen Chiang, 1991. "A Simultaneous Approach to the Whether, What and How Much to Buy Questions," Marketing Science, INFORMS, vol. 10(4), pages 297-315.
    5. Ransom, Michael R., 1987. "A comment on consumer demand systems with binding non-negativity constraints," Journal of Econometrics, Elsevier, vol. 34(3), pages 355-359, March.
    6. Lee, Lung-Fei, 1992. "On Efficiency of Methods of Simulated Moments and Maximum Simulated Likelihood Estimation of Discrete Response Models," Econometric Theory, Cambridge University Press, vol. 8(4), pages 518-552, December.
    7. Wales, T. J. & Woodland, A. D., 1983. "Estimation of consumer demand systems with binding non-negativity constraints," Journal of Econometrics, Elsevier, vol. 21(3), pages 263-285, April.
    8. Hausman, Jerry A & Wise, David A, 1978. "A Conditional Probit Model for Qualitative Choice: Discrete Decisions Recognizing Interdependence and Heterogeneous Preferences," Econometrica, Econometric Society, vol. 46(2), pages 403-426, March.
    9. Lee, Lung-Fei, 1995. "Asymptotic Bias in Simulated Maximum Likelihood Estimation of Discrete Choice Models," Econometric Theory, Cambridge University Press, vol. 11(3), pages 437-483, June.
    10. Keane, Michael P, 1994. "A Computationally Practical Simulation Estimator for Panel Data," Econometrica, Econometric Society, vol. 62(1), pages 95-116, January.
    11. Gourieroux, C & Laffont, J-J & Monfort, A, 1980. "Disequilibrium Econometrics in Simultaneous Equations Systems," Econometrica, Econometric Society, vol. 48(1), pages 75-96, January.
    12. Diewert, W E & Wales, T J, 1988. "Normalized Quadratic Systems of Consumer Demand Functions," Journal of Business & Economic Statistics, American Statistical Association, vol. 6(3), pages 303-312, July.
    13. Tripathi, Gautam, 2000. "Econometric Methods," Econometric Theory, Cambridge University Press, vol. 16(1), pages 139-142, February.
    14. Andersen, Torben G., 2000. "Simulation-Based Econometric Methods," Econometric Theory, Cambridge University Press, vol. 16(1), pages 131-138, February.
    15. Amemiya, Takeshi, 1974. "Multivariate Regression and Simultaneous Equation Models when the Dependent Variables Are Truncated Normal," Econometrica, Econometric Society, vol. 42(6), pages 999-1012, November.
    16. Lee, Lung-Fei & Pitt, Mark M, 1986. "Microeconometric Demand Systems with Binding Nonnegativity Constraints: The Dual Approach," Econometrica, Econometric Society, vol. 54(5), pages 1237-1242, September.
    17. McFadden, Daniel, 1989. "A Method of Simulated Moments for Estimation of Discrete Response Models without Numerical Integration," Econometrica, Econometric Society, vol. 57(5), pages 995-1026, September.
    18. Jeongwen Chiang, 1995. "Competing Coupon Promotions and Category Sales," Marketing Science, INFORMS, vol. 14(1), pages 105-122.
    19. Pollak, Robert A & Wales, Terrence J, 1969. "Estimation of the Linear Expenditure System," Econometrica, Econometric Society, vol. 37(4), pages 611-628, October.
    20. Christensen, Laurits R & Jorgenson, Dale W & Lau, Lawrence J, 1975. "Transcendental Logarithmic Utility Functions," American Economic Review, American Economic Association, vol. 65(3), pages 367-383, June.
    21. Diewert, Walter E & Wales, Terence J, 1987. "Flexible Functional Forms and Global Curvature Conditions," Econometrica, Econometric Society, vol. 55(1), pages 43-68, January.
    22. Lee, Lung-Fei & Pitt, Mark M., 1987. "Microeconometric models of rationing, imperfect markets, and non-negativity constraints," Journal of Econometrics, Elsevier, vol. 36(1-2), pages 89-110.
    23. repec:crs:wpaper:9315 is not listed on IDEAS
    24. Butler, J S & Moffitt, Robert, 1982. "A Computationally Efficient Quadrature Procedure for the One-Factor Multinomial Probit Model," Econometrica, Econometric Society, vol. 50(3), pages 761-764, May.
    25. Pakes, Ariel & Pollard, David, 1989. "Simulation and the Asymptotics of Optimization Estimators," Econometrica, Econometric Society, vol. 57(5), pages 1027-1057, September.
    26. Laroque, Guy & Salanie, B, 1993. "Simulation-Based Estimation of Models with Lagged Latent Variables," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 8(S), pages 119-133, Suppl. De.
    27. Deaton, Angus, 1974. "A Reconsideration of the Empirical Implications of Additive Preferences," Economic Journal, Royal Economic Society, vol. 84(334), pages 338-348, June.
    28. Mariano,Roberto & Schuermann,Til & Weeks,Melvyn J. (ed.), 2000. "Simulation-based Inference in Econometrics," Cambridge Books, Cambridge University Press, number 9780521591126, November.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. 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).
    2. Jean-Pierre H. Dubé, 2018. "Microeconometric Models of Consumer Demand," NBER Working Papers 25215, National Bureau of Economic Research, Inc.
    3. Nitin Mehta, 2015. "A Flexible Yet Globally Regular Multigood Demand System," Marketing Science, INFORMS, vol. 34(6), pages 843-863, November.
    4. Pan, Suwen & Mohanty, Samarendu & Welch, Mark, 2008. "India Edible Oil Consumption: A Censored Incomplete Demand Approach," Journal of Agricultural and Applied Economics, Cambridge University Press, vol. 40(3), pages 821-835, December.
    5. 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).
    6. 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.
    7. 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.
    8. Leonardo Galli & Alessandro Galligari & Marco Sciandrone, 2020. "A unified convergence framework for nonmonotone inexact decomposition methods," Computational Optimization and Applications, Springer, vol. 75(1), pages 113-144, January.
    9. Thomas, Alban & Chakir, Raja, 2020. "Unintended consequences of environmental policies: the case of set-aside and agricultural intensification," TSE Working Papers 20-1066, Toulouse School of Economics (TSE).
    10. Obafèmi P. Koutchadé & Alain Carpentier & Fabienne Femenia, 2021. "Modeling Corners, Kinks, and Jumps in Crop Acreage Choices: Impacts of the EU Support to Protein Crops," American Journal of Agricultural Economics, John Wiley & Sons, vol. 103(4), pages 1502-1524, August.
    11. Solon, Gary, 2010. "A simple microeconomic foundation for a Tobit model of consumer demand," Economics Letters, Elsevier, vol. 106(2), pages 131-132, February.
    12. Vithala R. Rao & Gary J. Russell & Hemant Bhargava & Alan Cooke & Tim Derdenger & Hwang Kim & Nanda Kumar & Irwin Levin & Yu Ma & Nitin Mehta & John Pracejus & R. Venkatesh, 2018. "Emerging Trends in Product Bundling: Investigating Consumer Choice and Firm Behavior," Customer Needs and Solutions, Springer;Institute for Sustainable Innovation and Growth (iSIG), vol. 5(1), pages 107-120, March.
    13. C. J. Lin & S. Lucidi & L. Palagi & A. Risi & M. Sciandrone, 2009. "Decomposition Algorithm Model for Singly Linearly-Constrained Problems Subject to Lower and Upper Bounds," Journal of Optimization Theory and Applications, Springer, vol. 141(1), pages 107-126, April.
    14. 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.
    15. 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.
    16. 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.
    17. Koutchad, P. & Carpentier, A. & Femenia, F., 2018. "Dealing with corner solutions in multi-crop micro-econometric models: an endogenous regime approach with regime fixed costs," 2018 Conference, July 28-August 2, 2018, Vancouver, British Columbia 277530, International Association of Agricultural Economists.
    18. 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).
    19. 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.
    20. 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.
    21. Andrea Manno & Laura Palagi & Simone Sagratella, 2018. "Parallel decomposition methods for linearly constrained problems subject to simple bound with application to the SVMs training," Computational Optimization and Applications, Springer, vol. 71(1), pages 115-145, September.
    22. 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.
    23. 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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. 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).
    2. 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.
    3. 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.
    4. Dong, Diansheng & Kaiser, Harry M., 2003. "Estimation of a Censored AIDS Model: A Simulated Amemiya-Tobin Approach," Research Bulletins 122113, Cornell University, Department of Applied Economics and Management.
    5. Lee, Lung-Fei, 1997. "Simulated maximum likelihood estimation of dynamic discrete choice statistical models some Monte Carlo results," Journal of Econometrics, Elsevier, vol. 82(1), pages 1-35.
    6. 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.
    7. Geweke, John F. & Keane, Michael P. & Runkle, David E., 1997. "Statistical inference in the multinomial multiperiod probit model," Journal of Econometrics, Elsevier, vol. 80(1), pages 125-165, September.
    8. Victoria Prowse, 2004. "Estimating Time Demand Elasticities Under Rationing," Economics Papers 2004-W22, Economics Group, Nuffield College, University of Oxford.
    9. 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.
    10. Bousquet, Alain & Ivaldi, Marc, 1998. "An individual choice model of energy mix," Resource and Energy Economics, Elsevier, vol. 20(3), pages 263-286, September.
    11. Jacques Huguenin & Florian Pelgrin & Alberto Holly, 2009. "Estimation of multivariate probit models by exact maximum likelihood," Working Papers 0902, University of Lausanne, Institute of Health Economics and Management (IEMS).
    12. Kristensen, Dennis & Salanié, Bernard, 2017. "Higher-order properties of approximate estimators," Journal of Econometrics, Elsevier, vol. 198(2), pages 189-208.
    13. Dennis Kristensen & Bernard Salanié, 2010. "Higher Order Improvements for Approximate Estimators," CAM Working Papers 2010-04, University of Copenhagen. Department of Economics. Centre for Applied Microeconometrics.
    14. Dong, Diansheng & Gould, Brian W. & Kaiser, Harry M., 2002. "The Structure Of Food Demand In Mexico: An Application Of The Amemiya-Tobin Approach To The Estimation Of A Censored System," 2002 Annual meeting, July 28-31, Long Beach, CA 19830, American Agricultural Economics Association (New Name 2008: Agricultural and Applied Economics Association).
    15. Jean-Pierre H. Dubé, 2018. "Microeconometric Models of Consumer Demand," NBER Working Papers 25215, National Bureau of Economic Research, Inc.
    16. Nitin Mehta, 2015. "A Flexible Yet Globally Regular Multigood Demand System," Marketing Science, INFORMS, vol. 34(6), pages 843-863, November.
    17. Lee, Lung-Fei, 1997. "A simulated likelihood estimator for qualitative response models with sufficient statistics," Economics Letters, Elsevier, vol. 57(1), pages 23-32, November.
    18. Kerem Tuzcuoglu, 2019. "Composite Likelihood Estimation of an Autoregressive Panel Probit Model with Random Effects," Staff Working Papers 19-16, Bank of Canada.
    19. Lee, Lung-Fei, 1997. "A smooth likelihood simulator for dynamic disequilibrium models," Journal of Econometrics, Elsevier, vol. 78(2), pages 257-294, June.
    20. Bolduc, Denis & Kaci, Mustapha, 1993. "Estimation des modèles probit polytomiques : un survol des techniques," L'Actualité Economique, Société Canadienne de Science Economique, vol. 69(3), pages 161-191, septembre.

    More about this item

    Keywords

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

    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

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:cuf:journl:y:2001:v:2:i:1:p:215-235. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Qiang Gao (email available below). General contact details of provider: https://edirc.repec.org/data/emcufcn.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.