Nothing Special   »   [go: up one dir, main page]
IDEAS home Printed from https://ideas.repec.org/p/cwl/cwldpp/1051.html
   My bibliography  Save this paper

Classical Estimation Methods for LDV Models Using Simulation

Author

Listed:
Abstract
This paper discusses estimation methods for limited dependent variable (LDV) models that employ Monte Carlo simulation techniques to overcome computational problems in such models. These difficulties take the form of high dimensional integrals that need to be calculated repeatedly but cannot be easily approximated by series expansions. In the past, investigators were forced to restrict attention to special classes of LDV models that are computationally manageable. The simulation estimation methods we discuss here make it possible to estimate LDV models that are computationally intractable using classical estimation methods. We first review the ways in which LDV models arise, describing the differences and similarities in censored and truncated data generating processes. Censoring and truncation give rise to the troublesome multivariate integrals. Following the LDV models, we described various simulation methods for evaluating such integrals. Naturally, censoring and truncation play roles in simulation as well. Finally, estimation methods that rely on simulation are described. We review three general approaches that combine estimation of LDV models and simulation: simulation of the log-likelihood function (MLS), simulation of moment functions (MSM), and simulation of the score (MSS). The MSS is a combination of ideas from MSL and MSM, treading the efficient score of the log-likelihood function as a moment function. We use the rank ordered probit model as an illustrative example to investigate the comparative properties of these simulation estimation approaches.

Suggested Citation

  • Vassilis A. Hajivassiliou & Paul A. Ruud, 1993. "Classical Estimation Methods for LDV Models Using Simulation," Cowles Foundation Discussion Papers 1051, Cowles Foundation for Research in Economics, Yale University.
    • Handle: RePEc:cwl:cwldpp:1051
    Note: See CFP 886
    as

    Download full text from publisher

    File URL: https://cowles.yale.edu/sites/default/files/files/pub/d10/d1051.pdf
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Geweke, John, 1989. "Bayesian Inference in Econometric Models Using Monte Carlo Integration," Econometrica, Econometric Society, vol. 57(6), pages 1317-1339, November.
    2. Hansen, Lars Peter, 1982. "Large Sample Properties of Generalized Method of Moments Estimators," Econometrica, Econometric Society, vol. 50(4), pages 1029-1054, July.
    3. Avery, Robert B & Hansen, Lars Peter & Hotz, V Joseph, 1983. "Multiperiod Probit Models and Orthogonality Condition Estimation," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 24(1), pages 21-35, February.
    4. Lee, Bong-Soo & Ingram, Beth Fisher, 1991. "Simulation estimation of time-series models," Journal of Econometrics, Elsevier, vol. 47(2-3), pages 197-205, February.
    5. Keane, Michael P, 1994. "A Computationally Practical Simulation Estimator for Panel Data," Econometrica, Econometric Society, vol. 62(1), pages 95-116, January.
    6. McFadden, Daniel L., 1984. "Econometric analysis of qualitative response models," Handbook of Econometrics, in: Z. Griliches† & M. D. Intriligator (ed.), Handbook of Econometrics, edition 1, volume 2, chapter 24, pages 1395-1457, Elsevier.
    7. Carlos F. Daganzo & Fernando Bouthelier & Yosef Sheffi, 1977. "Multinomial Probit and Qualitative Choice: A Computationally Efficient Algorithm," Transportation Science, INFORMS, vol. 11(4), pages 338-358, November.
    8. 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.
    9. Dale J. Poirier & Paul A. Ruud, 1988. "Probit with Dependent Observations," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 55(4), pages 593-614.
    10. Bolduc, D. & Kaci, M., 1991. "Multinomial Probit Models with Factor-Based Autoregressive Errors: A Computationally Efficient Estimation Approach," Papers 9118, Laval - Recherche en Energie.
    11. Rust, J., 1991. "Estimation of dynamic Structural Models: Problems and Prospects Part I : Discrete Decision Processes," Working papers 9106, Wisconsin Madison - Social Systems.
    12. Hans G. Bloemen & Arie Kapteyn, 1993. "The Joint Estimation of a Non-Linear Labour Supply Function and a Wage Equation Using Simulated Response Probabilities," Annals of Economics and Statistics, GENES, issue 29, pages 175-205.
    13. Lee, Lung-Fei, 1979. "Identification and Estimation in Binary Choice Models with Limited (Censored) Dependent Variables," Econometrica, Econometric Society, vol. 47(4), pages 977-996, July.
    14. 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.
    15. Duffie, Darrell & Singleton, Kenneth J, 1993. "Simulated Moments Estimation of Markov Models of Asset Prices," Econometrica, Econometric Society, vol. 61(4), pages 929-952, July.
    16. 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.
    17. Ruud, Paul A., 1991. "Extensions of estimation methods using the EM algorithm," Journal of Econometrics, Elsevier, vol. 49(3), pages 305-341, September.
    18. Gourieroux, Christian & Monfort, Alain & Trognon, Alain, 1984. "Pseudo Maximum Likelihood Methods: Theory," Econometrica, Econometric Society, vol. 52(3), pages 681-700, May.
    19. J. E. Dutt, 1976. "Numerical Aspects of Multivariate Normal Probabilities in Econometric Models," NBER Chapters, in: Annals of Economic and Social Measurement, Volume 5, number 4, pages 547-561, National Bureau of Economic Research, Inc.
    20. Laroque, Guy & Salanie, Bernard, 1989. "Estimation of Multi-market Fix-Price Models: An Application of Pseudo Maximum Likelihood Methods," Econometrica, Econometric Society, vol. 57(4), pages 831-860, July.
    21. Reuben Gronau, 1974. "The Effect of Children on the Housewife's Value of Time," NBER Chapters, in: Economics of the Family: Marriage, Children, and Human Capital, pages 457-490, National Bureau of Economic Research, Inc.
    22. Arulampalam, W. & Robin A. Naylor & Jeremy P. Smith, 2002. "University of Warwick," Royal Economic Society Annual Conference 2002 9, Royal Economic Society.
    23. McCulloch, Robert & Rossi, Peter E., 1994. "An exact likelihood analysis of the multinomial probit model," Journal of Econometrics, Elsevier, vol. 64(1-2), pages 207-240.
    24. Vassilis A. Hajivassiliou & Daniel L. McFadden, 1998. "The Method of Simulated Scores for the Estimation of LDV Models," Econometrica, Econometric Society, vol. 66(4), pages 863-896, July.
    25. Hendry, David F., 1984. "Monte carlo experimentation in econometrics," Handbook of Econometrics, in: Z. Griliches† & M. D. Intriligator (ed.), Handbook of Econometrics, edition 1, volume 2, chapter 16, pages 937-976, Elsevier.
    26. Ariel Pakes, 1991. "Dynamic Structural Models: Problems and Prospects. Mixed Continuous Discrete Controls and Market Interactions," Cowles Foundation Discussion Papers 984, Cowles Foundation for Research in Economics, Yale University.
    27. V. Joseph Hotz & Robert A. Miller, "undated". "Conditional Choice Probabilities and the Estimation of Dynamic Discrete Choice Models," University of Chicago - Population Research Center 89-2a, Chicago - Population Research Center.
    28. Bolduc, Denis, 1992. "Generalized autoregressive errors in the multinomial probit model," Transportation Research Part B: Methodological, Elsevier, vol. 26(2), pages 155-170, April.
    29. van Praag, B. M. S. & Hop, J. P., 1987. "Estimation Of Continuous Models On The Basis Of Set-Valued Observations," Econometric Institute Archives 272362, Erasmus University Rotterdam.
    30. R. F. Engle & D. McFadden (ed.), 1986. "Handbook of Econometrics," Handbook of Econometrics, Elsevier, edition 1, volume 4, number 4.
    31. Heckman, James, 2013. "Sample selection bias as a specification error," Applied Econometrics, Russian Presidential Academy of National Economy and Public Administration (RANEPA), vol. 31(3), pages 129-137.
    32. Vassilis A. Hajivassiliou & Daniel McFadden, 1990. "The Method of Simulated Scores for the Estimation of LDV Models with an Application to External Debt Crisis," Cowles Foundation Discussion Papers 967, Cowles Foundation for Research in Economics, Yale University.
    33. Berkovec, James & Stern, Steven, 1991. "Job Exit Behavior of Older Men," Econometrica, Econometric Society, vol. 59(1), pages 189-210, January.
    34. McFadden, Daniel & Ruud, Paul A, 1994. "Estimation by Simulation," The Review of Economics and Statistics, MIT Press, vol. 76(4), pages 591-608, November.
    35. Dubin, Jeffrey A & McFadden, Daniel L, 1984. "An Econometric Analysis of Residential Electric Appliance Holdings and Consumption," Econometrica, Econometric Society, vol. 52(2), pages 345-362, March.
    36. Chib, Siddhartha, 1993. "Bayes regression with autoregressive errors : A Gibbs sampling approach," Journal of Econometrics, Elsevier, vol. 58(3), pages 275-294, August.
    37. Kloek, Tuen & van Dijk, Herman K, 1978. "Bayesian Estimates of Equation System Parameters: An Application of Integration by Monte Carlo," Econometrica, Econometric Society, vol. 46(1), pages 1-19, January.
    38. Vassilis Argyrou Hajivassiliou, 1993. "Simulating Normal Rectangle Probabilities and Their Derivatives: The Effects of Vectorization," Working Papers _025, Yale University.
    39. Pakes, Ariel & Pollard, David, 1989. "Simulation and the Asymptotics of Optimization Estimators," Econometrica, Econometric Society, vol. 57(5), pages 1027-1057, September.
    40. Charles E. Clark, 1961. "The Greatest of a Finite Set of Random Variables," Operations Research, INFORMS, vol. 9(2), pages 145-162, April.
    41. Lee, Lung-Fei, 1978. "Unionism and Wage Rates: A Simultaneous Equations Model with Qualitative and Limited Dependent Variables," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 19(2), pages 415-433, June.
    42. Amemiya, Takeshi, 1984. "Tobit models: A survey," Journal of Econometrics, Elsevier, vol. 24(1-2), pages 3-61.
    43. Hausman, Jerry A & Wise, David A, 1979. "Attrition Bias in Experimental and Panel Data: The Gary Income Maintenance Experiment," Econometrica, Econometric Society, vol. 47(2), pages 455-473, March.
    44. Keane, Michael, 1993. "Simulation estimation for panel data models with limited dependent variables," MPRA Paper 53029, University Library of Munich, Germany.
    45. Gourieroux, Christian & Monfort, Alain & Trognon, Alain, 1984. "Pseudo Maximum Likelihood Methods: Applications to Poisson Models," Econometrica, Econometric Society, vol. 52(3), pages 701-720, May.
    46. Stern, Steven, 1992. "A Method for Smoothing Simulated Moments of Discrete Probabilities in Multinomial Probit Models," Econometrica, Econometric Society, vol. 60(4), pages 943-952, July.
    47. Goldfelfd, Stephen M. & Quandt, Richard E., 1975. "Estimation in a disequilibrium model and the value of information," Journal of Econometrics, Elsevier, vol. 3(4), pages 325-348, November.
    48. Heckman, James J, 1974. "Shadow Prices, Market Wages, and Labor Supply," Econometrica, Econometric Society, vol. 42(4), pages 679-694, July.
    49. Lewis, H Gregg, 1974. "Comments on Selectivity Biases in Wage Comparisons," Journal of Political Economy, University of Chicago Press, vol. 82(6), pages 1145-1155, Nov.-Dec..
    50. Beggs, S. & Cardell, S. & Hausman, J., 1981. "Assessing the potential demand for electric cars," Journal of Econometrics, Elsevier, vol. 17(1), pages 1-19, September.
    Full references (including those not matched with items on IDEAS)

    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. Vassilis A. Hajivassiliou, 1991. "Simulation Estimation Methods for Limited Dependent Variable Models," Cowles Foundation Discussion Papers 1007, Cowles Foundation for Research in Economics, Yale University.
    2. Vassilis A. Hajivassiliou, 1993. "Simulating Normal Rectangle Probabilities and Their Derivatives: The Effects of Vectorization," Cowles Foundation Discussion Papers 1049, Cowles Foundation for Research in Economics, Yale University.
    3. Daniel Ackerberg, 2009. "A new use of importance sampling to reduce computational burden in simulation estimation," Quantitative Marketing and Economics (QME), Springer, vol. 7(4), pages 343-376, December.
    4. Kerem Tuzcuoglu, 2019. "Composite Likelihood Estimation of an Autoregressive Panel Probit Model with Random Effects," Staff Working Papers 19-16, Bank of Canada.
    5. 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.
    6. Vijverberg, Wim P. M., 1997. "Monte Carlo evaluation of multivariate normal probabilities," Journal of Econometrics, Elsevier, vol. 76(1-2), pages 281-307.
    7. Geweke, J. & Joel Horowitz & Pesaran, M.H., 2006. "Econometrics: A Bird’s Eye View," Cambridge Working Papers in Economics 0655, Faculty of Economics, University of Cambridge.
    8. Inkmann, Joachim, 2000. "Misspecified heteroskedasticity in the panel probit model: A small sample comparison of GMM and SML estimators," Journal of Econometrics, Elsevier, vol. 97(2), pages 227-259, August.
    9. Hajivassiliou, Vassilis & McFadden, Daniel & Ruud, Paul, 1996. "Simulation of multivariate normal rectangle probabilities and their derivatives theoretical and computational results," Journal of Econometrics, Elsevier, vol. 72(1-2), pages 85-134.
    10. Vassilis A. Hajivassiliou & Daniel McFadden & Paul A. Ruud, 1994. "Simulation of Multivariate Normal Rectangle Probabilities: Theoretical and Computational Results," Cowles Foundation Discussion Papers 1021R, Cowles Foundation for Research in Economics, Yale University.
    11. Hanemann, W. Michael & Kanninen, Barbara, 1996. "The Statistical Analysis Of Discrete-Response Cv Data," CUDARE Working Papers 25022, University of California, Berkeley, Department of Agricultural and Resource Economics.
    12. Kamhon Kan & Chihwa Kao, 2005. "Simulation-Based Two-Step Estimation with Endogenous Regressors," Center for Policy Research Working Papers 76, Center for Policy Research, Maxwell School, Syracuse University.
    13. Keane, Michael, 1993. "Simulation estimation for panel data models with limited dependent variables," MPRA Paper 53029, University Library of Munich, Germany.
    14. Kenneth Train, "undated". "Simulation Methods for Probit and Related Models Based on Convenient Error Partitioning," Working Papers _009, University of California at Berkeley, Econometrics Laboratory Software Archive.
    15. 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.
    16. Ramdan Dridi & Eric Renault, 2000. "Semi-Parametric Indirect Inference," STICERD - Econometrics Paper Series 392, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
    17. Jesús Fernández-Villaverde & Juan F. Rubio-Ramírez, 2007. "Estimating Macroeconomic Models: A Likelihood Approach," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 74(4), pages 1059-1087.
    18. Gould, Brian W. & Dong, Diansheng, 2000. "The Decision Of When To Buy A Frequently Purchased Good: A Multi-Period Probit Model," Journal of Agricultural and Resource Economics, Western Agricultural Economics Association, vol. 25(2), pages 1-17, December.
    19. Horowitz, Joel & Keane, Michael & Bolduc, Denis & Divakar, Suresh & Geweke, John & Gonul, Fosun & Hajivassiliou, Vassilis & Koppelman, Frank & Matzkin, Rosa & Rossi, Peter & Ruud, Paul, 1994. "Advances in Random Utility Models," MPRA Paper 53026, University Library of Munich, Germany.
    20. Lee, Lung-Fei, 1997. "A smooth likelihood simulator for dynamic disequilibrium models," Journal of Econometrics, Elsevier, vol. 78(2), pages 257-294, June.

    More about this item

    Keywords

    Multivariate integration; limited dependent variable models; Monte Carlo simulation; maximum simulated likelihood; method of simulated moments; method of simulated scores;
    All these keywords.

    JEL classification:

    • C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General
    • C2 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables
    • C3 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables
    • C4 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics
    • C5 - Mathematical and Quantitative Methods - - Econometric Modeling
    • C8 - Mathematical and Quantitative Methods - - Data Collection and Data Estimation Methodology; Computer Programs

    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:cwl:cwldpp:1051. 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: Brittany Ladd (email available below). General contact details of provider: https://edirc.repec.org/data/cowleus.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.