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Smooth unbiased multivariate probability simulators for maximum likelihood estimation of limited dependent variable models

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  • Borsch-Supan, Axel
  • Hajivassiliou, Vassilis A.

Abstract

We apply a new simulation method that solves the multidimensional probability integrals that arise in maximum likelihood estimation of a broad class of limited dependent variable models. The simulation method has four key features: the simulated choice probabilities are unbiased; they are a continuous and differentiable function of the parameters of the model; they are bounded between 0 and 1; and their computation takes an effort that is nearly linear in the dimension of the probability integral, independent of the magnitudes of the true probabilities. We also show that the new simulation method produces probability estimates with substantially smaller variance than those generated by acceptance-rejection methods or by Stern's (1987) method. The simulated probabilities can therefore be used to revive the Lerman and Manski(1981) procedure of approximating the likelihood function using simulated choice probabilities by overcoming its computational disadvantages.

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Bibliographic Info

Article provided by Elsevier in its journal Journal of Econometrics.

Volume (Year): 58 (1993)
Issue (Month): 3 (August)
Pages: 347-368

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Handle: RePEc:eee:econom:v:58:y:1993:i:3:p:347-368

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Web page: http://www.elsevier.com/locate/jeconom

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  1. Chamberlain, Gary, 1984. "Panel data," Handbook of Econometrics, in: Z. Griliches† & M. D. Intriligator (ed.), Handbook of Econometrics, edition 1, volume 2, chapter 22, pages 1247-1318 Elsevier.
  2. V A Hajivassiliou & DL McFadden, 1997. "The Method of Simulated Scores for the Estimation of LDV Models," STICERD - Econometrics Paper Series /1997/328, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
  3. J. A. Hausman & D. A. Wise, 1976. "A Conditional Profit Model for Qualitative Choice: Discrete Decisions Recognizing Interdependence and Heterogeneous Preferences," Working papers 173, Massachusetts Institute of Technology (MIT), Department of Economics.
  4. Stern, Steven, 1992. "A Method for Smoothing Simulated Moments of Discrete Probabilities in Multinomial Probit Models," Econometrica, Econometric Society, vol. 60(4), pages 943-52, July.
  5. 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.
  6. Keane, Michael P, 1994. "A Computationally Practical Simulation Estimator for Panel Data," Econometrica, Econometric Society, vol. 62(1), pages 95-116, January.
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