Abstract
We outline a new estimation method for the multinomial probit model (MNP). The method is a differential evolution Markov chain algorithm that employs a Metropolis-within-Gibbs sampler with data augmentation and the Geweke–Hajivassiliou–Keane (GHK) probability simulator. The method lifts the curse of dimensionality in numerical integration as it neither requires simulation of the whole likelihood function nor the computation of its analytical or numerical derivatives. The method is applied to an unbalanced panel dataset of firms from the German business-related service sector over the period 1994–2000. In spite of its less restricted character, the MNP model is found not to provide more accurate estimates for explaining the performance of these firms than the multinomial logit model.
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Ben-Akiva M., McFadden D., Abe M., Böckenholt U., Bolduc D., Gopinath D. et al (1997) Modeling methods for discrete choice analysis. Marketing Letters 8: 273–286
Bolduc D. (1999) A practical technique to estimate multinomial probit models in transportation. Transportation Research Part B 33: 63–79
Börsch-Supan A., Hajivassiliou V. (1993) Smooth unbiased multivariate probability simulators for maximum likelihood estimation of limited dependent variable models. Journal of Econometrics 58: 347–368
Byatt D., Coope I. D., Price C. J. (2004) Effect of limited precision on the BFGS quasi-Newton algorithm. ANZIAM Journal 45: C283–C295
Cramer J. S. (1991) The Logit Model: An Introduction for Economists. Edward Arnold, London
Genz A. (1992) Numerical computation of multivariate normal probabilities. Journal of Computational and Graphical Statistics 1(2): 141–149
Geweke J. (1989) Bayesian inference in econometric models using Monte Carlo integration. Econometrica 57: 1317–1339
Geweke, J. (1991). Efficient simulation from the multivariate normal and student-t distributions subject to linear constraints. In E. M. Deramidas (Ed.), Computer science and statistics: Proceedings of the twenty-third symposium on the interface (pp. 571–578). Fairfax: Interface Foundation of North America, Inc.
Geweke J., Keane M., Runkle D. (1994) Alternative computational approaches to inference in the multinomial probit model. Review of Economics and Statistics 76: 609–632
Green W. H. (2008) Econometric Analysis, Sixth Edition. Prentice Hall, Upper Saddle River (NJ)
Hajivassiliou V., McFadden D. (1998) The method of simulated scores for the estimation of LDV models. Econometrica 66: 863–896
Hess S., Train K. W., Polak J. W. (2006) On the use of a Modified Latin Hypercube Sampling (MLHS) method in the estimation of a Mixed Logit Model for vehicle choice. Transportation Research Part B 40: 147–163
Keane, M. (1990). Four essays in empirical macro and labor economics. Ph.D. Thesis, Brown University.
Keane M. (1994) A computationally practical simulation estimator for panel data. Econometrica 62: 95–116
Koop G. (2003) Bayesian Econometrics. Wiley, Chichester
McFadden D. (1974) Conditional logit analysis of qualitative choice behavior. In: Zarembka P. (Ed.) Frontiers in Econometrics.. Academic Press, New York, pp 105–142
McCulloch R. E., Polson N. G., Rossi P. E. (2000) A Bayesian analysis of the multinomial probit model with fully identified parameters. Journal of Econometrics 99: 173–193
McFadden D. (1984) Econometric analysis of qualitative response models. In: Griliches Z., Intriligator M. (eds) Handbook of Econometrics, Vol. 2, Chap. 18.. North Holland, Amsterdam, pp 1395–1457
Monfardini C., Santos Silva J. M. C. (2008) What can we learn about correlations from multinomial probit estimates. Economics Bulletin 3(28): 1–9
Van Nguyen P., Laisney F., Kaiser U. (2004) The performance of German firms in the business-related service sector: a dynamic analysis. Journal of Business & Economic Statistics 22(3): 274–295
Nerlove, M. & Press, S. (1973). Univariate and multivariate log-linear and logistic models. RAND-R1306-EDA/NIH, Santa Monica.
Price K. V., Storn R. M, Lampinen J. A. (2005) Differential Evolution—A Practical Approach to Global Optimization. Springer, Berlin
Schervish M. (1984) Multivariate normal probabilities with error bound. Applied Statistics 33: 81–87
Storn, R., & Price, K. (1995), Differential Evolution—A simple and efficient adaptive scheme for global optimization over continuous spaces. International Computer Science Institute, Berkeley, TR-95-012. http://www.icsi.berkeley.edu~storn/litera.html
Storn R., Price K. (1997) Differential Evolution—A simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11: 341–359
Tanner M. A., Wong W. H. (1987) The calculation of posterior distributions by data augmentation. Journal of the American Statistical Association 82(398): 528–540
Ter Braak C. J. F. (2006) A Markov Chain Monte Carlo version of the genetic algorithm Differential Evolution: Easy Bayesian computing for real parameter spaces. Statistics and Computing 16: 239–249
Train K. (2009) Discrete Choice Methods with Simulation (2nd ed.). Cambridge University Press, Cambridge
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Open Access This is an open access article distributed under the terms of the Creative Commons Attribution Noncommercial License (https://creativecommons.org/licenses/by-nc/2.0), which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.
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Kuiper, W.E., Cozijnsen, A.J. The Performance of German Firms in the Business-Related Service Sectors Revisited: Differential Evolution Markov Chain Estimation of the Multinomial Probit Model. Comput Econ 37, 331–362 (2011). https://doi.org/10.1007/s10614-011-9259-x
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DOI: https://doi.org/10.1007/s10614-011-9259-x