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Simulation estimators (Lerman and Manski 1981; McFadden, Econometrica 57(5):995–1026, 1989; Pakes and Pollard, Econometrica 57:1027–1057, 1989) have been of great use to applied economists and marketers. They are simple and relatively easy to use, even for very complicated empirical models. That said, they can be computationally demanding, since these complicated models often need to be solved numerically, and these models need to be solved many times within an estimation procedure. This paper suggests methods that combine importance sampling techniques with changes-of-variables to address this caveat. These methods can dramatically reduce the number of times a particular model needs to be solved in an estimation procedure, significantly decreasing computational burden. The methods have other advantages as well, e.g. they can smooth otherwise non-smooth objective functions and can allow one to compute derivatives analytically. There are also caveats—if one is not careful, they can magnify simulation error. We illustrate with examples and a small Monte-Carlo study.
Ackerberg, D. (2001). A new use of importance sampling to reduce computational burden in simulation estimation. NBER working paper #T273
Ackerberg, D. (2003). Advertising, learning, and consumer choice in experience. Good markets: A structural empirical examination. International Economic Review, 44, 1007–1040. CrossRef
Aguirregabiria, V., & Mira, P. (2002). Swapping the nested fixed point algorithm: A class of estimators for discrete Markov decision models. Econometrica 70, 1519–1543. CrossRef
Aguirregabiria, V., & Mira, P. (2007). Sequential estimation of dynamic discrete games. Econometrica 75, 1–53. CrossRef
Bajari, P. (1998a). Econometrics of the first price auction with asymmetric bidders. Mimeo, Stanford Univ.
Bajari, P. (1998b). Econometrics of sealed bid auctions. In 1998 Proceedings of the Business and Economic Statistics Section of the American Statistical Association (pp. 41–49).
Bajari, P., Benkard, C. L., & Levin, J. (2007a). Estimating dynamic models of imperfect competition. Econometrica 75, 1331–1370. CrossRef
Bajari, P., Fox, J., & Ryan, S. (2007b). Linear regression estimation of discrete choice models with nonparametric random coefficient distributions. American Economic Review, 97, 459–463. CrossRef
Bajari, P., Chernozhukov, V., Hong, H., & Nekipelov, D. (2008). Nonparametric and semiparametric analysis of a dynamic game model. Unpublished working paper.
Bajari, P., Fox, J., Kim, K., & Ryan, S. (2009a). Discrete choice models with a nonparametric distribution of random coefficient. Mimeo, U. of MN.
Bajari, P., Hong, H., & Ryan, S. (2009b). Identification and estimation of discrete games of complete information. Econometrica, in press.
Berry, S. T. (1992). Estimation of a model of entry in the airline industry. Econometrica, 60, 889–917. CrossRef
Berry, S., Levinsohn, J., & Pakes, A. (1995). Automobile prices in market equilibrium. Econometrica, 63, 841–890. CrossRef
Crawford, G., & Shum, M. (2005). Uncertainty and learning in pharmaceutical demand. Econometrica, 73, 1135–1174. CrossRef
Davis, P. (2006). Estimation of quantity games in the presence of indivisibilities and heterogeous firms. Journal of Econometrics, 134, 187–214. CrossRef
Erdem, T., & Keane, M. (1996). Decision making under uncertainty: Capturing dynamic brand choice processes in turbulent consumer goods markets. Marketing Science, 15, 1–20. CrossRef
Gasmi, F., Laffont, J-J, & Vuong, Q. (1991). Econometric analysis of collusive behavior in a soft drink industry. Journal of Economics and Management Strategy, 1, 277–311.
Geweke, J. (1989). Efficient simulation from the multivariate normal distribution subject to linear inequality constraints and the evaluation of constraint probabilities. Econometrica, 57, 1317–1339. CrossRef
Goettler, R., & Clay, K. (2009). Tariff choice with consumer learning and switching costs. Mimeo, Chicago GSB.
Gourieroux, C., & Monfort, A. (1991). Simulation based inference in models with heterogeneity. Annales d’Economie et de Statistique, 20/21, 69–107.
Hansen, L. (1982). Large sample properties of generalized method of moments estimators. Econometrica, 50, 1029–1064. CrossRef
Hartmann, W. (2006). Intertemporal effects of consumption and their implications for demand elasticity estimates. Quantitative Marketing and Economics, 4, 325–349. CrossRef
Hendel, I., & Nevo, A. (2006). Measuring the implications of sales and consumer inventory behavior. Econometrica, 74, 1137–1173. CrossRef
Hotz, V. J., & Miller, R. A. (1993). Conditional choice probabilities and the estimation of dynamic models. Review of Economic Studies 60, 497–529. CrossRef
Hotz, V. J., Miller, R. A., Sanders, S., & Smith, J. (1994). A simulation estimator for dynamic models of discrete choice. Review of Economic Studies 61, 265–289. CrossRef
Imai, S., Jain, N., & Ching, A. (2009). Bayesian estimation of dynamic discrete choice models. Econometrica, in press.
Jofre-Bonet, M., & Pesendorfer, M. (2003). Estimation of a dynamic auction game. Econometrica 71, 1443–1489. CrossRef
Judd, K., & Su, C. (2008). Constrained optimization approaches to estimation of structural models. Mimeo, Stanford.
Keane, M., & Wolpin, K. (1994). The solution and estimation of discrete choice dynamic programming models by simulation and interpolation. Review of Economics and Statistics, 76, 648–72. CrossRef
Keane, M., & Wolpin, K. (2000). Estimating the effect of welfare on the education, employment, fertility and marraige decisions of women. Mimeo, UPenn.
Keane, M., & Wolpin, K. (2001). The effect of parental transfers and borrowing constraints on educational attainment. International Economic Review, 42, 1051–1103. CrossRef
Lerman, S., & Manski, C. (1981). On the use of simulated frequencies to approximate choice probabilities. In C. Manski & D. McFadden (Eds.) Structural analysis of discrete data with econometric applications. (pp. 305–319). Cambridge: MIT.
Maskin, E., & Riley, J. (1996). Existence of equilibrium in sealed, high bid auctions. Mimeo.
McFadden, D. (1989) A method of simulated moments for estimation of discrete response models without numerical integration. Econometrica, 57(5), 995–1026. CrossRef
Kloek, T., & Van Dijk, H. (1978): Bayesian estimation of equation system parameters: An application of integration by Monte-Carlo. Econometrica, 46, 1–20. CrossRef
Norets, A. (2009) Inference in dynamic discrete choice models with serially correlated unobserved state variables. Econometrica, in press.
Pakes, A., Ostrovsky, M., & Berry, S. (2007). Simple estimators for the parameters of discrete dynamic games, with entry/exit examples. RAND Journal of Economics 38, 373–399. CrossRef
Pakes, A., & Pollard, D. (1989). Simulation and the asymptotics of optimization estimators. Econometrica, 57, 1027–1057. CrossRef
Pantano, J. (2008). Labor market stigma in a forward looking model of criminal behavior. Mimeo, Washington U, St. Louis.
Pesendorfer, M., & Schmidt-Dengler, P. (2008). Asymptotic least squares estimators For dynamic games. Review of Economic Studies, 75, 901–928. CrossRef
Rust, J. (1987). Optimal replacement of GMC bus engines: An empirical model of Harold Zurcher. Econometrica, 55, 999–1033. CrossRef
Rust, J. (1997). Using randomization to break the curse of dimensionality. Econometrica, 65, 487–516. CrossRef
Train, K. (2003). Discrete choice methods with simulation. Cambridge: Cambridge University Press.
- A new use of importance sampling to reduce computational burden in simulation estimation
Daniel A. Ackerberg
- Springer US
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