JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms of scholarship. For more information about JSTOR, please contact support@jstor.org.. The Econometric Society is collaborating with JSTOR to digitize, preserve and extend access to Econometrica. This paper considers estimation of truncated and censored regression models with fixed effects in panel data. Up until now, no estimator has been shown to be consistent as the cross section dimension increases with the time dimension fixed. Trimmed least absolute deviations (LAD) and trimmed least squares estimators are proposed for the case where the panel is of length two, and it is proven that they are consistent and asymptotically normal under suitable regularity conditions. It is not necessary to maintain parametric assumptions on the error terms to obtain this result. Because three of the four estimators are defined as minimizers of nondifferentiable functions, traditional methods cannot be used to establish asymptotic normality. Instead, the approach of Pakes and Pollard (1989) is used. A small scale Monte Carlo study demonstrates that these estimators can perform well in small samples. Despite their nonlinear nature, the estimators are easy to calculate in practice, as are consistent estimators of their asymptotic variances. Generalization of the estimators to panels of arbitrary length is briefly discussed.Estimation of discrete choice models with fixed effects has been considered in the literature. If the underlying errors are independent with logistic distribution, then a conditional maximum likelihood estimator will be consistent and asymptotically normal (see Chamberlain (1984) for a discussion of this approach and for additional references). Manski (1987) has proposed a conditional maximum score estimator for the same model. The advantage of Manski's estimator is that it is consistent under assumptions that are much weaker than those needed for the conditional maximum likelihood estimator. This paper proposes estimators for limited dependent variable models with fixed effects. These models are usually estimated by maximizing a likelihood function over all the parameters, including the fixed effects. As mentioned, these estimators will generally not have the desired asymptotic properties. In contrast, the estimators proposed here are consistent and asymptotically normal as the number of individuals approaches infinity with the number of observations per individual fixed. The idea behind the estimators can be thought of as a bivariate generalization of the idea behind Powell's (1986) trimmed least squares estimators for Tobit models (without fixed effects). Like Powell's estimators, the estimators presented here are semiparametric. It is not necessary to assume a parametric form for the disturbances. Nor is it necessary to assume homoskedasticity across individ...

In this paper, we consider identification and estimation in panel data discrete choice models when the explanatory variable set includes strictly exogenous variables, lags of the endogenous dependent variable as well as unobservable individual-specific effects. For Ž . the binary logit model with the dependent variable lagged only once, Chamberlain 1993 gave conditions under which the model is not identified. We present a stronger set of conditions under which the parameters of the model are identified. The identification result suggests estimators of the model, and we show that these are consistent and asymptotically normal, although their rate of convergence is slower than the inverse of the square root of the sample size. We also consider identification in the semiparametric case where the logit assumption is relaxed. We propose an estimator in the spirit of the Ž Ž . . conditional maximum score estimator Manski 1987 , and we show that it is consistent. In addition, we discuss an extension of the identification result to multinomial discrete choice models, and to the case where the dependent variable is lagged twice. Finally, we present some Monte Carlo evidence on the small sample performance of the proposed estimators for the binary response model.

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Identification of dynamic nonlinear panel data models is an important and delicate problem in econometrics. In this paper we provide insights that shed light on the identification of parameters of some commonly used models. Using this insight, we are able to show through simple calculations that point identification often fails in these models. On the other hand, these calculations also suggest that the model restricts the parameter to lie in a region that is very small in many cases, and the failure of point identification may therefore be of little practical importance in those cases. Although the emphasis is on identification, our techniques are constructive in that they can easily form the basis for consistent estimates of the identified sets.