Trimmed Lad and Least Squares Estimation of Truncated and Censored Regression Models with Fixed Effects

Abstract

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...

Censored Data and Truncated Distributions

“…Moon's (1989) proposed estimator is not unrelated to this, and he, as these authors do, takes the CLAD estimator as a benchmark for comparison. Honore (1992) suggests how the CLAD estimator can be extended to accommodate panel data models with fixed effects. (It is worth noting, these estimators focus on estimation of a constant multiple of β.…”

A Two-Step First Difference Estimator for a Panel Data Tobit Model Under Conditional Mean Independence Assumptions

“…We conclude that the two-step first-difference Tobit estimator proposed in this study can be regarded as a very attractive alternative to the fixed effects Tobit estimator of Honoré (1992), since it allows one to calculate marginal effects, and as a bias reduction technique when applied to a random effects panel data Tobit model under conditional mean independence assumptions (Wooldridge, 1995).…”

“…The first is a fixed effects approach (Honoré, 1992, Kyriazidou, 1997 for which consistency does not require any assumptions on the individual specific effects but does require an additional distributional assumption, for instance the stationarity assumption in Honoré (1992). The second is a random effects approach (Nijman and Verbeek, 1992, Wooldridge, 1995, Rochina-Barrachina, 1999, Kalwij, 2003 for which consistency does not require an additional distributional assumption but does require a correct specification of the correlation between the individual specific effects and the explanatory variables, the so-called conditional mean independence assumption (Wooldrigde, 1995).…”

Estimation of a Transformation Model with Truncation, Interval Observation and Time-Varying Covariates

“…It is well understood that estimators of panel data models can be turned into estimators of cross-sectional models by considering all pairs of observations as units in a panel. See, for example, Honoré and Powell (1994), who apply the idea in Honoré (1992) 1 The assumption of log-concavity also appears elsewhere in the literature on truncated regression models.…”