Songnian Chen

Simple resampling methods for censored regression quantiles

Abstract Powell (Journal of Econometrics 25 (1984) 303–325; Journal of Econometrics 32 (1986) 143–155) considered censored regression quantile estimators. The asymptotic covariance matrices of his estimators depend on the error densities and are therefore difficult to estimate reliably. The difficulty may be avoided by applying the bootstrap method (Hahn, Econometric Theory 11 (1995) 105–121). Calculation of the estimators, however, requires solving a nonsmooth and nonconvex minimization problem, resulting in high computational costs in implementing the bootstrap. We propose in this paper computationally simple resampling methods by convexfying Powells approach in the resampling stage. A major advantage of the new methods is that they can be implemented by efficient linear programming. Simulation studies show that the methods are reliable even with moderate sample sizes.

SEMIPARAMETRIC ESTIMATION OF A PARTIALLY LINEAR CENSORED REGRESSION MODEL

In this paper we propose an estimation procedure for a censored regression model where the latent regression function has a partially linear form. Based on a conditional quantile restriction, we estimate the model by a two stage procedure. The first stage nonparametrically estimates the conditional quantile function at in-sample and appropriate out-of-sample points, and the second stage involves a simple weighted least squares procedure. The proposed procedure is shown to have desirable asymptotic properties under regularity conditions that are standard in the literature. A small scale simulation study indicates that the estimator performs well in moderately sized samples.

Semiparametric estimation of a heteroskedastic sample selection model

This paper considers estimation of a sample selection model subject to conditional heteroskedasticity in both the selection and outcome equations. The form of heteroskedasticity allowed for in each equation is multiplicative, and each of the two scale functions is left unspecified. A three-step estimator for the parameters of interest in the outcome equation is proposed. The first two stages involve nonparametric estimation of the “propensity score†and the conditional interquartile range of the outcome equation, respectively. The third stage reweights the data so that the conditional expectation of the reweighted dependent variable is of a partially linear form, and the parameters of interest are estimated by an approach analogous to that adopted in Ahn and Powell (1993, Journal of Econometrics 58, 3–29). Under standard regularity conditions the proposed estimator is shown to be -consistent and asymptotically normal, and the form of its limiting covariance matrix is derived.We are grateful to B. HonorA©, R. Klein, E. Kyriazidou, L.-F. Lee, J. Powell, two anonymous referees, and the co-editor D. Andrews and also to seminar participants at Princeton, Queens, UCLA, and the University of Toronto for helpful comments. Chens research was supported by RGC grant HKUST 6070/01H from the Research Grants Council of Hong Kong.

Distribution-free estimation of the random coefficient dummy endogenous variable model

This paper considers the estimation of the random coefficient dummy endogenous variable model under a symmetry and index condition for the error distribution. We follow a two-step approach.The selection equation is estimated first; in the second step an instrumental variables estimator is proposed for the ourcome equation through a pairwise comparison method. Our approach can be readily extended to the general switching regression model. In constrast to the existing literature on sample selection models, the exclusion restriction is not needed here for model identification; furthermore, the intercept term for the outcome equation can be estimated at the usual parametric rate.

Nonparametric Identification and Estimation of a Censored Location-Scale Regression Model

In this article we consider identification and estimation of a censored nonparametric location scale-model. We first show that in the case where the location function is strictly less than the (fixed) censoring point for all values in the support of the explanatory variables, the location function is not identified anywhere. In contrast, when the location function is greater or equal to the censoring point with positive probability, the location function is identified on the entire support, including the region where the location function is below the censoring point. In the latter case we propose a simple estimation procedure based on combining conditional quantile estimators for various higher quantiles. The new estimator is shown to converge at the optimal nonparametric rate with a limiting normal distribution. A small-scale simulation study indicates that the proposed estimation procedure performs well in finite samples. We also present an empirical illustration on unemployment insurance duration using administrative-level data from New Jersey.

Estimating censored regression models in the presence of nonparametric multiplicative heteroskedasticity

Abstract Powells (1984, Journal of Econometrics 25, 303–325) censored least absolute deviations (CLAD) estimator for the censored linear regression model has been regarded as a desirable alternative to maximum likelihood estimation methods due to its robustness to conditional heteroskedasticity and distributional misspecification of the error term. However, the CLAD estimation procedure has failed in certain empirical applications due to the restrictive nature of the ‘full rank’ condition it requires. This condition can be especially problematic when the data are heavily censored. In this paper we introduce estimation procedures for heteroskedastic censored linear regression models with a much weaker identification restriction than that required for the LCAD, and which are flexible enough to allow for various degrees of censoring. The new estimators are shown to have desirable asymptotic properties and perform well in small-scale simulation studies, and can thus be considered as viable alternatives for estimating censored regression models, especially for applications in which the CLAD fails.

Rates of convergence for estimating regression coefficients in heteroskedastic discrete response models

Abstract In this paper, we consider estimation of discrete response models exhibiting conditional heteroskedasticity of a multiplicative form, where the latent error term is assumed to be the product of an unknown scale function and a homoskedastic error term. It is first shown that for estimation of the slope coefficients in a binary choice model under this type of restriction, the semiparametric information bound is zero, even when the homoskedastic error term is parametrically specified. Hence, it is impossible to attain the parametric convergence rate for the parameters of interest. However, for ordered response models where the response variable can take at least three different values, the parameters of interest can be estimated at the parametric rate under the multiplicative heteroskedasticity assumption. Two estimation procedures are proposed. The first estimator, based on a parametric restriction on the homoskedastic component of the error term, is a two-step maximum likelihood estimators, where the unknown scale function is estimated nonparametrically in the first stage. The second procedure, which does not require the parametric restriction, estimates the parameters by a kernel weighted least-squares procedure. Under regularity conditions which are standard in the literature, both estimators are shown to be n -consistent and asymptotically normal.

Semiparametric estimation of the Type-3 Tobit model

Abstract This paper considers estimation of the Type-3 Tobit model with only some weak restrictions imposed on the distribution of the error terms. Two least-squares-type estimation approaches are proposed under the condition that the error terms and regressors are independent. Consistent estimators for the asymptotic covariance matrices are proposed to facilitate large sample inference, and a small Monte Carlo simulation is performed to investigate the finite sample behavior of the proposed estimators. Also, the semiparametric efficiency bound is derived for the Type-3 Tobit model under the independence restriction.

Semiparametric estimation of nonstationary censored panel data models with time varying factor loads

We propose an estimation procedure for a semiparametric panel data censored regression model in which the error terms may be subject to general forms of nonstationarity. Specifically, we allow for heteroskedasticity over time and a time varying factor load on the individual specific effect. Empirically, estimation of this model would be of interest to explore how returns to unobserved skills change over time—see, e.g., Chay (1995, manuscript, Princeton University) and Chay and Honore (1998, Journal of Human Resources 33, 4–38). We adopt a two-stage procedure based on nonparametric median regression, and the proposed estimator is shown to be null -consistent and asymptotically normal. The estimation procedure is also useful in the group effect setting, where estimation of the factor load would be empirically relevant in the study of the intergenerational correlation in income, explored in Solon (1992, American Economic Review 82, 393–408; 1999, Handbook of Labor Economics , vol. 3, 1761–1800) and Zimmerman (1992, American Economic Review 82, 409–429).

Rank estimation of a location parameter in the binary choice model

Abstract This paper proposes a rank-based estimator for a location parameter in the binary choice model under a monotonic index and symmetry condition, given an initial n -consistent estimator for the slope parameter. The estimator converges at the usual parametric rate. Compared with existing estimators, no nonparametric smoothing is needed here. A small Monte Carlo study illustrates the usefulness of the estimator. We also point out that the location and slope parameters can be jointly estimated.