Browsing by Author "Khan, S"

Now showing 1 - 13 of 13
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    Estimating censored regression models in the presence of nonparametric multiplicative heteroskedasticity
    (Journal of Econometrics, 2000-10-01) Chen, S; Khan, S
    Powell's (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 mis specification 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. © 2000 Elsevier Science S.A. All rights reserved.
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    Informational content of special regressors in heteroskedastic binary response models
    (Journal of Econometrics, 2016-07-01) Chen, S; Khan, S; Tang, X
    © 2016 Elsevier B.V.We quantify the informational content of special regressors in heteroskedastic binary response models with median-independent or conditionally symmetric errors. Based on Lewbel (1998), a special regressor is additively separable in the latent payoff and conditionally independent from the error term. We find that with median-independent errors a special regressor does not increase the identifying power by a criterion in Manski (1988) or lead to positive Fisher information for the coefficients, even though it does help recover the average structural function. With conditionally symmetric errors, a special regressor improves the identifying power, and the information for coefficients is positive under mild conditions. We propose two estimators for binary response models with conditionally symmetric errors and special regressors.
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    On Uniform Inference in Nonlinear Models with Endogeneity
    (Economic Research Initiatives at Duke (ERID), 2013-09-11) Khan, S; Nekipelov, D
    This paper explores the uniformity of inference for parameters of interest in nonlinear models with endogeneity. The notion of uniformity is fundamental in these models because due to potential endogeneity, the behavior of standard estimators of these parameters is shown to vary with where they lie in the parameter space. Consequently, uniform inference becomes nonstandard in a fashion that is loosely analogous to inference complications found in the unit root and weak instruments literature, as well as the models recently studied in Andrews and Cheng (2012a), Andrews and Cheng (2012b) and Chen, Ponomareva, and Tamer (2011). We illustrate this point with two models widely used in empirical work. The first is the standard sample selection model, where the parameter is the intercept term (Heckman (1990), Andrews and Schafgans (1998) and Lewbel (1997a)). We show that with selection on unobservables, asymptotic theory for this parameter is not standard in terms of there being nonparametric rates and non-gaussian limiting distributions. In contrast if the selection is on observables only, rates and asymptotic distribution are standard, and consequently an inference method that is uniform to both selection on observables and unobservables is required. As a second example, we consider the well studied treatment effect model in program evaluation (Rosenbaum and Rubin (1983) and Hirano, Imbens, and Ridder (2003)), where a parameter of interest is the ATE. Asymptotic behavior for existing estimators varies between standard and nonstandard across differing levels of treatment heterogeneity, thus also requiring new inference methods.
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    Partial rank estimation of duration models with general forms of censoring
    (Journal of Econometrics, 2007-01-01) Khan, S; Tamer, E
    In this paper we propose estimators for the regression coefficients in censored duration models which are distribution free, impose no parametric specification on the baseline hazard function, and can accommodate general forms of censoring. The estimators are shown to have desirable asymptotic properties and Monte Carlo simulations demonstrate good finite sample performance. Among the data features the new estimators can accommodate are covariate-dependent censoring, double censoring, and fixed (individual or group specific) effects. We also examine the behavior of the estimator in an empirical illustration. © 2006 Elsevier B.V. All rights reserved.
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    Quantile regression under random censoring
    (Journal of Econometrics, 2002-07-01) Honoré, B; Khan, S; Powell, JL
    Censored regression models have received a great deal of attention in both the theoretical and applied econometric literature. Most of the existing estimation procedures for either cross-sectional or panel data models are designed only for models with fixed censoring. In this paper, a new procedure for adapting these estimators designed for fixed censoring to models with random censoring is proposed. This procedure is then applied to the CLAD and quantile estimators of Powell (J. Econom. 25 (1984) 303, 32 (1986a) 143) to obtain an estimator of the coefficients under a mild conditional quantile restriction on the error term that is applicable to samples exhibiting fixed or random censoring. The resulting estimator is shown to have desirable asymptotic properties, and performs well in a small-scale simulation study. © 2002 Elsevier Science B.V. All rights reserved.
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    Rates of convergence for estimating regression coefficients in heteroskedastic discrete response models
    (Journal of Econometrics, 2003-12-01) Chen, S; Khan, S
    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. © 2003 Elsevier B.V. All rights reserved.
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    Semiparametric estimation of a heteroskedastic sample selection model
    (Econometric Theory, 2003-12-01) Chen, S; Khan, S
    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 √n-consistent and asymptotically normal, and the form of its limiting covariance matrix is derived.
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    Semiparametric estimation of a partially linear censored regression model
    (Econometric Theory, 2001-12-01) Chen, S; Khan, S
    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.
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    Semiparametric estimation of nonstationary censored panel data models with time varying factor loads
    (Econometric Theory, 2008-10-01) Chen, S; Khan, S
    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 Honoré (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 √n-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). © 2008 Cambridge University Press.
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    The impact of piped water provision on infant mortality in Brazil: A quantile panel data approach
    (Journal of Development Economics, 2010-07-01) Gamper-Rabindran, S; Khan, S; Timmins, C
    We examine the impact of piped water on the under-1 infant mortality rate (IMR) in Brazil using a recently developed econometric procedure for the estimation of quantile treatment effects with panel data. The provision of piped water in Brazil is highly correlated with other observable and unobservable determinants of IMR - the latter leading to an important source of bias. Instruments for piped water provision are not readily available, and fixed effects to control for time-invariant correlated unobservables are invalid in the simple quantile regression framework. Using the quantile panel data procedure in Chen and Khan [Chen, S., Khan, S., Semiparametric estimation of non-stationary censored panel model data models with time-varying factor. Econometric Theory 2007; forthcoming], our estimates indicate that the provision of piped water reduces infant mortality by significantly more at the higher conditional quantiles of the IMR distribution than at the lower conditional quantiles (except for cases of extreme underdevelopment). These results imply that targeting piped water intervention toward areas in the upper quantiles of the conditional IMR distribution, when accompanied by other basic public health inputs, can achieve significantly greater reductions in infant mortality. © 2009 Elsevier B.V.
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    Two-stage rank estimation of quantile index models
    (Journal of Econometrics, 2001-02-01) Khan, S
    This paper estimates a class of models which satisfy a monotonicity condition on the conditional quantile function of the response variable. This class includes as a special case the monotonic transformation model with the error term satisfying a conditional quantile restriction, thus allowing for very general forms of conditional heteroscedasticity. A two-stage approach is adopted to estimate the relevant parameters. In the first stage the conditional quantile function is estimated nonparametrically by the local polynomial estimator discussed in Chaudhuri (Journal of Multivariate Analysis 39 (1991a) 246-269; Annals of Statistics 19 (1991b) 760-777) and Cavanagh (1996, Preprint). In the second stage, the monotonicity of the quantile function is exploited to estimate the parameters of interest by maximizing a rank-based objective function. The proposed estimator is shown to have desirable asymptotic properties and can then also be used for dimensionality reduction or to estimate the unknown structural function in the context of a transformation model. © 2001 Elsevier Science S.A. All rights reserved.
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    Two-step estimation of semiparametric censored regression models
    (Journal of Econometrics, 2001-07-01) Khan, S; Powell, JL
    Root-n-consistent estimators of the regression coefficients in the linear censored regression model under conditional quantile restrictions on the error terms were proposed by Powell (Journal of Econometrics 25 (1984) 303-325, 32 (1986a) 143-155). While those estimators have desirable asymptotic properties under weak regularity conditions, simulation studies have shown these estimators to exhibit a small sample bias in the opposite direction of the least squares bias for censored data. This paper introduces two-step estimators for these models which minimize convex objective functions, and are designed to overcome this finite-sample bias. The paper gives regularity conditions under which the proposed two-step estimators are consistent and asymptotically normal; a Monte Carlo study compares the finite sample behavior of the proposed methods with their one-step counterparts. © 2001 Elsevier Science S.A. All rights reserved.
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    Weighted and two-stage least squares estimation of semiparametric truncated regression models
    (Econometric Theory, 2007-04-01) Khan, S; Lewbel, A
    This paper provides a root-n consistent, asymptotically normal weighted least squares estimator of the coefficients in a truncated regression model. The distribution of the errors is unknown and permits general forms of unknown heteroskedasticity. Also provided is an instrumental variables based two-stage least squares estimator for this model, which can be used when some regressors are endogenous, mismeasured, or otherwise correlated with the errors. A simulation study indicates that the new estimators perform well in finite samples. Our limiting distribution theory includes a new asymptotic trimming result addressing the boundary bias in first-stage density estimation without knowledge of the support boundary. © 2007 Cambridge University Press.