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Takuya Ishihara
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In this study, we develop a novel estimation method of the quantile treatment effects (QTE) under the rank invariance and rank stationarity assumptions. Ishihara (2020) explores identification of the nonseparable panel data model under these assumptions and propose a parametric estimation based on the minimum distance method. However, the minimum distance estimation using this process is computationally demanding when the dimensionality of covariates is large. To overcome this problem, we propose a two-step estimation method based on the quantile regression and minimum distance method. We then show consistency and asymptotic normality of our estimator. Monte Carlo studies indicate that our estimator performs well in finite samples. Last, we present two empirical illustrations, to estimate the distributional effects of insurance provision on household production and of TV watching on child cognitive development.
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Nonseparable panel models are important in a variety of economic settings, including discrete choice. This paper gives identification and estimation results for nonseparable models under time homogeneity conditions that are like time is randomly assigned or time is an instrument. Partial identification results for average and quantile effects are given for discrete regressors, under static or dynamic conditions, in fully nonparametric and in semiparametric models, with time effects. It is shown that the usual, linear, fixed-effects estimator is not a consistent estimator of the identified average effect, and a consistent estimator is given. A simple estimator of identified quantile treatment effects is given, providing a solution to the important problem of estimating quantile treatment effects from panel data. Bounds for overall effects in static and dynamic models are given. The dynamic bounds provide a partial identification solution to the important problem of estimating the effect of state dependence in the presence of unobserved heterogeneity. The impact of $T$, the number of time periods, is shown by deriving shrinkage rates for the identified set as $T$ grows. We also consider semiparametric, discrete-choice models and find that semiparametric panel bounds can be much tighter than nonparametric bounds. Computationally-convenient methods for semiparametric models are presented. We propose a novel inference method that applies in panel data and other settings and show that it produces uniformly valid confidence regions in large samples. We give empirical illustrations.
Factor structures or interactive effects are convenient devices to incorporate latent variables in panel data models. We consider fixed effect estimation of nonlinear panel single-index models with factor structures in the unobservables, which include logit, probit, ordered probit and Poisson specifications. We establish that fixed effect estimators of model parameters and average partial effects have normal distributions when the two dimensions of the panel grow large, but might suffer of incidental parameter bias. We show how models with factor structures can also be applied to capture important features of network data such as reciprocity, degree heterogeneity, homophily in latent variables and clustering. We illustrate this applicability with an empirical example to the estimation of a gravity equation of international trade between countries using a Poisson model with multiple factors.
In ordinary quantile regression, quantiles of different order are estimated one at a time. An alternative approach, which is referred to as quantile regression coefficients modeling (QRCM), is to model quantile regression coefficients as parametric functions of the order of the quantile. In this paper, we describe how the QRCM paradigm can be applied to longitudinal data. We introduce a two-level quantile function, in which two different quantile regression models are used to describe the (conditional) distribution of the within-subject response and that of the individual effects. We propose a novel type of penalized fixed-effects estimator, and discuss its advantages over standard methods based on $ell_1$ and $ell_2$ penalization. We provide model identifiability conditions, derive asymptotic properties, describe goodness-of-fit measures and model selection criteria, present simulation results, and discuss an application. The proposed method has been implemented in the R package qrcm.
In this paper, we develop a new censored quantile instrumental variable (CQIV) estimator and describe its properties and computation. The CQIV estimator combines Powell (1986) censored quantile regression (CQR) to deal with censoring, with a control variable approach to incorporate endogenous regressors. The CQIV estimator is obtained in two stages that are non-additive in the unobservables. The first stage estimates a non-additive model with infinite dimensional parameters for the control variable, such as a quantile or distribution regression model. The second stage estimates a non-additive censored quantile regression model for the response variable of interest, including the estimated control variable to deal with endogeneity. For computation, we extend the algorithm for CQR developed by Chernozhukov and Hong (2002) to incorporate the estimation of the control variable. We give generic regularity conditions for asymptotic normality of the CQIV estimator and for the validity of resampling methods to approximate its asymptotic distribution. We verify these conditions for quantile and distribution regression estimation of the control variable. Our analysis covers two-stage (uncensored) quantile regression with non-additive first stage as an important special case. We illustrate the computation and applicability of the CQIV estimator with a Monte-Carlo numerical example and an empirical application on estimation of Engel curves for alcohol.
This paper considers fixed effects estimation and inference in linear and nonlinear panel data models with random coefficients and endogenous regressors. The quantities of interest -- means, variances, and other moments of the random coefficients -- are estimated by cross sectional sample moments of GMM estimators applied separately to the time series of each individual. To deal with the incidental parameter problem introduced by the noise of the within-individual estimators in short panels, we develop bias corrections. These corrections are based on higher-order asymptotic expansions of the GMM estimators and produce improved point and interval estimates in moderately long panels. Under asymptotic sequences where the cross sectional and time series dimensions of the panel pass to infinity at the same rate, the uncorrected estimator has an asymptotic bias of the same order as the asymptotic variance. The bias corrections remove the bias without increasing variance. An empirical example on cigarette demand based on Becker, Grossman and Murphy (1994) shows significant heterogeneity in the price effect across U.S. states.
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