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.
Written by one of the world's leading experts on dynamic panel data reviews, this volume reviews most of the important topics in the subject. It deals with static models, dynamic models, discrete choice and related models.
This dissertation consists of three chapters that study unobserved heterogeneity in panel and network data models. In Chapter 1, I propose a semi-nonparametric panel data model with a latent group structure. I assume that individual parameters are heterogeneous across groups but homogeneous within a group while the group membership is unknown. I first approximate the infinite-dimensional function with a sieve expansion; then, I propose a Classifier-Lasso(C-Lasso) procedure to simultaneously identify the individuals' membership and estimate the group-specific parameters. I show that: (i) the classification exhibits uniform consistency; (ii) C-Lasso and post-Lasso estimators achieve oracle properties so that they are asymptotically equivalent to infeasible estimators as if the group membership is known; and (iii) the estimators are consistent and asymptotically normally distributed. Simulations demonstrate an excellent finite sample performance of this approach in both classification and estimation. In Chapter 2 (joint with Wenyu Zhou), we study a nonparametric additive panel regression model with grouped heterogeneity. The model can be regarded as a natural extension to the heterogeneous panel model studied in Su, Shi, and Phillips (2016). We propose to estimate the nonparametric components using a sieve-approximation-based Classifier-Lasso method. We establish the asymptotic properties of the estimator and show that they enjoy the so-called oracle property. In addition, we present the decision rule for group classification and establish its consistency. Then, a BIC-type information criterion is developed to determine the group pattern of each nonparametric component. We further investigate the finite sample performance of the estimation method and the information criterion through Monte Carlo simulations. Results show that both work well. Finally, we apply the model and the estimation method to study the demand for cigarettes in the United States using panel data of 46 states from 1963 to 1992. In Chapter 3, I study a network sample selection model in which 1) bilateral fixed effects enter the pairwise outcome equation additively; 2) link formation depends on latent variables from both sides nonparametrically. I first propose a four-cycle structure to difference out the fixed effects; next, utilizing the idea proposed in Auerbach (2019), I manage to use the kernel function to control for the selection bias. I then introduce estimators for the parameters of interest and characterize their asymptotic properties.
Microeconomic panel data, also known as longitudinal data or repeated measures, allow the researcher to observe the same individual across time. One of the advantages of panel data is that they allow the researcher to control for unobservable individual heterogeneity. The linear fixed effects model is the most commonly used method in empirical work to control for unobservable heterogeneity. Chapter 1 reviews the special features of the linear fixed effects model in detail, giving special attention to the definition of fixed effects and correlated random effects. It discusses the issues that arise when we move from a linear model to fully nonseparable models and reviews the two strands of the literature that are relevant for this dissertation: (1) the literature on nonlinear parametric panel data models with fixed effects, (2) the literature on nonparametric identification in nonseparable panel data models. Chapter 2 falls under the parametric nonlinear panel data models with fixed effects. Nonlinear panel data models with fixed effects are an important example in econometrics where the incidental parameter problem arises and the maximum likelihood estimator (MLE) is asymptotically biased. Bias correction of the MLE achieves consistency without increasing the asymptotic variance. Chapter 2 proposes a shrinkage estimator that combines that is shown to lead to a higher-order mean-square error improvement over the analytical bias-corrected estimator. Chapter 3 falls under the literature on nonparametric identification in nonseparable panel data models. Starting from a general DGP that exhibits nonseparability of the structural function, arbitrary individual and time heterogeneity, I give a necessary and sufficient condition for the point-identification of the APE for a subpopulation. This condition is then used to characterize the trade-off between assumptions on unobservable heterogeneity and the structural function that achieve identification. The identifying assumptions here have clear testable implications on the distribution of observables. I hence propose bootstrap-adjusted Kolmogorv-Smirnov and Cramer-von-Mises statistics to test these implications. Chapter 4 is an empirical paper that studies the issue of manipulation of air pollution data by Chinese cities. It applies tests similar in spirit to the tests proposed in Chapter 3 to test the presence of manipulation.
Contains 16 chapters authored by specialists in the field, covering topics such as: Missing-Data Imputation in Nonstationary Panel Data Models; Markov Switching Models in Empirical Finance; Bayesian Analysis of Multivariate Sample Selection Models Using Gaussian Copulas; and, Consistent Estimation and Orthogonality.
Panel or grouped data are often used to allow for unobserved individual heterogeneity in econometric models via fixed effects. In this paper, we discuss identification of a panel data model in which the unobserved heterogeneity both enters additively and interacts with treatment variables. We present identification and estimation methods for parameters of interest in this model under both strict and weak exogeneity assumptions. The key identification insight is that other periods' treatment variables are instruments for the unobserved fixed effects. We apply our proposed estimator to matched student-teacher data used to estimate value-added models of teacher quality. We show that the common assumption that the return to unobserved teacher quality is the same for all students is rejected by the data. We also present evidence that No Child Left Behind-era school accountability increased the effectiveness of teacher quality for lower performing students.
Using the models in Wooldridge (1999), We compare three main estimation methods for positive response variable-- FE method for log linear model (LFE), Poisson Quasi-Maximum Likelihood (PQML) and Generalized Method of Moment (GMM) -- by Mont Carlo Simulation and real life data set. It is not surprising that LFE estimator is not consistent when PQML is; however, we do find circumstance where both LFE and PQML estimators are consistent plus LFE is more efficient. With this regard, we introduce GMM to improve the efficiency of PQML estimator as well as keeping the consistency; this way also finds a solution to the problem raised in Wooldridge (1999). From the simulation results, we find that GMM can reduce the standard error of PQML estimator by almost a half. We also apply the GMM to a US domestic airlines data set and the result shows that GMM improves the efficiency by about $10 %$ compared with PQML. On the other hand, to make full use of the PQML method, We propose a semiparametric estimator of average partial effect after consistently estimating the parameters of interest; the result automatically extends the results in Ai and Norton (2008) from cross sectional setting to panel data models. In order to catch the positivity of the unknown conditional expectation function of the unobserved heterogeneity, we borrow the idea of power series approximation of unknown function in Newey(1993,1994) and develop an ``exponential sieves" estimator suggested in Wooldridge(1992a).
