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This paper studies the GMM estimation of short panel data models with interactive fixed effects. We demonstrate that the nonlinear moment conditions proposed by Ahn, Lee and Schmidt (2001, 2013) does not always satisfy the global identification assumption, which is necessary for consistency of GMM. Some numerical examples are provided to confirm this claim. We also demonstrate that the same problem happens for moment conditions proposed by Hayakawa (2012) and Robertson and Sarafidis (2015) since their moment conditions become identical to those of Ahn et al. (2001, 2013) in some cases. Finally, we conduct Monte Carlo simulation and show that the starting value used in the computation of non-linear GMM estimators has a significant effect on the performance.
This paper considers inference procedures for two types of dynamic linear panel data models with fixed effects (FE). First, it shows that the closures of stationary ARMAFE models can be consistently estimated by Conditional Maximum Likelihood Estimators and it derives their asymptotic distributions. Then it presents an asymptotically equivalent Minimum Distance Estimator which permits an analytic comparison between the CMLE for the ARFE (1) model and the GMM estimators that have been considered in the literature. The CMLE is shown to be asymptotically less efficient than the most efficient GMM estimator when N approaches the limit infinity but T is fixed. Under normality some of the moment conditions become asymptotically redundant and the CMLE attains the Cramer-Rao lowerbound when T approaches the limit infinity as well. The paper also presents likelihood based unit root tests. Finally, the properties of CML, GMM, and Modified ML estimators for dynamic panel data models that condition on the initial observations are studied and compared. It is shown that for finite T the MMLE is less efficient than the most efficient GMM estimator.
Panel Data Econometrics with R provides a tutorial for using R in the field of panel data econometrics. Illustrated throughout with examples in econometrics, political science, agriculture and epidemiology, this book presents classic methodology and applications as well as more advanced topics and recent developments in this field including error component models, spatial panels and dynamic models. They have developed the software programming in R and host replicable material on the book’s accompanying website.
This paper develops new estimation and inference procedures for dynamic panel data models with fixed effects and incidental trends. A simple consistent GMM estimation method is proposed that avoids the weak moment condition problem that is known to affect conventional GMM estimation when the autoregressive coefficient (rho) is near unity. In both panel and time series cases, the estimator has standard Gaussian asymptotics for all values of rho in (-1, 1] irrespective of how the composite cross section and time series sample sizes pass to infinity. Simulations reveal that the estimator has little bias even in very small samples. The approach is applied to panel unit root testing.
This paper considers GMM based estimation and testing procedures for two versions of the AR(1) model with Fixed Effects, henceforth abbreviated as ARFE(1): the conditional ARFE(1) model, and the inclusive ARFE(1) model, which contains the stationary ARFE(1) models and the ARFE(1) model with a unit root. First, the paper presents a two-step Optimal Linear GMM (OLGMM) estimator for the inclusive model, which is asymptotically equivalent to the optimal nonlinear GMM estimator of Ahn and Schmidt (1997). Then the paper examines the properties of the GMM estimators for both versions of the model when the data are persistent. Among other things, we find that the OLGMM estimator is superefficient in the unit root case. Furthermore, under stationarity the covariances of the instruments of the Arellano-Bond estimator and the first differences of the dependent variable are not weak. We also derive new approximations to the finite sample distributions of the Arellano-Bond estimator (for both versions of the model), the Arellano-Bover estimator, and the System estimator. We employ local-to-zero asymptotics (cf Staiger and Stock (1997)) for the Arellano-Bond estimator for the conditional model, because its instruments are weak in this context, and we employ local-to-unity asymptotics, which is developed in this paper, for the estimators for the stationary model. The new approximations agree well with the Monte Carlo evidence in terms of bias and variance. Finally, various GMM based unit root tests against stationary and conditional alternatives are proposed.
The second edition of a comprehensive state-of-the-art graduate level text on microeconometric methods, substantially revised and updated. The second edition of this acclaimed graduate text provides a unified treatment of two methods used in contemporary econometric research, cross section and data panel methods. By focusing on assumptions that can be given behavioral content, the book maintains an appropriate level of rigor while emphasizing intuitive thinking. The analysis covers both linear and nonlinear models, including models with dynamics and/or individual heterogeneity. In addition to general estimation frameworks (particular methods of moments and maximum likelihood), specific linear and nonlinear methods are covered in detail, including probit and logit models and their multivariate, Tobit models, models for count data, censored and missing data schemes, causal (or treatment) effects, and duration analysis. Econometric Analysis of Cross Section and Panel Data was the first graduate econometrics text to focus on microeconomic data structures, allowing assumptions to be separated into population and sampling assumptions. This second edition has been substantially updated and revised. Improvements include a broader class of models for missing data problems; more detailed treatment of cluster problems, an important topic for empirical researchers; expanded discussion of "generalized instrumental variables" (GIV) estimation; new coverage (based on the author's own recent research) of inverse probability weighting; a more complete framework for estimating treatment effects with panel data, and a firmly established link between econometric approaches to nonlinear panel data and the "generalized estimating equation" literature popular in statistics and other fields. New attention is given to explaining when particular econometric methods can be applied; the goal is not only to tell readers what does work, but why certain "obvious" procedures do not. The numerous included exercises, both theoretical and computer-based, allow the reader to extend methods covered in the text and discover new insights.
Written by one of the world's leading researchers and writers in the field, Econometric Analysis of Panel Data has become established as the leading textbook for postgraduate courses in panel data. This new edition reflects the rapid developments in the field covering the vast research that has been conducted on panel data since its initial publication. Featuring the most recent empirical examples from panel data literature, data sets are also provided as well as the programs to implement the estimation and testing procedures described in the book. These programs will be made available via an accompanying website which will also contain solutions to end of chapter exercises that will appear in the book. The text has been fully updated with new material on dynamic panel data models and recent results on non-linear panel models and in particular work on limited dependent variables panel data models.
This paper proposes new GMM estimators for the panel AR(1) model when the ratio of the variance of the individual effects to the variance of the idiosyncratic errors is large. First, we present a necessary condition for large N, fixed T consistency of any Fixed Effects or Random Effects estimator for this model. This condition is also sufficient for consistency of the FE estimators, which only depend on differences of the data. Next we show that RE estimators can still be consistent when the data is mean-stationary and the ratio of the variances is infinite. For instance, when T>3, the 2-step optimal System estimator is consistent provided that the elements of the weight matrix are consistently estimated. We argue that the RE Quasi ML estimator can be used for this purpose. The commonly used 1-step and 2-step System estimators are inconsistent in this case. We also propose local asymptotic approximations to the distributions of RE GMM estimators that are more accurate than conventional approximations when the data are mean-stationary and the ratio of the variances is large and we discuss conditions for redundancy of the moment conditions that include levels of the data. Finally, we conduct a Monte Carlo study into the finite sample properties of various estimators and related confidence intervals, and to illustrate the usefulness of our new System estimator we revisit the growth study of Levine et al. (2000).