This research deals with estimation and inference problems for dynamic panel-data models under time-varying individual heterogeneities and cross-sectional dependence (common shocks). An important aspect of these problems is that the individual heterogeneity and the common shocks are correlated with the explanatory variables. This correlation is fundamental for economic variables. Standard procedures such as within-group estimators will lead to inconsistent inferences. This research explores new estimation procedures and related inference problems. It also presents feasible implementation of the suggested procedures.
The last two decades have witnessed a huge development of panel data econometrics, as panel data techniques can solve issues that are hard to solve by either the cross section or time series procedures alone. With the increasing availability of panel data sets, the associated techniques have become the key tools of empirical researchers. The recent advancement and the importance of the panel techniques are summarized by three excellent monographs: Arellano (2003), Batagi (2006), and Hsiao (2003). Much of this literature has focused on the case of time-invariant individual heterogeneities.
Intellectual merit: The research considers models that allow the individual effects to be time varying, and the time effects (or common shocks) to have different impacts across individuals. Such models have both empirical and theoretical foundations, as detailed in the projection escription section. Moreover, the individual heterogeneities and the common shocks are allowed to be correlated with the regressors. This correlation arises naturally for economic variables when choice and decisions are involved. In this project, the PI will consider how to formulate the problem so that the estimation can be handled by the traditional methods such as the nonlinear generalized least squares or the quasi-maximum likelihood method. Careful analysis for small T (time periods) dynamic panel models will be rendered. Panel unit root and panel cointegration problems under both fixed T and large T will be considered. The corresponding inferential theory will be derived. Furthermore, models with heterogeneous slope coeffcients, their estimation, and inference will be studied. As in Alvarez and Arrelano (2005), robust likelihood that allows for changing variance will be considered, as the changing variance itself may be the object of interest. All the analysis will be conducted in the presence of time-varying heterogeneities and in the presence of correlation between the effects and regressors. This research will advance our knowledge and understanding of panel data models; it will enrich panel data analysis and result in additional tools for empirical studies.
Broader impact: This research deals with new methodologies and their implementations. Within economics, the methods are applicable in labor economics, industrial organization, and macroeconomics. These methods are also applicable outside the field of economics when panel data methods are called for. Computer programs will be made available to the general public. The proposed research will also enrich classroom teachings. NSF funding will help train graduate students for theoretical and computational work.
This project deals with estimation and inference problems for dynamic panel-data models with unobservable individual heterogeneities and cross-sectional dependence (common shocks). An important aspect of these problems is that the unobserved individual heterogeneity and the common shocks are correlated with the explanatory variables in the model, leading to an endogeneity problem. This type of correlation is fundamental for economic studies, in which decision variables are correlated with individual heterogeneity. Standard procedures such as the within-group estimator will lead to biased estimation and incorrect inferences. This project explores new estimation procedures and related inference problems. It also presents feasible implementation of the suggested procedures. This project developed new methods for data analysis and inference. These methods are being used by researchers in economics and statistics. This project has resulted in more than ten publications in leading journals of economics and statistics, including Econometrica, Journal of Econometrics, and Annals of Statistics. For example, "Fixed effects dynamic panel data models, a factor analytical approach" (published in Econometrica, 2013) considers an efficient estimation of dynamic panel data models in the presence of a large number of parameters (incidental parameters) in both dimensions: individual fixed-effects and time fixed-effects as well as incidental parameters in the variances. This paper uses the factor analytical approach by estimating the sample variance of individual effects rather than the effects themselves. In the presence of cross-sectional heteroskedasticity, the proposed method estimates the average of the cross-sectional variances instead of the individual variances. The method thereby eliminates the incidental-parameter problem in the means and in the variances over the cross-sectional dimension. While the time effects are treated as parameters, it is shown that estimating the time effects does not generate the incidental-parameter bias for the dynamic parameter. This research further considers incidental parameters in the variance over the time dimension. Efficient and robust estimation is obtained by jointly estimating heteroskedasticities. Unlike the within-group estimator, the proposed method is consistent under a small number of time periods. Unlike the generalized method of moment estimator, it does not have a bias in relating the cross-section dimension. Further departing from the existing methods, the proposed method uses data in levels despite the fixed-effects setup, avoiding information loss from differencing. Broadly speaking, the proposed method is consistent irrespective of whether the number of time period is fixed or large, and of the way in which the cross section dimension and the time dimension grow. This project has supported numerous graduate students, including women graduate students, in their research and teaching. The methods developed in this projects are being taught in classrooms, and had been presented in numerous university seminars and international conferences.
