Fixed Effects and Beyond. Bias Reduction, Groups, Shrinkage and Factors in Panel Data

Many traditional panel data methods are designed to estimate homogeneous coefficients. While a recent literature acknowledges the presence of coefficient heterogeneity, its main focus so far has been on average effects. In this paper we review various approaches that allow researchers to estimate heterogeneous coefficients, hence shedding light on how effects vary across units and over time. We start with traditional heterogeneous-coefficients fixed-effects methods, and point out some of their limitations. We then describe bias-correction methods, as well as two approaches that impose additional assumptions on the heterogeneity: grouping methods, and random-effects methods. We also review factor and grouped-factor methods that allow coefficients to vary over time. We illustrate these methods using panel data on temperature and corn yields in the United States, and find substantial heterogeneity across counties and over time in temperature impacts.