Three essays on robust inference for linear panel models with many time periods

This dissertation consists of three chapters. The first chapter is a critique on the two–way cluster–robust standard errors. In the presence of both cross–sectional correlation and serial correlation, traditional one–way cluster–robust standard errors are not valid. A new robust variance estimator called two–way cluster–robust standard errors is proposed by Thompson (2011) and Cameron et al. (2011) to conduct accurate inference when double clustering exists. However, this approach does not allow for correlation across different firms in different time periods. If such correlation exists, then the two–way cluster–robust standard errors will fail to work. Monte Carlo simulation results demonstrate that using two–way cluster–robust standard errors may lead to unreliable inference even when there is a simple AR(1) time effect. One solution to address this problem is proposed by Thompson (2011). He has improved the original formula for the two–way cluster–robust standard errors to account for correlation across different firms in different time periods. An alternative solution is the standard errors proposed by Driscoll and Kraay (1998) that are robust to cross–sectional correlation of general and unknown form as well as heteroskedasticity and serial correlation under covariance stationarity and weak dependence. The Driscoll and Kraay, 1998 (DK) standard errors perform well when firm dummies are included. Interestingly, without removing the firm effect, the DK standard errors do not behave well. Simulations results illustrate these interesting findings.;The second chapter provides an analysis of the standard errors proposed by Driscoll and Kraay (1998) in linear Difference–in–Differences (DD) models with fixed effects and individual–specific time trends. The analysis is accomplished within the fixed–b asymptotic framework developed by Kiefer and Vogelsang (2005) for heteroskedasticity and autocorrelation (HAC) robust covariance matrix estimator based tests. For the fixed–N, large–T case, it is shown that fixed–b asymptotic distributions of test statistics constructed using the DD estimator and the DK standard errors are different from the results found by Kiefer and Vogelsang (2005) and Vogelsang (2012). The newly derived fixed–b asymptotic distributions depend on the date of policy change, λ, individual-specific trend functions as well as the choice of kernel and bandwidth. Whether time period dummies are included does not affect the fixed–b limits. For other regressors that don't have a structural change, the usual fixed– b asymptotic distributions still apply. Monte Carlo simulations illustrate the performance of the fixed–b approximations in practice.;The third chapter studies finite sample properties of the naive moving blocks bootstrap (MBB) tests based on the DK standard errors in linear DD models with individual fixed effects. The naive bootstrap procedure is a bootstrap where the formula used to compute the standard errors on the resampling data is the same as the formula used on the original data. Following the approach in Gonçalves (2011), the so–called "panel MBB" method is used in this chapter. This method applies the standard MBB to the time series of vectors containing all the individual observations at each time period. Monte Carlo simulation results show that the bootstrap is much more accurate than the standard normal approximation, and it closely follows the new fixed–b approximation proposed in the second chapter. This improvement holds for the special case of Bartlett kernel. Results would look similar for other kernels. It even holds when the independent and identically distributed (i.i.d.) bootstrap is used, despite potential serial correlation in the data. Simulation results also show that if the block length is appropriately chosen, the bootstrap can outperform the fixed– b approximation when there is strong serial correlation.