Subsampling Under Two-way Clustering with Serial Correlation

We prove the validity of using subsampling method for inference under a two-way clustered panel in which the time effects are serially correlated. Subsamples should be drawn without replacement from randomly partitioned individual index set and consecutive blocks of time effects. We present two subsampling inference methods: estimating the quantiles directly and constructing the confidence interval by first estimating the asymptotic variance. The quantile method is very adaptive, allowing for non-Gaussian limit which invalidates all existing methods in two-way clustering with serial correlation. Although the variance method only works under Gaussian limit, it comes with a data-driven bandwidth selection algorithm and a bias-correction under suitable estimators. Monte Carlo simulations demonstrate our methods exhibiting the desired coverage level in the finite sample except when the serial correlation is extremely strong. This paper is the first one that allows for inference on non-Gaussian asymptotics under two-way clustering with serial correlation.