Confidence intervals for the shrinkage estimator

Shrinkage estimators have recently become popular in estimation of heterogeneous models on panel data. In this chapter we show that the estimated covariance matrix in the posterior distribution of the shrinkage estimator fails to include the variability of the hyperparameters. Hence, standard confidence intervals for the parameters based on the “estimated posterior” distribution, are too narrow and thus the t-statistic is upward biased. The bootstrap method, which incorporates some of the variability in the hyperparameters, is an alternative method to obtain confidence intervals for the parameters. Our empirical example shows that one has to be aware of the method used, since it can lead to significantly different economic conclusions.