II.1) Improving the Finite-Sample Estimators of Cointegrated Panel Models

Abstract

Though ordinary least square (OLS) estimates are super-consistent with cointegrated variables, their finite-T bias can be large in the presence of endogenous feedback. Fully modified OLS (FMOLS) are parsimonious tools to measure the cointegrating [long-run] slope between integrated variables in the presence of endogenous feedback, and correct the first-order OLS bias to the extent necessary to provide a nuisance parameter-free asymptotic distribution.Yet because FMOLS rely on a first-step OLS estimator that is biased, and has weak power and size, FMOLS also has poor finite-T properties. I show that FMOLS asymptotically leave an O(h/T) fraction of the OLS bias, where h is the selected bandwidth.I also propose an improved estimator, which corrects the first-order conditional bias and removes the residual O(h/T) FMOLS bias.I establish the maximal speed at which N can grow simultaneously to T for the tests statistics of panel group-mean of time-series estimators to be (asymptotically) nuisance parameter-free. My improved estimator permits analysing wider panels.In the scenarios reviewed by previous research, my finite-T FMOLS has lower bias and RMSE than the `asymptotic' FMOLS for all values of T and N.