Fixed-b Estimation and Inference in Heterogenous Dynamic Cointegrated Panels

We study semi-parametric estimation and inference in cointegrated panels with endogenous feedback, allowing for general time-series and cross-section dependence and heterogeneity.Central to this literature are the fully-modified OLS of Phillips and Hansen (1990) that use a spectral [non-parametric] estimation of the residual asymptotic covariance matrix to eliminate the bias. Despite their parsimony, these estimators are not T-consistent under fixed-b asymptotics, when the size of the bandwidth is a non-zero fraction of the sample size. Is the consequence benign? Test statistics are non-pivotal, and in panels always reject in the N-limit.Feasible FM-OLS are based on estimated OLS residuals, not on true unobserved residuals; this leads to complex asymptotics — even seemingly inextricable, see for instance Vogelsang and Wagner (2014).We introduce new, compact notations for the fixed-b limits of spectral covariance estimators. This permits us to construct T-consistent semi-parametric estimators: a simple estimator that estimates and subtracts the OLS bias, and a pseudo-exogenised estimator.These fixed-b robust estimators considerably improve the size statistics, reduce bias, and RMSE, compared to other semi-parametric estimators