Identification robust inference in cointegrating regressions

Abstract

In cointegrating regressions, estimators and test statistics are nuisance parameter dependent. This paper addresses this problem from an identification-robust perspective. Confidence sets for the long-run coefficient (denoted β) are proposed that invert LR-tests against an unrestricted or a cointegration-restricted alternative. For empirically relevant special cases, we provide analytical solutions to the inversion problem. A simulation study, imposing and relaxing strong exogeneity, analyzes our methods relative to standard Maximum Likelihood, Fully Modified and Dynamic OLS, and a stationarity-test based counterpart. In contrast with all the above, proposed methods have good size regardless of the identification status, and good power when β is identified.