Identication Robust Inference in Cointegrating Regressions

In cointegrating regressions, available estimators and test statistics are nuisance parameter dependent. This paper addresses this problem as an identi…cation failure. We focus on set estimation of long-run coe¢ cients (denoted ). We check whether and to what degree popular estimation methods, speci…cally the Maximum Likelihood of Johansen (1995), Fully Modi…ed OLS [Phillips and Hansen (1990); Phillips (1991, 1995)], Dynamic OLS [Stock and Watson (1993)], and the stationarity-test based method from Wright (2000)], su¤er from this problem and explore various robust solutions imposing and relaxing strong exogeneity. For the traditional cointegration case, we derive con…dence set estimates by inverting LR-type statistics and provide analytical solutions using the mathematics of quadrics as in Dufour and Taamouti (2005). Next, allowing for weak cointegration, we propose three size correction methods: a bounds-based critical value [based on Dufour (1989, 1997) and Dufour and Khalaf (2002)] and a data-dependent "Type 2 Robust" critical value [based on Andrews and Cheng (2011)], both of which preserve the analytical solution; and, a simulation-based method [based on Dufour (2006)] . Simulation results can be summarized as follows. The size of DOLS and FMOLS based t-tests exceeds 90% at the identi…cation boundary. Failure of weak-exogeneity causes severe distortions for DOLS as well as for FMOLS even when is identi…ed. The test from Wright (2000) is also oversized at the boundary. In contrast, even when weak exogeneity fails, all our proposed LR-based corrections have good size regardless of the identi…cation status, and good power when is identi…ed. J.E.L. Classi…cation Numbers: C32, C12. Keywords: Cointegration, Weak Identi…cation, Bound Test, Simulation-Based Inference.