Econometric Theory


Inference in Models with Nearly Integrated Regressors

Christopher L. Cavanagha1, Graham Elliotta2 and James H. Stocka3

a1 Columbia University

a2 University of California, San Diego

a3 Kennedy School of Government Harvard University and National Bureau of Economic Research


This paper examines regression tests of whether x forecasts y when the largest autoregressive root of the regressor is unknown. It is shown that previously proposed two-step procedures, with first stages that consistently classify x as I(1) or I(0), exhibit large size distortions when regressors have local-to-unit roots, because of asymptotic dependence on a nuisance parameter that cannot be estimated consistently. Several alternative procedures, based on Bonferroni and Scheffe methods, are therefore proposed and investigated. For many parameter values, the power loss from using these conservative tests is small.