Exact Inference Methods for First-Order Autoregressive Distributed Lag Models

Exact tests and confidence sets are obtained for general transformations of the coefficients in linear first-order autoregressive models with exogenous variables and i.i.d. disturbances. The tests proposed have known level and are either similar (constant rejection probability under all processes consistent with the null hypothesis) or use bounds which are free of nuisance parameters. Correspondingly, the confidence sets are either similar with known size or conservative. These exact methods are asymptotically valid under weak regularity conditions. Their usefulness is illustrated by power comparisons and by applications to a dynamic trend model of money velocity and a model of money demand.