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Exact Inference Methods for First-Order Autoregressive Distributed Lag Models

Jean-Marie Dufour
Jan F. Kiviet

Abstract

Methods are proposed to build exact tests and confidence sets in the linear first-order autoregressive distributed lag model with i.i.d. disturbances. For general linear hypotheses on the regression coefficients, inference procedures are obtained which have known level. The tests proposed are either similar (i.e., they have constant rejection probability for all data generating 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 (i.e., they have constant coverage probability) or conservative. We also develop exact tests and confidence sets for various nonlinear transformations of model parameters, such as long-run multipliers and mean lags. The practical usefulness of these exact methods, which are also asymptotically valid under weak regularity conditions, is illustrated by some power comparisons and with applications to a dynamic trend model of money velocity and a model of money demand.