Introduction

Econometric analysis of long-run relations has been the focus of much theoretical and empirical research in economics. In cases in which the variables in the long-run relation of interest are trend-stationary, the general practice has been to de-trend the series and to model the de-trended series as stationary autoregressive distributed-lag (ARDL) models. Estimation and inference concerning the long-run properties of the model have then been carried out using standard asymptotic normal theory. For a comprehensive review of this literature, see Hendry, Pagan, and Sargan (1984) and Wickens and Breusch (1988). The analysis becomes more complicated when the variables are difference-stationary, or integrated of order 1 [I(1) for short]. The recent literature on cointegration has been concerned with analysis of the long-run relations between I(1) variables, and its basic premise has been, at least implicitly, that in the presence of I(1) variables the traditional ARDL approach is no longer applicable. Consequently, large numbers of alternative estimation and hypothesis-testing procedures have been specifically developed for the analysis of I(1) variables. See the pioneering work of Engle and Granger (1987), Johansen (1991), Phillips (1991), Phillips and Hansen (1990), and Phillips and Loretan (1991).