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basic premise has been, at least implicitly, that in the presence of I (1) variables the traditional ARDL approach is no longer applicable.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).
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