Testing the long‐run response in time series environmetric and econometric models

Time series models are a common tool in both environmetrics and econometrics. Dynamic effects are accommodated by the inclusion of lagged variables. Tests of null hypotheses involving ‘long‐run’ effects are not invariant and, surprisingly, the most commonly used form involves a non‐linear hypothesis when an equivalent linear form is available. As examples we study a simple hydrological model of river flow, a simple electricity demand model and a number of artificially constructed data sets designed to illustrate the issues in a Monte Carlo context. We conclude that the differences due to test form may be large and (a) when it makes a difference, the linear form is to be preferred in terms of accuracy of test size; (b) even with the linear form, with trended data the size distortion may be so large that it may be necessary to simulate critical values for each problem; and (c) if the persistence in the dependent variable is large, test power can be very low. © 1998 John Wiley & Sons, Ltd.