Invariance and the Wald test

Many models and hypotheses of interest in econometrics are invariant to cer tain types of data transformations such as measurement unit changes. Dagena is and Dufour (Econometrica 59 (1991) 1601; Economics Letters 38 (1992) 251 ) and Dufour and Dagenais (J. Statist. Plann. Inference 32 (1992) 111) have shown that Wald tests are not invariant in general to such data transforma tions. In this paper, I provide a simple set of sufficient conditions to en sure that a Wald test for a null hypothesis is invariant to such a data tra nsformation. I then use this set of conditions to help account for certain features of the Monte Carlo results from Gregory and Weall (Economics Lette rs 22 (1986) 203) on the properties of a variety of Wald tests for Sargan's COMmon FACtor restriction (Sargan (Econometrica 48 (1980) 879)) in the fir st-order autoregressive distributed-lag model. (C) 2001 Published by Elsevi er Science S.A.