Journal of Econometrics 21 (1983) 53 - 70. North-Holland Publishing company TESTS FOR MODEL SPECIFICATION IN THE PRESENCE OF ALTERNATIVE HYPOTHESES Some Further Results* James G. MacKINNON zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPON Queen’s Umwsity, Kingston, Om. K7L 3N6, Canada Halbert WHITE Uniwsity of Coli/onuq Son Diego, Lo Jolla, CA 92093, USA , Russell DAVIDSON Queen’s University, Kingston, Ont. K7L 3N6, Canada In Davidson and MacKinnon (1981). two of the present authors proposed a novel and very slmple procedure for testing the spuiGcation of a nonlinear regression model against the evidence provided by a non-nested alternative. In this paper we extend their results in several directions. First, wc relax a numk of the assumptions of the previous paper, we admit the possibility that the nonliacar regression functions may depend on lagged dependent variables, and we do not require that the error terms be normally distributed. Second, we show how the earlier procedure may straightbwardly be generalid to the case where the two non-nested models involve diRrrent transformations of the dependent variable. Finally, we propose a simpk procedure for testing non-nested Linear regression modcls which have endogenous variables on the right-hand side, and have therefore been estimated by two-stage least squares. 1. Introduction In recent years several procedures have been proposed for testing the specification of a nonlinear regression model against the evidence provided by a non-nested alternative hypothesis, The first such tests were due to Pesaran (1974) and Pesaran and Deaton (1978), and were explicitly based on the classic work of Cox (1961, 1962). More recently, Davidson and MacKinnon (1981) proposed much simpler procedures based on artificial regression models, and showed the resulting tests are asymptotically equivalent to Cox tests. Indeed, White (1982) has shown that if one implements the Cox test in a straightforward fashion, one of the procedures of Davidson and MacKinnon is obtained directly. For a survey of this material, see MacKinnon (1982). *Davidwn and Mnd(innnn graIduUy acknowledge financial support for the research of this pap from the Social Scienas and Humanities Research Council of Canada, white’s panidpation was supponed by NSF grant JEs81-07552 and MacKinnon and White thank Ian Domowitz for numerous helpful discussons. 0 165-741 0/83/~/$03.OO zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA 0 1983 North-Holland