Testing nonnested models

Applied economic research often involves testing between onnested models. In such situations informal criteria re often used in preference toreadily available testing procedures. This article deals with regression-based t sts between onnested models, showing the development of the J- and JA-tests from the Cox principle. Testing between linear and log-linear models is discussed as an example of how tests can be constructed when the dependent variables of competing models have a monotonic functional relationship. An empirical example isgiven to illustrate the procedures. Key words: artificial regressions, JA-tests, J-tests, log-linear. Since the mid 1970s, much economet ¡ re-search has been devoted to procedures for test-ing empirical model specification. The present article deals with testing nonnested (or separate) models. Two models are said to be "nested " when one is a special case of the other, obtained by parameter restrictions. Thus, the Cobb-Douglas production function is nested within the constant elasticity of substitution (CES) production func-tion. If, on the other hand, one model cannot be expressed asa special case of the other by parameter estrictions, the models are "non-nested. " Applied economics gives rise to many instances in which nonnested models are appro-priate. (i) Models may differ in functional form. Oflen the competing functional forms will be nonnested; for example, the quadratic and Leontief (Diewert) production func-tions. (ii) Models may differ in explanatory vari-able definitions. For example, supply re-sponse models may use different defi-nitions of expected price (Shideed and White). In money demand studies, dif-ferent definitions of interest rate may be used. (iii) Different theories (e.g., about the con-sumption function) may be tested. (iv) Linear and log-linear formulations oflen are compared. Testing between Cobb