Empirical factor demand analysis is a topic in which a choice must be made among several competing non-nested functional forms. Each of the commonly used factor demand systems, such as Translog, Generalized Leontief, Quadratic, and Generalized McFadden, exhibits statistical inadequacy when tested for the absence of residual autocorrelation, homoskedasticity and normality. This does not necessarily imply that the whole system is invalid, especially if misspecification affects only a subset of the equations forming the entire system. Since there is no theoretical guidance on how to select the model which is most able to capture the relevant features of the data, formal testing procedures can be useful. In the literature, paired and joint univariate non-nested tests (e.g. Davidson-MacKinnon's J and P tests, Bera-McAleer test and Barten-McAleer test) have been discussed at length, whereas virtually no attention has been paid to multivariate non-nested tests. In this paper we show how multivariate non-nested tests can be derived from their univariate counterparts, and we apply these tests to compare alternative factor demand systems. Since the outcome of a non-nested test is likely to be influenced by the type of misspecification affecting the competing models, we investigate the empirical performance of a multivariate non-nested test using new Monte Carlo experiments. The competing models are compared indirectly via a statistically adequate model which is considered as if it were the DGP. Under such circumstances, the distribution of the non-nested test of an incorrect null, when it is evaluated at the DGP, tends to be closer to the distribution of the test under the correct null, at least in small samples. A non-nested test is expected to select the model which is closest to the DGP. Moreover, we investigate the empirical behaviour of a non-nested test when the DGP has, in turn, autoregressive, heteroskedastic and non-normal errors. Finally, we provide some suggestions for the applied researcher.
