The paper considers the problem of testing non-nested hypotheses by the application of the Lagrange Multiplier (LM) method to an exponentially combined likelihood function. It shows that the general test statistic derived by Atkinson (1970) and later by Breusch and Pagan (1980) can be regarded as an LM statistic only if it can be assumed that the parameters of the alternative model are known. When none of the parameters are known, the paper shows that a straightforward application of the LM method to testing non-nested hypotheses breaks down and it discusses the reasons for this failure. © 1981.
Pesaran, M. H. (1981). Pitfalls of testing non-nested hypotheses by the lagrange multiplier method. Journal of Econometrics, 17(3), 323–331. https://doi.org/10.1016/0304-4076(81)90005-1