A Modified Likelihood Approach for Models with Parameter-Dependent Support

In structural models with parameter-dependent support, maximum likelihood problems are non-regular. We reformulate these problems by parameter-dependent transformations and propose modified likelihood estimators that have regular asymptotic properties. We then describe several applications to search models, auction models and frontier production functions and demonstrate the performance of our method through Monte Carlo simulations. Lastly, we apply the method to a Vuong non-nested test of additive v.s. multiplicative separable auction-specific heterogeneity in Michigan Department of Transportation procurements.