Specification Testing When The Null Is Nonparametric Or Semiparametric

This paper discusses the problem of testing misspecifications in semiparametric regression models for a large family of econometric models under rather general conditions. We focus on two main issues that typically arise in econometrics. First, many econometric models are estimated through maximum likelihood or pseudo-ML methods like, for example, limited dependent variable or gravity models. Second, often one might not want to fully specify the null hypothesis. Instead, one would rather impose some structure like separability or monotonicity. In order to address these points we introduce an adaptive omnibus test. Special emphasis is given to practical issues like adaptive bandwidth choice, general but simple requirements on the estimates, and finite sample performance, including the resampling approximations.