A Practical Test for Misspecification in Regression: Functional Form, Separability and Distribution

This paper discusses the problem of testing misspecifications in semiparametric regression models for a large family of econometric models under rather general conditions on not further specified semiparametric estimators. We focus on mainly three issues that typically arise in econometrics. First, many econometric models are estimated through maximum likelihood like limited dependent variable models. Second, often the null hypothesis is only partly modeled parametrically. Third, under the null often some structure like separability is imposed on the nonparametric part. In order to address these points we introduce an adaptive omnibus test. Special emphasis is given on practical issues like bias reduction, adaptive bandwidth choice, rather general but simple requirements on the estimates, and finite sample performance, including the resampling approximations.