A Consistent Model Specification Test with Mixed Categorical and Continuous Data

• Activity Number: 130
• Type: Invited
• Date/Time: Monday, August 12, 2002 : 2:00 PM to 3:50 PM
• Sponsor: Section on Nonparametric Statistics*
• Author(s): Qi Li*+ and Cheng Hsiao and Jeff Racine
• Affiliation(s): Texas A&M University and University of Southern California and University of South Florida

Abstract

In this paper we propose a nonparametric kernel-based model specification test when the regression model contains both discrete and continuous variables. We smooth both the discrete and continuous variables using least-squares cross-validation methods. The test statistic is shown to have an asymptotic normal null distribution. We also prove the validity of using the wild bootstrap method to approximate the null distribution of the test statistic, the bootstrap being our preferred method for obtaining the null distribution in practice. Simulations show that the proposed test has significant power advantages over conventional kernel tests, which use frequency-based nonparametric estimators that require sample splitting to handle the presence of discrete variables. An application to a commonly used specification of earnings equations based on the latest CPS-ORG (Current Population Survey Outgoing Rotation Group) data demonstrates the utility of the proposed test in applied settings.