A CONSISTENT MODEL SPECIFICATION TEST BASED ON THE KERNEL SUM OF SQUARES OF RESIDUALS

ABSTRACT

This paper constructs a consistent model specification test based on the difference between the nonparametric kernel sum of squares of residuals and the sum of squares of residuals from a parametric null model. We establish the asymptotic normality of the proposed test statistic under the null hypothesis of correct parametric specification and show that the wild bootstrap method can be used to approximate the null distribution of the test statistic. Results from a small simulation study are reported to examine the finite sample performance of the proposed tests.

Keywords:

• Consistent test
• Kernel method
• Sum of squares of residuals
• Asymptotic normality
• Wild bootstrap
• Simulation
• JEL Classification Number: C12, C14

ACKNOWLEDGMENTS

The research of both authors is supported by grants from the Social Sciences and Humanities Research Council of Canada and the Natural Sciences and Engineering Research Council of Canada. Li's research is also supported by Ontario Premier's Research Excellence Awards, Texas A&M University Private Enterprise Research Center, and Bush program in Economics of Public Policy.