Nonparametric Bootstrap Specification Testing in Econometric Models

We consider three nonparametric tests for functional form, varying parameters, and omitted variables in regression models both of time series data and of cross-sectional data. The Þrst test is to compare the sums of squared residuals from the null and the alternative models and the second test is to compare the Þtted values of the null and alternative models. The third test is the nonparametric conditional moment test, which is to see if the residuals from the null model is related to the conditioning variables in the alternative models. Bootstrap procedures are used for these tests and their performance is examined via monte carlo experiments. Key Words: nonparametric test, nonlinearity, variable selection, lag selection, functional-coefficient model, conditional moment test, naive bootstrap, wild bootstrap, monte carlo. ∗We thank Zongwu Cai, Jianqing Fan, Qi Li for their programs and comments, and the UCR Academic Senate for the research support.