This paper introduces a conditional Kolmogorov test of model specifica
tion for parametric models with covariates (regressors). The test is a
n extension of the Kolmogorov test of goodness-of-fit for distribution
functions. The test is shown to have power against 1/root n local alt
ernatives and all fixed alternatives to the null hypothesis. A paramet
ric bootstrap procedure is used to obtain critical values for the test
.