Kernel smoothing end of sample instability tests P values

A Monte Carlo investigation shows that the rejection probability of the structural stability test of Andrews (2003) depends on several characteristics of the DGP, one of which is the length of the hypothesized break period. This is analyzed and found to be caused, at least in part, by the fact that the number of subsampling statistics used to compute the P value depends on the sample size and the length of the break period. Simulations show that kernel smoothed P values provide more accurate tests in small samples.