Bootstrap Inference for Partially Linear Model with Many Regressors

In this note, for the case that the disturbances are conditional homoskedastic, we show that a properly re-scaled residual bootstrap procedure is able to consistently estimate the limiting distribution of a series estimator in the partially linear model even when the number of regressors is of the same order as the sample size. Monte Carlo simulations show that the bootstrap procedure has superior �finite sample performance than asymptotic approximations when the sample size is small and the number of regressors is close to the sample size.