A new approach to bootstrap inference in functional coefficient models

We introduce a new, factor based bootstrap approach which is robust under heteroskedastic error terms for inference in functional coefficient models. Modeling the functional coefficient parametrically, the bootstrap approximation of a test statistic used for inference on parameter invariance is shown to hold asymptotically. In simulation studies, the factor based bootstrap inference outperforms the wild bootstrap and pairs bootstrap approach in small samples. Furthermore, in semiparametric modeling only testing by means of factor based bootstrap provides correct empirical size estimates. While via wild bootstrap based testing overrejects the null hypothesis for both homoand heteroskedastic error terms, tests via pair bootstrap underreject the null hypothesis under prevalence of homoskedastic error terms. Applying the functional coefficient model to a cross sectional investment regression on savings, the saving retention coefficient is found to depend on third variables as the population growth rate and the openness ratio.