Response surface regressions for critical value bounds and approximate p-values in equilibrium correction models
Sebastian Kripfganz (University of Exeter)
Daniel C. Schneider (Max Planck Institute for Demographic Research)
Single-equation conditional equilibrium correction models can be used to test for the existence of a level relationship among the variables of interest. The distributions of the respective test statistics are nonstandard under the null hypothesis of no such relationship and critical values need to be obtained with stochastic simulations. We run response surface regressions based on more than 95 billion F-statistics and 57 billion t-statistics to obtain precise finite-sample critical values and approximate p-values for the Pesaran, Shin, and Smith (2001, Journal of Applied Econometrics 16: 289-326) bounds test. Our estimates allow to compute critical value bounds and approximate p-values for any sample size, number of variables, and lag order. Response surfaces for the augmented Dickey-Fuller unit-root test statistics result as special cases.