Response Surface Regressions for Critical Value Bounds and Approximate p-values in Equilibrium Correction Models

We consider the popular 'bounds test' for the existence of a level relationship in conditional equilibrium correction models. By estimating response surface models based on about 95 billion simulatedF-statistics and 57 billiont-statistics, we improve upon and substantially extend the set of available critical values, covering the full range of possible sample sizes and lag orders, and allowing for any number of long-run forcing variables. By computing approximateP-values, we find that the bounds test can be easily oversized by more than 5 percentage points in small samples when using asymptotic critical values.