Response Surface Regressions for Critical Value Bounds and Approximate p‐values in Equilibrium Correction Models1

Abstract 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 simulated F ‐statistics and 57 billion t ‐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 approximate P ‐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.