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. 1 McNown et al. (2018) propose a bootstrap procedure for the Pesaran et al. (2001) test that allows for conclusive inference when the test statistic falls within the two bounds. 2 Previously tabulated CVs for a small set of sample sizes can be found in Fuller (1976) and Dickey (1976) for the univariable and Banerjee, Dolado and Mestre (1998) for the multivariable setting. 3 Cook (2001) compares the response surfaces from Cheung and Lai (1995a) with those from MacKinnon (1991) and concludes that adjusting for the lag order leads to a gain in power. RS estimates for finite-sample CVs of other unit-root tests are provided by Cheung

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