Numerical Distribution Functions of Likelihood Ratio Tests for Cointegration

This paper employs response surface regressions based on simulation experiments to calculate asymptotic distribution functions for the Johansen-type likelihood ratio tests for cointegration. These are carried out in the context of the models recently proposed by Pesaran, Shin, and Smith (1997) that allow for the possibility of exogenous variables integrated of order one. The paper calculates critical values that are very much more accurate than those available previously. The principal contributions of the paper are a set of data ®les that contain estimated asymptotic quantiles obtained from response surface estimation and a computer program for utilizing them. This program, which is freely available via the Internet, can be used to calculate both asymptotic critical values and P-values. Copyright # 1999 John Wiley & Sons, Ltd.