A Monte Carlo simulation is performed in order to investigate the effects of lagged relationship on the cointegration inference in a single equation. Given a small data sample the standard application of Engle–Granger cointegration testing procedure is significantly affected by the presence of lagged relationship. For instance, in a sample size of 30 observations, the power of the two-step Engle–Granger cointegration testing procedure, using the Dickey–Fuller (DF) or Augmented DF (ADF) test statistic in the second step, drops from almost one hundred percent, when the correct lag structure of cointegration relationship is respected, to around sixty percent, when the effect of 4 lags is ignored.
A simple parametric correction is proposed allowing avoiding the negative influence. When the cointegration parameters are known, the correction is applied directly to DF and ADF regressions. Whenever the parameters are estimated in the first step of Engle–Granger procedure, the cointegration regression should be modified instead in order to avoid the autocorrelation caused bias of parameter estimates. A Monte Carlo simulation reveals that such simple correction retains the power of the cointegration testing procedure without having a negative effect on the nominal size.
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