Cointegration Testing

The finding that many macro time series may contain a unit root has spurred the development of the theory of non-stationary time series analysis. Engle and Granger (1987) pointed out that a linear combination of two or more non-stationary series may be stationary. If such a stationary linear combination exists, the non-stationary time series are said to be cointegrated. The stationary linear combination is called the cointegrating equation and may be interpreted as a long-run equilibrium relationship among the variables.

This section describes several tools for testing for the presence of cointegrating relationships among non-stationary variables in non-panel and panel settings.

The first two parts of this discussion focus on cointegration tests employing the Johansen (1991, 1995) system framework or Engle-Granger (1987) or Phillips-Ouliaris (1990) residual based test statistics. The final section describes cointegration tests in panel settings where you may compute the Pedroni (1999), Pedroni (2004), and Kao (1999) tests as well as a Fisher-type test using an underlying Johansen methodology (Maddala and Wu, 1999).

The Johansen tests may be performed using a Group object or an estimated Var object. The residual tests may be computed using a Group object or an Equation object estimated using nonstationary regression methods. The panel tests may be conducted using a Pool object or a Group object in a panel workfile setting. Note that additional cointegration tests are offered as part of the diagnostics for an equation estimated using nonstationary methods. See “Testing for Cointegration”.

If cointegration is detected, Vector Error Correction (VEC) or nonstationary regression methods may be used to estimate the cointegrating equation. See “Vector Error Correction (VEC) Models” and “Cointegrating Regression” for details.