Multiple Testing for No Cointegration under Nonstationary Volatility

With cointegration tests often being oversized under time-varying error variance, it is possible, if not likely, to confuse error variance non-stationarity with cointegration. This paper takes an instrumental variable (IV) approach to establish individual-unit test statistics for no cointegration that are robust to variance non-stationarity. The sign of a fitted departure from long-run equilibrium is used as an instrument when estimating an error-correction model. The resulting IV-based test is shown to follow a chi-square limiting null distribution irrespective of the variance pattern of the data-generating process. In spite of this, the test proposed here has, unlike previous work relying on instrumental variables, competitive local power against sequences of local alternatives in 1/T-neighbourhoods of the null. The standard limiting null distribution motivates, using the single-unit tests in a multiple testing approach for cointegration in multi-country data sets by combining P-values from individual units. Simulations suggest good performance of the single-unit and multiple testing procedures under various plausible designs of cross-sectional correlation and cross-unit cointegration in the data. An application to the equilibrium relationship between short- and long-term interest rates illustrates the dramatic differences between results of robust and non-robust tests.