Estimating cointegrating vectors using near unit root variables

Abstract

This paper argues that the predominant method of estimating equilibrium relationships in macroeconometric models, namely the VECM system of Johansen, is severely flawed if the underlying variables are distributed as near unit root processes. Researchers may apply cointegration techniques to these processes, as the power of rejecting near unit roots using standard unit root tests is extremely low. Using Monte Carlo analysis, problematic behaviour of cointegration analysis is found in detecting the true underlying form of the connection between the near unit root processes. Furthermore the connecting vector is imprecisely estimated, resulting in problematic inference for error correction models.

Notes

To date over 1600 citation exists for this article, making it one of the most cited articles in the economic literature.

See also Abadir and Taylor (1999) and Elliott (1998).

For details on the GARMA model, the interested reader is referred to Chung (1996) and Bierens (2001). Diebold and Inoue (2001) show that the properties of certain regime switching processes are arbitrarily close to long memory. Thus, the results are likely to extend to a larger class of models, including those that are characterized by regime switching behaviour.

Following Robinson and Marinucci (2001), the study uses the property that the sum of a non-stationary series and a stationary series produces a non-stationary series by definition.

The rejection rate of the null of cointegration is not reported as this is generally consistent with the size of the tests for most cases in this table.

Tests on the form of the vector use an LR test and the standard χ² inference.

The results are conservative in that a number of lags are considered (up to 4) for both the trace and eigenvalue statistic, and the results reported for the specification and test that provide the least inferential problems for the Johansen procedure.

Similarly to Gonzalo and Lee (1998) it is also found that the inferential problem does not improve by a larger sample size.

An analysis was also conducted using the Engle–Granger test and it was found that the estimated RMSE was significantly smaller for the same processes as the results reported here.

For example, Cheung and Lai (1993) test for a long run connection between the nominal exchange rate, and domestic and foreign prices. They find estimates of the elements of the cointegrating vectors ranging from 0.35 to 25.422 (in absolute value), substantially different from the theoretical expected value of 1.