Cointegration in misspecified models

Abstract

This thesis examines analytically (using asymptotic theory) and via Monte Carlo simulations the effects of two types of misspecifications on the LR tests for cointegration proposed by Johansen (1988, 1996).

The first type of misspecification is intercept shifts, represented by step dummy variables. It is assumed that the DGP consists of I(1) processes which are cointegrated and some of them contain intercept shifts. The presence of intercept shifts is ignored in the construction of the statistical model (SM) used for cointegration testing. It is shown that under the above misspecification the tests overestimate the cointegrating rank with probability one as the sample size tends to infinity. An upper bound is found for the number of spurious cointegrating vectors that arise in the limit, and it is given by the number of distinct intercept shifts in the DGP. The attainment of the bound depends on the weak exogeneity status of the variables. Monte Carlo experiments designed in a way that allows control over the local power show that as the sample size and the magnitude of the shift become larger the frequency of accepting a bigger cointegrating rank than that in the DGP, increases. The impacts of intercept shifts are quite noticeable for sample sizes and model specifications used in empirical works.

The second type of misspecification is the presence of irrelevant variables in the SM or omission of relevant variables from the SM used for cointegration testing. We show that the inclusion of irrelevant variables does not affect the inference about the cointegrating rank or the consistency of the estimators of the cointegrating vectors, adjustment coefficients and variance of the errors, but simulations show a reduction in the power of the tests. We also show that the omission of relevant variables from the SM leads to either failure in detecting cointegration or underestimation of the cointegrating rank. Although in the latter case the estimator of the detected cointegrating vectors is shown to be consistent, this is not the case for the estimators of the adjustment coefficients and the variance of the errors.

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