### Discussion Paper

## Abstract

This paper demonstrates that unit root tests can suffer from inflated Type I error rates when data are cointegrated. Results from Monte Carlo simulations show that three commonly used unit root tests – the ADF, Phillips–Perron, and DF-GLS tests – frequently overreject the true null of a unit root for at least one of the cointegrated variables. The reason for this overrejection is that unit root tests, designed for random walk data, are often misspecified when data are cointegrated. While the addition of lagged differenced (LD) terms can eliminate the size distortion, this “success” is spurious, driven by collinearity between the lagged dependent variable and the LD explanatory variables. Accordingly, standard diagnostics such as (i) testing for serial correlation in the residuals and (ii) using information criteria to select among different lag specifications are futile. The implication of these results is that researchers should be conservative in the weight they attach to individual unit root tests when determining whether data are cointegrated.

## Comments and Questions

The paper is very well written, analyses the issue from every conceivable angle (so as to ensure correct conclusions), and has a very important conclusion that has serious implications for researchers: The methods we commonly use to identify the order of integration of series may be flawed; this raises the ...[more]

... issue of whether accepting a researcher's opinion is as good a guide as certain statistical tests to ascertain the order of integration of a series.

Summary: This (very short) paper makes a relevant point. Namely that univariate unit root tests can be misleading -- in

finite samples -- when the data is in fact generated by a multivariate cointegrated system. This point is made via a

simple simulation study. Overall, I think the conclusions in ...[more]

... this paper are relevant and interesting from the point of view

of empirical research.

Comments:

(1) The problem analyzed in this paper is a finite-sample problem. This should be emphasized. Asymptotically the

problem disappears.

(2) The analysis can be boiled down to the following problem: We observe a process, say X_t, which is generated as the

sum of a random walk, say Z_t, and a stationary process, say Y_t. That is, we observe X_t = Z_t + Y_t. It is well

known that in such a setup, the power of unit root tests on X_t depends on the signal-to-noise ratio and on the amount of

serial dependence in Y_t. In the present paper, these two features are essentially controlled by the cointegration

parameters. What I mean to say is that the problem is not new, but it is nevertheless interesting to analyze from the point

of view of cointegrated variables.

(3) Some of the conclusions should be toned down a bit. This relates for example to my point (1) above.

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