The finite sample effects of deterministic variables on conventional methods of lag-selection in unit root tests

In this paper we use numerical techniques to investigate the finite sample properties of data-based approaches to selecting the lag truncation order i n the context of the augmented Dickey-Fuller unit root test in a general au toregressive first-order integrated moving-average model. We focus on the w ell known Akaike and Schwarz information criteria and the recently suggeste d general-to-specific sequential approach. We find that in each case the re sulting unit root tests are highly sensitive to both the form of determinis tic variables inlcuded in the test-regression and to the lag structure adop ted, the latter of which will tend to be under-fitted under both informatio n-based and sequential rules. A strong interrelationship is highlighted bet ween these two aspects of the test regression. We also show that under data -based lag selection currently used finite sample critical values often rep resent a poor approximation to the finite sample null distribution of the u nit root test.