Reconsidering LM unit root testing

Non-rejection of a unit root hypothesis by usual Dickey & Fuller (1979) (DF, hereafter) or Phillips & Perron (1988) (hereafter PP) tests should not be taken as strong evidence in favour of unit root presence. There are less popular, but more powerful, unit root tests that should be employed instead of DF-PP tests. A prime example of an alternative test is the LM unit root test developed by Schmidt & Phillips (1992) (hereafter SP) and Schmidt & Lee (1991) (hereafter SL). LM unit root tests are easy to calculate and invariant (similar); they employ optimal detrending and are more powerful than usual DF-PP tests. Asymptotic theory and finite sample critical values (with inaccuracies that we correct in this paper) are available for SP-SL tests. However, the usefulness of LM tests is not fully understood, due to ambiguity over test type recommendation, as well as potentially inefficient derivation of the test that might confuse applied researchers. In this paper, we reconsider LM unit root testing in a model with linear trend. We derive asymptotic distribution theory (in a new fashion), as well as accurate appropriate critical values. We undertake Monte Carlo investigation of finite sample properties of SP-SL LM tests, along with applications to the Nelson & Plosser (1982) time series and real quarterly UK GDP.