The Effect of Recursive Detrending on Panel Unit Root Tests

This paper analyzes the properties of panel unit root tests based on recursively detrended
data. The analysis is conducted while allowing for a (potentially) non-linear
trend function, which represents a more general consideration than the current state of
affairs with (at most) a linear trend. A new test statistic is proposed whose asymptotic
behavior under the unit root null hypothesis, and the simplifying assumptions of a polynomial
trend and iid errors is shown to be surprisingly simple. Indeed, the test statistic is
not only asymptotically independent of the true trend polynomial, but is in fact unique
in that it is independent also of the degree of the fitted polynomial. However, this invariance
property does not carry over to the local alternative, under which it is shown that
local power is a decreasing function of the trend degree. But while power does decrease,
the rate of shrinking of the local alternative is generally constant in the trend degree,
which goes against the common belief that the rate of shrinking should be decreasing in
the trend degree. The above results are based on simplifying assumptions. To compensate
for this lack of generality, a second, robust, test statistic is proposed, whose validity
does not require that the trend function is a polynomial or that the errors are iid.