Generalized fixed‐T panel unit root tests

Abstract

Panel data unit root tests, which can be applied to data that do not have many time series observations, are based on very restrictive error and deterministic component specification assumptions. In this paper, we develop a new, doubly modified estimator, based on which we propose a panel unit root test that allows for multiple structural breaks, linear and nonlinear trends, heteroscedasticity, serial correlation, and error cross‐section heterogeneity, when the number of time series observations is finite. The test has the additional perk that it is invariant to the initial condition.

Panel unit-root tests with structural breaks

“…The limiting distribution of this statistic is shown to depend on the time dimension T . Following Karavias and Tzavalis (2019), the command implements a bootstrap algorithm to derive the critical values and p -values of min Z . The asymptotic distribution is valid for T fixed and N → ∞ .…”

“…The Karavias and Tzavalis (2014) tests are widely applicable and possess some unique optimality properties, as has been shown in Karavias and Tzavalis (2017, 2019). In terms of applicability, they can be used in both small- and large- T settings, where T is the number of time-series observations.…”

“…The breaks can affect the intercepts only or the intercepts and the linear trends of the series. If the dates of the breaks are unknown, then a bootstrap procedure described in Karavias and Tzavalis (2019) is used to derive the critical value and the p -value of the test. Other options include the allowance of cross-section heteroskedasticity, crosssection dependence as in O’Connell (1998), and normal errors.…”

“…The remainder of the article is organized as follows. In section 2, we present the panel unit-root tests as developed by Karavias and Tzavalis (2014) and their extension to two breaks along the lines of Karavias and Tzavalis (2019). This section also provides some Monte Carlo simulations on the behavior of the tests with two breaks.…”