Unit Root Tests for Dependent Micropanels

This paper proposes a new test for the null hypothesis of panel unit roots for micropanels with short time dimensions (T) and large cross-sections (N). There are several distinctive features of this test. First, the test is based on a panel AR(1) model allowing for cross-sectional dependency, which is introduced by a factor structure of the initial condition. Second, the test employs the panel AR(1) model with AR(1) coefficients that are heterogeneous for finite N. Third, the test can be used both for the alternative hypothesis of stationarity and for that of explosive roots. Fourth, the test does not use the AR(1) coefficient estimator. The effectiveness of the test rests on the fact that the initial condition has permanent effects on the trajectory of a time series in the presence of a unit root. To measure the effects of the initial condition, the present paper employs cross-sectional regressions using the first time-series observations as a regressor and the last as a dependent variable. If there is a unit root in every individual time series, the coefficient of the regressor is equal to one. The t-ratios for the coefficient are this paper’s test statistics and have a standard normal distribution in the limit. The t-ratios are based on the OLS estimator and the instrumental variables estimator that uses reshuffled regressors as instruments. The test proposed in this paper makes it possible to test for a unit root even at T = 2 as long as N is large. Simulation results show that test statistics have reasonable empirical size and power. The test is applied to college graduates’ monthly real wage in South Korea. The number of time-series observations for this data is only two. The null hypothesis of a unit root is rejected against the alternative of stationarity.