Unit Root Tests for Dependent and Heterogeneous Micropanels

Abstract

This paper proposes a panel unit root test for micropanels with short time dimension (T) and large cross section (N). There are several distinctive features of this test. First, the test is based on a panel AR(1) model, which allows for cross-sectional dependency, which is introduced by the initial condition's assumption of a factor structure. Second, the test employs the panel AR(1) model with heterogeneous AR(1) coefficients. Third, 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, this paper employs cross-sectional regression 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-ratio for the coefficient is this paper's test statistic and has a standard normal distribution in the limit. The t-ratio is based on the instrumental variables estimator that uses a reshuffled regressor as an instrument. 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 the test has 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 test rejects the null hypothesis of a unit root.