Unit root tests for dependent and heterogeneous micropanels∗
نویسنده
چکیده
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) coeffi cients. Third, the test does not use the AR(1) coeffi cient 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 coeffi cient of the regressor is equal to one. The t-ratio for the coeffi cient 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 reshuffl ed 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 ∗This paper was written while the author was visiting the Department of Economics, University of Texas, Austin. I thank Jason Abrevaya, Sukjin Han, Haiquing Xu and Stephen Douglas for their hospitality. A Matlab code for the empirical section of this paper can be obtained from the author upon request. †Sogang University, Seoul, Korea. Personal Webpage: http://inchoi.sogang.ac.kr. E-mail: [email protected], [email protected].
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