Unit root test for short panels with serially correlated errors

ABSTRACT

This paper proposes a unit root test for short panels with serially correlated errors. The proposed test is based on the instrumental variables (IVs) and the generalized method of moments (GMM) estimators. An advantage of the new test over other tests is that it allows for an ARMA-type serial correlation. A Monte Carlo simulation shows that the new test has good finite sample properties. Several methods to estimate the lag orders of the ARMA structure are briefly discussed.

KEYWORDS:

• GMM
• instrumental variables
• panel data
• unit root test.

Acknowledgments

The author is grateful to a referee for helpful comments. Part of this paper was written while the author was visiting the University of Cambridge as a JSPS Postdoctoral Fellow for Research Abroad. The author gratefully acknowledges the financial support from the JSPS Fellowship and the Grant-in-Aid for Scientific Research (KAKENHI, 22730178). All remaining errors are the author’s.

Notes

1 Blundell et al. (2008) also assumes a unit root for the income process.

2 We primarily consider these two models since Bond et al. (2005) show that the unit root tests based on these two models perform better than the others.

3 It is not theoretically difficult to include heterogeneous time trends. However, since unreported simulation results show poor power performance of the test proposed in this paper, we mainly focus on the no trend case. Further, we do not include the time effects for simplicity.

4 The level or system GMM estimators by Arellano and Bover (1995) and Blundell and Bond (1998) can be used to estimate model (6(6) ). Since ρ, the parameter of interest, appears in a non linear way in (6(6) ), we need to use a non linear GMM estimator, which is computationally cumbersome. Hence, we focus on model (5(5) ). However, model (6(6) ) is useful for selecting the lag orders p and q (see Sec. 4).

5 In a time series model, Hall (1989), Pantula and Hall (1991), and Lee and Schmidt (1994) use IVs to test for unit root.

6 We do not consider the IVs since y_i1, …, y_{i, t − q − 2} are redundant.

7 The asymptotic distribution is obtained by applying the general results on GMM to the moment conditions, , , , or . For the general results on the asymptotic distribution of the GMM estimator, see Newey and McFadden (1994, Sec. 3.3), Hall (2005, Chapter 3), or Cameron and Trivedi (2005, Chapter 6).

8 The rejection region is on the left side.

9 For a discussion on the robust standard error in panel data models, see Arellano (1987) and Petersen (2009).