This paper is concerned with estimation and inference for difference-in-difference regressions with errors that exhibit high serial dependence, including near unit roots, unit roots, and linear trends. We propose a couple of solutions based on a parametric formulation of the error covariance. First stage estimates of autoregressive structures are obtained by using the Han, Phillips, and Sul (2011, 2013) X-differencing transformation. The X-differencing method is simple to implement and is unbiased in large N settings. Compared to similar parametric methods, the approach is computationally simple and requires fewer restrictions on the permissible parameter space of the error process. Simulations suggest that our methods perform well in the finite sample across a wide range of panel dimensions and dependence structures.
This paper was written for the presentation at the 14th Advances in Econometrics Conference in honor of Peter C.B. Phillips at Southern Methodist University on November 1–3, 2014. We thank Tom Fomby for organizing the conference and Yoosoon Chang and Joon Y. Park for preparing the conference program. We also thank Badi Baltagi for helpful comments. Research by Han was supported by Korea University (K1222321).
Greenaway-McGrevy, R., Han, C. and Sul, D. (2014), "Efficient Estimation and Inference for Difference-In-Difference Regressions with Persistent Errors", Essays in Honor of Peter C. B. Phillips (Advances in Econometrics, Vol. 33), Emerald Group Publishing Limited, Leeds, pp. 281-302. https://doi.org/10.1108/S0731-905320140000033009
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