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A Simple and Trustworthy Asymptotic t Test in Difference-in-Differences Regressions

Cheng Liu and Yixiao Sun ()

University of California at San Diego, Economics Working Paper Series from Department of Economics, UC San Diego

Abstract: We propose an asymptotically valid t test that uses Student's t distribution as the reference distribution in a difference-in-differences regression. For the asymptotic variance estimation, we adopt the clustering-by-time approach to accommodate cross-sectional dependence. This approach often assumes the clusters to be independent across time, but we allow them to be temporally dependent. The proposed t test is based on a special heteroscedasticity and autocorrelation robust (HAR) variance estimator. We target the type I and type II errors and develop a testing-oriented method to select the underlying smoothing parameter. By capturing the estimation uncertainty of the HAR variance estimator, the t test has more accurate size than the corresponding normal test and is just as powerful as the latter. Compared to the nonstandard test developed in the literature, the standard t test is just as accurate but much more convenient to use. Model-based and empirical-data-based Monte Carlo simulations show that the t test works quite well in finite samples.

Keywords: Social and Behavioral Sciences; Basis Functions; Difference-in-Differences; Fixed-smoothing Asymptotics; Heteroscedasticity and Autocorrelation Robust; Student's t distribution; t test (search for similar items in EconPapers)
New Economics Papers: this item is included in nep-ecm and nep-ets
Date: 2019-03-12
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