Ferman, Bruno and Pinto, Cristine (2015): Inference in DifferencesinDifferences with Few Treated Groups and Heteroskedasticity.
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Abstract
DifferencesinDifferences (DID) is one of the most widely used identification strategies in applied economics. However, how to draw inferences in DID models when there are few treated groups remains an open question. We show that the usual inference methods used in DID models might not perform well when there are few treated groups and errors are heteroskedastic. In particular, when there is variation in the number of observations per group, inference methods designed to work when there are few treated groups tend to (under) overreject the null hypothesis when the treated groups are (large) small relative to the control groups. This happens because larger groups tend to have lower variance, generating heteroskedasticity in the group x time aggregate DID model. We provide evidence from Monte Carlo simulations and from placebo DID regressions with the American Community Survey (ACS) and the Current Population Survey (CPS) datasets to show that this problem is relevant even in datasets with large numbers of observations per group. We then derive an alternative inference method that provides accurate hypothesis testing in situations where there are few treated groups (or even just one) and many control groups in the presence of heteroskedasticity. Our method assumes that we can model the heteroskedasticity of a linear combination of the errors. We show that this assumption can be satisfied without imposing strong assumptions on the errors in common DID applications. Importantly, we do not need to specify the structure of the serial correlation of the errors. Our inference method can also be combined with feasible generalized least square (FGLS) estimation. This way, it is possible to attain an asymptotically uniformly most powerful (UMP) test if the FGLS ttest is asymptotically UMP, while still provide a test with correct size if the serial correlation is misspecified. With many pretreatment periods, we provide an alternative inference method that relies on strict stationarity and ergodicity of the time series instead of relying on the correct specification of the heteroskedasticity. Finally, we extend our inference methods to linear factor models when there are few treated groups.
Item Type:  MPRA Paper 

Original Title:  Inference in DifferencesinDifferences with Few Treated Groups and Heteroskedasticity 
Language:  English 
Keywords:  differencesindifferences; inference; heteroskedasticity; clustering; few clusters; bootstrap; randomization inference; linear factor model 
Subjects:  C  Mathematical and Quantitative Methods > C1  Econometric and Statistical Methods and Methodology: General > C12  Hypothesis Testing: General C  Mathematical and Quantitative Methods > C2  Single Equation Models ; Single Variables > C21  CrossSectional Models ; Spatial Models ; Treatment Effect Models ; Quantile Regressions C  Mathematical and Quantitative Methods > C3  Multiple or Simultaneous Equation Models ; Multiple Variables > C33  Panel Data Models ; Spatiotemporal Models 
Item ID:  73683 
Depositing User:  Bruno Ferman 
Date Deposited:  14 Sep 2016 06:00 
Last Modified:  27 Sep 2019 18:09 
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URI:  https://mpra.ub.unimuenchen.de/id/eprint/73683 
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Inference in DifferencesinDifferences with Few Treated Groups and Heteroskedasticity. (deposited 06 Nov 2015 15:26)

Inference in DifferencesinDifferences with Few Treated Groups and Heteroskedasticity. (deposited 08 Dec 2015 19:58)
 Inference in DifferencesinDifferences with Few Treated Groups and Heteroskedasticity. (deposited 14 Sep 2016 06:00) [Currently Displayed]

Inference in DifferencesinDifferences with Few Treated Groups and Heteroskedasticity. (deposited 08 Dec 2015 19:58)