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Register a new userEliminating Systematic Bias from Difference-in-Differences Design: A Permutational Detrending Strategy
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Added by
Xiaoming Wang
Publication date
2021
fields
Mathematical Statistics
and research's language is
English
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Since the initial work by Ashenfelter and Card in 1985, the use of difference-in-differences (DID) study design has become widespread. However, as pointed out in the literature, this popular quasi-experimental design also suffers estimation bias and inference bias, which could be very serious in some circumstances. In this study, we start by investigating potential sources of systemic bias from the DID design. Via analyzing their impact on statistical estimation and inference, we propose a remedy -- a permutational detrending (PD) strategy -- to overcome the challenges in both the estimation bias and the inference bias. We prove that the proposed PD DID method provides unbiased point estimates, confidence interval estimates, and significance tests. We illustrate its statistical proprieties using simulation experiments. We demonstrate its practical utility by applying it to the clinical data EASE (Elder-Friendly Approaches to the Surgical Environment) and the social-economical data CPS (Current Population Survey). We discuss the strengths and limitations of the proposed approach.
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We develop an analytical framework to study experimental design in two-sided marketplaces. Many of these experiments exhibit interference, where an intervention applied to one market participant influences the behavior of another participant. This interference leads to biased estimates of the treatment effect of the intervention. We develop a stochastic market model and associated mean field limit to capture dynamics in such experiments, and use our model to investigate how the performance of different designs and estimators is affected by marketplace interference effects. Platforms typically use two common experimental designs: demand-side (customer) randomization (CR) and supply-side (listing) randomization (LR), along with their associated estimators. We show that good experimental design depends on market balance: in highly demand-constrained markets, CR is unbiased, while LR is biased; conversely, in highly supply-constrained markets, LR is unbiased, while CR is biased. We also introduce and study a novel experimental design based on two-sided randomization (TSR) where both customers and listings are randomized to treatment and control. We show that appropriate choices of TSR designs can be unbiased in both extremes of market balance, while yielding relatively low bias in intermediate regimes of market balance.
Data can be collected in scientific studies via a controlled experiment or passive observation. Big data is often collected in a passive way, e.g. from social media. In studies of causation great efforts are made to guard against bias and hidden confounders or feedback which can destroy the identification of causation by corrupting or omitting counterfactuals (controls). Various solutions of these problems are discussed, including randomization.
Recent work has highlighted the difficulties of estimating difference-in-differences models when treatment timing occurs at different times for different units. This article introduces the R package did2s which implements the estimator introduced in Gardner (2021). The article provides an approachable review of the underlying econometric theory and introduces the syntax for the function did2s. Further, the package introduces a function, event_study, that provides a common syntax for all the modern event-study estimators and plot_event_study to plot the results of each estimator.
While difference-in-differences (DID) was originally developed with one pre- and one post-treatment periods, data from additional pre-treatment periods is often available. How can researchers improve the DID design with such multiple pre-treatment periods under what conditions? We first use potential outcomes to clarify three benefits of multiple pre-treatment periods: (1) assessing the parallel trends assumption, (2) improving estimation accuracy, and (3) allowing for a more flexible parallel trends assumption. We then propose a new estimator, double DID, which combines all the benefits through the generalized method of moments and contains the two-way fixed effects regression as a special case. In a wide range of applications where several pre-treatment periods are available, the double DID improves upon the standard DID both in terms of identification and estimation accuracy. We also generalize the double DID to the staggered adoption design where different units can receive the treatment in different time periods. We illustrate the proposed method with two empirical applications, covering both the basic DID and staggered adoption designs. We offer an open-source R package that implements the proposed methodologies.
We review recent literature that proposes to adapt ideas from classical model based optimal design of experiments to problems of data selection of large datasets. Special attention is given to bias reduction and to protection against confounders. Some new results are presented. Theoretical and computational comparisons are made.
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