Many estimators of the average treatment effect, including the difference-in-means, may be biased when clusters of units are allocated to treatment. This bias remains even when the number of units within each cluster grows asymptotically large. In this paper, we propose simple, unbiased, location-invariant, and covariate-adjusted estimators of the average treatment effect in experiments with random allocation of clusters, along with associated variance estimators. We then analyze a cluster-randomized field experiment on voter mobilization in the US, demonstrating that the proposed estimators have precision that is comparable, if not superior, to that of existing, biased estimators of the average treatment effect.

Di-(2-hydroxy-l-phenazinyl)methane, Phenazines, Bacterial Constituents, Pseudomonas aureofaciensThe structure elucidation of di-(2-hydroxy-l-phenazinyl)methane from Pseudomonas aureofaciens is described. In addition to the phenazine derivatives isolated earlier from this bacterium 2,3,4-trihydroxyphenazine-l-carboxylic acid and phenazine-1,6-dicarboxylic acid could be identified.

In the analysis of causal effects in non-experimental studies, conditioning on observable covariates is one way to try to reduce unobserved confounder bias. However, a developing literature has shown that conditioning on certain covariates may increase bias, and the mechanisms underlying this phenomenon have not been fully explored. We add to the literature on bias-increasing covariates by first introducing a way to decompose omitted variable bias into three constituent parts: bias due to an unobserved confounder, bias due toexcludingobserved covariates, and bias due to amplification. This leads to two important findings. Although instruments have been the primary focus of the bias amplification literature to date, we identify the fact that the popular approach of adding group fixed effects can lead to bias amplification as well. This is an important finding because many practitioners think that fixed effects are a convenient way to account for any and all group-level confounding and are at worst harmless. The second finding introduces the concept of biasunmaskingand shows how it can be even more insidious than bias amplification in some cases. After introducing these new results analytically, we use constructed observational placebo studies to illustrate bias amplification and bias unmasking with real data. Finally, we propose a way to add bias decomposition information to graphical displays for sensitivity analysis to help practitioners think through the potential for bias amplification and bias unmasking in actual applications.

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