Inference with a single treated cluster
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I introduce a generic method for inference about a scalar parameter in research designs with a finite number of heterogeneous clusters where only a single cluster received treatment. This situation is commonplace in difference-in-differences estimation but the test developed here applies more generally. I show that the test controls size and has power under asymptotics where the number of observations within each cluster is large but the number of clusters is fixed. The test combines weighted, approximately Gaussian parameter estimates with a rearrangement procedure to obtain its critical values. The weights needed for most empirically relevant situations are tabulated in the paper. Calculation of the critical values is computationally simple and does not require simulation or resampling. The rearrangement test is highly robust to situations where some clusters are much more variable than others. Examples and an empirical application are provided.
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