# Inference with Few Heterogeneous Clusters

*Rustam Ibragimov* and
*Ulrich K. Müller*

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Rustam Ibragimov: Imperial College Business School, Imperial College London

Ulrich K. Müller: Princeton University

*The Review of Economics and Statistics*, 2016, vol. 98, issue 1, 83-96

**Abstract:**
Suppose estimating a model on each of a small number of potentially heterogeneous clusters yields approximately independent, unbiased, and Gaussian parameter estimators. We make two contributions in this setup. First, we showhowto compare a scalar parameter of interest between treatment and control units using a two-sample t-statistic, extending previous results for the one-sample t-statistic. Second, we develop a test for the appropriate level of clustering; it tests the null hypothesis that clustered standard errors from a much finer partition are correct. We illustrate the approach by revisiting empirical studies involving clustered, time series, and spatially correlated data.

**Keywords:** Dependence; clustered standard errors; two-sample t-statistic; variance heterogeneity; difference-in-difference; structural breaks (search for similar items in EconPapers)

**JEL-codes:** C12 C14 C32 (search for similar items in EconPapers)

**Date:** 2016

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