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On the power properties of inference for parameters with interval identified sets

Author

Listed:
  • Federico A. Bugni
  • Mengsi Gao
  • Filip Obradovic
  • Amilcar Velez

Abstract

This paper studies the power properties of confidence intervals (CIs) for a partially-identified parameter of interest with an interval identified set. We assume the researcher has bounds estimators to construct the CIs proposed by Stoye (2009), referred to as CI1, CI2, and CI3. We also assume that these estimators are "ordered": the lower bound estimator is less than or equal to the upper bound estimator. Under these conditions, we establish two results. First, we show that CI1 and CI2 are equally powerful, and both dominate CI3. Second, we consider a favorable situation in which there are two possible bounds estimators to construct these CIs, and one is more efficient than the other. One would expect that the more efficient bounds estimator yields more powerful inference. We prove that this desirable result holds for CI1 and CI2, but not necessarily for CI3.

Suggested Citation

  • Federico A. Bugni & Mengsi Gao & Filip Obradovic & Amilcar Velez, 2024. "On the power properties of inference for parameters with interval identified sets," Papers 2407.20386, arXiv.org, revised Oct 2024.
    • Handle: RePEc:arx:papers:2407.20386
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    References listed on IDEAS

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    1. Keisuke Hirano & Guido W. Imbens & Geert Ridder, 2003. "Efficient Estimation of Average Treatment Effects Using the Estimated Propensity Score," Econometrica, Econometric Society, vol. 71(4), pages 1161-1189, July.
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