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Optimal Invariant Tests in an Instrumental Variables Regression With Heteroskedastic and Autocorrelated Errors

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  • Marcelo J. Moreira
  • Mahrad Sharifvaghefi
  • Geert Ridder

Abstract

This paper uses model symmetries in the instrumental variable (IV) regression to derive an invariant test for the causal structural parameter. Contrary to popular belief, we show that there exist model symmetries when equation errors are heteroskedastic and autocorrelated (HAC). Our theory is consistent with existing results for the homoskedastic model (Andrews, Moreira, and Stock (2006) and Chamberlain (2007)). We use these symmetries to propose the conditional integrated likelihood (CIL) test for the causality parameter in the over-identified model. Theoretical and numerical findings show that the CIL test performs well compared to other tests in terms of power and implementation. We recommend that practitioners use the Anderson-Rubin (AR) test in the just-identified model, and the CIL test in the over-identified model.

Suggested Citation

  • Marcelo J. Moreira & Mahrad Sharifvaghefi & Geert Ridder, 2017. "Optimal Invariant Tests in an Instrumental Variables Regression With Heteroskedastic and Autocorrelated Errors," Papers 1705.00231, arXiv.org, revised Aug 2021.
    • Handle: RePEc:arx:papers:1705.00231
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    References listed on IDEAS

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    1. Moreira, Humberto & Moreira, Marcelo J., 2019. "Optimal two-sided tests for instrumental variables regression with heteroskedastic and autocorrelated errors," Journal of Econometrics, Elsevier, vol. 213(2), pages 398-433.
    2. Gary Chamberlain, 2007. "Decision Theory Applied to an Instrumental Variables Model," Econometrica, Econometric Society, vol. 75(3), pages 609-652, May.
    3. Humberto Moreira & Marcelo Moreira, 2016. "Optimal two-sided tests for instrumental variables regression with heteroskedastic and autocorrelated errors," CeMMAP working papers 25/16, Institute for Fiscal Studies.
    4. Frank Kleibergen, 2005. "Testing Parameters in GMM Without Assuming that They Are Identified," Econometrica, Econometric Society, vol. 73(4), pages 1103-1123, July.
    5. Donald W. K. Andrews & Marcelo J. Moreira & James H. Stock, 2006. "Optimal Two-Sided Invariant Similar Tests for Instrumental Variables Regression," Econometrica, Econometric Society, vol. 74(3), pages 715-752, May.
    6. Isaiah Andrews, 2016. "Conditional Linear Combination Tests for Weakly Identified Models," Econometrica, Econometric Society, vol. 84, pages 2155-2182, November.
    7. Kadane, Joseph B, 1971. "Comparison of k-Class Estimators when the Disturbances are Small," Econometrica, Econometric Society, vol. 39(5), pages 723-737, September.
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