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The exact distribution of the conditional likelihood-ratio test in instrumental variables regression

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  • Malte Londschien

Abstract

We derive the exact asymptotic distribution of the conditional likelihood-ratio test in instrumental variables regression under weak instrument asymptotics and for multiple endogenous variables. The distribution is conditional on all eigenvalues of the concentration matrix, rather than only the smallest eigenvalue as in an existing asymptotic upper bound. This exact characterization leads to a substantially more powerful test if there are differently identified endogenous variables. We provide computational methods implementing the test and demonstrate the power gains through numerical analysis.

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  • Malte Londschien, 2025. "The exact distribution of the conditional likelihood-ratio test in instrumental variables regression," Papers 2509.04144, arXiv.org, revised Sep 2025.
    • Handle: RePEc:arx:papers:2509.04144
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    References listed on IDEAS

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    1. Kleibergen, Frank, 2021. "Efficient size correct subset inference in homoskedastic linear instrumental variables regression," Journal of Econometrics, Elsevier, vol. 221(1), pages 78-96.
    2. Kleibergen, Frank, 2007. "Generalizing weak instrument robust IV statistics towards multiple parameters, unrestricted covariance matrices and identification statistics," Journal of Econometrics, Elsevier, vol. 139(1), pages 181-216, July.
    3. Hillier, Grant, 2009. "On The Conditional Likelihood Ratio Test For Several Parameters In Iv Regression," Econometric Theory, Cambridge University Press, vol. 25(2), pages 305-335, April.
    4. Marcelo J. Moreira, 2003. "A Conditional Likelihood Ratio Test for Structural Models," Econometrica, Econometric Society, vol. 71(4), pages 1027-1048, July.
    5. Hillier, Grant, 2009. "Exact Properties Of The Conditional Likelihood Ratio Test In An Iv Regression Model," Econometric Theory, Cambridge University Press, vol. 25(4), pages 915-957, August.
    6. Frank Kleibergen, 2002. "Pivotal Statistics for Testing Structural Parameters in Instrumental Variables Regression," Econometrica, Econometric Society, vol. 70(5), pages 1781-1803, September.
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