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A Robust Test for Weak Instruments for 2SLS with Multiple Endogenous Regressors

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Abstract

We develop a test for instrument strength based on the bias of two-stage least squares (2SLS) that (1) generalizes the tests of Stock and Yogo (2005) and Sanderson and Windmeijer (2016) to be robust to heteroskedasticity and autocorrelation, and (2) extends the Montiel Olea and Pflueger (2013) robust test for models with a single endogenous regressor to multiple endogenous regressors. Our test can be based either on Stock and Yogo’s (2005) absolute bias criterion or on the 2SLS bias relative to Montiel Olea and Pflueger’s (2013) worst-case benchmark. We also develop extensions to test whether instruments are weak for individual 2SLS coefficients. In simulations, our test controls size and is powerful, and we provide efficient code packages for its practical implementation. We demonstrate our testing procedures in the context of the estimation of state-dependent fiscal multipliers as in Ramey and Zubairy (2018).

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  • Daniel J. Lewis & Karel Mertens, 2022. "A Robust Test for Weak Instruments for 2SLS with Multiple Endogenous Regressors," Working Papers 2208, Federal Reserve Bank of Dallas, revised 26 Sep 2024.
    • Handle: RePEc:fip:feddwp:94370
    DOI: 10.24149/wp2208r2
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    References listed on IDEAS

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    1. Kleibergen, Frank & Paap, Richard, 2006. "Generalized reduced rank tests using the singular value decomposition," Journal of Econometrics, Elsevier, vol. 133(1), pages 97-126, July.
    2. Gergely Ganics & Atsushi Inoue & Barbara Rossi, 2021. "Confidence Intervals for Bias and Size Distortion in IV and Local Projections-IV Models," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 39(1), pages 307-324, January.
    3. Whitney K. Newey & Kenneth D. West, 1994. "Automatic Lag Selection in Covariance Matrix Estimation," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 61(4), pages 631-653.
    4. Sanderson, Eleanor & Windmeijer, Frank, 2016. "A weak instrument F-test in linear IV models with multiple endogenous variables," Journal of Econometrics, Elsevier, vol. 190(2), pages 212-221.
    5. Phillips, P C B, 1980. "The Exact Distribution of Instrumental Variable Estimators in an Equation Containing n + 1 Endogenous Variables," Econometrica, Econometric Society, vol. 48(4), pages 861-878, May.
    6. Olivier Blanchard & Roberto Perotti, 2002. "An Empirical Characterization of the Dynamic Effects of Changes in Government Spending and Taxes on Output," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 117(4), pages 1329-1368.
    7. José Luis Montiel Olea & Carolin Pflueger, 2013. "A Robust Test for Weak Instruments," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 31(3), pages 358-369, July.
    8. Tönu Kollo & Dietrich Rosen, 1995. "Approximating by the Wishart distribution," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 47(4), pages 767-783, December.
    9. Valerie A. Ramey & Sarah Zubairy, 2018. "Government Spending Multipliers in Good Times and in Bad: Evidence from US Historical Data," Journal of Political Economy, University of Chicago Press, vol. 126(2), pages 850-901.
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    Cited by:

    1. Hack, Lukas & Istrefi, Klodiana & Meier, Matthias, 2023. "Identification of Systematic Monetary Policy," CEPR Discussion Papers 17999, C.E.P.R. Discussion Papers.
    2. Chang Liu & Yinxi Xie, 2023. "Understanding Inflation Dynamics: The Role of Government Expenditures," Staff Working Papers 23-30, Bank of Canada.
    3. Campbell, Douglas & Brodeur, Abel & Dreber, Anna & Johannesson, Magnus & Kopecky, Joseph & Lusher, Lester & Tsoy, Nikita, 2024. "The Robustness Reproducibility of the American Economic Review," I4R Discussion Paper Series 124, The Institute for Replication (I4R).

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    More about this item

    Keywords

    Instrumental Variables; Weak Instruments Test; Multiple Endogenous Regressors; Heteroskedasticity; Serial Correlation;
    All these keywords.

    JEL classification:

    • C26 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Instrumental Variables (IV) Estimation
    • C36 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Instrumental Variables (IV) Estimation

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