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Confidence Intervals for Bias and Size Distortion in IV and Local Projections–IV Models

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  • Gergely Ganics
  • Atsushi Inoue
  • Barbara Rossi

Abstract

In this paper we propose methods to construct confidence intervals for the bias of the two-stage least squares estimator, and the size distortion of the associated Wald test in instrumental variable models. Importantly our framework covers the local projections – instrumental variable model as well. Unlike tests for weak instruments, whose distributions are non-standard and depend on nuisance parameters that cannot be estimated consistently, the confidence intervals for the strength of identification are straightforward and computationally easy to calculate, as they are obtained from inverting a chi-squared distribution. Furthermore, they provide more information to researchers on instrument strength than the binary decision offered by tests. Monte Carlo simulations show that the confidence intervals have good small sample coverage. We illustrate the usefulness of the proposed methods to measure the strength of identification in two empirical situations: the estimation of the intertemporal elasticity of substitution in a linearized Euler equation, and government spending multipliers.

Suggested Citation

  • Gergely Ganics & Atsushi Inoue & Barbara Rossi, 2018. "Confidence Intervals for Bias and Size Distortion in IV and Local Projections–IV Models," Working Papers 1077, Barcelona School of Economics.
    • Handle: RePEc:bge:wpaper:1077
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    Cited by:

    1. 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.
    2. 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.
    3. Daniel J. Lewis & Karel Mertens, 2022. "A Robust Test for Weak Instruments with Multiple Endogenous Regressors," Staff Reports 1020, Federal Reserve Bank of New York.
    4. Barbara Rossi & Atsushi Inoue & Yiru Wang, 2024. "Has the Phillips curve flattened?," French Stata Users' Group Meetings 2024 22, Stata Users Group.
    5. Rossi, Barbara, 2019. "Identifying and Estimating the Effects of Unconventional Monetary Policy: How to Do It And What Have We Learned?," CEPR Discussion Papers 14064, C.E.P.R. Discussion Papers.
    6. Germano Ruisi, 2019. "Time-Varying Local Projections," Working Papers 891, Queen Mary University of London, School of Economics and Finance.
    7. Barbara Rossi, 2018. "Identifying and estimating the effects of unconventional monetary policy in the data: How to do It and what have we learned?," Economics Working Papers 1641, Department of Economics and Business, Universitat Pompeu Fabra, revised Jul 2020.
    8. Christis Katsouris, 2023. "Structural Analysis of Vector Autoregressive Models," Papers 2312.06402, arXiv.org, revised Feb 2024.
    9. Zhenhong Huang & Chen Wang & Jianfeng Yao, 2023. "The First-stage F Test with Many Weak Instruments," Papers 2302.14423, arXiv.org, revised Sep 2024.

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    More about this item

    Keywords

    Instrumental Variables; weak instruments; weak identification; concentration parameter; local projections;
    All these keywords.

    JEL classification:

    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection
    • C53 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Forecasting and Prediction Models; Simulation Methods

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