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Wild bootstrap inference for instrumental variables regressions with weak and few clusters

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  • Wang, Wenjie
  • Zhang, Yichong

Abstract

We study the wild bootstrap inference for instrumental variable regressions under an alternative asymptotic framework that the number of independent clusters is fixed, the size of each cluster diverges to infinity, and the within cluster dependence is sufficiently weak. We first show that the wild bootstrap Wald test controls size asymptotically up to a small error as long as the parameters of endogenous variables are strongly identified in at least one of the clusters. Second, we establish the conditions for the bootstrap tests to have power against local alternatives. We further develop a wild bootstrap Anderson–Rubin test for the full-vector inference and show that it controls size asymptotically even under weak identification in all clusters. We illustrate their good performance using simulations and provide an empirical application to a well-known dataset about US local labor markets.

Suggested Citation

  • Wang, Wenjie & Zhang, Yichong, 2024. "Wild bootstrap inference for instrumental variables regressions with weak and few clusters," Journal of Econometrics, Elsevier, vol. 241(1).
    • Handle: RePEc:eee:econom:v:241:y:2024:i:1:s0304407624000733
    DOI: 10.1016/j.jeconom.2024.105727
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    More about this item

    Keywords

    Wild bootstrap; Weak instrument; Clustered data; Randomization test;
    All these keywords.

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C26 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Instrumental Variables (IV) Estimation
    • C31 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models; Quantile Regressions; Social Interaction Models

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