Bootstrap and Higher-Order Expansion Validity When Instruments May Be Weak

  title={Bootstrap and Higher-Order Expansion Validity When Instruments May Be Weak},
  author={Marcelo Jovita Moreira and Jack R. Porter and Gustavo Adolfo Hernandez Suarez},
In this paper, we provide a framework for the bootstrap in the weakinstrument case. This framework yields a formal proof for the bootstrap validity of the Anderson-Rubin statistic, and bootstrap invalidity of the likelihood ratio (and Wald) statistic. Additionally, we propose two conditional bootstrap methods for the conditional likelihood ratio (CLR) test. Monte Carlo simulations show that the (conditional) bootstrap yields higher-order improvements with good instruments and is first-order… CONTINUE READING


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