A note on testing instrument validity for the identification of LATE


In this paper, we show that the testable implications derived in Huber and Mellace (Rev Econ Stat 97:398, 2015) are the best possible to detect invalid instruments in the presence of heterogeneous treatment effects and endogeneity. We also provide formal proof of the fact that those testable implications are only necessary, but not sufficient, conditions for instrument validity.

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  1. 1.

    By defining the potential outcomes, we implicitly assume that the usual Stable Unit Treatment Value Assumption (SUTVA) holds. Moreover, although the potential outcomes are allowed to be a function of Z, we omit the dependence on Z without loss of generality.

  2. 2.

    If \(\Pr (D=1|Z=1)<\Pr (D=1|Z=0)\) one can run the test on \(\tilde{Z}=1-Z\).


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Correspondence to Lukas Laffers.

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Laffers, L., Mellace, G. A note on testing instrument validity for the identification of LATE. Empir Econ 53, 1281–1286 (2017). https://doi.org/10.1007/s00181-016-1148-7

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  • Testing IV validity
  • Local average treatment effect
  • Moment inequalities
  • Bounds

JEL Classification

  • PC1
  • C4
  • C12