A note on testing instrument validity for the identification of LATE

Abstract

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.

This is a preview of subscription content, log in to check access.

Notes

  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 \(\tilde{Z}=1-Z\).

References

  1. Angrist J, Imbens G, Rubin D (1996) Identification of causal effects using instrumental variables. J Am Stat Assoc 91:444–472

    Article  Google Scholar 

  2. Horowitz JL, Manski CF (1995) Identification and robustness with contaminated and corrupted data. Econometrica 63:281–302

    Article  Google Scholar 

  3. Huber M, Laffers L, Mellace G Sharp IV bounds on average treatment effects on the treated and other populations under endogeneity and noncompliance. J Appl Econom (forthcoming)

  4. Huber M, Mellace G (2015) Testing instrument validity for LATE identification based on inequality moment constraints. Rev Econ Stat 97:398–411

    Article  Google Scholar 

  5. Imbens G, Angrist J (1994) Identification and estimation of local average treatment effects. Econometrica 62(2):467–475

    Article  Google Scholar 

  6. Kitagawa T (2015) A test for instrument validity. Econometrica 83(5):2043–2063

    Article  Google Scholar 

Download references

Author information

Affiliations

Authors

Corresponding author

Correspondence to Lukas Laffers.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

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

Download citation

Keywords

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

JEL Classification

  • PC1
  • C4
  • C12