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Sensitivity Analysis for Instrumental Variables Under Joint Relaxations of Monotonicity and Independence

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  • Pedro Picchetti

Abstract

In this paper I develop a breakdown frontier approach to assess the sensitivity of Local Average Treatment Effects (LATE) estimates to violations of monotonicity and independence of the instrument. I parametrize violations of independence using the concept of $c$-dependence from Masten & Poirier (2018) and allow for the share of defiers to be greater than zero but smaller than the share of compliers. I derive identified sets for the LATE and the Average Treatment Effect (ATE) in which the bounds are functions of these two sensitivity parameters. Using these bounds, I derive the breakdown frontier for the LATE, which is the weakest set of assumptions such that a conclusion regarding the LATE holds. I derive consistent sample analogue estimators for the breakdown frontiers and provide a valid bootstrap procedure for inference. Monte Carlo simulations show the desirable finite-sample properties of the estimators and an empirical application shows that the conclusions regarding the effect of family size on unemployment from Angrist & Evans (1998) are highly sensitive to violations of independence and monotonicity.

Suggested Citation

  • Pedro Picchetti, 2026. "Sensitivity Analysis for Instrumental Variables Under Joint Relaxations of Monotonicity and Independence," Papers 2603.25529, arXiv.org, revised Mar 2026.
    • Handle: RePEc:arx:papers:2603.25529
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    References listed on IDEAS

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