Monotonicity
The instrumental-variables assumption that the instrument moves everyone’s treatment status in the same (weak) direction — there are no “defiers” who do the opposite. Together with independence and the Exclusion-Restriction, monotonicity is what lets IV identify a clean weighted average of effects, the LATE; without it the IV estimand can mix effects with offsetting signs. A close analogue appears in changes-in-changes and fuzzy DiD, where a latent index is assumed monotone.
Relied on by
Instrumental variables (IV), fuzzy RD, changes-in-changes, fuzzy DiD.
Referenced by
- Angrist2022-EmpiricalStrategiesIlluminatingPath
- AngristKrueger1999-EmpiricalStrategiesLaborEconomics
- DeChaisemartinDHaultfoeuille2018-FuzzyDiD
- Method-buildout pass (2026-06-17): AngristKrueger2001-SearchForIdentification, Imbens2014-IVEconometriciansPerspective, Murray2006-WeakAndInvalidInstruments; fuzzy RD in LeeLemieux2010-RDDInEconomics, ImbensLemieux2008-RDDGuideToPractice, CattaneoEtAl2020-RDDHandbook; noncompliance in AtheyImbens2017-EconometricsOfRandomizedExperiments; ImbensWooldridge2009-ProgramEvaluation.