Abstract: This paper proposes a practical approach to recover causally interpretable linear instru-mental variable estimands when conventional monotonicity assumptions are too restrictive.We consider an ordered discrete treatment and multiple discrete instruments. Combining alocal version of the partial monotonicity of Mogstad et al. (2021) with the novel first-stagescalar partial monotonicity restriction, we show how propensity-score comparisons can beused to discover instrument regions that satisfy local monotonicity. Constructing simpleWald estimands on these regions yields parameters that identify a convex combination oflocal average treatment effects. An application to the estimation of returns to schooling ofCard (1993) illustrates instances where two-stage least squares can fail to be sign-preservingbecause of negative weighting, and demonstrates the practical implementation of the identification strategy. 
Draft_0414_2026_HeewonShin.pdfdiscussion (3).pdf 