Is Monotonicity in an IV and RD design testable? No, but you can still check it

Ben Edwards, Mario Fiorini, Katrien Stevens () and Matthew Taylor

No 2013-06, Working Papers from University of Sydney, School of Economics

Abstract: Whenever treatment effects are heterogeneous and there is sorting into treatment based on the gain, monotonicity is a condition that both Instrumental Variable and fuzzy Regression Discontinuity designs have to satisfy for their estimand to be interpretable as a LATE. Angrist and Imbens (1995) argue that the monotonicity assumption is testable whenever the treatment is multivalued. We show that their test is informative if counterfactuals are observed. Yet applying the test without observing counterfactuals, as it is generally done, is not. Nevertheless, we argue that monotonicity can and should be investigated using a mix of economic intuition and data patterns, just like other untestable assumptions in an IV or RD design. We provide examples in a variety of settings as a guide to practice.

Date: 2013-04
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Working Paper: Is Monotonicity in an IV and RD Design Testable? No, But You Can Still Check on it (2013)
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