Late again, whithout Monotonicity
Monotonicity is not necessary for the Wald ratio to identify a Local Average Treatment Effect. Under random assignment and exclusion restriction, if for every value of potential outcomes there are more compliers than defiers, the Wald ratio identifies the average treatment effect within a subpopulation of compliers. I use a simple Roy selection model to show that this "less defiers than compliers" condition is substantially weaker than monotonicity. It has two implications which are testable from the data, and it is closely related to those testable implications. Similarly, the local monotonicity condition in Huber & Mellace (2012) is not necessary for their identification results to hold and can also be replaced by a substantially weaker condition
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- Huber, Martin & Mellace, Giovanni, 2012. "Relaxing monotonicity in the identification of local average treatment effects," Economics Working Paper Series 1212, University of St. Gallen, School of Economics and Political Science.
- Clément De Chaisemartin & Xavier D'Haultfoeuille, 2012. "Late Again with Defiers," PSE Working Papers halshs-00699646, HAL.
- Klein, T.J., 2008.
"Heterogeneous Treatment Effects : Instrumental Variables Without Monotonicity?,"
2008-45, Tilburg University, Center for Economic Research.
- Klein, Tobias J., 2010. "Heterogeneous treatment effects: Instrumental variables without monotonicity?," Journal of Econometrics, Elsevier, vol. 155(2), pages 99-116, April.
- Klein, Tobias J., 2007. "Heterogeneous Treatment Effects: Instrumental Variables without Monotonicity?," IZA Discussion Papers 2738, Institute for the Study of Labor (IZA).
- Rashmi Barua & Kevin Lang, 2009.
"School Entry, Educational Attainment and Quarter of Birth: A Cautionary Tale of LATE,"
NBER Working Papers
15236, National Bureau of Economic Research, Inc.
- Kevin Lang & Rashmi Barua, 2010. "School Entry, Educational Attainment and Quarter of Birth: A Cautionary Tale of LATE," Boston University - Department of Economics - Working Papers Series WP2010-019, Boston University - Department of Economics.
- Abadie, Alberto, 2003. "Semiparametric instrumental variable estimation of treatment response models," Journal of Econometrics, Elsevier, vol. 113(2), pages 231-263, April.
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