Abstract: This paper presents a method of calculating sharp bounds on the average treatment effect using linear programming under identifying assumptions commonly used in the literature. This new method provides a sensitivity analysis of the identifying assumptions and missing data in two applications. The first application looks at the effect of parents’ schooling on children’s schooling, and the second application studies the effect of mandatory arrest policy on domestic violence recidivism. This paper shows that even a mild departure from identifying assumptions may substantially widen the bounds on average treatment effects. Allowing for a small fraction of the data to be missing also has a large impact on the results. (This research was supported by VEGA grant 1/0843/17)
Abstract: This paper provides a novel, simple, and computationally tractable method for determining an identified set that can account for a broad set of economic models when the economic variables are discrete. Using this method, we show using a simple example how imperfect instruments affect the size of the identified set when the assumption of strict exogeneity is relaxed. This knowledge is of great value, as it is interesting to know the extent to which the exogeneity assumption drives results, given it is often a matter of some controversy. Moreover, the flexibility obtained from our newly proposed method suggests that the determination of the identified set need no longer be application specific, with the analysis presenting a unifying framework that algorithmically approaches the question of identification. (This research was supported by VEGA grant 1/0843/17)
Sharp IV Bounds on Average Treatment Effects on the Treated and other Populations under Endogeneity and Noncompliance
Abstract: In the presence of an endogenous binary treatment and a valid binary instrument, causal effects are (nonparametrically) point identified only for the subpopulation of compliers, given that the treatment is monotone in the instrument. With the exception of the entire population, causal inference for further subpopulations has been widely ignored in econometrics. Therefore, we invoke treatment monotonicity and/or dominance assumptions on the mean potential outcomes across subpopulations to derive sharp bounds on the average treatment effects on the treated, who often bear considerable policy relevance, as well as on other groups (non-treated, entire population, compliers, always takers, and never takers). Furthermore, we use our methods to assess the educational impact of a school voucher program in Colombia on various subpopulations and also discuss testable implications of our assumptions.
Sensitivity of the Bounds on the ATE in the Presence of Sample Selection
Abstract: This paper reformulates the problem of bounding average treatment effects under sample selection studied in Lee (2009) as an optimization problem. This allows researchers to conduct sensitivity analysis of identifying assumptions easily, while the bounds remain sharp. We provide a mathematical formulation of the problem, replicate existing analytical results and extend them into sensitivity analysis. (This research was supported by VEGA grant 1/0843/17)
A Note on Testing Instrument Validity for the Identification of LATE
Abstract: In this paper we show that the testable implications derived in Huber and Mellace (2013) are the best possible to detect invalid instruments, in the presence of heterogeneous treatment effects and endogeneity. We also provide a formal proof of the fact that those testable implication are only necessary but not sufficient conditions for instrument validity.
Abstract: The monotone treatment selection (MTS) assumption together with the monotone instrumental variable (MIV) assumption imply bounds on average treatment effects that differ from those commonly reported in the applied literature. Instead, for the bounds to be correct, we should use an MTS assumption conditional on the value of a monotone instrument (cMTS). In this paper, we present an empirical example of bounding the effect of mothers education on children’s education, in which the MTS and cMTS assumptions lead to considerably different bounds on the treatment effects.