Generalized instrumental inequalities: testing the instrumental variable independence assumption

Mourifié

2021

In many set identified models, it is difficult to obtain a tractable characterization of the identified set, therefore, empirical works often construct confidence region based on an outer set of the identified set. Because an outer set is always a superset of the identified set, this practice is often viewed as conservative yet valid. However, this paper shows that, when the model is refuted by the data, a nonempty outer set could deliver conflicting results with another outer set derived from the same underlying model structure, so that the results of outer sets could be misleading in the presence of misspecification. We provide a sufficient condition for the existence of discordant outer sets which covers models characterized by intersection bounds and the Artstein (1983) inequalities. Furthermore, we develop a method to salvage misspecified models. We consider all minimum relaxations of a refuted model which restore data-consistency. We find that the union of the identified sets of these minimum relaxations is misspecification-robust and it has a new and intuitive empirical interpretation. Although this paper primarily focuses on discrete relaxations, our new interpretation also applies to continuous relaxations.

Section: Relation Between Misspecification Robust Bound and Falsification Adaptive Setsupporting

confidence: 59%

Discordant relaxations of misspecified models

Mourifié

2021

“…The data also contains a measure of ability we use to show some evidence that tuition is correlated with ability. Notice that Kédagni and Mourifié (2015) reject the independence assumption between potential earnings and tuition fees. Table 3 shows the descriptive statistics.…”

Section: Empirical Results: Returns To Collegementioning

confidence: 97%

Identification of Treatment Effects with Mismeasured Imperfect Instruments

2019

SSRN Journal

Self Cite

In this article, I develop a novel identification result for estimating the effect of an endogenous treatment using a proxy of an unobserved imperfect instrument. I show that the potential outcomes distributions are partially identified for the compliers. Therefore, I derive sharp bounds on the local average treatment effect. I write the identified set in the form of conditional moments inequalities, which can be implemented using existing inferential methods. I illustrate my methodology on the National Longitudinal Survey of Youth 1979 to evaluate the returns to college attendance using tuition as a proxy of the true cost of going to college. I find that the average return to college attendance for people who attend college only because the cost is low is between 29% and 78%.

“…For this reason, parents' education will not be a valid instrument. This fact is documented in Kédagni and Mourifié (2020), who provided evidence that even after controlling for a measure of ability, parental education is not a good instrument. This result is contrary to the Lemke and Rischall (2003) idea that controlling for some measure of child ability could make parental education a valid IV.…”

Section: Empirical Illustrationmentioning

confidence: 99%

Nonparametric Bounds on Treatment Effects with Imperfect Instruments

Ban

2020

SSRN Journal

Self Cite

This paper extends the identification results in Nevo and Rosen (2012) to nonparametric models. We derive nonparametric bounds on the average treatment effect when an imperfect instrument is available. As in Nevo and Rosen (2012), we assume that the correlation between the imperfect instrument and the unobserved latent variables has the same sign as the correlation between the endogenous variable and the latent variables. We show that the monotone treatment selection and monotone instrumental variable restrictions, introduced by Manski and Pepper (2000, 2009), jointly imply this assumption. We introduce the concept of comonotone instrumental variable, which also satisfies this assumption. Moreover, we show how the assumption that the imperfect instrument is less endogenous than the treatment variable can help tighten the bounds. We also use the monotone treatment response assumption to get tighter bounds. The identified set can be written in the form of intersection bounds, which is more conducive to inference. We illustrate our methodology using the National Longitudinal Survey of Young Men data to estimate returns to schooling.