Nonparametric bounds on treatment effects with imperfect instruments

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. Moreover, we show how the monotone treatment response assumption can help tighten the 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.

Giniinc: A Stata Package for Measuring Inequality from Incomplete Income and Survival Data

Often, observed income and survival data are incomplete because of left- or right-censoring or left- or right-truncation. Measuring inequality (for instance, by the Gini index of concentration) from incomplete data like these will produce biased results. We describe the package giniinc, which contains three independent commands to estimate the Gini concentration index under different conditions. First, survgini computes a test statistic for comparing two (survival) distributions based on the nonparametric estimation of the restricted Gini index for right-censored data, using both asymptotic and permutation inference. Second, survbound computes nonparametric bounds for the unrestricted Gini index from censored data. Finally, survlsl implements maximum likelihood estimation for three commonly used parametric models to estimate the unrestricted Gini index, both from censored and truncated data. We briefly discuss the methods, describe the package, and illustrate its use through simulated data and examples from an oncology and a historical income study.

ASYMPTOTICALLY EFFICIENT ESTIMATION OF WEIGHTED AVERAGE DERIVATIVES WITH AN INTERVAL CENSORED VARIABLE

This paper studies the identification and estimation of weighted average derivatives of conditional location functionals including conditional mean and conditional quantiles in settings where either the outcome variable or a regressor is interval-valued. Building on Manski and Tamer (2002, Econometrica 70(2), 519–546) who study nonparametric bounds for mean regression with interval data, we characterize the identified set of weighted average derivatives of regression functions. Since the weighted average derivatives do not rely on parametric specifications for the regression functions, the identified set is well-defined without any functional-form assumptions. Under general conditions, the identified set is compact and convex and hence admits characterization by its support function. Using this characterization, we derive the semiparametric efficiency bound of the support function when the outcome variable is interval-valued. Using mean regression as an example, we further demonstrate that the support function can be estimated in a regular manner by a computationally simple estimator and that the efficiency bound can be achieved.

COMPLEMENTARITY AND IDENTIFICATION

This paper examines the identification power of assumptions that formalize the notion of complementarity in the context of a nonparametric bounds analysis of treatment response. I extend the literature on partial identification via shape restrictions by exploiting cross-dimensional restrictions on treatment response when treatments are multidimensional; the assumption of supermodularity can strengthen bounds on average treatment effects in studies of policy complementarity. This restriction can be combined with a statistical independence assumption to derive improved bounds on treatment effect distributions, aiding in the evaluation of complex randomized controlled trials. Complementarities arising from treatment effect heterogeneity can be incorporated through supermodular instrumental variables to strengthen identification in studies with one or multiple treatments. An application examining the long-run impact of zoning on the evolution of urban spatial structure illustrates the value of the proposed identification methods.