This paper considers the practically important case of nonparametrically estimating heterogeneous average treatment effects that vary with a limited number of discrete and continuous covariates in a selection-on-observables framework where the number of possible confounders is very large. We propose a two-step estimator for which the first step is estimated by machine learning. We show that this estimator has desirable statistical properties like consistency, asymptotic normality and rate double robustness. In particular, we derive the coupled convergence conditions between the nonparametric and the machine learning steps. We also show that estimating population average treatment effects by averaging the estimated heterogeneous effects is semi-parametrically efficient. The new estimator is an empirical example of the effects of mothers' smoking during pregnancy on the resulting birth weight.
One of the most important empirical findings in microeconometrics is the pervasiveness of heterogeneity in economic behaviour (cf. Heckman 2001). This paper shows that cumulative distribution functions and quantiles of the nonparametric unobserved heterogeneity have an infinite efficiency bound in many structural economic models of interest. The paper presents a relatively simple check of this fact. The usefulness of the theory is demonstrated with several relevant examples in economics, including, among others, the proportion of individuals with severe long term unemployment duration, the ave…
Finite mixture models are useful in applied econometrics. They can be used to model unobserved heterogeneity, which plays major roles in labor economics, industrial organization and other fields. Mixtures are also convenient in dealing with contaminated sampling models and models with multiple equilibria. This paper shows that finite mixture models are nonparametrically identified under weak assumptions that are plausible in economic applications. The key is to utilize the identification power implied by information in covariates variation. First, three identification approaches are presented,…
We consider an index model of dyadic link formation with a homophily effect index and a degree heterogeneity index. We provide nonparametric identification results in a single large network setting for the potentially nonparametric homophily effect function, the realizations of unobserved individual fixed effects and the unknown distribution of idiosyncratic pairwise shocks, up to normalization, for each possible true value of the unknown parameters. We propose a novel form of scale normalization on an arbitrary interquantile range, which is not only theoretically robust but also proves partic…
This article proposes different tests for treatment effect heterogeneity when the outcome of interest, typically a duration variable, may be right-censored. The proposed tests study whether a policy 1) has zero distributional (average) effect for all subpopulations defined by covariate values, and 2) has homogeneous average effect across different subpopulations. The proposed tests are based on two-step Kaplan-Meier integrals and do not rely on parametric distributional assumptions, shape restrictions, or on restricting the potential treatment effect heterogeneity across different subpopulatio…
Spatial association and heterogeneity are two critical areas in the research about spatial analysis, geography, statistics and so on. Though large amounts of outstanding methods has been proposed and studied, there are few of them tend to study spatial association under heterogeneous environment. Additionally, most of the traditional methods are based on distance statistic and spatial weighted matrix. However, in some abstract spatial situations, distance statistic can not be applied since we can not even observe the geographical locations directly. Meanwhile, under these circumstances, due to…
This study proposes a mixed logit model with multivariate nonparametric finite mixture distributions. The support of the distribution is specified as a high-dimensional grid over the coefficient space, with equal or unequal intervals between successive points along the same dimension; the location of each point on the grid and the probability mass at that point are model parameters that need to be estimated. The framework does not require the analyst to specify the shape of the distribution prior to model estimation, but can approximate any multivariate probability distribution function to any…
Negative control is a strategy for learning the causal relationship between treatment and outcome in the presence of unmeasured confounding. The treatment effect can nonetheless be identified if two auxiliary variables are available: a negative control treatment (which has no effect on the actual outcome), and a negative control outcome (which is not affected by the actual treatment). These auxiliary variables can also be viewed as proxies for a traditional set of control variables, and they bear resemblance to instrumental variables. I propose a family of algorithms based on kernel ridge regr…
This paper analyzes the effect of a discrete treatment Z on a duration T. The treatment is not randomly assigned. The confounding issue is treated using a discrete instrumental variable explaining the treatment and independent of the error term of the model. Our framework is nonparametric and allows for random right censoring. This specification generates a nonlinear inverse problem and the average treatment effect is derived from its solution. We provide local and global identification properties that rely on a nonlinear system of equations. We propose an estimation procedure to solve this sy…
Causal inference is difficult in the presence of unobserved confounders. We introduce the instrumented common confounding (ICC) approach to (nonparametrically) identify causal effects with instruments, which are exogenous only conditional on some unobserved common confounders. The ICC approach is most useful in rich observational data with multiple sources of unobserved confounding, where instruments are at most exogenous conditional on some unobserved common confounders. Suitable examples of this setting are various identification problems in the social sciences, nonlinear dynamic panels, and…
Quantile-Optimal Policy Learning under Unmeasured Confounding
Department of Statistics and Data Science, Yale University（统计与数据科学系，耶鲁大学）；Department of Decision Sciences, George Washington University（决策科学系，乔治华盛顿大学）；Cowles Foundation for Research in Economics, Yale University（经济学研究基金会，耶鲁大学）
