Distributional Effects of a Continuous Treatment with an Application on Intergenerational Mobility

35 Pages Posted: 7 Oct 2020

See all articles by Brantly Callaway

Brantly Callaway

University of Mississippi - Department of Economics

Weige Huang

Zhongnan University of Economics and Law

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Date Written: August 1, 2020

Abstract

This paper considers the effect of a continuous treatment on the entire distribution of outcomes after adjusting for differences in the distribution of covariates across different levels of the treatment. Our methodology encompasses dose‐response functions, counterfactual distributions, and ‘distributional policy effects’ depending on the assumptions invoked by the researcher. We propose a three‐step estimator that consists of (i) estimating the distribution of the outcome conditional on the treatment and other covariates using quantile regression; (ii) for each value of the treatment, averaging over a counterfactual distribution of the covariates holding the treatment fixed; (iii) converting the resulting counterfactual distribution into parameters of interest that are easy to interpret. We show that our estimators converge uniformly to Gaussian processes and that the empirical bootstrap can be used to conduct uniformly valid inference across a range of values of the treatment. We use our method to study intergenerational income mobility where we consider effects of parents’ income on features of their child's income distribution such as (i) the fraction of children with income below the poverty line; (ii) the variance of child's income; and (iii) the inter‐quantile range of child's income–all as a function of parents’ income.

Suggested Citation

Callaway, Brantly and Huang, Weige, Distributional Effects of a Continuous Treatment with an Application on Intergenerational Mobility (August 1, 2020). Oxford Bulletin of Economics and Statistics, Vol. 82, Issue 4, pp. 808-842, 2020, Available at SSRN: https://ssrn.com/abstract=3706185 or http://dx.doi.org/10.1111/obes.12355

Brantly Callaway (Contact Author)

University of Mississippi - Department of Economics ( email )

371 Holman Hall
University, MS 38677
United States

Weige Huang

Zhongnan University of Economics and Law ( email )

No.143, Wuluo Road
Wuhan, Hubei 430073
China

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