Nonparametric Difference-in-Differences in Repeated Cross-Sections with Continuous Treatments

TL;DR

This paper introduces a new nonparametric difference-in-differences method for identifying causal effects of continuous treatments using repeated cross-sectional data, accommodating endogeneity and heterogeneity without restrictive assumptions.

Contribution

It develops a novel nonparametric approach that allows for endogenous continuous treatments and heterogeneous effects in repeated cross-sections, without functional form restrictions.

Findings

Successfully identified causal effects of income on consumption.

Provided estimators with proven asymptotic properties.

Demonstrated the method on real data showing practical applicability.

Abstract

This paper studies the identification of causal effects of a continuous treatment using a new difference-in-difference strategy. Our approach allows for endogeneity of the treatment, and employs repeated cross-sections. It requires an exogenous change over time which affects the treatment in a heterogeneous way, stationarity of the distribution of unobservables and a rank invariance condition on the time trend. On the other hand, we do not impose any functional form restrictions or an additive time trend, and we are invariant to the scaling of the dependent variable. Under our conditions, the time trend can be identified using a control group, as in the binary difference-in-differences literature. In our scenario, however, this control group is defined by the data. We then identify average and quantile treatment effect parameters. We develop corresponding nonparametric estimators and study their asymptotic properties. Finally, we apply our results to the effect of disposable income on consumption.