Modeling Distributional Treatment Effects with Misreported Discrete Survey Data – An Application to Marijuana Legalization in the U.S.

• Applicant: Professor Daniel Gutknecht, Ph.D.
• Subject Area: Statistics and Econometrics ; Economic Policy, Applied Economics
• Term: since 2021
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 463916029

The primary objective of this project is to develop statistical methods to estimate and make inference about distributional effects of a treatment (e.g., a policy reform) on a discrete outcome variable, when the latter is potentially underreported (a form of measurement error) and treatment may influence the underreporting behavior itself. More specifically, the identification and estimation arguments will allow the underreporting to depend on individual level characteristics in a flexible, nonlinear manner, but will not rely on distributional assumptions for the error term of the semiparametric regression model. In a second step, the project will use these results to establish a new estimator for treatment effects on discrete outcomes from repeated cross-section or panel data when underreporting may vary by treatment status. Importantly, the focus will lie on estimating treatment effects not only at the mean, but across the entire (conditional) distribution of the discretely measured outcome. The procedures developed in this project will be applicable to various fields of applied economics. Examples include studies on the effects of a change in the legal status of abortion on the incidence of reported abortions or on the effects of a tax reform on self-reported tax evasion incidences. The proposed estimators and inference methods will also complement and extend more conventional policy evaluation tools for repeated cross-section or panel data such as linear Difference-in-Differences methods by allowing treatment effects to differ across individuals (“heterogeneous treatment effects”). The secondary objective is the application of the statistical methods to repeated cross-sectional data to study legalization effects of recreational drug use for adults across several U.S. states on the (conditional) distribution of marijuana consumption among high school students over a period ranging from 2012 to 2018. Here, underreporting is likely to feature heavily in the self-reported marijuana consumption data, and understanding differences in the effects of marijuana legalization across adolescent consumers (e.g., first time, “low” or “high frequency” consumers) is important for an informed policy debate. For instance, since evidence suggests that marijuana consumers are most vulnerable to the harms of consumption during their teenage years (see proposal for references), focusing on the statistical significance and size of effects for more “regular” and “high frequency” consumers might be of particular interest from a health policy perspective. Indeed, such effect differences could remain undetected in a more conventional analysis of the conditional mean.The third objective is to produce freely accessible and user-friendly software codes for the statistical procedures developed in this project. The code will be written in R and Stata, two widely used statistical software languages, and shared through journal submissions and a Github webpage.

• DFG Programme: Research Grants
• International Connection: United Kingdom
• Cooperation Partners: Professorin Dr. Wiji Arulampalam; Professorin Dr. Valentina Corradi