Treatment effects beyond the mean using distributional regression: Methods and guidance

Abstract

This paper introduces distributional regression also known as generalized additive models for location, scale and shape (GAMLSS) as a modeling framework for analyzing treatment effects beyond the mean. In contrast to mean regression models, GAMLSS relate each distributional parameter to covariates. Therefore, they can be used to model the treatment effect not only on the mean but on the whole conditional distribution. Since they encompass a wide range of different distributions, GAMLSS provide a flexible framework for modeling non-normal outcomes in which additionally nonlinear and spatial effects can easily be incorporated. We elaborate on the combination of GAMLSS with program evaluation methods including randomized controlled trials, panel data techniques, difference in differences, instrumental variables, and regression discontinuity design. We provide practical guidance on the usage of GAMLSS by reanalyzing data from the Mexican Progresa program. Contrary to expectations, no significant effects of a cash transfer on the conditional consumption inequality level between treatment and control group are found.

Subjective returns to education: Rational expectations of disadvantaged groups in India

“…Similarly, OBC and SC-ST groups show significantly higher earnings relative to male upper caste groups for college education in the OLS specification. As described in Section 3.3, when the analysis does not entail a clean treatment and control comparison, and other explanatory variables are used in the final analysis, there are shortcomings where only point estimates are provided (Hohberg et al 2017). This is true for the current study.…”

“…A subgroup analysis or interaction term can be used to observe the average linear effect of a specific covariate. However, both of these techniques have a shortcoming-the former reduces the sample size, and the latter is problematic if the variable that determines membership of the individual (such as gender or religion) is also one of the outcomes of interest Hohberg et al (2017).…”

“…As an alternative to point estimates or averages, this study uses DR as a methodological contribution. DR (Hohberg et al 2017;Stasinopoulos et al 2018) goes beyond the mean and takes into account variation over the entire distribution of the dependent variable for the covariates of interest. Using a maximum likelihood estimation, the distribution of the outcome y i can be described as a density function…”

“…Thus, consistent and comparable measures are estimated since it is from the same model. Finally, as Hohberg et al (2017) point out, if the aim of the study is to only compare distributions of the outcome variable for the treatment and control, we do not require DR, since we can compare the histograms or kernel densities. However, since this study does not compare only treatment and control groups but estimates the effects of nonlinear covariates in the final analysis, the implementation of the method is a useful contribution to the literature.…”

“…By using the novel distributional regression (DR) technique, we are able to analyse the differential effect of belonging to a specific social identity not only on the mean outcome variable (subjective returns to education), but on the entire conditional distribution of the outcome. This method is developed as a complementary technique to ordinary least squares (OLS) estimation that only observes a linear change of explanatory variables on point esti-mates of the outcome (Hohberg et al 2017;Stasinopoulos et al 2018). Finally, as a comparison to the Huntington-Klein (2015) study, I correlate the inflation-adjusted actual earnings for the three levels of education with the subjective earnings reported by the students.…”