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.
Highlights
Program evaluation typically identifies the effect of a policy or a program on the mean of the response variable of interest
This paper introduces GAMLSS as a modeling framework for analyzing treatment effects beyond the mean in various research areas, including economics, which is the focus of this paper, medicine, and epidemiology
Going beyond mean effects is relevant if the evaluator or the researcher is interested in treatment effects on the whole conditional distribution or derived measures that take parameters other than the mean into account
Summary
Program evaluation typically identifies the effect of a policy or a program on the mean of the response variable of interest. Of treatment effects on all functionals of the response distribution, we introduce generalized additive models for location, scale and shape (GAMLSS, [2]) to the evaluation literature. Shen [16] proposed a nonparametric approach based on kernel functions to estimate the effect of minimum wages on the conditional income distribution She points out that the flexibility of estimating distributional effects conditional on the other covariates is useful for the regression discontinuity design (RDD). By applying GAMLSS to the evaluation context, we provide a flexible, parametric complement to the existing approaches The advantage of this approach is that it provides one coherent model for the conditional distribution which estimates simultaneously the effect on all distributional parameters avoiding crossing quantiles or crossing predictions.
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