Flexible Instrumental Variable Distributional Regression

Abstract

We tackle two limitations of standard instrumental variable regression in experimental and observational studies: restricted estimation to the conditional mean of the outcome and the assumption of a linear relationship between regressors and outcome. More flexible regression approaches that solve these limitations have already been developed but have not yet been adopted in causality analysis. The paper develops an instrumental variable estimation procedure building on the framework of generalized additive models for location, scale and shape. This enables modelling all distributional parameters of potentially complex response distributions and non-linear relationships between the explanatory variables, instrument and outcome. The approach shows good performance in simulations and is applied to a study that estimates the effect of rural electrification on the employment of females and males in the South African province of KwaZulu-Natal. We find positive marginal effects for the mean for employment of females rates, negative effects for employment of males and a reduced conditional standard deviation for both, indicating homogenization in employment rates due to the electrification programme. Although none of the effects are statistically significant, the application demonstrates the potentials of using generalized additive models for location, scale and shape in instrumental variable regression for both to account for endogeneity and to estimate treatment effects beyond the mean.

Distributional regression modeling via generalized additive models for location, scale, and shape: An overview through a data set from learning analytics

“…That is, GAMLSS are a distributional regression framework “geared toward causality” (Bühlmann, 2020a ) in that it can be used to examine stabilization of estimated fits across perturbations (in relation to cross‐validation, it is important to note that causal models are not suitable for prediction if there is no distribution shift between training and validation data since including noncausal covariates improves prediction). A recent proposal has demonstrated that combining instrumental variable estimation with GAMLSS is also a fruitful step in this front (Briseño‐Sánchez et al, 2020 ).…”

Tree species richness and evenness affect forest biomass differently across biogeographic regions

“…However, since all available methods to deal with spatial confounding are derived from linear assumptions, we included the linear models for comparison. The two-stage structure of the spatial+ model makes it particularly amenable to the use of non-linear trends in the final stage and our approach here closely resembles non-linear strategies used in the context of two-stage instrumental variables models (Marra and Radice, 2011, Briseño Sanchez et al, 2020). All analyses were done in R, using the packages ‘nlme’ (Pinheiro et al, 2023), ‘mgcv’ (Wood, 2019), and ‘tidyverse’ (Wickham et al, 2019).…”

A review of predictive uncertainty estimation with machine learning

“…Other models: The case of using instrumental variables in distributional regression has been investigated by Briseño Sanchez et al (2020). Efficient estimation of censored or truncated dependent variables has been implemented by Messner et al (2016).…”