Title: Instrumental variable estimation in compositional regression
Authors: Andrej Srakar - University of Ljubljana (Slovenia) [presenting]
Abstract: In an increasing number of empirical studies, the dimensionality (i.e. size of the parameter space) can be very large. In functional data analysis, the appropriate setting to analyze such problems is a functional linear model in which the covariates belong to Hilbert spaces. This has been previously extended to the cases where covariates are endogenous (functional instrumental variables/FIV). This is now extended to the compositional (with extensions also to histogram, i.e. empirical distributional) data setting, with most of the analysis based on compositional regression using additive log-ratio transformation where either or both independent and dependent variables are compositional. We show that estimation leads to an ill-posed inverse problem with a data-dependent operator. We use and extend the notion of instrument strength to compositional and distributional settings and discuss generalized versions of the estimators when the problem is premultiplied by an instrument-dependent operator. We establish appropriate central limit theorems and study the finite sample performance in a Monte Carlo simulation setting. Our application studies the relationship between long term care provision to relatives and paid work, using a recent time use survey from the Survey of Health, Ageing and Retirement in Europe (SHARE). In conclusion, we discuss extensions to other causal inference approaches in the line of distributional synthetic control.