Primary Submission Category: Instrumental Variables
Instrumental Variable Estimation in Compositional Regression for Time-Use Surveys in Health and Long-Term Care
Authors: Andrej Srakar,
Presenting Author: Andrej Srakar*
Time use surveys are used in many areas of economics, including economics of health and long-term care. If analyzed in a regression context, time use survey data suffer from the problem of spurious correlation noted in early works of Aitchison (1986). This problem leads to a need for compositional regression perspective on a geometric simplex. We develop an instrumental variable compositional regression model, building on two strands of literature with applications for health economics and economics of long-term care. We extend Florens and Van Bellegem (2015) functional instrumental variables model to compositional data setting where either or both independent and dependent variables are of compositional nature. We show there exist two ways of deriving compositional IV’s, one using isometric log-ratio transform and Chesher et al. (2013)’s IV model of multiple discrete choice; and another deriving from the recent literature on compositional functional data in Bayes spaces (Machalova et al., 2021). We show that estimation leads to an ill-posed inverse problem with a data-dependent operator and we use and extend the notion of instrument strength to compositional setting. We establish appropriate functional CLT’s and study the finite sample performance in a Monte Carlo simulation setting. Our application studies relationship between long term care for older people and paid work, using recent time use survey from Survey of Health, Ageing and Retirement in Europe (SHARE).