Estimating Dynamic Discrete Choice Models With Hyperbolic Discounting, With an Application to Mammography Decisions

Abstract

This paper extends the semi-parametric identification and estimation method for dynamic discrete choice models using Hotz and Miller's (1993) conditional choice probability (CCP) approach to the setting where individuals may have hyperbolic discounting time preferences and may be naive about their time inconsistency. We implement the proposed estimation method to the decisions of undertaking mammography to evaluate the importance of present bias and naivety in the under-utilization of mammography. Preliminary results show evidence for both present bias and naivety.

Discount Rates and the Education Gradient in Mammography in the Uk

“…Some of the specification checks of Sections 4.4.1 and 4.4.3 address these issues. The estimated discount factor is close to the result of Fang and Wang (2010), even though they use US data and different modelling assumptions. There is no significant difference in the discount factor between the two education groups, although women having secondary or higher education are estimated to have a lower discount rate.…”

“…The model is a semiparametric long-time-horizon model, which avoids the heavy dependence on functional-form assumptions. It is in a sense simpler than the related models of Hotz and Miller (1993) and Fang and Wang (2010) as I assume a finite time horizon and do not consider hyperbolic discounting but utilise the 3-year recommended frequency of breast cancer screening. The approach of Fang and Wang is not applicable to the UK sample as women in the UK generally do not have to make decisions on mammography each year.…”

“…In the empirical analysis, I normalise u(x, i = 1) = 0, that is, I estimate the influencing factors of u(x, i = 0) À u(x, i = 1), which I call the disutility of screening. The prerequisites of identification are based on Magnac and Thesmar (2002) and are similar to those in the model of Fang and Wang (2010). The model is identified only if there is at least one variable that affects the transition probabilities but that has no influence on the disutility of screening (i.e.…”

“…9 Many studies found a small but positive effect of breast cancer screening on longevity (among others Stout et al, 2006;Mandelblatt et al, 2009;Glasziou and Houssami, 2011). Fang and Wang (2010) also found that undertaking mammography significantly reduces the 2-year probability of dying. On the other hand, Gotzsche and Olsen (2000) stated that there is no evidence that breast cancer screening would decrease mortality due to breast cancer.…”

“…Fuchs (1982) also addressed the relationship between health behaviours, health and time preferences, but he used survey measures on time preferences. Fang and Wang (2010) provided an empirical analysis of preventive care utilisation based on a dynamic discrete-choice model, where individuals are allowed to have hyperbolic discounting and to be naive about their time inconsistency. Their application is also to mammography decisions, using data from the US Health and Retirement Study.…”