Discount rate heterogeneity among older households: a puzzle?

J Popul Econ (2017) 30:647–680 DOI 10.1007/s00148-016-0623-y ORIGINAL PAPER Discount rate heterogeneity among older households: a puzzle? Antoine Bozio1,2 · Guy Laroque2,3 · Cormac O’Dea2 Received: 17 February 2016 / Accepted: 13 October 2016 / Published online: 23 November 2016 © The Author(s) 2016. This article is published with open access at Springerlink.com Abstract We put forward a method for estimating discount rates using wealth and income data. We build consumption from these data using the budget constraint. Consumption transitions yield discount rates by household groups. Applying this technique to a sample of older households, we find a similar distribution to those previously estimated using field data, though with a much lower mean than those found using experiments. Surprisingly, among this older population, patience is negatively correlated with education and numeracy. This goes against the positive correlation found for younger populations in experiments and some field studies. We discuss potential explanations for this result. Keywords Time preference · Discount rate · Consumption JEL Classifications D12 · D31 · D91 · E21 Responsible editor: Alessandro Cigno  Cormac O’Dea Antoine Bozio Guy Laroque 1 Paris School of Economics (PSE), Paris, France 2 Institute for Fiscal Studies (IFS), London, UK 3 University College London (UCL), London, UK 648 C. O’Dea et al. 1 Introduction In many situations, individuals make decisions that involve a comparison of present and future circumstances. They must decide how much to invest in education, how much to save for retirement, how much to invest in health, etc. In each case, these decisions are based on some assessment of the potential welfare at different periods under different scenarios. Following Samuelson (1937), economists have largely adopted a discountedutility model which assumes that preferences over time can be condensed into one major parameter, the geometric discount rate (see Frederick et al. 2002 for a critical review and Hall 2010 for a review of recent research developed using this approach). To estimate discount rates, both field data and experiments are found in the literature. Experimental studies are by far the most numerous. Among the 42 studies surveyed by Frederick et al. (2002), 34 use experimental methods. A typical approach is for individuals to be offered a menu of (real or hypothetical) choices between a quantity of money now and a different quantity of money at some point in the future. Respondents’ choices are used to estimate a discount rate. Our paper fits into a much smaller literature that estimates discount rates using field data on aspects of behaviour and a lifecycle model of consumption and saving. A typical way to estimate preference parameters in such models, though not the one that we will take, has been to solve numerically the intertemporal optimisation problem that the agents in a particular population are assumed to face. Estimates of parameters such as the discount rate are chosen such that the model’s predictions are close, in some metric and according to some data, to those seen in reality. Such studies vary in the extent to which heterogeneity in the discount factor is admitted into the model. Some papers assume homogenous discounting behaviour, like French (2005) and Edwards (2013) where discounting is exponential and Laibson et al. (2007) where discounting is quasi-hyperbolic. More flexibility was allowed by Attanasio et al. (1999) who estimate a version of the lifecycle model where the discount rate varies stochastically with the composition of the household while even more is allowed by Samwick (1998) and Gustman and Steinmeier (2005) who estimate a different discount rate for every household. These papers fully specify a lifecycle model and solve it. The method we employ does not do this but rather uses the first-order condition to that solution—the Euler equation. We first generate longitudinal observations on consumption using a procedure introduced by Ziliak (1998) and Browning and Leth-Petersen (2003). This involves calculating consumption using comprehensive and high quality data on assets and income and the intertemporal budget constraint. Our resulting distribution of consumption is shown to be remarkably similar to that derived from the UK’s household budget survey. Using the Euler equation and consumption transitions at the household level, we estimate average discount rates for groups of households. Such an approach has typically been precluded in the past by the absence of good quality panel data on consumption—a problem discussed in detail by Browning et al. (2003). Our approach has some parallels with papers that have previously relied on the Euler equation to estimate parameters, in particular the elasticity of intertemporal substitution. Estimation in this manner was carried out by Campbell and Mankiw Discount rate heterogeneity 649 (1989) and Attanasio and Weber (1995) among others. For a lively criticism of this approach, see Carroll (2001) and for a defense see Attanasio and Low (2004). Our approach differs from these papers in three principal ways. First, we are able to use consumption transitions at the household level rather than relying on aggregate or cohort-level data. Second, our use of household rather than cohort level consumption data allows us to use the exact Euler equation in our estimation, rather than relying on Taylor series approximations. Third, we do not assume that the discount rate is the same for each individual in our sample, nor do we assume that it is unchanging across the lifecycle. We apply the procedure outlined above to a representative sample of older English households using the English Longitudinal Survey of Ageing (ELSA). We show, unsurprisingly, that there is substantial heterogeneity in discounting in that population. The typical levels of discount rates that we estimate are of similar magnitude to those estimated in other papers based on the lifecycle model of consumption and saving. These rates imply substantially less discounting than is implied by the results of experimental studies. Our most surprising result is that discount rates tend to rise with education and levels of numerical ability (i.e. those with less education and those who are less numerically able tend to be the most patient). This result is contrary to that found in the literature that measures the extent to which individuals discount future income streams (see for instance Warner and Pleeter 2001; Harrison et al. 2002; Dohmen et al. 2010). These papers differ in their empirical approach—the first uses data on the choices of departing military personnel over whether they will take their severance payment in a lump-sum or in the form of an annuity payment, while the second and third papers use laboratory experiments. The literature using field data offers less conclusive evidence. Gourinchas and Parker (2002) solve a l (...truncated)