A test of risk vulnerability in the wider population

Theory and Decision https://doi.org/10.1007/s11238-019-09708-5 A test of risk vulnerability in the wider population Philomena M. Bacon1 · Anna Conte2 · Peter G. Moffatt1 © The Author(s) 2019 Abstract Panel data from the German SOEP is used to test for risk vulnerability (RV) in the wider population. Two different survey responses are analysed: the response to the question about willingness-to-take risk in general and the chosen investment in a hypothetical lottery. A convenient indicator of background risk is the VDAX index, an established measure of volatility in the German stock market. This is used as an explanatory variable in conjunction with HDAX, the stock market index, which proxies wealth. The impacts of these measures on risk attitude are identifiable by exploiting the time dimension of the panel and matching survey months with corresponding observations from these time-varying factors. Both of the survey responses allow us to test for decreasing absolute risk aversion (DARA); in one case, we find strong evidence of DARA, while in the other, we do not. Both survey responses also allow us to test for RV, and in both cases we find strong evidence. In the case of the hypothetical lottery response, we are also able to estimate a “coefficient of risk vulnerability” (CRV). This is defined as the absolute amount by which absolute risk aversion rises in response to a doubling of background risk. We estimate CRV to be between 1.03 and 1.27. Keywords Risk vulnerability · Background risk · Panel data · Survey data We acknowledge access to the German Socio-Economic Panel (SOEP) for use in this research under licence number: 2596. B Peter G. Moffatt Philomena M. Bacon Anna Conte 1 School of Economics, University of East Anglia, Norwich NR4 7TJ, UK 2 Department of Statistical Sciences, Sapienza University of Rome, Rome, Italy 123 P. M. Bacon et al. 1 Introduction There is much empirical evidence of decreasing absolute risk aversion (DARA), the phenomenon of an individual becoming more willing to take risk when their wealth increases by an absolute amount. This evidence comes from both the field (e.g. Hamal and Anderson 1982) and the laboratory (e.g. Levy 1994). A related concept is risk vulnerability (RV) (Gollier and Pratt 1996). This is the phenomenon of an individual becoming less willing to take risk when mean-zero background risk (independent of other risks) is added to their wealth. Risk vulnerability is an important hypothesis, especially in the light of the 2008 global financial crisis, and the global recession that followed. The period of (and immediately following) the crisis amounted to a textbook example of a period of abnormally high background risk. It is important to understand the impact of this on individuals’ risk attitude in order to gain greater insight into our understanding of the overall impact of the crisis for future reference. It has been shown, for example, that risk-vulnerable agents respond to an increase in background risk by adjusting their portfolio in favour of safe assets and by demanding more insurance (Gollier and Pratt 1996). Risk Vulnerability has even been put forward as an explanation for the well-known equity premium puzzle (Mehra and Prescott 1985; Weil 1992). In many theoretical studies, RV is assumed. For example, Heaton and Lucas (2000) invoke the assumption in their explanations of portfolio puzzles. However, perhaps surprisingly, there is comparatively little empirical evidence of RV. Experimental evidence of RV has been found by Beaud and Willinger (2015), Lusk and Coble (2008) and others. In this paper, we instead use survey data drawn from the wider population. It may be argued that in the present context survey data have considerable advantages over experimental data with regard to external validity. Aside from the standard advantages of a larger and more representative sample, it is reasonable to expect that measures of background risk that might be used in the context of survey data (e.g. measures of macroeconomic uncertainty) have greater external validity than the types of background risk typically induced in a laboratory setting. Guiso and Paiella (2008) find evidence of RV from a cross section sample of Italian individuals, where the chosen measure of background risk is the variance (over time) in per-capita GDP in the individual’s province of residence. West and Worthington (2014) estimate the impact of macroeconomic conditions on risk attitude using an Australian panel data set. Although they do not explicitly refer to background risk and RV, our analysis is similar to theirs in respect of exploiting a panel data set, and introducing time-varying factors. The panel data we use is the German Socio-Economic Panel (SOEP). This consists of repeated data on a large number of individuals. We focus on two outcome variables. The first is the response to the direct question about willingness to take risks in general. This response is provided on a 0–10 Likert scale (Likert 1932). Hence, the random effects ordered probit model is used for the analysis of this outcome. The second outcome is the response to a hypothetical lottery investment question. An individual’s response to this question may be taken to imply that that individual’s coefficient of absolute risk aversion lies in a particular interval. Consequently, the random effects interval regression model is used for the analysis of this outcome. 123 A test of risk vulnerability in the wider population In order to test for DARA and RV, we match repeated responses to these riskrelated questions in the panel, to observations (from the month immediately preceding the survey date) on the time-varying factors, HDAX and VDAX. HDAX is the German stock market index, which acts as a proxy for wealth, and hence, a test of the impact of HDAX on risk attitude amounts to a test of DARA. VDAX is an established indicator of volatility in the German stock market,1 thereby having a direct interpretation as a measure of background risk prevailing in any given time period. Consequently, a test of the impact of VDAX on risk attitude may be interpreted as a test of RV. In addition to testing for risk vulnerability in the manner described above, we will go a step further by deducing an estimate of the “coefficient of risk vulnerability” (CRV), which will be defined in due course. To our knowledge, this is the first attempt at the empirical quantification of risk vulnerability. The paper is organized as follows: Sect. 2 describes the data; Sect. 3 discusses the modelling strategies; Sect. 4 reports and discusses the results, and also constructs an estimate of the CRV; and Sect. 5 concludes. 2 The SOEP data set The German Socio-Economic Panel Survey (SOEP) has been running since 1984 and surveys a cohort of approximately 20,000 households annually, inquiring into lifestyle and economic activities (Frick et al. 2007; Jürgen and Gert 2007).2 In 2004, the survey broadened to (...truncated)