Risk Theory Society

RTS Proceedings

2018 RTS Proceedings

Responses to Saving Commitments: Evidence from Mortgage Run-offs

We study consumers’ responses to removing a saving constraint. Mortgage run-offs predictably relax a saving constraint for borrowers whose mortgage committed them to save by paying down principal. Using the entire Danish population, we identify mortgages on
track to run off between 1995 and 2014. We measure the effect of run-offs on earnings and the household balance sheet. We find that borrowers use 39 percent of previous mortgage payments to decrease labor income, and use 53 percent to pay down other debts. Borrowers run up non-mortgage debt prior to the run-off and this run-up stops once the mortgage is repaid.

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Consumption Does Not Evolve As a Random Walk Around Small Income Shocks in Life-Cycle Models

While Hall (1978) argues that the solution for consumption of a life-cycle model with uncertainty and isoelastic preferences evolves as a random walk in first order approximation around small income shocks, I show that it does not. First, I explain that the solution for consumption departs from a random walk because of precautionary behavior. A prudent household facing uncertainty allocates more
of its resources to the uncertain future, raising its future consumption growth to an extent that depends on its current variables. This precautionary component of consumption growth does not disappear in first order approximation around small realized income shocks because it relates to the magnitude of the uncertainty ex-ante, not to the magnitude of the realized shocks ex-post. Second, I account for the previous literature that finds consumption to evolve approximately as a random walk: I show that there is an element of circular reasoning in the derivation of a random walk expression. Third, I assess the importance of the correlation of assets, total income and transitory income with subsequent consumption growth in a calibrated life-cycle model. I find all correlations to be highly significant.

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The Moral Hazard of Lifesaving Innovations: Naloxone Access, Opioid Abuse, and Crime

The United States is experiencing an epidemic of opioid abuse. In response, many states have increased access to naloxone, a drug that can save lives when administered during an overdose. However, naloxone access may unintentionally increase opioid abuse through two channels: (1) reducing the risk of death per use, thereby making riskier opioid use more appealing, and (2) saving the lives of active drug users, who survive to continue abusing opioids. By increasing the number of opioid abusers who need to fund their drug purchases, naloxone access laws may also increase theft. We exploit the staggered timing of naloxone access laws to estimate the total effects of these laws. We find that broadening naloxone access led to more opioid-related emergency room visits and more opioid-related theft, with no reduction in opioid-related mortality. These e↵ects are driven by urban areas and vary by region. We find the
most detrimental effects in the Midwest, including a 14% increase in opioid-related mortality in that region. We also find suggestive evidence that broadening naloxone access increased the use of fentanyl, a particularly potent opioid. While naloxone has great potential as a harm-reduction strategy, our analysis is consistent with the hypothesis that broadening access to naloxone encourages riskier behaviors with respect to opioid abuse.

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The Efficiency of Voluntary Risk Classification in Insurance Markets

It has been established that categorical discrimination based on observable characteristics such as gender, age, or ethnicity enhances efficiency. We consider a different form of risk classification where there exists some cost less yet imperfectly informative test on risk types, with the test outcome unknown to the agents ex-ante. We show that a voluntary risk classification where agents are given the option to take the test always increases efficiency compared with no risk classification. Moreover, voluntary risk classification also Pareto dominates the regime of compulsory risk classification in which all agents are required to take the test.

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It’s All About Speed and Costs: The Impact of Digital Technology on the Insurance Market Structure

Digital technology is costly, but it allows insurers to more quickly learn about the risk type of their policyholders. We study the implications of this speed-versus-cost trade off for equilibrium pricing and coverage decisions in an insurance market featuring adverse selection. In particular, we develop a theoretical model of dynamic competitive equilibrium featuring individuals who differ in their privately known risk types, and a large number of two types of insurers: conventional insurers and “tech” insurers who employ digital technologies. We consider three distinct dynamic equilibrium concepts: a finite horizon structure with foresight, an infinite horizon “overlapping generations”
structure, and an infinite horizon myopic structure. Equilibrium in each setting features a sorting of low-risk types into tech firms and high-risk types into conventional firms. Depending on the setting, however, the equilibrium tech-firm market share may negatively or positively correlate with the learning speed of conventional insurers.

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Insurers as Asset Managers and Systemic Risk

Financial intermediaries often provide guarantees that resemble out-of-the-money put options, exposing them to tail risk. Using the U.S. life insurance industry as a laboratory, we present a model in which variable annuity (VA) guarantees and associated hedging operate within the regulatory capital framework to create incentives for insurers to overweight illiquid bonds (“reach-for-yield”). We then calibrate the model to insurer-level data, and show that the VA-writing insurers’ collective allocation to illiquid bonds exacerbates system-wide fire sales in the event of negative asset shocks, plausibly erasing up to 20-70% of insurers’ equity capital.

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The Dark Side of Liquid Bonds in Fire Sales

We investigate which bonds institutional investors sell in fire sales. We find that these are mostly bonds that were trading in liquid markets before the fire sale, and that they are sold by other institutions as well. Somewhat surprisingly, the
price impacts in these markets are higher than in bonds that were trading in less liquid markets before the fire sale, but are also liquidated during fire sales. It appears as if liquid bonds in fire-sales exhibit larger price impacts than less liquid
bonds. We argue this is because institutions fail to fully account for the effect of selling common bonds on other market participants. Controlling for commonality of bonds, we find that liquid bonds have smaller price impacts in fire sales. This
result matters for the measurement of systemic risk: the commonality of liquid bonds exacerbates fire sales losses, as they are sold more in fire sales. Measures of portfolio similarity should thus overweight liquid bonds overlap, not underweight it.

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Information and Risk Preferences: The Case of Insurance Choice

Despite standard economic models that assume stability of preferences, empirical work on insurance choice has documented a surprising lack of stability of risk preferences across domains. We hypothesize that informational differences can partly explain the observed empirical regularities, and test our hypothesis by conducting lab and field experiments with over 4,000 participants. We exogenously vary the information subjects receive about the underlying risk they face and elicit willingness to pay for insurance. We have three major findings:

  1. information plays a significant role – willingness to pay for insurance is higher in settings with more complex or ambiguous information;
  2. both risk aversion and aversion to complex or ambiguous information are decreasing in the underlying
    risk probability; and
  3. risk aversion and aversion to complex or ambiguous information are negatively correlated, with the correlation coefficient being remarkably invariant to underlying risk and sociodemographic characteristics.

Using demand simulation techniques, we illustrate how informational effects can bias the empirical estimation of risk preferences and have a large impact on the allocative efficiency of insurance markets.

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The Lifetime Costs of Bad Health

Health shocks are an important source of risk. People in bad health work less, earn less, face higher medical expenses, die earlier, and accumulate less wealth. Importantly, the dynamics of health are richer than those implied by a low-order
Markov process. We first show that these dynamics can be parsimoniously captured by a combination of some lag-dependence and ex-ante heterogeneity. We then study the effects of health shocks in a structural life-cycle model that can reproduce the observed inequality in economic outcomes by health status. Our model has several implications concerning the pecuniary and non-pecuniary effects of health shocks. The lifetime costs of bad health are very concentrated, with the largest component of these costs being the loss in labor earnings. The non-pecuniary effects of health are very important along two dimensions. First,
individuals value good health mostly because it extends life expectancy. Second, health uncertainty substantially increases lifetime inequality.

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Mortality Risk, Insurance, and the Value of Life

A substantial body of research finds that consumers are far from fully annuitized, but the conventional economic theory on the value of life assumes otherwise. We develop and apply a new framework for valuing health and longevity improvements that relaxes this assumption, and describe several novel implications. First, in contrast to the conventional theory, a given mortality improvement may be worth more, not less, to patients facing shorter lives. This result helps reconcile economic theory with evidence that consumers prefer to award a fixed longevity gain to the patients with the bleakest survival prospects, and also implies that existing economic analysis may undervalue the treatment of severe illnesses relative to mild ones. Second, we introduce the value of statistical illness, which quantifies the value of preventing illness and includes the value of statistical life as a special case. Using detailed microdata, we calculate that treating illnesses such as cancer and heart disease is worth several times more to consumers than saving an equivalent number of life-years by preventing these conditions. Finally, we show that public annuity programs boost demand for life-extension. For instance, US Social
Security adds $11.5 trillion (10.5 percent) to the current value of post-1940 longevity gains.

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2017 RTS Proceedings

Simplifying Health Insurance Choice with Consequence Graphs

Standard theories of insurance demand are based on the idea that people select plans that maximize expected utility over the distribution of final wealth outcomes determined by the plan choice. However, a number of recent empirical studies in health insurance markets document patterns of sub-optimal choices that cannot be rationalized by standard models. These seemingly inefficient
choices may be linked to consumers’ poor understanding of insurance and the complexity involved in mapping the cost-sharing features of plans to their distribution of financial consequences. We develop an approach that we call “consequence graphs” to presenting health insurance options that combines information about the ex-ante distribution of medical spending needs with plan cost sharing rules to present each plan option graphically. The resulting consequence graphs show the distribution of total spending generated by each plan option. We use an incentivized laboratory experiment to compare consequence graphs to providing information on cost-sharing features
(e.g., deductibles and coinsurance rates) of plans. We find that when plan menus have options that are financially dominated, the majority of people violate financial dominance when choosing with typical feature-based information displays, but very few do so with consequence graphs. We interpret this result as clear evidence of the role that poor understanding of financial consequences
plays in health-insurance choice patterns. The consequence-graph approach also provides a practical way to simplify and clarify health insurance options.

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Adverse Selection in LowIncome Health Insurance Markets: Evidence from a largescale RCT in Pakistan

Around the world, there is a growing interest to provide insurance policies to low income households. Selection of high-risk individuals into the insurance pool is an often cited impediment for the sustainability of such schemes, though. We provide robust evidence on
the presence of adverse selection from a large randomized control trial on health insurance in rural Pakistan. Our experimental setup allows us to separate adverse selection from moral hazard, to estimate how selection changes at different points of the demand curve and to test measures against adverse selection. The results suggest that there is substantial adverse selection if health insurance coverage can be individually assigned. In particular, adverse selection tends to become worse with higher premium prices, creating a trade-off between cost recovery and the quality of the insurance pool. In contrast, adverse selection is mitigated when bundling insurance policies at the household or higher levels. Further analyses suggest that adverse selection in individual products has non-negligible welfare consequences and that these are less pronounced in relative terms when bundling policies.

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