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Using a structural life-cycle model and data on school visits from Safegraph and school closures from Burbio, we quantify the heterogeneous impact of school closures during the Corona crisis on children affected at different ages and coming from households with different parental characteristics. Our data suggests that secondary schools were closed for in-person learning for longer periods than elementary schools (implying that younger children experienced less school closures than older children), and that private schools experienced shorter closures than public schools, and schools in poorer U.S. counties experienced shorter school closures. We then extend the structural life cycle model of private and public schooling investments studied in Fuchs-Schündeln, Krueger, Ludwig, and Popova (2021) to include the choice of parents whether to send their children to private schools, empirically discipline it with data on parental investments from the PSID, and then feed into the model the school closure measures from our empirical analysis to quantify the long-run consequences of the Covid-19 school closures on the cohorts of children currently in school. Future earnings- and welfare losses are largest for children that started public secondary schools at the onset of the Covid-19 crisis. Comparing children from the topto children from the bottom quartile of the income distribution, welfare losses are ca. 0.8 percentage points larger for the poorer children if school closures were unrelated to income. Accounting for the longer school closures in richer counties reduces this gap by about 1/3. A policy intervention that extends schools by 3 months (6 weeks in the next two summers) generates significant welfare gains for the children and raises future tax revenues approximately sufficient to pay for the cost of this schooling expansion.
Using a structural life-cycle model, we quantify the heterogeneous impact of school closures during the Corona crisis on children affected at different ages and coming from households with different parental characteristics. In the model, public investment through schooling is combined with parental time and resource investments in the production of child human capital at different stages in the children’s development process. We quantitatively characterize the long-term consequences from a Covid-19 induced loss of schooling, and find average losses in the present discounted value of lifetime earnings of the affected children of close to 1%, as well as welfare losses equivalent to about 0.6% of permanent consumption. Due to self-productivity in the human capital production function, skill attainment at a younger stage of the life cycle raises skill attainment at later stages, and thus younger children are hurt more by the school closures than older children. We find that parental reactions reduce the negative impact of the school closures, but do not fully offset it. The negative impact of the crisis on children’s welfare is especially severe for those with parents with low educational attainment and low assets. The school closures themselves are primarily responsible for the negative impact of the Covid-19 shock on the long-run welfare of the children, with the pandemic-induced income shock to parents playing a secondary role.
We characterize the optimal linear tax on capital in an Overlapping Generations model with two period lived households facing uninsurable idiosyncratic labor income risk. The Ramsey government internalizes the general equilibrium effects of private precautionary saving on factor prices and taxes capital unless the weight on future generations in the social welfare function is sufficiently high. For logarithmic utility a complete analytical solution of the Ramsey problem exhibits an optimal aggregate saving rate that is independent of income risk, whereas the optimal time-invariant tax on capital implementing this saving rate is increasing in income risk. The optimal saving rate is constant along the transition and its sign depends on the magnitude of risk and on the Pareto weight of future generations. If the Ramsey tax rate that maximizes steady state utility is positive, then implementing this tax rate permanently induces a Pareto-improving transition even if the initial equilibrium capital stock is below the golden rule.
Households buy life insurance as part of their liquidity management. The option to surrender such a policy can serve as a buffer when a household faces a liquidity need. In this study, we investigate empirically which individual and household specific sociodemographic factors influence the surrender behavior of life insurance policyholders. Based on the Socio-Economic Panel (SOEP), an ongoing wide-ranging representative longitudinal study of around 11,000 private households in Germany, we construct a proxy to identify life insurance surrender in the data. We use this proxy to conduct fixed effect regressions and support the results with survival analyses. We find that life events that possibly impose a liquidity shock to the household, such as birth of a child and divorce increase the likelihood to surrender an existing life insurance policy for an average household in the panel. The acquisition of a dwelling and unemployment are further aspects that can foster life insurance surrender. Our results are robust with respect to different models and hold conditioning on region specific trends; they vary however for different age groups. Our analyses contribute to the existing literature supporting the emergency fund hypothesis. The findings obtained in this study can help life insurers and regulators to detect and understand industry specific challenges of the demographic change.
Telemonitoring devices can be used to screen consumer characteristics and mitigate information asymmetries that lead to adverse selection in insurance markets. Nevertheless, some consumers value their privacy and dislike sharing private information with insurers. In a secondbest efficient Miyazaki-Wilson-Spence (MWS) framework, we allow consumers to reveal their risk type for an individual subjective cost and show analytically how this affects insurance market equilibria as well as social welfare. We find that information disclosure can substitute deductibles for consumers whose transparency aversion is sufficiently low. This can lead to a Pareto improvement of social welfare. Yet, if all consumers are offered cross-subsidizing contracts, the introduction of a screening contract decreases or even eliminates cross-subsidies. Given the prior existence of a cross-subsidizing MWS equilibrium, utility is shifted from individuals who do not reveal their private information to those who choose to reveal. Our analysis informs the discussion on consumer protection in the context of digitalization. It shows that new technologies challenge cross-subsidization in insurance markets, and it stresses the negative externalities that digitalization has on consumers who are unwilling to take part in this
development
What are the aggregate and distributional consequences of the relationship be-tween an individual’s social network and financial decisions? Motivated by several well-documented facts about the influence of social connections on financial decisions, we build and calibrate a model of stock market participation with a social network that emphasizes the interplay between connectivity and network structure. Since connections to informed agents help spread information, there is a pivotal role for factors that determine sorting among agents. An increase in the average number of connections raises the average participation rate, mostly due to richer agents. A higher degree of sorting benefits richer agents by creating clusters where information spreads more efficiently. We show empirical evidence consistent with the importance of connectivity and sorting. We discuss several new avenues for future research into the aggregate impact of peer effects in finance.
Telemonitoring devices can be used to screen consumer characteristics and mitigate information asymmetries that lead to adverse selection in insurance markets. Nevertheless, some consumers value their privacy and dislike sharing private information with insurers. In a secondbest efficient Miyazaki-Wilson-Spence (MWS) framework, we allow consumers to reveal their risk type for an individual subjective cost and show analytically how this affects insurance market equilibria as well as social welfare. We find that information disclosure can substitute deductibles for consumers whose transparency aversion is sufficiently low. This can lead to a Pareto improvement of social welfare. Yet, if all consumers are offered cross-subsidizing contracts, the introduction of a screening contract decreases or even eliminates cross-subsidies. Given the prior existence of a cross-subsidizing MWS equilibrium, utility is shifted from individuals who do not reveal their private information to those who choose to reveal. Our analysis informs the discussion on consumer protection in the context of digitalization. It shows that new technologies challenge cross-subsidization in insurance markets, and it stresses the negative externalities that digitalization has on consumers who are unwilling to take part in this development.
This paper uses laboratory experiments to provide a systematic analysis of how di↵erent presentation formats a↵ect individuals’ investment decisions. The results indicate that the type of presentation as well as personal characteristics influence both, the consistency of decisions and the riskiness of investment choices. However, while personal characteristics have a larger impact on consistency, the chosen risk level is determined more by framing e↵ects. On the level of personal characteristics, participants’ decisions show that better financial literacy and a better understanding of the presentation format enhance consistency and thus decision quality. Moreover, female participants on average make less consistent decisions and tend to prefer less risky alternatives. On the level of framing dimensions, subjects choose riskier investments when possible outcomes are shown in absolute values rather than rates of return and when the loss potential is less obvious. In particular, reducing the emphasis on downside risk and upside potential simultaneously leads to a substantial increase in risk taking.
In this paper I assess the effect of interest rate risk and longevity risk on the solvency position of a life insurer selling policies with minimum guaranteed rate of return, profit participation and annuitization option at maturity. The life insurer is assumed to be based in Germany and therefore subject to German regulation as well as to Solvency II regulation. The model features an existing back book of policies and an existing asset allocation calibrated on observed data, which are then projected forward under stochastic financial markets and stochastic mortality developments. Different scenarios are proposed, with particular focus on a prolonged period of low interest rates and strong reduction in mortality rates. Results suggest that interest rate risk is by far the greatest threat for life insurers, whereas longevity risk can be more easily mitigated and thereby is less detrimental. Introducing a dynamic demand for new policies, i.e. assuming that lower offered guarantees are less attractive to savers, show that a decreasing demand may even be beneficial for the insurer in a protracted period of low interest rates. Introducing stochastic annuitization rates, i.e. allowing for deviations from the expected annuitization rate, the solvency position of the life insurer worsen substantially. Also profitability strongly declines over time, casting doubts on the sustainability of traditional life business going forward with the low interest rate environment. In general, in the proposed framework it is possible to study the evolution over time of an existing book of policies when underlying financial market conditions and mortality developments drastically change. This feature could be of particular interest for regulatory and supervisory authorities within their financial stability mandate, who could better evaluate micro- and macro-prudential policy interventions in light of the persistent low interest rate environment.
Socially responsible investing (SRI) continues to gain momentum in the financial market space for various reasons, starting with the looming effect of climate change and the drive toward a net-zero economy. Existing SRI approaches have included environmental, social, and governance (ESG) criteria as a further dimension to portfolio selection, but these approaches focus on classical investors and do not account for specific aspects of insurance companies. In this paper, we consider the stock selection problem of life insurance companies. In addition to stock risk, our model set-up includes other important market risk categories of insurers, namely interest rate risk and credit risk. In line with common standards in insurance solvency regulation, such as Solvency II, we measure risk using the solvency ratio, i.e. the ratio of the insurer’s market-based equity capital to the Value-at-Risk of all modeled risk categories. As a consequence, we employ a modification of Markowitz’s Portfolio Selection Theory by choosing the “solvency ratio” as a downside risk measure to obtain a feasible set of optimal portfolios in a three-dimensional (risk, return, and ESG) capital allocation plane. We find that for a given solvency ratio, stock portfolios with a moderate ESG level can lead to a higher expected return than those with a low ESG level. A highly ambitious ESG level, however, reduces the expected return. Because of the specific nature of a life insurer’s business model, the impact of the ESG level on the expected return of life insurers can substantially differ from the corresponding impact for classical investors.
Low interest rates are becoming a threat to the stability of the life insurance industry, especially in countries such as Germany, where products with relatively high guaranteed returns sold in the past still represent a prominent share of the total portfolio. This contribution aims to assess and quantify the effects of the current low interest rate phase on the balance sheet of a representative German life insurer, given the current asset allocation and the outstanding liabilities. To do so, we generate a stochastic term structure of interest rates as well as stock market returns to simulate investment returns of a stylized life insurance business portfolio in a multi-period setting. Based on empirically calibrated parameters, we can observe the evolution of the life insurers’ balance sheet over time with a special focus on their solvency situation. To account for different scenarios and in order to check the robustness of our findings, we calibrate different capital market settings and different initial situations of capital endowment. Our results suggest that a prolonged period of low interest rates would markedly affect the solvency situation of life insurers, leading to a relatively high cumulative probability of default, especially for less capitalized companies. In addition, the new reform of the German life insurance regulation has a beneficial effect on the cumulative probability of default, as a direct consequence of the reduction of the payouts to policyholders.
We prove the existence of an equilibrium in competitive markets with adverse selection in the sense of Miyazaki (1977), Wilson (1977), and Spence (1978) when the distribution of unobservable risk types is continuous. Our proof leverages the finite-type proof in Spence (1978) and a limiting argument akin to Hellwig (2007)’s study of optimal taxation.
Different insurance activities exhibit different levels of persistence of shocks and volatility. For example, life insurance is typically more persistent but less volatile than non-life insurance. We examine how diversification among life, non-life insurance, and active reinsurance business affects an insurer's contribution and exposure to the risk of other companies. Our model shows that a counterparty's credit risk exposure to an insurance group substantially depends on the relative proportion of the insurance group's life and non-life business. The empirical analysis confirms this finding with respect to several measures for spillover risk. The optimal proportion of life business that minimizes spillover risk decreases with leverage of the insurance group, and increases with active reinsurance business.
This paper studies insurance demand for individuals with limited financial literacy. We propose uncertainty about insurance payouts, resulting from contract complexity, as a novel channel that affects decision-making of financially illiterate individuals. Then, a trade-off between second-order (risk aversion) and third-order (prudence) risk preferences drives insurance demand. Sufficiently prudent individuals raise insurance demand upon an increase in contract complexity, while the effect is reversed for less prudent individuals. We characterize competitive market equilibria that feature complex contracts since firms face costs to reduce complexity. Based on the equilibrium analysis, we propose a monetary measure for the welfare cost of financial illiteracy and show that it is mainly driven by individuals’ risk aversion. Finally, we discuss implications for regulation and consumer protection.
Telemonitoring devices can be used to screen consumers' characteristics and mitigate information asymmetries that lead to adverse selection in insurance markets. However, some consumers value their privacy and dislike sharing private information with insurers. In the second-best efficient Wilson-Miyazaki-Spence framework, we allow for consumers to reveal their risk type for an individual subjective cost and show analytically how this affects insurance market equilibria as well as utilitarian social welfare. Our analysis shows that the choice of information disclosure with respect to revelation of their risk type can substitute deductibles for consumers whose transparency aversion is sufficiently low. This can lead to a Pareto improvement of social welfare and a Pareto efficient market allocation. However, if all consumers are offered cross-subsidizing contracts, the introduction of a transparency contract decreases or even eliminates cross-subsidies. Given the prior existence of a WMS equilibrium, utility is shifted from individuals who do not reveal their private information to those who choose to reveal. Our analysis provides a theoretical foundation for the discussion on consumer protection in the context of digitalization. It shows that new technologies bring new ways to challenge crosssubsidization in insurance markets and stresses the negative externalities that digitalization has on consumers who are not willing to take part in this development.
The modern tontine: an innovative instrument for longevity risk management in an aging society
(2016)
The changing social, financial and regulatory frameworks, such as an increasingly aging society, the current low interest rate environment, as well as the implementation of Solvency II, lead to the search for new product forms for private pension provision. In order to address the various issues, these product forms should reduce or avoid investment guarantees and risks stemming from longevity, still provide reliable insurance benefits and simultaneously take account of the increasing financial resources required for very high ages. In this context, we examine whether a historical concept of insurance, the tontine, entails enough innovative potential to extend and improve the prevailing privately funded pension solutions in a modern way. The tontine basically generates an age-increasing cash flow, which can help to match the increasing financing needs at old ages. However, the tontine generates volatile cash flows, so that - especially in the context of an aging society - the insurance character of the tontine cannot be guaranteed in every situation. We show that partial tontinization of retirement wealth can serve as a reliable supplement to existing pension products.
The Solvency II standard formula employs an approximate Value-at-Risk approach to define risk-based capital requirements. This paper investigates how the standard formula’s stock risk calibration influences the equity position and investment strategy of a shareholder-value-maximizing insurer with limited liability. The capital requirement for stock risks is determined by multiplying a regulation-defined stock risk parameter by the value of the insurer’s stock portfolio. Intuitively, a higher stock risk parameter should reduce risky investments as well as insolvency risk. However, we find that the default probability does not necessarily decrease when reducing the investment risk (by increasing the stock investment risk parameter). We also find that depending on the precise interaction between assets and liabilities, some insurers will invest conservatively, whereas others will prefer a very risky investment strategy, and a slight change of the stock risk parameter may lead from a conservative to a high risk asset allocation.
European insurers are allowed to make discretionary decisions in the calculation of Solvency II capital requirements. These choices include the design of risk models (ranging from a standard formula to a full internal model) and the use of long-term guarantees measures. This article examines the impact and the drivers of discretionary decisions with respect to capital requirements for market risks. In a first step of our analysis, we assess the risk profiles of 49 stock insurers using daily market data. In a second step, we exploit hand-collected Solvency II data for the years 2016 to 2020. We find that long-term guarantees measures substantially influence the reported solvency ratios. The measures are chosen particularly by less solvent insurers and firms with high interest rate and credit spread sensitivities. Internal models are used more frequently by large insurers and especially for risks for which the firms have already found adequate immunization strategies.
A greater firm-level transparency through enhanced disclosure provides more information regarding the risk situation of an insurer to its outside stakeholders such as stock investors and policyholders. The disclosure of the insurer's risktaking can result in negative influences on, for example, its stock performance and insurance demand when stock investors and policyholders are risk-averse. Insurers, which are concerned about the potential ex post adverse effects of risk-taking under greater transparency, are thus inclined to limit their risks ex ante. In other words, improved firm-level transparency can induce less risktaking incentive of insurers. This article investigates empirically the relationship between firm-level transparency and insurers' strategies on capitalization and risky investments. By exploring the disclosure levels and the risk behavior of 52 European stock insurance companies from 2005 to 2012, the results show that insurers tend to hold more equity capital under the anticipation of greater transparency, and this strategy on capital-holding is consistent for different types of insurance businesses. When considering the influence of improved transparency on the investment policy of insurers, the results are mixed for different types of insurers.
This article explores life insurance consumption in 31 European countries from 2003 to 2012 and aims to investigate the extent to which market transparency can affect life insurance demand. The cross-country evidence for the entire sample period shows that greater market transparency, which resolves asymmetric information, can generate a higher demand for life insurance. However, when considering the financial crisis period (2008-2012) separately, the results suggest a negative impact of enhanced market transparency on life insurance consumption. The mixed findings imply a trade-off between the reduction in adverse selection under greater market transparency and the possible negative effects on life insurance consumption during the crisis period due to more effective market discipline. Furthermore, this article studies the extent to which transparency can influence the reaction of life insurance demand to bad market outcomes: i.e., low solvency ratios or low profitability. The results indicate that the markets with bad outcomes generate higher life insurance demand under greater transparency compared to the markets that also experience bad outcomes but are less transparent.