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This paper characterizes the stationary equilibrium of a continuous-time neoclassical production economy with capital accumulation in which households can insure against idiosyncratic income risk through long-term insurance contracts. Insurance companies operating in perfectly competitive markets can commit to future contractual obligations, whereas households cannot. For the case in which household labor productivity takes two values, one of which is zero, and where households have logutility we provide a complete analytical characterization of the optimal consumption insurance contract, the stationary consumption distribution and the equilibrium aggregate capital stock and interest rate. Under parameter restrictions, there is a unique stationary equilibrium with partial consumption insurance and a stationary consumption distribution that takes a truncated Pareto form. The unique equilibrium interest rate (capital stock) is strictly decreasing (increasing) in income risk. The paper provides an analytically tractable alternative to the standard incomplete markets general equilibrium model developed in Aiyagari (1994) by retaining its physical structure, but substituting the assumed incomplete asset markets structure with one in which limits to consumption insurance emerge endogenously, as in Krueger and Uhlig (2006).
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.
Historical evidence like the global financial crisis from 2007-09 highlights that sector concentration risk can play an important role for the solvency of insurers. However, current microprudential frameworks like the US RBC framework and Solvency II consider only name concentration risk explicitly in their solvency capital requirements for asset concentration risk and neglect sector concentration risk. We show by means of US insurers’ asset holdings from 2009 to 2018 that substantial sectoral asset concentrations exist in the financial, public and real estate sector, and find indicative evidence for a sectoral search for yield behavior. Based on a theoretical solvency capital allocation scheme, we demonstrate that the current regulatory approaches can lead to inappropriate and biased levels of solvency capital for asset concentration risk, and should be revised. Our findings have also important implications on the ongoing discussion of asset concentration risk in the context of macroprudential insurance regulation.
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 feedback of private precautionary saving. For logarithmic utility our full analytical solution of the Ramsey problem shows that the optimal aggregate saving rate is independent of income risk. The optimal time-invariant tax on capital is increasing in income risk. Its sign depends on the extent 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 generates a Pareto-improving transition even if the initial equilibrium is dynamically efficient. We generalize our results to Epstein-Zin-Weil utility and show that the optimal steady state saving rate is increasing in income risk if and only if the intertemporal elasticity of substitution is smaller than 1.