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Working Paper
Insurance and Inequality with Persistent Private Information
We study optimal insurance contracts for an agent with Markovian private information. Our main results characterize the implications of constrained efficiency for long-run welfare and inequality. Under minimal technical conditions, there is Absolute Immiseration: in the long run, the agent?s consumption and utility converge to their lower bounds. When types are persistent and utility is unbounded below, there is Relative Immiseration: low-type agents are immiserated at a faster rate than high-type agents, and ?pathwise welfare inequality? grows without bound. These results extend and ...
Working Paper
Insurance and Inequality with Persistent Private Information
This paper studies the optimal tradeoff between insurance and inequality in economies with persistent private information.We consider a principal-agent model in which the principal insures the agent against privately-observed shocks to his endowment, which follows an ergodic finite-state Markov chain that may exhibit arbitrary serial correlation. The optimal contract always induces immiseration: the agent’s consumption and utility become arbitrarily negative in the long run. When the endowment is positively serially correlated, the optimal contract provides increasingly high-powered ...
Working Paper
Insurance and Inequality with Persistent Private Information
This paper studies the implications of optimal insurance provision for long-run welfare and inequality in economies with persistent private information. We consider a model in which a principal insures an agent whose privately observed endowment follows an ergodic, finite Markov chain. The optimal contract always induces immiseration: the agent’s consumption and utility decrease without bound. Under positive serial correlation, the optimal contract also features backloaded high-powered incentives: the sensitivity of the agent’s utility with respect to his report increases without bound. ...
Working Paper
Insurance and Inequality with Persistent Private Information
This paper studies the implications of optimal insurance provision for long-run welfare and inequality in economies with persistent private information. We consider a model in which a principal insures an agent whose privately observed endowment follows an ergodic, finite Markov chain. The optimal contract always induces immiseration: the agent’s consumption and utility decrease without bound. Under positive serial correlation, the optimal contract also features backloaded high-powered incentives: the sensitivity of the agent’s utility with respect to his report increases without bound. ...
Working Paper
Insurance and Inequality with Persistent Private Information
We study the implications of optimal insurance provision for long-run welfare and inequality in economies with persistent private information. A principal insures an agent whose private type follows an ergodic, finite-state Markov chain. The optimal contract always induces immiseration: the agent’s consumption and utility decrease without bound. Under positive serial correlation, it also backloads high-powered incentives: the sensitivity of the agent’s utility with respect to his reports increases without bound. These results extend—and help elucidate the limits of—the hallmark ...
Working Paper
Insurance and Inequality with Persistent Private Information
We study the implications of optimal insurance provision for long-run welfare and inequality in economies with persistent private information. A principal insures an agent whose private type follows an ergodic, finite-state Markov chain. The optimal contract always induces immiseration: the agent’s consumption and utility decrease without bound. Under positive serial correlation, it also backloads high-powered incentives: the sensitivity of the agent’s utility with respect to his reports increases without bound. These results extend—and help elucidate the limits of—the hallmark ...
Working Paper
Extended Supplement to “Insurance and Inequality with Persistent Private Information”
This supplement contains auxiliary technical results and proofs omitted from Bloedel, Krishna, and Leukhina (2025) (henceforth BKL) and its Supplemental Appendix (henceforth SA). First, Section I proves parts (a)–(c) and (e)–(f) of Theorem 3 from Appendix B.1 of BKL. (Part (d) of Theorem 3 is proved in SA-E.1 of BKL.) Second, Section J proves Proposition 3.2 from Section 3.3 of BKL and Lemma B.2 from Appendix B.2 of BKL. Finally, Section K proves supporting facts for Properties (a)–(e) from Section 5.2 of BKL. Throughout, we follow the numbering and labeling conventions from BKL and its ...
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Rollover risk as market discipline: a two-sided inefficiency
Why does the market discipline that financial intermediaries face seem too weak during booms and too strong during crises? This paper shows in a general equilibrium setting that rollover risk as a disciplining device is effective only if all intermediaries face purely idiosyncratic risk. However, if assets are correlated, a two-sided inefficiency arises: Good aggregate states have intermediaries taking excessive risks, while bad aggregate states suffer from costly fire sales. The driving force behind this inefficiency is an amplifying feedback loop between asset values and market discipline. ...
Working Paper
Continuous Markov equilibria with quasi-geometric discounting
We prove that the standard quasi-geometric discounting model used in dynamic consumer theory and political economics does not possess continuous Markov perfect equilibria (MPE) if there is a strictly positive lower bound on wealth. We also show that, at points of discontinuity, the decision maker strictly prefers lotteries over the next period's assets. We then extend the standard model to have lotteries and establish the existence of an MPE with continuous decision rules. The models with and without lotteries are numerically compared, and it is shown that the model with lotteries behaves ...
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Signaling with Private Monitoring
A sender signals her private information to a receiver who privately monitors the sender’s behavior, while the receiver transmits his private inferences back through an imperfect public signal of his actions. In a linear-quadratic-Gaussian setup in continuous time, we construct linear Markov equilibria, where the state variables are the players’ beliefs up to the sender’s second order belief. This state is an explicit function of the sender’s past play—hence, her private information—which leads to separation through the second-order belief channel. We examine the implications of ...