Optimal risk sharing and borrowing constraints in a continuous-time model with limited commitment

We study a continuous-time version of the optimal risk-sharing problem with one-sided commitment. In the optimal contract, the agent's consumption is a time-invariant, strictly increasing function of a single state variable: the maximal level of the agent's income realized to date. We characterize this function in terms of the agent's outside option value function and the discounted amount of time in which the agent's income process is expected to reach a new to-date maximum. Under constant relative risk aversion we solve the model in closed-form: optimal consumption of the agent equals a constant fraction of his maximal income realized to date. In the complete-markets implementation of the optimal contract, the Alvarez-Jermann solvency constraints take the form of a simple borrowing constraint familiar from the Bewley-Aiyagari incomplete-markets models

Borrowing Constraint as an Optimal Contract

We study a continuous-time version of the optimal risk-sharing problem with one-sided commitment. In the optimal contract, the agent's consumption is non-decreasing and depends only on the maximal level of the agent's income realized to date. In the complete-markets implementation of the optimal contract, the Alvarez-Jermann solvency constraints take the form of a simple borrowing constraint familiar from the Bewley-Aiyagari incomplete-markets models. Unlike in the incomplete-markets models, however, the asset buffer stock held by the agent is negatively correlated with income.Borrowing constraint, limited commitment

Repeated Two-Sided Moral Hazard

In this paper I study a class of repeated two-sided moral hazard problems with discounting. I consider two agents who are involved in multiperiod, and possibly infinite-horizon, contractual relationships. In every period, the agents simultaneously take hidden actions, each of which independently affects the distribution of a separate random public signal. The realizations of the public signals jointly determine the output of a perishable final good, which the agents consume. This abstract framework can be used to analyze contractual relations within a variety of institutions, such as partnership firms, households, or cooperatives, in which bilateral moral hazard is an essential feature. I examine the nature of Pareto optimal contracts in this environment that respect both technological and informational constraints. After establishing the existence of optimal contracts, I show that every continuation contract of an optimal contract is itself optimal. Using this recursive property, next I derive a partial, but fairly general, characterization of optimal consumption allocations. It is an equation that links the ratio of marginal utilities of the agents in the current period to the same ratio in the next period. Moreover, optimal contracts imply that the sequence of ratios of marginal utilities in each period is a submartingale. I provide sufficient conditions for the submartingale to converge. Finally, using this result, I identify conditions under which one agent receives all surplus in the long run.

Competitive Risk Sharing Contracts with One-Sided Commitment

This paper analyzes dynamic equilibrium risk sharing contracts between profit-maximizing intermediaries and a large pool of ex-ante identical agents that face idiosyncratic income uncertainty that makes them heterogeneous ex-post. In any given period, after having observed her income, the agent can walk away from the contract, while the intermediary cannot, i.e. there is one-sided commitment. We consider the extreme scenario that the agents face no costs to walking away, and can sign up with any competing intermediary without any reputational losses. We demonstrate that not only autarky, but also partial and full insurance can obtain, depending on the relative patience of agents and financial intermediaries. Insurance can be provided because in an equilibrium contract an up-front payment effectively locks in the agent with an intermediary. We then show that our contract economy is equivalent to a consumption-savings economy with one-period Arrow securities and a short-sale constraint, similar to Bulow and Rogoff (1989). From this equivalence and our characterization of dynamic contracts it immediately follows that without cost of switching financial intermediaries debt contracts are not sustainable, even though a risk allocation superior to autarky can be achieved.Long-term contracts, Risk Sharing, Limited Commitment, Competition

Competitive Risk Sharing Contracts with One-Sided Commitment

This paper analyzes dynamic equilibrium risk sharing contracts between profit-maximizing intermediaries and a large pool of ex-ante identical agents that face idiosyncratic income uncertainty that makes them heterogeneous ex-post. In any given period, after having observed her income, the agent can walk away from the contract, while the intermediary cannot, i.e. there is one-sided commitment. We consider the extreme scenario that the agents face no costs to walking away, and can sign up with any competing intermediary without any reputational losses. We demonstrate that not only autarky, but also partial and full insurance can obtain, depending on the relative patience of agents and financial intermediaries. Insurance can be provided because in an equilibrium contract an up-front payment e.ectively locks in the agent with an intermediary. We then show that our contract economy is equivalent to a consumption-savings economy with one-period Arrow securities and a short-sale constraint, similar to Bulow and Rogo. (1989). From this equivalence and our characterization of dynamic contracts it immediately follows that without cost of switching financial intermediaries debt contracts are not sustainable, even though a risk allocation superior to autarky can be achieved.Long-term Contracts, Risk Sharing, Limited Commitment, Competition

Competitive Equilibria with Production and Limited Commitment

This paper studies a production economy with aggregate uncertainty where consumers have limited commitment on their financial liabilities. Markets are endogenously incomplete due to the fact that the borrowing constraints are determined endogenously. We first show that, if competitive financial intermediaries are allowed to set the borrowing limits, then the ones that prevent default will be an equilibrium outcome. The equilibrium allocations in this economy are not constrained efficient due to the fact that intermediaries do not internalize the adverse effects of capital on default incentives. We also isolate and quantifiy this new source of inefficiency by comparing the competitive equilibrium allocations to the constrained efficient ones both qualitatively and quantitatively. We tend to observe higher capital accumulation in the competitive equilibrium, implying that agents may enjoy higher (average) welfare in the long run than in the constrained efficient allocation.Enforcement Constraints, Intermediation, Risk Sharing, Capital Accumulation.

Credit and inflation under borrower’s lack of commitment

Here we investigate the existence of credit in a cash-in-advance economy where there are complete markets but for the fact that agents cannot commit to repay their debts. Defectors are banned from the credit market but they can use money balances for saving purposes. Without uncertainty, deflation crowds out credit completely. The equilibrium allocation, however, is efficient if the government deflates at the time preference rate. Efficiency can also be restored with positive inflation. For any non negative inflation rate below the optimal level, the volume of credit and the real interest rate increase with inflation. Our results hold when idiosyncratic uncertainty is introduced and households are sufficiently impatient but in one instance: efficiency cannot be restored if the deflation rate is nearby the rate of time preference. Our numerical examples suggest that the optimal inflation rate is not too large for reasonable levels of patience and risk aversion. Finally, we present a framework where the use of money arises endogenously and show that it is tantamount to our cash-in-advance framework. Our results hold in this modified environment

Competitive Risk Sharing Contracts with One-Sided Commitment

This paper analyzes dynamic equilibrium risk sharing contracts between profit-maximizing intermediaries and a large pool of ex-ante identical agents that face idiosyncratic income uncertainty that makes them heterogeneous ex-post. In any given period, after having observed her income, the agent can walk away from the contract, while the intermediary cannot, i.e. there is one-sided commitment. We consider the extreme scenario that the agents face no costs to walking away, and can sign up with any competing intermediary without any reputational losses. Contrary to intuition, we demonstrate that not only autarky, but also partial and full insurance can obtain, depending on the relative patience of agents and financial intermediaries. Insurance can be provided because in an equilibrium contract an up-front payment effectively locks in the agent with an intermediary. We then show that our contract economy is equivalent to a consumption-savings economy with one-period Arrow securities and a short-sale constraint, similar to Bulow and Rogoff (1989). From this equivalence and our characterization of dynamic contracts it immediately follows that without cost of switching financial intermediaries debt contracts are not sustainable, even though a risk allocation superior to autarky can be achieved.

Misallocation of Capital in a Model of Endogenous Financial Intermediation and Insurance

In this paper we analyze productivity and welfare losses from capital misallocation in a general equilibrium model of occupational choice and endogenous financial intermediation. We study the effects of borrowing and lending, insurance, and risk sharing on the optimal allocation of resources. We find that financial markets together with general equilibrium effects have large impact on entrepreneurs' entry and firm-size decisions. Efficiency gains are increasing in the quality of financial markets, particularly in their ability to alleviate a financing constraint by providing insurance against idiosyncratic risk.Financial markets and the macroeconomy; Occupational choice; Personal income and wealth and their distributions