Efficient allocations with moral hazard and hidden borrowing and lending: A recursive formulation

Abstract

We propose a tractable recursive framework to study the optimal allocation of consumption and e¤ort in a dynamic setting with moral hazard where agents have secret access to the credit market or to storage. The recursive structure is based on a generalized …rst order approach, whose validity must be veri…ed ex-post. Thanks to the recursive formulation of the optimal contract, the veri…cation procedure turns out to be numerically parsimonious as it can be performed using standard dynamic programming techniques with only one endogenous state variable: The agent's level of assets. We study the performance of our ex-post veri…cation test in practice by solving numerically three representative in…nite horizon examples.

Structural Experimentation to Distinguish between Models of Risk Sharing with Frictions in Rural Paraguay

“…Ábrahám et al (2011) give sufficient conditions in a model with hidden investments such as Problem 2, but with only two periods. No conditions sufficient to guarantee the validity of the first order approach in the infinite period case are known, but Werning (2001) andÁbrahám andPavoni (2008) argue for an approach which assumes the validity of the first order approach to compute proposed solutions, and verifies the correctness of these solutions. In this same spirit, we offer the following first order characterization of the solution to Problem 2.…”

Unemployment insurance with hidden savings

“…Our paper is related to both Werning [9,10] and Abraham and Pavoni [1,2], who use the first-order approach to study models with hidden savings and borrowing. Briefly speaking, the first-order approach studies a relaxed problem, which replaces the incentive constraints in the original problem with some first-order conditions of the agent.…”

“…1 The fundamental trade-off is between search time and quality of match (in terms of wages). They find that the optimal contract has constant benefits (for CARA utility, and approximately so for constant relative risk-aversion (CRRA) utility), and keeps the agent on the Euler equation.…”

Quantitative Macroeconomics with Heterogeneous Households

“…Caselli and Ventura (2000) add heterogeneity in initial tastes and skills, and characterize the joint evolution of distributions and averages for consumption, income, and wealth. 2 Maliar and Maliar (2003) is another example. They extend the Chatterjee environment to allow for id-Relying on the assumption of complete markets is unattractive for a number of reasons.…”