Linda Cohen, Steven Matthews; Constrained Plott Equilibria, Directional Equilibria and Global Cycling Sets, The Review of Economic Studies, Volume 47, Issu

We study different solutions to a simple one-dimensional linear quadratic game with a large number of private agents and a government. A “time-consistent” solution is defined as a solution to the Hamilton-Jacobi-Bellman equation, i.e. as a policy for which the government has noprecommitment capability. This solution is compared to a policy where the government has an “instantaneous” pre-commitment, i.e. an equilibrium in which the government has a period by period leadership. In both cases, we show how control theory should be applied to calculate the equilibrium and how to relate these equilibria to the differential game literature.

Abstract How do consumer credit markets affect the allocation of workers to firms, output, and labour productivity? We address this question in two steps. First, we use new micro-data to estimate empirical elasticities of job search patterns to credit. Second, we estimate our novel theory of sorting under risk aversion to match these elasticities, and then we conduct aggregate counterfactuals. Empirically, we show that an increase in credit limits worth 10% of prior annual earnings allows individuals to take 0.33 weeks longer to find a job. Conditional on finding a job, they earn 1.85% more and work at higher paying firms. We also find that young and high-utilization individuals are more responsive to credit. Theoretically, we integrate risk aversion and borrowing into a model with worker and firm heterogeneity. We estimate the model to match our new empirical elasticities, and we then measure how the credit expansion from 1964 to 2004 affected sorting and output. Sorting improves as credit expands since constrained workers—in particular constrained, young, high human capital workers—find more capital-intensive jobs.