Stationary measures for some Markov chain models in ecology and economics

Summary. Let continuous, exists in for x in . Let be an i.i.d. sequence from F and X₀ be a nonnegative random variable independent of . Let be the Markov chain generated by the iteration of random maps by . Such Markov chains arise in population ecology and growth models in economics. This paper studies the existence of nondegenerate stationary measures for {X_n}. A set of necessary conditions and two sets of sufficient conditions are provided. There are some convergence results also. The present paper is a generalization of the work on random logistics maps by Athreya and Dai (2000).Received: 20 March 2002, Revised: 4 December 2002, JEL Classification Numbers: C22, D9.The author wishes to thank Professor Mukul Majumdar and the referees for several useful suggestions.     

Unsecured credit markets are not insurance markets

We study the extent to which unsecured credit markets have altered the transmission of increased income risk to consumption variability over the past several decades. We find that unsecured credit markets pass through increased income risk to consumption, irrespective of bankruptcy policy and the information possessed by lenders. If risk sharing has indeed improved over this period, the reasons do not therefore lie in the unsecured credit market.     

On the efficiency of ‘single window’

In many countries, the process of obtaining government approval for different projects involves interaction with multiple government agencies at various levels. This often makes the approval process inefficient by unnecessary lengthening it. In this paper we study the effect of a re-organization of the approval process towards making it a single window clearance system, on the efficiency of the entire process. We have used the expected queue length and the expected waiting time in the system at the stochastic steady state as measures of inefficiency of an approval system.     

Self-employment rates and business size: the roles of occupational choice and credit market frictions

Self-employment rates and project size vary greatly across countries. The main message of this paper is that these broad regularities are consistent with an environment in which a common self-employment technology is available worldwide, but where (a) financial intermediation costs and (b) alternatives in “paid” work differ greatly. Our model indicates that alternatives in paid work are crucial for explaining self-employment rates, whereas high financial intermediation costs primarily affect the scale of projects. We also show that credit use is not informative for predicting either rates of self-employment or the scale of self-employment projects.     

A note on closing the windows: Some lessons from queuing theory

Consider two departments of a government each serving customers of a particular type. We explore conditions under which a reorganization leading to both departments serving both types of customers leads to an enhancement of "efficiency" defined in terms of the expected queue size in a stochstic equilibrium.     

Unsecured debt with public insurance: From bad to worse

In U.S. data, income interruptions, the receipt of public insurance, and the incidence of personal bankruptcy are all closely related. The central contribution of this paper is to evaluate bankruptcy protection and public insurance in a unified setting where each program alters incentives in the other. Our analysis delivers two striking conclusions. First, we find that U.S. personal bankruptcy law is an important barrier that prevents the public insurance system from improving welfare. Second, contrary to popular belief, we find that increases in the generosity of public insurance will lead to more, not less, bankruptcy.     

BANKRUPTCY AND DELINQUENCY IN A MODEL OF UNSECURED DEBT

This article documents and interprets a fact central to the dynamics of informal consumer debt default. We observe that for individuals 60– 90 days late on payments, (i) 85% make payments during the next quarter, and (ii) 40% reduce their debt. To understand these facts, we develop a quantitative model of debt delinquency and bankruptcy. Our model reproduces the dynamics of delinquency and suggests an interpretation of the data in which lenders frequently reset loan terms for delinquent borrowers, typically offering partial debt forgiveness, instead of a blanket imposition of the “penalty rates” most unsecured credit contracts specify.     

Estimating the stationary distribution of a Markov chain

Summary. Let be a Markov chain with a unique stationary distribution . Let h be a bounded measurable function. Write and . This paper explores conditions for the consistency and asymptotic normality of the estimate of of assuming the existence of a solution to the Poisson equation . Our framework covers the case of nonirreducible Markov chains arising in many growth models in economics. Received: October 8, 2001; revised version: April 8, 2002 RID="*" ID="*" Thanks are due to Professors Rabi Bhattacharya, Nicholas Kiefer and Timothy Vogelsang on an earlier draft for helpful conversations, and a referee for insightful comments. Correspondence to: M.Majumdar