matching08final - 1 Labor Market Matching Models The Hansen...

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1 Labor Market Matching Models The Hansen lotteries model is not a great framework to understand per- sistent equilibrium unemployment (the lottery is iid). The seminal work to understand equilibrium unemployment is Mortensen (1982) and Pissarides (1990). The material here is closer to Cole and Rogerson (1999) and Ljunqvist and Sargent (Ch. 26.3). Th ek eyadd i t iontoth emod e l sw ehav ea l r eadys tud i edi sth ein t ro - duction of a matching technology that takes job seekers (those who are unemployed) and vacancies as inputs and the output is a match. The typ- ical technology assumed is CRS, so matches are increasing in job seekers and vacancies. 1.1 Mortensen-Pissarides 1.1.1 Simplest Environment Pop: A unit measure of workers and a continuum of managers. Prefs: Both workers and managers are risk neutral and discount the future at rate β. Prod Tech: Managers own a technology y t = z t h t where h t { 0 , 1 } is worker input. If a manager is matched (hires) with a worker, the pair generates output z t but if the manager does not hire a worker, they generate zero output. Output is nonstochastic since we will assume z t = z . If a manager is not matched with a worker, it costs c to post a vacancy (job opening). If a worker is not matched with a manager (i.e. if the worker is unem- ployed), he receives the utility b<z (this could be home production or the “replacement rate”). Once a manager and a worker are matched, there is an exogenous probability δ that the technology breaks down and the match is de- stroyed. There is free entry by managers. Match Tech: The measure of successful matches in a period is given by M ( u t ,v t ) where u t and v t are aggregate unemployment and vacancies, respec- tively. Since there is a unit measure of workers, 1= u t + n t where n t is aggregate per capita employment. 1
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We will take it to be a Cobb-Douglas technology M ( u t ,v t )= u α t v 1 α t , which is increasing in both arguments, homogeneous of degree 1. The parameter α measures the elasticity of the matching function with respect to unemployment. 1 The assumption of constant returns to scale is consistent with em- pirical f ndings by Blanchard and Diamond (1989) “The Beveridge Curve”, Brookings Papers on Economic Activity, p. 1-60. They found evidence for CRS by regressing data for log(new hires), a mea- sure of matches, on data for log unemployment and log vacancies and testing that the coe cients were α and (1 α ) respectively. The probability of f lling a vacancy is denoted q ( θ t M ( u t t ) v t = θ α t (1) where θ t = v t u t is a measure of “labor market tightness”. By this de f nition, if unemployment is low or vacancies (job openings) is high, the labor market it tight (it is hard for “ f rms” to f nd workers). Since q 0 ( θ t αθ ( α +1) t < 0 , we know that if the labor market gets tighter, the probability of f lling a job falls.
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matching08final - 1 Labor Market Matching Models The Hansen...

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