On the Efficiency of Matching and Related Models of Search and Unemployment by Arthur J. Hosios

On the Efficiency of Matching and Related Models of Search and Unemployment

Arthur J. Hosios

The Review of Economic Studies

Vol. 57, No. 2 (Apr., 1990), pp. 279-298

Published by: Oxford University Press

Stable URL: http://www.jstor.org/stable/2297382

Abstract:  This paper describes a simple framework for evaluating the allocative performance of economies characterized by trading frictions and unemployment. This framework integrates the normative results of earlier Diamond-Mortensen-Pissarides bilateral matching-bargaining models of trade coordination and price-setting, and consists of a set of general conditions for constrained Pareto efficient resource allocation that are applicable to conventional natural rate models. To illustrate, several conventional models of the labour market are reformulated as matching- bargaining problems and analyzed using this framework.

Hosios (1990) derives the conditions which the matching function and surplus-sharing rule must satisfy to be internalized. Intuitively, how the externalities of congestion in the labor market, represented by the matching function ($m(u,v)$), and the way the surplus (economic profits) is shared has to exactly balance. In the literature, these conditions are known as the Hosios' Condition. 

Hosios' Conditions + Pareto Efficiency 

imply 

Agent's social contributions = Private Gains  

  These conditions are:

Entry/Exit Externalities:

Entry to be efficient requires that unattached agents of each type received their social marginal profit. Which is equivalent to say that the share of unemployed workers and vacant firms in the surplus of the match is equal to the elasticity of matching function with respect  to the search input (unemployed workers and vacant firms):

$m_{u}=\gamma \frac{m(u,v)}{u}$

$m_{v}=(1-\gamma) \frac{m(u,v)}{v}$

Job Acceptance:

Sharing rule and the matching technology must satisfy:

$m_{u}+m_{v}=\gamma \frac{m(u,v)}{u}+(1-\gamma) \frac{m(u,v)}{v}$

Search/Recruitment externality:

To be efficient has to equate the marginal social and private benefits for matching of search and recruitment. 

Assessing the Economic Effects of Environmental Regulations: A General Equilibrium Approach (2013) by Richard Rogerson

"Abstract: I describe standard macroeconomic methods for assessing the effects of policy on allocations and welfare. I then embed a version of a benchmark industry equilibrium model into an otherwise standard version of the one sector growth model and describe how this setting provides a useful structure for the analysis of environmental regulations that impact on one particular sector but which might reasonably have important aggregate effects."

 Key contributions:
It is a comprehensive review of two standard macroeconomic models that are commonly used to analyze policies and welfare in any context: A general equilibrium, the one sector growth model, and a partial equilibrium, the industry equilibrium model based on Hopenhayn(1992). And then he combines the models. Environmental Regulations are an application on where you can use this type of frameworks.

Key weaknesses:
One key effect that is recognized in the literature as an important economic effect of environmental regulations is the welfare effects of job layoffs and the transitional costs of finding a new job. Is important to acknowledge that he recognizes it, and mentions, in section 4.4, as the natural extension of his paper.

Possible Extensions:
Given what I expressed in the last point and as he mentions in the paper the most important extension is to include features that help to measure the welfare effects of  the sectoral reallocation of workers.