Matching Functions
Stocks and flows

Standard matching function models of the labour market, in which stocks of vacancies and unemployed relate to each other, assume in effect that those looking for work search at random, while in practice most unemployed workers will check newspapers and job centres systematically for information on suitable vacancies. In Discussion Paper No. 939, Melvyn Coles develops a matching function based on microeconomic behaviour with directly testable implications, which incorporates these `information channels' and worker heterogeneity. In this framework, the unemployed have already sampled the stock of vacancies and not found a suitable match, so the stock of unemployed matches the flow of new vacancies (and the stock of `old' vacancies similarly matches the flow of newly unemployed workers). `New' vacancies are also much more likely than `old' ones to match the current stock of unemployed, who have not yet sampled them. CobbDouglas matching functions are also misspecified and empirical work based on them may indicate the presence of decreasing returns, even when such returns are in fact increasing.

This framework also provides an important pointer for future empirical work. Increasing returns to matching may account for the pattern of ruralurban migration that arises from industrialization, which ceases when the congestion costs of living in cities exceed the returns to greater matching (specialization) there. This matching paradigm may also be generalized to other markets such as antique furniture and rental accommodation, in which prospective purchasers ignore the pieces or properties they have already seen, while new entrants to the market initially select those warranting closer inspection from the entire currently available stock on the market.

Understanding the Matching Function: The Role of Newspapers and Job Agencies
Melvyn G Coles

Discussion Paper No. 939, April 1994 (HR)