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Matching theory (macroeconomics)
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In macroeconomics, matching theory, also known as search and matching theory,
is a mathematical framework describing the formation of mutually beneficial relationships
over time. It offers a way of modeling markets in which frictions prevent instantaneous adjustment of the level of economic activity. Among other applications, it has been used as a framework for studying frictional unemployment.
The key element that distinguishes matching theory from other approaches to
macroeconomic modeling is the presence of a matching function.
Matching theory has been especially influential in labor economics,
where it has been used to describe the formation of new jobs, as well as to describe other
human relationships like marriage.
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Encyclopedia
In macroeconomics, matching theory, also known as search and matching theory,
is a mathematical framework describing the formation of mutually beneficial relationships
over time. It offers a way of modeling markets in which frictions prevent instantaneous adjustment of the level of economic activity. Among other applications, it has been used as a framework for studying frictional unemployment.
The key element that distinguishes matching theory from other approaches to
macroeconomic modeling is the presence of a matching function.
Matching theory has been especially influential in labor economics,
where it has been used to describe the formation of new jobs, as well as to describe other
human relationships like marriage. Matching theory is closely related to an earlier framework
called search theory which is somewhat more commonly applied in microeconomics.
One of the founders of matching theory is Dale T. Mortensen of Northwestern University.
A textbook treatment of the matching approach to labor markets is Christopher A. Pissarides'
book Equilibrium Unemployment Theory.
The matching function
A matching function is a mathematical relationship
that describes the formation of new relationships (also called 'matches')
from unmatched agents of the appropriate types.
For example, in the context of job formation, matching functions are sometimes assumed
to have the following 'Cobb-Douglas' form:
where , , and are positive constants.
In this equation, represents the number of unemployed
job seekers in the economy at a given time , and
is the number of vacant jobs firms are trying to fill.
The number of new relationships (matches) created (per unit of time) is given by
.
A matching function is in general analogous to a production function.
But whereas a production function usually represents the production of
goods and services from inputs like labor and capital, a matching
function represents the formation of new relationships from the pools of available
unmatched individuals. Estimates of the labor market matching function suggest that it has
constant returns to scale, that is, .
If the fraction of jobs that separate (due to firing, quits, and so forth)
from one period to the next is ,
then to calculate the change in employment from one period to the next we must
add the formation of new matches and subtract off the separation of old matches.
A period may be treated as a week, a month, a quarter, or some other convenient period of time,
depending on the data under consideration. (For simplicity, we are ignoring the entry
of new workers into the labor force, and death or retirement of old workers,
but these issues can be accounted for as well.)
Suppose we write the number of workers employed in period as ,
where is the labor force in period .
Then given the matching function described above,
the dynamics of employment over time would be given by
For simplicity, many studies treat as a fixed constant.
But the fraction of workers separating per period of time can be determined
endogenously if we assume that the value of being matched
varies over time for each worker-firm pair (due, for example, to changes
in productivity).
Applications
Matching theory has been applied in many economic contexts, including:
- Formation of jobs, from unemployed workers and vacancies opened by firms
- Formation of marriages, from unmatched men and women
- Allocation of loans from banks to entrepreneurs
- The role of money in facilitating sales when sellers and buyers meet
Controversy
Matching theory has been widely accepted as one of the best available descriptions
of the frictions in the labor market, but some economists
have recently questioned its quantitative accuracy. While unemployment exhibits large
fluctuations over the business cycle, Robert Shimer has demonstrated that
standard versions of matching models predict much smaller fluctuations in
unemployment.
See also
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