Matching theory (macroeconomics)
Encyclopedia
In macroeconomics
, matching theory, also known as search and matching theory,
is a mathematical framework attempting to describe 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 evolved from an earlier framework called 'search theory
'. Where search theory studies the microeconomic decision of an individual searcher, matching theory studies the macroeconomic outcome when one or more types of searchers interact.
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. Mortensen and Pissarides, together with Peter A. Diamond
, won the 2010 Nobel Prize in Economics for 'fundamental contributions to search and matching theory'.
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
).
, Robert Shimer
has demonstrated that standard versions of matching models predict much smaller fluctuations in unemployment.
Macroeconomics
Macroeconomics is a branch of economics dealing with the performance, structure, behavior, and decision-making of the whole economy. This includes a national, regional, or global economy...
, matching theory, also known as search and matching theory,
is a mathematical framework attempting to describe 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
Marriage
Marriage is a social union or legal contract between people that creates kinship. It is an institution in which interpersonal relationships, usually intimate and sexual, are acknowledged in a variety of ways, depending on the culture or subculture in which it is found...
. Matching theory evolved from an earlier framework called 'search theory
Search theory
In microeconomics, search theory studies buyers or sellers who cannot instantly find a trading partner, and must therefore search for a partner prior to transacting....
'. Where search theory studies the microeconomic decision of an individual searcher, matching theory studies the macroeconomic outcome when one or more types of searchers interact.
One of the founders of matching theory is Dale T. Mortensen
Dale T. Mortensen
Dale Thomas Mortensen is an American economist. He received his B.A. in economics from Willamette University and his Ph.D. in Economics from Carnegie Mellon University. He is a member of the Beta Theta Pi fraternity...
of Northwestern University
Northwestern University
Northwestern University is a private research university in Evanston and Chicago, Illinois, USA. Northwestern has eleven undergraduate, graduate, and professional schools offering 124 undergraduate degrees and 145 graduate and professional degrees....
. A textbook treatment of the matching approach to labor markets is Christopher A. Pissarides
Christopher A. Pissarides
Christopher Antoniou Pissarides F.B.A. is a Cypriot economist. He currently holds the Norman Sosnow Chair in Economics at the London School of Economics. His research interests focus on several topics of macroeconomics, notably labor, economic growth, and economic policy. In 2010, he was awarded...
' book Equilibrium Unemployment Theory. Mortensen and Pissarides, together with Peter A. Diamond
Peter A. Diamond
Peter Arthur Diamond is an American economist known for his analysis of U.S. Social Security policy and his work as an advisor to the Advisory Council on Social Security in the late 1980s and 1990s. He was awarded the Nobel Memorial Prize in Economic Sciences in 2010, along with Dale T. Mortensen...
, won the 2010 Nobel Prize in Economics for 'fundamental contributions to search and matching theory'.
The matching function
A matching function is a mathematical relationship that describes the formation of new relationships (also called 'matches') from unmatched agentsAgent (economics)
In economics, an agent is an actor and decision maker in a model. Typically, every agent makes decisions by solving a well or ill defined optimization/choice problem. The term agent can also be seen as equivalent to player in game theory....
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
Production function
In microeconomics and macroeconomics, a production function is a function that specifies the output of a firm, an industry, or an entire economy for all combinations of inputs...
. 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 forceLabor force
In economics, a labor force or labour force is a region's combined civilian workforce, including both the employed and unemployed.Normally, the labor force of a country consists of everyone of working age In economics, a labor force or labour force is a region's combined civilian workforce,...
in period
. Then given the matching function described above, the dynamics of employment over time would be given byFor simplicity, many studies treat
as a fixed constant. But the fraction of workers separating per period of time can be determined endogenouslyEndogeneity (economics)
In an econometric model, a parameter or variable is said to be endogenous when there is a correlation between the parameter or variable and the error term. Endogeneity can arise as a result of measurement error, autoregression with autocorrelated errors, simultaneity, omitted variables, and sample...
if we assume that the value of being matched varies over time for each worker-firm pair (due, for example, to changes in productivity
Productivity
Productivity is a measure of the efficiency of production. Productivity is a ratio of what is produced to what is required to produce it. Usually this ratio is in the form of an average, expressing the total output divided by the total input...
).
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 individuals
- 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 cycleBusiness cycle
The term business cycle refers to economy-wide fluctuations in production or economic activity over several months or years...
, Robert Shimer
Robert Shimer
Robert Shimer is an American macroeconomist and labor economist who currently holds the Alvin H. Baum Chair in the Economics Department of the University of Chicago. He is an editor of the Journal of Political Economy. His research focuses on the search and matching approach to labor economics...
has demonstrated that standard versions of matching models predict much smaller fluctuations in unemployment.
See also
- Search theorySearch theoryIn microeconomics, search theory studies buyers or sellers who cannot instantly find a trading partner, and must therefore search for a partner prior to transacting....
- Beveridge curveBeveridge curveA Beveridge curve, or UV-curve, is a graphical representation of the relationship between unemployment and the job vacancy rate . It typically has vacancies on the vertical axis and unemployment on the horizontal...
- Labor economics
- Monetary economics
- Nash bargaining game