Matching theory (economics) 1

Matching theory (economics)Not to be confused with the matching approach in applied statistics.In economics, matching theory, also known as search and matching theory, is a mathematical frameworkattempting to describe the formation of mutually beneficial relationships over time.Matching theory has been especially influential in labor economics, where it has been used to describe the formationof new jobs, as well as to describe other human relationships like marriage. Matching theory evolved from an earlierframework 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.[citation needed] Itoffers a way of modeling markets in which frictions prevent instantaneous adjustment of the level of economicactivity. Among other applications, it has been used as a framework for studying frictional unemployment.One of the founders of matching theory is Dale T. Mortensen of Northwestern University. A textbook treatment ofthe 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'.[1]

The matching functionA 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, matchingfunctions are sometimes assumed to have the following 'Cobb–Douglas' form:

where , , and are positive constants. In this equation, represents the number of unemployed job seekersin the economy at a given time , and is the number of vacant jobs firms are trying to fill. The number of newrelationships (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 usuallyrepresents the production of goods and services from inputs like labor and capital, a matching function represents theformation of new relationships from the pools of available unmatched individuals. Estimates of the labor marketmatching 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 tocalculate the change in employment from one period to the next we must add the formation of new matches andsubtract off the separation of old matches. A period may be treated as a week, a month, a quarter, or some otherconvenient period of time, depending on the data under consideration. (For simplicity, we are ignoring the entry ofnew workers into the labor force, and death or retirement of old workers, but these issues can be accounted for aswell.) Suppose we write the number of workers employed in period as , where is the laborforce in period . Then given the matching function described above, the dynamics of employment over time wouldbe given by

For simplicity, many studies treat as a fixed constant. But the fraction of workers separating per period of timecan be determined endogenously if we assume that the value of being matched varies over time for each worker-firmpair (due, for example, to changes in productivity).

Matching theory (economics) 2

ApplicationsMatching 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

ControversyMatching theory has been widely accepted as one of the best available descriptions of the frictions in the labormarket, but some economists have recently questioned its quantitative accuracy. While unemployment exhibits largefluctuations over the business cycle, Robert Shimer has demonstrated that standard versions of matching modelspredict much smaller fluctuations in unemployment.

References[1] Economic Prize Committee of the Royal Swedish Academy of Sciences, 'Scientific Background', page 2. (http:/ / www. nobelprize. org/

nobel_prizes/ economics/ laureates/ 2010/ advanced-economicsciences2010. pdf)

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Article Sources and ContributorsMatching theory (economics)  Source: http://en.wikipedia.org/w/index.php?oldid=607020532  Contributors: Bender235, Byelf2007, CronopioFlotante, Dreispt, John Quiggin, Karl432,Kazvorpal, Kjuto, Lihaas, Omnipaedista, Rinconsoleao, Rjwilmsi, Zaslav, 3 anonymous edits

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