Matching theory (economics)

Last updated

In economics, matching theory, also known as search and matching theory, is a mathematical framework attempting 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 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.[ citation needed ] 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.

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. [1] Mortensen and Pissarides, together with Peter A. Diamond, were awarded the 2010 Nobel Prize in Economics for 'fundamental contributions to search and matching theory'. [2]

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, . [3]

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). [4]


Matching theory has been applied in many economic contexts, including:


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. [7]

See also

Related Research Articles

Labour economics Study of the markets for wage labour

Labour economics seeks to understand the functioning and dynamics of the markets for wage labour. Labour is a commodity that is supplied by labourers in exchange for a wage paid by demanding firms. Because these labourers exist as parts of a social, institutional, or political system, labour economics is often regarded as a sociology or political science.

Macroeconomics Study of an economy as a whole

Macroeconomics is a branch of economics dealing with performance, structure, behavior, and decision-making of an economy as a whole. For example, using interest rates, taxes, and government spending to regulate an economy’s growth and stability. This includes regional, national, and global economies. According to a 2018 assessment by economists Emi Nakamura and Jón Steinsson, economic "evidence regarding the consequences of different macroeconomic policies is still highly imperfect and open to serious criticism."

A minimum wage is the lowest remuneration that employers can legally pay their employees—the price floor below which employees may not sell their labor. Most countries had introduced minimum wage legislation by the end of the 20th century. Because minimum wages increase the cost of labor, companies often try to avoid minimum wage laws by using gig workers, by moving labor to locations with lower or nonexistent minimum wages, or by automating job functions.

Full employment is a situation in which there is no cyclical or deficient-demand unemployment. Full employment does not entail the disappearance of all unemployment, as other kinds of unemployment, namely structural and frictional, may remain. For instance, workers who are "between jobs" for short periods of time as they search for better employment are not counted against full employment, as such unemployment is frictional rather than cyclical. An economy with full employment might also have unemployment or underemployment where part-time workers cannot find jobs appropriate to their skill level, as such unemployment is considered structural rather than cyclical. Full employment marks the point past which expansionary fiscal and/or monetary policy cannot reduce unemployment any further without causing inflation.

Rational expectations

In economics, "rational expectations" are model-consistent expectations, in that agents inside the model are assumed to "know the model" and on average take the model's predictions as valid. Rational expectations ensure internal consistency in models involving uncertainty. To obtain consistency within a model, the predictions of future values of economically relevant variables from the model are assumed to be the same as that of the decision-makers in the model, given their information set, the nature of the random processes involved, and model structure. The rational expectations assumption is used especially in many contemporary macroeconomic models.

New Keynesian economics

New Keynesian economics is a school of macroeconomics that strives to provide microeconomic foundations for Keynesian economics. It developed partly as a response to criticisms of Keynesian macroeconomics by adherents of new classical macroeconomics.

Phillips curve Single-equation economic model relating wages to unemployment

The Phillips curve is a single-equation economic model, named after William Phillips, hypothesizing an inverse relationship between rates of unemployment and corresponding rates of rises in wages that result within an economy. Stated simply, decreased unemployment, in an economy will correlate with higher rates of wage rises. Phillips did not himself state there was any relationship between employment and inflation; this notion was a trivial deduction from his statistical findings. Paul Samuelson and Robert Solow made the connection explicit and subsequently Milton Friedman and Edmund Phelps put the theoretical structure in place. In so doing, Friedman was to successfully predict the imminent collapse of Phillips' a-theoretic correlation.

In Keynesian economics, underemployment equilibrium is a situation with a persistent shortfall relative to full employment and potential output so that unemployment is higher than at the NAIRU or the "natural" rate of unemployment.

James Meade British economist who won Nobel in Economics in 1977

James Edward Meade, was a British economist and winner of the 1977 Nobel Memorial Prize in Economic Sciences jointly with the Swedish economist Bertil Ohlin for their "pathbreaking contribution to the theory of international trade and international capital movements".

Frictional unemployment is a type of unemployment. It is sometimes called search unemployment and can be based on the circumstances of the individual. It is time spent between jobs when a worker is searching for a job or transferring from one job to another. Frictional unemployment is one of the three broad categories of unemployment, the others being structural unemployment and cyclical unemployment. A person may be looking for a job change for better opportunities, services, salary and wages, or because of dissatisfaction with the previous job. Strikes by trade unions also give rise to frictional unemployment.

Beveridge curve Graphical representation of the relationship between unemployment and the job vacancy rate

A Beveridge curve, or UV curve, is a graphical representation of the relationship between unemployment and the job vacancy rate, the number of unfilled jobs expressed as a proportion of the labour force. It typically has vacancies on the vertical axis and unemployment on the horizontal. The curve, named after William Beveridge, is hyperbolic-shaped and slopes downward, as a higher rate of unemployment normally occurs with a lower rate of vacancies. If it moves outward over time, a given level of vacancies would be associated with higher and higher levels of unemployment, which would imply decreasing efficiency in the labour market. Inefficient labour markets are caused by mismatches between available jobs and the unemployed and an immobile labour force.

Dale T. Mortensen American economist

Dale Thomas Mortensen was an American economist and Nobel laureate.

Christopher A. Pissarides

Sir Christopher Antoniou Pissarides is a Cypriot economist. He is the School Professor of Economics & Political Science and Regius Professor of Economics at the London School of Economics, and Professor of European Studies at the University of Cyprus. His research focuses on topics of macroeconomics, notably labour, economic growth, and economic policy. In 2010, he was awarded the Nobel Prize in Economics, jointly with Peter A. Diamond and Dale Mortensen, "for their analysis of markets with theory of search frictions."

Peter 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 and Christopher A. Pissarides. He is an Institute Professor at the Massachusetts Institute of Technology. On June 6, 2011, he withdrew his nomination to serve on the Federal Reserve's board of governors, citing intractable Republican opposition for 14 months.

Tournament theory is the theory in personnel economics used to describe certain situations where wage differences are based not on marginal productivity but instead upon relative differences between the individuals. This theory was invented by economists Edward Lazear and Sherwin Rosen.

Employment protection legislation (EPL) includes all types of employment protection measures, whether grounded primarily in legislation, court rulings, collectively bargained conditions of employment, or customary practice. The term is common among circles of economists. Employment protection refers both to regulations concerning hiring and firing.

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.

Étienne Wasmer French professor and economist (born 1970)

Étienne Wasmer is a French professor and economist currently holding a Professorship at New York University in Abu Dhabi. Wasmer mainly focuses on the fields of labor economics, job search theory, discrimination and human capital. He teaches microeconomics and labor economics.

NAIRU Level of unemployment below which inflation would be expected to rise

Non-accelerating inflation rate of unemployment (NAIRU) is a theoretical level of unemployment below which inflation would be expected to rise. It was first introduced as NIRU by Franco Modigliani and Lucas Papademos in 1975, as an improvement over the "natural rate of unemployment" concept, which was proposed earlier by Milton Friedman.

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 was an editor of the Journal of Political Economy from 2004 to 2012. His research focuses on the search and matching approach to labor economics. He is especially known for arguing that the standard labor market matching model predicts fluctuations in the unemployment rate much smaller than those actually observed over the business cycle, an observation which has sometimes been called the Shimer puzzle. His book Labor Markets and Business Cycles was published in 2010 by Princeton University Press, and was recommended by Robert Hall:


  1. 1 2 Pissarides, Christopher (2000). Equilibrium Unemployment Theory (2nd ed.). MIT Press. ISBN   978-0-262-16187-9.
  2. Economic Prize Committee of the Royal Swedish Academy of Sciences, 'The Sveriges Riksbank Prize in Economic Sciences in Memory of Alfred Nobel 2010'
  3. Petrongolo, Barbara; Pissarides, Christopher (2001). "Looking into the black box: a survey of the matching function" (PDF). Journal of Economic Literature. 39 (2): 390–431. doi:10.1257/jel.39.2.390. JSTOR   2698244.
  4. 1 2 Mortensen, Dale; Pissarides, Christopher (1994). "Job creation and job destruction in the theory of unemployment". Review of Economic Studies . 61 (3): 397–415. doi:10.2307/2297896. JSTOR   2297896.
  5. Haan, Wouter den; Ramey, Garey; Watson, Joel (2003). "Liquidity flows and the fragility of business enterprises" (PDF). Journal of Monetary Economics . 50 (6): 1215–1241. doi:10.1016/S0304-3932(03)00077-1. S2CID   10864047.
  6. Kiyotaki, Nobuhiro; Wright, Randall (1993). "A search-theoretic approach to monetary economics". American Economic Review . 83 (1): 63–77. JSTOR   2117496.
  7. Shimer, Robert (2005). "The cyclical behavior of equilibrium unemployment and vacancies". American Economic Review. 95 (1): 25–49. CiteSeerX . doi:10.1257/0002828053828572.