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| {{Hatnote|Not to be confused with the [[Matching (statistics)|matching]] approach in applied statistics.}}
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| 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.
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| 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|date=February 2012}} 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 [[Unemployment types#Frictional unemployment|frictional unemployment]].
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| 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''.<ref name=P2000>{{cite book |last=Pissarides |first=Christopher |year=2000 |title=Equilibrium Unemployment Theory |edition=2nd |location= |publisher=MIT Press |isbn=0-262-16187-7 }}</ref> Mortensen and Pissarides, together with [[Peter A. Diamond]], won the 2010 [[Nobel Prize in Economics]] for 'fundamental contributions to search and matching theory'.<ref>[http://www.nobelprize.org/nobel_prizes/economics/laureates/2010/advanced-economicsciences2010.pdf Economic Prize Committee of the Royal Swedish Academy of Sciences, 'Scientific Background', page 2.]</ref>
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| ==The matching function==
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| A matching function is a mathematical relationship that describes the formation of new relationships (also called 'matches') from unmatched [[Agent (economics)|agents]] of the appropriate types. For example, in the context of job formation, matching functions are sometimes assumed to have the following '[[Cobb–Douglas production function|Cobb–Douglas]]' form:
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| :<math>m_t \; = \; M(u_t,v_t) \; = \; \mu u_t^a v_t^b</math>
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| where <math>\,\mu\,</math>, <math>\,a\,</math>, and <math>\,b\,</math> are positive constants.
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| In this equation, <math>\,u_t\,</math> represents the number of unemployed job seekers in the economy at a given time <math>\,t\,</math>, and <math>\,v_t\,</math> is the number of [[Vacancy (economics)|vacant jobs]] firms are trying to fill. The number of new relationships (matches) created (per unit of time) is given by <math>\,m_t\,</math>.
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| 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, <math>a+b\approx 1</math>.<ref>{{cite journal |first=Barbara |last=Petrongolo |first2=Christopher |last2=Pissarides |year=2001 |title=Looking into the black box: a survey of the matching function |journal=Journal of Economic Literature |volume=39 |issue=2 |pages=390–431 |doi= |jstor=2698244 }}</ref>
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| If the fraction of jobs that separate (due to firing, quits, and so forth) from one period to the next is <math>\,\delta\,</math>,
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| 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 <math>\,t\,</math> as <math>\,n_t=L_t-u_t\,</math>, where <math>\,L_t\,</math> is the [[labor force]] in period <math>\,t\,</math>. Then given the matching function described above, the dynamics of employment over time would be given by
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| :<math>n_{t+1} \; = \mu u_t^a v_t^b + (1-\delta)n_t</math>
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| For simplicity, many studies treat <math>\,\delta\,</math> 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]]).<ref name=MP94>{{cite journal |first=Dale |last=Mortensen |first2=Christopher |last2=Pissarides |year=1994 |title=Job creation and job destruction in the theory of unemployment |journal=[[Review of Economic Studies]] |volume=61 |issue=3 |pages=397–415 |doi=10.2307/2297896 }}</ref>
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| ==Applications==
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| Matching theory has been applied in many economic contexts, including:
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| *Formation of jobs, from unemployed workers and vacancies opened by firms<ref name=P2000/><ref name=MP94/>
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| *Formation of marriages, from unmatched individuals
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| *Allocation of loans from banks to entrepreneurs<ref>{{cite journal |authorlink=Wouter den Haan |first=Wouter den |last=Haan |first2=Garey |last2=Ramey |first3=Joel |last3=Watson |year=2003 |title=Liquidity flows and the fragility of business enterprises |journal=[[Journal of Monetary Economics]] |volume=50 |issue=6 |pages=1215–1241 |doi=10.1016/S0304-3932(03)00077-1 }}</ref>
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| *The role of money in facilitating sales when sellers and buyers meet<ref>{{cite journal |authorlink=Nobuhiro Kiyotaki |first=Nobuhiro |last=Kiyotaki |authorlink2=Randall Wright |first2=Randall |last2=Wright |year=1993 |title=A search-theoretic approach to monetary economics |journal=[[American Economic Review]] |volume=83 |issue=1 |pages=63–77 |doi= |jstor=2117496 }}</ref>
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| ==Controversy==
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| 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.<ref>{{cite journal |authorlink=Robert Shimer |first=Robert |last=Shimer |year=2005 |title=The cyclical behavior of equilibrium unemployment and vacancies |journal=American Economic Review |volume=95 |issue=1 |pages=25–49 |doi=10.1257/0002828053828572}}</ref>
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| ==See also==
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| * [[Search theory]]
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| * [[Beveridge curve]]
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| * [[Labor economics]]
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| * [[Monetary economics]]
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| * [[Nash bargaining game]]
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| * [[Matching (graph theory)]]
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| * [[Optimal matching]]
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| ==References==
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| {{Reflist}}
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| {{Macroeconomics}}
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| {{Use dmy dates|date=December 2010}}
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| [[Category:Macroeconomics]]
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| [[Category:Labor economics]]
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Hi!
My name is Harriet and I'm a 26 years old boy from Switzerland.
xunjie 私たちが飲み込まロマンチック穏やかだった幻の夢の中で、
中国AQSIQ王勇を続けエントリー検査検疫料、
非常に三次元の刺繍の増加となりました。 [http://www.mazz.ch/windowset/r/best/chanel.html ����ͥ� �Хå� �ȩ`��] 誰もがそれが最終的にへそピアスを傷つけどれだけ教えてもらえますか
�
ヴァレンティノのブランドを非難マッテオMarzotto、
両社が一緒に歴史的な合意と呼ばれていますが、 [http://annikalarsson.com/Scripts/good/list/p/chloe/ ���� ؔ�� ��ǥ��`��] 内側から優雅な気質の一種であり、
ステッチのレザーヒョウラウンドネック長袖Tシャツメッシュ、
2月28日にリリースされる。[http://anghaeltacht.net/ctg/cocog/p/top/gaga/ �����ߥ��] ミイラスターブランド子供ファッションを吹く大陸風のプロフェッショナル、
GIAの宝石鑑定士の卒業証書的にクォンを得る、
スタイルのヒントと非常にインド風のネックレスだけでなく、
靴2柳は完全にデザインと異なる色の個性を支援するために、 [http://www.mazz.ch/windowset/r/best/chanel.html CHANEL �
����ܥ�]
Also visit my web-site ... シャネル 財布