Random Matching Model Research Articles

Unemployment and market size

Without strong empirical support, labour market matching models typically assume constant returns to scale in matching. We construct a tractable equilibrium random matching model with a general matching technology, introducing market size effects: the job‐finding rate varies with unemployment. Stable steady‐states may occur in regions of increasing or decreasing returns, and multiple equilibria are welfare‐ranked by market size. While the standard model relies on high‐frequency shocks to the steady state to explain the co‐movement of unemployment and job‐finding, locally decreasing returns in matching generate plausible adjustment dynamics and slower convergence. Lastly, an extension of the Hosios condition internalises search externalities.

Investments in education and welfare in a two-sector, random matching economy

We consider a random matching model where heterogeneous agents choose optimally to invest time and real resources in education. Generically, there is a steady state equilibrium where some agents, but not all of them, invest. Regular steady state equilibria are constrained inefficient in a strong sense. The Hosios (1990) condition is neither necessary nor sufficient for constrained efficiency. We also provide restrictions on the fundamentals sufficient to guarantee that equilibria are characterized by overeducation (or undereducation), present some results on their comparative statics properties, and discuss the nature of welfare improving policies.

Search and matching in the housing market

Housing markets clear partly through the time buyers and sellers spend on the market, and the readiness with which they transact with each other. Applying a random matching model to unique multi-year, multi-market survey data on both buyers and sellers, we examine how demand affects housing market liquidity. We find that buyer time on the market, the number of homes buyers visit, and especially seller time on the market all decrease with demand, with a much greater sensitivity to demand growth than its level. This is consistent with a straightforward matching model with a lag in seller response. Our findings imply that the elasticity of the hazard that any given seller will be contacted by a buyer, with respect to the buyer–seller ratio, is 0.84, assuming a constant returns to scale matching function.

Independent random matching

Random matching models with a continuum population are widely used in economics to study environments where agents interact in small coalitions. This paper provides foundations to such models. In particular, the paper establishes an existence result for random matchings that are universal in the sense that certain desirable properties are satisfied for any assignment of types to agents. The result applies to infinitely many types of agents, thus covering random matching models which are currently used in the literature without a foundation. Furthermore, the paper provides conditions guaranteeing uniqueness of random matching.

Existence of a continuum of equilibria in a monetary random-matching model

In this paper, we study a monetary random-matching model where both goods and money are perfectly divisible, production is costly, and there is no exogenous upper bound on agents' money holdings, information on which is private to the agent. We show that there is a continuum of stationary equilibria where agents have either no money or a set amount, and buyers spend all their money. As in the previous studies, the equilibrium value function is step-like, which emerges as a self-fulfilling prophecy. The endogenous upper bound on agents' money holdings is the result of private information on agents' money holdings. Buyers post an offer that is accepted only by sellers without money, who set a higher value on money.

Investments in Education and Welfare in a Two-Sector, Random Matching Economy

We consider a random matching model where heterogeneous agents choose optimally to invest time and real resources in education. Generically, there is a steady state equilibrium, where some agents, but not all of them, invest. Regular steady state equilibria are constrained inefficient in a strong sense. The Hosios (1990) condition is neither necessary, nor sufficient, for constrained efficiency. We also provide restrictions on the fundamentals sufficient to guarantee that equilibria are characterized by overeducation (or undereducation), present some results on their comparative statics properties, and discuss the nature of welfare improving policies.

Search Theory; Current Perspectives

Search Theory is an analysis of resource allocation in economic environments with trading frictions. These frictions include the difficulty of bringing potential traders together, coordinating agents’ decisions, informing agents of trading opportunities, and keeping records of agents’ trading histories. In the market, trading frictions appear in various forms of transactions cost and they generate important regularities in quantities and prices. For example, there are unemployed workers, under-utilized capital, and unsold goods in inventory, which indicate that markets are unable to exhaust all potentially desirable trades. Also, the law of one price predicted for a frictionless economy is at odds with the dispersion of prices often observed for similar goods. Earlier models of search theory introduced two elements to capture search frictions (see Diamond, 1987). One element is a matching function, which generates the frequency of matches between agents. The other element is a mechanism to determine prices in individual trades. Two types of models incorporated these elements. One is sequential search models, in which agents on one side of the market post prices. Agents on the other side receive price quotes at an exogenous rate and decide sequentially whether to accept the quotes. The other type is random-matching models, in which the matching frequency is a function of the ratio of the numbers of agents on the two sides of the market. Such models determine price by Nash bargaining. We will refer to these models as models of random search or undirected search, because agents in the models take the matching frequency as given. With undirected search, the 1 This article is written as an entry to the Palgrave Dictionary of Economics. I thank the Social Sciences and Humanities Research Council of Canada for research support.

Categorization and correlation in a random-matching game

We consider a random-matching model in which every agent has a categorization (partition) of his potential opponents. In equilibrium, the strategy of each player i is a best response to the distribution of strategies of his opponents (when they face i) in each category of his categorization. We provide equivalence theorems between distributions generated by equilibrium profiles and correlated equilibria of the underlying game.

Directed search, unemployment and public policy

Abstract We examine the effects of public policy parameters in a simple directed search model of the labour market, and contrast them with those in standard random matching models with Nash bargaining. Both finite and limit versions of the directed search model are considered, and the value of the limit model as an approximation of the finite one is assessed. As with the random matching model, job creation is the key channel through which the policy parameters affect the equilibrium of the directed search model. Both comparative static effects of the policy parameters and optimal configurations are identified.

Matching models with a conservation law: The existence and global structure of the set of stationary equilibria

We study random matching models where there is a set of infinitely lived agents, and in each period agents are pairwise matched to each other and play a stage game. We investigate the basic structure of equilibria in such models: the existence of equilibria and the global structure of the set of equilibria. Specifically, we focus on models with a conservation law, which typically holds in economies having some assets, such as money. In such models, under certain regularity conditions the set of equilibria is one-dimensional and each connected component of it is a piecewise smooth one-dimensional manifold being homeomorphic to either the unit circle or the unit interval. Moreover, in an endpoint of an interval all agents have the same amount of assets.

The Neutrality of Money Revisited with a Bottom-Up Approach: Decentralisation, Limited Information and Bounded Rationality

In the mainstream top-down approach, money is neutral except with special assumptions. Intending to make money "essential", random-matching models introduced decentralisation by considering pair-wise transactions. Nevertheless, in both cases top-level equilibrium constrains agents' behaviour. Instead, here we use a bottom-up approach. In a competitive market, decentralised autonomous agents meet and exchange a commodity for money. Their decisions use minimal information. They are triggered by simple rules founded on a "satisficing" procedure and on a random decision process that simulates bounded rationality. The conclusions are, first, that non-monetary costs are essential to avoid collapse of the economy. Second, mainly "price setters" who are adequately satisfied achieve equilibrium protecting themselves by evolving advantages to avoid competition that is too tough. Third, and the most important conclusion is that money ceases to be neutral as soon as competition arises between individual firms.

The theory of fiat money and private money as alternative media of exchange

A random-matching model with a clearinghouse is constructed to investigate the impact of private money on economic efficiency and social welfare in three monetary regimes. A subset of agents, called bankers, whose credit histories are recorded by the clearinghouse, are allowed to issue private banknotes in order to consume. Those private liabilities may serve as media of exchange, either by themselves, or alongside a stock of fiat money. Under certain conditions, welfare in a monetary steady state with private money is strictly higher than that attained in a steady state where private money is prohibited.

Counterfeiting as Private Money in Mechanism Design

We describe counterfeiting activity as the issuance of private money, one which is difficult to monitor. Our approach, which amends the basic random-matching model of money in mechanism design, allows a tractable welfare analysis of currency competition. We show that it is not efficient to eliminate counterfeiting activity completely. We do not appeal to lottery devices, and we argue that this is consistent with imperfect monitoring.

MATCHING FUNCTION FOR THE JAPANESE LABOUR MARKET: RANDOM OR STOCK–FLOW?

ABSTRACTThis paper estimates outflow equations for the unemployed and job vacancies under random and stock–flow matching using Japanese data. We find that for the outflow of the unemployed, the stock–flow matching model fits better than the random matching model at the quarterly frequency, but not at the monthly frequency. In contrast, the outflow of vacancies is affected by the stock of the unemployed as well as its inflow at both monthly and quarterly frequencies. In addition, we calculate the exit rates of the unemployed and job vacancies to show the relationship between the exit rates and the durations of unemployment and job vacancies.

Imperfect Monitoring and the Discounting of Inside Money

One of the fundamental questions concerning inside money is whether its issuers should be regulated and how. This paper evaluates the efficiency of one prevalent regulatory recommendation -- a requirement that private issuers redeem inside money on demand at par -- in a random-matching model of money where the issuers of inside money are only imperfectly monitored. I find that for sufficiently imperfect monitoring, a par redemption requirement leads to lower social welfare than if private money were redeemed at a discount. A central message of the paper is that if inside money and outside money are not perfect substitutes for one another, as is the case if there is sufficiently imperfect monitoring, a par redemption requirement may not be socially optimal because such a requirement effectively binds them to circulate as if they are. Such an outcome is a version of Gresham's law that bad money drives out good money.

Some Benefits of Cyclical Monetary Policy

In this paper, we present a simple random-matching model in which different seasons translate into different propensities to consume and produce. We find that the cyclical creation and destruction of money is beneficial for welfare under a wide variety of circumstances. Our model of seasons can be interpreted as providing support for the creation of the Federal Reserve System, with its mandate of supplying an elastic currency for the nation.

Categorization and Correlation in a Random-Matching Game

We consider a random-matching model in which every agent has a categorization (partition) of his potential opponents. In equilibrium, the strategy of each player is a best response to the distribution of actions of his opponents in each category of his categorization. We provide equivalence theorems between distributions generated by equilibrium profiles and correlated equilibria of the underlying game.

Class, gender and marriage

This paper estimates the contributions of differential fecundity, social heterogeneity, assortative matching and search frictions to aggregate marriage behavior in 18th century Quebec. The reduced form estimates show that a simple random matching model of the marriage market, in which there are gains to assortative matching and women may leave the marriage market at a higher rate than men, can explain these data. The estimates also show that the marriage market was segmented by social status.

A model of banknote discounts

Prior to 1863, state-chartered banks in the United States issued notes—dollar-denominated promises to pay specie to the bearer on demand. Although these notes circulated at par locally, they usually were quoted at a discount outside the local area. These discounts varied by both the location of the bank and the location where the discount was being quoted. Further, these discounts were asymmetric across locations, meaning that the discounts quoted in location A on the notes of banks in location B generally differed from the discounts quoted in location B on the notes of banks in location A. Also, discounts generally increased when banks suspended payments on their notes. In this paper we construct a random matching model to qualitatively match these facts about banknote discounts. To attempt to account for locational differences, the model has agents that come from two distinct locations. Each location also has bankers that can issue notes. Banknotes are accepted in exchange because banks are required to produce when a banknote is presented for redemption and their past actions are public information. Overall, the model delivers predictions consistent with the behavior of discounts.

Imperfect Monitoring and the Discounting of Inside Money

One of the fundamental questions concerning inside money is whether its issuers should be regulated and how. This paper evaluates the efficiency of one prevalent regulatory recommendation -- a requirement that private issuers redeem inside money on demand at par -- in a random-matching model of money where the issuers of inside money are only imperfectly monitored. I find that for sufficiently imperfect monitoring, a par redemption requirement leads to lower social welfare than if private money were redeemed at a discount. A central message of the paper is that if inside money and outside money are not perfect substitutes for one another, as is the case if there is sufficiently imperfect monitoring, a par redemption requirement may not be socially optimal because such a requirement effectively binds them to circulate as if they are. Such an outcome is a version of Gresham's law that bad money drives out good money.