Random Matching Model Research Articles

A MODEL IN WHICH OUTSIDE AND INSIDE MONEY ARE ESSENTIAL

I present an environment for which both outside and inside money are essential as means of payment. The key model feature is that there is imperfect monitoring of issuers of inside money. I use a random-matching model of money where some agents have private trading histories and others have trading histories that can be publicly observed only after a lag. I show via an example that for lags that are neither too long nor too short, there exist allocations that use both types of money that cannot be duplicated when only one type is used. Inside money provides liquidity that increases the frequency of trades, but incentive constraints restrict the amount of output that can be traded. Outside money is immune to such constraints and can trade for higher levels of output.

Money with partially directed search

Partially directed search replaces the total randomness of monetary search models. Agents choose whether to stay in their production location or visit other locations. Each visiting agent randomly chooses one shop among many in each location. As in random matching models, a commodity or fiat object can endogenously become money, but the details are richer and conform better with evidence: any commodity can be money; the “best” commodity is the most likely money; fiat money can totally crowd out commodity money in an asymmetric environment; going shopping is more likely than door-to-door sales. The model nests Walrasian equilibria.

A Model in Which Outside and Inside Money are Essential

I present an environment for which both outside and inside money are essential as means of payment. The key model feature is that there is imperfect monitoring of issuers of inside money. I use a random matching model of money where some agents have private trading histories and others have trading histories that can be publicly observed only after a lag. I show via an example that for lags that are neither too long nor too short, there exist allocations that use both types of money that cannot be duplicated when only one type is used. Inside money provides liquidity that increases the frequency of trades, but incentive constraints restrict the amount of output that can be traded. Outside money is immune to such constraints and can trade for higher levels of output.

Minorities and Endogenous Segregation

A theoretical analysis is proposed of segregation as an equilibrium phenomenon in a randommatching model of the marriage market. Otherwise identical partners possess a pay-off-irrelevant characteristic, colour. We derive the set of colour-blind equilibria and show that they are generically constrained inefficient. Equilibrium segregation strategies are strategies that condition actions on the type of match. It is shown that distributions of types exist such that segregation equilibrium pay-offs Pareto dominate colour-blind pay-offs. For other distributions, segregation also generates conflict, where the majority unambiguously gains, while the minority group may lose. Giving preferential treatment, that is, minority bias, can increase overall welfare.

PASCV Membership

This paper investigates the dynamic foundation of a competitive equilibrium, studying a sequence of random matching models between ex ante heterogeneous buyers and sellers under two-sided incomplete information with no entry, where each agent is endowed with non-transferable utility. The economy is populated with two sets of infinitesimal agents, buyers and sellers, who have private information about their own valuations of the object. In each period, buyers and sellers in the pool are matched to draw randomly a pair of expected payoffs, which will realize if the long term relationship is formed. Each player decides whether or not to agree to form a long term relationship, conditioned on his private information. If both parties agree, then they leave the pool, receiving the expected payoff in each period while the long term relationship continues. The existing long term relationship is terminated either by will or by a random shock, upon which both parties return to the respective pools of agents. We quantify the amount of friction by the time span of each period. We demonstrate that as the friction vanishes, any sequence of stationary equilibrium outcomes, in which trade occurs with a positive probability, converges to the competitive equilibrium, under a general two sided incomplete information about the private valuation of each agent.

Search and leisure with idiosyncratic endowment shocks in a random-matching model

Agents who realize idiosyncratic endowment shocks (High and Low) choose between leisure and searching for a trading partner. In the non-monetary economy there are two cases: everyone enjoys leisure or everyone enters the market to barter. In the first case, money can generate an equilibrium in which all agents enter the market. In the second, money can generate an outcome impossible without money, in which High agents trade while Low agents rest. Money affects the real side of the economy by driving Low quality goods out of the market, improving the quality of traded goods.

Existence of a monetary steady state in a matching model: divisible money

Existence of a monetary steady state is established in a random matching model with divisible goods, divisible money, an arbitrary bound on individual money holdings, and take-it-or-leave-it offers by consumers. The monetary steady state shown to exist has nice properties: the value function, defined on money holdings, is strictly increasing and strictly concave, and the distribution over money holdings has full support. The approach is to show that the “limit” of the nice steady states for indivisible money, existence of which was established in an earlier paper, as the unit of money goes to zero is a monetary steady state for divisible money. For indivisible money, the marginal utility of consumption at zero was assumed to be large; for divisible money it is assumed to be large and finite.

General Preferences for Consumption Goods in the Random Matching Model of Commodity Money

This paper generalizes the original random matching model of money by Kiyotaki and Wright (1989) (KW) in two aspects: first, the economy is characterized by an arbitrary distribution of agents who specialize in producing a particular consumption good; and second, these agents have preferences such that they want to consume any good with some probability. The results depend crucially on the size of the fraction of producers of each good and the probability with which different agents want to consume each good. KW and other related models are shown to be parameterizations of this more general one.

Price distribution in a random matching model

We derive a price distribution for a homogeneous good in a symmetric economy where sellers are in locations and choose prices, and buyers choose locations randomly. The equilibrium strategy of the sellers is a non-atomic distribution.

Wage-Tenure Contracts in a Frictional Labour Market: Firms' Strategies for Recruitment and Retention

A common assumption in equilibrium search and matching models of the labour market is that each firm posts a wage, to be paid to any worker hired. This paper considers the implications of firms posting contracts, in a random matching model with on-the-job search. More complex contracts enable firms to address both recruitment and retention problems by, for example, increasing the wage with tenure. The effect on the labour market is to reduce turnover, below the level required for efficient matching of workers to firms. Copyright 2004, Wiley-Blackwell.

A Model in which Outside and Inside Money are Essential

I present an environment for which both outside and inside money are essential as means of payment. The key model feature is that there is imperfect monitoring of issuers of inside money. I use a random-matching model of money where some agents have private trading histories and others have trading histories that can be publicly observed only after a lag. I show via an example that for lags that are neither too long nor too short, there exist allocations that use both types of money that cannot be duplicated when only one type is used. Inside money provides liquidity that increases the frequency of trades, but incentive constraints restrict the amount of output that can be traded. Outside money is immune to such constraints and can trade for higher levels of output.

When trade requires coordination

We consider a random matching model in which agents exchange endowments. Agents choose a standard of behavior from a given set of standards, with the knowledge that the gains from trade are higher if two trading agents have chosen the same standard. Agents have different preferences over these standards. There are two communities with uneven sizes. In one community, a particular standard is preferred by its members, while in the other, another standard is preferred. Using this framework, we study conditions under which, when we account for these inherent preferences over a set of standards, total welfare of a minority community decreases when a trade barrier between the two communities is lifted. J. Japanese Int. Economies 18 (3) (2004) 440–461.

Existence of a monetary steady state in a matching model: indivisible money

Existence of a monetary steady state is established for a random matching model with divisible goods, indivisible money, an arbitrary bound on individual money holdings, and take-it-or-leave-it offers by consumers. The background environment is that in papers by Shi and by Trejos and Wright. The monetary steady state shown to exist has nice properties: the value function, defined on money holdings, is strictly increasing and strictly concave, and the measure over money holdings has full support.

Does commodity money eliminate the indeterminacy of equilibrium?

Previous studies have shown that a random-matching model with divisible fiat money and without constraint on agents’ money inventories possesses a continuum of stationary single-price equilibria. Wallace (J. Econom. Theory 81 (1998) 223) conjectures that the indeterminacy can be eliminated by the use of commodity money. Instead, I find that in a similar random-matching model with dividend-yielding commodity money, a continuum of stationary single-price equilibria exists when the utility of dividend is not too high. This result casts doubt on the conventional belief that the indeterminacy of monetary equilibrium is be caused only by the nominal nature of money.

Output and price level effects of monetary uncertainty in a matching model

Monetary uncertainty and information lags are put into a random matching model so that the resulting setting has some meetings in which producers are relatively informed and others in which consumers are relatively informed. For that setting, the ex ante socially optimal way to conduct trade is characterized. The optimum can display a variety of relationships between money and total output and the price level. While the price level is always sticky, even the direction of its response and that of total output depend on the magnitude of the lag and on subtle features of the serial correlation properties of the money supply.

Comparison of Auctions and Posted Prices in a Finite Random Matching Model

I determine the steady state equilibrium in a random matching model with a finite number of buyers and sellers. Two trading mechanisms, namely, auctions and posted prices are compared. Auctions depict a situation where the sellers are unable to commit to a reserve price, whereas posted prices depict a situation where the sellers commit to a publicly announced price. In the corresponding infinite agent model the two mechanisms are equivalent, while in the finite case posted prices are preferred by sellers and auctions by buyers.

About market structure

I study an economy where sellers choose locations, and buyers choose which location to visit. All sellers in one location correspond to the Walrasian market while each seller in a separate location corresponds to the standard random matching model. Trades are consummated in auctions, and it turns out that the Walrasian market is not an equilibrium market structure. Rather, the sellers choose to distribute themselves in several locations endogenously creating the imperfectness of markets. I determine the number of sellers per location in equilibrium as a function of the ratio of buyers to sellers.

Discrete time dynamics in a random matching monetary model

Under take-it-or-leave-it offers, dynamic equilibria in the discrete time random matching model of money are a “translation” of dynamic equilibria in the standard overlapping generations model. This formalizes earlier conjectures about the equivalence of dynamic behavior in the two models and implies the indeterminacy of dynamic equilibria in the random matching model. As in the overlapping generations model, the indeterminacy disappears if an arbitrarily small utility to holding money is introduced. We introduce a different pricing mechanism, one that puts into sharp focus that agents are forward-looking when they interact.

On the Distribution of Money Holdings in a Random-Matching Model*

This article studies stationary and nonstationary distributions of money holdings in a random-matching model. The first part characterizes the stationary distributions of money holdings and derives the optimum quantity of money. The second part considers nonstationary distributions of the optimum quantity of money to show that if the production costs are not too large, any distribution of the optimum quantity of money converges asymptotically to the uniform distribution.

The size of meetings and the role of money

I extend the random-matching model of money by allowing the number of people in a random meeting to be greater than two, a parameter N. I prove that any beneficial role of money disappears as N→∞.