A Model of Money With Multilateral Matching, Second Version

2010

Search-theoretic models of money assume that sellers can produce any amount of goods on demand. However, a majority of goods are produced in advance by sellers. In this paper we propose a new model of monetary search in which sellers produce partially durable goods in advance and then strive to …nd customers. This has two implications. First, sellers have the option to produce for themselves (home production) or for customers in exchange for money (market production). Second, both sides of the market take a risk: buyers invest in money which depreciates because of in ‡ation, sellers produce perishable output in advance and none is sure to trade. We obtain three types of equilibria. Type I Equilibrium is a nonmonetary pure-strategy equilibrium in which the seller produces only for himself and nothing for the market. Type II Equilibrium is a pure-strategy monetary equilibrium in which the seller produces, sells a fraction and keeps the leftover for himself. Type III Equilibrium has two parts, both of which are mixed-strategy monetary equilibria. In the …rst one buyers bring a unique amount of money and sellers randomize between two levels of output. In the second, the buyer brings multiple amounts of money with positive probabilities and likewise the seller brings multiple amounts of output with positive probabilities. Thus, with some probability this equilibrium gives rise to the buyer bringing more money than he spends.

2002

I review in this paper some recent literature that deals with the coexistence of inside and outside money in a matching model of money à la Kiyotaki and Wright. I examine first a class of models that introduce credit by assuming that some agents' actions can be monitored and punished by the other agents in the economy. I then turn to a model in which agents can (costly) commit to keep their promises. I also analyse a literature that introduces banks and private money in the model, to evaluate the Hayek-Friedman debate on the private vs. public provision of money. The very last part of the paper is devoted to the issue of coexistence of money and nominal bonds with a higher rate of return.

2015

We propose a new search-based model of monetary exchange with indivisible assets, based on price posting by sellers, rather than bargaining. The approach generates price dispersion, is consistent with sticky nominal prices, and is well-suited for the study of nonstationary monetary equilibria. The paper also contributes to the literature on general price dispersion, by having buyers constrained by their asset positions, which matters for the number and nature of equilibria. Once some technical results are established, the framework is tractable, and parametric cases can be solved explicitly. In general, we characterize stationary and dynamic equilibria, including sunspot equilibria.

Review of Economic Dynamics, 2000

In this paper we take as given that market economies are characterized by a set of stylized responses to increases in the stock of money. Innovations to the stock of money lead to increased output and reductions in short term interest rates in the short run and only in the long run do nominal prices respond. These features of the monetary transmission mechanism have been discussed at least since David Hume. Most authors have attributed the real effects of money in the short run either to mistaken expectations or to non-market clearing or both. In this paper we argue that neither of these channels is needed to explain the facts. We show that a competitive market clearing model in which money enters the production function is fully capable of mimicking the broad features of the data. Our argument relies on an explanation of "price stickiness" that exploits a multiplicity of equilibria in a rational expectations model.

2005

We construct a simple model of monetary exchange where, as in , trades take place in both centralized and decentralized markets. However, in constrast to Lagos and Wright, we allow for general preferences and introduce nonconvexities (indivisiblities) and sunspots. In the centralized market, agents can trade statecontingent commodities. We show that nonconvexities and sunspots make the model tractable by reducing the heterogeneity generated by the randomness of the trading process in the decentralized market. We show that the allocations in the centralized and decentralized markets are determined independently. In particular, the unemployment rate in the centralized market is indenpendent of inflation. While the allocation in the centralized market is efficient, the allocation in the decentralized market is in general inefficient. * We thank the participants of the FRB-Cleveland Monetary Theory Workshop August 2004. The views expressed herein are those of the authors and not necessarily those of the Federal Reserve Bank of Cleveland or the Federal Reserve System.

2000

This paper investigates the relationship between money growth, inflation, and productive activity in a general equilibrium model of search. The use of a multiple-matching technique, where trade frictions are captured by limited consumption variety, allows us to study price determination in a search-theoretic environment with divisible money and goods. In our basic framework, productive activity and matching in the goods market are endogenized by a time allocation decision of work and shopping effort. We find that in such an environment, a positive feedback between shopping and work effort decisions creates a channel by which inflation can positively influence productive activity. This feature also creates the possibility of multiple steady state equilibria when household preferences for variety is sufficiently great. We also consider an alternative means of endogenizing the matching technology through endogenous firm entry. Consistent with the findings of our basic framework, the importance of search frictions continues to be essential for the non-uniqueness of equilibria and an additional channel which links money growth to real activity.

1998

This paper investigates the relationship between money growth, inflation, and productive activity in a general equilibrium model where search frictions motivate the transactions role of money. The use of a multiple matching technique, where search frictions are captured by limited consumption variety, allows us to study price determination in a search-theoretic environment with divisible money and goods. We find that in such a setting, a positive feedback between work and shopping effort decisions create a channel by which inflation can positively influence real activity. This feature also creates the possibility of multiple steady state equilibria. We also analzye the impact of inflation on capital accumulation, the role search frictions play in determining the extent to which inflation distorts relative prices, and the effect of money growth on firm entry on trade frictions. In doing so, we demonstrate that a multiple matching model of money is amendable to study a wide range of traditional issues in monetary theory.

Physica A: Statistical Mechanics and its Applications, 2003

The impact of money supply on the real variables and on utility is an important question in monetary economics. Most previous works study this impact in representative agent economies, often under perfect foresight. With such a framework, however, the use of ÿat money as a medium of exchange cannot be endogenously explained. This paper, by contrast, considers an economy where ÿat money is intrinsically necessary for exchange, due to the local structure of interaction among agents. It investigates the transitory and permanent impact of local or global injections of money on the dynamics of exchanged quantities, prices, and individual welfares, and the mechanisms that explain this evolution.

SSRN Electronic Journal, 2002

We show that monetary trading is simple, self-enforcing, symmetric, and irreducible in a natural framework. Furthermore, we will show that the utility for each economic agent is at least as big under the monetary system as under any other simple, self-enforcing, symmetric, and irreducible trading system of the same complexity. Thus, we rationalize the monetary nature of real-world trade as being an efficient way to achieve those properties. "The search for a means of exchange is almost as old as mankind."-The Economist, December 22nd 2001, page 87. * This paper is an heavily revised version of Chapter 4 of my Ph.D. thesis. I wish to thank my advisors, Narayana Kocherlakota, and Marcel K. Richter, for their guidance, encouragement, and very helpful comments and suggestions. I wish also to thank Beth

One implication of the concept of monetary equilibrium is that the money supply should vary with money demand. In a recent paper, Bagus and Howden (Rev Austrian Econ 24:383–402, 2011) argue that this conclusion is predicated on the assumption of price stickiness. The purpose of this paper is to suggest that the foundation of monetary equilibrium is the role of money as a medium of exchange. As such, changes in the demand for money result in changes in both nominal and real spending that are welfare-reducing. This proposition is then used to examine whether a monetary policy in which the central bank varies the money supply in response to money demand can be considered optimal. In addition, the paper considers how a free banking system with competitive note issuance would vary the money supply in response to changes in money demand. In both cases, the results are consistent with the concept of monetary equilibrium. In addition, these results can be obtained even when prices are perfectly flexible if trade is decentralized (i.e. not conducted in Walrasian markets). Price stickiness is therefore not a necessary condition to suggest that the money supply should vary with money demand.

2017

Whether currency can be efficiently provided by private competitive money suppliers is arguably one of the fundamental questions in monetary theory. It is also one with practical relevance because of the emergence of multiple competing financial assets as well as competing cryptocurrencies as means of payments in certain class of transactions. In this paper, a dual currency version of Lagos and Wright (2005) money search model is used to explore the answer to this question. The centralized market sub-period is modeled as infinitely repeated game between two long lived players (money suppliers) and a short lived player (a continuum of agents), where longetivity of the players refers to the ability to influence aggregate outcomes. There are multiple equilibria, however we show that equilibrium featuring lowest inflation tax is weakly renegotiation proof, suggesting that better inflation outcome is possible in an environment with currency competition.

This paper uses a New Monetarist framework to study the trade of indivisible goods with divisible money in a frictional market. We …rst derive conditions under which stationary equilibrium exists, and then show that if equilibrium exits, it is unique. The uniqueness result is due to the commitment and coordination nature of the pricing mechanisms. Money is superneutral in the model with generalized Nash bargaining, but not with competitive search. Because of the superneutrality of money, monetary equilibrium in the generalized Nash bargaining model only exists for low values of nominal interest rate. With competitive search, monetary equilibrium exists for all i > 0.

Economic Theory, 2010

We define continuous-time dynamics for exchange economies with fiat money. Traders have locally rational expectations, face a cash-in-advance constraint, and continuously adjust their short-run dominant strategy in a monetary strategic market game involving a double-auction with limit-price orders. Money has a positive value except on optimal rest-points where it becomes a “veil” and trade vanishes. Typically, there is a piecewise globally unique trade-and-price curve both in real and in nominal variables. Money is not neutral, either in the short-run or long-run and a localized version of the quantity theory of money holds in the short-run. An optimal money growth rate is derived, which enables monetary trade curves to converge towards Pareto optimal rest-points. Below this growth rate, the economy enters a (sub- optimal) liquidity trap where monetary policy is ineffective; above this threshold inflation rises. Finally, market liquidity, measured through the speed of real trades, can be linked to gains-to-trade, households’ expectations, and the quantity of circulating money.

Macroeconomic Dynamics, 2010

International Economic Review, 2012

This article presents a microfounded model of money with a consumption and an investment market. We consider an economy in which only part of the investment returns can be pledged. A liquidity constraint arises when the pledgeable part of the returns are not enough to pay for investment costs. We show that when the liquidity constraint is binding, agents may make a cash downpayment and money can perform two roles—as a provider of liquidity services and exchange services. The liquidity constraint constitutes a channel though which underinvestment occurs even at low inflation rates.