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.     

A Matching Model with Bounded Holdings of Indivisible Money

Recent versions of pairwise random matching models of money with divisible and perishable goods are amended to allow individuals to hold more than one unit of an indivisible asset. The asset resembles a fiat asset, except that nominal holdings of it yield a small amount of utility. There is a general upper bound on the number of units of the asset that individuals can hold. A steady state with trade is shown to exist. The model is applied to study numerically the effect on welfare of the degree to which the asset is divisible.     

Stationary monetary equilibria with strictly increasing value functions and non-discrete money holdings distributions: An indeterminacy result

In this paper, we present a search model with divisible money in which there exists a continuum of monetary equilibria with strictly increasing continuous value functions and with non-discrete money holdings distributions.     

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.     

Multiple reserve requirements in a monetary growth model

Summary. This paper considers a monetary growth model in which banks provide liquidity, and in which a government finances a deficit by printing money and selling bonds. In this context, I examine the possibility that the government may want to impose binding reserve requirements on banks' holdings of both money and government bonds. Conditions are established under which doing so increases steady state welfare and reduces the scope for indeterminacies. Furthermore, under a binding system of multiple reserve requirements we have that money is superneutral. On the other hand, if reserve requirements are imposed on cash holdings alone, increases in the steady state inflation rate adversely affect capital accumulation and long run real activity. Thus systems of multiple binding reserve requirements can insulate real activity from the consequences of inflationary taxation. Received: June 30, 2000; revised version: January 31, 2001     

A monetary theory with non-degenerate distributions

We construct and analyze a tractable search model of money with a non-degenerate distribution of money holdings. Analytical tractability comes from modeling decentralized exchange as directed search, which makes the monetary steady state block recursive. By adapting lattice-theoretic techniques, we characterize individuals? policy and value functions, and show that these functions satisfy the standard conditions of optimization. We prove that a unique monetary steady state exists and provide conditions under which the steady-state distribution of buyers over money balances is non-degenerate. Moreover, we analyze the properties of this distribution.     

Individual and Aggregate Real Balances in a Random-Matching Model

This article investigates the characteristics of stationary single-price equilibrium in a monetary random-matching model where agents can hold an arbitrary amount of divisible money and where production is costly. At such an equilibrium, agents' money holdings are endogenously determined and uniformly bounded. A refinement of weakly undominated strategies is argued to be necessary. It is shown that a continuum of single-price equilibria indexed by the aggregate real-money balance exists if one such equilibrium exists. Equilibria with different money-holdings upper bounds, hence different distributions, but with identical aggregate real-money balances can coexist.     

STRATEGY PROOF AND PRIVACY PRESERVING FAIR ALLOCATION MECHANISM*

We study a fair division problem with indivisible objects such as jobs, houses and one divisible good like money. It is required that each agent be assigned with exactly one object and a certain amount of money. Agents are assumed to have quasi‐linear utilities in money but their reservation values over the objects are private information. A dynamic mechanism is proposed that induces all agents to act honestly rather than strategically and assigns the objects with money to agents efficiently and fairly; at the same time it achieves privacy protection for the agents.     

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.     

Money and the gains from trade*

This article studies the role of money in environments where in each meeting there is a double coincidence of real wants. Traders who meet at random finance their purchases through current production, the sale of divisible money or both. It is shown that in the absence of valued money if traders have asymmetric tastes for each other's good, they produce and exchange socially inefficient quantities. With valued money, however, traders exchange efficient quantities if the asymmetry of tastes is not too large. It is shown that the gains from trade in the monetary economy are strictly greater than those in the corresponding barter economy, that the Friedman rule holds, and that the allocation of resources in the monetary economy converges to the allocation in the barter economy as the growth rate of the money supply is increased.     

Capital market imperfections in a monetary growth model

Summary. We consider a monetary growth model essentially identical to that of Diamond (1965) and Tirole (1985), except that we explicitly model credit markets, a credit market friction, and an allocative function for financial intermediaries. These changes yield substantially different results than those obtained in more standard models. In particular, if any monetary steady state equilibria exist, there are generally two of them; one of these has a low capital stock and output level, and it is necessarily a saddle. The other steady state has a high capital stock and output level; either it is necessarily a sink, or its stability properties depend on the rate of money creation. It follows that monetary equilibria can be indeterminate, and nonconvergence phenomena can be observed. Increases in the rate of money creation reduce the capital stock in the high-capital-stock steady state. If the high-capital-stock steady state is not a sink for all rates of money growth, then increases in the rate of money growth can induce a Hopf bifurcation. Hence dynamical equilibria can display damped oscillation as a steady state equilibrium is approached, and limit cycles can be observed as well. In addition, in the latter case, high enough rates of inflation induce the kinds of “crises” noted by Bruno and Easterly (1995): when inflation is too high there are no equilibrium paths approaching the high-activity steady state. Received: November 18, 1995; revised version: March 26, 1996     

A theory of optimal denominations for government liabilities

Summary The design and implementation of monetary arrangements has important implications for the welfare and determinacy properties of equilibria that arise under competitive monetary exchange. In this paper we consider one particular feature of a monetary arrangement. We ask whether a government should issue its liabilities so that they are imperfectly divisible and whether they should at the same time regulate private intermediation. We argue that the answer is affirmative. We then consider the optimal minimum denomination for government liabilities given that the social planner would like to implement a particular equilibrium. We show that generically the steady state equilibria supported by minimum denominations that result in Pareto optimal allocations are indeterminate. We then pose the question, what is the best (in a Pareto sense) stationary equilibrium that can be supported, subject to the constraint that the equilibrium display certain minimal determinacy properties? The existence of an optimum in this sense is established. Such equilibria are supported by having the government issue indivisible liabilities with appropriately chosen minimum denominations.Research supported in part by NSF Grant SES-8921346. We have benefitted from conversations with Stan Engerman, Rod Garratt, Glenn MacDonald, Anne Villamil, Neil Wallace and Warren Weber, and from the comments of seminar participants at Cornell and Rochester. We are especially grateful to Ed Prescott for his suggestions.     

WEALTH,ASSET PORTFOLIO,MONEY DEMAND AND POLICY RULE

I look at the linkages between monetary policy and asset wealth using quarterly data for the USA. I show that a positive interest rate shock leads to a fall in aggregate wealth and an important change in portfolio composition: housing wealth gradually decreases, but the effects are very persistent; and financial wealth quickly shrinks, but the impact is short‐lived. I also find that the money market can be characterized as follows: (i) the money demand has a large interest elasticity and a small output elasticity; and (ii) the estimated monetary policy reaction function highlights the special focus given by the central bank to developments in monetary aggregates. These features call for an approach whereby monetary authorities put more emphasis on tracking wealth developments, in particular, given the asset portfolio rebalancing between money holdings and financial and/or housing assets.     

Bidding for money

We analyze monetary exchange in a model that allows for directed search and multilateral matches. We consider environments with divisible goods and indivisible money, and compare the results with those in models that use random matching and bilateral bargaining. Two different pricing mechanisms are used: ex ante price posting, and ex post bidding (auctions). Also, we consider settings both with and without lotteries. We find that the model generates very simple and intuitive equilibrium allocations that are similar to those with random matching and bargaining, but with different comparative static and welfare properties.     

Money-Hoarding as a Behaviour Towards Uninsured Idiosyncratic Risk

This paper explores the implications of the presence of uninsured idiosyncratic risks for the hoarding of intrinsically useless fiat money in an overlapping-generations model. It is shown that: (a) monetary equilibria exist in almost all cases; (b) the valuation of money is not necessarily Pareto-improving since the non-monetary steady state may Pareto-dominate the monetary one; and (c) the accelerating inflation may, moreover, reduce the long-run capital stock.
JEL Classification Number: E41.     

Assessing excess liquidity in the euro area: the role of sectoral distribution of money

The strong and prolonged deviation of money growth from its reference value since 2001 has caused concern among policy-makers about the upside risks to price stability from monetary developments. In this article we provide evidence that these risks might have been smaller until 2005 than regularly assumed. Three basic findings support this view. First, a sectoral breakdown of money holdings shows that current excess liquidity conditions have been partly related to the acceleration of nonbank financial intermediaries’ money demand, as well as to the accumulation of marketable instruments. Such increases are likely to be associated more to portfolio choices than to transaction motives. Second, evidence from balance sheet data on investment funds points to a general increase in the relative importance of this sector in the economy, rather than to a higher degree of liquidity of their asset positions, thus reflecting, to a large extent, a permanent change in the financial structure of the economy. Third, excess liquidity measures that exclude nonbank financial intermediaries’ money holdings have more predictive power for future inflation at medium-term horizons than those that include them.     

Collateral fluctuations in a monetary economy

This paper studies economy-wide fluctuations that occur endogenously in the presence of monetary and real assets. Using a standard monetary search model, we consider an economy in which agents can increase consumption, over and above what their liquid monetary asset holdings would allow, pledging real assets as collateral for monetary loans. It is shown that, if the liquidation value of real assets is below full market value, a stable cyclical equilibrium can emerge in consumption and capital around the unstable steady state. We also provide conditions for the existence of cycles of higher order, chaos and sunspot equilibria.     

Existence and Welfare Properties of Equilibrium in an Exchange Economy with Multiple Divisible and Indivisible Commodities and Linear Production Technologies

In this paper we consider a class of economies with a finite number of divisible commodities, linear production technologies, and indivisible goods and a finite number of agents. This class contains several well-known economies with indivisible goods and money as special cases. It is shown that if the utility functions are continuous on the divisible commodities and are weakly monotonic both on one of the divisible commodities and on all the indivisible commodities, if each agent initially owns a sufficient amount of one of the divisible commodities, and if a “no production without input”-like assumption on the production sector holds, then there exists a competitive equilibrium for any economy in this class. The usual convexity assumption is not needed here. Furthermore, by imposing strong monotonicity on one of the divisible commodities we show that any competitive equilibrium is in the core of the economy and therefore the first theorem of welfare also holds. We further obtain a second welfare theorem stating that under some conditions a Pareto efficient allocation can be sustained by a competitive equilibrium allocation for some well-chosen redistribution of the total initial endowments. Journal of Economic Literature Classification Numbers: D4, D46, D5, D51, D6, D61.     

Re‐vitalizing money demand in the Euro area. Still valid at the zero‐lower bound

The analysis of monetary developments has always been a cornerstone of the ECB's monetary analysis and, thus, of its overall monetary policy strategy. In this respect, money demand models provide a framework for explaining monetary developments and assessing price stability over the medium term. It is a well‐documented fact in the literature that, when interest rates are at the zero‐lower bound, the analysis of money stocks become even more important for monetary policy. Therefore, this paper re‐investigates the stability properties of M3 demand in the euro area in the light of the recent economic crisis. A cointegration analysis is performed over the sample period 1983 Q1 and 2015 Q1 and leads to a well‐identified model comprising real money balances, income, the long‐term interest rate and the own rate of M3 holdings. The specification appears to be robust against the Lucas critique of a policy dependent parameter regime, in the sense that no signs of breaks can be found when interest rates reach the zero‐lower bound. Furthermore, deviations of M3 from its equilibrium level do not point to substantial inflation pressure at the end of the sample. Excess liquidity models turn out to outperform the autoregressive benchmark, as they deliver more accurate CPI inflation forecasts, especially at the longer horizons. The inclusion of unconventional monetary policy measures does not contradict these findings.     

Liquidity, Quality, Production Cost, and Welfare in a Search Model of Money

This paper examines a search model of money with divisible commodities of high and low quality, while keeping the assumptions of indivisible money and unit-inventory constraint. With no direct barter and a higher fixed cost of producing high relative to low quality, an increase in the money stock encourages the production of high-quality output by trading off the larger trading opportunities against the significance of higher fixed cost. As long as the fixed-cost differential between high and low quality is sufficiently small relative to the utility gain from high-quality consumption, the quality improvement outweighs the negative effect of higher money stocks on aggregate production, and hence implies higher welfare.