M AY / JU N E 1 9 9 6 Alberto Trejos is an assistant professor at Northwestern University. Randall Wright is professor of economics at the University of Pennsylvania, and consultant to the Federal Reserve Banks of Cleveland and Minneapolis. backed by central bank reserves in Search- U.S. dollars (as in Argentina)? Theoretic • Should more Latin American coun- tries simply abandon their local cur- Models of rency and switch to U.S. dollars (as International Panama did)? Though we do not claim to be ready Currency to provide definitive answers to all of these important questions at this time, we do Alberto Trejos and think that search-theoretic models are in Randall Wright principle well suited to address these types of issues. More traditional theory, includ- ing models that include cash-in-advance earch-based theories of the exchange or money-in-the-utility-function type as- process provide economists with a sumptions, are clearly ill suited in this re- Sway of formalizing the microfounda- gard. They are ill suited because too much tions of monetary economics and to dis- is decided by assumption. In particular, cuss a variety of issues in monetary the- the answer to the question, “Which ory and policy in a new light.1 Many monies circulate in which countries?” is questions that cannot even be formulated determined at the outset by the modeler in more traditional monetary models can when he chooses which money to put be profitably analyzed in these new mod- in which cash-in-advance constraint or in els. In this essay, we propose to review re- which utility function. In contrast, cent developments using search-based search models are designed to determine models to study some international mone- endogenously which monies circulate tary issues. where. There seems little doubt that interna- We begin by reviewing a version of tional monetary economics is of central the model in Matsuyama, Kiyotaki, and importance today. Of the types of ques- Matsui (1993). Basically, it can be de- tions one would ultimately like to answer, scribed as follows. There are two countries, consider these: each of which issues its own currency. There is a meeting or matching technology • Should Europe adopt a common that describes the frequency with which a currency? given individual interacts with other indi- viduals, both locals and foreigners (it is as- • If so, should individual countries sumed that one interacts with individuals continue to issue local currencies? from one’s own country more often than a foreigner interacts with these same indi- • If a state or province separates from viduals). When two agents meet, one 1 a nation (as Quebec periodically with money and the other with real output See, for example, in addition to the work discussed below, discusses in Canada), how should it for sale, they have to decide whether to Kiyotaki and Wright (1989, design its monetary system? trade. Parameter values, as well as expecta- 1991, and 1993), Aiyagari tions regarding other agents’ behavior, and Wallace (1991 and • Should more Latin American coun- jointly determine this decision and thereby 1992), Williamson and Wright tries adopt currency boards, where determine the realm of circulation for each (1994), Trejos (forthcoming) each unit of local currency is currency. Potentially there are three dis- and Ritter (1995). F E D E R A L R E S E RV E B A N K O F S T. L O U I S M AY / J U N E 1 9 9 6 tinct types of equilibria—or regimes—in • How does the fact that a currency which we are interested, where none, one, circulates internationally affect its or both of the currencies circulate interna- purchasing power at home? tionally. This model allows one to answer ques- • Where does an international cur- tions like the following: rency purchase more—at home or abroad? • What features of a country make it possible, or likely, for its currency to • What are the effects on seigniorage circulate internationally? and welfare in each country when one money becomes an interna- • How and when can local currencies tional currency? survive in the presence of a univer- sally accepted international cur- • How are policies designed to maxi- rency? mize either seigniorage or welfare affected by concerns of currency • Does an international currency substitution? emerge naturally as economies be- come integrated? • How are national monetary policies connected, and what is the scope • What are the costs and benefits to a for international cooperation? country of having its currency serve as an international medium of ex- In the next section, we outline the change? basic assumptions on which the model is built. The third section presents the indi- • An extension of this model in Zhou visible output version of the model in (1994) additionally allows one to Matsuyama, Kiyotaki, and Matsui (1993). study the issue of when agents We then present the divisible output would want to exchange currencies model with bargaining in Trejos and in such a world. Wright (1995b), followed by a discussion of some policy implications. The final sec- There are shortcomings with the mod- tion presents some brief conclusions. els mentioned in the previous paragraph. Perhaps the most obvious is that in these models, as in all of the first-generation THE BASIC MODEL search-based models of money, every ex- The economy consists of two coun- change is assumed to be a one-for-one tries, labeled i = 1, 2. One’s country is im- trade. This simplifying assumption makes portant in that it determines the frequency it possible to discuss the process of ex- with which one interacts with other change—and, in particular, which objects agents. Individuals interact, or meet, bilat- circulate as media of exchange among erally according to a random matching which agents—without tackling the deter- process in continuous time, and ˆ ij de- mination of the relative values of these ob- notes the Poisson arrival rate at which a jects. Unfortunately, however, it obviously citizen of Country i meets citizens of also makes it impossible to talk about Country j. We assume that ˆ ³ ˆ for 2 ii ji Bargaining was first introduced prices or exchange rates. Therefore, we j ¹ i. This simply says that, for example, a into (one-country) search mod- els of money in Trejos and also present the extension of the model in Mexican meets Mexicans more frequently Wright (1995a) and Shi Trejos and Wright (1995b) designed to en- than an American meets Mexicans. 2 (1995b). Other recent applica- dogenize prices using bargaining theory. Each country starts with a large num- tions include Aiyagari et al. This extension allows us to raise a ber of citizens, and the fraction of individ- (1996), Trejos (1994), and whole range of new issues, including the uals from Country i is Ni with N1 + N2 = 1. Shi (1995a). following: Thereafter, both populations grow at the FE D E R A L R E S E RV E B A N K O F S T. L O U I S 118 M AY / J U N E 1 9 9 6 same rate ³ 0. The population sizes and class of models under consideration from the meeting technology parameters are not ones with particular cash-in-advance or independent because we have the identity money-in-the-utility-function assumptions 4 N1 ˆ 12 = N2 ˆ 21 (both sides of the equality imposed exogenously. give the total number of international Fiat money is introduced by the gov- meetings per unit time). Here we take ˆ ij ernment of Country j issuing one unit of as primitive and let the populations be free Currency j to some fraction Mj Î (0,1) of to satisfy this identity. A special case is the its newborn citizens, at each point in time, specification actually used in Matsuyama, in exchange for some amount of real out- Kiyotaki, and Matsui (1993), which has put (how much real output depends on ˆ ii = N1 and ˆ ij = *Nj, with * < . Thus, what assumptions we make). Issuing arrival rates are proportional to country money in this way yields a continuous flow size, but they are smaller across countries of seigniorage, although notice that the than they are within countries. As * gets only time private agents interact with the closer to , the two countries become government is when they first enter the more integrated.3 economy. In the special case where = 0, Agents are distinguished not only by the government simply issues an input of their country and date of birth, but also by currency to some fraction of its citizens their tastes and technologies. As in the at the initial date and then shuts down. 3 In this model one does not typical monetary search model, we need to To keep things tractable, we make the physically travel between one adopt some notion of specialization. Here, following assumptions. First, we assume country and another, nor does for simplicity, it is assumed that there are that an agent holding a unit of currency one choose in any other way to K ³ 3 goods and the population of each always spends it all at once, which could interact with foreigners instead country contains equal numbers of K obviously be guaranteed if we simply say of fellow citizens. It is simply types, where each Type k consumes only that the monetary object is indivisible. that you sometimes meet for- Good k and produces only Good k +1 This implies that no one holding currency eigners in your daily routine. (modulo K; that is, Type K produces Good ever holds less than one unit.