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John Duffy is an assistant professor of at the University of Pittsburgh and a visiting scholar at the Federal Reserve Bank of St. Louis. The author thanks Jack Ochs, Michael Pakko, and Joseph Ritter for helpful comments, Nick Meggos for research assistance, and Denise Hazlett and for permission to reproduce figures from their papers.

that the scale of macroeconomic phenomena Monetary is perceived to be too great to be tested in controlled laboratory with small Theory in groups of subjects. That would almost cer- tainly be the view, for example, among the Laboratory applied macroeconomists working with field data. Today, however, most macroeco- John Duffy nomic theorists work with models that build on explicit for the behavior of individuals. These models often INTRODUCTION impose artificial restrictions on individuals’ behavior that are not embodied in any avail- uring the past few decades, an able field data. Consequently, it often is not increasing number of possible to empirically test the aggregate Dhave begun conducting controlled predictions that emerge from these models. laboratory experiments with paid human Even in those cases where the aggregate subjects in an effort to test theories of eco- predictions of microfoundation models can nomic behavior. Economists have turned be tested using field data, it is not always to laboratory experiments because in many possible to use field data to verify whether instances they lack the appropriate nonex- behavior at the individual level adheres to perimental field data that are required to the predictions or assumptions of these models. test their theories. Economic experiments On the other hand, controlled labora- usually involve groups of subjects, tory experiments can be used to test both typically college students, who play simple the aggregate and individual predictions of economic decision-making games and are microfoundation models. Though econo- paid on the basis of the decisions they mists need to be wary of generalizing from make. The games subjects play and the the results of laboratory experiments that monetary rewards they can earn in the involve small groups of subjects to aggre- are constructed in a manner gate macroeconomic activity, there should that approximates the theoretical environ- be somewhat less objection to using exper- ment being studied so that the data iments to test the predictions of individual collected from the experiment can be used behavior in macroeconomic models with to prove or disprove the theory. explicit microfoundations. Because the To date, the experimental methodology predictions of these macroeconomic has been used primarily by microeconomists models stand on their assumptions of how and game theorists to test theories of indi- individuals behave, laboratory evidence vidual or strategic behavior in various can test the reasonableness of a particular economic environments.1 Using laboratory model as a characterization of some experiments, researchers have made substan- macroeconomic activity. And in the tial inroads in these fields; microeconomists increasing number of macroeconomic and game theorists now readily acknowledge models that admit multiple equilibria, the relevance of using experiments to test laboratory evidence can be used to guide theory and have begun to develop new theo- researchers toward those equilibria that ries to explain experimental findings that subjects perceive as more relevant. Finally, are at odds with existing theories. macroeconomists can use laboratory By contrast, there has been relatively methods to conduct policy experiments 1 For a recent survey, see, for little use of the experimental methodology that would be impossible to conduct out- example, Kagel and Roth in . A likely explanation is side of the laboratory. (1995).

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For these and other reasons, a few as a Store of researchers have begun to use laboratory For money to serve as a , experiments, as well as survey questionnaires, economic agents must believe that money to test both the assumptions and predictions will have value in the future. A necessary of modern macroeconomic models. This condition for such a belief is that there be paper describes some of these studies, a future. Suppose it was known that the focusing on laboratory tests of various dif- world would end at a certain future date. ferent models of money.2 Though the Would individuals continue to hold money? major emphasis is on the results obtained According to economic theory, no rational from laboratory studies of monetary theo- individual would choose to hold money ries, some attention is also devoted to the day before the world ended, as money issues of experimental design. would be worthless the next day. By the same kind of logic, no one would choose to hold money two days before the world ended, and THE ROLES AND TYPES therefore no one would choose to hold money OF MONEY three days before the world ended, and so Monetary theorists have no single uni- on. This argument, based on backward fied theory of money and do not appear induction, implies that if the end of the world close to achieving any kind of consensus were known with certainty, individuals on what a reasonable theory might entail. would cease holding money. Do human Instead, there are several different and subjects behave in accordance with this

2 competing models of money. Each model prediction? This is a good example of a Some of this literature is also can account for some, but not all, of the question that is difficult to address outside discussed in surveys by Marimon (1997), Ochs important roles that money plays in the of a controlled laboratory setting. (1995), and Sargent (1993). . In reviewing laboratory tests of these theories it is useful to organize the 3 While there have been many discussion around the three major roles of Testing Backward Induction experiments involving tests of money. Money serves as a store of value, as McCabe (1989) conducted an experi- backward induction, (see, for a , and as a unit of ment that attempted to test for backward example, Smith, Suchanek, 3 and Williams [1988] and account. Money is a store of value because induction. In his experiment, a population McKelvey and Palfrey [1992]), it is believed to retain purchasing power of players is divided up equally into three McCabe’s (1989) is the only over time. Money is a medium of exchange types. The players then engage in a simple one to consider whether sub- because it is readily accepted in exchange trading game that lasts six rounds. In each jects apply backward induction for or services. Finally, money is a round of this game, two of the three player in assessing the value of money. in that of goods and types are endowed with a unit of a good that 4 Wallace (1998) proposes that services are quoted all in terms of units yields a cash payoff at the end of the money should not be a primi- of money. round, but which ceases to have any value tive in theories of money. In In the discussion that follows, we will in the following round. One can think of experimental tests of monetary also make reference to two different types these goods as perishable, like fish or theories there is a similar dic- of money: fiat money and commodity money. bananas. Furthermore, one out of every tum: The goods that are candi- is unbacked, intrinsically worth- three players also possesses a ticket that dates to play the roles of less liabilities issued by the government can be used to buy one unit of any perish- money should not be referred to and declared money by the government’s able good. Tickets are not perishable and as money; this prevents fiat power. Dollar bills are an example of can be potentially used over and over triggering any preconceived fiat money. Commodity money is an again to purchase perishable goods. Like notions that experimental sub- intrinsically valued good, the value of fiat money, these tickets have no intrinsic jects might have regarding the proper role of a money object. which serves as the value of money. Gold value—they yield no cash payoff to their 4 Hence McCabe and other exper- coins are an example of commodity holders. In every round of the game, a imenters testing theories of money. Most of the experimental studies of ticket holder may use a ticket to buy one money use more neutral terms money have focused on fiat money because unit of any good, but only if there is another like tickets to refer to objects that is the type of money most commonly player willing to sell a good for a ticket. that may serve as money. used in the world today. Barter exchanges of goods for goods are not

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10 S EPTEMBER/OCTOBER 1998 allowed. All offers and exchanges are made players do not have sufficient experience with anonymously through a centralized clearing- the implications that a finite horizon has for house (the experimenter). After any the value of their fiat money holdings. exchanges occur, players are paid the cash Though subjects clearly failed to apply value of any goods they are holding at the backward induction, there are certain end of the round. The cash value from features of McCabe’s experimental environ- holding goods varies in a systematic way ment that may have served to promote the over the six rounds of the game and always use of tickets as a store of value. In particular, differs across the three player types. the of tickets in terms of goods was Holding goods yields a cash payoff to each known to be fixed at one-for-one, so even player type of either $0.50, $0.25, or $0 though there was regarding the depending on the round number, and this acceptability of tickets, there was no uncer- information is common knowledge. Simi- tainty regarding the exchange rate of tickets larly, the endowment pattern of goods for goods if tickets were accepted in . varies in a systematic manner that is also Moreover, tickets were the only means of common knowledge. The cash values of transferring goods; barter exchanges of goods goods and the timing of the endowment of for goods were not allowed. these goods are such that, if the game con- tinued without end, all players would maximize their earnings by offering to buy Overlapping Generations Models or sell tickets in certain rounds of the game. of Money That is, the use of tickets (fiat money) in Historically, when fiat money has ceased this game is Pareto improving. The game, to serve as a store of value, the explanation however, does not continue forever. In round 6, has not been that the fiat object was known which all players know is the final round to have zero value at a certain future date. of the game, no player will want to remain Rather, the explanation is always that there holding a ticket because a ticket has no has been a rapid erosion of money’s purchasing future use or cash value. By backward power caused by inflation, as in a very high induction, no player should offer to trade inflation, or hyperinflation. One theory of for a ticket in any round and therefore no hyperinflation suggests that such events may exchanges should ever be observed. be the result of self-fulfilling expectations. Indi- What happens in the experiment? viduals expect that future prices will be higher McCabe reports that in contrast to the the- and make and decisions oretical prediction of no exchange, there is in accordance with this expectation. Conse- a substantial volume of trade in tickets, quently, their expectations of future inflation however, this trading volume does diminish become ratified in an actual inflation that is somewhat as the end of a six-round game consistent with their expectations. Laboratory approaches. When the same six-round tests of this theory have been conducted using game is repeated 10 to 20 times with the Samuelson’s overlapping generations model same group of subjects, these results are of money, which we briefly summarize. unchanged. It was only after McCabe At every date t, a generation of n identical brought the same group of subjects back agents that live for two periods is born; in for two additional experimental sessions, period t they are young and in period t + 1 y each a week apart, that he was able to they are old. Each consumes ct units obtain a collapse of all exchange in tickets of a single, perishable consumption good o from the start of a six-round game. Before when young and ct+1 units of this good when McCabe obtained this result, subjects old. All agents are endowed with ey units played the six-round game 45 times! of the consumption good when young and

McCabe’s experiment suggests that a eo units of this good when old, with ey > eo. fiat object, a ticket, may serve as a store of In addition, each member of the old gener- value for some period of time even when ation has a constant m units of a durable there is a certain, known finite horizon, if but intrinsically worthless fiat object, or

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money, that they acquired in their youth. Figure 1 These old agents may use their fiat money holdings to purchase some of the young A Self-fulfilling, agents’ endowment of the consumption Hyperinflationary Path for Prices good at an endogenously determined per unit price of pt. Because old agents will not p t+1 f(p ) be alive in the next period, they will trade t 45o all of their fiat money holdings for m/pt units of the consumption good held by young agents. Assuming that lifetime is given y o y o by u(ct , ct +1) = ct . ct +1, and that agents have perfect foresight knowledge (rational 0 p– p p expectations) of future prices, the ' t – 2m representative young agent’s problem is to eo

y o max c .c + y o t t 1, ct , ct+1 subject to a pair of budget constraints, one simply consume their endowments. In this for each period of life as follows: case, individuals rationally forecast that the will rise by an ever-increasing y = − ct ey mt / pt , amount in every period, and their forecasts o are always correct—hence the name self- c = e + m / p . t o t t +1 fulfilling model of hyperinflation. The first-order conditions imply that Lucas (1986) noted that the multiplicity in equilibrium, of nonstationary equilibrium paths for prices predicted by this model might be 2mt ey (1) p + = f (p ) = − + p . ruled out by assuming that agents did not t 1 t e e t o o possess , but instead Equation 1 is a first-order difference formed their expectations of future prices equation for the evolution of equilibrium in an adaptive manner. In particular, if price sequences. The specification of the young agents’ time t expectation of next e model is completed by assuming (for now) period’s price level, pt+1, is given by some that mt is set equal to a constant m > 0 for weighted average of past prices and all t. Given this assumption, the model has forecasts, for example, if a unique stationary solution that is given e = α + ( − α) e α ∈( ) as follows: pt +1 pt −1 1 pt , 0, 1 , 2m p = . e − e then one can_ show that the stationary y o solution, p, will be the long-run price An illustration of Equation 1 and the level of the economy. Replacing the stationary solution is provided in Figure 1. assumption of rational expectations with Figure 1 plots the price level at time t + 1 affects the stability against the price level at time t. We see properties of the stationary solution, that unless_ pt is equal to the stationary changing it from an unstable equilibrium solution, p, the equilibrium path of prices to a stable one. will be nonstationary. For instance, if Lucas argued that the question of = > pt p© p, the equilibrium path for which type of equilibrium path for prices prices, as illustrated in Figure 1, is explo- was more likely (stationary or sive, and in the limit, fiat money holdings nonstationary-hyperinflationary) could be are worthless and no exchange occurs addressed in a controlled laboratory exper- between young and old agents—they iment. Following up on Lucas’ suggestion,

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Lim, Prescott, and Sunder (1994) designed agents. Young agents were asked to an experiment that aimed to effectively provide a schedule of the quantity of chips implement the overlapping generations they would supply at various different environment and address the question prices. The chip supply schedules from all posed by Lucas. In every period of Lim et young agents were then aggregated to form al.’s experimental sessions, a group of sub- a supply schedule. The market jects of size n was chosen from an N-member demand for chips was the amount of chips subject pool to take a two-period turn in that could be bought with the total quan- the model environment. Subjects entered tity of francs held by all members of the first as a member of the young generation, old generation (that is, old agents and in the next period they were members passively offered all of their francs for of the old generation. Thus in every period chips). The price at which aggregate of a session there were 2n subjects partici- supply equaled was pating in the model environment and N – announced as the market-clearing, 2n > n subjects who were idle. Each agent equilibrium price level. This price was in the young generation was endowed with used to determine the quantity of chips ey chips and each old agent was endowed supplied by each young agent (according with eo chips (ey > eo). In addition, the ini- to their individual supply schedules), the tial old generation of subjects (who, unlike lifetime utility of old agents who would other participants, were only in the model then exit the model environment, and the environment for one period), were each winner of the price forecasting game endowed with m francs. At the end of a among those agents who were not partici- two-period turn in the model environment, pating as members of either the young or each subject earned cash payments that old generation. were proportional to the lifetime utility In all of Lim et al.’s experimental sessions objective of cy . co, where c y and c o were the price level fluctuated somewhat as agents the amount of chips a subject acquired learned how to make good decisions, but when young and old, respectively. Subjects it was never explosive. Indeed, near the end who were idle in any period played a fore- of the experiments, the price level was close casting game in which they earned cash to, though never precisely_ equal to, the payments according to how well they fore- unique stationary value p 6. The authors cast the market clearing price level that conclude from their experimental findings would prevail in the next period, that is, that stationary solutions for prices are good how close their expectations of next candidates for the equilibria of overlapping e period’s price level, pt +1, were to the actual generations models and that explosive self- 5 price level pt +1. Because of the backward fulfilling hyperinflationary equilibria Of course, subjects were aware induction problem, the experimenters did appear unlikely. that the experimental session not want to reveal to subjects when the In some respects, this conclusion is would last for a finite period— experimental session would end.5 When not too surprising. As previously noted, no more than a couple of experimenters finally did announce the Lucas (as well as others) argued that if hours. They did not know, however, precisely when the end of the session, they used the average individuals did not possess rational expec- game they were playing would forecast of the future price level, as deter- tations of future prices and instead formed end. mined by the nonparticipating subjects, to their expectations adaptively, then the_ sta- determine the value of all money holdings bility of stationary equilibria such as p 6 In fact, the price level was in terms of chips. They thus prevented the might well be altered. Surprisingly, Lim et even closer to another station- backward induction problem and had a al. did not analyze or report forecasted ary where players take account of the size final period price level that was prices from their experiment, preferring to of the group of buyers and sell- endogenously determined by the subjects concentrate their attention on the behavior ers and do not behave as if themselves. of the market price level. They did note, they are atomistic in their abili- After some experimentation, Lim et al. however, that forecasts appeared to be ty to affect prices. This equilib- settled on a mechanism for the exchange adaptive, an observation that might rium is close to the stationary of chips for francs between young and old account for their findings. equilibrium –p.

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Setting aside the issue of whether indi- What happens when subjects are viduals have rational expectations, one placed in this environment? Do they coor- may question the self-fulfilling theory of dinate their expectations in such a way as π π hyperinflation that Lim et al. tested on to achieve high , low or some explosive other grounds. In particular, this theory path for inflation? Marimon and Sunder ignores any causal relationship between (1993) sought to address these questions the growth rate of the and using an experimental design that was the rate of inflation of the price level. similar to that of Lim et al. (1994). One Inflation occurs even though the stock of difference was that nonparticipating 7 The derivation of this equation money is constant. Historically, most subjects now forecast the future inflation makes use of the fact that hyperinflations have been ended by some rate rather than the price level. effort to reduce the growth rate of the Furthermore, the government’s means of m / p = e − cà , t t y t money stock (see, for example, Sargent financing its consumption requirement by [1986]), which suggests that a growing issuing more francs in every period was where cÃt is the young agent’s optimal consumption decision. money stock should be a prerequisite for a made common knowledge. The function hyperinflation to occur. Marimon and Sunder report that in Marimon and Sunder (1993, 1994, contrast to the rational expectations e + e − 2d g(π ) = o y and 1995) have conducted a series of prediction, the actual path for inflation in t e o experiments involving versions of the all of their experimental sessions is always e − y . e π overlapping generations model where the in the neighborhood around the low-inflation o t π stock of fiat money is allowed to grow over stationary equilibrium, low . In particular,

8 time. In these experiments there exists a inflation rates were never observed around Experimental results are replicated government (the experimenter) that seeks the high-inflation steady state, π , nor when qualitatively similar results high are obtained using the same to purchase a constant per capita amount, were they ever explosive. Figure 3 provides experimental design and treat- d, of the consumption good (chips) in a representative illustration of the actual ment variables but with different every period. The government purchases d inflation path from one of Marimon and groups of subjects. This notion chips at price pt by expanding the money Sunder’s experimental sessions (No. 7C). of replications differs from that supply (the amount of francs per capita) m Marimon and Sunder’s findings using the of Dewald, Thursby and Anderson as follows: policy rule, Equation 2, have been replicated (1986), where replication refers in an independent experimental study con- to the ability of different ∆ = − = 8 (2) m mt mt −1 ptd. ducted by Arifovic (1995). researchers to duplicate the same As in Lim et al’s. experiment, Marimon numerical results using the Using the policy rule, Equation 2, in com- and Sunder’s (1993) finding can be explained same techniques on the same bination with Equation 1 and assuming by subjects’ use of some kind of adaptive set of non-experimental data. rational expectations, one can derive a law rather than rational expectations.9 Marimon 9 Marcet and Sargent (1989), for of motion for gross inflation, defined by and Sunder explore this possibility and instance, showed that the low π = t pt / pt −1, of the form: conclude that though no single adaptive inflation stationary equilibrium, rule explains behavior in all of their exper- π , would be stable and π = π e low t +1 g ( t ). iments, a rule for expected inflation, π , of the high inflation stationary the type suggested by Cagan (1956), that is, equilibrium, π , would be high 7 π e = π e + α (π −π e ) < α < unstable if agents forecast infla- This equation is illustrated in Figure 2. t +1 t t −1 t , 0 1, fits tion by running a least squares In this version of the model, if d is the data from many sessions reasonably well. small enough, there exist two stationary When estimated versions of such rules autoregression on past prices. π < π inflation rates, low high . Under the are used in place of rational expectations, 10 Similarly, Arifovic (1995) argues π assumption that agents possess rational the low-inflation steady state, low , is that the experimental findings expectations, the higher of these two locally stable and the high inflation steady are similar to those generated π by a genetic algorithm—an stationary values is predicted to be the state, high , is locally unstable, thereby π 10 adaptive, stochastic search limit of all equilibrium sequences for infla- explaining the attractiveness of low . process based on principles of tion starting from any initial value for Using the same experimental design, π > π population genetics, which also t low ; Figure 2, illustrates one such Marimon and Sunder (1994) conducted converges to a neighborhood of equilibrium sequence with an initial infla- further overlapping generations experiments the low inflation steady state. tion rate of π´. in an effort to understand the effect that

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different government policies might have Figure 2 on subject behavior. They consider as an alternative to Equation 2 a monetary Dynamics in policy of the following form: the Model with a Growing Stock of Fiat Money ∆ = − = π * − (3) m mt mt −1 ( 1)mt −1, π t+1 45o * π where π is the government’s constant gross g ( t) inflation target.11 With Equation 3 in place of the constant government expenditure rule, (Equation 2), there is again the possi- bility of two stationary equilibrium values for inflation. The lower of these two stationary * 0 π π π π inflation rates is π , the government’s low ' high t targeted value, and the higher stationary inflation rate, π **, is one in which fiat money ceases to have value and individuals merely consume their endowments. As in Equation 2, under rational expectations, Figure 3 the higher stationary inflation rate, π **, is The Path of Inflation in Marimon predicted as the limiting inflation rate for and Sunder's (1993) Experimental most initial conditions. Session 7C Marimon and Sunder (1994) report that when the policy rule, Equation 3 is used in Inflation (Percent Per Period) place of Equation 2, and the government’s 250 target, π * , is common knowledge, the infla- π tion rate generated by the experimental 200 high subjects’ decisions is again in a neighbor- hood of the low-inflation stationary 150 π * equilibrium—in this case, . They also 100 π considered whether preannounced changes low * in the two policy variables, d or π , have 50 any effect on the decisions of experimental subjects. The rational expectations predic- 0 tion is that a decrease (increase) in either d 0 2 4 6 8 10 12 14 16 18 20 or π * leads to a decrease (increase) in the Periods low-inflation stationary equilibrium value π π * for inflation (( low or ). Marimon and these two rules is preferable from a policy Sunder report that preannounced decreases perspective. For example, which rule in these policy parameters do not have leads to lower volatility in inflation? This much of an anticipatory effect on subject is the kind of question that would be difficult behavior. Nevertheless, the inflation rate gen- to ask outside of a controlled laboratory erated in the laboratory experiments did setting, as natural experiments that could gradually drift downward to a neighborhood be used to address such questions are rather of the new lower stationary equilibrium, and difficult to arrange. And even if such natural the timing of this change was coincident with experiments could be arranged, it would the actual change in policy. be difficult to disentangle the public’s reac- 11 Under this constant money Given that the two policy rules, Equa- tion from issues surrounding the government’s growth rule, government rev- tion 2 and 3, seem to lead to the same commitment to its new policy. In the labo- enue is now endogenously experimental result, namely coordination ratory, however, the policy rule is under determined according to = ( π * − π * ) . near a stationary, low-inflation equilibrium, the direct control of a non-elected official gt ( 1) / a natural question that arises is which of (the experimenter)—a fact that serves to mt −1 / pt −1.

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minimize, though perhaps not eliminate there is no tendency for increasing coordi- credibility issues. Such control makes it a nation of inflation forecasts around the relatively easy task to consider the perfor- announced inflation target value, π *. mance of different rules. The issue of whether This evidence might be taken to suggest the policy rule described by Equation 2 or that a policy of inflation targeting is not by Equation 3 leads to lower inflation any better at coordinating inflationary volatility is addressed in another paper by expectations than constant money growth Marimon and Sunder (1995). rules. Indeed, because inflation-targeting In this experiment, Marimon and regimes are relatively new, there is little in 12 Marimon and Sunder rule out Sunder considered a parameterization of the the way of nonexperimental, empirical evi- the possibility that agents have overlapping generations model where the dence to suggest that inflation-targeting coordinated on some kind of inflation target, π *, under the constant policies are any better at coordinating stationary sunspot equilibrium because they did not include a money growth rule, Equation 3, is nearly inflationary expectations than earlier policy the same as the low-inflation steady state regimes. See, for example, Mishkin and sunspot variable (a purely π extrinsic variable) for individu- value, low , under the constant government Posen (1997). Hence experimental evidence als to condition on. In expenditure rule, Equation 2. They then of the sort presented by Marimon and Sunder Marimon, Spear, and Sunder asked whether one of the two announced might be useful in these sorts of policy dis- (1993), a two-state sunspot policy rules is better at stabilizing inflation. cussions. variable was introduced into an In this set of experiments, Marimon and In extrapolating from experimental experimental overlapping gen- Sunder (1995) simplified their experimental results to aggregate macroeconomic activity, erations economy. Realizations design considerably so that young agents however, much caution seems warranted. of this variable were not found only provided an inflation forecast (along First, the amount of time that subjects have to play a role in subjects’ with nonparticipating agents). This to learn about policies in the laboratory is expectations. However, when the realizations of the sunspot inflation forecast was used by the computer not really comparable to the amount of time variable were correlated with program to determine the optimal quantity the general public would have available to real shocks for awhile, the of chips that each young agent sells for react to these same policies. Experimental sunspot variable did appear to francs. Thus the game is now one in which economists seek to lessen this problem by be a factor in subject’s expecta- optimization decisions are entirely absent having subjects play many rounds of the tions even after the real shocks and agents are simply concerned with fore- same game, in an attempt to compress the had ended. casting the one-step-ahead inflation rate as amount of time it takes them to learn. 13 In particular, they find evidence closely as possible. There is no guarantee, however, that this of learning equilibrium as Though Marimon and Sunder (1995) compression of learning is a good approxi- described in Bullard (1994). claim, on the basis of their experimental mation of the learning process that occurs

14 evidence, that there is relatively lower outside the laboratory. Second, the policy Other overlapping generations volatility in inflation under the simpler rules themselves are highly simplified experiments, which test the effectiveness of different mone- constant money supply growth rule, Equa- characterizations (some would say carica- tary policy regimes, include tion 3, than under the less transparent tures) of actual monetary regimes. For Bernasconi and Kirchkamp constant government expenditure rule, instance, under either policy rule, Equation (1997), who test whether the Equation 2, the evidence they present does 2 or 3, all government expenditures are labeling of policy regimes mat- not clearly demonstrate any significant dif- financed through seigniorage, a rather ters and Evans, Honkaphja, and ference. Under both policy rules, Marimon unrealistic assumption. Still, Marimon and Marimon (1998), who consid- and Sunder report a few experimental ses- Sunder are only testing models that theorists er whether constitutional sions in which inflation rates persistently themselves have used to characterize mon- restraints on the amount of cycle around the low-inflation steady state, etary policy regimes. Following a grand government seigniorage can be even though cyclic behavior for inflation tradition in economic research, these models used to lower the stationary does not constitute a rational expectations (and experimental results from tests of equilibrium value of inflation. 12 Arifovic (1996) implements an equilibrium. They show that the cyclical these models) are best viewed as abstract 14 experimental overlapping gen- behavior of inflation in these cases is tied versions of reality. erations economy with two cur- to the adaptive forecast processes that agents In the overlapping generations experi- rencies and examines the appear to be using.13 Moreover, they do ments reported thus far, explosive paths behavior of the endogenously not find that inflation forecasts differ much for inflation have not been observed. How- determined exchanged rate. under the two policy regimes. In particular, ever, there is no disputing the fact that,

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though infrequent, there have been historical Figure 4 episodes of hyperinflation and collapse. How might such hyperinflationary The Path of Inflation in Hazlett paths be generated in the laboratory? Ochs and Kernen's (1997) Experimental (1995) suggested that rather than adhering Session 2B to just one or two constant money growth Inflation (Percent Per Period) rates or expenditure levels, what may be 250 required to generate hyperinflationary paths is a policy regime in which the growth rate π 200 high of the money supply accelerates for some period. Here we have an example of histor- 150 ical evidence (on the likely source of π hyperinflationary episodes) affecting exper- 100 low imental design. Following up on Och’s suggestion, Hazlett and Kernen (1997) 50 conducted overlapping generations experi- 0 ments using the Marimon and Sunder 0 2 4 6 8 10 12 14 16 (1995) experimental design, in which they Periods steadily increased the value of government Period 16 inflation: 20,841 percent. Period 17: currency collapses. expenditures, d, over the first 10 periods of an experimental session and then held d constant. This has the effect of increasing the low stationary equilibrium value for tions around the low-inflation stationary inflation, but decreasing the high stationary value for inflation and tracked this value equilibrium value for inflation, before both rather closely, even after government stationary values level off. Subjects were expenditures, d, had stopped increasing. informed in advance of the number of chips This last finding suggests that hyperinfla- (d) that the government would buy in every tionary currency collapses may be sobering period. Though the level of d always remained affairs, having a lasting impact on the below the maximum sustainable level, the way individuals evaluate government steady increase in d did lead to a hyperin- policies and update their expectations. flationary path for prices and a currency One can also interpret this finding as collapse in two out of three sessions with support for the notion that agents eventu- inexperienced subjects. One of these two ally learn to form rational expectations sessions is illustrated in Figure 4. in the sense that they avoid making We see that in this session, actual systematic mistakes. inflation tracks the stationary low-inflation In all of the overlapping generations equilibrium rather well through Period 11. experiments where two stationary, rational When the government ceases to increase expectations equilibria coexist, it is always its chip consumption after Period 11 (so reported that either individuals coordinate that d is constant), inflation nevertheless on the stationary equilibrium with the lower continues to increase. After Period 16, the inflation rate or there is an explosive hyper- currency collapses, as young players’ infla- inflation and currency collapse. Coordination tion forecasts were so high that it was optimal on the high-inflation stationary rational for them not to exchange any of their con- expectations equilibrium never occurs. sumption good for francs. Interestingly, One might ask why the stationary, high- Hazlett and Kernen found that the currency inflation equilibrium is ever focal under collapse outcome was possible only with any expectations scheme, as it is a Pareto inexperienced subjects. When they brought inferior outcome and is associated with experienced subjects back to play the same counterfactual policy prescriptions: A game, they found that the experienced reduction in government spending, d, or subjects always coordinated their expecta- the money growth rate, π *, leads to an

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π increase in the stationary value of high Table 1 or π ** . Experimental evidence suggests an alternative possibility: The Each Type’s Consumption lack of attractiveness of the high inflation and Production Goods stationary equilibrium is caused by Player Type individuals’ use of some kind of adaptive learning process as opposed to rational 1 2 3 expectations. That is, under a variety of Desire to Consume Good: 1 2 3 adaptive expectations schemes, the low But Produces Good: 2 3 1 inflation stationary equilibrium is locally stable and the high-inflation stationary equilibrium is locally unstable. Under this interpretation, the classical policy prescrip- theoretic model of money as a medium of tion within the overlapping generations exchange and the predictions that emerge framework—that a reduction in the money from this theory. growth rate is associated with lower infla- In Kiyotaki and Wright’s (1989) tion—is one that presumes that agents learn model, a population of agents is divided over time in an adaptive manner. equally into three different types, labeled as Types 1, 2, or 3. In addition, there are three different goods, labeled as Goods 1, Money as a Medium of Exchange 2, or 3. Each player, Type i, desires to con- In McCabe’s exchange game and in the sume the good corresponding to his type, overlapping generations experiments, the Good i, but produces some other good, primary role of money is as a store of j ≠ i . Suppose that the of value. If, as has been shown, the money production goods over types is as given in good serves as a store of value, then it also Table 1. Notice that, by design, in the absence serves as a medium of exchange because the of trade there is never a double coincidence money good is the only means of storing of wants between any two players; that is, wealth from one period to the next in all of no agent produces the good desired by the these .15 However, as Ostroy and player type who produces his consumption Starr (1990) have pointed out, though good. For trade to occur, some individuals goods that serve as media of exchange must must accept a good they do not want to necessarily be stores of value, the reverse is consume with the expectation that they will not true—stores of value are not be able to use this good to obtain a good necessarily media of exchange. For they do want to consume. We will refer to example, old master paintings or baseball a good used for such exchange purposes as cards might be excellent stores of value a medium of exchange. Agents in this model but adopting them as commodity monies are able to store a single unit of any good would require that these goods be conven- in any period, but storage of goods is costly. tionally used in trade. To understand the Kiyotaki and Wright suppose that the conditions under which a store of value storage costs of Goods i = 1,2,3, denoted

comes to serve as a medium of exchange, by ci, are such that: what is needed is a model with multiple 0 < c < c < c < u, competing stores of value along with some 1 2 3 motive for individuals to engage in trade. where u is the utility that all three types get Kiyotaki and Wright (1989) have proposed from consuming the good corresponding to 15 Similarly, in the experimental economy studied by Lian and such a model and have characterized the their type. In every period, agents in this Plott (1998), a cash-in- conditions under which certain stores of model are paired randomly with one another. advance requirement for pur- value may come to serve as media of The decision they face is whether to trade chases ensures that money exchange. Before we can discuss the good they currently have in storage for serves as a medium of experimental tests of this model, it will be the good the agent with whom they are paired exchange. useful to have a brief sketch of the search- has in storage. must be mutually

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18 S EPTEMBER/OCTOBER 1998 agreed on and involve simple one-for-one The optimal trading of Type 1 swaps of goods in inventory. If a player players depends on parameter conditions. successfully trades for his consumption Type 1 players play the fundamental good, he immediately consumes that good strategy of refusing to trade their produc- and produces a new unit of his production tion Good 2 for Good 3, which is more good, which becomes the good he has in costly to store, provided that storage. In this case the player earns a pos- β − > ( − ) u itive payoff equal to u – cj, where cj is (4) c3 c2 p31 p21 . the storage cost of his production good. If 3 trade is not mutually agreed on or a player Here, pi1 denotes the fraction of agents of trades for a good that is not his consump- Type i = 2, 3 holding Good 1; β ∈ (0, 1) tion good, his net payoff for the period is is the constant discount factor. The right

–cj, where cj is the storage cost of the good hand side of this inequality represents the he has in storage at the end of the period. discounted, expected difference in utility In the theoretical model, each player’s from having Good 3, rather than Good 2 − trading decision involves weighing the cost in storage. The left hand side, (c3 c2 ), of not trading and incurring the cost of the denotes the additional storage cost of good currently held in storage against the Good 3 over Good 2. If this storage cost expected net utility benefit from trading for difference outweighs the expected gain in the good held by the other player. If the other utility, then it is optimal for Type 1 players player’s good is the desired consumption to play fundamentally and refuse to trade good, then, by design, it is always optimal Good 2 for Good 3. to offer to trade for this good. The more Provided the inequality in Equation 4 interesting trading situations are those in holds, the unique equilibrium prediction is which a player meets a good in trade that is that all three types play fundamental strate- not his consumption good and that is dif- gies. The pattern of exchange in this ferent from the good he currently has in fundamental equilibrium is depicted in storage. In such cases, the expected bene- Figure 5. Type 2 players trade Good 3 to fits from trade involve an analysis of the Type 3 players in exchange for Good 1. relative marketability of the good the player Type 2 players then trade Good 1 to Type 1 currently has in storage and the good that players in exchange for Good 2. Because his trading partner has in storage. These Type 2 players do not value Good 1 for expected benefits must be weighed against consumption purposes, but nevertheless the difference in storage costs between the agree to trade for it, Good 1 may be regarded two goods. as a commodity medium of exchange in this Kiyotaki and Wright focus on steady-state, environment. pure-strategy Nash equilibria. They show If the inequality in Equation 4 is that for all valid parameterizations of this reversed, there is a different unique pure- model, Type 2 and Type 3 players maximize strategy Nash equilibrium in which Types their utility by adhering to fundamental, or 2 and 3 adhere to fundamental trading cost-reducing, pure strategies in which they strategies but Type 1 players choose a agree to trade for goods other than their con- speculative trading strategy, offering to sumption good only if these goods have lower trade their production Good 2 to Type 2 storage costs than the good they currently players in exchange for the more costly-to- have in storage. Thus Type 3 players will store Good 3. Type 1 players then trade never offer to trade their production Good Good 3 with Type 3 players in exchange 1 for any good other than Good 3, because for Good 1, which Type 3 players produce. a trade of Good 1 for Good 2 would increase (See the illustration of this speculative their storage costs. On the other hand, Type 2 equilibrium in Figure 6.) In this specula- players will always offer to trade their pro- tive equilibrium, there are two commodity duction Good 3 for Good 1, because this media of exchange, Goods 1 and 3. Further- trade lowers Type 2’s storage costs. more, because Good 3 is more costly to

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Figure 5 beliefs as the theory presumes, but who must nevertheless adjust their strategies to their evolving historical experiences within The Pattern of Exchange in the Fundamental Equilibrium the given structure of the model. Several experimental studies of the Kiyotaki-Wright environment have been conducted by Brown Type 1 (1996) and Duffy and Ochs (1998a and 1998b) in an effort to address this question. 1 Brown (1996) considered a parameter- od Go d 2 oo ization of the Kiyotaki-Wright model in which G the unique Nash equilibrium prediction was for Type 1 players to speculate in the Good 1 high cost Good 3, but for Type 2 and 3 players Type 2 Good 3 Type 3 to play fundamental strategies, as illustrated by the pattern of exchange shown in Figure 6. Brown conducted two experiments in this environment in which one-third of the pool of 18 subjects were assigned the role of Figure 6 Type 1, one-third the role of Type 2, and one-third the role of Type 3. Subjects were The Pattern of Exchange in the informed of each type’s objectives, told which Speculative Equilibrium good they currently had in storage, and then asked to submit trading strategies for Type 1 all possible encounters with other agents. That is, would they offer to trade the good 3 d Go oo od they currently had in storage if they met G 1 1 d Go oo od Type i with Good j ≠ i in storage? Sub- G 2 3 od Go jects were then paired randomly and their trading strategies were implemented. They Good 1 were informed of the results of these trading Type 2 Good 3 Type 3 encounters—for instance, whether the good they had in storage had changed—and they were also informed of the dollar amount they had won or lost for the round. They then would have the opportunity to change their trading strategies before the next store than Good 1, Good 3 is dominated in round. Subjects played approximately rate of return as a medium of exchange by 50 rounds, with the end to a session deter- Good 1. The notion that a medium of mined randomly. exchange or money may be dominated in Brown reports that nearly all subjects rate of return by other assets (in this case offered to trade for their consumption good by another medium of exchange) is a real- when given the opportunity. Furthermore, world feature that is captured by Kiyotaki 99 percent of Type 2s offered to trade their and Wright’s model but is not so easily production Good 3 for the less costly-to- obtained in other models of money. store Good 1 when faced with the opportunity. Kiyotaki and Wright (1989) provide Hence, Good 1 served as a medium of only a characterization of the kinds of exchange in the experimental economy. equilibria that are possible in their model. Brown also found, however, that only 31 An important but unanswered question percent of Type 1 players offered to trade is whether these equilibria might ever be their production Good 2 for the more achieved by agents who do not begin a process costly-to-store Good 3, even though the of social interaction with equilibrium parameterization of the model was such

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that Type 1 players’ equilibrium best response Figure 7 was always to agree to such trades. Duffy and Ochs (1998a) also tested Aggregate Results From the previously described version of the Duffy and Ochs (1998a) Kiyotaki-Wright model in a laboratory set- ting but sought to provide subjects with Type 1 Offers Good 2 for Good 3 more information than was available in the Fundamental Parameterization Brown study. In particular, they provided (70.0%) subjects with population-wide information on the distribution of goods held in storage by each player type. They thought this information would help subjects assess the (30.0%) relative marketability of the goods they might meet in trade. In the theory, such Offer Refuse information is common knowledge. More- over, Duffy and Ochs allowed subjects to observe the type of player they were matched with and the good that this player Type 1 Offers Good 2 for Good 3 Speculative Parameterization type had in storage, before deciding whether to trade the good they currently had in (64.0%) storage. Finally, these authors made some effort to implement discounting of future payoffs, as the theory assumes, and to con- (36.0%) trol for subjects’ different attitudes toward risk. Subjects began a game with 100 Offer Refuse points and gained or lost points based on the outcome of their trading decisions using known storage costs and other para- meter values. Subjects’ probability of winning a high cash prize was a linear Type 2 Offers Good 3 for Good 1 Fundamental Parameterization function of their end-of-game point totals. Duffy and Ochs considered two different (97.0%) parameterizations of the model—in particular, two different values for u, the utility value of consumption. One value was consistent (3.0%) with the fundamental equilibrium as depicted in Figure 5 and the other with the speculative Offer Refuse equilibrium as depicted in Figure 6. For each parameterization, they report the results of five experimental sessions, each involving 24 to 30 subjects who participated in an Type 2 Offers Good 3 for Good 1 average of 100 trading rounds. Like the Brown Speculative Parameterization (1996) study, Duffy and Ochs found that nearly all subjects offered to trade for their (93.0%) consumption good when given the oppor- tunity. Some of their other main findings are summarized in Figure 7, which reports (7.0%) average aggregate offer frequencies from five sessions in which the fundamental equilib- Offer Refuse rium was the unique Nash equilibrium and five sessions in which the speculative equi- librium was the unique Nash equilibrium.

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In the parameterization consistent with the Thus agents in this environment face an speculative equilibrium, they found results interesting coordination problem: Whether that were similar to those of Brown (1996). to avoid the use of an intrinsically worth- An average of 93 percent of Type 2 players less object as a medium of exchange in offered to trade Good 3 for Good 1, favor of a valued commodity object or to whereas an average of only 36 percent of use both as media of exchange. Duffy and Type 1 players chose to speculate by Ochs (1998b) report that in the experimental offering to trade Good 2 for Good 3. When economy there is, in fact, a substantial the parameterization of the model was volume of trade in the fiat object, Good 0, changed so that the unique Nash equilib- which is accepted anywhere from 80 percent rium was the fundamental equilibrium, to 95 percent of the time. Moreover, Good Duffy and Ochs found that these aggregate 1 remains a medium of exchange as well. offer frequencies were not significantly dif- The findings that emerge from these ferent. Nearly all Type 2 players, 97 percent, experimental studies of money search continued to offer to trade Good 3 for Good 1, models provide somewhat mixed support as predicted in the fundamental equilibrium. for the theory. On the one hand, goods may Thirty percent of Type 1 players, however, serve as media of exchange if they have speculated in Good 3, despite the fact that relatively low storage costs compared with such speculation did not constitute a steady other goods. Moreover, like fiat money, state best response. Duffy and Ochs attempted these low-storage-cost goods need not be to uncover the motivations for players’ intrinsically valued. These findings are actions (especially those of Type 1 players). consistent with equilibria in which all Using a simple learning model, they showed players play according to fundamental, that subjects were motivated mainly by the cost-reducing strategies. However, in para- payoff success of past actions and not by meterizations in which some players are the marketability concerns that the theory predicted to play speculative trading emphasizes. strategies in equilibrium (Type 1 players in Duffy and Ochs (1998b) considered a the version of the model described here) modification to the Kiyotaki-Wright envi- using relatively high-storage-cost goods as ronment in which an intrinsically worthless, media of exchange, the experimental but perfectly durable, fiat object, Good 0, evidence appears at odds with these theo- was added to the model. This Good 0 could retical predictions. Further experiments in not be produced, consumed, or discarded search-theoretic environments might help by any player type. The fiat object was resolve these issues. On the other hand, introduced into the economy by endowing these experimental findings might serve to a fraction, m, of each player type with motivate further theoretical explanations Good 0 and endowing the remaining frac- for why money is held despite being domi- tion, 1 – m, with their production good. In nated in rate of return by other assets. one of the experimental treatments, the storage cost of Good 0 was set at zero, making it the least costly-to-store good; Money as a Unit of Account the storage costs of the other goods were Finally, we consider the role of money unchanged. In this case there is an equilib- as a unit of account. There is no question rium in which Good 0 is always accepted that money serves as a unit of account, that when offered in trade. There is another is, as a common measure of the value of all equilibrium, however, in which no one . Indeed, most of us do believes that Good 0 has any value. This not hesitate to think of the value of all goods belief becomes self-fulfilling because no and services in terms of the number of agent offers to trade for Good 0. In either money units it takes to purchase them— case, Good 1 continues to circulate as a that is, in terms of prices. However, when commodity medium of exchange in the it comes to thinking about the value of fundamental equilibrium of the model. goods and services over time, taking infla-

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22 S EPTEMBER/OCTOBER 1998 tion (or deflation) of prices into account, as well as with various Americans, (including casual empiricism suggests that individuals his own dentist!) to buttress his frequently think in nominal, or current-dollar, contention that money illusion was perva- terms, rather than in real, or constant-dollar, sive. Since Fisher’s (1928) book, however, terms as is assumed in economic theories. economists have largely ignored the empir- For example, the U.S. financial press is ical question of whether individuals suffer fond of reporting on changes in the benchmark from money illusion, preferring to believe Dow Jones Industrial Average (DJIA), which that there can be no such illusion. As is the current-dollar, weighted average Howitt (1987) notes, money illusion con- price of 30 Blue Chip stocks. If there is tradicts economists’ assumptions of inflation of the price level then, over time, rational, utility, or profit-maximizing the value of the DJIA will reflect this infla- agents, and for this reason economists tion as well. What stock market investors tend to dismiss the possibility of money should care about is changes in the value illusion out of hand. of the DJIA in constant dollars, that is, in Recently, the question of the extent to dollars adjusted for inflation (as measured which individuals may suffer from money by changes in a price ). But that is illusion has been reconsidered by Shafir, not the figure that gets reported. Diamond, and Tversky (1997). Going (1928) defined money beyond the casual empiricism of Fisher illusion as the “failure to perceive that the and others, these authors have sought to dollar, or any other unit of money, expands document, through the use of survey ques- or shrinks in value.” Fisher argued that tionnaires, the extent to which individuals money illusion was a serious problem think in nominal rather than real terms.16 because economic contracts are nearly Though the use of survey questions is always specified in money units, and the prone to a number of biases and differs in parties to such contracts must recognize many respects from controlled laboratory the possibility of inflation or deflation of environments where individuals are paid prices over the length of the contract to on the basis of the decisions that they properly judge whether the contract is make, the idea of attempting to quantify likely to result in a real gain or loss. the extent of money illusion by asking the Because Fisher thought that money public how they think about economic illusion was pervasive, he argued that it decisions is similar to the experimental was the task of the monetary authority to methodology. stabilize the level of prices and therefore Shafir et al. used a variety of different the purchasing power of money. He survey questions that were designed to detect likened this task to government efforts to the presence or absence of money illusion in standardize weights and measures to economic decision-making. The questions prevent cheating. “If,” Fisher argued, “we were presented to large groups of people are at such pains to standardize or stabilize (typically 100 or more) at two New Jersey 16 Similarly, Bewley (1998) uses the yard, the pound and every other goods- shopping malls, the Newark International surveys of firm behavior to exam- unit, having—as we do—official settlers of Airport, and to Princeton undergraduates. ine the extent to which labor mar- weights and measures to prevent the cheating In most cases, the answers given by the various kets suffer from a related illusion, of the public because of changes in those groups were similar. The authors conclude namely resistance to nominal goods-units, how much more important is that the answers to these survey questions cuts. Shiller (1997a) it to stabilize the unit of money, applying indicate that “money illusion is a widespread uses survey evidence to explain as it does to every purchase and sale.” phenomenon in the United States.” why there is resistance to indexation of long-term con- Fisher’s argument for price stability is Consider for example, the following tracts. In another paper, Shiller predicated on the notion that the public question, which is typical of the survey (1997b) uses survey evidence suffers from money illusion, but what is questions in the Shafir et al. study: to demonstrate that econo- the hard evidence for this claim? Fisher mists’ mental models of infla- himself related conversations he had with “Two competing bookstores have in stock tion are substantially different Germans he met while touring Germany, an identical leather-bound edition of from those of non-economists.

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Oscar Wilde’s collected writings. Store A theorizing. As Shafir et al. point out, there bought its copies for $20 each. Tom, who are ways of providing more neutral frames, works for Store A, has just sold 100 copies which eschew terms such as real. Using of the book to a local high school for $44 these more neutral frames, the authors a copy. Store B bought its copies a year after report that the incidence of money illusion Store A. Because of a 10% yearly inflation, is only somewhat diminished. Store B paid $22 per copy. Joe, who works A stronger critique of Shafir et al.’s survey for Store B, has just sold 100 copies of results is that the decisions subjects were the book to another school for $45 a asked to make were, in all cases, hypothet- copy. Who do you think made a better ical, and with one exception, subjects were deal selling the books, Tom or Joe?” not paid according to the answers they provided.17 In fact, most subjects were not Shafir et al. report that 87 percent of a paid anything to answer the survey questions, group of 130 subjects incorrectly chose which might make us wonder whether Tom. The authors hypothesize that these they were sufficiently motivated to think subjects focused on the fact that Tom’s hard about their responses. It thus remains nominal profit of $24 was higher than Joe’s to be seen whether these same kinds of nominal profit of $23, even though in real results will continue to be obtained when terms Joe earned more than Tom. an individual’s decisions have direct and Some might argue that findings of this significant payoff consequences as they do sort are simply a result of the manner in in actual markets.18 Indeed, one can think which the problem is framed, or presented, of the survey findings as a kind of pilot to subjects. Indeed, Shafir et al. address test for controlled laboratory experiments; the possibility of framing effects at some if the survey results did not reveal evidence length. The framing problem—that results of money illusion, then it seems unlikely that may differ under different frames—is one paying subjects according to their decisions that plagues all research, not just survey would lead to significantly different results. or experimental methods. Indeed, it is dif- Casual empiricism of the type alluded to ficult to imagine developing any model of earlier suggests that it should be possible 17 The exception is an experiment behavior that does not rest on some partic- to find evidence of money illusion with conducted by Thaler, Tversky, ular framing of a problem. paid human subjects in controlled labora- Kahneman, and Schwartz To illustrate the potential importance of tory settings.19 (1997) which is discussed in framing effects, suppose the wording of the Shafir et al. (1997). preceding question was changed as follows: 18 Tversky and other psychologists CONCLUSION have argued that in many (but “Tom and Joe both paid the same real What, if anything, can we learn from not all) cases, subjects’ price for 100 copies of an identical these experimental studies? Can experimental responses to hypothetical sur- leather-bound edition of Oscar Wilde’s evidence be used to confirm or refute a vey questions do not depend collected writings. Tom has just sold his particular monetary model or equilibrium on whether the subjects are 100 copies to a local high school for $44 prediction? Some might argue that the the- paid according to their respons- es. Experimental economists, while Joe has just sold his 100 copies to oretical environments examined, especially for example, Smith and Walker another school for $45. Who do you the overlapping generations and search (1993), have disputed this think made the better deal selling the theoretic models of money, are too complex view, with experiments that books, Tom or Joe?” for subjects to comprehend, and for this show that paying subjects reason, these theories cannot be tested in the according to the decisions they With this new wording, I would laboratory. This argument, however, begs the make does make a big differ- hazard that most would find the correct question of just what type of behavior these ence in behavior and nearly answer (Joe) rather obvious. The new theories seek to describe. If a theory cannot always reduces the variance of wording of the problem, however, is such be tested, because of a lack of non-experi- observed actions. that there is no possibility for money illu- mental data and because laboratory tests of 19 See, for example, the work of sion to occur—that is, the problem has it are judged to be impossible, then what one Fehr and Tyran (1998). been assumed away, as in most economic has, essentially, is a vacuous theory.

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A more reasonable critique is that the REFERENCES experimental environment is not complex Arifovic, Jasmina. “The Behavior of the Exchange Rate in the Genetic enough or that it leaves out many real Algorithm and Experimental Economies,” Journal of world features—for example, communica- (June 1996), pp. 510-41. tion or observation of the decisions of others, which, if allowed, would serve to ______. “Genetic Algorithms and Inflationary Economies,” Journal further promote the adoption of money as of (December 1995), pp. 219-43. a store of value, as a medium of exchange, Bernasconi, Michele, and Oliver Kirchkamp. “The Name of Inflation: An or as a unit of account in accordance with Experimental Study of , Inflation and Monetary Policies in an the theoretical predictions. But this same Overlapping Generations Economy,” Universitat Manneheim Working critique can be made of the theory itself, Paper (September 1997). which does not allow for, or more typically Bewley, Truman F. “Listening to Business: A Study of Wage Rigidity,” has nothing to say about, such real-world fea- Yale University Unpublished Manuscript (January 1998). tures and is itself only an approximation to Brown, Paul M. “Experimental Evidence on Money as a Medium of some observed real-world phenomena. Exchange,” Journal of Economic Dynamics and Control (April 1996), The approach of experimental researchers pp. 583-600. is to attempt to approximate the theoretical Bullard, James. “Learning Equilibria,” Journal of Economic Theory environment as closely as possible and then (December 1994), pp. 468-85. argue that the experimental results from the Cagan, Phillip. “The Monetary Dynamics of Hyperinflation,” Studies in approximated environment can be used to the Quantity Theory of Money, , ed., University of test the theory. In many cases, as we have Chicago Press, 1956, pp. 25-117. seen, these laboratory approximations deliver Dewald, William.G., Jerry G. Thursby, and Richard G. Anderson. results that are consistent with some of the “Replication in Empirical Economics: The Journal of Money, Credit and theoretical predictions. Furthermore, in Banking Project,” American Economic Review (September 1986), the overlapping generations and search- pp. 587-603. theoretic environments where multiple Duffy, John and Jack Ochs. “Emergence of Money as a Medium of equilibria are possible, evidence from labo- Exchange: Experimental Evidence,” University of Pittsburgh Working Paper ratory experiments can be used to resolve the (January 1998a) and American Economic Review, forthcoming. question of which equilibrium is likely to ______and ______. “Fiat Money as a Medium of Exchange: be more focal, and therefore more relevant, Experimental Evidence,” University of Pittsburgh Working Paper for policy purposes or theoretical extensions. (March 1998b). In cases where the experimental results Evans, George W., Seppo Honkapohja, and Ramon Marimon. “Fiscal are at odds with the theory, there is always Constraints and Monetary Stability,” University of Oregon Working the possibility that further refinements of Paper 217, 1998. the experimental environment—for instance, changes in the manner in which problems Fehr, Ernst and Jean-Robert Tyran, “Does Money Illusion Matter? An Experimental Approach,” Discussion Paper No. 9802, (February are framed—may serve to deliver experimental 1998), University of St. Gallen results that ultimately confirm the theoret- ical predictions. There should also, however, Fisher, Irving. “The Money Illusion”, Adelphi, 1928. be feedback from experimental results to Hazlett, Denise, and Amanda Kernen. “Hyperinflation and Seigniorage theoretical modeling, especially when in an Experimental Overlapping Generations Economy,” Whitman experimental results are continually found College Working Paper (September 1997). at odds with a particular theory. Howitt, Peter. “Money Illusion,” The New Palgrave: A Dictionary of The experimental studies discussed in Economics, vol. 3, John Eatwell et al., ed., The Macmillam Press, this paper provide some support for several 1987, pp. 518-19. different theories of money, but large gaps Kagel, John H., and Alvin E. Roth eds. “The Handbook of Experimental still remain in our understanding of why Economics, Princeton University Press, 1995. money is held and how decisions involving Kiyotaki, Nobuhiro, and Randall Wright. “On Money as a Medium of money are made. Further theoretical work, Exchange,” Journal of the Political Economy (August 1989), pp. 927-54. in combination with laboratory experiments Lian, Peng, and Charles R. Plott, “General Equilibrium, Markets, can serve only to deepen our understanding Macroeconomics and Money in a Laboratory Experimental Environment,” of this important topic. Economic Theory, 12 (July 1998), pp. 21-75

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Lim, Suk S., Edward C. Prescott, and Shyam Sunder. “Stationary Solution Shiller, Robert J. “Public Resistance to Indexation: A Puzzle,” Brookings to the Overlapping Generations Model of Fiat Money: Experimental Papers on Economic Activity 1, (1997a), pp. 159-228. Evidence,'' Empirical Economics 19(2), 1994, pp. 255-77. ______. “Why Do People Dislike Inflation?” Reducing Inflation: Lucas, Robert E. Jr. “Adaptive Behavior and Economic Theory,” Journal Motivation and Strategy, Christina Romer and David Romer, eds., of Business (October 1986), pp. S401-S426. Reprinted in Rational University of Chicago Press (1997b), pp. 3-65. Choice: the Contrast Between Economics and Psychology, Robin Smith, Vernon L., Gerry L. Suchanek and Arlington W. Williams. Hogarth and Melvin Reder eds., Chicago: University of Chicago Press, “Bubbles, Crashes and Endogenous Expectations in Experimental Spot 1986, pp. 217-42. Asset Markets,” Econometrica (September 1988), pp. 1119-51. Marcet, Albert, and Thomas J. Sargent. “Least-Squares Learning and Smith, Vernon L. and James M. Walker. “Monetary Rewards and the Dynamics of Hyperinflation,” Economic Complexity: Chaos, Decision Cost in Experimental Economics,” Economic Inquiry (April , Bubbles, and Nonlinearity, William A. Barnett et al., eds., 1993), pp. 245-61. Cambridge: Cambridge University Press, 1989, pp. 119-37. Thaler, Richard H., , , and Alan Schwartz. Marimon, Ramon. “Learning From Learning in Economics,” Advances in “The Effect of on Risk Taking: An Experimental Test,” Economics and : Theory and Applications, vol. 1, David Quarterly Journal of Economics (May 1997), pp. 647-61. M. Kreps and Kenneth F. Wallis, eds., Cambridge University Press, 1997. Wallace, Neil. “A Dictum for Monetary Theory,” Federal Reserve Bank Marimon, Ramon, Stephen Spear, and Shyam Sunder. “Expectationally of Minneapolis Quarterly Review (Winter 1998), pp. 20-26. Driven Market Volatility: An Experimental Study,” Journal of Economic Theory (October 1993), pp. 74-103. Marimon, Ramon, and Shyam Sunder. “Expectations and Learning Under Alternative Monetary Regimes,” Economic Theory (January 1994), pp. 131-62. ______and ______. “Indeterminacy of Equilibria in a Hyperinflationary World: Experimental Evidence,” Econometrica (September 1993), pp. 1073-107. ______and ______. “Does a Constant Money Growth Rule Help Stabilize Inflation? Experimental Evidence,” Carnegie Rochester Conference Series on Public Policy, 1995, pp. 111-56. McCabe, Kevin A. “Fiat Money as a Store of Value in an Experimental Market,” Journal of Economic Behavior and Organization (October 1989), pp. 215-31. McKelvey, Richard D., and Thomas R. Palfrey. “An Experimental Study of the ,” Econometrica (July 1992), pp. 803-36. Mishkin, Fredric S. and Adam S. Posen. “Inflation Targeting: Lessons From Four Countries,” Federal Reserve Bank of New York Review (August 1997), pp. 9-110. Ochs, Jack. “Coordination Problems,” The Handbook of Experimental Economics, John H. Kagel and Alvin E. Roth, eds., Princeton University Press, 1995, pp. 195-251. Ostroy, Joseph M., and Ross M. Starr, “The Transactions Role of Money,” Handbook of Monetary Economics, vol. 1, Benjamin M. Friedman and Frank H. Hahn, eds., Elsevier Science Publishers, 1990, pp. 3-62. Sargent, Thomas J. Bounded Rationality in Macroeconomics, Oxford University Press, 1993. ______. “The Ends of Four Big Inflations,” Rational Expectations and Inflation, Thomas J. Sargent, ed., New York: Harper and Row, 1986, pp. 40-109. Shafir, Eldar, , and Amos Tversky. “Money Illusion,” Quarterly Journal of Economics (May 1997), pp. 341-74.

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