A Monetary Policy Simulation Game for the Classroom∗ Y VAN L ENGWILER† February 2003 Abstract A computer game is presented that puts the player into the shoes of a central bank governor. The game is a stochastic simulation of a standard reduced form macro model, and the user interacts with this simulation by manipulating the interest rate. The decision problem that the player faces is in many ways quite realistic, in the following sense: Just as a real monetary authority, the player is confronted with a constant stream of shocks he cannot unambiguously identify, and his decisions affect the economy only with a considerable lag. These are two ingredients that make monetary policy decisions so challenging in reality, and that also make playing this game successfully rather difficult. The game can be used for undergraduate or continuing education classes. An “advanced mode” allows the teacher (or the student) to customize many aspects of the simulation, and to experiment with different calibrations or different monetary feedback rules. (JEL codes: A2, C88, E52.) Key words: computer game, monetary policy, stochastic simulation.
The Monetary Policy Simulation Game, or short, MoPoS,1 was built with two aims in mind: First, the game provides a simulation of the decision problem of the monetary authority which is in many ways quite realistic. The user has to decide about the appropriate interest rate based on very limited and not perfectly reliable information. He cannot observe the shocks that hit the economy, and must try to infer them from the time series at his disposal. His decisions interact with a simulated virtual economy in complex ways, and the effects of these decisions are often visible only with a considerable lag, just as in a real economy. These two ingredients (unobservable sequence of shocks and long lags) make monetary policymaking so difficult in reality, and these ∗
This article was published by the Journal of Economic Education, Spring 2004, vol 35 (2), 175–183. University of Basel, Dept. of Economics (WWZ), Petersgraben 51, CH–4003 Basel, Switzerland (
[email protected]), former Economic Adviser of the Swiss National Bank. I thank Georg Rich and Carlos Lenz and the referees of this journal for helpful comments. 1 The game and a user’s guide can be downloaded for free from the website of the Swiss National Bank, see http://www.snb.ch/e/publikationen/publi.html?file=text_mopos.html. The game was the subject of articles in the New York Times (June 4, 2001), Frankfurter Allgemeine Zeitung (August 11, 2001), and many other newspapers. It has been downloaded or ordered more than 20,000 times since April 2001. †
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very same ingredients are present in this game, and make playing it successfully far from trivial. Second, the game provides an alternative to the usual curve-shifting exercises we usually do in beginning economics courses. Rather than analyzing the effects of shocks and policy measures in a comparative static way, the user of MoPoS is confronted with a constant flow of shocks, and experiences the dynamics of his policy decisions through time. This interaction with a stochastic simulation provides a different view of the most important macroeconomic relationships, such as the IS or the Phillips curve, a view that focuses on correlations rather than abstract curves. By providing this different view, the stochastic simulator can be a useful supplement to the traditional teaching method. The game is quite flexible because many aspects of the simulation model can be customized. Yet, the game unfortunately also has significant limitations. First, it cannot accommodate systematic fiscal policy. As such, no interaction between fiscal and monetary policy can be studied with the model. Second, MoPoS’ virtual economy is closed. No international linkages or erratic exchange rate movements make the monetary policy maker’s life difficult. These two limitations may seriously restrict the usefulness of the simulator for more advanced classes. THE MODEL MoPoS implements a fairly simple orthodox model of a closed economy without government sector. The model is calibrated on a quarterly basis. All variables, except interest and inflation rates, are in logs. The core of the model consists of (1) a stochastic trend for potential output, (2) a Phillips curve relating inflation to inflation expectations and (lagged) output gap, and (3) an IS curve relating the output gap to lagged output gap and (lagged) real interest rates. ∆y ∗ = g + ε y ,
(1) "
π = E(π) +
4 X t =0
# ∗ αt (y−t − y−t ) · 4 + επ ,
∗ y − y ∗ = φ · (y−1 − y−1 )−
4 X
βt (i−t − E(π−t ) − r ∗ ) + εd .
(2) (3)
t =0
g in equation (1) is the long run trend growth rate. The Phillips curve in equation (2) has a distributed lag structure, α0 , . . . , α4 . The sum of these coefficients determines the strength of the influence of the output gap on inflation.2 The distribution of this total effect on the five α-coefficients determines the time lag of this effect. The same is true for the IS relation in equation (3). Here, too, the five β-coefficients determine the strength and the time lag by which the real interest rate affects the output gap. In addition, the φ-coefficient is an autoregressive term of the output gap, which is used for implementing sufficient persistence of the business cycle. 2
I multiply in equation (2) the effect of the output gap on inflation by four because π is the annualized quarterly growth rate of the price level.
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Three additional equations, governing E(π), r ∗ , and i , are required to close this system. We first consider inflation expectations. We assume E(π) = λπols + (1 − λ)π−1 .
(4)
According to this equation, inflation expectations are a convex combination of lagged inflation (π−1 ) and an inflation forecast (πols ), which is computed in each period with a rolling regression of current inflation on lagged inflation, real output growth, and money growth (all explanatory variables enter with one to four lags). λ is a measure of inflation stickiness. The smaller λ is, the more inflation is dominated by the autoregressive term, and the less quickly it can change. A large λ, on the other hand, means that realized inflation is not much influenced by its past realizations, but more dominated by the inflation forecast. Quasi-rational expectations (here, OLS expectations) requires λ = 1. The other extreme, λ = 0, makes expectations completely adaptive. Empirically, an intermediate degree of stickiness, 0 < λ < 1, appears to fit the data best (Roberts 1997), and MoPoS’s standard parameter file sets λ equal to one half.3 r ∗ in equation (3) is what Taylor (1993, 202) calls the “equilibrium” real rate. This is the real interest rate that does not cause the output gap to either increase or decrease. In a general equilibrium macro model with firm microfoundations this rate would be related to the time preference of the representative agent and the curvature of his utility function, and to the natural growth rate of the economy (and thus to technical progress). Here, we simply assume that the equilibrium real interest rate fluctuates stochastically around its mean r ∗∗ , r ∗ = r ∗∗ + εr .
(5)
Finally, the nominal interest rate is either set exogenously by the user, in which case the interest rate is exogenous, or the user can choose to use an auto-pilot, which is the standard Taylor (1993) rule,4 i = r ∗∗ + (p−1 − p−5 ) + τπ (p−1 − p−5 − π∗ ) + τ y E(gap).
(6)
The price level is given by the definition5 p = p−1 + π/4.
(7)
p−1 − p−5 in equation (6) is the yearly inflation rate (given the information up to last quarter), so this is the same as (π−1 + π−2 + π−3 + π−4 )/4. E(gap) is the deviation of output from its log-linear trend, which is re-estimated every period. Following Taylor’s 3
Two theoretical reasons for these less than rational expectations have been proposed in the literature. Fuhrer and Moore (1995) argue that the structure of wage setting may be responsible for this stickiness. Gali and Gertler (1999) argue that, in the presence of costly information accumulation, a fraction of the population may simply use inherited inflation as a rule-of-thumb for forming inflation expectations. 4 In fact, the interest rate i , whether it is controlled by Taylor’s rule or by the user, is also subject to shocks in the simulation, indicating imperfect control over the relevant interest rate. 5 We divide by four because π is the annualized quarterly inflation rate.
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original formulation of his rule, the default parameters are τπ = τ y = 0.5, and the inflation target π∗ is set to 2 percent. The model is almost closed now except that monetary growth enters the inflation forecast. So we add a monetary block, in essence an LM curve with a trend velocity plus stochastic velocity shocks, m − p = γy − δi − v.
(8)
∆v = w + εv .
(9)
w is the velocity trend growth rate, and εv are money demand shocks. Note that log velocity, measured as p + y − m, equals (1 − γ)y + δi + v. The standard parameters set the income elasticity of money demand equal to unity (γ = 1). With this choice, the cyclical component of velocity (after removing the velocity trend w) is procyclical if and only if the interest rate is procyclical, as is the case, for instance, with the Taylor rule. All shocks in the model are AR(1) processes with innovations that are normally distributed, or, in the case of ε y , επ , and εd , can have fat tails. On top of this fairly standard structure, we implement observation errors. It is a fact of life that macroeconomic time series are far from perfect and are often revised. The final data are often available only with a substantial delay. Yet, the monetary authority needs to make decisions using the imperfect data it has. We allow for observation errors of the price level and the output, ( p + νp before revision, observed p = (10) p after revision, ( y + ν y before revision, observed y = (11) y after revision. The initial observations of output and price level are subject to noise, νp and ν y . The idea is that the true y and p become available only after some lag (in the standard parameter file after four quarters). It may be somewhat unusual to implement this particular information problem of a monetary authority into an otherwise mainstream model. Yet, it is my belief that the impact of measurement errors is actually quite significant. Orphanides (2001) demonstrated that measurement errors considerably weaken the performance of the Taylor rule as a guide for monetary policy. Users who prefer not to deal with this slightly exotic aspect may turn it off by setting the revision lags to zero (see section “Customizing the game” on how to do that). EXPECTATIONS AND CREDIBILITY Just like a real monetary authority, the user controls the interest rate in this virtual economy, so changes of the interest rate — whether effected by hand or controlled by the Taylor rule — correspond to monetary policy decisions. These monetary policy moves affect the economy in two ways. The first effect is direct, changing the real 4
interest rate and thus affecting the output gap through the IS curve and ultimately the inflation rate through the Phillips curve. The second effect is indirect. Money growth enters the OLS inflation forecast regression, which is recomputed for every simulated period.6 Money growth is immediately affected by the nominal interest rate that the user chooses through the LM relation. If the player follows a completely random interest rate policy, the estimated coefficient of the money growth in the inflation forecast regression will not be significant. Accordingly, interest rate changes will have only a marginal effect on inflation expectations. If, on the other hand, the interest rate policy of the user follows some pattern (a rule?), the coefficient of money growth will be significant and interest changes will also affect the equilibrium of the system through expectations. The user has to build this effect by providing the economy with a long enough, stable pattern for the regression to recognize it. This is similar to building a reputation. For instance, if the user follows the rule to increase the interest rate (and therefore decrease money growth) whenever the inflation rate exceeds some given value, and accordingly thereby quickly reduces inflation, the coefficient of money growth in the inflation forecast equation will be positive and significant. As a result, such a user will find it easier to fight inflation because whenever he raises interest rates, he not only reduces the gap, but also the inflation expectations. Through this simple mechanism, the game implements the idea that a credible central bank — one that has repeatedly demonstrated that it means business — has an easier job. PLAYING THE GAME MoPoS is implemented as an Excel Visual Basic for Applications program. After loading the workbook (and “Enabling macros” in case Excel asks for permission), the user sees a control panel (Figure 1). The panel contains four graphs showing the real growth rate, the inflation rate, the nominal interest rate, and the (ex post) real interest rate [clockwise from top left]. On the right-hand side there is a lever to control the interest rate, and there are a few buttons for specifying the speed of the simulation, and whether the auto-pilot (the Taylor rule) should be turned on or not. On the top right there is a large yellow face. This face, which we call “smiley,” is happy in an inflationless boom. The smaller the real growth rate is, and the farther away we are from price 6
Money is completely passive in this model. The central bank controls the interest rate, and money supply just adapts to the money demand which is determined by nominal output, the nominal interest rate, and money demand shocks according to equation (8). So why would anyone use money to forecast inflation? I believe there are two answers to this: First, in data of real economies (as well as in data of the virtual economy simulated by MoPoS) there is undeniably a strong correlation between money growth and lagged inflation. For an agent who does not know the “true” model it would certainly make sense to use information about monetary aggregates when trying to forecast inflation (especially because economists have advocated in the last forty-odd years that “inflation is a monetary phenomenon” (Friedman 1956)). Second, even within the MoPoS-model it would not be rational to ignore money. Money demand is affected by the true nominal output, net of observation errors. For that reason, monetary statistics contain information that is not contained in any other observable variable.
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Figure 1: The MoPoS control panel. stability, the grimmer it looks.7 The workbook adds a menu, “Simulator,” to Excel’s menu bar. With this menu, the user can save and reload simulations from the disk, and he can switch to an “advanced mode” that offers more possibilities (more on that later). Several simulations come with the game, that correspond to situations that a real central bank may encounter. For instance, there is a boom scenario where the user is called upon to engineer a soft landing. There is also a recession scenario in which the player can try to shorten the recession, but he has to be careful not to overreact and slip into an inflation. Other scenarios are stability, stagflation, inflation, and new economy. The student can also generate new, completely random simulations. In essence, this is all the user needs to know to play the game.8 POSSIBLE EXERCISES The game can be used by complete lay persons on a pure trial-and-error basis. Ideally, however, a user should have had at least some exposure to macroeconomic theory. It is my belief that the game can be put to its most productive use within an undergraduate macro or a principles class. Recently, I have adapted the game on request from the Reserve Bank of New Zealand, see http: //www.rbnz.govt.nz/education/0116902.html The main difference of the New Zealand version is 7
that “smiley” reacts only to the inflation rate, in accordance with the RBNZ inflation target. It shows how well the central bank fulfills its own target. It does not show how satisfied the population is with the overall performance of the economy. 8 For a detailed description of all the features of the program, see the description of the game that comes with the download.
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I have used the game in undergraduate courses at the university, for continuing education courses, and for executive MBA courses. My experience is that the learning experience can be much enhanced by requiring the students to make a protocol of their observations and actions. Playing becomes slower, and the students make a bigger effort in trying to find the best policy if they have to write it down. One simple exercise I usually start with is to ask the students to make “smiley” happy for as long as possible. Of course, this task cannot be achieved for very long, for engineering a boom (which makes “smiley” happy) will eventually lead to high inflation, and a very grim look. I start with this task because it takes out the obvious temptation to see a happy face. Moreover, it demonstrates to the students that in the long run, monetary policy cannot produce miracles. The long-run Phillips curve is vertical in this model, which translates into the fact that, in the long run, “smiley” will not always be happy. A second exercise is to let the students load a fairly easy scenario, such as “stability.sim.” In this scenario, everything is more or less fine. Inflation is under control, it seems, and we are neither in an extreme boom nor in a recession. The only task I give to the students is to try to avoid messing up the situation. Of course, shocks will come along that will require good timing and dosage of action. The student learns that forward looking behavior and, in some cases, preemptive strikes at the first sight of a boom or recession, constitutes good policy. A third exercise is to use the scenario “boom.sim,” and to ask the students to perform a soft landing. Even more difficult is the “stagflation.sim” scenario. The student is also free to produce new random scenarios. Another exercise is to simply observe the evolution of the economy using the Taylor rule. I ask the students to search for patterns. They should write down what “stylized facts” they find. Do they recognize the Phillips curve relationship or the IS curve? This exercise provides for an alternative view of these key relations they have learned in class, a view that is more focused on correlations and lags rather than abstract curves in a coordinate system. Then I ask them if they understand why the Taylor rule moves the interest rate in the way it does. This can help the students understand the rationale of the Taylor rule: React to both, inflation and the output gap, because the output gap will eventually (through the Phillips curve) affect inflation. This is what forward looking monetary policy is about. CUSTOMIZING THE GAME MoPoS has an “advanced mode.” This mode differs most visibly from the simple mode by offering more graphs. There is a graph of monetary growth, and there are graphs of the level of real output, prices, and money stock, together with their trends. More importantly, however, this mode allows the user to tamper with the parameters of the model, and to change the stochastic properties of the shocks, such as their variance and autocorrelation. Also, the sequence of unobservable shocks can be made visible, which can be helpful for understanding the events during a simulation in hindsight. In addition, a new monetary policy feedback rule can also be programmed. With these
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additional possibilities, the teacher can customize many aspects of the simulations, and certain exercises for more advanced classes are conceivable. • A class could be given the task to compare the performance of different parameters in the Taylor rule. What is the optimal weight given to the inflation and the gap component? This can be tested with a series of simulations. Start with, say, 20 10-year-long simulations9 using the standard Taylor rule. For each of these simulations, the results can be copied into an empty worksheet. Redo this for other parameters of the Taylor rule. After that, compute a graph showing the variance of real growth versus the variance (or the average level) of inflation. Which parameter combination works best on average? • The teacher can change the stochastic properties of the shocks or the parameters of the model, for instance in order to match the stochastic properties of a particular economy, or to study the influence of a particular parameter on the performance of different monetary feedback rules. As an example, changing the persistence of shocks has a very strong effect on the behavior of the model. Another experiment is to vary the lengths of the time lags built into the transmission mechanism. This can be done by manipulating the distributed lag parameters in the IS and Phillips curves. • The program also has built in functions for shocks with fat tails. Even more, the parameters of the model can themselves be made stochastic, thereby allowing the implementation of the idea of variable (random) lags (Friedman 1968)10 and the study of robust control problems (Sargent 1998). Such customizations of the parameters of the model can be saved into a parameter file, thereby allowing the user to switch between different calibrations. Besides changing the parameters, the “advanced mode” also allows the teacher to implement a whole new policy feedback rule. There is a cell in the “data” worksheet that accepts a formula that represents your own feedback rule. For instance, one can try to implement an interest rate feedback rule that stabilizes money growth, or one can implement the non linear inflation targeting rule of Orphanides and Wieland (2000). Moreover, the “data” worksheet also allows the user to create additional graphs. For instance, it can be instructive to study under what circumstances money is a good leading indicator. To do that it may be helpful to monitor velocity, yet there is no graph depicting velocity. Such a graph can easily be added, though. Compute velocity as p + y − m in one of the free columns of the “data” worksheet and make a graph with these data. When you run the simulation you can see how velocity evolves through time. 9
Ten years of simulation can be generated with one mouse click using a corresponding menu item in the Simulator menu in “advanced mode.” 10 The parameter file “variable lag.par” features random lags in the IS equation.
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CONCLUSION MoPoS is clearly not designed to replace a study of monetary policy along more standard lines. It is a complement, not a substitute. It provides a “hands-on” experience of the monetary policy decision problem, and it exposes the students to stochastic simulations, which give a rather different view of the workings of the standard AD-AS model than what they are used to. But the biggest advantage is that students can learn and have fun at the same time. It is a perfect antidote against “dry theory” so despised by many students. Using it should make your classes more attractive. REFERENCES Friedman, M. 1956. The quantity theory of money — A restatement. In Studies in the Quantity Theory of Money, Chicago: University of Chicago Press, 3–24. Friedman, M. 1968. The role of monetary policy. American Economic Review 58 (1): 1–17. Fuhrer, J. and G. Moore 1995. Inflation persistence. Quarterly Journal of Economics 110 (1): 127–160. Gali, J. and M. Gertler 1999. Inflation dynamics: A structural econometric analysis. Journal of Monetary Economics 44 (2). Orphanides, A. 2001. Monetary policy rules based on real-time data. Economic Review 91 (4): 964–985.
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Orphanides, A. and V. Wieland 2000. Inflation zone targeting. European Economic Review 44 (7): 1351–1387. Roberts, J. 1997. Is inflation sticky? Journal of Monetary Economics 39 (2): 173–196. Sargent, T. J. 1998. Discussion of ‘Policy rules for open economies’ by Laurence Ball. Working paper, University of Chicago and Hoover Institution. Taylor, J. B. 1993. Discretion versus policy rules in practice. Conference Series on Public Policy 39 (December): 195–214.
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Carnegie Rochester
