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This reprint is provided for personal and noncommercial use. For any other use, please send a request Brian Hayes by electronic mail to [email protected]. Computing Science

Everything Is Under Control

Brian Hayes

n 1949, faculty and students at The basic idea in Keynesian econom- I the London School of Economics Can control theory ic policy is to counteract any oscillatory gathered to observe a demonstration. tendencies. When an economy over- At the front of the room was a seven- heats, with business activity growing foot-tall contraption assembled out of save the economy at an unsustainable pace, the central plastic pipes, tanks, valves and other bank raises interest rates and thereby plumbing hardware. The device, later from going restricts the money supply. At the same dubbed the MONIAC, was a hydraulic time, governments raise taxes or reduce analog computer for modeling the flow down the tubes? spending, which also cools the econo- of money through a national economy. my. Conversely, when business slumps, When the machine was powered up, the aim is to spur growth by lowering colored water gurgled through the worth revisiting, especially at a time interest rates and by letting the govern- transparent tubes and sloshed into res- when real economies are leaking liq- ment run a deficit, spending more than ervoirs. Various streams represented uid assets at an alarming rate. it takes in through taxes. consumption, investment, taxes, sav- Keynes has gone in and out of fash- ings, imports and exports. Crank- Engineering the Economy ion, but even many of his detractors now wheels and adjustable cams allowed The principal architect (and plumber) accept the idea that controlling wild ex- the water levels and flows to be regu- of the MONIAC was A. W. H. Phillips, cursions of the business cycle is an ap- lated—the hydraulic equivalent of set- a New Zealander who had been an propriate policy goal. In the current eco- ting interest rates or tax policies. This electrical engineer before he turned to nomic downturn, it is taken for granted was real trickle-down economics! economics. It’s easy to see the influ- that governments will do their best to The MONIAC attracted much atten- ence of his engineering background. A speed recovery and mitigate damage. tion, and it lives on in folklore. Later hydraulic simulation of the economy In the U.S., both the recently departed generations of students called it the makes sense only if you believe that the Republican administration and the new “pink lemonade national income ma- circulation of money through a soci- Democratic one have enacted huge chine.” Punch magazine tried to satirize ety obeys definite, mathematical laws, “stimulus” plans, and the Federal Re- the device, but their cartoon was really like those that govern real fluids and serve has cut interest rates to near zero. no more outlandish than the construc- other physical systems. And the crank- Everyone waits anxiously to see how tion drawings for the machine itself. wheels and cams on the MONIAC im- well these measures will work. There are tales of leaks; according to ply that the behavior of an economy is The economics profession, naturally, one source, the machine couldn’t cope not only predictable but also controlla- has much to say about these matters, with inflation, which caused red fluid ble. If we twiddle the knobs and nudge but there is another intellectual tradition to squirt out through a hole in one of the levers in just the right way, all the that may also offer useful counsel: con- the cylinders. And then there’s the streams will flow smoothly and the trol theory, the branch of applied math- story about the Chancellor of the Ex- various basins where wealth accumu- ematics and engineering that deals with chequer and the Governor of the Bank lates will never run dry or overflow. feedback systems. Devising a scheme of England; when they were given a This notion of engineering an econ- to suppress oscillations, like those seen turn at the controls, the results showed omy was and is controversial. Adam in the business cycle, is a common task “why the U.K. economy was in the Smith and other classical economists for control theorists. The theory also state it was.” had argued that markets are self- identifies certain unfortunate situations This is all good fun, but the correcting; meddling with them can where attempts to impose control can MONIAC was not just a toy or a joke. only impair their efficiency. By the actually make matters worse, destabi- It embodied a style of thinking about 1930s, however, the British economist lizing a system that might otherwise economic problems that may still be John Maynard Keynes was making a have found its own equilibrium. case for a specific kind of intervention Brian Hayes is senior writer for American Scien- by governments and central banks: Control Freaks tist. Additional material related to the “Computing They could and should act to stabi- On first acquaintance, the idea of feed- Science” column appears in Hayes’s blog at http:// lize economies, he said—to smooth out back control seems straightforward bit-player.org. Address: 211 Dacian Avenue, Dur- cycles of boom and bust. Phillips was enough. Consider the design of a cruise- ham, NC 27701. Internet: [email protected] one of Keynes’s many followers. control system for an automobile. A

© 2009 Brian Hayes. Reproduction with permission only. 186 American Scientist, Volume 97 Contact [email protected]. minimal version measures the current speed of the car, compares it with the desired speed, then adjusts the throttle by an amount proportional to the difference. If the car slows somewhat— perhaps on an upgrade—the controller senses the discrepancy and opens the throttle wider, so that the car regains some of the lost speed. But there is more to control theory than this simple proportional-feedback mechanism. A drawback of pure proportional control is that the car never quite attains the requested speed; as the error diminishes, so does the feedback signal, and the system settles into a state with some nonzero offset from the correct velocity. The offset can be eliminated by another form of feedback, based not on the error itself but on the integral of the error with respect to time. In effect, the integral measures the cu- mulative error, which keeps growing if the speed differs even slightly from the set point. Thus integral control ensures that over the long term the net error approaches zero and the average speed converges on the set-point speed. Yet integral control has drawbacks of its own. Suppose the car cannot main- tain a commanded speed of 60 on an upgrade; an integral controller might compensate by going 80 on the other side of the hill, which could get you a speeding ticket. More generally, integral control has a tendency to overshoot and oscillate around the set point. A remedy is to add still another form of feedback, based on the time derivative of the error signal. Derivative feedback opposes rapid changes in speed and thus tends to damp out oscillations.

Running Hot and Cold Proportional, integral and derivative Colored water in transparent plastic pipes control (together known as PID) are ba- modeled the flow of money through an economy in a hydraulic computer built in 1949 sic tools of control theory. In designing cam a control system, an engineer sets the by the British economist A. W. H. Phillips. “gain” of each type of feedback—the Fluid pumped to the top of the main circuit represented income; it streamed back down valve amount of correction applied for a giv- as consumption, with amounts diverted into en error magnitude. High gains yield taxes and savings. The flows were regulated a sensitive controller that promptly by feedback devices, such as the one depicted detects and corrects any disturbance. in the diagram at right: A float in a reservoir But a controller that responds too vig- operated a valve, which controlled the rate at orously risks destabilizing the system, which the reservoir filled. The drawing above, float magnifying departures from the set which shows an Americanized version of the point rather than suppressing them. Phillips computer, is in the James Meade Ar- reservoir The hazard of controller-induced chive of the London School of Economics. instability is most acute when there are delays, or time lags, built into the the water is too cool, so you twist the little more. When the hot water finally feedback circuit. The nature of this temperature-control valve counter- makes its way to the shower head, you problem is familiar in everyday life. clockwise. Nothing happens for a few find you’ve gone too far. You dial the You step into the shower and find that seconds, and so you turn the valve a valve back a little, but the water con-

© 2009 Brian Hayes. Reproduction with permission only. www.americanscientist.org 2009 May–June 187 Contact [email protected]. tinues to get hotter, so you turn the might need to regulate temperature, control law that comes closest to satis- control further clockwise. Soon, you’re pressure and several flow rates. Again, fying a given criterion. shivering. The temperature oscillations the variables cannot be considered A number of further variations have can keep growing until the shower is separately; turning up the heat alters grown out of optimal control. Robust alternately emitting the hottest and the pressures and flows. control finds laws that deliver reason- coldest water available. (In this situa- Solving such multivariable control able performance even if the real system tion the average temperature might be problems was difficult and tedious with differs somewhat from the mathemati- just right, but no one would count that early design methods, which are now cal model that represents it. Stochastic a success of the control system.) characterized as classical control theory. control tolerates noise or errors in the Cruise control and a shower valve Those methods assess the performance measurements of the system’s state. are examples of control systems that of any given control law but leave to Adaptive control applies the feedback regulate a single variable, such as the intuition of the engineer the task of principle to the control laws them- speed or temperature. An aircraft auto- choosing which laws to test. Beginning selves, allowing the controller to con- pilot, in contrast, might have to main- in the 1960s, modern control theory in- tinue working as the system evolves. tain a constant altitude and heading as troduced a new computer-intensive well as controlling motion around the methodology that not only evaluates An Invisible Hand on the Controls roll, pitch and yaw axes. All of these given laws but also searches for the Even without any external controls, variables are coupled; a change in one best attainable laws under stated con- economic systems are laced with mul- affects others. Similarly, a controller for straints. This collection of techniques, tiple feedback loops. Adam Smith’s a distilling column in an oil refinery known as optimal control, identifies the price mechanism is the best-known example: When demand exceeds supply, gains prices rise, thereby curtailing demand kp set lag and allowing prices to fall back toward point e their original level. This is a negative- e k ∫ i  feedback loop, which has a stabilizing de influence. Other loops introduce posi- kd dt tive feedback, as with the inflationary lag spiral: Rising prices bring demands spending production  for higher wages, which lead to still income higher prices. Smith believed that built-in feedback Concepts from control theory underlie an economic model devised by Phillips in 1954. At the mechanisms are the best possible regu- bottom of the block diagram is a feedback loop representing the operation of the economy lator of an economy; left alone, the sys- itself: Spending by consumers results in demand for production, which after a time lag gener- tem will find its own equilibrium, bal- ates income, which in turn is spent to create still more demand. The rest of the diagram shows ancing production and consumption. a hypothetical control circuit meant to stabilize the economy. The difference between actual Keynes agreed that economies tend income and a set point produces an error signal, e, that is transformed to become a negative toward equilibrium, but he pointed out feedback applied to production. Three forms of control feedback are included, namely signals that the same economy might wind up proportional to e, proportional to the integral of e and proportional to the time derivative of e. at many different points of equilibrium. A thriving economy has a high level of proportional + integral + derivative control production balanced by a high level of consumption; for a depressed economy, 0 supply and demand remain in balance, but both are at lower levels. The aim of proportional + integral control Keynesian economic policy is to nudge –1 us from a recessionary equilibrium toward a more prosperous one. proportional control Keynes did not formulate his ideas –2 in the vocabulary of control theory, but some of his followers did. Phillips took this approach not only in the design

change in economic output –3 of the MONIAC but also in later essays that explore PID control laws for economic variables. At about the same uncorrected behavior time, Arnold Tustin, a British engineer, –4 published a treatise on “the problem of 0 1 2 3 4 5 years economic stabilisation from the point of view of control-system engineer- Feedback control prevents fluctuations in output in the Phillips model. The graph shows the economy’s response to an abrupt downward shift in demand. Without a stabilizing controller, ing.” These works and a few others production falls off and remains at a new, lower equilibrium. With proportional control only, from the same era include block dia- output remains below the original level. The combination of proportional and integral control grams and stability graphs that would returns to the original level but then overshoots and oscillates. Including derivative control sup- be perfectly at home in a text on indus- presses the oscillations. But a real economy is more challenging than this simplistic model. trial control problems.

© 2009 Brian Hayes. Reproduction with permission only. 188 American Scientist, Volume 97 Contact [email protected]. With the advent of optimal control a decade later, there was another surge 2.5 of interest in control theory as a tool lag = 6 for solving economic problems. In the 2.0 early 1970s a series of joint conferences brought economists together with control engineers, and dozens of publica- 1.5 lag = 4 tions explored the synergies of the two disciplines. Furthermore, the Federal lag = 3 Reserve began experimenting with 1.0 control-theory methods in the suite lag=1 of statistical and mathematical tools 0.5 that inform its policy deliberations. A

1974 review article by Michael Athans system state (arbitrary units) of MIT (a control theorist) and David 0 Kendrick of the University of Texas at Austin (an economist) remarked on the atmosphere of excitement in a new –0.5 interdisciplinary area that seemed to 0 10 20 30 40 50 60 have bright prospects. time (months) 2.0 Economic Sensors and Actuators To create a control system for an economy, a first step is to identify economic 1.5 lag = 6 equivalents of engineering concepts such as sensors and actuators. Filling the role of economic sensors are mea- 1.0 lag = 4 surements of business activity, such lag = 3 as employment levels, trade balances 0.5 and statistics on income, savings and lag=1 spending. The actuators are monetary and fiscal policies. Monetary policy is 0 how a central bank controls the supply system state (arbitrary units) of money. (Printing currency is a minor part of this process; the major part is –0.5 regulating terms of credit.) Fiscal poli- 0 10 20 30 40 50 60 cy has to do with government revenues time (months) and expenditures, and especially the Time lags in a control system can have a disastrous effect on stability. The graphs show the balance between these amounts. Be- response of a hypothetical system governed by a simple controller when the set point is cause the government is typically the abruptly changed from 0 to 1 (in some arbitrary units). In the upper graph the gain of the largest single participant in the market, controller is 0.3; in other words, if the measured state of the system differs from the set point a government surplus or deficit can by an amount x, the controller applies a correction of –0.3x. The four curves differ in the time have a decisive effect on the overall lag between when the state is measured and when the correction is applied. With a lag of one demand for goods and services. month the system settles smoothly to a new steady state; a lag of three months causes some As control tasks go, regulating a na- overshoot, and a lag of four months induces damped oscillations. When the lag reaches six tional economy looks to be a major months, the system is unstable, with oscillations that grow in amplitude. In the lower graph the lags are the same but the gain has been reduced by half, to 0.15. Now the system is stable, challenge. One notable difficulty is the but it takes many months to readjust after a change in the set point. wide range of time scales. Some economic events play out in a matter of hours or days (the 1987 stock market set annually. Because of all these time business activity. Control actions have crash, the collapse of Lehman Broth- lags, regulators can never really know different effects on lenders vs. borrowers). At the other end of the spectrum, the current state of the economy they ers, workers vs. investors, tenants vs. major trends can last for a decade or are trying to control; they have to act landowners, importers vs. exporters. more (the Great Depression). Data on the basis of measurements made A boon to farmers may be a burden from stock markets and commodity over an interval that extends months to food buyers. The effects on various exchanges flow in minute by minute, into the past, and their actions will not sectors of the economy cannot be ad- but other statistics (retail sales, un- produce their full effects for months justed independently; all the variables employment, corporate earnings) are into the future. interact, much like temperature and calculated on a weekly, monthly or Another issue is that economic con- pressure in an industrial process. quarterly basis. On the actuator side trol is a multivariable problem, even Still another question is whether of the control process, monetary policy though policymakers often speak as if governments and central banks actual- is usually revised every month or two, there were a single dial, like a thermo- ly have the power to tame the business but most aspects of fiscal policy are stat, that governs the overall pace of cycle. No algorithm can keep a car up

© 2009 Brian Hayes. Reproduction with permission only. www.americanscientist.org 2009 May–June 189 Contact [email protected]. to speed if the engine lacks the oomph interest rates are a blade with only one lenders will anticipate any changes in to climb a hill. Likewise, agencies try- edge: You can raise them as high as rates, adjusting their behavior in ways ing to correct a severe economic down- you wish, but you cannot lower them that tend to neutralize the effect of the turn may simply lack the resources to below zero. (On the other hand, bail- policy change. It’s as if the supertanker, restore prosperity. In the case of mon- out packages for banks are tantamount with a mind of its own, could change etary policy, it is often pointed out that to a negative interest rate: The banks the shape of the rudder in order to re- are being paid to borrow.) sist commands from the helm. Among all these impediments to ef- The Lucas critique attacks not just gross domestic product 12 fective control, the most worrisome control theory and mathematical (trillion $) are the time lags between measuring modeling but any reasoned strategy 11 the state of the economy and applying for managing an economy. The most 10 corrections. Such delays, if combined extreme form of the thesis holds that 9 with overly zealous control actions, if a policy can be predicted, it will be bring a risk of controller-induced oscil- undermined and rendered ineffective. 8 lations—of getting scalded or frozen in Thus the attempt to regulate the econ- 7 the shower. We might still be trying to omy becomes a futile spiral in which stimulate a sluggish economy when it people adjust to new policies, the poli- unemployment rate (percent) is already on the verge of overheating; cies are adjusted to account for those 8 then in the next phase of the cycle we adjustments, and so on. 7 might overreact in the other direction. Within the context of control theory, Control theory offers well-defined however, the kind of circularity cited 6 criteria for deciding whether a system by Lucas is not anything out of the or- will eventually settle down to a steady dinary. In any system with closed-loop 5 state or will enter some runaway regime feedback control—animate or inani- 4 of exponential growth or unbounded mate—the controller affects the state oscillations. Control engineers employ of the plant, which in turn affects the 8 interest rate (percent) those methods to calculate stability state of the controller, which affects the margins—a measure of how closely the plant, and so on. The circularity is an 6 system approaches the edge of insta- essential part of the design and does 4 bility. As far as I know, such stability not lead to undefined behavior or an analyses are not routinely performed endless round of readjustments. As- 2 for monetary and fiscal controls applied suming that stability criteria are satis- to major economies. Perhaps it is not fied, the combined system of controller 0 possible to do so given our imperfect and plant converges on some definite knowledge of the state of the economy; and predictable equilibrium state. 2 government if that’s the case, however, then we also Another branch of mathemat- surplus cannot know how the economy will ics reaches a similar conclusion from 0 (hundred billion $) respond to our policies. somewhat different premises. In game –2 theory, a contest like the one between a Second Guessing regulator and a population of econom- –4 Viewing economics through the lens of ic agents generally has a fixed point control theory amounts to treating the (called a Nash equilibrium), where –6 economy as a machine. The machine neither party can gain by making fur- 1990 1995 2000 2005 2010 may be an unwieldy one—something ther changes in strategy. This idea has like a heavily laden supertanker, slow developed into a theory of “policy A model of the U.S. economy created by Ray to start and stop, difficult to steer—but games,” which strive to identify those C. Fair of Yale University could be viewed as it still obeys deterministic laws of mo- economic models that remain control- an updated version of the MONIAC, with- tion. In particular, a machine never tries lable even when the players don’t wish out the gurgling and splashing. The model consists of 127 equations, defining relations to second-guess or outwit the controller. to be controlled. among quantities such as industrial produc- But a human society is not a machine. From a more pragmatic point of tion, consumer spending and interest rates. In 1976 Robert E. Lucas, Jr., of the view, it’s not clear that real-world For the period up to the end of 2008, the coef- University of Chicago presented a caus- economic agents are as strongly moti- ficients of the equations are fitted to empirical tic critique of mathematical modeling vated to “game the system” as Lucas data; beyond that date (purple region of graphs) as a tool for setting economic policy. supposed. Ray C. Fair of Yale Univer- the model runs in a forecasting mode. The Models, he said, predict the effect of sity, using a model of the U.S. economy first two variables plotted above—gross do- policy changes without acknowledg- based on decades of empirical data, mestic product and the unemployment rate— ing that rational agents will alter their tested variations of the model in which are measures of economic health. The other behavior under the new policies in agents could look ahead and base their two variables—the interest rate on short-term Treasury notes and the government surplus ways that invalidate the assumptions behavior on predictions of future regu- or deficit—are instruments of monetary and on which the models were built. For latory policies. The results suggest that fiscal policy often employed to counteract ad- example, if everyone knows (or can such activity is not common in the real verse trends. The model is available online at infer) the rule by which the Federal Re- economy. Another series of studies by http://fairmodel.econ.yale.edu/main2.htm. serve sets interest rates, borrowers and Glenn D. Rudebusch of the Federal Re-

© 2009 Brian Hayes. Reproduction with permission only. 190 American Scientist, Volume 97 Contact [email protected]. serve Bank of San Francisco reached a student of the Great Depression, has economic wellbeing should be opti- similar conclusion. argued that timid and misguided poli- mized—is the intellectually difficult Whatever the merits of the Lucas cies of the Federal Reserve were partly and politically contentious part of the critique, it had the collateral effect of to blame for the length and severity of process. Maybe the answer is to power dampening enthusiasm for applica- the 1930s depression. Bernanke is now up the MONIAC again. We can let the tions of control theory in macroeco- chairman of the Fed, and he has pre- cascade of colored water tell us how nomics. Research in the area did not sided over a monetary response that far to twist the hot and cold faucets. end entirely, but the undertaking lost is anything but timid. Since September momentum, and control theory has 2008 the Fed has injected well over a Bibliography never again been fully in the main- trillion dollars into the U.S. economy. Åström, Karl Johan, and Richard M. Murray. stream of economic thought. Nor has Not all economists see timidity as 2008. Feedback Systems: An Introduction for it become a common tool of those who the main peril. Athanasios Orphanides Scientists and Engineers. Princeton: Princeton University Press. put policy into practice. of the Federal Reserve has argued Athans, Michael, and David Kendrick. 1974. that overaggressive corrections in the Control theory and economics: A survey, The Great Moderation 1970s contributed to the “stagflation” forecast, and speculations. IEEE Transactions With or without control theory, govern- of that decade. And still another fac- on Automatic Control 19:518–524. ments and central banks have not given tion questions whether monetary ad- Barr, Nicholas. 2000. The history of the Phillips up on attempts to smooth out business justments really have much effect at machine. In Leeson, 2000, pp. 89–114. cycles. On the contrary, every major all. Through an ingenious computer Bernanke, Ben S. 2004. Essays on the Great Depres- sion. Princeton: Princeton University Press. recession and inflationary episode in simulation, Christopher A. Sims of Bissell, Chris. 2007. Historical perspectives: recent years has been met with a “coun- Yale imposed the policies of the mod- The Moniac: A hydromechanical analog ter-cyclical” response, regardless of the ern Fed on the economy of the 1930s, computer of the 1950s. IEEE Control Systems political ideology of those in power. and vice versa. Swapping the strate- Magazine 27(1):69–74. Feedback principles have probably gies had little effect on the outcome. Fair, Ray C. 2004. Estimating How the Macro- helped to frame some of those counter- I don’t know what to make of all economy Works. Cambridge, Mass.: Harvard University Press. See also http://fairmodel. cyclical actions. In 1993 John B. Tay- these seemingly contradictory observa- econ.yale.edu/main2.htm lor of Stanford University proposed tions, and I find it unnerving that in a Kendrick, David A. 1988. Feedback: A New mathematical rules for setting central- matter of such consequence there is so Framework for Macroeconomic Policy. Boston: bank interest rates in response to in- little consensus on basic principles. If Kluwer Academic Publishers. flation and economic growth—rules the designers of an airplane disagreed Kendrick, David Andrew. 2005. Stochastic con- that may well have influenced Fed- so vehemently about the engineering of trol for economic models: Past, present and the paths ahead. Journal of Economic Dynam- eral Reserve decisions over the past the flight-control system, the airplane ics and Control 29:3–30. decade. The Taylor rules constitute a would not leave the ground until the Leeson, Robert (editor). 2000. A. W. H. Phillips: rudimentary feedback mechanism. On conflict had been resolved. But ground- Collected Works in Contemporary Perspective. the other hand, they do not exploit the ing the economy is not an option. Cambridge: Cambridge University Press. full power of modern control theory. In It was the economic catastrophe of Lucas, Robert E., Jr. 1976. Econometric policy eval- particular, Taylor’s formulas ignore the the 1930s that led Keynes to propose uation: A critique. Carnegie-Rochester Confer- ence Series on Public Policy, Vol. 1, pp. 19–46. question of controller-induced insta- a mechanism for moderating cycles of Orphanides, Athanasios, and John C. Williams. bility, and they take no account of the growth and contraction. Perhaps the 2005. The decline of activist stabilization uncertainties that enter into stochastic current crisis will inspire a further ex- policy: Natural rate misperceptions, learn- and robust control methods. amination of strategies for managing ing, and expectations. Journal of Economic Until recently, the economic strate- these fluctuations. The precepts of con- Dynamics and Control 29:1927–1950. gies of governments and banks seemed trol theory suggest that one useful goal Phillips, A. W. 1954. Stabilisation policy in a closed economy. The Economic Journal to be working rather well. The peaks would be to reduce time lags in the 64(254):290–323. Reprinted in Leeson, 2000. and troughs of the business cycle have feedback loop. On the sensor side, this Rudebusch, Glenn D. 2002. Assessing the Lucas been shallow, with only mild inflation. would mean quicker collection and critique in monetary policy models. Federal By 2002, economists were calling our evaluation of basic business data, such Reserve Bank of San Francisco, Working era the Great Moderation. as price levels and employment sta- Paper 2002–02. http://www.frbsf.org/pub- But confidence in a perpetually tistics. Speeding up the actuator side lications/economics/papers/2002/wp02- 02bk.pdf purring economy has been swept away might be more problematic. Although Sims, Christopher A. 1998. The role of interest by the financial crisis of the past year. the Fed and other central banks can act rate policy in the generation and propaga- Governments have taken extraordi- promptly on monetary policy, many tion of business cycles: What has changed nary measures in an effort to stabilize aspects of fiscal policy are tied to the since the ’30s? In Beyond Shocks: What Causes the system. One would like to believe legislative calendar. The most promis- Business Cycles?, edited by Jeffrey C. Fuhrer and Scott Schuh. Boston: Federal Reserve that those interventions were guided ing approach may be greater reliance Bank of Boston, Conference Series No. 42. by scientific principles of some kind— on “safety net” mechanisms such as Taylor, John B. 1993. Discretion versus policy that the timing and the magnitude of unemployment compensation, which rules in practice. Carnegie-Rochester Con- the stimulus plans were calibrated to function automatically, without any ference Series on Public Policy, Vol. 39, pp. produce the fastest possible recovery need to enact new laws. 195–214. without the kind of overcorrection that Standing in the middle between sen- Tustin, Arnold. 1953. The Mechanism of Eco- nomic Systems: An Approach to the Problem of might bring oscillations. sors and actuators are the control al- Economic Stabilization from the Point of View Needless to say, the cost of miscal- gorithms. Finding the optimal control of Control-System Engineering. Cambridge, culation is high. Ben S. Bernanke, a law—and deciding what measure of Mass.: Harvard University Press.