Gazdasági Ismeretek | Közgazdaságtan » Should Control Theory be Used for Economic Stabilization

SHOULD CONTROL THEORY FOR ECONOMIC Edward C. Prescott Carnegie-Mellon In a genetic-historical in outlook view which natural science nature are exhortation, of the like which deception, characteristically that men must that i.e, the inert subject since drawn natural be like natural objects to of persuasion, etc., but are “inexorable” we have to combat an inference, race, revolution of modem men, of our fundamental the real beginning was the discovery coercion, The position University represents not BE USED STABILIZATION?* seems to rest upon by the objects objects “best are not (Knight, minds” like men, 1941, p. 121) I. INTRODUCTION Modern management control trajectories with significant efficiency It has become economic Many if not most There have been Currently, Governors techniques simplified tradition gains a useful manned reduced takes be used to improve in the profession numerous models of the to

the studies can Kalchbrenner version over time. scheduling be and Tinsley Federal Reserve design of macro of the Fed-MIT at its best and was designed It has made possible that naturally of a market the answer when arises is, economy? to this question have demonstrated effectively control. and firm behavior The question believe more individual and by finding and inventory the performance which engineering on the moon fuel requirements. in production place tool in both landings the basic tool used to describe theory econometric has become It made possible dramatically activity can control theory science. is yes. convincingly controlled through that its use.’ (1975), staff members of the Board System, are applying optimal stabilization model, specifically which policy. reflects for policy * of control They are using the econometric a evaluation. Revised January 1977. I would like to acknowledge valuable

discussions with several of my colleagues, in particular Allan Meltzer and Robert Townsend. TIE views presented are my own 1 See Kendrick (1976) for a survey of cwr ninety such applications. 13 Ill fd, in actual economy decisions way informal what has been used in an informal have looked to evaluate employment, selection, at the current of Given that control better considered as Kalchbrenncr the consequences and prices. it is surely is generally waq state of tile that it be applied to bc the brst and Tinsley in econometric advocate, than in the way it has and is being used. (1953) economctricians predicts they efforts do. of and magnitude fine tuning the contributing Federal growth in the money theory invariant models economy not of monetary have and that He has argued and tested be attempted. rules is preferable the attack economy of the econometric of a detailed System instability, fundamental to stabilize use of

caution. having policy He argues had the a neutral that and that. that thr perverse policy that theory best effect of of a constant to the use of macro models and methods. A more structure should supply a note of the effects Reserve to economic control theory has sounded are a long way from the timing macro theory law of motion output, evaluation, Friedman the upon using for policy model not control Policymakers is being used for policy a formal until time, Some selection. and used an implicit alternative theory for policy upon model describing to the policy rule. are worthless in assessing economic under theory alternative the best operating the LW of macro models is due to Lucas (1 976). and that the that policy using is the major rules. He advocates operatin, 0 characteristics rules and the selection the of the economy simulations alternative to predict policy the motion policy and control Hc

argues of the of a rule which yields characteristics. In commenting on Lucas’s essay, Gordon (1976) has suggested that if changes in policy change the law of motion (i.e structure of the econometric model) only in a predictable take (1977) into attempt dynamic games continuation nature. is inappropriate At this point fluctuations economy be better and optimal evaluate that the control alternative the rational I would can still be policy. policy One need and I Kydland impossible. Even in is inconsistent. in subsequent periods plan over the reniainder expectations used. equilibrium Unlike is not the of the planning paradigm, optimal selection. like to emphasize can or should that the issue is not whether be rcducCd. The question stabilized through theory or through stabilization optimal plan optimal for policy theory in designing and find it logically the optimal of the first period economic control situations, If one

accepts control then such changes to do precisely deterministic against horizon. way, consideration the use of econometric the LIX of dynamic rules? Given the enonnoux 14 is, rather. can the simulation economic models theory costs associated to with unsuccessful tation macro to resolve been performed model to policy, it seems this debate. are neither simulate the application economy, invariant to the way policy analyses tests of the alternative or self-fulfilling expectations Control theory being expository current time Neither experimen- and tests” They a fixed law of motion are my and Kydland’s paradigms, that have all use an econometric assuming OF STOCHASTIC presupposes the In discrete and because class-next position nor test. scientific to consider as in both nor Lucas’s cases a rational world is assumed. controlled. simplicity the discrete ludicrous “applications thereby is selected. II. A

REVIEW system almost The so-called existence THEORY of a law of motion time--which virtually period’s xt. the action CONTROL will be all quantitative position or state of the controller for the assumed macro xt+l here models depends for are in upon ut, and an independent the shock e t; that is, xt+] (1) = F(xt>ut. Et) In a macroeconomic application, an econometric model. for most models, macro and certain used obvious to translate a first-order The Tinbergen F of on the or if there and an objective developed was linear, methods production advocated difference were with These desired function scheduling applied instruments must and errors, form of as is the case these lagged variables procedure with a single variable demand management a set of target variables path. computationally first one, into n variables. If there are costs of adjusting with additive include equation aggregate in whose scheme are

selected. variable than added to F. This is just the well-known order quantitative variables (1957) nth father instruments, offs, must equation of instruments target the state difference (1956), F would be the reduced of lags is greater identities an the function If the order are adjusted are more and the objective (Holt, inventory Modigliani, control. that they be used for macroeconomic 15 there Simon techniques when function Muth, and Subsequently, planning. is so as to keep the target instruments, be introduced. feasible policy and an equal number variables than will be trade- (1956) and Theil the law of motion quadratic. Simon, Theil These 1960) to (1964) If the Taylor quadratic of motion law series expansions functions relevant systems are used then, before to form to approximate the objective optimally these whether and magnitude of the effects uncertainty, attempts at of contributing analogue When are

ill understood (for example, best control is not practice and only when science physical to attempt fine argument systems the perverse has a direct with transients steel making tuning. moves in the timing given this great to have This some continuous the process over the stochastic or engineering. and that, arc likely instability. controlling that infrequently supply, stabilization economic function is great uncertainty of the money active to in engineering. that there Similarly, used to control arise in management has argued these techniques, approximations. This is the basic method (1953) applying linear range of outcomes. Friedman effect is nonlinear, are used processes), Adjustments arc made out of some acceptable control range. Builders deduce the of macro fonn of econometric relationships The nature of the adjustment empirically by starching which provides Silverman models, the Unlike probability model

Chow worked errors of this found if the the Wharton data, model suggesting the type. Wharton well when Wharton for the one McCuire, model may and econometric process is high. robustness policy model hand, stocks. has not been shown The only that optimal On the other performed adjustment theory to is determined sizes used in estimating an incorrect ( 1976),2 poorly stock lag relationships of control theory or stationary work by Geiscl. for sample a lack of robustness. desired to the desired econometric of selecting to specification suggesting from that, economic of distributed the performance I am aware, Michigan the indicates forecasting, be robust which a space static LISP detennining of the actual the best fit. Recent (1975) models study derived the Michigan be more the policy model robust of from the generated the optimal to data, derived generated for control purposes. If the theory can specifying the

decision 2John programming facing the expected is augmented unknown in the be effectively the law of motion the dynamic maximize uncertainty still brought law of motion The F of Bellman controller is well value of some criterion specifying there is a well-defined this work to my attention. 16 is moderate, uncertainty is represented methods by a set of variables parameters, B. Taylor the system’s applied. in the by a prior distribution. (1957) defined, and Blackwell the function. objective Using (1965). being to When the state variable the controller’s law of motion. control parameters distribution on the Practical engineering assume methods and functions objective are based are independent quadratic, and selecting coefficients. determining next the This decision observing the result, in dealing uncertainty found profile is not necessarily control have state decision of state variables. This current prior the

prior is updated indicate before this procedure worked been many of the population, inapplicable. to structures with control subject accepts the view that the economy motion and if one has sufficient question that modern control coefficients. selection to a policy is governed knowledge theory well Wallace, in policy, as the demo- optimal Zellner control adaptive (1971), and problem. is an increasingly invariant and the changing such (1973) have extended Similarly, when relationships Provided factors, into the control theory and more 1975). Rolnick, unstable. a and way (e.g, MacRae, in finding Muench, and not by changes varying optimal systems very successful exogenous of has been made perform (see PJorman, model, effect is obtained, progress however, Sarris and Athans model expected in a practical of the relationships changing the By using an instrument of its effect developed, not by slowly have incorporated

for controlling optimal which would be optimal Some modest element procedures To summarize, 3 estimate in the future. Even for the Fed-MIT is caused value in the the controller’s ignores is great, and the gains seem modest Weiler (1974) others, from Tests however, experimental the over time. computing of the coefficients. a more precise Econometricians structure draws unknown programming are linear with hundreds decision. knowledge this of coefficients, After each observation, is possible with None rules with If the coefficients the dynamic decision systems procedure, future control of motion observations. was moderate. decision upon effective law and decisions. 3 The methods at each stage that decision period’s well when uncertainty graphic a linear were independent on the unknown in the economics optimal following optimal even for complex suggests if the coefficients stable and on the Thus, as for the

case of known observation independently draws from some distribution, are rules is feasible 1972). developed to find approximately a quadratic coefficients variable. were literatures powerful law of motion. by some policy invariant of this law of motion, there tool If one law of is no should be used for macro planning. In the economics literature,, I first used these methods in 1967; I was unable to determine when they first the engineeringhterature. For further details on the methods, see Chow (1975, ch 11) appeared in 17 III. DOES A POLICY Many that social constructs years ago Knight problems could which This warning the have produced that arguing dynamic that economic what happens, knowledge, and the models. which are inconsistent If it is not, an underlying rejected. invariant the basic considerations result As before. depends in addition sciences. Lucas (1976) attacked with or structural everything where now economic

relationship known actors agents as having about care of the models, about are public expectations of the model? of control theory to the way policy in the following the actions that there is selected reformulation there is a law of motion, upon the of the natural assumption invariant to assume sciences triumphs Lucas asks, to model problem. state variable to the social or even the predictions law of motion Such it was a fallacy behavioral with the predictions then EXIST? More recently, In situations is it reasonable, stabilization the celebrated inconsistent theory. that by applying unheeded. a policy it was LAW OF MOTION (194 1) argued be solved has gone largely assumption exists, INVARIANT be of the but the motion dt of the private is must of the economic agents: = F(xt+dt. (2) xt+l Given a policy also possible) et). rule (here which assumed specifies deterministic, but randomized the values of the control

as a function strategies are of the state variable, (3) and ut = p(xt) relation private 1 (2), the determination agents is. like all competitive If the structure of preference of the is recursive, of the form: (4) equilibrium equilibrium dt = 6,(x,) 18 these analyses, decision rules of the a fixed point problem. rules will be time invariant and The corresponds 6, are indexed law of motion under 71 which policy to the behavioral by the policy In his critique policy yields of current equations rule. Equations rule of econometric models, (2), (3), and (4) define ?T. The policy desirable operating econometric policy design problem characteristics evaluation, but the system’s is to find a for the economy. Lucas (1976) advocates this approach. In commenting in the policy control these just theory period changes. and found situation and a correct position, predict situation, functions agent’s to predict theory

to rationalize changes that choice, they do, results as indicated to do and the end of strategies policy. policy. which in searching that policy case the only plausible use utility of empirical induced a static for the that one for an optimal only framework, static optimal tax policy taxation may strictly consider only non- This leads inescapably alternative player and with the fundamental need policy. solutions, solution. the reaction being small, behave by is selected, is a game if agents maximize arc many one is the dominant agents, in a randomized takes into consideration while the many in behavior This is at variance selection use utility agents policy. Even specify there private say, a set of tax rates, that advisers) and uses them to There is a wealth out A policy, the With gaming problems, the policymaker carried his economic If policymakers choice? of future has shown theory to the conclusion

policy. way, then attempted choice that by changes are given (1976) control randomized if changes given the current outcomes (actually, not assume social the best deterministic of action, individual environments. why a problem. maximize Stiglitz dominate and I (1977) current rationalize in new then analyses are not agents problem, that, takes into consideration The best the policymaker and predict policy expectations Kydland of both in the public’s expectations Most and above, which choice theory evidence suggests in a predictable the controller impossible. evaluation (1976) equations is not optimal. utility the As noted it logically In a dynamic constructs Gordon the behavioral can still be used, provided induced that on this critique, rule change for given but in this In selecting of agents noncooperatively policy, to his decision, and maximize for given policy. The applicability to a spirited problem

empirically behavior expectations debate facing of the hypothesis agents determined than can of rationality as to its “plausibility.” in dynamic uncertain disequilibrium rational equilibrium There 19 rules equilibria? are, 1 think, has led of the forecasting environments behavioral expectations obtained? of expectations Is the complexity so can How great better is answers a that predict rational to these questions. being Competitive obtained economic even if the introduce an assumption indicators of expectations, anticipations. casts Given are sought. about how economic obtained, there future policy, behavior. Unless is unlikely policy in an equilibrium Forecasters will be selected of consumers’ the rational in the competitive the same reason that the stock market and sales the best fore- expectations expectations anticipations both and observe confidence anticipations, the basis for people’s

between to exist result understood. plans, and form will be a discrepancy a discrepancy will likely is not such as measures expected But, the forecasts aggregate much forecasting structure of solution and forecasts. forecasting is Such business is efficient--profitable for opportunities would exist. Consistent policy A consistent which specifies time. The elements. motion, policy rules For finite fundamental games, (1976) optimal policv Given resulted control question takes patent realizes that should into with of the world at that given the subsequent Blackwell has demonstrated policies invariant policy to infinite the period, a policy and any optimal established time For (1965) has extended horizon that problems, a consistent are not necessarily same law of is consistent. result when For policy consistent. he found the was inconsistent. resources products protection optimal the state problems theory for

each is optimal and discounting, (1975) one examule in new patent policy each and that optimal independently monetary Patent decision of control Kydland optimal upon that is optimal. returns result is not generally Calvo period policy of rules, contingent the property with bounded dynamic is a sequence action have a consistent problems this policy have for existing theory consideration monopoly effects of alternative selected. allocated the inventions. solution be posed protection been or processes. of the the incentive and the loss in consumer rent. In other policy words, policy No one would to be reasonable. in terms both to inventive efficient Most optimal economic consider would agree that life policy, activity that results theory this the which provided when by someone is used to predict rules and a rule with good operating 20 which to permit seriously patent for inventive surplus activity is not

the characteristics Dynamic taxation In recent policy example years, is optimal constraint that a large optimal if it maximizes agents supply taxation some labor literature social welfare optimally has developed.4 criterion, A tax subject to the given tax and wage rates. The optimal taxation literature has abstracted from the savings decision and focuses only on labor supply and consumption. Once the time dimension is introduced, optimal taxation principle of policy, consumption decisions Suppose there the (expected) is the behavior depend tax rates income In subsequent on labor is zero future maximizes in the both optimal current become given tax policy of this consumer, and the Assuming are not labor period and that must be financed, expenditures and capital solution the current utility The optimal will be taxed in the initial period, periods, The supply who maximizes the welfare expenditures of the periods

consumer labor tax rates. and labor incomes. which is not consistent. current future given the tax policy, The inconsistency eventually because upon expected of government of the consumer, inelastically. or deterministic, hold on capital of tax stream random not is a representative too large, only capital taxed. does tax rates sequence given some whether optimality as it is supplied incomes arises because and positive will be the optimal in future ones, but one. Other examples The inconsistency problem provides the rationale contracts and for certain legal principles such as grandfather policy debates, however, the principle is ignored, for example, crop the shortfall, product’s the government future price, controls or when current the for price promising government enforceable clauses. In many when, following a imposes not to control rent controls on existing rental units but not on new units. Similarly, no rational private

agent would stockpile oil speculating on another embargo because he would realize that, in such an event, the government would almost surely again control the price of oil. Use of control Control scheduling which theory in management theory production> equates from physical next has proved The reason period’s considerations stock science useful in controlling it has succeeded to current and is invariant inventory stocks plus net additions to policy selection. 4See t&nsey (1927), Diamond and Mirrlees (1971), and Stigtitz and Dasgupta (1971). 21 and in is that the law of motion is derived If the problem is modified to make price a decision appropriate, price to tile extent but on anticipated monopoly pricing power current future prices. rely on a pricing The tenn that in control “control” and monitoring in terms clearly control not is no longer only why and do not recognize control operating that the policy of

alternative theory policy the should on current firms with some use control theory for economy of dynamic nearly controllers want to go in different suggestion monetary wage contracts.6 which is not to guiding has Activist been If, characteristics of the economy Let w supply the rule. n=770-771 ‘Cyert and D&root an to predict theory The inert rocket is that problem rocket ship when of ship. the two taken I~XPICTATIOIVS if expectations enter the are rational, into long-term to mean wage, is a mistake, hand, may even if agents policy, argument nominal the monetary action as the example below is that the operating for some -rule other rule, then there is no disagreement. w maximizes be superior wage, and assume the expected to supply log of labor demand (w-p)+ planning. to guiding that, nominal other given he is committed wage. The assumed is judged Accountants theory equilibrium AND RATIONAL be the log

of the nominal given the policy firm. equilibrium a dual-control 5 made monetary demonstrates. money on is a set of rules system directions. is appropriate is best given the current constant analogous CONTRACTS policy of the USE for economic but more The is to be used the activist characteristics problem system of a particular rules. stabilizing analogous but its USC is very different control implication not IV. LONG-TERM in accounting, An accounting The effectiveness resulting To summarize, 6See optimal depends This is probably policy is used theory. procedures. of the the effect (5) then drmand decisions. from worker, variable, that utility all the labor it is set efficiently of the representative the firm wants n is e, (1977) consider such a dual-controller problem. Fischer (1977), Modigliani(1977), Phelps and Taylor (1977), and Taylor (1976). 22 than the at that where p e is an aggregate is the function

demand log of the price or supply level. for the individual, and shock and has mean zero, and where Letting u(. , ) be the appropriate E the expectations operator, objective the w selected is the one which maximizes (6) Ep n[u(w-P.n)l, subject to (5). approximated u(w-pn) (7) Substituting (8) It is further by the quadratic assumed that the objective function can be function: = w~(~-P) + (n - F 1I2 for n and taking the expectations I-(~(w-P) + Differentiating [v. - v 1 (w-pe) with respect to - P yields 1I 2 + var (E) + w, setting zero, and solving for w, the nominal the wage selected v;var resulting (PI + 2771 expression COV(C,P). equal to is w = pe + (7)o - ~1-/421)1)/77] (9) Without knowledge basis for forming Control theory of the way in which policy will be selected, is no price expectations. or discretionary With this solution, solution the rate of inflation that will be selected to be best relative to

some social objective function demand (5), the function representative there worker and the value and a democratic function and the worker’s answers, including utility the observation of society, function differ? s(n,p), realized 23 shock. why should Phelps that labor income given can be said w, the labor If there is a the social objective (1972) is subject provides to income some tax, which for will result in an oversubstitution market-produced wedge between optimal the private (10) using of home-produced goods unemployment insurance addition, and social quadratic s(n,p) = (n-02)” Another question objective product and leisure drives a of search, resulting in less than to be addressed the social objective function arrangements price problem. is that is are predicated policy of evidence If this perception choice that the price level in the social the U.S and many level instability in a democracy, is

a wealth convince is, why introduce One reason are changed, is that, approximations. + oO(p-01)~ function? and institutional there In employment. Again, these goods. upon stable imposes should is not rational, real costs. reflect the public other prices, Another the people’s perceives then tax systems and that, until inflation it behooves argument preference; as a serious economists to so the people. Maximizing the social objective to the labor demand function (lo), with respect to p, subject (5), yields 2 (11) p= The expected (12) price prior to observing Substituting Best policy this (9), and + 00). W)/(Vl then 2 +Q). solving wage for the control theory w, the rational best. It is not optimal because for yields policy. rule The control the into nominal w)i(?l: e is, therefore, 2 pe=(u@r~-7JO77~+771a2+rll expectations upon +77la2-77lf+771 (rJOo]-40’71 policymaker the selected theory policy fails to

take nominal is not in general into wage consideration w. There 24 the effect will exist a policy of his policy -rule rule of the form (13) p=7r()+Ir1 E) provides a higher which expected value for the social objective function. With be maximized with such a rule, (14) Pe = K(), and (16) n=no-nl The expected respect (~-710-7~1 value model way, and the conclusion control finding theory characteristics.8 analysis would rule These theory is inappropriate not addressed wage rigidities The problem yields assumed good that be much more complicated, trivial. complications should is that such rigidities selection. which If it were function to (14) - (16).7 incorporates derived for policy a policy E of the social objective to rro and ~1, subject The assumed e )+ only reinforce if expectations here is that the nature or, in the simplest do not justify is one of policy in this possible the use of design, namely, case, best

operating wage contracts are overlapping, and the control theory the argument are rational. of the contract that Another solution optimal problem is likely to change the non- control that is if policy changes. ‘I have not proved here that the best policy lies within the class of linear response functions nor would I be surprised if it did not. I have established that the control theory solution could be dominated by an element of the class. ‘These conclusions are implicit in F’helps and Taylor (1977, p. 163) when they recognize that monetary authorities should sometimes penalize the economy in the short run for the sake of beneficial effects of the rule upon the economy’s operating characteristics. 25 V. NONNEUTRALITIES The equilibrium that anticipated demonstrates whether through representative supplied. view of business macro that the policy way issuing household (17) (ct -pint where Og<l maximizes is no proportional to

proportionality The expenditures does matter. depend example are financed, The example upon consumption in period the expected imply following t, and nt labor assumes a and labor supplied, the value of the function -p2nt), is the discount There or taxation, whose preferences POLICY does not necessarily effect. government ct be consumption representative ~t,j+ fluctuations is without in which debt consumer Letting WITH ANTICIPATED rate, and the cli are positive capital, labor and input; constant the production measuring may be taken parameters. relationship output units is output yt appropriately, to be one, and the production the function is simply (18) y =n t t Government expenditures the relationship private The bills which u d tt+1 The policy above +rn tt its due the next the government’s and household’s do not affect intertemporal expenditures period. and Letting constraint debt obligations of

real purchasing dt be the debt coming tax rate, and at the price budget past and the issuance due of a real bill coming is =gt+dt. instruments constraint instrument, finances t, rt the proportional due next period, the representative tax on labor income come exogenously choice. government a proportional in period (19) rationalizes consumption-leisure through power which gt are determined are the tax rate and the amount precludes their independent manipulation, which will be taken to be the tax rate. 26 of the bills issued. The so there is but one For simplicity, known it is assumed distribution financing policy with in period and on government Given these that the gt are independent a finite second t depends expenditures; assumptions, draws from some It is further only upon debt coming that the state moment. is, rt = r(gt,dt), variables, assumed and dt+l or position that due in that period = d(gt,dt). of the economy,

are the pair (gt,dt). The perfect corner production the competitive rule nt = n,(gt,dt). will change the for with problem equilibrium in the policy the ratio of the marginal elastic constant function no at real wage 1. returns is to determine to scale for a given employment is subscripted utility (assuming need not be considered. labor nr ct+l be 0. For the assumed is infinitely along function as a result of changes ct must so share ownership equilibrium r(gt,dt) The employment Equating supplied assumption point ut for labor and dividends, = of equilibrium the demand fixed rt assumption that competitive zero profits policy (20) implies function, Further, implies The substitutability solutions) by function r because it r(gt,df). of ct and the disutility of labor to the ratio of their prices, one obtains l 1 =-, -( 1-rt) -pl-2P2nt or l-P*1 (21) Labor that 1 -7, 2fl2 n=- t 2P2 employed period. in period Tax

receipts ut = /3, the equilibrium (22)dt+l =’p [gt+dt-rt t t is a decreasing are rtnt, law of motion (2 and linear from is obtained: - 27 z)]. (20), function of the tax rate in (21), and the result that Because affect of the very special current labor consumption functions. (23) -g l-/J1 ct=n t do not depend relevant, the financing as the expected household depends upon the policy be the expected t forward which debt increasing function v,(g,d) (24) vr(g,d) where n if the policy remains function is decreasing n-g 7 = 64 d’ = /3-‘(d+g-rn), define and Nonetheless, policy is flows for the representative rule followed. discounted utility is rt = r(gt,dt). with in d. Proof: realized I restrict certainty; and r(g,d) function by the household tax policies next period’s is increasing By the recursivity to those debt in d. Result: is an The principle, ) there conditions is a unique point that a

function of g. The right-hand of bounded (measurable) The fixed points to verify to this fixed decreasing rule followed. value of utility debt; a mapping the same set of functions. it maps do not GT = that policies employment 1 C It is trivial of future equilibrium - and F(.) is the distribution conclude the = c - p ln - p2n2 + p / vr(z,d’)dF(z) l-1*1 (24). policy bounded of current = 2p2 constraints expectations is why discounted Let v,(gt,dt) from period for 39 upon This 1 rt - gt . 21-12 - =- t assumption, supply. decreasing in that argument. of this mapping of (g,d) into M are solutions to of theorem 5 of Blackwell (1965) to and that M” v EM (M nl- v) converges solution, for all functions side of (24) and the functions v(g,d). The operator in its second This proves the result. 28 argument M has the property into a function also Discussion If the taxpayer representative matter? The depends on the

answer is that is less welfare expenditures. government expenditures constraint that expenditures. constraint total expenditures and receipts An interesting would followed policy debt. next The control the government taxation control. solution, then, in the would ready of be bent a considerable many the theory of the in chemistry the present situations that value when rather insisting of the only than matching upon an equality is that the representative defaulted to honor on its existing future of household’s debt and then debt obligations. The inconsistency problem Such a of the optimal will again fail to honor existing markets. THE ALTERNATIVE any single being elapses appear mixture required observation accepted acceptance Einstein’s observations demise equals is never to honor or of a new prediction by the gravitational period of government constraints existing debt and, as a result, The result is inefficient

loss to society. that hypothesis confirmation and then will not have access to capital It is unlikely the constant when it is small, for every t, with the single in static the government VI. TESTING results sources promising period and a dead-weight expectations rtnt of tax revenues of this model by optimal is that replaces as a and welfare a relatively a given stream markets if the government a given debt policy is implied solution with financing and for each match. feature increase problem equal total expenditures, to revenue debt of debt financing gt is large and surpluses gain realized receipts types welfare when value same expenditures taxation equal tax receipts the present government By maintaining to capital gt It is the is that is an optimal deficits access the why does the amount of taxation. loss associated Having owns then this efficiency tax rate, and by running there household is liable for its

payment, will rejected. theory from result An or paradigm, relativity a new theory inconsistent with and a generation, 29 the the in the rational observation theory force of the sun, is a rarity. before theory PARADIGMS which such that as the light rays More typically, is accepted, and even then new For acceptance as described theory. example, of Dalton’s atomic by Kuhn (1970, p. 135): Chemists could not, on the evidence, even after therefore, for much accepting the theory, into line, a process When of well-known Similarly, assuming beats as the maximizing percentage was different. period with rational paradigm assumption, once the subject The will elapse expectations may be considered to be fundamental. information sets efficiently assumption when surveys before the theory, be and or, for the matter, in the same spirit debate in economics, expectations by hypothesizing that used test if some of much

The rational maximizing. cannot One can only expectations the another will remain. the maximizing and even a considerable into conformity augmented observed, done, took almost compounds expectations considered hypothesis. was it is accepted, even then many puzzles theory Instead, had changed. nature The rational it Dalton’s they had still to beat nature in the event, composition economist but now which, generation. data themselves simply accept of that was still negative. Like utility, to test theory, irrational the whether assumption agents use their expectations are not rational expectations it incorporates expectations, rational is or is not consistent with observations. In science, theories. But, to stabilize controlled experiments this is hardly the economy-the paradigm equilibrium phenomena or the which economic fluctuations views policy invariant trade-off law between experiment of motion. economics

expectations theorists contributing to uncertainty. predictions of the buy lower unemployment There nonmaximizing confidently occurred. income notable macro economic predicted function was mistaken. as close hope this procedure a perceived to a controlled for. The predictions of would by fail and that. unemployment supporters that science. determined at exploiting are even increase curve physical as were fulfilled. higher inflation would were not confirmed. is another for This prediction consumption attempts as one might might Phillips from of be used fluctuations by an empirically inflation that should economic borrowed Recent and used in the testing hypothesis views as generated employment in aggregate which which paradigm, the rational The are frequently the way to test the example the depression, post-World was proved which of the failure theory: related New maximizing War 30 and which to current of

consumption accepted economists the empirically consumption theories which II period, wrong because current of a generally so never determined disposable were developed by Modigliani this failure. and Brumberg These theories the prediction, subsequently would have minimal stabilization difference Bogaard rapid recovery more sophisticated known. verified, “tests (1957) in response well since then, generating, that the temporary and applications” have appeared equations, example, and by Friedman to for example, tax surcharge of 1968 effect. Many suggested macro (1954) have forecast sometimes and Theil’s from stochastic, (1959) the Great tests to Depression model simulate would 1967) with the have been did not random theory for They have all used a set of economy. use of the Klein I model (Prescott, An econometric of the use of control in the literature. possible. assume shocks For to show that a the was

used Slightly model to be to generate an historical data set. This data set was then used to draw inferences from the model, and adaptive control methods were used to select policy actions during the control tion worthless into period. procedure One could to obtain in choosing the simulated such tests can economists tine tune go one step further more demanding between the alternative environment, assess the is a policy validity of do not have sufficiently the economy, paradigms Friedman’s because, (1953) selec- such tests are incorporated law of motion. knowledge until they the model But, even then, invariant precise and that, and simulate tests. At best, contention that of the law of motion do, they should to rely on a neutral policy. Kydland within rapid the and I (1977) rational adjustment by assuming equilibrium in capacity that capacity of the expenditures We simulated was makers use control theory assumption to

the policy rule used. economy Econometricians there has been determine moves the function, the shift in the investment tax credit to change, new equilibrium of the investment and the policymaker in turn induces function policy investment rule. The change in policy which period. is recognized. 31 stabilization induces policy investment They to the implementation the with some fraction also relationship which the equilibrium Subsequent describing policy. investment to determine that with introduced in such an environment. passive revise their estimate structural a new policy the investment this estimated the incorrect the control associated lags were two periods, policies and the rest in the second, and that the function given have required in the first, tax credit costs Distributed that a passive investment in the past, econometricians Increasing assumed. expansion the use of optimal equilibrium, a class of

investment framework. were occurring The tests assume was pursued evaluated behavior assume and that that policy- rule is optimal, under function is invariant of this policy investment function, rule, function. reasoning uses optimal still another a change in the policy that control change to in rule once The tests examples, found this performance initially eventually that the iterative process application of control simulated (e.g, early to a policy converging tax credit policy. For other and iteration resulted each process captures increase theory economic environments, not equilibrium observations between problem existence of a stable size one cannot as the sixties choose shift viewed that the and can very well that, for equilibrium planning, but do as an equilibrium consistent the theories, or dis- rational paradigms financing expectations with rather severe requiring us to reject as occurred in

policy. in the late theories which warrant to test for an output-inflation there being none. Sargent classical hypotheses and variables Similarly, the differ. the key hypotheses and fiscal-policy predict how large the sample of the theories evidence consistent (p. 236) both be used to ’ A fundamental Only if there is a change inflationary of cannot approaches. rule do the predictions the data rate” experiments and that no matter uses international monetary or the interest a policy incorporating evidence government given tests and finds a model (1976) turns of the model do not cause LIP that unemployment one can find laws of motion which are with the data. VII. The primary but economic of a policy purpose to discuss planning. invariant when CONCLUSION of this paper whether optimal The use of optimal if expectations recognized demonstrate that simulation between are two trade-off exist as this iterative

tests indicate is hazardous is best effects, no-investment did not converge, Insofar these and the equilibrium to peacetime Lucas (1973) debate, tests law of motion, and early seventies, There “little suggest is that mention. tests process not be used for economic economy the control inference such the should to the process. These choose These theory economic had detrimental economy. stabilization fluctuations. whether the iterative For some improved was inferior of what is happening, for macro control indicate examples, converged. theory but then which in a less stable the essence use of control iterations), typically the law of motion, are rational. situation is not control control which The to enter into is an appropriate is predicated economic predicts of control such device for upon the existence theory inapplicability is well understood, the monetarist will not theory as for patent is policy 9 I

proposed the use of simulation experiments with many players assuming the roles of households, firms, banks, forecasters, and policymakers. The near unanimity of opinion among my coUeagues that results of such experiments would tell one nothing led me to retract this proposal. 32 and management. from physics determined objects It is only for aggregate the concept is unlikely to those obtained rational to achieve purpose effect, all theories for some policy economy will be preferred the foremost example, inflations, affects until predict utilizing to others, of the paradigm, and uncorrelated comparable the fallacy anticipated that because monetary policy imply that active policy to economic operating is precisely instability. Quite the characteristics what Lucas of the (1976) wage contracts the unanticipated the anticipated, of the equilibrium of the be used to be as inert component yet the policy of rule followed of output. theory not be

attempted. the in social science this paradigm with The implication currency people argues. For the long-term a tested is available, that which correlated with law of motion modeling as unlike people. rules, the equilibrium is perfectly the variance stabilization stable advocate output that triumphs objects or will contribute contrary; invariant warned celebrated physical theories be ineffectual policy (1941) that the norm is to borrow of the essay is to correct expectations will have little will either Knight by treating A secondary some of a fixed empirically. economics business Reliance price and constant implication to predict the view of business cycle is available on a policy economy’s operating policy rules, and that one with good characteristics 33 is that active of maintaining tax rates is appropriate. of the equilibrium fluctuations it is best that a relatively Once a tested view is that characteristics be

selected. economic under theory theory alternative REFERENCES Bellman, R. (1957) Dynamic Programming. Princeton: Princeton University Press. Blackwell, D. (1965), Mathematical Bogaard, “Discounted Statistics, P.JM van den, and Theil, An Application Economy Calvo, of Strategy of the United A.G (1976), “On Monetary Economy,” Economics, Columbia Chow, G.C (1975). Dynamic Programming,” Annals of 36: 871-90. H. (1959), and States, the “Macrodynamic Certainty Equivalence 1933-36,” Time Metroeconomica, Inconsistency discussion Policy paper of to the 11: 149-67. Optimal 76-7704, Making: Concepts Policy in a Department of University. Analysis and Control of Dynamic Systems. New York: John Wiley and Sons. (1976), Stabilization “Usefulness of Imperfect Department Policies,” Models for the Formulating of Economics, Princeton of University. Mimeographed. Cyert, R.M, and DeGroot, Problems,” Diamond,

Theory P.A, Production,” Friedman, and Mirrlees, American M. (1953), A Formal University of Chicago (1957). Fischer, S. (1977), Optimal Money J.A (197 l), Review, Strategies in Dual Control “Optimal Taxation in Essays and Public 61: 8-27 and 261-78. of a Full Employment Analysis,” Policy in Positive on Economic Economics. Chicago: Press. A Theory University “Sequential forthcoming. Economic “The Effect Stability: Princeton M.H (1977), and Decision, of the Consumption Function. Princeton: Press. “Long-Term Supply Rule,” Contracts, Journal 34 Rational of Political Expectations Economy, and the 85: 191-206. Geisel, MS., McGuire, Box-Jenkins Procedures Carnegie-Mellon Gordon, R.J Holt, CC., “Can “Evaluation working of the paper 46-75-76, Decision Journal Modigliani, Policy Evaluation Curve and Labor Markets, be Salvaged?: A eds. K Brunner and Stabilization and North-Holland. “Linear

Quarterly Production, Analysis,” Econometric Amsterdam: (1962) Growth,” L.P (1975), for Time-Series ” in The Phillips A.H Meltzer, C.C and Silverman, University. (1976), Comment, Holt, T.W, F., for Economic of Economics, Muth, Inventories, Rules J.F, 76: 20-45. and and Work Force. Simon, H. Englewood (1960). Planning Cliffs, N.J: Prentice- Hall. Kalchbrenner, J.H, and Tinsley, P.A (1975), in the Design of Monetary on the Monetary Washington, Kendrick, in D. (1976), of Amsterdam: On Theory 3, “Social History and University F.E F.E, Science,” Method of Reserve Board, to Macroeconomics,” ed. M.D Intrilligator, The Structure of Scientific of Chicago (1975), “Equilibrium discussion and The Inconsistency in Ethics, 5 1. Reprinted Economics: Selected in Knight, Essays (1956). of Chicago Press. University Administration, Kydland. of Control Economics, (194 l), Models,” Control Conference

North-Holland. T.S (1970) Kydland, Federal Quantitative the Chicago: in Open Economies, “Applications F.H Chicago: Kuhn, Mechanism “On the Use of Optimal Paper read at the Helsinki D.C Mimeographed Frontiers Knight, Policy.” paper, Journal Prescott, Solutions Norwegian of Economic E.C of Optimal Revolutions, 2nd. ed, enlarged Press. Theory, (1977), Plans,” 473-92. 35 in Dynamic School Player and Business forthcoming. “Rules Journal Dominant of Economics Rather Than of Political Discretion: Economy, 83: Lucas, R.E Jr. Trade-Offs,” (1973), Curve Amsterdam: McCallum, and Labor B.T (1977) Economy, Policy Markets, Evidence of Output-Inflation 63: 326-34. Evaluation: eds. A Critique,” K. Brunner and in The Meltzer, A.H “Price-Level Policy Stickiness with Rational “Linear Decision and the Feasibility Expectations, of Monetary ” Journal of Political 85: 627-34. E.C (1972), Economic

Modigliani, Review, North-Holland. Stabilization MacRae, International Economic “Econometric (1976). Phillips “Some American with and Social Measurement, F. (1977), Stabilization “The Policies?” Experimentation,” Annals of 1: 437-47. Monetarist American Controversy Economic or Should Review, We Forsake 67: l-19. Modigliani, F., and Brumberg, R (1954), “Utility Analysis and the Consumption Function,” in Post Keynesian Economics, ed. KK Kurihara, New Brunswick, Muench, N.J: Rutgers T., Rolnick, Structural Change Structural Models,” Norman, A.L Department Models Annals E.S Approach Wallace, W., and Intervals of the U.S: of Economic Policy W. (1974), Control, “Tests for the Reduced-Forms Fed-MIT and Estimation University on Stochastic to Monetary The Weiler, Michigan and Social Measurement, “Alternative of Economics, (1972). Press. and Prediction (1975). NBER Conference Phelps, A., University and of

Texas. and Unemployment Planning. London: Control Strategies,” read at the Fourth Mass. Theory: Macmillan Quarterly 3: 491-5 19. Paper Cambridge, for of Two The Cost-Benefit Co. Powers of Monetary Policy Phelps, E.S, and Taylor, JB (1977), “Stabilizing under Rational Expectations,” Journal of Political Economy, 85: 163-90. 36 Phillips, A.W (1954), Journal -’ Prescott, “Stabilization Policy in a Closed Economy,” Economic 64: 290-323. E.C (1967), “Adaptive Ph.D dissertation, Graduate Decision Rules for Macroeconomic School Planning.” of Industrial Administration, to the Theory of Taxation,” Carnegie- Mellon University. Ramsey, F.P (1927), Journal -T Sargent, T.J Journal A.H, Taylor, the Adaptive Control United Methods paper No. 24, Computer and Management Science, NBER, Programming under Function,” Econometrica, 24: 74-8 1. “Utilization technical report and Dasgupta, J.B P.S (1971),

Expectations,” H. (1957), “A Note for Research 575 Technology, during and Control working (1964). Optimal Decision Public Goods, 38: 151-74. Studies, a Transition to Rational 83: 1009-2 1. of a Macroeconomic Equivalence Rules North-Holland. 37 a The Case for Random Taxation, paper, Columbia on Certainty with University. Economic Economy, Uncertainty Model with University. in Dynamic Planning,” 25 : 346-49. Econometrica, Amsterdam: of Policy of Political “Estimation Equity: “Differential Review “Monetary Journal (1976), and Horizontal No. 2 14, Stanford Efficiency,” (1975), Expectations,” Theil, “Optimal working “Dynamic Economic Rational for 84: 207-37. (1956), J.E (1976) J.E, Model Criterion Taxation,” and Economic Mass. 02139 H.A Stiglitz, Economy, Systems,” for Economics Quadratic Stiglitz, Macroeconometric M. (1973), Varying Cambridge, Simon, of Political and Athans,

Structurally Center “A Classical (1976), States,” Sarris, “A Contribution 37: 47-61. for Government and Industry. Tinbergen, J. (1956) Economic Policy: Principle and Design. Amsterdam: North-Holland. Zellner, A. (1971) New York: An Introduction to Bayesian John Wiley and Sons. 38 Inference in Econometrics