Annual Reviews in Control 33 (2009) 79–88

Control theory and economic policy: Balance and perspectives

Reinhard Neck *

Department of Economics, Klagenfurt University, Universitaetsstrasse 65–67, A-9020 Klagenfurt, Austria

A R T I C L E I N F O

Article history:

Received 20 September 2008

Accepted 8 March 2009

Keywords:

Economics

Economic policy

Optimum control

Stochastic control

Dynamic games

Robust control

A B S T R A C T

This paper provides a selective survey of applications of control theory to the analysis of economic policy

problems. We discuss applications of closed-loop control and of optimum control theory, including

deterministic, stochastic and decentralized optimum control. Promising areas of mutual cooperation

between control theorists and economists such as robust control and dynamic game theory are

identified. A critical evaluation is given of different control theory approaches to an empirically useful

theory of economic policy.

� 2009 Elsevier Ltd. All rights reserved.

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1. Introduction

For more than 50 years, methods which were originally createdby control engineers and later fully developed by control theoristsand applied mathematicians have been used to extend the theoryof economic policy and its applications. Control theory can beregarded as a collection of methods to be used by economists, likestatistics or some other fields of applied mathematics.

A great number of economic applications of control theory relateto theoretical issues, such as growth theory, the theory ofexhaustible resources, intergenerational allocation problems, etc.This work has greatly enhanced economists’ insights into a variety ofproblems of economic theory, but it is not immediately helpful forreal applications to practical problems of economic policy. On theother hand, for short-term stabilization policy problems there is along tradition of and experience in applying numerical economicmodels, and in this field control theory applications have proved tobe of direct practical relevance. By stabilization policy we meaneconomic policy with a short time horizon (up to 5 years) that aimsto influence macroeconomic variables such as output, (un-)employ-ment and the price level (inflation), etc., in other words policy that isdirected towards goals relevant for an entire economy. Althoughcontrol theory can be applied to other fields of economic policy (andto more general economic problems) as well, we will concentrate onapplications to problems of stabilization policy in this paper.

Looking at the development of control theory applications toeconomic policy in this area, we can distinguish between three

* Tel.: +43 463 2700 4121; fax: +43 463 2700 4191.

E-mail address: reinhard.neck@uni-klu.ac.at.

1367-5788/$ – see front matter � 2009 Elsevier Ltd. All rights reserved.

doi:10.1016/j.arcontrol.2009.03.004

periods, which partially correspond to different methodologicalapproaches in control theory and certain theories in macroeco-nomics:

(1) Up to the end of the 1950s, problems concerning the stability ofcontrol systems were analyzed, mainly by means of transferfunction methods. At that time, macroeconomic theory andpolicy were both dominated by Keynesian ideas; analogiesbetween engineering and social systems were emphasized;and both were assumed to be easily subject to manipulation byan external controller.

(2) With the discovery of the maximum principle by Pontryagin andco-authors and of dynamic programming by Bellman (andIsaacs), the era of optimum (or optimal) control theory began,which parallels the use of state-space methods (pioneered byKalman). From now on, questions like the controllability,observability and optimality of dynamic systems were inves-tigated, which are mostly represented in the time domain asdifference or differential equations. At the beginning, this theorywas only capable of solving deterministic optimization pro-blems, but later on several methods for the analysis of stochasticeconomic problems became available. These breakthroughs incontrol theory occurred at a time when large-scale econometricmodels were being increasingly used for policy purposes, andoptimism was high that decision technologies for policy-makerscould be developed, enabling them to fine-tune economies.

(3) Due to severe criticisms raised by the New Classical Macro-economists and to the less than perfect results of the stabilizationpolicies, the reputation of optimum control analyses of economicproblems declined during the late 1970s and following. Largeeconometric models also fell out of fashion, their construction

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being regarded as a routine task for applied economists instead ofa challenge for economists active at the frontline of innovativeresearch. More recently, however, economists have started torealize that many critical points can be dealt with by using andextending the control theorist’s methodological toolbox. Exam-ples of these tools are robust control theory and dynamic gametheory.

This paper attempts to survey these developments and evaluatethem critically. Section 2 reports on economic applications of‘‘classical’’ control theory, especially closed-loop control. Economicpolicy applications of deterministic and stochastic optimumcontrol theory are the subjects of Sections 3 and 4, respectively.Section 5 deals with a somewhat neglected field, economic policyapplications of decentralized control theory. Two more areaswhere control methods have been applied to economic policy inrecent times are briefly discussed in Section 6: dynamic gametheory and robust control theory. An evaluation of the impact ofcontrol theory on the theory of economic policy is attempted inSection 7.

2. Economic policy as a problem of closed-loop system control

The first attempt to analyze economic policy problems from thepoint of view of a control theorist and electrical engineer was byTustin (1953). He proposed starting with analogies betweeneconomic models and technical systems, tentatively applying thetheory of automatic regulation. Such analogies can clearly be seenby drawing schemes of dependence for aggregate quantities, thatis, by representing macroeconomic models with block diagrams asis usual in electrical circuit theory and in other applications ofclosed-loop control systems. In this way, Tustin investigatedseveral macroeconomic models; notions like feedback or thestability of closed-loop systems and methods like harmonicanalysis and transfer functions (especially the theory of theLaplace transform), among others, were applied to these simplemodels. Although all these methods had widespread applicationsin the physical sciences and in engineering, the possibility ofapplying them to problems of economic policy remained ratherlimited. The tendency of Tustin’s work was continued only inmodels by Phillips (1954, 1957; cf. also Allen (1967)), who becamemore famous for inventing the Phillips curve. A recent evaluationof Phillips’s work, including his biography as an engineer-turned-economist, together with some of his previously unpublished (yethighly relevant) papers can be found in Leeson (2000).

The reason why only relatively little work was done on directlyapplying traditional methods of electrical engineering to econom-ics may be found in the fact that the conditions of systemconstruction differ between economists and engineers. In engi-neering, as in economics, the goal of achieving a stable system isattained by modifying the workings of the system, which consistseither in changing the dependences within the system or addingfurther dependences for the purpose of stabilization. Thedifferences arise when performing this task: while the engineercan typically modify his experimental design if he is not satisfiedwith its result, the economist cannot usually exert influence on theinternal relations of the system.

In some cases, however, the assumption is also justified that theeconomist as a planner or politician has some possibilities at hand tomodify even the internal relations of the system. More specifically,with respect to the problem of time lags examined by Phillips, it ispossible to influence (and especially to shorten) the information lagby changing the communication structure of the planning system, toaffect the decision lag by changing the process of making decisions(coordination, centralization), and to influence the execution lag bychanging the political infrastructure. These and similar measures

can exert direct influence on the behavior of the system, not only onthe time structure but on system relations in general; likewise,political measures with a longer time perspective may have such aneffect. For the engineer, however, the question of how to change hisexperimental design in order to improve his results is not asimportant and not as complex as the corresponding question for theeconomist who asks how and by what means he can influence thereactions of the system to achieve an improvement. It was probablyfor this reason that the methods of engineers in this field did notprove fruitful for economic problems.

The other possibility of arriving at stable behavior for a system,namely by adding further supplementary feedback loops to thesystem, was the only one which was developed systematically byengineers and economists alike. In the models of Phillips, thismeans adding government expenditures to the national incomeidentity; these government expenditures can then take arbitraryvalues according to the politician’s target to limit oscillations innational income. But this is also something that belongs to the classof problems relating to the ‘‘design’’ of a control system: by thatterm, engineers mean questions that are related to the planningand setting up of an experiment (a mechanism, a system) which isto have certain desired properties (in our case, stability). As aninterpretation of the Phillips model, this question was generallynot regarded as a problem of synthesis, but instead in the sense ofan input–output scheme with a black-box structure. But this isonly possible because the Phillips model, by adding the term forgovernment expenditures to the national income identity, hasbecome an open system, precisely because it has received an inputpossibility for an exogenous control variable. This addition ofgovernment expenditures may be interpreted in economic termsas the ‘‘installment of stabilization policy’’ or the ‘‘abandonment ofa laissez-faire attitude’’, as a change in the structure which makesthe previously closed system (with government expendituresbeing one of several components of national income) an open one—this in fact can be regarded as analogue to the formal manipulationof an engineer adding a supplementary feedback loop. Thusincreased stability of the system in the last resort can be said to beachieved only by manipulating the structure of the system, not bymerely introducing quantitative changes of inputs.

3. Economic policy as a problem of optimum control

One of the most important results of the application of‘‘classical’’ methods of control theory by Phillips was the insightthat under the influence of certain kinds of ‘‘intuitive’’ stabilizationpolicies, simple macroeconomic multiplier–accelerator interactionmodels can display undesired instabilities. This is even moreprobable for complicated models and in economic reality. For ananalysis of larger and more realistic models, however, theapproach developed by Tustin and Phillips is not well suitedbecause it consists in ‘‘trial-and-error methods’’ which cannoteasily be extended to more complicated models. In addition thenotion of ‘‘stability’’ of a system, which plays a crucial role in thework of Tustin and Phillips, is not made sufficiently operational bythem. Moreover, further developments in control theory showedthat stability, although generally a necessary condition for a goodsystems design, does not in itself necessarily guarantee a designwith further desirable properties.

Economists therefore realized that admissible control shouldalso have an optimizing feature in some sense. By acknowledgingthis, the decisive step towards the theory of optimum control wastaken. Here the optimality property of a control is defined by theminimization or maximization of a criterion function (perfor-mance measure, performance integral; in economic terms:objective function, i.e. cost or welfare function). Optimality isseen to be at least as important as the property of stability, which

R. Neck / Annual Reviews in Control 33 (2009) 79–88 81

under rather general conditions can be shown to follow fromoptimality as optimized systems in general are also stable.

The optimum control problem in its deterministic versionconsists in choosing time paths for variables (control variables)from a given class of time paths (control set) where the time pathsfor the variables describing the system (state variables) are givenby a set of difference or differential equations (equations ofmotion); this choice has to be made in such a way that a givenfunctional which depends on the time paths of the control andstate variables (objective functional) is to be maximized orminimized. The static analogue to the problem of optimal controlis the problem of mathematical programming. In the discrete-timecase it is possible to derive solutions for the problem of optimumcontrol from the solution of a static programming problem byredefining the variables.

Many results are available in the control theory literature on theexistence of a solution to the problem of optimal control as well ason how to find such an optimal solution. The main approaches tothe solution of the optimum control problem are the calculus ofvariations, dynamic programming (Bellman, 1957), and themaximum principle (Pontryagin et al., 1962). Using these methods,it is possible to analytically determine an optimal solution forseveral control problems, such as, for instance, the problem ofoptimizing a quadratic performance criterion with a linear system.Considerable difficulties, however, arise with a more complicatedobjective function and with nonlinear systems.

Among the economic applications of control theory, methodsderiving from Pontryagin’s maximum principle have been usedmost frequently for theoretical purposes, paralleled by dynamicprogramming. The first genuine control theoretic analysis ofeconomic policy problems was extensions to the Phillips model,which was augmented by an objective function (Fox, Sengupta &Thorbecke, 1966; Sengupta, 1970; Turnovsky, 1973). Mathema-tical difficulties arising at the beginning of these developments (cf.Preston, 1972; Turnovsky, 1974) were due to the fact that somesufficient conditions for the existence of stable optimal policieshad not yet been adequately identified by economists (Aoki, 1973).These were the controllability of the model, i.e. the ability of thecontrol variables to carry the state vector of the system to anyneighboring state, and its observability, which in terms ofeconomic policy applications can be interpreted as requiring thatthe objective function contain all variables ‘‘relevant’’ forgenerating optimal stabilization policies.

The notions of controllability and observability were firstformulated in the control theory literature by Kalman (1960), whoalso derived the conditions under which these properties aresatisfied for linear systems (Kalman, Ho, & Narendra, 1963). For thetheory of economic policy, the possibility of interpreting controll-ability as a dynamic analogue to Tinbergen’s (1952, 1956) notion ofthe existence of a policy for a given system is interesting (Aoki,1975; Preston, 1974). This was later extended to develop adynamic theory of economic policy, which makes extensive use ofconcepts and results from systems and control theory (Preston &Pagan, 1982; Preston & Sieper, 1977; see also Hughes Hallett, 1989;Hughes Hallett & Rees, 1983; Petit, 1990). Recently, interest in thistheory has re-emerged in the context of policy problems with morethan one decision-maker; see Acocella and Di Bartolomeo (2008),Acocella, Di Bartolomeo, and Hughes Hallett (2007).

However, optimum control theory does not only provide ageneralization of the theory of economic policy to the dynamiccase; it is also a tool that contributes to handling practical andempirical problems of short-term economic policy with the help ofeconometric models. This idea was disseminated in the practice ofpolicy-making to such an extent that from September 1972, thescientific staff of the Federal Reserve Board (FRB) used optimumcontrol methods, especially linear-quadratic methods (control of

linear systems with quadratic criteria), in order to arrive atrecommendations for economic policy-makers in the case of trade-offs between unemployment and inflation (Athans & Kendrick,1974).

The path-breaking work in this direction was carried out byPindyck (1973b) and it quickly spread among control engineers(Pindyck, 1972) and economists (Pindyck, 1973a). Pindyckconstructed a small quarterly linear econometric model for theUSA after the Korean War with the usual macroeconomic basicvariables in the Keynesian sense. Such a model can be regarded, incontrol-theoretic terms, as representing a linear discrete-timetime-invariant system. It is used as a constraint when minimizing aquadratic cost criterion. For the cost function, it is assumed that theprimary aim of stabilization policy consists not in preventingoscillations in economic variables but instead in driving thevariables along ‘‘ideal’’ paths, for instance, with low unemploy-ment and inflation. Preventing oscillations is a secondary goal here,which is achieved to some extent simultaneously when theeconomy follows the desired trajectory. As a result, Pindyckobtains not only optimal stabilization policies for different costfunctions but also essential insights into the dynamic behavior ofhis econometric model. These could, in principle, also be obtainedby simulation experiments, but only if a sufficient number ofsimulations were performed; the approach of looking for optimalpolicies is thus more efficient and more systematic than that ofsimulating policies with an econometric model.

A comparison of Pindyck’s model with a similar work by Livesey(1971), who investigated a nonlinear model for the UK with aquadratic objective function along these lines, also shows that alinear model, although not really supported by economic theory, isgenerally to be preferred to a nonlinear one because of muchgreater ease of computability, which was of major concern in earlyeconomic control applications (the ‘‘curse of dimensionality’’).Nonlinearities were, however, introduced into optimum controlanalyses for econometric models by Chow (1975, 1981). Hisapproach consists in linearizing nonlinear models along atrajectory instead of at a given time point, thus retaining as manyof the nonlinearity features as possible when resorting tolinearization is inevitable (as is the case with larger models ineconomic control applications).

Another question discussed in the economics literature relatesto the assumption of a quadratic cost function as used by Pindyckand Livesey, which may be regarded as being too restrictive.Indeed, the specification of a quadratic preference or welfarefunction has been widely used in economics because by applying itto constraints in the form of a linear system, it yields lineardecision rules (Holt, 1962). But the idea of symmetry, which isoften entailed by a quadratic objective function, is certainlyrestrictive because it implies that overshooting a target gives riseto the same costs as undershooting it by the same amount. It is,however, not clear whether ‘‘overshooting’’ even exists for certaineconomic policy targets. For instance, if we look at the problem ofmaintaining full employment, there is no agreement as to whetherthis target can be overshot, that is, whether something like ‘‘overemployment’’ exists in the first place. In any case, it cannot bedenied that considerable numbers of unemployed and excessdemand for labor to the same extent are two different socialphenomena, which have also different political consequences.

Relaxing the assumption of a quadratic objective function andmodifying it to more general cost functions therefore seemappropriate. Friedman (1974) performed such an investigation,assuming a piecewise quadratic cost function with asymmetriccosts for overshooting and undershooting the targets. However, inthis case as well it is questionable whether the considerably highernumber of calculations arising from this modification is worth-while. In general, it can be said that the definition of targets and

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preferences for a society in functional form is probably morecomplicated and problematic than the specification of such afunction. If we believe such a definition to be possible at all, then aquadratic specification does not seem that implausible and can bejustified to a certain extent, at least by computational advantages.

4. Economic policy applications of stochastic control theory

Another problem arises from the fact that in the literaturereported so far, a deterministic specification and solution of theoptimum control problem was given, which should pertain to adeterministic economic model. In fact, however, the estimatedcoefficients of an econometric model, and hence the elements ofthe system matrices derived from them, are themselves randomvariables. Furthermore, each equation of the structural form of themodel has an additive error term. A solution to a general stochasticcontrol problem that takes full account of the stochastic nature ofthe economic model is not obtainable. There are, however, severalapproaches in existence, and some results for problems ofstochastic control were developed by control engineers. Thecharacteristic feature of real disturbances in engineering andeconomics alike is the impossibility of exactly predicting futurevalues. Hence they cannot be represented in a model as analyticalfunctions, but only as sequences of random variables. Ifdisturbances are thus described as stochastic processes, thestatistical tools of time series analysis can be applied.

Stochastic control theory deals with stochastic dynamicsystems, which are represented by stochastic difference ordifferential equations, i.e. they are subject to disturbancescharacterized by stochastic processes. Stochastic optimum controlproblems require finding a control law optimizing (maximizing orminimizing) a given criterion with a given stochastic dynamicsystem as a constraint. While in the theory of optimal control ofdeterministic systems there is no difference between a controlstrategy and a control program, or between the performance of aclosed-loop and an open-loop system, in a stochastic frameworkthis is different: an optimizing control has to be found as a functionof the current state of the system. In addition, only in stochastictheory does it become clear that the performance of the systemcrucially depends on the information available at the time at whichthe value of the control is determined. For instance, it can be shownthat a delay in observing or measuring the state makes theperformance of the system deteriorate.

In stochastic control theory, it is well known that the predictionproblem and the linear-quadratic stochastic control problem aremathematically dual. A link between the theories of estimating,filtering and predicting the state of the system and the theories ofcontrolling a stochastic system is provided by results in theengineering and mathematics literature called separation theo-rems. They show that in LQG problems (linear system, quadraticcriterion, normally or Gaussian distributed additive disturbances),the optimal control strategy can be separated into two parts: thestate estimator, which produces the best estimation of the systemstate vector from the observations, and a linear feedback law,which gives the control vector as a linear function of the estimatedstate. This linear control law is the same as if there were nodisturbances and the state vector were known with certainty. Thefirst proof of such a separation theorem was given by Joseph andTou (1961); it is interesting to note that similar results for specialcases were found earlier in the econometric literature, where theywere called ‘‘certainty equivalence theorems’’ (Simon, 1956; Theil,1957).

There are several examples of applications of stochastic controltheory to problems of stabilization policy. The issues discussed inthe literature include, among others, the optimization of quadraticobjective functions with linear econometric models whose

parameters are random variables (Chow, 1975, 1981; Kendrick,1981), various applications of the Kalman filter (to economicpolicy: Vishwakarma, 1974), the optimization of nonlinearstochastic control models (Chow, 1981), and comparisons betweenthe performance of an economic policy under a deterministic and astochastic specification, respectively (Kendrick, 1981; Turnovsky,1973, 1977).

A shortcoming of many applications of stochastic control theoryis the following: usually only the expected value of a criterionfunction is maximized, without regarding higher moments, forinstance. This is only useful, however, if we want to achieve ourobjective optimally in the long run on average. But if short-termobjectives are of interest, as is especially the case for stabilizationpolicy, then another objective function may be more reasonable.We can, for example, require economic policy to have a probabilityof 90% for reaching a certain target, and maximize under thisconstraint. It is also possible to look for a minimum variancecontrol strategy which minimizes the variance of certain variablesof the model over time. Such questions of risk aversion, which arefamiliar from portfolio selection analysis (Markowitz, 1959), arerelevant for problems of economic policy as well and have beendealt with in the literature on risk-sensitive control (see Section 6.2below).

As general solutions of stochastic optimum control problemsare not available and approximations to the optimum are the bestone can hope for, computational aspects of stochastic optimumcontrol become very important. So far, only a few algorithmsdealing with the calculation of (approximate) solutions tostochastic optimum control problems are available; in particular,one for nonlinear systems with additive disturbances (Chow, 1981)and one for linear systems with a more general stochastic structure(Kendrick, 1981). An attempt to combine the capabilities of bothhas been made by Matulka and Neck (1992). They developed theOPTCON algorithm, designed to approximate optimal solutions tostochastic control problems for nonlinear systems under multi-plicative (uncertain parameters) and additive uncertainty. Itdelivers solutions to problems with a quadratic intertemporalobjective function and (rather general) nonlinear dynamic systemswhich are representations of the economic (mostly econometric)models of the economy under consideration. The former is of the‘‘tracking’’ form, penalizing deviations of state and controlvariables from ‘‘ideal’’ paths; the latter are approximatedrepeatedly during the calculation of the approximately optimalsolution by time-varying linear systems. The OPTCON algorithmhas been used to determine optimal macroeconomic policies forAustria and Slovenia, both under certainty and under the fullstochastic assumptions detailed above. See Neck and Karbuz(1997), Weyerstrass, Haber, and Neck (2000) for some results.

5. Economic policy applications of decentralized control theory

In the optimum stochastic control problem, the control actionsat different points in time must be set as functions of the availabledata. Usually it is assumed that all actions which have to be done ata certain time must be based on the same data and that all dataavailable at time t will also be available at any later time t0 > t, asituation which has been called a classical information pattern(structure) by Witsenhausen (1968).

In contrast to this, a problem with non-classical informationpattern exists whenever the ‘‘memory’’ of the controller is limited;for example, it is possible to determine an optimal controllerwithout memory such that every control action depends just onthe last observation of the state. Another possibility is theinterpretation of communication problems as control processes;in this case, too, the information pattern is never a classical onebecause there are at least two control stations (agents) who do not

R. Neck / Annual Reviews in Control 33 (2009) 79–88 83

have access to the same data. Finally, non-classical informationstructures can be found whenever the system to be controlled islarge or consists of several subsystems; also in these cases, theactions of the controllers at any point in time are not based on thesame data, even if every control station has perfect memory, sincethe chains of communication between the stations are subject tolags, disturbances and cost constraints. From a methodologicalpoint of view, these chains of communication can be regarded aspart of the controlled system and the communication policy as partof the control policy.

The investigation of different information patterns in the wayindicated above is the subject of decentralized control theory(Jamshidi, 1983; Siljak, 1991; Singh, 1981). Mathematical resultsare available only for special cases. However, Witsenhausen (1971)developed a rather general model showing the formulation ofdiscrete-time decentralized control problems, i.e. of models forsystems with several controllers. The essential point here is thatseveral controllers, who have non-identical information about thestructure of the system, the state vector, the parameters, etc., acttogether in controlling the same system.

In economics, similar problems of decisions in organizationswhose members share common goals have been discussed in theliterature for many years; the relevant theory is called the theory ofteams. A team is a group of persons, each of whom makes decisionson different problems but who gets a common reward as a result ofall these decisions (Marschak & Radner, 1972). The issuesdiscussed in team theory are very similar to those occurring indecentralized control theory; in particular, the investigation ofinformation structures and of the influence of information on theoptimal value of the criterion is of major concern in both cases. Themain difference is that the theory of teams by Marschak undRadner is mostly static while decentralized control theory isessentially dynamic.

Dynamic generalizations of methods of the theory of teams andtheir application to problems of optimal control with a decen-tralized decision structure therefore appeared to be an obvioussolution. However, it was necessary to set extremely restrictiveassumptions in order to keep the computational efforts withinreasonable limits. The main difficulties stem from the interactionbetween information and control, because the actual decision of anagent (controller) at any time depends on the previous actions ofthe other members of the team; these actions, however, arethemselves part of the solution to be determined as a result of theproblem. A limitation to the methods of team theory is theconstraint that the same decision-maker cannot decide more thanonce at each point in time.

In principle, for decentralized systems with non-classicalinformation patterns, the same questions were investigated asin classical control theory; however, solutions are only availablefor some special cases. Intensive investigations have beendedicated especially to the questions of stability of the controlledsystem, optimality of the control design, and the relation betweendifferent information patterns. Apart from this, several methodsshould be mentioned in this connection which were developed inorder to describe complex systems and also seem to be applicableto decentralized systems, such as the theory of hierarchicalsystems (Singh, 1977), the theory of composite systems, investiga-tions into the decoupling and the assignment problems (Morse &Wonham, 1971), and the application of the concept of aggregationto coupled systems (Aoki, 1968).

The issue of decentralized planning has been recognized as arelevant problem by economists for a long time, especially sincethe ‘‘Socialist controversy’’ of the inter-war period between Mises,Hayek, Lange and others. It continued in the theory of allocationmechanisms developed after World War II (see, e.g., Hurwicz &Reiter, 2006). This economic theory of decentralization, however,

is fully directed towards the problems of allocation and cannot bedirectly applied to the problems of short-run stabilization policyover time; furthermore, these methods are mostly static ones.

On the other hand, economic policy interpretations of somemodels of decentralized dynamic control systems can provide newinsights. The different controllers can be interpreted as policy-making persons or institutions which have to bear responsibilityfor different tasks of stabilization policy, like, for instance thegovernment, the central bank, social insurance companies, etc. Thequestions of transmission of information, which can be analyzedby decentralized control theory, are of great practical interest asdelays and disturbances in the communication and transmission ofinformation between all these institutions are omnipresent. Someof the few economic policy applications of decentralized controltheory are Aoki (1974) and Neck (1983, 1987).

Treating the problems of stabilization policy in the form of abasically team-theoretic model (with a common objective functionfor all controllers) is, however, only justified when only thoseinstances are regarded as controllers that are dependent ongovernment in some form or another. Institutions like trade unions,employers’ associations and even independent central banks withtheir own objectives then cannot be regarded as controllers,although they obviously have a decisive influence on economicpolicy decisions. In order to incorporate such institutions, it isnecessary to use a game-theoretic approach, which allows for theanalysis of cooperation as well as of conflicts between these agents.Control theory methods differ from those of game theory mainly inthat the former incorporate only one single decision-maker as beingeventually decisive. Although this decision-maker is no longerexplicitly present in problems of decentralized control theory, thisapproach essentially assumes the existence of somebody above allcontrollers (in engineering applications, for instance, the experi-menter) who defines the control laws and the objective function andsupervises the workings of the system. In economic terms,decentralized control can be called a topic in the organization ofan economic policy; indeed, for questions of organizing an activity,the approach of team theory is well suited. Conflicts of goals orinterests between several groups, on the other hand, cannot betackled by these instruments.

6. Recent developments in economic policy controlapplications

Recently, it has been increasingly recognized that manyproblems of economic policy cannot be solved by uncriticaladoption of optimum control concepts. In particular, economicpolicy problems are typically characterized by a multitude ofdecision-makers with non-identical interests. Moreover, disillu-sion with Keynesian activist policies have raised severe doubtabout the possibilities of controlling an economy in a similar wayto a physical object such as a rocket, for instance. Hence,economists have started to look for alternative sources ofinspiration for their scientific work, such as biology, appliedbusiness and management, or psychology, for instance. Never-theless, there is still a need for a framework for quantitativeeconomic policy problems. In this section, we argue that dynamicgame theory, which also originated from engineering and extendsoptimum control theory, can provide such a framework. Moreover,robust control theory can provide important insights into theproblems of designing stabilization policies when uncertaintyabout the specification of the economic model is present.

6.1. Economic policy applications of dynamic game theory

Dynamic game theory is the most appropriate tool for analyzingproblems with several decision-makers who have non-identical

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interests. It is a methodology which was largely developed byengineers and control theorists and which has gradually found itsway into economics. Within the game theory paradigm, theproblem of stabilization policy is no longer regarded as a problemof optimization but of equilibrium among agents with (at leastpartially) conflicting interests. Several solution concepts have beendefined for dynamic games, such as Nash, Stackelberg and Pareto,open-loop and feedback (or Markov perfect) solutions, dependingon the ability (or lack thereof) of the decision-makers to committhemselves to certain courses of action, and on the cooperative ornon-cooperative character of the games, etc. See Basar and Olsder(1999), Mehlmann (1988), Dockner, Jorgensen, Long, and Sorger(2000), for more details. It is easy to see that dynamic games arevery appropriate for many economic problems. The classicalmicroeconomic oligopoly problem, in which two or more (but notmany) firms compete against each other, is a typical game situationas these firms obviously have conflicting interests, although theseinterests are not necessarily completely antagonistic. This meansthat their situation can be best described as a non-zero-sumgame—a model that is more complicated than a zero-sum game, inwhich each player’s gains are exactly the other player’s losses. Thesame is true for a large variety of economic (and even most othersocial) problems.

In the area of macroeconomics and the theory of stabilizationpolicy, there are several possibilities to introduce decision-makerswith different interests (see, among others, Petit, 1990). Inparticular, different policy-making institutions, which are respon-sible for specific policy instruments and/or areas, may differ withrespect to their preferences. At a national level, there may beconflicts between the government (which is usually responsible forfiscal policy) and the central bank, to which monetary policy isentrusted. For example, central banks are often highly adverse toinflation, while governments frequently put more emphasis ongoals like full employment or high GDP growth. In an internationalcontext, governments of different countries may have differentobjectives, and problems of international policy coordination mayarise. In this case, policy-makers in different countries mayprimarily pursue their own national interests and not care aboutspillovers of their actions to other countries or even engage in‘‘beggar-thy-neighbor’’ policies. Stabilization theory sometimeseven covers conflicts of interest between the government of acountry and the (aggregate) private sector of that country or atleast between the decisions of a country’s policy-makers and thepreferences of the majority of its citizens. Several other scenarioswith divergent interests are conceivable, and dynamic gametheory is a very appropriate tool to analyze (and sometimes helpresolve) the resulting conflict situations.

An especially interesting problem of strategic interactionsarises in the case of a monetary union, of which the EuropeanEconomic and Monetary Union (EMU) is a prominent example. In amonetary union, national currencies (national central banks) havebeen completely replaced by a common currency (common centralbank). This implies that the exchange rate between the members ofa monetary union is no longer available as an instrument ofadjustment. It can be shown that the results of different solutionconcepts for a dynamic game between the common central bankand national fiscal policy-makers provide insights into thestructure of a policy conflict and its consequences under differentassumptions about policy-makers’ behavior in such a union. Fordetails see, among others, Haber, Neck, and McKibbin (2002), Aarlevan, Di Bartolomeo, Engwerda, and Plasmans (2002), Neck andBehrens (2004).

Dynamic game models are usually much more complex thanoptimum control problems; hence only in rare cases are analyticalsolutions available for these models. Therefore, even for smallmacroeconomic models, numerical solutions or approximations to

them are the best one can hope for. One of the few algorithmsavailable for obtaining such solutions of dynamic games is theOPTGAME algorithm (Behrens & Neck, 2008). The OPTGAMEalgorithm is designed to approximate solutions of dynamic gameswith a finite planning horizon. It solves discrete-time LQ (linear-quadratic) games, and approximates the solutions of nonlinear-quadratic difference games by iteration. At present, the algorithmcalculates approximations to the open-loop and the feedback Nashand Stackelberg equilibrium solutions and the cooperative Pareto-optimal solutions for an arbitrary number of players.

6.2. Economic policy applications of robust control theory

A serious criticism often raised against many applications ofoptimum control theory to problems of economic stabilizationpolicies relates to the quality and reliability of the models of theeconomy to be controlled. It is well known that forecasts witheconometric or other economic models often fail to come close tothe actual values of the variables of interest, and the problem ofmisspecification of economic models is well known to modelbuilders and users alike. If such models are not very reliable, canwe then dare to trust in policy recommendations derived from adecision support system of which such models are an essentialpart? This question is more relevant in economics than inengineering uses of control theory because economic modelbuilders have much fewer possibilities to influence the environ-ment of the system to be controlled, less information about the‘‘laws’’ governing the system, and less data to validate their modelsthan scientists working with physical systems. Experiments arevirtually impossible in a macroeconomic context, with severalcompeting theories trying to explain macroeconomic phenomenaand consequently several (often ideologically biased) policyrecommendations and often a variety of models without clear-cut possibilities of discriminating between them.

In principle, this situation can be dealt with by assuming someprior probability distribution of possible models and determiningoptimal policies by taking expectations over the class of possiblemodels in a Bayesian manner. However, such an approach may notbe feasible when no such probability distribution is available.Moreover, policy recommendations based on a likely but never-theless not perfectly known model may be rather dangerous if themodel then fails to deliver an accurate description of the economyunder control. Policy-makers are usually risk-averse and mayattach higher negative weights to possible deteriorations in theeconomic situation caused by misguided policies than to possibleimprovements occurring when the model is (at least approxi-mately) valid (Whittle, 2002). Robust control theory, which hasbeen an active field of research in the control engineeringcommunity during the last decade, can provide the tools to dealwith such problems. For instance, H1 control, which takes themost pessimistic view of nature (in the case of economic policyproblems, of the validity of the economic model), may be superiorto just optimizing an expected value of the objective function givensome probability distribution of possible economic models,although in some cases, decisions derived by robust controlmethods may seem too pessimistic (cf. Tucci, 2006).

Over the last few years, several studies have used methods andconcepts from robust control theory to determine economicpolicies which are not too risk-sensitive but which can never-theless achieve some improvement over an uncontrolled devel-opment. This literature returns to the old question of policy designunder uncertainty, but uses concepts and tools that do not assumemuch knowledge about the reliability of the economic model. Astudy by Onatski and Stock (2002), for example, showed thatrobust policies in most cases (at least in their framework) weremore active than under certainty, a result which is somewhat

R. Neck / Annual Reviews in Control 33 (2009) 79–88 85

unexpected. Their result is contradicted by Zakovic, Rustem, andWieland (2005), but confirmed by Zhang and Semmler (2005) andLeitemo and Soderstrom (2008). Another line of research comparesrobust policies to those obtained when assuming that private-sector agents (and possibly also policy-makers) learn about themodel during the process in which the economy is beingcontrolled. This is especially relevant in the context of an economicenvironment where agents are assumed to have rational expecta-tions, which is now a standard assumption of both New Classicaland New Keynesian macroeconomics. In this case, robust controltheory has to be extended to the non-causal dynamic systemsimplied by rational expectations, resulting in a fruitful exchange ofideas between control and economics research. The recent book byHansen and Sargent (2008) is an excellent example of this kind ofmutual enhancement. For an explicit model of learning processesin the context of robust monetary policy design, see Tetlow andvon zur Muehlen (2009). We expect a lot of interesting furtherwork at the interface of robust control theory and macroeconomicpolicy to appear over the next few years.

7. Possibilities and limitations of control theory models ineconomic policy

‘‘Economists experimenting with the decision-makingapproach of ‘optimal control theory’ hope that it will becomefully operational in economics in the next few years. If it does, theywill have at their disposal a mathematical supertool that, whenused together with econometric models, could substantiallyadvance the science of economic and financial management.Control theory has swept into the economics profession so rapidlyin the past 2 or 3 years that most economists are only dimly awarethat it is around. But for econometricians and mathematicaleconomists, and for the companies and government agencies thatuse their skills, it promises an improved ability to manage short-run economic stabilization, long-run economic growth, invest-ment portfolios, and corporate cash positions’’ (Business Week 19May 1973; quoted in Athans & Kendrick, 1974). This optimisticview of the possibilities of control theory from the early days of itsapplications to economic policy problems, came soon under theinfluence of the ‘‘Lucas critique’’ (Lucas, 1976) and the demonstra-tion of the possible time-inconsistency of optimum control results(Kydland & Prescott, 1977; Prescott, 1977) and gave way to a morepessimistic view a decade later, asking whether economic policyand control theory were engaging in a ‘‘failed partnership’’ (Currie,1985). What can be said now, more than two decades later?

In evaluating control theory applications to problems ofeconomic policy, one can say that in some respect the approachof control theory, especially optimum control theory, is veryflexible. For instance, there are no difficulties formulating time-varying linear systems with systems matrices being dependent ontime; also the weighting matrices of the objective function may betime-dependent without any problems. This also includes the casewhere certain variables become relevant targets only at certainpoints in time and others cease to be targets at certain points intime. The approach of optimum control theory is also flexible in thesense that it is not absolutely necessary to specify the idealtrajectories of the target and instrument variables for the entireplanning period in advance. It is possible to feed back the ‘‘ideal’’ tothe actual values; this would not cause principal difficulties butonly computational ones.

The fact that both state variables (‘‘targets’’) and controlvariables (‘‘instruments’’) may be contained as arguments in theobjective function also has some importance for the dichotomybetween targets and instruments, which was the subject ofdiscussions within the theory of economic policy about the so-called ‘‘teleological fallacy’’. Tinbergen’s theory of economic policy

is taxonomic in the sense that it distinguishes between target andinstrument variables for the model under consideration; thisdistinction is seen by some critics of this approach as using a ratherspecial and mostly arbitrary scheme of classification. The optimumcontrol approach, and more generally an optimization approach,meets this criticism if it also contains the instrument variables inthe objective function. Then it becomes possible for all variables ofthe model to become ‘‘target variables’’ in a wider sense (usuallycalled ‘‘objective variables’’) as their desired (optimal) values canbe determined. On the other hand, it is also possible to assume asmany variables as ‘‘instruments’’ as we like (with a minimum ofone); it only has to be presumed that these variables are under thecontrol of the planner.

The high degree of uncertainty regarding policy effects hasoften been used as the main argument against discretionaryeconomic policy-making; likewise the argument that highinformational requirements make rational planning impossiblehas been advanced against economic planning. Both aspects can becaptured by control theory approaches, at least conceptually, andthe recent interest in robust control theory by economists and theapplications of this theory to problems of stabilization policy showthat one can in fact design policies that are robust againstmisspecifications of the model of the economic system underconsideration.

On the other hand, the dichotomization between exogenousand endogenous variables is required and even essential, also foroptimum control considerations. Distinguishing between endo-genous and exogenous variables supposes that the system is‘‘open’’, that is to say that it has relations to an environment whichis different and distinct from the system itself. In contrast to thisstands the idea in systems theory (e.g., Kade, Ipsen, & Hujer, 1968)that observation and control compel us as observers andcontrollers to become part of the system ourselves: in the processof observing, some of the information necessary for observation isdestroyed. Goal-seeking behavior, which includes observation aswell as control, among others, therefore has to be representedalways as some sort of closed circuit. Hence the question ‘‘in whichdirection’’ the system is open is in no way trivial, and just thisrepresentation is not given in control theory. The decision-makeror controller is principally assumed to be exogenous to the system.Although being influenced by the results of the system (especiallyunder feedback control, closed-loop control or adaptive control),the decision-maker is not himself part of the system. Apart fromthe exogenous variables, which are either given in a deterministicway or affect the motion of the system as stochastic disturbances,there are variables that are exogenous insofar as a consciously andrationally acting individual manipulates them in a certain mannerfreely determined by him, in order to optimize an objectivefunction whose structure and even existence also exclusivelydepends on this individual.

A possible interpretation of control theory models and ofoptimization models in general can be given by regarding them asconsistency models: if somebody sets some targets (an objectivefunction), how do we have to specify the controls in order toguarantee optimal fulfillment of these targets? Such a consistencyanalysis is not, however, of much use for practical purposes unlessit is also stated who shall or can bring about these conditions andwho regards the goals as desirable. For problems of economicpolicy, the objective function is often interpreted as a ‘‘collective(social) welfare function’’ allegedly reflecting all costs and benefitsto the society. But it is well known from social choice theory thateven with plausible and not very restrictive assumptions about thepreferences of the members of a society, no social welfare functionexists that can be derived from these preferences. Most macro-econometric models were built for democratic societies; hence thisinsight is important for the optimum control approach to economic

R. Neck / Annual Reviews in Control 33 (2009) 79–8886

policy. The objective function cannot easily be interpreted ashaving been brought about by democratic methods of definingsocial welfare. On the other hand, this need not be required for anindirect democracy: there the citizens elect persons who, for acertain period of time, are trusted to put into effect their own goalsand targets. Thus the objective function merely reflects thepreferences of the politicians or planners, which for a fixed periodof time can be implemented. We need not discuss whether thismodel of democracy adequately reflects the political realities of thecountries of Europe or Northern America, for example; in any case,the objections raised by social choice theory against social welfarefunctions do not necessarily appear as impediments to applyingthe optimization approach to economic policy.

There is, however, another problem that is closely connected tothe one just mentioned: if the objective function only reflects thepreferences of the planners, who should these planners andpoliticians be? Is it only the elected representatives of the people,especially the government? Can these planners be modeled as onesingle unit, or are there conflicts between them or other reasonswhy we must assume a multiplicity of planners, even in a simplemodel? Control theory first considered one decision-maker only;in decentralized control models, several controllers are taken intoconsideration. But even there, one basic assumption continues: theexistence of a single objective function common to all controllers.The problem then is to create an ‘‘optimal design’’ of the team, as iscommon in organization theory when organizing machines orhuman work in industrial firms. In doing so, the economic systemitself is regarded as a variable and the goal is to organize thissystem in such a way that it performs optimally. The objectivefunction is, in this sense, part of the ‘‘design’’ created by the‘‘designer’’ of the system (the economic system mechanism).

This should rather clearly reveal the ideas underlying thetraditional control theory models; but here, as well, their inherentdifficulties become clear. Apart from presuming extensive abilitiesto manipulate the system, it is not quite clear who in the last resortis responsible for designing the stable system, optimizing theobjective function, organizing the team. An experimenter in theelectrical engineering sense does not usually exist in socialsystems, at least if we disregard extremely powerful dictators (asituation that – alongside questions as to its desirability – does notseem realistic even for countries with very totalitarian govern-ments and centrally planned economies). The idea of designing asystem therefore seems to be more appropriate to engineeringthan to economics. In economic systems, there is always a varietyof individuals and groups performing several control activitieswith different targets and goals, but these are themselves parts ofthe system and must be represented within it. Both in centrallyplanned and in market economies, agents with different aims andtargets must be taken into consideration, and the institutionsresponsible for planning and economic policy are also integralparts of the economic system; these two aspects, however, cannotbe represented in traditional control theory models. In economicpolicy-making, there are several planners with different targets,themselves being parts of the system. The idea of a singleexogenous planner determining the design of the system is notrealistic since in such a case even more ‘‘omniscience’’ and‘‘omnipotence’’ would have to be assumed of such a planner thaneven in the case of completely deterministic models. Instead,economic policy problems can be best modeled in terms ofdynamic game theory, and the applications of these methodsalready have shown that one can gain important insights into theevolution of economic policy decision processes on a national or aninternational level.

The reason why insufficient attention has been paid to thisaspect in the literature on control applications to economic policyfor a long time is due to the fact that issues like transforming an

economic policy into reality, exercise of power, and differences ininterests have been strongly neglected in economic theory. Onemay ask whether the logical structure of economic models does notgrasp certain relevant aspects only for ideological reasons orwhether there are also reasons for this neglect that are inherent toscience. In fact, the last possibility might be true; mathematicaland analytical economists have taken physics and other highlydeveloped natural sciences as a prototype in building their modelsand have often carried over the models of those sciencesuncritically. The only mathematical theory that has been devel-oped with a specific economic (or, more generally, social science)aim might be game theory. Since control engineering also had astandard that was superior to economic theories of planning asregards formal methods, it was a natural development to occupythis theory with minor modifications for economic policy modelbuilding as well. A frequent cause for the inadequacy of somemodels is the requirement that the model must be solvable; oftenit is possible to recognize what is or could be missing, but it isimpossible to formulate those aspects for the specific model or tosolve an extended (and more realistic) model.

Here it is interesting that the concepts of optimization andstabilization induce a very particular focus for the theory ofeconomic policy, assuming an essential unity of policy-makers’preferences. But different policy-making institutions can best bemodeled by assuming different objective functions for them. Hereconcepts of game theory provide a promising alternative,especially the theory of dynamic games for dynamic problems,which has a rigorous mathematical foundation and was eveninitiated by control theorists and engineers. Even the problem oftime inconsistency can be adequately treated within the frame-work of dynamic game theory (see, e.g., Dockner & Neck, 2008).From a methodological point of view, a research program for atheory of economic policy based on dynamic game theory (ofwhich the control-theory based approach will be a one-decision-maker special case) could even settle the old dispute between‘‘institutionalism’’ and ‘‘analytical economics’’ because institu-tional problems would then be investigated by means ofanalytical methods. Such a theory, however, would no longerbe a normative one but purely positive; it is an open questionwhether it should be still termed a ‘‘theory of economic policy’’ orrather ‘‘political economy’’. In any case, such a theory would holdan intermediate position between theoretical economics on theone hand and political science on the other one; it would be moreuseful for the problems of the stable development of an economythan those optimum control concepts derived from engineeringwhich are interesting as consistency models but cannot provide atheoretical foundation for an empirically useful theory ofeconomic policy.

Acknowledgements

Thanks are due to the Jubilaeumsfonds der OesterreichischenNationalbank (project no. 12166) for financial support and to JanosGertler, Andrew Hughes Hallett, Gerhard Sorger, Klaus Weyer-strass and Peter Winker for helpful comments on an earlier draft.The usual caveat applies.

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Reinhard Neck was born on 19 May 1951 in Vienna. From 1970 to 1975, he studiedeconomics and social and economic statistics at the University of Vienna, where heobtained his Ph.D. in 1975 sub auspiciis praesidentis (with special distinctions). He wasassistant professor at the University of Fribourg, Switzerland, and at the ViennaUniversity of Economics and Business Administration, Austria, where he was awardedthe Habilitation in 1991. He was Joseph Schumpeter research fellow at Harvard

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University, Cambridge, MA (USA) from 1991 to 1992, and Austrian visiting professor atStanford University, Stanford, CA (USA) in 2001. From 1992 to 1995 he was professor ofeconomics (Quantitative Economic Policy) at the University of Bielefeld, Germany,from 1995 to 1997 full professor of economics (Public Economics) at the University ofOsnabrueck, Germany. He is full professor of economics at Klagenfurt University,

Klagenfurt, Austria, since 1997. He has edited 30 books and has published about250 papers in scientific journals and books, which deal with issues of economic policy,macroeconomics, applied econometrics, public economics and European integration,among others. From 1999 to 2008, he was Chairman of the IFAC TC on Economic andManagement Systems.