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Control theory and stabilization policy
Journal or Economic Dynamics and Control 1 (1979) 111-l 16. 0 North-Holland
CONTROL
THEORY
AND
STABILIZATION
A Review of the Report of the Committee
POLICY
on Policy Optimisation
Franklin R. SHUPP Unioersity
of Illinois,
Urbana,
IL
61801,
USA
Received August 1978
The potential of optimal control theory both to influence and shape stabilization policy is carefully and critically examined in this excellent study’ authorized by Parliament. While the report focuses on policy formation at the British Treasury and makes certain recommendations specific to that institution, much of the report is of a sufficiently general character to be of interest to anyone concerned with macroeconomic policy determination. The formal charge to the Conimittee which serves as a basis for this study is as follows: To consider the present state of development of optimal control techniques as applied to macroeconomic policy. To make recommendations concerning the feasibility and value of applying these techniques within Her Majesty’s Treasury. In interpreting this charge’ the committee wisely restricted macroeconomic policy to include only those measures which ‘focus primarily on the problems of stabilizing behavior of employment, prices, and balance of payments around a long term trend’. In addition the committee chose to emphasize the social u&e rather than the technical feusibility of applying control theory to macroeconomic decision making, and further distinguished between direct and indirect benefits. Broadly speaking direct benefits are defined as ‘contributions to the ministerial or @2icial decision making process’ while indirect benefits are defined as ‘contributions at the technical level’. In its major finding the committee concludes that the direct benefits of applying control techniques in this area are likely to be limited, but that the indirect benefits should be substantial. Put more baldly, it is the committee’s judgment that optimization techniques cannot profitably be used to generate specific policy ‘Reporr
London).
?J f/w
Cornrniffw
m
Po/k,r
Opriruistrrior~.
1978 (Her Majesty’s Stationery Office,
112
F.R.
Shupp.
Control
theory
and stabilization
polic)
directives in the same way that they have been used to guide rockets. On the other hand, the committee is optimistic about the potential use of control techniques to provide insights leading to better econometric models and improved policy structures. The committee’s reluctance to endorse the direct use of control theory derives from two arguments: (i) existing macroeconomic models are neither sufficiently comprehensive nor sufficiently reliable, and (ii) social welfare functions which adequately reflect the Chancellor’s preferences are extremely difficult, if not impossible, to design. Each of these arguments is treated separately below., The report recognizes that the track record of large scale econometric models is quite good, and, in particular, that the forecasts of the Treasury model compare favorably with those of the London Business School and the National Institute for Economic and Social Research. Like these other models, however, the Treasury model appears to overemphasize the channels through which policy operates and to slight certain private sector behavior, including changes in this behavior. Consequently, forecast accuracy depends crucially on the model builders’ own judgment as to the value over the next several quarters of such parameters as the propensity to spend. It follows that policies indicated by these econometric models are, in reality, policies largely dictated by this judgment. There is no guarantee that the Chancellor’s judgment will be more accurate or more comprehensive, but he may be able to intuit recent changes in attitudes or behavior which are difficult to incorporate immediately into the model. The study also cites the criticism that the lack of agreement, particularly between fiscalists and monetarists, about even the most basic structural mechanisms of the economy implies that policies derived from control models are necessarily deficient. The committee copes with this objection by arguing that the Chancellor most likely has a personal view of the basic underlying economic forces and would logically employ a model consistent with this view. Even if this were not the case, an optimal policy could still be calculated. Suppose, for example, that the Chancellor believes that a liscalist model given by eq. (I) below is twice as probable as a monetarist model given by eq. (2). Suppose further that the only target variable is the full employment level of output y:. The appropriate policy could then be generated by minimizing
D= i 0.67(~5,-y:)~+O.33(y,,-y:)~, I=1 subject to
F.R.
Shupp,
Control
theory
and stabilization
policy
113
yut+,,=w,,+b,g,,
(1)
where Y,, g, and m, denote respectively the level of aggregate output, fiscal stimulus, and money stock. While the committee notes several other reasons for its reluctance to use its existing econometric models as the primary basis for policy &termination, major reservation about the direct employment of optimal control techniques stems from its conviction that it would be very diffcult to construct an appropriate welfare function. In part this reflects the committee’s view that the Chancellor might prove unwilling to reveal his preferences regarding alternative outcomes. Furthermore, even if he should, his preferences might prove incomplete, subject to rapid change, or possibly be internally inconsistent. In addition, the committee itself seems to have had some difficulty in identifying target values for a hypothetical welfare function. In paragraph 52 of the report the implied target path consists of the ‘long run trend values’ of the relevant variables, whereas in paragraph 207 the target path is restrained only by the requirement that it ‘be realistic, but not feasible’. In some instances these statements can be reconciled, but this is not always possible as is shown in an interesting study by Palash. In any event it is clear that identifying appropriate targets for the welfare function is a rather complex problem. A further problem related to formal optimization is the determination of the appropriate planning horizon. Should the length of the horizon be 3 years or 5 years? Or should it be dictated by the projected return of the economy to equilibrium, or even by political exigencies? Only in the case of rapid policy convergence is the answer to these questions unimportant. It should be clear from these illustrations that further research is needed before a satisfactory welfare function can be formulated, thus allowing the direct application of optimal control models. Now to the more positive side of the report. As noted above, the central conclusion of the report is that control theory’s major contribution in the near future will be (i) to assist in the formulation of improved econometric models, and (ii) to facilitate the generation of simulations directed towards the achievement of macroeconomic targets. In the first of these areas control theory techniques can be used to ‘road test’ new models by subjecting them to a formal optimization procedure. If both the indicated optimal policies and the corresponding trajectories of the state variables prove to be plausible in a series of simulations employing %. Palash, 1977, On the specification of unemployment function, Annals of Economic and Social Measurement 6, p. 276.
and
inflation
in
the
objective
114
F.R.
Shupp,
Control
theory
mrd stubilizctrio~r
policy
both various criterion functions and various shocks. the new model can be assumed road worthy. On the other hand, if either the indicated policy behavior or the corresponding dynamics of the system is grossly counterintuitive, the model should be subjected to further reexamination. In this event, the simulated trajectories may prove useful in identifying a structural weakness or in prompting a more appropriate specification. In the area defined by (ii) above, the model is assumed to be correctly specified and the objective is to identify policy sets consistent with some prescribed target set. If optimization methods are not used, repeated simulations are required. For large scale models like the Treasury model these simulations are very costly. However, the number of simulations can be greatly reduced if control techniques are tirst used to identify an optimal policy set for the given target set. The study also suggests that it may be even more efficient to apply control theory to a smaller model and then to use the indicated optimal policies as a basis for simulation studies on the more comprehensive Treasury model. This smaller model might be estimated directly or it might be artificially constructed from ‘ready reckoners’ derived from the large Treasury model. These ready reckoners are reduced form relationships, generated by the large model, of changes in the target variables induced by changes in the policy variables. There is a second and equally important reason for applying control theory to smaller models-a reason which I believe receives inadequate attention in the report. Explicit policy rules can be derived from these models, and these rules often provide insights or emphases which suggest appropriate policy simulations for larger scale econometric models. Consider the following simple reduced form model: min D = c qxf + sx,u, + ruf, 1=l
subject to X ,+I
=ax,+bu,+c,,
where x, and u, represent deviations from the targeted levels of the state and policy variables respectively. The optimal policy rule for this problem is of the form
U,=e,,X,+e~~C,+ej,c,+,+e,,c,+,+
. . ..
This specification differs from the widely held conviction that the appropriate policy response should be proportional to the gap between the prevailing and
F.R.
Shupp.
Control
theory
and stubilizucion
policy
115
targeted values of the state variable, e.g., the size of the full employment budget deficit should be proportional to the level of the unemployment gap. This specification is given by p, =0,x,.
Two differences between (4) and (5) are immediately apparent. First specification (5) calls for a constant coefficient policy rule whereas specification (4) calls for a uuriable coefficient policy rule, i.e., f3,, varies over time. In other words the optimal policy requires a different (more vigorous) response to, for example, 6% unemployment early in a recession than it does to that same 6% unemployment late in a recession. Similarly if we consider a wage-price control model in which x, denotes price increases and u, denotes controlled wage increases, then 8, represents the allowable fractional wage compensation for any price increase. The optimal control rule indicates that or, should increase over time. This contrasts with the most widely held ad koc rule in which 8, is time invariant. The other obvious difference between (4) and (5) is the inclusion of forecasted exogenous economic behavior (the c, trajectory) in the former and its exclusion in the latter. Although policy authorities have always been aware of the need to consider forecasts of autonomous economic behavior, some have tended to place too much emphasis on the current state of the economy as suggested by rule (5). A second control theory result, which may influence policy makers, obtains when the model given by (3) above is modified to allow for uncertainties. This can be done by making a, b, and c, of (3) stochastic. It is a commonly held belief that in the face of uncertainty, policy makers should proceed very conservatively, i.e., that 6, should be smaller for the stochastic case than it is for the corresponding deterministic case. Control theory however suggests that if the uncertainty resides primarily in a, then the opposite result rna~r obtain, i.e., a more vigorous policy may be indicated for the stochastic situation. This insight may reduce the tendency for some policy authorities to move too cautiously in the face of uncertainty. Optimal policy rules can also be derived for simple models which are characterized by adaptive or rational expectations. Here as elsewhere, these derived rules are suggestive only and need to be further tested by simulations on more comprehensive models.3 While the major conclusion of this study is that control theory’s primary contributions will be indirect (or possibly qualitative) rather than direct, the study offers many other interesting insights which justify a careful reading of ‘For a more complete and ad hoc stabilization
discussion of some ol these arguments, see F. Shupp. policy rules, Economic Inquiry 15, p. 183.
1977, On
optimal
116
F.R.
Shupp,
Control
theory
and stabilization
policy
the entire report. Several topics are listed below to suggest the scope of the report’s coverage. (1) Since data from the most recent quarter are often unreliable and subject to substantial revisions, forecasting models might be improved by deemphasizing this statistic. (2) Since frequent changes in policy behavior create confusion and dampen investment spending, policy makers should try to abstain from this behavior, and control models should penalize such changes. (3) Responses to a 10% rate of inflation may be qualitatively responses to a 5% rate; consequently ministers and model should be alert to possible implied structural changes.
different from builders alike
(4) In commenting on the extreme monetarist position the committee stated that it ‘did not feel that any of the arguments put forward provided a prima racie case against macroeconomic intervention in the economy, and the exercise of discretionary fiscal and monetary policy’. (5) ‘There are several different ways of approximating the effects of uncertainty on our economic policies. If sufficient funds were available to carry out precisely the different techniques advocated for dealing with uncertainty, they would all lead to very similar results’. In summary, this is an excellent study written in non-technical distinguished and knowledgeable scholars and practitioners. ranging and fair and has much to recommend it.
language by It is wide
CONTROL
THEORY
AND
STABILIZATION
A Review of the Report of the Committee
POLICY
on Policy Optimisation
Franklin R. SHUPP Unioersity
of Illinois,
Urbana,
IL
61801,
USA
Received August 1978
The potential of optimal control theory both to influence and shape stabilization policy is carefully and critically examined in this excellent study’ authorized by Parliament. While the report focuses on policy formation at the British Treasury and makes certain recommendations specific to that institution, much of the report is of a sufficiently general character to be of interest to anyone concerned with macroeconomic policy determination. The formal charge to the Conimittee which serves as a basis for this study is as follows: To consider the present state of development of optimal control techniques as applied to macroeconomic policy. To make recommendations concerning the feasibility and value of applying these techniques within Her Majesty’s Treasury. In interpreting this charge’ the committee wisely restricted macroeconomic policy to include only those measures which ‘focus primarily on the problems of stabilizing behavior of employment, prices, and balance of payments around a long term trend’. In addition the committee chose to emphasize the social u&e rather than the technical feusibility of applying control theory to macroeconomic decision making, and further distinguished between direct and indirect benefits. Broadly speaking direct benefits are defined as ‘contributions to the ministerial or @2icial decision making process’ while indirect benefits are defined as ‘contributions at the technical level’. In its major finding the committee concludes that the direct benefits of applying control techniques in this area are likely to be limited, but that the indirect benefits should be substantial. Put more baldly, it is the committee’s judgment that optimization techniques cannot profitably be used to generate specific policy ‘Reporr
London).
?J f/w
Cornrniffw
m
Po/k,r
Opriruistrrior~.
1978 (Her Majesty’s Stationery Office,
112
F.R.
Shupp.
Control
theory
and stabilization
polic)
directives in the same way that they have been used to guide rockets. On the other hand, the committee is optimistic about the potential use of control techniques to provide insights leading to better econometric models and improved policy structures. The committee’s reluctance to endorse the direct use of control theory derives from two arguments: (i) existing macroeconomic models are neither sufficiently comprehensive nor sufficiently reliable, and (ii) social welfare functions which adequately reflect the Chancellor’s preferences are extremely difficult, if not impossible, to design. Each of these arguments is treated separately below., The report recognizes that the track record of large scale econometric models is quite good, and, in particular, that the forecasts of the Treasury model compare favorably with those of the London Business School and the National Institute for Economic and Social Research. Like these other models, however, the Treasury model appears to overemphasize the channels through which policy operates and to slight certain private sector behavior, including changes in this behavior. Consequently, forecast accuracy depends crucially on the model builders’ own judgment as to the value over the next several quarters of such parameters as the propensity to spend. It follows that policies indicated by these econometric models are, in reality, policies largely dictated by this judgment. There is no guarantee that the Chancellor’s judgment will be more accurate or more comprehensive, but he may be able to intuit recent changes in attitudes or behavior which are difficult to incorporate immediately into the model. The study also cites the criticism that the lack of agreement, particularly between fiscalists and monetarists, about even the most basic structural mechanisms of the economy implies that policies derived from control models are necessarily deficient. The committee copes with this objection by arguing that the Chancellor most likely has a personal view of the basic underlying economic forces and would logically employ a model consistent with this view. Even if this were not the case, an optimal policy could still be calculated. Suppose, for example, that the Chancellor believes that a liscalist model given by eq. (I) below is twice as probable as a monetarist model given by eq. (2). Suppose further that the only target variable is the full employment level of output y:. The appropriate policy could then be generated by minimizing
D= i 0.67(~5,-y:)~+O.33(y,,-y:)~, I=1 subject to
F.R.
Shupp,
Control
theory
and stabilization
policy
113
yut+,,=w,,+b,g,,
(1)
where Y,, g, and m, denote respectively the level of aggregate output, fiscal stimulus, and money stock. While the committee notes several other reasons for its reluctance to use its existing econometric models as the primary basis for policy &termination, major reservation about the direct employment of optimal control techniques stems from its conviction that it would be very diffcult to construct an appropriate welfare function. In part this reflects the committee’s view that the Chancellor might prove unwilling to reveal his preferences regarding alternative outcomes. Furthermore, even if he should, his preferences might prove incomplete, subject to rapid change, or possibly be internally inconsistent. In addition, the committee itself seems to have had some difficulty in identifying target values for a hypothetical welfare function. In paragraph 52 of the report the implied target path consists of the ‘long run trend values’ of the relevant variables, whereas in paragraph 207 the target path is restrained only by the requirement that it ‘be realistic, but not feasible’. In some instances these statements can be reconciled, but this is not always possible as is shown in an interesting study by Palash. In any event it is clear that identifying appropriate targets for the welfare function is a rather complex problem. A further problem related to formal optimization is the determination of the appropriate planning horizon. Should the length of the horizon be 3 years or 5 years? Or should it be dictated by the projected return of the economy to equilibrium, or even by political exigencies? Only in the case of rapid policy convergence is the answer to these questions unimportant. It should be clear from these illustrations that further research is needed before a satisfactory welfare function can be formulated, thus allowing the direct application of optimal control models. Now to the more positive side of the report. As noted above, the central conclusion of the report is that control theory’s major contribution in the near future will be (i) to assist in the formulation of improved econometric models, and (ii) to facilitate the generation of simulations directed towards the achievement of macroeconomic targets. In the first of these areas control theory techniques can be used to ‘road test’ new models by subjecting them to a formal optimization procedure. If both the indicated optimal policies and the corresponding trajectories of the state variables prove to be plausible in a series of simulations employing %. Palash, 1977, On the specification of unemployment function, Annals of Economic and Social Measurement 6, p. 276.
and
inflation
in
the
objective
114
F.R.
Shupp,
Control
theory
mrd stubilizctrio~r
policy
both various criterion functions and various shocks. the new model can be assumed road worthy. On the other hand, if either the indicated policy behavior or the corresponding dynamics of the system is grossly counterintuitive, the model should be subjected to further reexamination. In this event, the simulated trajectories may prove useful in identifying a structural weakness or in prompting a more appropriate specification. In the area defined by (ii) above, the model is assumed to be correctly specified and the objective is to identify policy sets consistent with some prescribed target set. If optimization methods are not used, repeated simulations are required. For large scale models like the Treasury model these simulations are very costly. However, the number of simulations can be greatly reduced if control techniques are tirst used to identify an optimal policy set for the given target set. The study also suggests that it may be even more efficient to apply control theory to a smaller model and then to use the indicated optimal policies as a basis for simulation studies on the more comprehensive Treasury model. This smaller model might be estimated directly or it might be artificially constructed from ‘ready reckoners’ derived from the large Treasury model. These ready reckoners are reduced form relationships, generated by the large model, of changes in the target variables induced by changes in the policy variables. There is a second and equally important reason for applying control theory to smaller models-a reason which I believe receives inadequate attention in the report. Explicit policy rules can be derived from these models, and these rules often provide insights or emphases which suggest appropriate policy simulations for larger scale econometric models. Consider the following simple reduced form model: min D = c qxf + sx,u, + ruf, 1=l
subject to X ,+I
=ax,+bu,+c,,
where x, and u, represent deviations from the targeted levels of the state and policy variables respectively. The optimal policy rule for this problem is of the form
U,=e,,X,+e~~C,+ej,c,+,+e,,c,+,+
. . ..
This specification differs from the widely held conviction that the appropriate policy response should be proportional to the gap between the prevailing and
F.R.
Shupp.
Control
theory
and stubilizucion
policy
115
targeted values of the state variable, e.g., the size of the full employment budget deficit should be proportional to the level of the unemployment gap. This specification is given by p, =0,x,.
Two differences between (4) and (5) are immediately apparent. First specification (5) calls for a constant coefficient policy rule whereas specification (4) calls for a uuriable coefficient policy rule, i.e., f3,, varies over time. In other words the optimal policy requires a different (more vigorous) response to, for example, 6% unemployment early in a recession than it does to that same 6% unemployment late in a recession. Similarly if we consider a wage-price control model in which x, denotes price increases and u, denotes controlled wage increases, then 8, represents the allowable fractional wage compensation for any price increase. The optimal control rule indicates that or, should increase over time. This contrasts with the most widely held ad koc rule in which 8, is time invariant. The other obvious difference between (4) and (5) is the inclusion of forecasted exogenous economic behavior (the c, trajectory) in the former and its exclusion in the latter. Although policy authorities have always been aware of the need to consider forecasts of autonomous economic behavior, some have tended to place too much emphasis on the current state of the economy as suggested by rule (5). A second control theory result, which may influence policy makers, obtains when the model given by (3) above is modified to allow for uncertainties. This can be done by making a, b, and c, of (3) stochastic. It is a commonly held belief that in the face of uncertainty, policy makers should proceed very conservatively, i.e., that 6, should be smaller for the stochastic case than it is for the corresponding deterministic case. Control theory however suggests that if the uncertainty resides primarily in a, then the opposite result rna~r obtain, i.e., a more vigorous policy may be indicated for the stochastic situation. This insight may reduce the tendency for some policy authorities to move too cautiously in the face of uncertainty. Optimal policy rules can also be derived for simple models which are characterized by adaptive or rational expectations. Here as elsewhere, these derived rules are suggestive only and need to be further tested by simulations on more comprehensive models.3 While the major conclusion of this study is that control theory’s primary contributions will be indirect (or possibly qualitative) rather than direct, the study offers many other interesting insights which justify a careful reading of ‘For a more complete and ad hoc stabilization
discussion of some ol these arguments, see F. Shupp. policy rules, Economic Inquiry 15, p. 183.
1977, On
optimal
116
F.R.
Shupp,
Control
theory
and stabilization
policy
the entire report. Several topics are listed below to suggest the scope of the report’s coverage. (1) Since data from the most recent quarter are often unreliable and subject to substantial revisions, forecasting models might be improved by deemphasizing this statistic. (2) Since frequent changes in policy behavior create confusion and dampen investment spending, policy makers should try to abstain from this behavior, and control models should penalize such changes. (3) Responses to a 10% rate of inflation may be qualitatively responses to a 5% rate; consequently ministers and model should be alert to possible implied structural changes.
different from builders alike
(4) In commenting on the extreme monetarist position the committee stated that it ‘did not feel that any of the arguments put forward provided a prima racie case against macroeconomic intervention in the economy, and the exercise of discretionary fiscal and monetary policy’. (5) ‘There are several different ways of approximating the effects of uncertainty on our economic policies. If sufficient funds were available to carry out precisely the different techniques advocated for dealing with uncertainty, they would all lead to very similar results’. In summary, this is an excellent study written in non-technical distinguished and knowledgeable scholars and practitioners. ranging and fair and has much to recommend it.
language by It is wide