The role of macroeconomic models in the policy design process.

Westaway, Peter F.

Introduction

This note examines the role of macroeconomic models in the policy design process. It discusses some of the general issues that need to be addressed if macroeconomic models are to make an important contribution to the policy debate. More topically, it illustrates the role that can be played by using policy optimisation techniques on the National Institute UK model to examine some of the macroeconomic policy options currently facing policymakers.

The need for some form of tool to analyse the broad problems of macroeconomic policy should be self-evident. For policymakers, their calculation of the appropriate response to a particular problem will always depend on their precise objectives and on how they think the economy will react under different policy settings. Taking the current conjuncture, a number of questions must be faced. How quickly should interest rates be raised in response to current or prospective inflationary pressure? How soon should interest rates be lowered again as inflation subsides? How far can unemployment be expected to fall and what can policy do to influence this? How quickly should the public finances be returned towards balance? How much scope is there for tax cuts? What policies can be implemented to improve the long-run rate of growth of the UK economy?

As acknowledged in a recent report by the ESRC Macromodelling Consortium,

'There is no alternative to the use of models of the full economy when seeking answers to these and other questions. No non-model shortcuts are available, despite the appeal of back-of-the-envelope methods.'

Of course, it must also be acknowledged that some of these questions are not easily addressed in the framework of an econometrically estimated macroeconomic model. One of the purposes of this paper, therefore, is to draw attention to the limitations that should be placed on the use of macromodels in the policy design process. Nevertheless, there have been many important issues which have been illuminated by the use of macroeconomic models. At the National Institute, we have used our own models to contribute to the policy debate in a number of different areas. In Wren-Lewis et al. (1991), we calculated the 'optimal' entry rate of sterling into the ERM, suggesting that the rate which was eventually chosen would be too high, and would imply severe output costs. In Westaway (1992a), we analysed the problem of how to choose whether to abandon the ERM. Barrell et al. (1994) examined the consequences of the eventual decision to suspend membership. In the sphere of fiscal policy, Pain et al. (1993, 1994) exhaustively analysed the prospects for the public finances, focusing in particular on the importance of the distinction between current and capital spending. In Blake and Westaway (1993), we examined the possible costs and benefits of delegating the control of monetary policy to an independent Bank of England.

Because of the role that macroeconomic models can play in the policy debate, it has been suggested by the ESRC Macromodelling Consortium that the policy advice given by the macromodelling groups should be standardised in the same way that simulation comparisons have been made by the ESRC Macroeconomic Modelling Bureau at Warwick (see Church et al., 1993, for example). A comparative policy optimisation exercise by Bray et al. (1993) has been cited as an example of how this might be done. One purpose of this note is to consider how such an exercise might be designed. As will be argued below, while we are strongly supportive of the increased use of macroeconomic models to inform the policy debate, we have our own views on how this exercise should best be carried out. In particular, we would emphasise the limitations that should be placed on the type of questions that macromodels, in their current form, should be expected to answer.

Of course, it is well known that macromodels have been subjected to considerable criticism in recent years mainly due to their poor forecasting record and critics have claimed that this invalidates their use as a tool to inform and guide policy. In fact, Britton and Pain (1992) have shown that macroeconomic models have performed no worse than any of the competing forecasting methods; indeed, since the departure of sterling from the ERM at the end of 1992, the forecasting record of our own model at the Institute has been remarkably good. Nevertheless, we agree that it is important for macromodellers to remain humble in their attempts to explain how the economy works but we would argue that the structural approach offered by macromodels is still the most appropriate vehicle for forecasting the economy and analysing policy. Moreover, recent developments in economic modelling, for example relating to the treatment of credibility and expectations have, if anything, strengthened the case for the use of an 'optimisation' framework for policymakers. In practice, policymakers may resort to the use of short-term indicators both to reinforce the credibility of their policy and to guide them on a day to day basis. However, crucially this does not preclude an explicit consideration of final objectives and the trade-off between them as shown by an estimated macroeconomic model. For a more complete discussion of these issues, see Westaway and Wren-Lewis, (1993).

The policy optimisation problem

Since 1980, the government has set down in broad terms the objectives of policy and the policy instruments that it intends to use in order to achieve them. This framework, published annually in the 'Red Book' as the Medium Term Financial Strategy, represents the most complete account of the government's macroeconomic policy aims and objectives although important changes in the emphasis of policy are often announced elsewhere. For example, Nigel Lawson's highly influential Mais lecture in 1984 represented an important statement of policy while in the wake of the departure from the ERM, the decision to announce an explicit inflation target was contained in a letter to the Treasury and Civil Service Committee. Nevertheless, by setting down objectives in this way, the problem of policy design lends itself naturally to the techniques of policy optimisation. If the government were to state the relative priorities on different objectives explicitly and if it were to take a view on which model of the economy is the most accurate, then the calculation of the appropriate settings for fiscal and monetary policy would appear to be a merely technical exercise, (for a useful introduction to the use of optimal control techniques in economic applications, see Whitley, 1994). In practice, of course, the practical problem of macroeconomic policy design is rather more complicated than this. In this paper, an attempt is made to define more precisely the nature and extent of the role which macroeconomic models should be expected to play in the policy design process. To do this, we need to define more carefully the objectives of policy and the targets and instruments which might be used to achieve them.

Standard textbook treatments of the policy design problem are not necessarily very helpful. In some tightly specified theoretical models, for example those based on the notion of infinitely lived economic agents, the choice of 'target' for the government or 'central planner' is straightforward since policy simply involves maximising the discounted utility of the representative consumer (see Blanchard and Fisher (1990) for a clear exposition of this type of model). Even when these models are made more realistic by introducing overlapping generations of finitely-lived representative economic agents who do not have strong bequest motives and the appropriate choice of social welfare function becomes more complicated because of issues of intergenerational distribution, the problem of reconciling the interests of different social groups remains unresolved. An explicit utility-maximising approach is more difficult to take when econometrically based models are adopted since the underlying utility functions are usually implicit, although an approximation to utility maximisation can be taken by maximising the discounted flow of consumption. The difficulties of computing this discounted sum to the limit have led some to include wealth as part of the objective function (see Weale et al., 1989).

In practice, the macroeconomic policy design problem rarely focuses on the ultimate sources of 'utility' suggested by the theoretical models, but instead pays attention to variables such as inflation, output and unemployment. How should policy be appropriately designed with respect to these variables? One point should be made at the outset: if the policy design problem is to be tackled formally as an optimal control exercise, it is important to draw a distinction between the final objectives of policy on the one hand, and intermediate objectives and constraints on policy on the other. In principle, this distinction should be straightforward. In practice, however, the status of a variable as a final objective may depend on the model being used.

To illustrate, consider the MTFS. The aims of policy are stated as being to provide an environment of low inflation and sound public finances in order to provide the conditions for sustained economic growth (see FSBR, 1994). Stated like this, the ultimate objective of policy would appear to be the level of output. In designing policy as an optimisation problem, therefore, policy instruments would only need to be set with respect to a cost function which includes output but not inflation or the PSBR. Then, if the model being used is one where low inflation and sound public finances promote growth, then these will automatically occur as a consequence of the optimal policy. But importantly, not because they are treated as targets of policy. Of course, it is possible that for the particular econometric model being used, a fall in price inflation will not actually stimulate growth, since the decline in uncertainty which would be expected to be the main channel through which low inflation would stimulate growth is generally absent in macroeconomic models. (In fact, in the NIESR model, a fall in inflation will cause GDP to rise slightly in the long run because of a resulting fall in borrowing constraints on consumption). Similarly, a tightening in the fiscal stance will not necessarily improve the supply side performance. In such circumstances, it may be necessary to set up the policy design problem as if inflation and public borrowing were also ultimate objectives. It should be acknowledged, of course, that this is a second best solution. It would be preferable to conduct a policy analysis using a model which fully articulated the influence of inflation and public borrowing.

Let us consider how a policy optimisation exercise should be carried out if, as far as is possible, an attempt is made to capture the macroeconomic objectives of the current government as stated in the MTFS and elsewhere. This will be carried out using the National Institute econometric model of the UK economy (NIDEM). The targets of policy will be taken to be price inflation, GDP growth and public sector borrowing which will be steered towards their desired values by the manipulation of interest rates, government procurement spending and the level of income tax. A number of issues relating to this target-instrument assignment require clarification:

Defining the inflation target - The target range of 1-4 per cent per annum for price inflation in the MTFS is defined in terms of the RPI excluding mortgage interest payments. This definition will be adopted in our empirical work. Since the government's stated intention is to drive inflation into the lower half of this range by the end of the current parliament, the 'bliss value' for this variable will be taken to be 2 per cent. This also happens to be consistent with the widely accepted notion that a 2 per cent rate of measured price inflation is actually consistent with stable underlying inflation once account is taken of price rises due to quality changes (although Oulton, 1995, suggests that this figure may be an over-estimate of these effects).

Monetary policy and the determinacy of the price level - The rule determining nominal interest rates has a crucial role to play since it effectively determines the price level. Since the real equilibrium of the economy is independent of the price level itself, the price level will be indeterminate unless a particular trajectory is tied down by the monetary policy assumption. In general, this will be achieved by a rule which relates the nominal interest rate to any nominal variable, either the price level itself or else an intermediate nominal target such as the money supply; an 'integral control rule' which relates the change in interest rates to the rate of inflation will similarly tie down the price level. Importantly, a rule designed to move nominal interest rates so that real interest rates are held fixed will not tie down the price level. Since the fully optimal control rule for any policy instrument automatically feeds back on every state variable in the model, price level determinacy will be achieved for the optimal control policy. These issues are discussed in more detail in Blake and Westaway (1994).

Level or rate of change of prices - If inflation overshoots its target in any period, should policy be set to claw back the price level slippage? The MTFS itself does not address this issue which probably implies that such slippage will be ignored in practice. Whether this is appropriate or not depends on why inflation is included as a target variable in the first place. If low inflation is preferred because it is thought to minimise general uncertainty or because it avoids undesirable redistributive effects which might arise from unexpected inflation or imperfect indexing, then there is a good case for ignoring past overshooting. On the other hand, if an inflation target is set to provide a reference trajectory for the price level against which nominal contracts should be written, then a commitment to maintaining the target level will increase the credibility of the reference path.

For one particularly simple class of policy regimes which will be analysed below, the choice between price level and inflation targets does not matter. Consider a simple integral control policy rule of the form

[Delta]r = [Theta](inf - [inf.sup.*])

which is used to manipulate interest rates to control inflation (where r is the nominal interest rate, inf and [inf.sup.*] are the actual and desired inflation rates and [Delta] is the first difference operator). It is easy to show that this will be equivalent to a proportional control rule on the price level, i.e.

r = [Theta](p - [p.sup.*])

and there will be no price level slippage so long as the inflation target is unaltered. However, once a more general form of policy rule is considered, for example

[Delta]r = [[Theta].sub.1](inf - [inf.sup.*]) + [[Theta].sub.2](x - [x.sup.*])

where x is some other target variable which always returns to some natural rate [x.sup.*], then the amount of price level slippage will be determined by the transition path of variable x (see Blake and Westaway, 1994). Since the fully optimal control solution is itself a more general from of this type of rule where the policy instrument reacts to every state in the model then in any policy optimisation exercise, the choice between a price level and inflation target will affect the results.

A target for GDP growth - Although GDP growth is accorded the status of a target variable, it differs from inflation in that, for a wide range of models including the National Institute's to be used here, its long-run value can not be altered by changing interest rates, government spending or tax rates. Typically, long-run growth is assumed to be determined by technical progress and population growth which are both set exogenously. In the Institute model, this implies a 'natural growth rate' of approximately 2.5 per cent a year although this can vary as the composition of the economy shifts between low and high productivity sectors. Following the work of Romer (1986) and others, attempts have been made to endogenise the growth process so that policy variables can affect long-run growth either through investment in the process of research and development, or via the encouragement of education and training. So far, these types of model have not been developed into econometrically estimated macromodels amenable to the type of policy optimisation exercise described in this paper.

The resulting inability to change the long-run growth rate has one important implication for the policy optimisation exercise. Any attempt to target GDP growth above its natural rate will compromise the achievement of any other target variables. In our context, it will introduce an 'inflationary bias'. Such an effect is most easily illustrated in the context of a simple interest rate feedback rule on inflation and growth, as follows;

[Delta]r = [[Theta].sub.1](inf - [inf.sup.*]) + [[Theta].sub.2]([g.sup.*] - g)

Since interest rates must stabilise in the long run, the inflationary bias is given by

bias = inf - [inf.sup.*] = [[Theta].sub.1]/[[Theta].sub.2](g - [g.sup.*])

which will only be zero if the target growth rate, [g.sup.*], is set equal to the true long-run rate, g. In that case, it is easy to show that the price level slippage in the face of any shock will be given by the cumulated value of [[Theta].sub.1]/[[Theta].sub.2](g - [g.sup.*]) which is equivalent to [[Theta].sub.1]/[[Theta].sub.2] multiplied by the transient deviation of output from its steady state. Interestingly, this type of inflationary bias is reminiscent of those which arise in the simple models of monetary policy proposed by Barro and Gordon, (1983) for example, but the effect described here does not require the presence of forward-looking expectations.

Level or rate of change of GDP - The preceding discussion of the MTFS has assumed that the ultimate aim of policy is to improve living standards, suggesting that the level of GDP rather than its rate of growth should be included as a final objective of policy. This would seem to be logical since even temporary increases in output above the natural rate are likely to be valued (see Westaway and Wren-Lewis, 1993, for a more complete account of this argument). In practice, however, specifying a target for output in terms of its level raises a number of questions. Even if the natural rate of growth is known with certainty, the natural level may be more difficult to pin down accurately, especially if that level is subjected to random shocks to technical progress. If the wrong level is chosen as the natural rate, then an inflationary (or deflationary) bias may be unwittingly incorporated in policy outcomes. In practical policy optimisation exercises, therefore, it is often safer to incorporate a target for GDP growth, subject to the caveats noted above. Such a growth target is adopted in the empirical work to be described here.

The implications of conflicting targets - Of course, the effect of a non-achievable GDP growth or level target on the outturn for inflation is a specific example of the more general problem of conflicting targets. In the empirical exercise to be described below, this problem is avoided by setting the desired value of GDP growth equal to its natural rate and including no other primary targets. By contrast, in the comparative policy optimisation exercise described in Bray et al. (1993), five different objectives are specified, some of them potentially conflicting, namely to drive inflation towards zero, to maximise growth, to minimise unemployment, to bring the PSBR below 2 per cent of GDP and to drive the current account of the balance of payments to zero by the end of the century. Given the preceding discussion, this type of approach is likely to be problematic since it runs the risk of compromising the achievement of final objectives which are achievable with ultimately futile attempts to alter target variables such as growth and unemployment which can not be affected in the long run. This is not to say that such attempts will always be wrong, and under certain circumstances, it may still be desirable to attempt to drive output above its natural rate (see Rogoff, 1985). For a wide class of models where agents are forward-looking, however, it will be optimal for policymakers to implement policy as if their bliss value for the infeasible target was actually at its natural rate; indeed, much of the case for the delegation of monetary policy to a conservative Central Bank rests on this argument (see Barro and Gordon, 1983, Blake and Westaway, 1993).

The role of the current account target in the Bray exercise raises a different issue. This has only been included there to ensure that all of the models reach a sensible equilibrium in the medium term. The model itself should ensure that such a long-run property is achieved. This device of modifying the optimal control problem to compensate for the shortcomings in a particular model has a long history (see the discussion in the Ball report, Committee on Policy Optimisation, 1978, for example). In fact, this type of modification should not be necessary if the model is adequate. For example, in the NIESR model, a long-run constraint on the balance of payments would not need to be artificially included as an 'objective' in the optimal control exercise. This is because long-run stock-flow equilibrium is ensured by the behavioural private sector equations. In conjunction with the target on the PSBR, this will already guarantee national solvency. Indeed, to attempt to drive the current account to zero may actually be inconsistent with the long-run desired saving plans implied by the government and private sector.

Fiscal policy and the determination of optimal borrowing - The role of fiscal policy in a policy optimisation exercise presents yet another set of problems. In choosing the appropriate levels of government spending and tax rates, a number of considerations come into play. More government spending will usually be preferred to less, ceteris paribus. Similarly, people would rather pay lower taxes which are changed infrequently. Of course, both these considerations must be balanced against the solvency constraint of the government which will impose a debt financing burden on future generations of taxpayers. Clearly, many aspects of these fiscal policy choices are likely to depend on criteria which lie outside the scope of the macroeconomic model. Consequently, it is often sensible to assume that the optimal structure of government spending and taxation has been determined in a prior optimisation exercise which determines the medium-term trajectory for government borrowing. This can be characterised as a medium-term constraint on the PSBR which will itself tie down the long-run debt to income ratio of the government. For a more detailed discussion of the issues underlying the calculation of the 'optimal PSBR' (see Pain et al., 1993, 1994).

This is not to say that fiscal policy instruments can not be manipulated as short-term instruments of demand management, as discussed in Westaway and Wren-Lewis (1993), although as illustrated below, this fine-tuning role may need to be constrained in practice to prevent overly disruptive movements in tax rates or government spending programmes which can not be adjusted frequently.

The role of intermediate targets (the exchange rate, money supply) - So far, no mention has been made of the role of the intermediate targets of policy. In practice, such variables often play an important, if not the predominant role. During the 1980s in the early years of the MTFS in the UK, monetary policy was primarily dictated by the growth of certain monetary aggregates relative to their pre-announced target range. More recently, before and during UK membership of the ERM, the exchange rate was effectively treated as an intermediate target which determined movements in interest rates. In both these episodes, it was argued that the final objective of inflation control would be better achieved indirectly via control of the intermediate target rather than directly by reacting to inflation itself.

It is sometimes argued that this approach may bestow more credibility on the anti-inflationary policy, perhaps because the chosen intermediate target is easier to control than the final objective itself or because the data for the intermediate target are more timely. In fact, these arguments are often fallacious; the former simply shifts the problem on to the link between the intermediate target and the final objective, while in the latter case, the new information contained in the timely indicator variable should more properly be incorporated into the macroeconomic model itself. (This is not to deny that there may be some intermediate target regimes which are more credible because of altered institutional arrangements, for example the ERM). Consequently, in a full policy optimisation exercise, there is no obvious role for intermediate targets. This issue will be discussed briefly again below in the discussion of the design of simple feedback rules where such variables might be useful.

Empirical exercise on the NIESR model

In this section, optimal control techniques are used to illustrate a limited range of options currently available to policymakers in the Treasury and Bank of England. The arguments of the previous section have suggested that the techniques of policy optimisation within a macroeconomic model do not provide an appropriate vehicle for the optimal determination of the medium-term stance of fiscal policy. Accordingly, it is assumed that the rate of income tax remains constant, and that uprating of current grants and allowances will be preserved as in the NIESR November forecast (for more details, see Young, 1994). Government spending will be moved as a policy instrument operating under the medium-term constraint that the PSBR to GDP ratio is driven to balance by the early years of the next century, although in the short term some role for fiscal fine-tuning is permitted. Primarily, then, the focus of attention in this exercise is on the 'optimal' determination of interest rates.

Policymakers are assumed to derive a setting for nominal interest rates (the base rate) and government procurement spending to minimise the following cost function which is assumed to capture the objectives of the government;

C = [summation of] 1/2[[Delta].sup.t][a[(inf - [inf.sup.*]).sup.2] + b[(g - [g.sup.*]).sup.2] where t = 95Q1 to 09Q4 + c[(PSBRY - [PRBRY.sup.*]).sup.2] + d[Delta][r.sup.2] + e([Delta][G.sup.2])]

* inf and [inf.sup.*] are taken to be the actual and desired values of inflation (defined using the RPI excluding mortgage interest payments), where [inf.sup.*] = 2 as explained above.

* Similarly, g and [g.sup.*] refer to actual and desired GDP growth. [g.sup.*] is set equal to 2.5 per cent, equal to the assumed long-run growth rate of the UK economy.

* PSBRY and [PSBRY.sup.*] are the actual and desired value of the PSBR to GDP ratio. The desired value is set equal to zero after 99q4.

* Rate of change terms on the nominal interest rate (the base rate) and government spending are included to ensure that the resulting interest rate outcome is plausible (technically, some degree of damping is required on the policy instruments to deliver a determinate solution).

* Policy instruments are manipulated actively from 190195q1 to 2009q4. Thereafter, each policy instrument has a 'tail' whereby they are set to a neutral trajectory for the rest of the optimisation period. This is done so as to avoid implausible movements in the instruments near the terminal period which can have disruptive effects on the optimisation results; for more on these technical details, see Blake and Westaway (1995a).

* All costs are assumed to be discounted at 1 per cent a quarter i.e. [Delta] = 0.99. This assumption is essentially arbitrary, although it can be justified as being roughly consistent with the observed annual real interest rate of 4 per cent. The optimisation horizon is taken to be 2009Q4.

The policy optimisation techniques described here do contain one important innovation. Since the National Institute model can not be simulated under the assumption of fixed nominal interest rates (unless the exchange rate is also exogenised) for reasons implied by the previous discussion of price level determinacy, the conventional optimal control algorithms for use with large scale non-linear models can not be used. This is because to calculate the derivatives of policy targets with respect to changes in policy instruments, the model is required to be solved in open-loop mode, that is with policy instruments held exogenous and successively shocked. A general technique for solving any such problem where the open-loop model is either indeterminate or even unstable is described in Blake and Westaway (1995b); briefly, the policy instrument concerned must be divided into an exogenous and endogenous component where the latter constitutes a feedback rule which must both remove the indeterminacy/instability and be contained within the fully optimal feedback rule. An example of such a stabilising rule in the case of monetary policy which is used in the empirical work here is a simple integral feedback from interest rates feeding back on the deviation of inflation from its target value.

As a benchmark, all solutions derived from the optimisation process are compared with the November forecast. There, interest rates are largely taken from the forward-markets and are therefore assumed to be broadly consistent with expectations prevailing in the private sector. On this basis, short-term interest rates were expected to rise from the prevailing level in November of 5.75 per cent to reach 8 per cent by 1997 before settling down at 7.5 per cent in the long run, reflecting a difference of around 0.5 per cent with a trade-weighted average of competitors' interest rates. Since the exchange rate equation in the Institute model is simply based on the open arbitrage condition, the effective exchange rate will accordingly depreciate by that amount under the maintained assumption of model of rational expectations. Given the associated profile for overseas inflation, which is forecast to be just above 3 per cent a year by the end of the century, UK inflation is predicted to rise to the top of the target range of 1 to 4 per cent, before settling down at an average rate of around 4 per cent in the early years of the next century. Clearly, since inflation is expected to rise near to the top or even outside its target range, it can not be the case that the government's commitment to that range is entirely credible.

We now turn to the optimal control results. Can an optimally derived solution deliver an improved outcome on the basis of the assumed government objective function?

First, it is assumed that the government attribute no weight to output growth or to changes in the exchange rate (the weights in the objective function are a = 1, d = 0.01, e = 0.000001). Charts 1(a)-(d) how the resulting outcomes for inflation, interest rates, GDP growth and the PSBR to GDP ratio. Table 1 gives the resulting costs compared with the outcome from the November forecast. The inflation cost is shown to have fallen by 99 per cent, while movements in government spending are now ensuring that the medium-term solvency condition on the PSBR ratio is hit more accurately towards the end of the optimisation period.

On superficial scrutiny, these 'optimal' results appear to be paradoxical. Interest rates are lower throughout, yet inflation falls sharply as a consequence of a sharp 5 per cent appreciation of the nominal exchange rate. The initial output consequences are slightly adverse but over the whole optimisation horizon, GDP costs are roughly unchanged. How can this be? In fact, this outcome arises because of the implicit change in the inflation target from 3.5 per cent to 2 per cent which implies a sharp tightening of policy. Because this more severe reaction to inflation is perfectly anticipated, however, nominal interest rates are [TABULAR DATA FOR TABLE 1 OMITTED] now expected to be lower in the long run and immediately begin to fall accordingly, although real interest rates do rise in the short run (In Blake and Westaway (1994), this counter-intuitive response of nominal interest rates in the face of a lower inflation target is illustrated more clearly for both an analytic model and on the NIESR model). It is easy to show how the 'optimal policy' will adjust if the weights in the objective function are altered. Charts 1 (a)-(d) and table 1 also show the implications of incorporating a weight of b = 10 on the deviation of output from its natural rate. Inflation control is slightly worse in the late 1990s while GDP is slightly higher as a result, although in the long run, as discussed earlier, GDP returns to its previous trajectory, as does inflation. Most importantly, however, the improved control over inflation relative to the November forecast base is maintained.

It is worth discussing the nature of these results in more detail. Two features stand out;

First, they illustrate starkly that it is crucial to interpret prospective movements in policy instruments in a closed-loop context (i.e. as the outcome of policy rules) rather than as open-loop policy settings. Clearly, it would be nonsensical for the government to announce the new lower trajectory for nominal interest rates on the basis that this is the optimal policy. Such a strategy would be meaningless without an accompanying explanation of the basis on which the interest rate path was to be set. Yet this presents a practical problem since it is extremely difficult to characterise the fully optimal policy as a rule since it has been derived numerically and even for a linear model would involve the announcement of a feedback rule which reacted to every variable in the model (see Blake and Westaway, 1994).

Second, it shows that it is not valid to consider optimal policy unless some account is taken of credibility. The large fall in inflation only comes about because the commitment to the new inflation target is believed immediately and completely. Suppose, however, that the private sector did not greet the government's announcement with such unquestioning trust. In fact, there are two quite separate senses in which credibility might be considered;

* First, even if the private sector perceives correctly the objective function of the government, there will be still an incentive for governments to re-optimise after an initial policy announcement; this is known as the problem of time-inconsistency, first noted in the macroeconomic policy context by Kydland and Prescott (1978). If private agents anticipate this continual process of re-optimisation, an inferior time-consistent solution results. Such a solution has been computed for this example using the technique described in Westaway (1989). The results are shown in charts 2(a)-(b). In fact, although the necessary rise in interest rates is slightly larger and the resulting control of inflation slightly poorer, the inherent degree of time-inconsistency is rather small in this case, mainly because the target level of inflation is achieved relatively quickly (for an example where the difference between the time-inconsistent and time consistent outcomes are much larger, see Westaway and Wren-Lewis, 1990).

* Alternatively, suppose that the private sector initially does not believe that the government is actually prepared to stick to its announced inflation target, and will only believe that such a policy is in operation when it has been observed over a number of periods.

This would imply that the private sector learns about the governments true policy stance. There are two alternative ways to analysing this problem. One is to assume that private sector agents use a Kalman filter learning rule to form their expectations, eventually homing in on a solution which will be consistent with the rational expectations solution (see Hall, 1993, for example). Computationally, this approach is rather burdensome and implicitly does not distinguish between learning about the policy rule and learning about the workings of the whole model. Instead, a form of model consistent learning is adopted (explained in Westaway, 1992b) where the private sector is gradually assumed to learn about the true policy reaction function itself, and the solution is obtained by a series of 'stacked' consistent expectations solutions (where ex post, expectations are not model consistent because of the initial expectational errors).

The problem of deriving an optimal policy under the assumption of learning by the private sector is extremely complicated and will not be attempted here (see Backus and Driffill, 1985, for a discussion of some of the issues involved). Instead, it will be assumed that the fully optimal policy is actually approximated by a simple rule which feeds back on the inflation error alone. This was found to be most closely proxied by

[Delta]r = 0.25(inf - 2)

Charts 2(a)-(b) show how surprisingly similar the results are for the simpler feedback rule compared to the fully optimal strategy. It should be emphasised that despite the simplicity of this rule in only reacting to the current level of inflation, the rule is effectively forward-looking since all future deviations in inflation will be reflected in future interest rates, and hence will be brought forward on to the current exchange rate. Of course, as has been argued by others (see Currie and Levine, 1985, for example), the announcement of a rule in simple form has other advantages since it will be clearly understood and easily monitored.

Charts 3(a)-(b) compare the results for the simple rule (instantly believed) with the results of assuming that private sector expectations adjust slowly over a period of 10 and 20 quarters from the original feedback rule (embodied in interest rate futures) to the simple-optimal rule. Throughout, the government is assumed to follow the simple-optimal rule. Under learning, interest rates do not fall immediately, but instead rise for a few quarters until it becomes clear that the government's inflation target has indeed fallen. Output costs are higher in the short term as the rise in nominal interest rates needs to be greater to have the same effect in bringing down inflation.

Policy conclusions

This note has attempted to illustrate the role that empirically based macroeconomic models can play in the practical policy design process. A number of conclusions should be emphasised.

The main focus of attention has been on the design of monetary policy. It has been shown how optimal control techniques can provide a useful benchmark in determining how well inflation can be controlled via the manipulation of interest rates. Moreover, a simple rule has been designed for interest rates feeding back on inflation alone which would be both easy to understand and transparent to monitor which has been shown to mimic many of the desirable features of the fully optimal policy. More work is required, however, to check the robustness of these simple rules to different assumptions within the model, and to inclusion in different models. In particular, a more systematic investigation is required of the role of forward-looking indicators which policymakers currently claim to be using. The results of this paper and the analysis of Blake and Westaway (1994) suggest that, when expectations are forward-looking, the need for such anticipatory behaviour may be over-exaggerated since the influence of future policy is already reflected in the current tightness of monetary policy via its effect on the exchange rate.

The time inconsistency problem has been shown to be relatively unimportant in the particular example described but consideration of the evolving credibility of anti-inflationary policy has been shown to have an important bearing on the interpretation of results. This, it is argued here, would tend to reinforce the case for an announced policy rule which is easy to understand and readily monitored.

On fiscal policy, a path has been derived for government spending which, at current tax rates, will drive public sector borrowing back towards balance by the early years of the next century. It has been argued, however, that although fiscal policy can have a short-term fine-tuning rule, the calculation of 'optimal' taxation and public spending (both current and capital) is best addressed outside the macromodelling framework as currently defined. This is not to say that in the future, macroeconomic models may not be expanded to address these questions. Similarly, the role of macroeconomic policy instruments in stimulating economic growth or alleviating unemployment can only be analysed for their short to medium-term effects since, in the long run, both will return to their natural levels. Again, it is expected that models with an endogenous growth process may eventually allow these questions to be addressed more comprehensively. Unfortunately, this does mean that many of the most important macropolicy questions regarding optimal public sector debt, the appropriate level of taxes, the determination of the natural rate of unemployment and long-run growth can not be comprehensively addressed using standard macromodels. There is still a need for a greater understanding of microeconomic processes underlying these macro variables and how they should be incorporated within a larger analytical framework.

To conclude, it is worthwhile re-emphasising the argument that policymakers will always need to employ some form of macroeconomic model to aid their own process of policy design. Some 'practical' men would have us believe otherwise, but they are mistaken.

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