COMPARATIVE PROPERTIES OF MODELS OF THE UK ECONOMY.

Church, Keith B. ; Sault, Joanne E. ; Sgherri, Silvia 等

Kenneth F. Wallis [*]

This article analyses the properties of five leading macroeconometric models of the UK economy, as revealed in four simulation experiments. These are carried out in a common operating environment that reflects the broad objectives of current policy -- sound public finances and low inflation -- by using feedback rules for income tax and interest rates. Developments in the structure of the models as revealed by the series of such exercises carried out during the lifetime of the ESRC Macroeconomic Modelling Bureau (1983-99) are described. The development of the research methods through which models' properties were elucidated and analysed is also reviewed.

Introduction

Comparative analysis of macroeconometric models took a significant step forward in 1983 with the establishment of the ESRC Macroeconomic Modelling Bureau. This was an important initiative by the Macroeconomic Modelling Consortium, itself newly established to coordinate support for a programme of research in macroeconomic modelling provided by the Research Council, HM Treasury and the Bank of England, and to manage this on a four-year cycle. Both developments resulted from the acceptance in June 1981 by the then Social Science Research Council of the recommendations of a subcommittee on macroeconomic research chaired by Michael Posner (SSRC, 1981). In the course of its deliberations the subcommittee had considered the case for setting up a new centre, to undertake comparative research on existing models of the UK economy and to help achieve greater openness and understanding of the models and their associated forecasts and policy analysis. It was supported in this by the House of Commons Select Committee on th e Treasury and Civil Service which, in the course of its enquiry into monetary policy, was "not satisfied that present arrangements produce the most useful model-based evidence for the Committee, for Parliament, or for the public" (Treasury and Civil Service Committee, Session 1980-81, Ch.1O). The Bureau was funded by the Consortium in each of its four four-year phases, until the research programme was discontinued in 1999, and the Bureau closed on 30 September 1999.

Regular comparative studies of overall model properties gave a first look at dynamic multipliers and policy ready-reckoners, and the reasons for differences between them across different models. These studies initially appeared as chapters in annual review volumes (Wallis et al., 1984-87) and subsequently as articles in this Review, at first annually and then biennially; the last exercise in this sequence appears in the fourth section of the present article. These accounts of overall model properties, based on standard simulation experiments, met the initial demand for information about the models and the reasons for differences between them, and also focussed Bureau research on specific features of the models that might be responsible for these differences. How these research methods developed is briefly reviewed in the following section.

Macroeconomic models evolve, in response to developments in economic theory and econometric methods, new statistical evidence, changes in legislative and institutional arrangements and changes in the economic policy questions asked of the models. A look back over the Bureau's regular comparative studies gives a clear view of this development process, and three major elements are described in the third section. The models are now better grounded in economic theory, have firmer econometric foundations, and are better suited to the analysis of the current monetary and fiscal policy environment than was the case sixteen years ago.

The general properties of the current versions of five models of the UK economy are analysed in the fourth section. One is the model of HM Treasury, while four received support from the Consortium. Two of these modelling groups, namely those at the London Business School (LBS) and the National Institute of Economic and Social Research (NIESR) were, like the Bureau, supported in all four phases of the Consortium's research programme, while the 'COMPACT' model group led by Simon Wren-Lewis of the University of Exeter and the Cambridge University Small UK Model (CUSUM), directed by Sean Holly, appeared in the later phases of the programme. Our analysis is based on the versions of these models deposited at the Bureau in late 1998-early 1999; for HM Treasury this is the annual release of the public model. The final section concludes.

Research methods

Empirical economics is commonly criticised for not paying enough attention to discriminating between competing explanations of the same phenomena. Macroeconomic modelling is the area where most comparative work has been done, however, perhaps as a result of the high public profile of the models and the forecasts and policy analyses based on them. The model comparison literature extends back to the 1950s, and covers all dimensions of the models and their uses, from the specification of single equations to full-system responses, and from forecasting and counterfactual analysis to policy optimisation. Most of this literature is in the form of conference proceedings, with papers on their models or the results of a specified model application contributed by model proprietors, and commentary and related work contributed by other researchers. In the United Kingdom, for example, a sequence of such conferences was initiated by the Economics Committee of the Social Science Research Council soon after it began work in 1 966, given that in economic modelling it had decided to support a number of separate projects rather than put all its eggs into one basket.

Comparison conferences seldom reach clear conclusions, however. Differences among models are commonly observed, but there are few serious attempts to explain them. It is often noted that part of the observed differences may be due to differences in the way that different modellers carried out the assigned exercise on their own model, but the extent of this cannot be assessed in this framework. The opportunities for comparative analysis by third parties are limited by their lack of access to the models, and there is little testing of competing views and little attempt to learn from one exercise to the next.

The establishment of the Bureau was an attempt to remedy these deficiencies. As an independent third party with whom complete models and associated databases were deposited, the Bureau was able to undertake direct comparisons across models of the UK economy at all stages of a comparative exercise -- design, execution, analysis and testing. This was not without controversy. The US Model Comparison Seminar, for example, had explicitly decided to leave matters in the hands of the model proprietors (Fromm and Klein, 1976), although Christ, in his classic commentary, was then unable to determine "which of them are wrong...and which (if any) are right" (Christ, 1975, p.54). Similar views had been expressed by UK modellers. In an important precursor to the Bureau's comparative studies, also published in this Review, Laury et al. (1978) looked forward to regular comparative studies "by those most familiar with the operational complexities of the various models".

The Bureau's first objective was to standardise comparisons of overall model properties, and so eliminate differences in the results that might have resulted from different model proprietors making different side assumptions or setting up the fiscal and monetary policy environment for the simulation experiment in different ways. The sources of important differences that emerge in these standard simulation exercises are then tracked down in the model structures, often using diagnostic simulations in which the importance of a particular transmission mechanism is assessed by means of a variant simulation in which it is closed off. Such partial simulations -- or "response dissections", introduced by Helliwell and Higgins (1976) -- are difficult to specify ex ante and difficult to standardise across models, hence scarcely feature in the comparison conference set-up. But their main purpose is not directly comparative: they play an essential part in detective work, and through their use differences in model properti es often reduce to rather precise questions about particular model equations or even a particular coefficient within an equation. Econometric evaluation can then proceed, in an encompassing spirit (Hendry, 1988). Although there are several UK models, there is only one UK economy, to which the different models are simply different approximations, and their adequacy for particular purposes can be assessed statistically.

Sometimes comparative testing may lead to a preferred and/or improved specification. The sensitivity of overall model properties can then be checked by replacing the various original specifications by the preferred specification and observing the impact of this change on the comparative simulation results. Sometimes the available data cannot discriminate between competing specifications, but at least the model user is then clear about where the uncertainty lies, and can base a choice on whatever other grounds may be appropriate to the particular application. This combination of simulation analysis of overall model properties and econometric analysis of individual model equations or groups of equations in the context of cross-model comparisons proved to be a productive methodological development, with applications covering several sectors of the models. Although systematic econometric evaluations of particular equations in the models had begun to appear before the Bureau came into being (see Brooks, 1981, for example), and indeed were continued by the Bureau, their relation to the full-system behaviour of the models had not hitherto been developed.

Model evolution

In this section some important developments in the models are described under three main headings -- their theoretical structure, the treatment of expectations, and the modelling of policy variables. Pervading all three topics and hence also an area of development is the notion of the long-run or steady-state properties of a model. Important parallel developments in time-series econometrics of considerable influence in macroeconomic model-building concern the treatment of integrated and cointegrated series and the connection with the popular error correction model. This provides a convenient distinction between the long-run implications of a dynamic equation and its short-run adjustment process, and hence facilitates the analysis of the long-run properties of a model. As with any econometric technique, however, it may not automatically provide a complete answer, for example when variables that feature in the economist's long-run relationship do not appear in the statistician's cointegrating vector, for one re ason or another.

The theoretical paradigm

Of the six models that appeared in the Bureau's first review (Wallis et al., 1984), four -- the LBS, NIESR, HMT and Cambridge Growth Project models -- could be described as 'mainstream', a classification also used by Britton (1983) in introducing his edited volume on the NIESR model. We focus on developments in the mainstream, noting the influence of the other two models -- the City University Business School (CUBS) and Liverpool models -- in passing.

The mainstream models were developed around the income-expenditure framework for the determination of effective demand in real terms, thus the level of output was determined through the components of the national income identity: consumers' expenditure, fixed investment, stockbuilding, government current expenditure, and exports minus imports. With government expenditure predetermined, other components were largely demand-driven: consumers' expenditure as a function of real income, with an allowance for changes in credit conditions; fixed investment as an accelerator relationship; stockbuilding with reference to a target stock--output ratio; and exports and imports as functions of aggregate demand, foreign or domestic, and relative prices or costs. The implicit assumption was that the aggregate supply schedule was fairly elastic up to the 'full employment' level of unemployment, but this was not explicitly modelled. The labour market structure was likewise incomplete, with no modelling of supply and employmen t equations often based on inverted production functions. Like the investment functions, these labour demand equations contained no factor price effects.

This picture soon began to change, in response to internal and external criticism, and modellers sought to achieve greater theoretical consistency: in respect of a better articulated macroeconomic framework incorporating both demand and supply; in respect of internal consistency, for example in the joint determination of output, prices, and the demand for factors of production; and paying attention to stock-flow equilibria. Implicit criticism in some respects came from within the modelling community, being provided by the contrasting positions adopted by the CUBS and Liverpool models. The CUBS model represented an attempt to implement the textbook economics of demand-and-supply within a small macroeconomic system. It abandoned the income-expenditure framework and explicitly determined the supply of output via a production function. This identified four factors of production -- capital, labour, energy and raw materials -- and factor demands were based on an assumption of profit maximisation within a perfectly competitive framework.

The Liverpool model was a practical attempt to use New Classical ideas in building an empirical structural model. In the theoretical models of the New Classical school deviations of output from trend are the result of random disturbances of the price level from its expected value in the structural form, or a consequence of unanticipated changes in monetary and other policies in the reduced form. In these models the aggregate supply schedule is constrained to be vertical in both the short and the long run, so that anticipated demand shocks do not change the levels of output and unemployment, but increase the price level (or inflation). This happens quickly, thanks to the assumption of rational expectations. The characteristic market clearing assumptions imply very rapid relative price adjustment, so that only demand and supply functions are required, with no need for a price adjustment equation. However the Liverpool model departed from its theoretical counterparts by allowing for real rigidities in adjustment , notably in the labour market, where the convergence to market clearing was very slow. Nevertheless, the eventual equilibrium or 'natural rate' values of employment, output and real wages were now endogenous. Further classical features were given by an emphasis on stocks rather than flows, for example, the use of wealth rather than income in modelling expenditure decisions.

Both the CUBS and Liverpool models had some influence in leading other modellers to take the supply-side view seriously, but their econometric credentials were often questioned and the major influence was the supply-side model of Layard and Nickell (1986). This treats goods and labour markets as imperfectly competitive, and was quickly adopted by mainstream modellers. Prices are set by imperfectly competitive firms, given the demand they face, and their demand for labour depends on both the real product wage and the level of real aggregate demand. Wages are determined in a bargaining process and if firms have the 'right to manage' they set employment, given the wage, although wage behaviour is relatively insensitive to the particular specification of the bargaining model. Key questions about the long-run properties of a large-scale model, such as whether the aggregate supply schedule is vertical and what causes it to shift, can then be addressed by analysing a core supply-side framework consisting of the stea dy-state versions of the wage and price equations together with, in an open-economy context, the response of the exchange rate, as shown by Joyce and Wren-Lewis (1991) for the NIESR model and Turner (1991) for the Treasury model. With various elaborations of detail this remained the leading approach through the rest of the decade.

The prevailing paradigm is thus one in which a broadly neoclassical view of macroeconomic equilibrium coexists with a new Keynesian view of short-to-medium-term adjustment. In respect of the long-run equilibrium, the level of real activity is found to be independent of the price level and the steady-state inflation rate, whereas in the short run there is considerable real and nominal inertia. Adjustment costs and contractual arrangements imply that markets do not clear instantaneously and there is a relatively slow process of dynamic adjustment to equilibrium. This is by no means a full-employment equilibrium, however, and the questions of whether a model possesses a non-accelerating- inflation rate of unemployment (NAIRU) and, if so, what are its determinants, can be analysed as described in the preceding paragraph. It is often found that the NAIRU is independent of the steady-state inflation rate and so is the 'natural' rate of unemployment, as a result of the dynamic homogeneity or inflation neutrality of the price and wage equations. The NAIRU may, however, depend on the rate of productivity growth.

Expectations

Expectations or anticipations of future values of endogenous variables, such as exchange rates and inflation, are often important determinants of current behaviour, and their influence has been incorporated into macro-econometric models in various ways. One possibility is to use direct observations on anticipations and expectations, obtained by surveys, for example, but reliable quantitative data on expectations are relatively rare. In any event, in forecasting and policy analysis exercises these expectations have themselves to be projected, hence modellers have turned to the use of auxiliary hypotheses about the formation of expectations.

A traditional way of dealing with unobserved expectations variables is to assume that they are functions of the current and lagged values of a few observed variables, the simplest example being the adaptive expectations hypothesis. The unobserved expectations variables are then substituted out, giving a conventional backward-looking dynamic or distributed lag model. This confounds the description of the expectations-formation process with the description of economic behaviour given expectations. It results in equations that are unlikely to remain invariant across policy regimes and hence likely to give wrong estimates of the macroeconomic consequences of a change in policy regime -- this is the 'Lucas critique' of econometric policy evaluation. One response was to question the relevance of the critique by noting that model-based policy analysis often consisted of estimating the consequences of changes in the settings of policy instruments, rather than complete changes of regime. A more direct response was to keep the description of the formation of expectations separate from the model of economic behaviour given expectations, although the first way in which this was done, by assuming that expectations are formed 'rationally', still gives the model an important role.

The rational expectations hypothesis is that expectations coincide with the conditional expectations of the variable given 'all available information', which includes knowledge of the underlying economic system. Its foundation in optimising behaviour led to its incorporation into equilibrium business cycle models and its advocacy as part of New Classical macroeconomics, and hence its adoption by the Liverpool model since its first appearance in 1980. The distinction between the theoretical stance of the model in which expectations variables appear and the theory of expectations which is adopted was nevertheless appreciated, and the rational expectations hypothesis had been incorporated into more mainstream models by the mid-1980s.

The practical solution of a model for the endogenous variable values over a forecast period now requires an internally consistent forward-looking solution sequence to be calculated, in which each period's future expectations variables coincide with the model's forecasts for the future period. With this implementation the approach is more accurately and perhaps less controversially termed 'model-consistent' expectations. In parallel to the requirement for an initial condition when solving a conventional difference equation, there is also a need for terminal or transversality conditions that specify forecast values and expectations at the forecast horizon. If the steady-state properties of the model are known, as in the Liverpool model, then the terminal conditions may explicitly incorporate this knowledge. This may require a relatively long solution period, however, to ensure that the model has reached an approximate equilibrium. In the absence of such knowledge, or in a shorter solution period, terminal condi tions are typically specified to approximate a stable convergence to equilibrium by requiring constant growth rates of relevant variables.

The full information assumption may be inappropriate or unacceptable in some circumstances, and various hybrid ways of treating expectations have resulted. Empirical analysis of observed expectations or forecasts does not always find them to be unbiased and efficient, as predicted by the rational expectations hypothesis, while 'all available information' is clearly an extreme characterisation, and modifications such as 'bounded rationality' or 'economically rational expectations' have appeared. A model proprietor is typically uncertain about the model, not only due to sampling error in its coefficient estimates but also due to available choices of competing specifications. Moreover in some policy discussions the question of the credibility of policy is a central concern. Thus various kinds of learning mechanisms have been developed, sometimes with respect to the model itself and sometimes with respect to its external environment. In these exercises the rational expectations assumption often continues to serve as a baseline, not only in the sense that many of the learning schemes are designed to converge on the full information scenario, but also as a comparator for the alternative solution trajectory, allowing the gains from the full credibility of policy to be evaluated, for example.

Fiscal and monetary policy

Traditional policy analysis with macroeconometric models consists of 'what-if' exercises. These address the question of what would be the macroeconomic consequences if policy settings, treated as exogenous, were altered. In rational expectations models an accompanying assumption about agents' anticipations of policy actions is needed, and whether such actions are regarded as temporary or permanent. A tendency in recent years has been a move away from an exogeneity assumption towards an endogenisation of policy or 'closing' of the model, with simple policy rules. To some extent the challenge of VAR modellers, who from the beginning abandoned the endogenous/exogenous distinction, provoked this response, but important stimuli were the changes in practical policy-making in both fiscal and monetary policy, which we discuss in turn.

The government expenditure simulation has over the years been the simulation exercise which most modellers run first, to begin to study the properties of their models. The classic article by Christ (1968) drew attention to the importance of the government budget constraint and the implication that the government expenditure multiplier cannot be defined without an assumption about how the expenditure is to be financed. The two polar side conditions that subsequently appeared were unchanged interest rates and unchanged monetary aggregates, the first representing an assumption of full accommodation of increases in money demand, with the rest of the deficit financed by issuing bonds, the second assuming pure bond finance. In the absence of complete stock-flow accounting, however, the debt stock position was often not monitored, and it was possible to remain blithely unaware of the debt explosion that a simulation experiment might be causing. It is unrealistic to assume that investors remain willing to purchase go vernment bonds indefinitely in such circumstances, and more realistic to assume some feedback from the state of the public finances onto fiscal policy. The actual reality of the debt explosion in many countries in the 1980s also placed the intertemporal government budget constraint, that the government remain solvent or policy remain sustainable, onto the policy modelling agenda.

Different ways of incorporating the constraint appear in several of the multi-country models featuring in the model comparison projects sponsored by the Brookings Institution (Bryant et al., 1988, 1993). These are the models that also adopt a forward-looking treatment of expectations, where a consistent treatment of the long run is essential. One approach, adopted in models with a highly aggregate treatment of the public sector accounts, is to incorporate financing assumptions that maintain policy sustainability directly into the representation of the accounts; this had also been done in the Liverpool model of the domestic economy. An alternative approach, initiated by Paul Masson and colleagues at the IMF, is to replace an exogeneity assumption for a fiscal instrument with a closure rule describing its adjustment in response to financial disequilibria. This has been the preferred approach in models of the UK economy, motivated by the same combination of modelling developments and policy objectives, and fisca l closure rules first appeared in Bureau comparative studies in 1995.

The intertemporal government budget constraint is typically represented as a stability condition for the debt/GDP ratio and/or deficit/GDP ratio. The ratio form reflects both the definition of a steady state in terms of constant growth rates for aggregate real and nominal variables of the model (with constant inflation), and the practical expression of the Masstricht Treaty's fiscal requirements. The period-by-period government budget constraint is silent on the question of which of the government's income and expenditure variables should be adjusted in the face of a disequilibrium - it is an identity, not a behavioural equation. In practice, model-based analyses take tax revenues or the average tax rate to be the relevant policy instrument. Equally, the solvency requirement does not specify the time path of any necessary adjustment, but simply that an adjustment must occur, sooner or later. Again, in practice, adjustment is assumed to take place continuously, by specifying a policy rule or reaction function that describes how the instrument is altered period-by-period in response to deviations of the target variable from its desired value. Nevertheless different formulations appear in different models - tax levels or first differences, debt or deficit targets - resulting in the suspicion that these differences contribute to observed differences in simulation results. Recent Bureau research (Mitchell et al., 2000) has established equivalences between these rules, in respect of both their long-run equilibria and their disequilibrium dynamics, which will assist both the design of the rules and the interpretation of results.

Monetary policy modelling has followed the changing fashions in monetary policy-making, in turn targeting the money supply, the exchange rate and finally, and directly, inflation, through the setting of official interest rates. The explicit focus on the control of inflation in several OECD countries was accompanied over the last decade by an explosion of research on the design and evaluation of monetary policy rules. While much of this research used theoretical models or simple stylised empirical models as the research vehicle, the rules have also been incorporated into large-scale models to improve their representation of practical policy-making, and they also appeared in Bureau comparative studies for the first time in 1995.

The rules considered, like the fiscal policy rules above, include both change and level formulations. The former sets the change in the short-term nominal interest rate as a function of deviations of inflation from target and, possibly, output from potential output. The latter sets the level of the interest rate as a function of similar arguments; this includes the form known as the 'Taylor' rule, found to provide a reasonable approximation to actual US policy-making. A further development associated with the name of Svensson (1997) is the inclusion of terms in the deviation of forecast future inflation from target, such forward-looking rules probably being closer to central bank practice. A first question concerns the circumstances in which the target is achieved, for example, whether an exogenous change in the target value produces the same change in actual inflation, with a long-run change in the nominal interest rate also of the same amount, leaving the real rate of interest unaltered, as in a standard Do rnbusch model. After that there is an important shift in the main focus of attention between the respective fiscal and monetary policy studies, from first moments to second moments, statistically speaking. Neither the small stylised models used in this research nor typical large-scale models, as discussed above, admit a long-run trade-off between the levels of output and inflation, and policies are evaluated in terms of the variances of outcomes.

Long run and steady state

The notion of the long-run or steady-state properties of a model provides motivation for and connections between the three topics discussed in this section, as noted at the outset. The supply side of a model determines its long-run properties, hence developments in one imply developments in the other. Consistency with economic theory is often sought in relation to a comparative static economy theory, in terms of the long-run or equilibrium properties of a dynamic model, neglecting its short-run adjustment properties. Attention to stock and flow equilibria and a complete specification of the public sector accounts raises the issue of the long-run sustainability of policy and the use of fiscal closure rules.

In the present context of models used in short-to-medium-term forecasting and policy analysis, 'long-run implications' means the steady-state properties of a system of dynamic equations and so represents only a subset of what economists more generally might wish to consider as long-run issues. The nature of the long-run equilibrium is a steady-state growth path, with the real growth rate equated to the 'natural' rate of growth of the standard neoclassical growth model, given as the rate of (labour-augmenting) technical progress plus the growth rate of the population. The models follow the neoclassical growth model in treating both of these as exogenous, and do not address a range of issues arising in a second generation of growth models, known as endogenous growth models, such as the role of education, knowledge and human capital. Nominal equilibrium is 'anchored' by specifying a target, again exogenously, for a nominal variable such as inflation, and a feedback rule for nominal interest rates seeks to achiev e the target value.

In a model with consistent forward-looking expectations, the long-run effects of exogenous shocks may influence short-run behaviour, hence it is again important that these be properly modelled, even in a context of short-to-medium-term analysis. The use of backward-looking treatments of expectations may have contributed to the previous neglect of asset stock equilibria, a debt explosion in the remote future having no effect on projections two-to-five years ahead in this case.

Standard simulations

Four simulation experiments on the five models are analysed and interpreted in this section. The first is a monetary policy simulation, namely a change in the inflation target. Two fiscal policy experiments follow, an increase in government expenditure and a reduction in the basic rate of income tax. The final experiment, an increase in the level of technical progress, is a supply-side shock. This is a newcomer to the set of 'standard' simulations although it was used for comparisons across three of these models in the course of a substantive investigation of the role of technical progress in a previous article (Church et al., 1998).

The macroeconomic responses to these shocks are estimated by comparing the results of two solutions of a model, one a base run and the other a perturbed run in which the indicated variable, treated as exogenous, is perturbed from its base-run values. The responses may include changes in inflation and the state of the public finances, and the policy environment is one in which the interest rate and the basic rate of income tax are used to target the inflation rate and to ensure fiscal solvency. As noted above, this representation of the current policy regime first appeared in our studies of model properties in 1995, and a fuller discussion can be found in the two preceding comparative properties articles (Church et al., 1995, 1997). To focus on model properties we suspend the fiscal closure rule for the period of the fiscal policy shocks -- five years in each case -- and reintroduce it once the perturbation is removed, to ensure long-run sustainability. The monetary policy and technical progress shocks are per manent, not temporary.

General results on the main macroeconomic indicators for our four experiments are presented in Tables A1-A4. For three of the models (LBS, NIESR, CUSUM) the base run corresponds to a published forecast, although it is typically extended well beyond the published forecast horizon. The base run supplied by the COMPACT model proprietors is constructed for simulation purposes and does not represent a published forecast. Results for the inflation targeting, government expenditure and income tax simulations on the HMT model relative to its own base, which is not published, are kindly provided by the Treasury. While numerical results are shown over the first ten years of the simulation, in all models except HMT the base is longer than this, and our discussion sometimes refers to the 'long-run' outcome that obtains at the end of the simulation period.

Reduction in the inflation target

In this simulation the inflation target is set at half a percentage point below the base-line values of inflation throughout the simulation period. In the NIESR model, this led to non-convergence of the model solution software. In this case we conduct a half a percentage point increase in the target and reverse the sign of all the responses so that comparisons can be made with the other models.

Taking the HMT, NIESR and COMPACT models first, the results in Table A1 show that the inflation rate is initially reduced in all three cases, and then settles down around the new target in the NIESR and COMPACT models. The HMT model has clearly not reached equilibrium by the end of the simulation, and this difference mainly reflects the expectations regimes under which the models operate. The new inflation target is reached quickly in the NIESR model, with inflation 0.5 percentage points below baseline during the third year of the simulation. Adjustment is protracted in the COMPACT model, with inflation only reaching the new target towards the end of the seventy-year simulation horizon.

In each model the short-term interest rate is the policy instrument that delivers the desired inflation target. This falls below baseline values in the first year in the NIESR and COMPACT models, remaining there for the entire simulation horizon. The long-run position for the nominal rate, 0.5 percentage points below baseline, is achieved most quickly in the NIESR model, corresponding to the speed with which the long-run inflation position is reached in this model. The real interest rate in the long run is unchanged in both COMPACT and NIESR models, supporting the theoretical proposition that changing the steady-state inflation rate leaves real variables unchanged in the long run. By contrast, the short-term interest rate in the HMT model is above baseline for two-thirds of the simulation period.

This need for different interest rate paths in order to generate the same outcome for inflation can be explained by the different roles of the exchange rate. Generating a permanent drop in the inflation rate requires continuous appreciation of the nominal exchange rate. This then feeds, via import prices, to domestic prices. In each model, the differential between domestic and foreign interest rates is an important determinant of the exchange rate response, via some form of uncovered interest parity or open arbitrage condition. Generally, an increase in domestic rates with foreign rates unchanged gives the appreciation that drives prices down. The other important influence on the current level of the exchange rate is the expected exchange rate one period ahead. In both models where real interest rates are unchanged in the long run, the expected future exchange rate is treated in an explicit forward-looking manner, with the future expectation set equal to the actual solution value for that period. The exchange rate jumps at the start of the simulation in response to anticipated future events, in this case the lower future rate of inflation. Here, it is the expectations term that is driving the exchange rate appreciation. Interest rates, which play no role in the rise in the exchange rate, are then free to fall to their new long-run level, in a manner determined by the monetary policy rule, although there is overshooting in the short-to-medium term because of some sluggish behaviour in wages and prices.

The direction of the initial jump in the nominal exchange rate differs between the NIESR and COMPACT models, because the key exchange rate relationship in the COMPACT model is expressed in real terms, whereas the variable that jumps in the NIESR model is the nominal exchange rate. In COMPACT the real exchange rate immediately depreciates by 2 per cent in the first year. The long-run outcome is tied down by the equilibrium of the model and in this case the real exchange rate must be back at base by the final period. The nominal exchange rate moves in line with the real rate. In order to achieve the required appreciation, the real exchange rate must therefore increase over time, and the only way it can do this and return to base at the end of the simulation is to jump down in the first period before gradually climbing back. This real exchange rate trajectory drags the nominal rate some 1.7 per cent below base in the first quarter, with the subsequent appreciation taking the rate above baseline values during the fourth year.

In the exchange rate equation in the HMT model expectations are backward looking, and the model relies on the interest rate to deliver the required appreciation in the nominal exchange rate. Interest rates immediately rise when the cut in the target is introduced, reaching 0.55 percentage points above base by the second year. This ensures that the inflation rate hits its new target during the sixth year of the simulation, but the subsequent overshooting of the target brings interest rates down sharply, dipping below baseline values in years 7-9. In the tenth and final year of the simulation, inflation is slightly below target and interest rates 0.14 percentage points above and rising.

Inflation in the CUSUM and LBS models fails to settle down at the new target. One feature of all the LBS results presented here is the presence of large cycles in both nominal and real variables. Given that the only major change to the model since our last comparative exercise is the inclusion of a newly estimated supply-side block, it is likely that this is at least partly responsible. Examination of the dynamic characteristics of the equation for total costs reveals that it generates an eight-year cycle in response to a shock. But this does not explain the large amplitude of these cycles, and so other elements within the new supply side, possibly interacting with the interest rate reaction function, must also be important. In common with the HMT model, expectations within the exchange rate equation are backward looking and it is the interest rate that delivers the required exchange rate appreciation. The inflation rate never settles at its desired long-run position, instead it cycles around it for the full 27 years of the simulation. The cycle does dampen over time, and it may be the case that at some point in the future the steady-state outcome is achieved.

In CUSUM, inflation falls almost one percentage point by the second year, following the large appreciation of the exchange rate in the first year. However, despite modelling the nominal exchange rate in a similar way to the NIESR and COMPACT models, the interest rate response is very different, remaining above baseline throughout the whole simulation horizon. The new inflation target is not achieved, and it is this differential between actual and target rates that ensures that the interest rate stays above base. As in our previous comparative exercise, the wage and price equations in the CUSUM model lack dynamic homogeneity, such that exchange rate movements are not passed on fully to prices.

In the three models that deliver an increase in interest rates, there is a loss of output in the short term, whereas in the NIESR and COMPACT models lower interest rates help stimulate higher output. However, even though their short-to-medium-term GDP responses are similar, closer examination of consumption, investment and the trade balance reveals different compositional effects. In Table Al, these components are expressed in terms of their actual deviation as a proportion of baseline GDP, so that when summed these effects should be approximately equal to the GDP response as shown. Consumption is permanently higher in the NIESR model, some 0.6 per cent of baseline GDP higher after 31 years. In the COMPACT model, consumers' expenditure, which is forward looking, immediately jumps down around half a per cent of baseline GDP in the first year, before rising slowly thereafter, settling around 0.2 per cent higher after the full 71 years of the simulation. The investment response also differs, increasing by 0.1 per cent of baseline GDP in the NIESR model and remaining above baseline, at 0.2 per cent of baseline GDP in the final year, whereas in the COMPACT model investment hardly moves in the short-to-medium term, but is slightly below base during the second half of the simulation period. In the COMPACT model these responses are dictated by the real post-tax interest rate, which increases as inflation and nominal interest rates are both lower, in turn reducing both consumption and investment; in this model it is net trade that lies behind the increase in output. The fall in the real exchange rate described above improves the trade balance in the short run, more than countering the consumption and investment responses. Meanwhile, the real exchange rate appreciation in the early years of the NIESR simulation worsens its trade balance.

Increase in government expenditure

The second simulation experiment is a five-year increase in government spending of [pounds]2 billion (1995 prices) per annum, which is approximately equal to a quarter of one per cent of baseline GDP. The fiscal closure rules in the models are suppressed for the duration of the expenditure increase, so that a 'live now, pay later' approach is adopted. The rules are activated at the start of the sixth year.

One consequence of adopting the prevailing theoretical paradigm described above is the inability of the government to alter the equilibrium level of output, this instead being determined by the growth rates of technical progress and the working population. The absence of non-neutralities in wages and prices explains why policy-makers cannot shift the equilibrium level of activity by changing the inflation rate, but in the short-to-medium term, the dynamics of wage and price reactions are sluggish, giving the opportunity of a role for a counter-cyclical government spending policy.

The results in Table A2 show that the impact government expenditure multiplier is around unity in the NIESR model, with GDP 0.25 per cent higher in the first year. This compares with a multiplier of around half this size in the COMPACT model, where the initial response of GDP is an increase of 0.13 per cent. Crowding out in both models reduces the benefits of this early expansion over the next four years, although the speed at which this happens differs. During the sixth year, GDP falls below base in both models, but the reduction in the COMPACT model is far less dramatic. This sudden unwinding of the GDP rise is a combination of two factors. First, government spending returns to baseline values. Second, the fiscal closure rules are introduced, tax rates increase, and a fiscal contraction ensues. GDP does eventually recover and is virtually back at baseline values after ten years in both models.

The difference in the impact GDP multiplier is explained by the differing response of consumers' expenditure. Consumption rises by a maximum 0.1 per cent of baseline GDP by the second year in the NIESR model whereas the COMPACT results show a peak fall of over 0.2 per cent at the same time, almost completely countering the increase in government spending. However, the recovery in GDP during years 4 and 5 is a result of consumers' expenditure returning back towards baseline values. This response can be traced to both increasing interest rates and the modelling of consumer behaviour in the COMPACT model. The majority of consumers in COMPACT are forward looking. They foresee the higher taxes of the future and save at first, smoothing their consumption: they do not always increase consumption in line with increases in disposable income. Consumers in the NIESR model are less forward looking and spend more of the gains, despite a similar rise in interest rates.

This increase in nominal interest rates in both models is required to control the inflation that results from the increased demand in the economy. With real interest rates rising, there is initially an appreciation in the real exchange rate, which worsens the trade balance, with this effect strongest in the NIESR model. This exerts downward pressure on GDP. As output is reduced inflation declines, and nominal and real rates return to baseline.

There are short-term increases in output in the LBS, HMT and CUSUM models, which in all cases diminish over time. The cycles present in the inflation targeting simulation in the LBS model also appear here, although once again it is possible that these are damped around a sensible equilibrium. In the HMT model the government expenditure multiplier is around a half. The increase in GDP that does occur is entirely attributable to the impact of the higher government expenditure, as the other main components of GDP drag the response down. Although investment is slightly higher in the first year in reaction to higher output, it starts to fall below base in the second year in response to higher interest rates. This increase in rates, which is required to keep inflation down, also hits consumers' expenditure and the trade balance, the latter effect coming through the appreciation in the real exchange rate. The nature of the long-run position in the HMT model is unclear. The inflation rate is below base in the tenth y ear, along with interest rates. Consequently output, consumers' expenditure and investment are all rising in the final year. In the CUSUM model, both nominal and real interest rates are permanently above base, mirrored by investment and consumption responses that are permanently lower. GDP has almost returned to baseline values in this model by the sixteenth and final year of the simulation, as net trade almost exactly offsets the negative influences of the other major GDP components.

During the first five years of the simulation, tax rates are fixed. The public finances worsen in each model during this period, with the greatest deterioration in the COMPACT model. The tax rate then increases by some 0.6 percentage points during year 6 in this model, and the rise in the debt ratio is immediately reversed, but still takes 30 years to get close to baseline values. The NIESR results give some indication of how the choice of a less activist rule can influence simulation results. The debt ratio continues to climb after the rule starts operating, reaching 1.5 percentage points above base in the tenth year, remaining 0.5 percentage points above base in year 31. The income tax rate barely changes throughout the simulation period; the maximum increase is only slightly over 0.1 percentage points. The fiscal solvency rule in the HMT model targets the PSNCR to GDP ratio to baseline values in each period. Initially, the basic rate of income tax increases sharply, reinforcing the fall in consumers' expen diture described above. Here, unlike in the NIESR model, the operation of the tax rule ensures that the deficit is maintained at baseline levels in every single period. In the CUSUM model, there is a substantial increase in the tax rate, some 2.0 percentage points in the long run. But the debt ratio is still 0.6 percentage points above baseline at the end of the simulation with no sign of diminishing.

Reduction in the basic rate of income tax

The results of a two-point reduction in the basic rate of income tax, sustained for five years, are shown in Table A3. As with the government spending simulation, the fiscal closure rules are suppressed for the duration of the shock and then allowed to operate from the beginning of the sixth year. Two main channels can be identified through which the tax cut may affect the economy. The first is uncontroversial: higher real personal disposable income will in turn increase consumers' expenditure. The second is by changing the behaviour of workers through its impact on wage bargaining, and here there is disagreement across models.

This simulation illustrates clearly the extent of consumption smoothing and the near Ricardian behaviour in the COMPACT model. Consumption rises very little in the short term with a peak of 0.17 per cent of baseline GDP above base in year 5, much less than the increase in real disposable income. It is the fact that some consumers are liquidity-constrained and do increase spending after the tax cut that ensures that Ricardian equivalence is not complete. By contrast, consumption in the NIESR model rises much more, reaching 1.4 per cent of baseline GDP above base in the fourth year.

After five years of lower tax rates the basic rate reverts to the control of the public finances and the reversal of any deterioration that has occurred as a result of the tax cut. The tax rate in the COMPACT model has to rise sharply, as in the previous experiment, here increasing by 1.6 percentage points by year 6, before returning smoothly back towards baseline. This need for a large increase reflects the failure of the tax cut to boost employment and increase government receipts. Consumers also anticipate future higher tax rates during the first five years, saving more in the short term to compensate for the future loss of disposable income. In the NIESR model, taxes are higher once the solvency rule is implemented, although again the magnitude of change is much smaller, as is the impact on the debt to GDP ratio. Higher taxes help to drive consumption 0.8 per cent of baseline GDP below base during the medium term.

The second channel through which the lower tax rate may have an impact is through changes in wage bargaining. A lower tax rate reduces the wedge between employers' real wage costs and employees' real consumption wages, which may have an impact on the bargained wage outcome and hence on the NAIRU. The HMT model is the only one of these five to feature a tax wedge term in the long-run specification of the wage equation; this does not appear in the other models, which conform to the view that, in the long run, changes in the wedge are borne entirely by labour. Short-run wedge effects may nevertheless be important and rather persistent, and in the NIESR model the change in the wedge appears in the error correction form of the wage equation. Here the tax cut puts downwards pressure on real wages, causing the numbers unemployed to fall by 29,000 by year 3, reinforcing the demand-side impact of the tax cut described above.

In the HMT model the long-run wedge effect puts greater downward pressure on the real wage, and unemployment is reduced by 132,000 by year 6. However, at this point the temporary shock has ended and tax increases are implemented to ensure that the PSNCR/GDP ratio is returned to baseline values. The increase in the tax rate that follows has the opposite impact on the labour market from the initial tax cut. The reductions in unemployment are reversed, and with the tax rate 1.2 percentage points above base in year 10, the number of unemployed rises to some 98,000 above baseline values. The presence of these effects in the wage equation also has a short-lived effect on price inflation in both models.

Increase in the level of technical progress

The final simulation is a permanent 1 per cent increase in the level of technical progress. This shock is a supply-side shock and draws attention to the determinants of equilibrium output in the models. Technical progress increases the potential supply of output, and with sufficiently flexible factor and product markets this potential is realised, resulting in increased consumption, investment and real wages. It is important to note that this is a domestic shock, with technical progress in the rest of the world unchanged, hence exports might also be expected to contribute to the realisation of the potential increase in GDP. In the neoclassical growth model technical progress is assumed to be Harrod-neutral or labour-augmenting, the model's steady state then conforming to the stylised fact of a constant investment/output ratio, and the same assumption is adopted in the empirical models.

The results in Table A4 show that the NIESR and COMPACT models deliver increased output in the first ten years, and in both models GDP does eventually rise by 1 per cent, as predicted by theory. But this takes 20 years for the NIESR model and 24 years for the COMPACT model. Neither the LBS or CUSUM models deliver the expected results. Unemployment rises dramatically in the LBS model and shows little sign of a return to base, remaining 170,000 higher after 24 years. Although there is some technological unemployment created in the NIESR and COMPACT models, it is only in the short-to-medium term. The NIESR results show employment falling by 0.3 per cent by year 4 and then increasing slowly in line with output, finally moving above base in year 26. In the COMPACT model the maximum difference in employment from base, -0.4 per cent, does not occur until the tenth year, but employment returns to its baseline values by the start of year 22. Given the responses of output and employment described above, it follows that the 1 per cent increase in technical progress is fully reflected in the level of productivity, although adjustment in both models is protracted. In the COMPACT model this is due to the vintage or 'putty-clay' model of production in which, once a new vintage of capital equipment is installed, there are no factor substitution possibilities. Thus the improvement in technical progress is only gradually embodied into the capital stock through the acquisition of new mach ines. In the NIESR model, which assumes that factor proportions are continuously variable, the costs of adjustment of the capital stock that appear in the investment functions prevent quick adjustment.

In both NIESR and COMPACT models, investment, consumption and the trade balance are above baseline in equilibrium. The extra output produced has to be consumed somewhere and in both cases much of it flows abroad. In order to sell these goods overseas, the relative price faced by foreign buyers has to fall, which is achieved by a depreciation of the exchange rate. In the neoclassical growth model investment would be expected to rise by 1 per cent along with output. This occurs in neither model, however, as total investment includes components which are unaffected by the increase in technical progress. In the COMPACT model, investment in oil does not change, while investment in petroleum, natural gas and public sector dwellings is unaffected by technical progress in the NIESR model.

This model-based analysis of technical progress and its potential relation to analysis of the 'New Paradigm' is bedevilled by the same measurement problems that affect analysis of these issues at any level. The measurement of real investment in the face of falling prices of computer hardware and software and the measurement of real output in parts of the public sector and the services sector where output measurement is traditionally based on measures of labour input are the leading problem areas. To improve the analysis of the macroeconomic consequences of technical progress better data are required, more than better economic theory or econometrics.

Conclusion

Macroeconometric models provide an internally consistent quantitative account of the main macroeconomic responses to external shocks and policy innovations. This internal consistency has a number of dimensions, with respect to the national accounting system, for example, increasingly viewed from an intertemporal perspective, and with respect to prevailing macroeconomic theory. This article reviews the properties of the current versions of five models of the UK economy, in the light of their behaviour in simulation experiments and of their general development over the lifetime of the ESRC Macroeconomic Modelling Bureau, a unique model comparison project. Some models have been everpresent in the Bureau's portfolio, and there have also been new entries and exits. There have been remarkable developments in macroeconometric models over this period, both in their theoretical structures and in the econometric methods used to quantify those structures. This is clearly evident in what can be identified as the mainstre am throughout this period, and also with the appearance of new models such as the COMPACT model, which is explicitly designed to embody recent macroeconomic theory.

Similar developments have occurred in models of the UK economy outside the Bureau's portfolio, indeed in models of other national economies and in multicountry models constructed and maintained both in the UK and overseas. Research supported by the Macroeconomic Modelling Consortium has clearly influenced modelling principles and practice on a wider canvas. The Bank of England (1999), for example, explicitly places its macroeconometric model in this new mainstream, and recent versions of the models of the Federal Reserve Board, IMF, and OECD reflect the same developments. A fully specified macroeconometric model is essential for the quantitative assessment of policy options -- there is no alternative, as the Bureau continuously maintained -- and policy analysts have benefited from the considerable developments of the past sixteen years.

(*.) This article concludes the series of surveys published in the National Institute Economic Review by the ESRC Macroeconomic Modelling Bureau at the University of Warwick. Editorial responsibility is taken by the authors, not by the Editorial Board of the Review. Comments should be addressed to the last-named author at Department of Economics, University of Warwick, Coventry CV4 7AL (K.F.Wallis@warwick.ac.uk).

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 Inflation target simulation: reduction of
 0.5 percentage points
 Year LBS NIESR HMT COMPACT CUSUM
GDP [a] 1 -0.32 0.10 -0.10 -0.23 -0.01
 3 -0.81 0.10 -0.40 0.10 -0.49
 5 -0.73 0.11 -0.62 0.15 -0.57
 7 -0.50 0.13 -0.56 0.19 -0.50
 10 -0.90 0.19 0.21 0.24 -0.46
Consumers' expenditure [b] 1 -0.10 0.12 -0.19 -0.56 0.05
 3 -0.46 0.29 -0.48 -0.29 -0.13
 5 -0.13 0.35 -0.62 -0.21 -0.45
 7 0.03 0.38 -0.46 -0.14 -0.46
 10 -0.55 0.48 0.12 -0.03 -0.41
Investment [b] 1 -0.15 0.12 -0.24 0.00 0.00
 3 -0.25 0.15 -0.96 -0.01 -0.06
 5 -0.10 0.17 -1.35 -0.01 -0.16
 7 0.03 0.19 -1.15 -0.01 -0.18
 10 -0.21 0.22 -0.06 0.00 -0.17
Real trade balance [b] [c] 1 0.01 -0.15 -0.02 0.28 0.31
 3 -0.09 -0.34 0.00 0.34 0.25
 5 -0.54 -0.41 -0.01 0.34 0.30
 7 -0.59 -0.44 -0.06 0.31 0.50
 10 -0.12 -0.51 -0.25 0.27 0.83
Unemployment [d] 1 7 -1 3 0 2
 3 62 -1 27 -10 53
 5 109 0 64 -23 109
 7 115 1 80 -38 94
 10 109 1 -11 -58 68
Nominal interest rate [a] 1 1.28 -0.30 0.45 -0.37 0.16
 3 0.12 -0.48 0.53 -0.59 0.90
 5 -1.26 -0.50 0.26 -0.65 0.55
 7 -1.15 -0.53 -0.08 -0.69 0.43
 10 0.70 -0.57 0.14 -0.79 0.47
Inflation rate [e] 1 -0.08 -0.41 -0.01 -0.39 -0.18
 3 -0.67 -0.51 -0.24 -0.57 -0.58
 5 -1.05 -0.51 -0.47 -0.62 -0.07
 7 -0.57 -0.51 -0.68 -0.64 -0.12
 10 0.00 -0.51 -0.43 -0.71 -0.15
Price level [a] 1 -0.09 -0.40 -0.01 -0.37 -0.17
 3 -1.12 -1.45 -0.37 -1.46 -1.53
 5 -3.06 -2.47 -1.19 -2.61 -1.79
 7 -4.38 -3.51 -2.46 -3.81 -1.97
 10 -4.55 -5.09 -4.12 -5.74 -2.39
Nominal exchange rate [a] 1 0.81 1.39 0.26 -1.58 3.90
 3 3.03 2.26 1.39 -0.54 4.34
 5 4.77 3.18 2.27 0.65 3.06
 7 4.98 4.14 2.56 1.96 3.12
 10 5.43 5.64 1.74 4.15 3.87
Basic rate of income tax [e] 1 0.01 0.00 0.00 0.24 0.00
 3 0.10 -0.07 0.50 0.25 -0.01
 5 0.19 -0.15 0.63 0.15 -0.12
 7 0.17 -0.23 0.25 0.07 0.04
 10 0.20 -0.36 -1.10 -0.05 0.34
Deb/IGDP ratio [e] [f] 1 0.18 0.08 -3 0.61 0.00
 3 1.17 0.27 -38 0.61 -0.17
 5 1.71 0.33 105 0.38 0.20
 7 1.31 0.35 155 0.18 0.28
 10 1.84 0.28 -99 -0.11 0.19
 Government expenditure simulation: increase of [pounds]2bn
 (1995 prices) per annum for 5 years
 Year LBS NIESR HMT COMPACT CUSUM
GDP [a] 1 0.24 0.25 0.12 0.13 0.28
 3 0.23 0.12 0.01 0.03 -0.18
 5 0.20 0.05 -0.21 0.12 -0.13
 7 0.03 -0.25 -0.45 -0.06 0.00
 10 0.15 -0.07 0.12 -0.04 0.07
Consumers' expenditure [b] 1 0.03 0.06 -0.03 -0.17 0.05
 3 0.10 0.09 -0.15 -0.20 -0.07
 5 0.20 0.02 -0.17 -0.05 -0.23
 7 0.32 -0.15 -0.34 -0.04 -0.14
 10 0.29 -0.08 0.12 -0.03 -0.03
Investment [b] 1 0.02 -0.02 0.04 -0.01 0.00
 3 0.03 -0.05 -0.26 -0.04 -0.08
 5 0.02 -0.06 -0.64 -0.04 -0.14
 7 0.01 -0.07 -0.68 -0.02 -0.13
 10 0.08 -0.02 0.85 -0.01 -0.09
Real trade balance [b][c] 1 -0.07 -0.05 -0.17 -0.04 0.12
 3 -0.16 -0.16 -0.19 -0.05 0.00
 5 -0.26 -0.14 -0.27 -0.07 -0.05
 7 -0.31 -0.02 -0.04 -0.02 0.03
 10 -0.22 0.04 -0.15 -0.01 0.12
Unemployment [d] 1 -9 -6 -13 -2 -30
 3 -31 -12 -28 -7 28
 5 -44 -12 -12 -12 63
 7 -28 1 41 -6 45
 10 -11 5 53 1 22
Nominal interest rate [e] 1 0.05 -0.02 0.24 0.25 0.14
 3 0.29 0.16 0.58 0.36 0.74
 5 0.23 0.20 0.56 0.21 0.34
 7 -0.26 0.09 -0.03 0.02 0.21
 10 -0.46 -0.01 -1.03 0.02 0.24
Inflation rate [e] 1 0.01 -0.01 0.04 0.23 -0.14
 3 0.08 0.07 0.08 0.27 -0.42
 5 0.00 0.02 0.03 0.11 0.04
 7 -0.17 -0.05 -0.05 -0.02 -0.03
 10 -0.03 -0.02 -0.15 0.00 -0.06
Price level [a] 1 0.01 -0.01 0.04 0.22 -0.14
 3 0.16 0.11 0.19 0.77 -1.16
 5 0.21 0.18 0.29 1.09 -1.20
 7 -0.05 0.11 0.22 1.05 -1.20
 10 -0.39 0.00 -0.26 1.09 -1.35
Nominal exchange rate [a] 1 0.01 0.70 -0.01 0.41 3.11
 3 0.13 0.58 0.53 -0.27 2.94
 5 0.46 0.20 1.21 -0.88 1.55
 7 0.73 -0.10 1.08 -1.03 1.56
 10 0.15 -0.19 -1.54 -1.13 2.02
Basic rate of income tax [e] 1 0.00 0.00 0.00 0.00 0.00
 3 0.00 0.00 0.00 0.00 0.00
 5 0.00 0.00 0.00 0.00 0.00
 7 0.00 0.02 0.53 0.50 0.33
 10 -0.05 0.08 -0.13 0.31 0.95
Debt/GDP ratio [e][f] 1 0.03 -0.01 1520 0.05 0.18
 3 0.48 0.30 1840 0.76 0.18
 5 0.93 0.81 3124 1.41 0.49
 7 0.99 1.29 11 1.25 0.54
 10 0.35 1.47 -17 0.76 0.45
 Income tax simulation: 2 percentage point
 reduction in the basic rate
 Years LBS NIESR HMT COMPACT CUSUM
GDP [a] 1 0.10 0.51 0.23 0.01 0.50
 3 0.63 0.81 0.60 -0.01 0.62
 5 0.61 0.35 0.64 0.04 0.78
 7 0.07 -0.75 -0.13 -0.03 0.95
 10 0.14 -0.68 -1.11 -0.03 1.06
Consumers' expenditure [b] 1 0.10 0.68 0.53 0.05 0.72
 3 0.84 1.40 0.77 0.08 1.11
 5 1.08 1.13 0.71 0.17 1.14
 7 0.82 -0.32 -0.53 0.02 1.30
 10 0.79 -0.76 -0.41 -0.01 1.49
Investment [b] 1 0.01 0.08 0.26 0.00 0.02
 3 0.14 0.04 0.60 -0.02 0.17
 5 0.11 -0.10 0.14 -0.03 0.21
 7 -0.01 -0.24 -1.67 -0.02 0.29
 10 0.16 -0.16 -1.24 -0.01 0.37
Real trade balance [b][c] 1 -0.02 -0.29 -0.08 -0.03 -0.11
 3 -0.35 -0.67 -0.14 -0.06 -0.53
 5 -0.56 -0.67 -0.20 -0.08 -0.81
 7 -0.73 -0.13 0.07 -0.03 -0.98
 10 -0.85 0.26 -0.29 -0.01 -1.25
Unemployment [d] 1 -2 -8 -6 0 -27
 3 -49 -25 -59 0 -101
 5 -108 -29 -119 -3 -113
 7 -106 -5 -96 0 -119
 10 -15 19.00 98 1 -123
Nominal interest rate [e] 1 0.01 -0.25 -0.56 0.08 0.14
 3 0.32 -0.14 0.02 0.15 0.74
 5 0.89 0.31 0.77 0.15 0.34
 7 0.38 0.55 1.35 0.07 0.21
 10 -1.86 0.16 0.07 0.05 0.24
Inflation rate [e] 1 0.00 -0.16 -0.08 0.07 -0.15
 3 0.10 0.08 0.02 0.12 -0.24
 5 0.22 0.20 0.08 0.10 0.25
 7 -0.12 0.10 0.12 0.04 0.11
 10 -0.59 -0.12 -0.04 0.03 0.01
Price level [a] 1 0.00 -0.16 -0.08 0.07 -0.14
 3 0.14 -0.17 -0.09 0.28 -0.93
 5 0.53 0.18 0.07 0.50 -0.55
 7 0.48 0.48 0.46 0.59 -0.22
 10 -1.09 0.23 0.42 0.69 -0.13
Nominal exchange rate [a] 1 0.00 0.78 -0.31 0.26 3.11
 3 0.10 1.35 -1.21 0.02 2.94
 5 0.60 1.24 -0.78 -0.30 1.55
 7 1.62 0.33 1.81 -0.49 1.56
 10 1.51 -0.76 2.04 -0.68 2.02
Basic rate of income tax [e] 1 -2.00 -2.00 -2.00 -2.00 -2.00
 3 -2.00 -2.00 -2.00 -2.00 -2.00
 5 -2.00 -2.00 -2.00 -2.00 -2.00
 7 0.01 0.01 0.45 1.44 -1.99
 10 -0.04 0.26 1.20 0.85 -1.98
Debt/GDP ratio [e][f] 1 0.05 0.33 3955 0.59 0.58
 3 0.48 1.11 3830 2.49 0.51
 5 0.79 2.10 4809 4.41 0.79
 7 0.98 2.98 -25 3.59 0.92
 10 0.19 4.08 17 2.13 0.91
 Increase of 1 per cent in the level of technical progress
 Year LBS NIESR COMPACT CUSUM
GDP [a] 1 0.02 0.10 0.05 0.01
 3 -0.06 0.35 0.02 -0.26
 5 -0.10 0.59 0.06 0.00
 7 -0.07 0.78 0.12 0.16
 10 -0.05 0.89 0.23 0.22
Consumers' expenditure [b] 1 0.00 -0.06 0.11 0.06
 3 -0.08 -0.06 0.08 0.03
 5 -0.09 0.05 0.11 0.15
 7 -0.11 0.20 0.14 0.27
 10 -0.21 0.32 0.17 0.34
Investment [b] 1 0.01 0.07 0.00 0.00
 3 0.02 0.09 0.02 -0.03
 5 0.01 0.13 0.03 -0.05
 7 0.02 0.15 0.06 0.02
 10 0.01 0.15 0.10 0.06
Real trade balance [b] 1 0.00 0.07 -0.05 0.24
 3 0.00 0.29 -0.07 0.10
 5 -0.01 0.38 -0.07 -0.09
 7 0.02 0.40 -0.05 -0.09
 10 0.15 0.39 -0.02 -0.05
Unemployment [d] 1 32 8 4 1
 3 184 19 24 36
 5 202 21 47 51
 7 193 19 74 33
 10 188 13 99 14
Nominal interest rate [e] 1 -0.05 0.15 0.10 0.14
 3 -0.15 0.07 0.21 0.74
 5 -0.16 -0.03 0.24 0.34
 7 -0.16 -0.05 0.30 0.21
 10 0.04 -0.03 0.42 0.24
Inflation rate [e] 1 -0.02 0.10 0.10 -0.18
 3 -0.04 -0.04 0.16 -0.46
 5 -0.01 -0.04 0.17 0.09
 7 0.00 -0.01 0.22 0.04
 10 0.05 0.01 0.30 -0.04
Price level [a] 1 -0.02 0.09 0.09 -0.17
 3 -0.08 0.09 0.39 -1.31
 5 -0.11 0.00 0.72 -1.31
 7 -0.12 -0.04 1.11 -1.15
 10 0.00 -0.04 1.91 -1.23
Nominal exchange rate [a] 1 -0.01 -1.37 0.26 3.11
 3 -0.07 -1.65 -0.07 2.94
 5 -0.23 -1.69 -0.50 1.55
 7 -0.47 -1.61 -1.00 1.56
 10 -0.74 -1.48 -1.99 2.02
Basic rate of income tax [e] 1 0.00 0.00 -0.05 0.00
 3 0.02 0.00 -0.03 -0.02
 5 0.04 -0.04 -0.01 -0.17
 7 0.07 -0.09 0.02 -0.17
 10 0.12 -0.19 0.06 -0.11
Debt/GDP ratio [e] 1 -0.01 -0.02 -0.11 -0.01
 3 0.18 -0.04 -0.09 -0.22
 5 0.46 -0.19 -0.01 -0.01
 7 0.71 -0.46 0.06 0.08
 10 1.16 -0.94 0.15 -0.01

Notes: (a.)Percentage difference. (b.)Difference as proportion of baseline GDP, except HMT which is percentage difference. (c.) Percentage points difference from base of current account/GDP ratio for HMT model. (d.) Difference from base ('000s). (e.) Percentage points difference. (f.) Difference from base of PSNCR ([pounds] million) for HMT model.