Comparative properties of models of the UK economy.

Church, Keith B. ; Mitchell, Peter R. ; Sault, Joanne E. 等

This article analyses the properties of five leading macroeconometric models of the UK economy, in the light of the current discussion of monetary and fiscal policy-making. In simulation experiments, the interest rate and the basic rate of income tax are used to target the inflation rate and to ensure fiscal solvency. Our results show that monetary shocks soon affect the response of quantity variables, and fiscal shocks bare monetary consequences, thus the operation of monetary and fiscal policy cannot be separated. Although the Bank of England's view is that it takes two years for monetary policy to bare its maximum effect on inflation, our results show that this depends on the approach taken to the modelling of expectations.

1. Introduction

Sound public finances and the control of inflation remain at the top of the government's macroeconomic policy agenda, through the recent change in its political complexion. The new arrangements for monetary policy, in which the Bank of England is given operational responsibility for setting interest rates, were completed by the Chancellor in his Mansion House speech on 12 June 1997. He reasserted a target inflation rate of 2.5 per cent, and added a requirement that the Bank should report publicly on its actions whenever inflation deviates from this target by more than one percentage point in either direction. Similar precision with respect to the fiscal objective is lacking, however, whether or not the government were to adopt the Maastricht Treaty's targets for the size of the general government financial deficit and the volume of debt, as proportions of GDP. That the apparent exactitude of these targets is spurious is clear from the debate in several European countries about the specific accounting conventions to be applied. Nevertheless both objectives condition the outlook of macroeconomic policy analysts and forecasters, and they are also reflected in the models that provide the quantitative framework for such analysis, which are the subject of this article.

The leading paradigm among both policy analyst-advisers and macroeconometric modellers in many OECD economies is one in which a broadly neo-classical view of macroeconomic equilibrium coexists with a new Keynesian view of short-to-medium term adjustment. Thus, at least in respect of the long-run equilibrium, the level of real activity is independent of the steady-state inflation rate, whereas in the short run, adjustment costs and contractual arrangements imply that markets do not clear instantaneously and there is a relatively slow process of dynamic adjustment to equilibrium. The potential persistence in output and employment disequilibria may then leave considerable scope for fiscal policy whose effects, strictly speaking, are nevertheless only temporary.

How these broad general views are developed in the specifications of five major models of the UK economy is the subject of Section 2 of this article. Section 3 then considers the explicit channels of the monetary policy transmission mechanism, and Section 4 analyses the issues involved in undertaking policy exercises on macroeconomic models. The results of four simulation experiments are discussed in Section 5; these experiments are carried out under standardised conditions, so that differences in the estimated macroeconomic responses genuinely represent differences in the models. Section 6 contains concluding comments.

2. Modelling the UK economy

Five models of the UK economy are considered in this article. One is the model of Her Majesty's Treasury (HMT), while four receive support from the ESRC Macroeconomic Modelling Consortium, which also supports the Bureau. These are the London Business School (LBS) and the National Institute of Economic and Social Research (NIESR), together with the `COMPACT' model group led by Simon Wren-Lewis of the University of Exeter and a new entrant known as `CUSUM'--the Cambridge University Small UK Model--directed by Sean Holly. Our analysis is based on the versions of these models deposited at the Bureau at the end of 1996; for the Treasury this is the annual release of the public model.

A general trend in recent model development is towards a more compact core structure with more transparent theoretical foundations, within the overall paradigm noted above. Downward sloping demand curves in imperfectly competitive goods and labour markets determine the quantity of output traded and the level of employment, and price setting and wage bargaining equations determine domestic prices and wages. Markets do not clear instantaneously because wages and prices are sticky, reflecting adjustment costs; and fluctuations in output largely reflect fluctuations in aggregate demand. The supply side is relatively unimportant for the determination of output in the short run, but is crucial for the longer run properties of the model. A key feature is the homogeneity of the price and wage equations, which delivers long-run inflation-neutrality. The sustainable level of output is, in principle, tied down by the NAIRU. In most models the long-run rate of growth of output is determined by exogenous productivity trends and the rate of population growth. They focus on short-to-medium term developments and typically lack any of the endogenous growth mechanisms, through human capital and so on, which are currently the subject of much academic research.

The Treasury model has recently undergone substantial slimming, the new version of the model, first used for the 1995 Summer Economic Forecast and described by Chan et al (1995), having only some 30 genuine behavioural equations. The CUSUM model, as its name suggests, is yet smaller, with only 15 behavioural equations. It is comparable in size to the model used by the Bank of England in preparing its inflation forecasts, although this model has not been documented and is not made available to us for comparative study. The main distinguishing feature of CUSUM is that growth occurs only through the capital accumulation process, rather than through exogenous technical progress trends. The model also includes a number of forward-looking variables: the effective exchange rate, the price of equity and the long-term interest rate.

The main change in the NIESR model since our previous study (Church et al, 1995) is the abandonment of the vintage capital model of production in the non-oil private sector of the economy, and the incorporation of a new system of factor demand equations. The vintage or `putty-clay' model assumes that, once a new vintage of capital is installed by a firm, there are no factor substitution possibilities. The optimal choice of factor proportions prior to installation then depends on expected future factor prices over the equipment's entire lifetime, while consistent pricing behaviour is related in a complicated way to the costs of operating the various vintages of capital equipment. Desired labour input also reflects the age profile of the capital stock. Young (1996) gives several reasons for the abandonment of the vintage approach: the fit of the labour demand equation was poor and could be at least equalled by much simpler structures; the complexity of the system made comprehension of full-model properties difficult and acted as a barrier to other innovations on the supply side; the vintage system introduced certain unusual features into simulation results, due to the interaction of investment and the scrapping of capital equipment.

This change to the NIESR model means that the COM PACT model is now alone among these five in using a vintage production system, which is itself implemented more comprehensively than in the previous NIESR model. Revisions to the COMPACT model since our previous study include a new investment equation which imposes the same forward-looking dynamic structure that features in the employment and price equations. Recent revisions to the LBS model involve re-estimation of the price equations. The non-homogeneity noted by Church et al (1997) has been removed, increasing the clarity of the model's long-run properties.

3. How monetary policy works

It takes two years for monetary policy to have its maximum effect on inflation, according to the Bank of England. The monetary policy transmission mechanism is essentially an interest rate transmission process. The official short-term interest rate influences other interest rates, asset prices and the exchange rate, and these financial variables then affect output and prices through the various expenditure components. A rise in the official short-term interest rate has its initial impact on domestic inflation through an appreciation of sterling, while the effects on the components of aggregate demand work through more slowly. In this section we describe how these various channels are represented in the models.

The chief mechanism by which the models achieve changes in the inflation rate is through the exchange rate, which in all cases is modelled through some form of uncovered interest parity condition. Thus the current level of the exchange rate is explained in terms of its expected future level and the differential between domestic and foreign interest rates. In the NIESR, COMPACT and CUSUM models the expected future exchange rate is treated in an explicit forward-looking model-consistent manner, and the model's solution sequence is internally consistent in the sense that each period's future expectations coincide with the solution values for those future periods. The exchange rate may then `jump' in the current period in response to anticipated future events. On the other hand the HMT model has a backward-looking treatment of expectations, equating the expected future value to the lagged value of the exchange rate. (We focus on the public model, although the Treasury's own work shows that the model can also be solved under model-consistent expectations, as illustrated by Chan et al (1995).) The LBS model includes both future and past exchange rates, but the expected future variable is then determined by lagged variables, so that the overall treatment is backward looking; these variables include a risk premium proxy and an additional interest rate term, making this model more sensitive to interest rate changes. The only other model with a risk premium term is the CUSUM model.

An appreciation in the exchange rate lowers the domestic-currency cost of imports, reducing the price of manufactured goods and hence, both directly and indirectly, the overall price level. Any change in the exchange rate is fully reflected by corresponding changes in domestic prices in all models, ensuring that policies involving attempts at a `competitive devaluation' cannot succeed because the real exchange rate is ultimately unchanged. However, prices and wages react slowly and this nominal inertia allows indirect short-run employment and output responses.

Several direct domestic channels of interest rate transmission are usually distinguished in theoretical discussion. The four main effects are: an income effect, in which interest rate changes influence the flow of dividend and interest payments, and hence spending decisions; a substitution effect, in which interest rate changes affect the intertemporal allocation of private consumption and saving; a wealth effect, in which the value of personal sector wealth is influenced by interest rate changes through their effect on financial asset prices and house prices; and a user-cost-of-capital effect. The extent to which these effects are elaborated in empirical models varies with the amount of detail in the financial accounts, the level of aggregation, and the econometric specification. The substitution effect is usually represented as a direct impact of interest rates in the consumption function, and a rise in the short-term interest rate permanently reduces consumers' expenditure in all models except HMT, where the reduction is short-lived. The COMPACT model uses a real interest rate variable in modelling consumer behaviour. This is measured after tax.

Private sector fixed investment responds to interest rate changes through their influence on the cost of capital. In the LBS and HMT models both long and short rates appear, reflecting the mix of financing opportunities available to firms, whereas in the NIESR model only the short rate appears. In the COMPACT model's vintage system a higher real post-tax rate of interest makes newer technology less attractive to install and older but less productive vintages more viable. These four models all have a separate treatment of housing investment, with the interest cost variable measured in slightly different ways. The CUSUM model explains total private sector investment, but a change in interest rates has no long-run direct effect on this aggregate investment variable.

4. Policy exercises with macroeconomic models

Our comparisons of overall model properties are based on four simulation experiments conducted in a common policy framework. This reflects the broad objectives of current policy by using interest rates to target inflation and by ensuring sustainable public finances. The simulations comprise a change in the inflation target, an external shock to the foreign interest rate, and two fiscal policy shocks. In each case macroeconomic responses to a shock are estimated by comparing the results of two solutions of a model, one a base run and the other a perturbed run in which a relevant 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 different results may be obtained simply due to different assumptions about the way in which policy reacts, which we accordingly standardise as far as possible.

In four models the monetary policy rule sets the nominal short-term interest rate as a function of the deviation of inflation from its target. In the NIESR model this simply relates the change in the interest rate directly to the inflation deviation, and we implement a rule of the same form in the CUSUM model. In the LBS model additional terms in the change and rate of change of the inflation rate are included, in order to prevent instability in the model. In the COMPACT model an additional term involves the deviation of the price level from its base-run value.

Fiscal closure rules ensure the sustainability of policy, in particular ruling out the possibility of an explosion of government debt. In principle any government income or expenditure variable could be altered to achieve a desired fiscal adjustment or, perhaps more realistically, a package of changes in taxation and expenditure could be constructed, but in practice the models use the direct tax rate as the policy instrument, following earlier work on fiscal closure rules on the IMF's MULTIMOD model (Masson et al, 1990). In the LBS and NIESR models the basic rate of income tax is adjusted whenever the PSBR/GDP ratio deviates from its target value, and we implement a similar rule in the CUSUM model; in the COMPACT model the target variable is the debt/GDP ratio.

In the HMT model it has not proved possible to find correspondingly simple fiscal and monetary policy rules that perform well in all our simulation experiments, and so we apply optimal control techniques, with an objective function that reflects the same policy framework. This penalises (squared) deviations of the inflation rate and the PSBR/GDP ratio from their target values, together with changes in the interest rate and income tax rate instruments, as is conventional in this approach, in order to avoid excessive and unrealistic movements in these policy instruments. Thus, unlike the other models, there is not a one-to-one target-instrument assignment, recognising the fact that the setting of fiscal policy has an impact on the inflation rate and that interest rates influence the public finances. While the separate rules implemented on the other models represent a separation of authority that reflects recent moves towards Bank autonomy, it is in practice important to consider the two arms of policy together.

The target values used in these exercises are in general set equal to the base-run values of inflation and the relevant fiscal indicator respectively. This ensures comparability across the models, given that there are differences in their base-run solutions. Assigning an absolute target, such as an inflation rate of 2.5 per cent, would distort comparisons since differences in the base imply that policy instruments have a different amount of work to do for this reason alone, irrespective of any differences in the models' transmission mechanisms. Accordingly, in the inflation target simulation, where a change in the target is itself the perturbation under study, the objective of policy is specified as the achievement of an inflation rate that is I per cent lower than in the base solution. Whereas this is a permanent shock, the other three perturbations are temporary, being removed after five years. A permanent change in the foreign interest rate causes instability in at least one forward-looking model, and we again wish to retain comparability. With respect to the fiscal shocks, permanent changes to government expenditure or personal taxation within an internally consistent scenario require accommodating changes to the fiscal targets, and there is no consensus on how these should be assigned. Correspondingly, the fiscal policy rule is itself suspended for the duration of these shocks.

5. Simulation results

General results on the main macroeconomic indicators for our four experiments are reported in Tables A1-A4. For four of the models (LBS, NIESR, CUSUM, HMT) the base run corresponds to a published forecast; in the last case, however, the Treasury does not make its forecast assumptions available, and the base run is the forecast of the Ernst and Young ITEM (Independent Treasury Economic Model) Club, kindly provided by the Club. For the COMPACT model a base run constructed for simulation purposes is supplied by the model proprietors. The length of the base varies between models, and while results are reported up to ten years in Tables Al-A4 our discussion also refers on occasion to the full horizons over which we run the models, namely 12, 16, 23, 33 and 71 years in the HMT, CUSUM, LBS, NIESR and COMPACT models respectively.

Table A1. Inflation target simulation:
reduction of 1 percentage point

Year LBS NIESR HMT COMPACT CUSUM

GDP(a)

1 -0.08 0.20 -0.37 -1.99 -0.96
3 -0.66 0.51 -0.69 -0.37 -2.56
5 -0.57 0.51 -0.95 0.05 -3.67
7 0.14 0.45 -1.27 0.19 -4.07
10 0.66 0.41 -1.62 0.13 -4.00

Consumers' expenditure(b)

1 -0.03 0.31 -0.42 -1.81 -0.41
3 -0.35 1.10 -0.41 -1.20 -1.70
5 0.47 1.05 -0.67 -0.94 -3.48
7 1.96 0.83 -0.98 -0.72 -4.36
10 3.02 0.62 -1.24 -0.62 -4.85

Investment(b)

1 -0.06 0.25 -0.15 -0.63 -0.44
3 -0.28 0.31 -0.47 -0.33 -0.93
5 -0.14 0.30 -0.73 -0.25 -1.13
7 0.19 0.31 -0.87 -0.23 -1.12
10 0.34 0.31 -0.99 -0.28 -0.97

Real trade balance(b)

1 0.01 -0.35 0.20 0.71 -0.02
3 -0.01 -0.68 0.17 0.83 0.26
5 -0.90 -0.63 0.33 0.98 1.02
7 -2.01 -0.54 0.40 0.98 1.45
10 -2.71 -0.44 0.35 0.93 1.85

Unemployment(c)

1 12 -7 11 36 57
3 134 -52 63 72 316
5 192 -78 77 57 608
7 88 -77 106 4 656
10 -76 -60 152 -92 460

Nominal interest rate(d)

1 0.48 -0.52 1.18 -1.00 0.07
3 0.29 -0.76 0.24 -1.00 -0.34
5 -0.67 -0.90 0.30 -1.00 -0.89
7 -0.99 -0.96 0.51 -1.00 -0.87
10 -0.52 -0.98 0.70 -1.00 -0.12

Inflation rate(d)

1 -0.09 -0.66 -0.07 -2.45 -0.74
3 --0.94 -0.97 -0.75 -2.33 -1.22
5 -1.38 -1.07 -0.89 -1.36 -2.00
7 -1.18 -1.06 -0.90 -0.99 -2.30
10 -0.86 -1.02 -0.89 -0.89 -1.28

Price level(a)

1 -0.03 -0.65 -0.07 -2.30 -0.72
3 -1.09 -2.48 -1.32 -7.51 -3.27
5 -3.70 -4.46 -2.93 -10.23 -6.61
7 -6.50 -6.43 -4.63 -12.05 -10.66
10 -9.44 -9.22 -7.08 -14.39 -15.10

Nominal exchange rate(a)

1 0.47 2.65 0.73 0.62 9.62
3 4.28 4.06 2.36 2.65 9.71
5 9.35 5.73 2.98 4.71 10.96
7 13.03 7.64 3.93 6.81 13.32
10 17.01 10.68 5.63 10.05 16.26

Basic rate of income tax(d)

1 0.00 0.01 0.28 0.96 0.19
3 0.05 -0.11 1.14 1.28 1.56
5 0.14 -0.14 1.23 1.12 3.11
7 0.15 -0.12 1.29 0.84 3.88
10 -0.02 -0.06 1.36 0.54 4.27

Debt/GDP ratio(d)

1 0.00 0.09 0.21 2.41 0.45
3 0.25 0.35 0.98 3.20 2.69
5 0.68 1.11 2.16 2.80 5.14
7 0.33 1.99 3.39 2.10 7.32
10 -1.72 3.18 5.18 1.35 8.64

Notes: (a) Percentage difference from base. (b) Difference from base as proportion of baseline GDP. (c) Difference from base (000s). (d) Percentage points difference from base.

Table A2. Foreign interest rate simulation:
increase for 5 years of 1 percentage point

Year LBS NIESR HMT COMPACT CUSUM

1 0.00 -0.11 -0.12 0.32 -0.13
3 -0.19 -0.26 -0.12 0.17 0.03
5 -0.50 -0.17 -0.23 0.15 -0.11
7 -0.54 -0.08 -0.24 0.03 -0.54
10 0.15 0.00 -0.20 0.01 -0.65

Consumers' expenditure(b)

1 -0.01 -0.24 -0.18 -0.03 -0.26
3 -0.44 -0.64 -0.25 0.05 -0.32
5 -1.01 -0.31 -0.32 0.37 -0.13
7 -1.01 0.02 -0.12 0.41 -0.42
10 0.17 0.11 -0.10 0.39 -0.68

Investment(b)

1 -0.02 -0.18 -0.06 0.09 -0.11
3 -0.16 -0.19 -0.14 0.05 -0.04
5 -0.30 -0.10 -0.19 0.05 -0.12
7 -0.25 --0.05 -0.11 0.00 -0.27
10 0.07 -0.01 -0.04 -0.03 -0.20

Real trade balance(b)

1 0.02 0.31 0.11 0.13 0.26
3 0.43 0.47 0.21 0.11 0.36
5 0.84 0.18 0.23 -0.18 0.16
7 0.73 -0.05 -0.02 -0.31 0.18
10 -0.10 -0.09 -0.10 -0.30 0.23

Unemployment(c)

1 -4 4 4 -7 -7
3 9 27 7 -23 -41
5 68 30 -1 -33 -82
7 118 17 -13 -28 -6
10 18 -2 0 -7 104

Nominal interest rate(d)

1 0.24 0.45 0.53 0.66 0.58
3 0.93 0.46 0.60 0.90 0.09
5 1.18 0.20 0.97 0.4.5 0.37
7 0.44 0.03 0.56 0.09 0.26
10 -0.07 0.00 -0.45 -0.09 -0.66

Inflation rate(d)

1 0.06 0.36 0.01 0.65 0.42
3 0.25 0.10 0.01 0.85 0.38
5 0.13 -0.13 -0.01 0.38 0.45
7 -0.24 -0.14 0.01 0.02 0.18
10 -0.11 -0.04 0.01 -0.16 -0.76

Price level(a)

1 0.03 0.35 0.01 0.61 0.41
3 0.49 0.73 -0.04 2.38 1.43
5 1.04 0.58 -0.03 3.38 2.31
7 0.95 0.28 -0.02 3.54 2.88
10 -0.05 0.07 0.02 3.20 1.53

Nominal exchange rate(a)

1 -0.72 -2.34 -0.21 -2.56 -4.20
3 -2.28 -1.46 -0.76 -2.46 -2.62
5 -2.80 -0.25 -0.31 -1.94 -1.49
7 -0.95 0.16 0.89 -1.84 -1.55
10 0.54 0.14 0.32 -1.81 -0.62

Basic rate of income tax(a)

1 0.00 0.01 0.08 -0.13 0.11
3 0.02 0.10 -0.03 -0.06 0.05
5 0.11 0.13 0.14 -0.03 -0.21
7 0.26 0.12 0.38 -0.03 -0.06
10 0.42 0.10 0.50 -0.05 0.18

Debt/GDP ratio(a)

1 0.08 0.03 0.07 -0.34 -0.04
3 0.58 0.27 0.13 -0.14 -0.60
5 1.67 0.36 0.13 -0.09 -0.99
7 2.89 0.37 0.05 -0.07 -1.00
10 3.77 0.30 0.06 -0.13 -0.32

Notes: see Table A1

Table A3. Government expenditure simulation:
increase of 2bn [pounds sterling] (1990 prices) per annum

Year LBS NIESR HMT COMPACT CUSUM

GDP(a)

 1 0.16 0.30 0.25 0.36 0.44
 3 0.11 0.23 0.15 0.18 0.75
 5 0.15 0.16 0.13 -0.08 0.79
 7 0.06 -0.16 -0.26 0.00 -0.12
10 0.05 -0.04 -0.15 0.01 0.31

Consumers' expenditure(b)

 1 -0.04 0.09 -0.03 -0.15 -0.03
 3 -0.08 0.14 0.13 -0.19 0.21
 5 0.01 0.02 0.29 0.03 0.29
 7 0.18 -0.15 -0.08 0.00 -0.49
10 0.15 -0.06 -0.47 0.01 -0.44

Investment(b)

 1 -0.01 0.04 -0.03 0.10 0.12
 3 0.00 -0.01 -0.11 0.04 0.23
 5 0.02 -0.02 -0.14 -0.05 0.20
 7 0.02 -0.05 -0.09 -0.04 -0.16
10 0.02 -0.01 0.10 -0.04 0.10

Real trade balance(b)

 1 -0.08 -0.19 -0.05 -0.05 -0.06
 3 -0.09 -0.20 -0.17 -0.03 -0.05
 5 -0.15 -0.14 -0.32 0.03 -0.01
 7 -0.14 0.01 -0.14 0.04 0.58
10 -0.12 0.01 0.14 0.03 0.59

Unemployment(c)

 1 -16 -11 -30 -6 -15
 3 -16 -51 -40 -21 -76
 5 -22 -64 -38 -23 -156
 7 -12 -26 20 -19 -144
10 -12 16 58 -5 -175

Nominal interest rate(d)

 1 0.27 0.02 0.62 0.37 0.28
 3 -0.02 0.21 0.48 0.44 0.11
 5 0.04 0.16 -0.12 -0.11 0.76
 7 -0.05 -0.02 -0.69 -0.17 1.36
10 -0.01 -0.02 -0.22 -0.19 1.37

Inflation rate(d)

 1 0.10 0.02 0.04 0.36 0.15
 3 -0.02 0.11 0.06 0.41 0.32
 5 -0.02 0.00 0.06 -0.14 0.86
 7 0.01 -0.11 0.05 -0.18 1.47
10 0.02 -0.02 -0.06 -0.19 1.71

Price level(a)

 1 0.06 0.02 0.04 0.34 0.15
 3 0.03 0.24 0.09 1.26 0.76
 5 -0.04 0.30 0.19 1.26 2.17
 7 -0.14 0.13 0.33 0.93 4.90
10 -0.09 -0.01 0.24 0.33 9.95

Nominal exchange rate(a)

 1 0.13 0.70 0.23 0.01 -2.32
 3 0.25 0.44 0.89 -0.98 -2.77
 5 0.42 0.05 0.72 -1.35 -4.33
 7 0.43 -0.10 -0.50 -1.09 -6.82
10 0.21 0.00 -1.81 -0.56 -11.40

Basic rate of income tax(d)

 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 -0.03 0.50 0.41 0.95
10 -0.02 0.01 0.20 0.24 0.39

Debt/GDP ratio(d)

 1 0.07 -0.02 -0.02 -0.12 0.07
 3 0.07 0.29 0.33 0.72 0.65
 5 0.07 0.73 0.76 1.42 1.03
 7 -0.02 1.00 0.95 1.02 0.32
10 -0.18 1.05 0.85 0.60 -1.69

Notes: see Table A1

Table A4. Income tax simulation:
2 percentage point reduction in the standard rate

Year LBS NIESR HMT COMPACT CUSUM

GDP(a)

 1 0.07 0.33 0.17 0.11 0.48
 3 0.31 0.62 0.35 0.05 1.29
 5 0.32 0.53 0.61 0.17 1.35
 7 0.16 0.35 0.08 0.04 -0.2
10 0.16 0.13 0.13 0.01 -0.7

Consumers' expenditure(b)

 1 0.09 0.50 0.27 0.11 0.47
 3 0.49 1.26 0.43 0.11 1.32
 5 0.62 1.29 0.79 0.25 1.46
 7 0.50 1.06 0.26 0.02 -0.22
10 0.49 0.67 0.10 0.00 -1.27

Investment(b)

 1 0.01 0.13 0.02 0.03 0.11
 3 0.06 0.13 0.06 0.02 0.37
 5 0.07 0.07 0.26 0.04 0.31
 7 0.07 0.02 0.07 -0.01 -0.30
10 0.08 -0.02 -0.04 -0.03 -0.36

Real trade balance(b)

 1 -0.03 -0.27 -0.11 -0.05 -0.17
 3 -0.24 -0.60 -0.11 -0.06 -0.44
 5 -0.36 -0.63 -0.35 -0.09 -0.42
 7 -0.41 -0.56 -0.51 0.01 -0.45
10 -0.41 -0.40 0.09 0.03 -0.91

Unemployment(c)

 1 -8 -13 -6 -2 -13
 3 -46 -78 -54 -7 -103
 5 -57 -119 -102 -14 -137
 7 -36 -119 -77 -13 -50
10 -33 -93 -27 -7 1

Nominal interest rate(d)

 1 0.16 -0.15 -6 0.20 0.17
 3 0.35 0.05 0.67 0.36 -0.07
 5 0.20 0.10 0.58 0.15 0.38
 7 -0.28 0.10 0.68 -0.07 0.77
10 -43.17 0.07 -0.70 -0.16 0.60

Inflation rate(d)

 1 0.04 -0.12 -0.05 0.20 0.06
 3 0.08 0.08 0.07 0.34 0.13
 5 -0.04 0.06 0.27 0.12 0.43
 7 -0.18 0.02 0.15 -0.09 0.77
10 0.04 -0.01 0.00 -0.17 0.73

Price level(a)

 1 0.01 -0.11 -0.05 0.19 0.06
 3 0.14 -0.03 -0.06 0.84 0.32
 5 0.06 0.09 0.26 1.23 1.03
 7 -0.23 0.15 0.72 1.08 2.49
10 -0.40 0.15 0.69 0.61 4.61

Nominal exchange rate(a)

 1 0.03 1.02 -0.10 0.02 -1.32
 3 0.38 1.18 -0.31 -0.60 -1.62
 5 0.99 1.03 -0.24 -1.17 -2.64
 7 1.31 0.84 0.98 -1.18 -4.09
10 0.74 0.60 -0.43 -0.83 -6.51

Basic rate of income tax(d)

 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 -1.85 0.36 1.39 0.95
10 -0.05 -1.55 0.61 0.82 1.42

Debt/GDP ratio(d)

 1 0.06 0.29 0.18 0.47 0.57
 3 0.52 0.83 1.03 2.38 2.03
 5 0.83 1.45 1.46 4.25 3.62
 7 0.81 2.24 1.49 3.49 3.72
10 0.41 3.39 1.38 2.05 2.57

Notes: see Table A1

Reduction in the inflation target

In this simulation the inflation target is set at one percentage point below the base-run values of inflation throughout the simulation period, as discussed above. In the COMPACT model, however, this led to non-convergence of the model solution algorithm. Instead we suppress the interest rate reaction function and the exchange rate equation in this model and impose interest rate and exchange rate trajectories consistent with the required reduction in inflation.

The results in Table A1 show that inflation is reduced in each of the models, although only the NIESR model has settled down by the tenth year of the simulation, the other models displaying more cyclical behaviour. The key difference between the models is the reaction of the exchange rate. The forward-looking equation in the NIESR model gives an immediate jump in the exchange rate. The new target for inflation is fully credible and determines the behaviour of the exchange rate, which is driven higher by expectations of higher rates in the future. This appreciation reduces the price level leading to inflation overshooting its target level so that the interest rate falls. In the long run the reduction in the interest rate is one percentage point leaving the real rate unchanged.

The LBS and HMT models both feature backward-looking expectations hence the exchange rate cannot jump by a large amount at the start of the simulation and the movement of inflation towards its new target is relatively sluggish. It is the interest rate that has to deliver the required exchange rate appreciation in these models rather than the expectations mechanism. In the LBS model the real interest rate enters the exchange rate equation, and although the nominal rate eventually falls, a higher real rate gives the required appreciation. This appreciation is far greater than that required in the other models to achieve a similar inflation outcome, which is due to the sluggish adjustment of private sector average earnings. The two other components of the key producer cost variable, namely the price of fuel and the price of non-fuel imports, fully reflect exchange rate changes in approximately a quarter of the time. The nominal interest rate in the HMT model rises by more than in the LBS model to deliver the exchange rate appreciation but in contrast prices react quickly. Indeed, the real exchange rate falls by 1.6 per cent by the end of the tenth year compared to an appreciation of 7.9 per cent by the same period in the LBS model.

Demand side responses dominate the results by the tenth year of the simulation, although this is a pure monetary shock. The real exchange rate reactions are often important in explaining the overall response of demand. In this case, however, despite the appreciation of the real exchange rate in the LBS model output eventually rises, and in the HMT model, where an improvement in competitiveness occurs, output falls. Initially the higher interest rate in the LBS model reduces expenditure, but inflation overshoots its target by year 4 so the nominal interest rate is then below base. This, together with higher real income and wealth, produces a large consumption response which outweighs the worsening trade balance.

The improvement in competitiveness in the HMT model which commences midway through the simulation is countered by the combination of higher interest and tax rates. However, the tax base is falling and the deficit is not controlled, nor has the inflation rate reached its target by the end of the simulation. The movements in the policy instruments reduce consumers' expenditure and investment, hence GDP falls.

In the COMPACT model the requisite exchange rate and interest rate trajectories are imposed, as noted above, and these ensure that the inflation rate is reduced by one percentage point in the long run. There is a substantial amount of cycling, however, not only in prices but also in quantity variables, through the operation of the vintage production system. The results for the first ten years reflect short-term fluctuations in consumption, investment and output, but not their long-run outcomes. By the end of the simulation, the GDP response has converged to -0.6 per cent. The real interest rate is unchanged as the nominal rate and inflation fall by the same amount, but in these circumstances the real post-tax interest rate increases. This implies a lower equilibrium capital/labour ratio and with an unchanged natural rate of unemployment this is achieved through reduced investment and output.

In the CUSUM model the exchange rate is determined in a similar manner to the NIESR model, but its initial movement is substantially greater, and as this feeds through, inflation overshoots its target. The real exchange rate and the real interest rate are above base throughout the simulation, reducing equity prices. The model's price and wage equations lack dynamic homogeneity, hence this model is not inflation neutral, and the unemployment response can be interpreted as an increase in the NAIRU.

Increase in the foreign interest rate

A forward-looking uncovered interest parity condition, as used in the NIESR, COMPACT and CUSUM models, implies that an increase of one percentage point in the foreign interest rate leads to a fall in the exchange rate of one per cent per annum, in the absence of any domestic interest rate response. Maintaining this shock for a period of five years then implies that the exchange rate should jump down by 5 per cent in the first quarter. In fact the depreciation is 2.2 per cent, 2.8 per cent and 4.3 per cent in the NIESR, COMPACT and CUSUM models respectively, reflecting some narrowing of the interest differential. The exchange rate is then expected to return to base gradually, although the speed with which this occurs varies greatly across the models. In the NIESR model the exchange rate is back to base in year 6 but in the COMPACT model after 71 years it is still 0.5 per cent lower while all other variables in the model, with the exception of prices which reflect the changes in the exchange rate, have returned to base. We do not observe a convergent path in the CUSUM model, which may be due to its sluggish price adjustment combined with a simulation horizon that is relatively short among these forward-looking models. In the LBS and HMT models the exchange rate does not jump but depreciates gradually.

The jump in the exchange rate in the forward-looking models gives an upward push to the price level through sharply rising import prices. Whereas the price level hardly moves in the LBS and HMT models in the first quarter, it rises by 0.2 per cent in the other three models. In all five models a general pattern emerges of the exchange rate fuelling inflation, which necessitates an increase in the domestic interest rate. In the HMT model the sharp initial rise in the interest rate is sufficient to subdue the inflation rate immediately, whereas in the LBS model the interest rate reaction function gives a comparatively slow response. The exchange rate in the LBS model is in any event more sensitive to interest rates, as noted above, but this does not manifest itself in a large inflation problem, as prices react very slowly to exchange rate movements.

The results of the shock on the real side of the economy again depend on the direct influence of interest rates on the components of GDP and the second round impact on demand. An obvious impact of an exchange rate depreciation is on the trade volumes. The initial improvement in the real trade balance that is seen across the models is outweighed by the effect of interest rates on consumption and investment. In both LBS and HMT models it is consumers' expenditure which makes the largest contribution to the fall in GDP, the overall magnitude of the decrease being greatest in the LBS model where the peak interest rate rise is the largest. The COMPACT model is an outlier in respect of the demand-side effects as output actually increases throughout the early part of the simulation that is reported in Table A2. The initial increase in GDP is attributable to improvements in the real trade balance, a small increase in investment and a large initial jump in stockbuilding.

In contrast GDP declines continuously in the CUSUM model, mirroring the response of consumers' expenditure, whose own fall is due to lower real income and wealth. Part of the revaluation of personal sector wealth is in line with movements in equity prices which fall dramatically, declining by 20 per cent in real terms in ten years. This collapse in equity prices combined with lower output and higher nominal interest rates also reduces private sector investment, reinforcing the overall GDP response.

Increase in government expenditure

The increase in central government current expenditure on goods and services is 2bn [pounds sterling] per annum in 1990 prices, approximately 0.3 per cent of GDP. It is allocated proportionately between procurement and employment in the HMT model, the only model to make such a distinction. The increase is maintained for five years, after which expenditure returns to baseline values and the fiscal solvency rules are reimposed. The results are shown in Table A3.

Each of the models in this comparison now possesses static homogeneity throughout their price and wage systems. Consequently it is not possible for the government to choose a policy that changes the price level and hence the natural rate of economic activity. As noted above, with the exception of the CUSUM model, where dynamic homogeneity does not hold, it is also impossible for the authorities to manipulate the inflation rate in order to change the natural rate. However the response of wages and prices is sluggish and markets are not in equilibrium in every period, so there is a possible role for countercyclical policy and by increasing expenditure the government can achieve worthwhile short-term benefits.

The initial positive multiplier on output in all models is almost entirely attributable to the increase in government expenditure, and there is some agreement about the size of the first-quarter impact. There is also some agreement about the persistence of the improvement, with GDP returning to base in 5-7 years in four models, although in the LBS model this takes 13 years. We should note, however, that in the CUSUM model GDP returns to base only briefly before increasing over the remaining years of the simulation, despite removal of the initial shock.

The NIESR and COMPACT models show no long-term change in equilibrium following the shock, with all quantity variables returning to base, in accordance with the theoretical framework outlined above. Although the dynamic responses appear to be similar the decomposition of aggregate demand does reveal some differences. The real exchange rate appreciates in the NIESR model giving a fall in the real trade balance in the first five years, whereas in the COMPACT model no such effect exists. Consumers' expenditure falls in the COMPACT model during the first five years, but shows a slight increase in the NIESR model as the effects of the government fiscal stimulus permeate through to other sectors of the economy.

The LBS results are characterised by a small but sustained improvement in GDP. In this and the HMT model there is partial crowding out of private sector investment and consumption expenditure through increased nominal and real interest rates. Real personal disposable income reacts very slowly in the LBS model, reaching a maximum of 0.2 per cent above base after eight years, which explains the sluggish response of consumers' expenditure. In the HMT model, even though nominal interest rates remain above base for longer, increased disposable income dominates and consumption is higher until year 7. In the HMT model the larger initial increase in interest rates keeps investment below base until the end of year 8, while it hardly moves in the LBS simulation.

The extent to which tax rates are required to move to ensure fiscal solvency depends on how the public sector finances have changed as a result of the shock. The increase in expenditure increases the deficit but generates higher revenue through the short-term expansion in the tax base. In the LBS model, however, the changes in the public finances following the initial expansion of the economy are negligible. Consequently there is virtually no movement in the tax rate when the solvency rule begins to operate in year 6. In contrast the basic rate of income tax rises sharply in the HMT model at this point, rising by 0.68 percentage points in the first quarter before falling gradually back to base by the year 11. During the period of increased government expenditure, the PSBR/GDP ratio peaks at 0.30 percentage points above base in year 5, but returns to and remains at its baseline values as soon as the targeting regime commences. The debt/GDP ratio starts its decline back towards base at the same point.

The inflationary consequences of the expenditure increase are quickly subdued in three models, but in the COMPACT simulation there is a big initial jump in the inflation rate which is not brought back to base by interest rates until the end of year 4. Together with the initial output gains this leads, unusually, to an immediate but temporary improvement in the debt ratio. In CUSUM inflation is not controlled, and with real GDP also stimulated by reduced real interest rates, the debt/GDP ratio fall rapidly in the latter part of the simulation; the NAIRU also falls.

Although the behaviour of the exchange rate is the dominant influence in simulations of monetary shocks, it also plays a part in fiscal policy simulations, as interest rates react to control any inflation response, with foreign exchange consequences. Several of the features of our first two simulations are therefore relevant to the fiscal experiment; in the current policy environment the distinction between monetary and fiscal policy is blurred.

Income tax cut

There are two main channels through which this two-pence reduction in the income tax rate might affect the economy. First, cutting the basic rate leads to a direct increase in personal disposable income and hence consumers' expenditure. This is true across all the models. Secondly, the reduction might change the behaviour of workers through its impact on wage bargaining. The lower tax rate reduces the wedge between employers' real costs and workers' real wages, which may reduce the equilibrium real wage and hence the NAIRU. Only in the HMT model, however, does a long-run tax wedge effect appear in the wage equation, so that a permanent cut in the basic rate of income tax would deliver a sustained reduction in the NAIRU. The NIESR model includes the change in the tax wedge in its wage equation, giving short-run effects. We consider only a temporary shock, nevertheless these wedge effects, absent from the other models, still have an important role. The tax cut puts downward pressure on real wages causing unemployment to fall, reinforcing the demand-side effects.

The wedge effects in the NIESR and HMT models result in an initial downward movement in inflation and the interest rate, in contrast to the other models. The expansion of demand tends to fuel inflation, but with the direct impact of the tax rate in the wage equation pushing in the opposite direction the need for any substantial rise in interest rates to control inflation is subdued until the start of the third year in the HMT model, while only minor tightening is ever required in the NIESR simulation. The absence of interest rate rises in the first few years manifests itself in slightly higher initial GDP responses and much larger reductions in unemployment by the fifth year in these two models, compared to the LBS and COMPACT models.

In the LBS model the initial GDP response is relatively small. The first-year increases in consumers' expenditure and disposable income are modest, given the reduction in the tax rate, and are quickly dampened by the increase in the nominal interest rate. Price movements, again modest, are quickly brought under control by the exchange rate appreciation, although there is some overshooting of the inflation target after year 4. As a result, both nominal and real short-term interest rates fall below base, stimulating investment and consumption expenditure during years 7-10. The first-year consumption response in COMPACT is also small, but for different reasons, the income effect being offset by an increase in the real post-tax interest rate.

The models demonstrate a clear lack of Ricardian equivalence. If Ricardian equivalence holds then consumers save the complete proceeds of the tax cut in the knowledge that to ensure stable public finances the government will simply raise future tax rates to finance the current policy. An important reason why this might not hold in practice is the existence of credit-constrained consumers who would like to, but cannot, borrow to finance expenditure. These people regard the tax cut as a means of achieving this borrowing with the government assuming the role of lender. This feature is explicitly modelled in the COMPACT model.

After five years of lower tax rates, the basic rate reverts to its fiscal solvency role, and three of the models then require substantial tax increases to rectify the deterioration in the public finances. The COMPACT model shows the largest increase reflecting the failure of the tax cut to boost employment and thus increase government receipts. The peak reduction in unemployment in the COMPACT model is 15,000 at the end of the fifth year, substantially smaller than the reductions achieved in the other models. The HMT and CUSUM models also required tax increases, despite more beneficial outcomes of the fiscal stimulus. Thus these three models do display an amount of Ricardian equivalence. In contrast the LBS and NIESR models suggest that the government can reduce taxes for a period with no requirement to eventually raise them above original levels. In the LBS model the tax rate remains just below base when solvency is introduced; the deficit ratio is already returning to base at the end of year 5. The NIESR model suggests that the initial tax cut is reversed gradually, bringing the PSBR/GDP ratio gradually back towards base while the debt/GDP ratio eventually stabilises around 5 percentage points higher.

6. Conclusion

Although it is the Bank of England view that it takes two years for monetary policy to have its maximum effect on inflation, our results show that this view is clearly dependent on the approach taken to the modelling of expectations. The overall dynamic response to a shock comprises both expectations and adjustment effects. Sluggish adjustment due to contractual arrangements and so forth is represented in all of the models, but there is a clear distinction between forward-looking and backward-looking treatments of expectations. Our simulations provide several examples in which forward-looking variables jump towards their new equilibrium outcomes rather than displaying protracted adaptation. The assumption that new policy is immediately credible and completely understood, implicit in a full model-consistent treatment of expectations, may be controversial and may be modified to incorporate learning about the new policy and its effects. Nevertheless, as the Bank of England noted in its May 1997 Inflation Report, the announcement of the new monetary policy arrangements immediately lowered inflation expectations by around half a per cent.

Our simulations show that shocks originating on the monetary side of the economy soon affect the response of quantity variables. The impact of these changes on the public finances then leads to a reaction in the fiscal instrument to ensure that the intertemporal government budget constraint is satisfied. Similarly, fiscal shocks have monetary consequences. Thus the operation of monetary and fiscal policy cannot be separated, at least conceptually. There are some differences in the way in which the policy environment is represented in the models, yet some representation is essential; in its absence the models could give only partial answers to important policy questions.

REFERENCES

Bank of England (1997), Inflation Report, May.

Chan, A., D. Savage and R. Whittaker (1995), The new Treasury model', Government Economic Service Working Paper no. 128, HM Treasury.

Church, K.B., P.R. Mitchell, P.N. Smith and K.E Wallis (1995), `Comparative properties of models of the UK economy', National Institute Economic Review, August, no. 153, pp. 59-72.

Church, K.B., P.R. Mitchell and K.E Wallis (1997), `Short-run rigidities and long-run equilibrium in large-scale macroeconometric models', in Market Behaviour and Macroeconomic Modelling (S. Brakman, H. van Ees and S.K. Kuipers, eds), Macmillan, forthcoming.

Masson, P.R., S. Symansky and G. Meredith (1990), `MULTIMOD Mark II: A revised and extended model', Occasional Paper no. 71, International Monetary Fund, Washington DC.

Young, G. (1996), `A new system of factor demand equations for the NIESR domestic model', presented at the ESRC Macroeconomic Modelling Seminar, University of Warwick, July 1996.

Statistical Appendix

Data are included up to the end of the latest quarter, if they are available at the time of going to press.

[TABULAR DATA 1-20 NOT REPRODUCIBLE IN ASCII]

(*) Correspondence should be addressed to the authors at the ESRC Macroeconomic Modelling Bureau, University of Warwick, Coventry, CV47AL. This article continues 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.