Technical progress and the natural rate in models of the UK economy.

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

1. Introduction

What are the macroeconomic consequences of technological (or technical) change? The standard neoclassical growth model gives a clear answer. In the long run, the natural rate of growth of the economy is equal to the rate of technical progress plus the growth rate of the population. Technical progress increases the potential supply of output, and given sufficiently flexible factor and product markets this potential can be realised, resulting in increased consumption, investment and real wages. These prognostications of beneficial outcomes nevertheless may not assuage more classical concerns about the possibility of permanent technological unemployment. And even with a beneficial view of long-run equilibrium, the processes of adjustment to the introduction of new technologies may be sufficiently protracted that substantial unemployment costs are incurred.

Macroeconometric models are useful devices for quantifying some of these effects. They provide estimates of the relevant long-run responses and the nature of the intervening adjustments to a change in the rate of technical progress. This is done at a relatively high level of aggregation, and macroeconometric models are typically silent on compositional and distributional questions, such as the impact of new technologies on employment and investment in different industries. Nor is technical progress itself explained by these models, instead the rate of technical progress is exogenous and typically constant.

In this article we undertake simulations of changes in the rate of technical progress on three models of the UK economy in order to answer the question posed in our opening sentence. The models considered are those of Her Majesty's Treasury (HMT), the National Institute of Economic and Social Research (NIESR), and the 'COMPACT' model group, as deposited at the ESRC Macroeconomic Modelling Bureau in late 1996; their general properties are reviewed along with those of two further models by Church et al (1997). As is usual in the Bureau's research programme, our analysis focuses not only on answering the substantive economic question posed above, but also on using it as a case study for cross-model comparisons. In general the models conform to what is now the leading paradigm among both policy analyst-advisers and macroeconometric modellers in many OECD economies, in which a broadly neoclassical 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. This is by no means a full-employment equilibrium, however, and an important question is what determines the non-accelerating-inflation rate of unemployment (NAIRU). The NAIRU is often independent of the steady-state inflation rate and so becomes the 'natural' rate of unemployment; it may, however, depend on the rate of productivity growth. These and other possible differences are explored in the remainder of this article.

A technical progress shock is essentially a supply-side shock and so draws attention to the supply-side specifications of the models. These have seen substantial developments in the last decade or two, redressing an important imbalance in the demand-oriented models of the 1970s. The forecasting failures of those models in the face of supply-side shocks, a desire for greater theoretical consistency in the models, and a shift in the emphasis of policy all pointed towards such a reorientation. However model-based analyses have addressed only a small range of the resulting issues. They have typically focused on measures that impact directly on costs, a popular simulation in the light of the experience of the 1970s being a change in the world price of oil. Relatively less attention has been given to technical progress, despite the debate about the causes and consequences of the slowdown in productivity growth in the 1970s. The OECD's INTERLINK model seems to have been the only model used to address this question (Englander and Mittelstadt, 1988; Torres and Martin, 1990; Giorno et al, 1995) until a recent comparative study of Australian models (Hargreaves, 1994) and an initial investigation of two UK models (Church et al, 1998). The present article further develops this line of research.

The article proceeds as follows. In section 2 we briefly describe how key features of the supply side are represented in the models, with particular attention to the production technology and the determination of the NAIRU. This provides a framework for interpreting the results of simulations of changes in technical progress, which are presented in section 3. It is seen that several of the 'natural rate' propositions are reflected in the results, although there are substantial differences in short-run dynamics and some of the unemployment responses are scarcely beneficial, if not perverse. Since these are national-economy models and the shock is applied on the same basis, terms of trade responses are also an important factor. Section 4 contains concluding comments.

2. Technical Progress and the Supply Side of Macroeconometric Models

2.1 The Production Function and Factor Demands

The basic description of technology within the models is a two-factor production function with constant returns to scale, of either the Cobb-Douglas or constant elasticity of substitution (CES) form. Technical progress is assumed to be Harrod-neutral or labour-augmenting, the model's steady state then conforming to the stylized fact of a constant investment/output ratio; technical progress proceeds at a constant exponential rate. The production function thus has the general form

[Y.sub.t] = F([K.sub.t], [L.sub.t] [e.sup.[Beta]t]). (2.1)

In none of the present models is a production function estimated as such, rather the estimated factor demand equations are based on the underlying production function, and technical progress then appears in those equations as time-trends. We now describe how this is done in the three models.

HM Treasury In the HMT model firms are assumed to choose factor input levels to minimise current costs given the expected level of output, subject to a Cobb-Douglas production function with labour elasticity [Alpha]. The first-order conditions yield log-linear equations for employment and investment each containing the trend term [Alpha][Beta]t, although the implied cross-equation restriction is not imposed in estimation. Indeed, in the manufacturing employment equation this is estimated as a split time-trend, with a lower rate of growth over 1975-80. The treatment of expectations uses the CBI/NIESR series for expected manufacturing output.

NIESR In the NIESR model the firm's objective is to maximise the present discounted value of future expected net cash flows, subject to a CES production function. The cash flow variable includes a quadratic cost of adjusting the capital stock. The resulting investment equation involves future expected investment, which is one of the forward-looking variables treated as 'rational' or 'model-consistent' expectations in solving this model. The analysis uses an 'effective' labour measure throughout, implicitly treating the second argument of the production function (2.1) as a single variable. Technical change is thus measured as an index of labour efficiency, calculated as the residual output growth unexplained by growth in the two primary factor inputs, at an average annual rate which varies by sector.

COMPACT Whereas the HMT and NIESR models assume that factor proportions are continuously variable, the COMPACT model adopts a vintage or 'putty-clay' model of production in which, once a new vintage of capital investment is installed, 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, within an ex ante Cobb-Douglas technology. The age profile of the capital stock in use then determines the required labour input. Technical progress enters as in (2.1), but any change in technical progress is only gradually embodied in the capital stock as a result of its vintage structure.

2.2 Prices, Wages and the NAIRU

Prices are determined as a mark-up on costs, and the wage equation is generated by a bargaining model as described by Layard and Nickell (1985). Both equations are usually estimated in error correction form and exhibit static and dynamic homogeneity, and so can be solved to obtain an expression for the NAIRU, as in Joyce and Wren-Lewis (1991) and Turner (1991). The long run of a typical wage equation may be written as

w - p + [t.sup.e] = pr + [Theta]([t.sup.i] + [t.sup.e] + [t.sup.d] + [t.sup.m]) - yu + [z.sup.w] (2.2)

where w, p and pr are (log) nominal earnings, producer prices and average labour productivity respectively, u is the unemployment rate, [t.sup.d], [t.sup.i] and [t.sup.e] are the average direct, indirect and employers' tax rates (per cent) respectively, and [t.sub.m] is the 'tax' imposed by high import prices or the real exchange rate. These four terms drive a 'wedge' between employers' real wage costs and employees' real consumption wages, whose long-run impact on the bargained wage outcome and consequently on the NAIRU is measured by the parameter [Theta]. In the HMT model [Theta] = 0.5, whereas in the other two models [Theta] = 0 so a permanent change in any of the wedge terms has no effect on the NAIRU. Finally other wage pressure variables may be included in [z.sup.w], such as the replacement ratio and a measure of union power.

The earnings equations in the HMT and COMPACT models are statically but not dynamically homogeneous with respect to productivity. Thus in a dynamic steady state with real wage growth occurring at the rate of growth of productivity, this steady-state productivity growth rate also affects the level of real wages and hence the NAIRU in these models: an increase in productivity growth leads to a fall in the NAIRU. (This response is not observed in simulations of the COMPACT model, however, since in the model code a constant trend productivity growth number rather than an endogenous productivity growth variable appears at the relevant point.) The underlying effect is consistent with evidence presented by Manning (1992) that the slowdown in productivity growth is an important explanation of the increase in unemployment in many OECD countries; Turner et al (1993) study the G3 economies and report a similar finding for Germany, but not for Japan or the United States. No such effect occurs in the NIESR model; on the other hand, in this model the NAIRU is a function of the rate of change of the wedge, together with the cost of stock-holding and the proportion of long-term unemployment.

It should be noted that the average labour productivity measure considered in this section can be immediately equated to the labour efficiency measure discussed in the preceding section only in the steady state of the simple growth model. In a full-model simulation of changes in technical progress, feedbacks from the rest of the model to employment, notably from output and relative factor prices, also influence the labour productivity outcome, and the adjustment to a new steady state may be protracted.

2.3 Aggregation

In the COMPACT model the features discussed above are treated at the level of the non-oil private sector of the economy, whereas the other two models disaggregate this. In the HMT model separate factor demand equations are estimated for manufacturing and non-manufacturing, and the latter is further disaggregated in the NIESR model, into business services, distribution and 'other'. A more aggregate model is more transparent and easier to maintain, ceteris paribus, although information is lost whenever different components of an aggregate behave differently and these different behaviours can be successfully modelled.

The technical progress measure in the NIESR model, analogous to the parameter [Beta] in (2.1), takes different values across the four sectors, as noted above; these are, at annual rates, manufacturing 3.2 per cent, distribution 0.032 per cent, business services 0.92 per cent, other 5.92 per cent, compared to the single aggregate figure in the COMPACT model of 1.96 per cent. The corresponding estimates of productivity trends derived from the HMT model's manufacturing and non-manufacturing employment and investment equations are not directly comparable, since they are functions of movements in relative factor prices as well as technical progress. Chan et al (1995, p.36) give these as, in manufacturing, 2.6 per cent over 1970-75, 2.1 per cent over 1975-80 and 3.7 per cent over 1981-92, and in non-manufacturing 1.0 per cent.

3. Simulation Experiments

3.1 Experimental Design

Macroeconomic responses to a technical progress shock are estimated by comparing the results of two solutions of each model, one a base run and the other a perturbed run in which the relevant technical progress variable is assigned values that deviate from its base-run values. Two shocks are considered. The first is an increase in the level of labour-augmenting technical progress of 1 per cent. The second is an increase in the annual growth rate of technical progress, analogous to the parameter [Beta] in equation (2.1), of 0.1 percentage points. This is a permanent change, and the first shock can be equivalently considered to be a temporary shock to the growth rate. In the NIESR and COMPACT models explicit labour efficiency trends appear, which can be directly perturbed. In the HMT model, equivalent perturbations are applied to the manufacturing and non-manufacturing employment and investment equations.

The base run in the NIESR model corresponds to a published forecast, extended to a horizon of 33 years for simulation purposes. The COMPACT model is not used for forecasting, and a 71-year simulation base is supplied by its proprietors. The public release of the HMT model does not include a forecast or simulation base, and we use the forecast of the Ernst and Young ITEM (Independent Treasury Economic Model) Club, kindly provided by the Club, which has a horizon of 12 1/2 years. All three models operate at a quarterly data frequency.

The macroeconomic responses to a shock may include changes in inflation and the state of the public finances, which may in turn induce changes in monetary and fiscal policy, since the models operate in a policy framework that reflects the broad objectives of current policy, namely low inflation and sound public finances. In the NIESR and COMPACT models the monetary policy rule sets the nominal short-term interest rate as a function of the deviation of inflation from its target, which in our perturbed run is taken to be the base-run values of inflation. The fiscal closure rules adjust the direct tax rate whenever the PSBR/GDP ratio (NIESR) or debt/GDP ratio (COMPACT) deviates from its target value, again the base-run values. For the HMT model we are not able to find correspondingly simple rules that perform well in all our experiments (see also Church et al, 1997), 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 base-run values, together with (-squared) changes in the interest rate and income tax instruments, as is conventional in this approach, in order to avoid excessive and unrealistic movements in these policy instruments.

An implication of the fiscal policy rule together with the maintenance of (exogenous) government expenditure at its base-run values is that any beneficial effect of increased technical progress on the public finances is passed on to the personal sector in the form of lower taxation. Other possibilities, such as increasing public expenditure or reducing the 'Maastricht' target ratios, remain for future study.

3.2 An Increase in the Level of Technical Progress

The economy-wide responses of output, employment, investment and productivity in the first simulation are shown in Charts 1-4, where annual averages of quarterly data are presented. Only the first forty years of the COMPACT solution are shown in the Charts, the remaining thirty years exhibiting little further change in variables of interest. The results show that productivity does eventually increase by about 1 per cent in each of the models although some uncertainty remains in the case of the HMT model that this is the long-run outcome. The adjustment in the COMPACT model is protracted due in part to the vintage system, whereas the NIESR model has a slow but very smooth path to the new equilibrium.

Identical outcomes in terms of productivity behaviour can be achieved through different combinations of employment and output responses. In the HMT and COMPACT models the productivity increase is driven by an increase in output with employment returning to base, although in the case of the HMT model it seems likely that there is some cyclical behaviour still to unwind. In the COMPACT model we do see the neutrality of the natural rate to changes in the level of productivity discussed above. By contrast in the NIESR model output is not a full 1 per cent higher but the productivity gain is achieved with a permanent reduction in the level of employment. Investment increases in line with output in each of the models although the determination of investment behaviour is different in each case as described below.

In the HMT model the 1 per cent increase in the level of technical progress has an immediate effect on output. Both manufacturing and non-manufacturing output are above base throughout the simulation period, ending at levels 1.34 per cent and 0.52 per cent above base respectively in the final quarter. Taken together with the employment responses, average labour productivity in both sectors increases, peaking in quarters 25 (manufacturing) and 21 (non-manufacturing) at values 1.18 per cent and 1.21 per cent above base, before diminishing as the reductions in employment at the beginning of the simulation are reversed. In the final quarter productivity remains 0.86 per cent (manufacturing) and 0.66 per cent (non-manufacturing) above base, employment in manufacturing being 0.47 per cent above base at this point, while in non-manufacturing employment is virtually back at base.

In the NIESR model output and investment increase sharply in the first year of the simulation while employment declines, being 0.4 per cent below base even after 33 years. This means that average productivity increases by 1 per cent, although the employment/output mix that achieves this is different to the other models. This result can in part be explained by looking at the results at the sectoral level. In the NIESR model the determination of public sector employment differs to that in other parts of the economy. For manufacturing, distribution, business services and 'other' sectors the effective labour input is determined by inverting the production function where actual hours worked adjust only slowly towards target hours, hence after 33 years employment is still 0.2-0.3 per cent below base. Employment in public services falls equiproportionately with increases in technology and rises in line with output. In this simulation public sector employment falls about 0.9 per cent below base whereas output in this sector increases by 0.1 per cent in the long run producing a 1 per cent increase in public sector productivity.

The results from the COMPACT model are dominated by the properties of the vintage system of production. The responses of output, investment and employment are notably slower than in the other models, reflecting the fact that the improvement in technical progress gradually increases the level of the capital stock over a long period of time. Firms are faced with a choice between investing in the new more productive machinery which requires shifting forward capital expenditure or continuing to produce output using old machines. Wages depend on average output per head and thus increase as the new machinery is introduced. When firms decide on the current investment mix the expectation of higher future wage rates is an important influence. This gives a lower labour to capital ratio in current investment and hence employment falls below base for 10 years before recovering back towards its original values as marginal costs finally reflect the improvement in technical progress. After about 30 years output has risen by 1 per cent reflecting the 20 years it takes the new technology to be embodied in all machines. However although the neutrality of the NAIRU with respect to a change in the level of productivity appears to hold eventually, there is a substantial 'cost' arising from the incorporation of new technology as it is fifty years before the unemployment rate returns to its baseline level.

Charts 5 and 6 show the impact of an increase in the level of technical progress on unemployment and real wage behaviour allowing comparisons across models with our a priori expectation that the level of the real wage should fully reflect the improvement in technical progress and that the NAIRU is invariant to the increase in the level of technical progress, although the shock may affect tax rates and the terms of trade which in the HMT model in turn affect the NAIRU.

Falling prices along with a higher unemployment level in the HMT model counter any positive effects that the increase in productivity has on average earnings during the first 3 years of the simulation. As the productivity increase feeds through, average earnings rise slightly above base for around 2 years before declining back below base for the remainder of the simulation, finishing 0.64 per cent below base in both the manufacturing and non-manufacturing sectors. The RPI falls by 1.3 per cent, giving an increase in real wages of 0.66 per cent, although these quantities have not settled down by this time.

Relative factor prices are an important determinant of employment levels in the HMT model. As prices change the interest rate adjusts in order to target inflation, and these interest rate changes have implications for the cost of capital in both sectors. An initial fall is reversed after about 5 years, the cost of capital peaking at 3.36 per cent (manufacturing) and 2.88 per cent (non-manufacturing) above base after about 7 1/2 years. The cost of capital response dominates that of wage costs, which explains the employment dynamics in Chart 2, the positive output effect only beginning to emerge at the end of the simulation period. The unemployment rate in Chart 5 is almost a mirror image. In the HMT model the NAIRU is affected by the wedge, in particular its income tax rate and real exchange rate components in this simulation. The income tax rate falls in order to target the deficit ratio back to base, while rising export prices and falling import prices worsen the terms of trade; these two effects offset one another throughout the simulation.

The unemployment rate in the NIESR model also peaks in year 5 at about the same rate as in the HMT model. Thereafter a small and protracted decline occurs with the unemployment rate still about 0.3 percentage points higher by the end of the simulation. The effect of the increase in the level of technical progress on the wage bargain is an increase in the real wage of around 0.6 per cent in the first six years of the simulation followed by a period of slower growth, such that the increase is just 0.8 per cent by the end of the simulation compared to the 1 per cent increase expected from the core supply-side framework.

3.3 An Increase in the Growth Rate of Technical Progress

The results of a 0.1 per cent percentage point increase in the growth rate of technical progress for output, employment, investment and productivity growth are shown in Charts 7-10. The rate of technical progress determines the overall growth of the economy so we would expect to see the economy move to a new steady state at a higher growth rate.

In the HMT model the growth rates of output, employment, investment and in turn productivity, fluctuate for the first 5 years of the simulation before reaching relatively stable paths. In the final quarter the productivity growth rate is 0.13 percentage points above base (manufacturing) and 0.09 percentage points above base (non-manufacturing). The increase in the growth rate of technical progress is more than fully reflected by investment decisions in both sectors, although the growth rate responses do not seem to have settled down at constant levels by the end of the simulation period. The improvement in the growth rate of output in the manufacturing sector reaches a similar level to that of investment, 0.27 percentage points above base in the final quarter, although in the non-manufacturing sector the output growth response is only half of this. Changes in the growth rate of employment are much smaller than those of output and investment. In the non-manufacturing sector the growth rate falls and then slowly returns back towards base. The lost growth is never recouped during the course of the simulation, leaving employment levels around 0.5 per cent below base during the second half of the simulation.

In the NIESR model employment and output growth decline in the first two years although productivity growth increases as the fall in output is less than that in employment. From year 3 output growth climbs above base but the employment growth rate remains below. By the end of the simulation output growth is about 0.08 percentage points higher and still increasing very gradually towards equality with the increment in the growth rate of technical progress. Employment growth also appears to be adjusting back towards base at the end of the simulation. As in the previous simulation the explanation of the aggregate employment response is found in the behaviour of the public sector where employment growth declines throughout the simulation ending up at a constant difference from base of around -0.08 percentage points, in contrast to the other sectors where employment growth returns to base in the long run, leaving 'effective labour' growth increased by 0.1 percentage points.

In the COMPACT model the longer simulation horizon does allow the improvement in the growth rate of technical progress to manifest itself completely in the behaviour of output and investment, both of which show the full 0.1 percentage point increase in growth. Although the growth rate of employment returns to its base-run value, the level of employment never returns to its original values and instead settles down some 0.5 per cent lower. As in the first experiment the adjustment of the COMPACT model to the new equilibrium is protracted, with large short-run fluctuations occurring before equilibrium is reached. The growth rates of output and investment both jump sharply in the first quarter by 0.53 per cent and 1.04 per cent respectively, increase again in the second quarter but then fall back for the following year. Both increase steadily for the rest of the simulation. By contrast employment changes very little, increasing to a maximum response 0.07 per cent above base after three quarters. This small employment gain is eliminated by the end of year 5. The initial volatility of output is reflected in productivity growth itself, before the model starts to settle down.

The increase in the growth rate of technical progress is assumed to be confined to the UK economy. In each of the models the level of employment is lower as a result of the shift in technology, but output is higher, its level continuously diverging from base-run values. Clearly this extra output has to be consumed either by the domestic market or overseas, and these compositional effects differ across the models, as shown in Chart 11.

In the HMT model lower prices and higher interest rates lead to initial nominal and real appreciations of the exchange rate. The real appreciation worsens competitiveness stimulating imports and depressing exports. This has an adverse effect on the terms of trade, pushing up unemployment. However, the interest rate falls below base in quarter 5, so the nominal exchange rate depreciates. Prices fall by less, giving a real depreciation. The increase in competitiveness which results helps exports recover quickly, and the improvement in the terms of trade position helps dampen unemployment.

The income tax rate moves to target the deficit ratio, with a downward trend in the basic rate during the second part of the simulation, corresponding to the increase in the tax base. This gives higher real personal disposable income and hence increases in consumers' expenditure, which is 0.66 per cent above base in the final quarter. The lower income tax rate assists in dampening unemployment through its role in the wedge variable.

In the NIESR model interest rates are 0.1 percentage points higher in each of the first three years of the simulation, then continue to rise very gradually, being 0.2 percentage points higher by the end of the simulation. This ensures that the small initial increase in inflation is eliminated by the fifth year. Although this interest rate profile might lead us to expect a slight appreciation of the nominal exchange rate, both nominal and real rates decline, ending up 5 per cent and 2 per cent lower respectively in the final period. This exchange rate response accounts for the behaviour of net export demand, which increases steadily as a proportion of the increase in GDP, accounting for 78 per cent of this by the end of the simulation compared to 14 per cent and 7 per cent for investment and consumption, as shown in Chart 11. The contribution of consumption is negative for the first 14 years of the simulation, while that for investment is virtually zero.

Consumption growth is 0.1 percentage points higher by the end of the simulation as higher real personal disposable income and wealth offset the depressing effect on consumers' expenditure of increased unemployment. The rise in disposable income is enhanced by the fiscal solvency rule which, after a short-lived increase in the basic rate of income tax of about 0.1 pence, reduces the tax rate to 0.3 pence below base by the end of the simulation. The fiscal policy rule aims to hold the PSBR/GDP ratio at its base-run values, and higher GDP growth not only improves the public finances, ceteris paribus, as noted above, but also reduces the ratio, ceteris paribus.

In the COMPACT model a long-run depreciation of the real exchange rate is required to bridge the gap between domestic demand and output. Immediately after the shock is implemented there is a large fall in the nominal exchange rate and a corresponding jump in prices and hence the inflation rate. Interest rates increase in line with inflation and this moderates and then reverses the depreciation. The inflation rate falls below base in the thirteenth year, but finally returns to its original level at the very end of the simulation horizon. Both the nominal exchange rate and the price level eventually reach new lower levels just below base, giving a long-run real depreciation of about 4.3 per cent.

This improvement in competitiveness ensures that the increase in technical progress is fully reflected in output as exports increase throughout the simulation. In the HMT and COMPACT export equations the presence of a term in cumulated investment of the UK relative to the rest of the world, representing 'quality' (Owen and Wren-Lewis, 1993), reinforces the competitiveness effect. In the COMPACT model non-oil exports increase by 3.85 per cent by the final quarter of the simulation. Despite both competitiveness and cumulated investment terms working in the opposite direction and the absence of any improvement in technical progress elsewhere, non-oil imports also increase in the COMPACT model.

The increase in the growth rate of output expands the tax base and in order to satisfy the debt ratio target the basic rate of income tax has to fall. By the end of the simulation the basic rate is 3.63 percentage points lower in the COMPACT model. The combined impact of this tax cut and the increase in real wages described above stimulates domestic demand ensuring that most of the increase in output is consumed at home. Consumers' expenditure is below base for the first thirteen years reflecting both initial higher interest and tax rates, but once the interest rate returns to base and the tax rate starts falling, consumers' expenditure increases steadily, finishing 7.44 per cent higher at the end of the simulation. This increase in domestic demand combined with the real exchange rate depreciation sucks in imports which are eventually 2.15 per cent higher However, the response of exports ensures improvement in the domestic trading position.

The responses of unemployment and real wages are shown in Charts 12 and 13. In the NIESR model the level of the real wage increases steadily throughout the simulation as does real wage growth which ends up around 0.1 percentage points higher by the last year of the simulation. The unemployment rate and the 'population needing work' ratio increase throughout the simulation without appearing to stabilize at a new higher level.

For the first 11 years of the COMPACT simulation wages and prices rise in line with each other. They then decline, but wages lag behind prices and finish permanently higher giving a final increase in average real wages of 5.92 per cent. The level of the wage bargain achieved reflects the level of average productivity while the price level depends on the change in marginal productivity. The increase in the NAIRU in this simulation mirrors the increase in the ratio of average to marginal productivity, this worsening occurring despite a reduction in the maximum vintage of machinery in use which by itself would tend to reduce marginal costs and hence the natural rate. With lower employment fewer people enjoy the increased real wage or the reduction in the basic rate of income tax that also occurs in this simulation.

For the HMT model average earnings fall during the initial stages of the simulation, but this is soon reversed and average earnings rise throughout the remainder of the simulation, stimulated by the continual increase in the level of productivity. The growth rate exceeds that of prices, hence real wage growth is increased, by an amount which matches the increase in technical progress at the end of the simulation. The unemployment profile in Chart 12 suggests that the beneficial effect on the NAIRU in this model of an increase in productivity growth is beginning to appear by the end of the simulation.

4. Conclusion

In the textbook neoclassical growth model it is the growth rate of technical progress, together with that of the population, that determines the overall rate of economic growth. Our conclusion from the results presented in this article is that this is also broadly true of three economy-wide empirical models of the UK economy. Increases in technical progress are fully reflected by increases in productivity and hence by increases in the real wage received by workers. However the models also suggest that the transition to a new equilibrium following a technology shock is protracted and may possibly result in permanent technological unemployment.

An increase of 1 per cent in the level of technical progress is expected to leave the natural rate of unemployment unchanged. Only in the COMPACT model is this clearly the case, where employment does eventually recover to its original level and the 1 per cent increase in productivity is achieved through an equivalent increase in output. The NIESR model suggests that the same productivity increase is achieved with a smaller workforce and an increase in output of less than 1 per cent, a result which is due to the reaction of the public sector. An increase in the growth rate of technical progress results in an increase in the growth rate of output in each of the models. However it is only in the HMT model that this change might reduce the NAIRU. The other two models show a substantial permanent increase in the unemployment rate although those remaining in work enjoy increased growth in their real wages.

Macroeconometric models provide an internally consistent account of the main macroeconomic responses to an external shock. Their system-wide perspective is their main distinguishing feature from partial empirical analyses that focus more sharply on specific questions, but difficulties of measurement and explanation are common to both modes of analysis. For the technical progress question, a key measurement issue is that of accurately recording and evaluating improvements in the quality of output, which assumes particular importance in parts of the public sector and the services sector where output measurement is based on measures of labour input. Whereas an economy-wide aggregate treatment might mask distortions of this kind, a more disaggregate treatment that attempts to distinguish possibly different behaviour in these sectors is potentially at risk from the mismeasurement of the contribution of technical progress. Some of the model-based results reported above are no more or less at risk from this issue than other kinds of analysis. Explanations of technical progress at the macroeconomic level are similarly difficult to obtain, hence in model-based analysis it is treated as an exogenous variable. Attempts to explain it by relating it to such variables as research and development expenditure or indicators of patenting activity at levels of aggregation much beyond individual case studies have not proved successful, and endogenising it in this way in an economywide model would in turn require explanations of those "explanatory" variables.

The models considered in the present article are national-economy models, with the rest of the world treated as exogenous, and the changes in technical progress that are implemented in the models apply only to the UK economy. These exercises provide useful insights into the supply-side responses of the models, but to the extent that technological change is a global phenomenon, with innovation being rapidly transmitted among the industrialised nations, our results do not represent accurate forecasts. Equivalent technical progress shocks in the UK's trading partners might be expected to produce similar supply responses, but demand might respond more quickly thanks to the trade mechanism. Nevertheless single-country competitiveness gains should no longer be a feature, hence the export share of growth might be expected to be less than that shown in our results. Findings along these lines are reported by Giorni et al (1995), who compare the results of single-economy and area-wide changes in trend productivity using the OECD's INTERLINK model and show that overall adjustment towards long-run equilibrium is significantly speeded up in the case of an area-wide shock. The extension of our analysis to the domestic effects of global technological changes is a future research task.

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