Explaining price inflation in the UK: 1971-92.

Soteri, Soterios ; Westaway, Peter

Introduction

The late-1950s and 1960s were, by recent standards, a period of low and stable inflation(1). Since then, however, inflation has been both higher and more volatile peaking above 24 per cent in 1975 in the wake of the quadrupling in the world price of oil. As a consequence, the control of price inflation has become a central concern of macroeconomic policymakers. In the 1970s, the policy response was often to rely on some form of direct control of prices and earnings through incomes policies. By contrast, the Conservative administration from 1979 onwards eschewed all forms of market interference instead relying on the more explicitly macroeconomic policies of monetary control. At first, these took the form of announced targets for the broad monetary aggregates (initially |pounds~M3), but through the 1980s the specification of the Medium Term Financial Strategy (MTFS) evolved to allow a more flexible assessment of 'monetary conditions' which allowed a wider range of indicators to be monitored. Nevertheless, the primary aim of policy remained the control of inflation. The commitment of sterling to the exchange rate mechanism in February 1990 was a logical extension to this approach. The failure to maintain this policy is, by now, well known and the subsequent relaxation of policy in the wake of ERM departure has clearly represented a shift in emphasis away from pure inflation targeting towards a more active concern for the maintenance of output. Nevertheless, recent policy statements, in particular with the announcement of an inflation target of 1-4 per cent for the forthcoming year, have been at pains to preserve the role of the inflation objective in the overall policy framework.

If inflation is to play such an important role in the policy framework, it is crucial to be able to explain its behavior. The objective of this note is to do this by employing the system of estimated wage and price equations embodied in the National Institute macroeconomic model. Obviously, inspection of the individual equations alone cannot tell the whole story since wages and prices are simultaneously determined. Consequently, one needs to derive the reduced form of the wage-price system in order to decompose the explanation of the inflation path into contributions from each of the explanatory variables and residuals in the system. We adopt a similar methodology to that described for the Treasury model in Rowlatt (1993) although our analysis differs in an important way because of the forward-looking nature of our system. As in this previous exercise, our explanation of inflation concentrates on its proximate causes, since we treat all the non-price variables, e.g. unemployment, world prices, capacity utilisation, as exogenous to the wage-price system despite the fact that many of these are endogenous in the full Institute model. This will tend to overstate the predictive power of the complete model and indeed, on this basis, the short term forecasting ability of the system is fairly accurate. This is especially the case if we assume that the lagged value of inflation is known. It is more informative, in seeking to 'explain' the prevailing rate of inflation, if we decompose both the lagged and contemporaneous effects into the 'quasi-exogenous' factors. This allows us to decompose the historical trajectory of inflation into those effects arising from world price movements, domestically generated influences and an unexplained category.

The plan of the rest of the note is as follows. First, we briefly describe the main measures of price inflation and how differences in definition have recently caused variations amongst the most commonly adopted inflation measures. We describe an underlying measure of inflation which largely resolves these definitional differences. Secondly, we describe the wage-price system of the National Institute model, with particular reference to the theoretical framework of imperfect competition in goods and labour markets. Finally, we conduct a diagnostic breakdown of inflation conditioned on the variables used in the wage and price equations.

Inflationary profile

The two most common measures of the UK's inflation rate are the annual growth rates of the retail price index (RPI) and the consumer expenditure deflator (CED). The RPI is a chain-linked monthly base weighted index for a representative basket of goods and services, where the weights are updated each January. By contrast, the CED is a current weighted quarterly price deflator which applies to all consumers' expenditure. The most important difference in coverage applies to the treatment of the consumption of private housing services; the RPI includes a component to capture mortgage interest payments while the CED includes an imputed rent component.(2) For more definitional details, see HM Treasury (1990).

Both measures, given in Chart 1, show a similar profile of rising inflation in the 1970s followed by a subsiding rate in the 1980s. However the severe tightening in monetary policy, which produced a jump in base rates from 7.5 to 15 per cent in the space of 18 months, and the subsequent dramatic easing in policy following sterling's withdrawal from the exchange rate mechanism has caused the two series to diverge significantly since 1988.

Treating the community charge in the same manner as the original household rates series in the CED, thereby making it consistent with the way it is treated in the RPI, and excluding the consumption of private housing services from both series, yields a measure of underlying inflation. This eliminates the factors which account for most of the divergence between the two series, as indicated by Chart 2. This measure of underlying inflation will be the main focus of the empirical analysis in this note.

Wage and price determination in the National Institute model

The underlying rate of price movements in the Institute model is captured by appealing to the theoretical price setting behaviour of profit maximising firms which negotiate their labour costs within an imperfectly competitive environment. This 'structural' approach deliberately conditions on those variables which impinge on the wage and price setting decisions. This means, of course, that we are only investigating the proximate causes of inflation but it does allow us to ask what effect the 'quasi-exogenous' variables such as foreign prices, the exchange rate, capacity utilisation or unemployment have had on the profile of inflation. It precludes however, an investigation of the more fundamental causes of the inflationary process which could include an investigation of the effects of monetary policy on these 'quasi-exogenous' variables. It is perhaps worth emphasising, therefore, that the analysis of this note neither confirms nor contradicts a monetarist analysis of the inflationary process which attributes a causal link between the rate of growth of the money supply and the rate of change of prices.

We begin by describing the theoretical framework within which our estimated price and wage equations may be interpreted.

Price setting

The price setting behaviour of firms is based on the imperfectly competitive framework described in Layard and Nickell (1986). It is assumed that firms possess Cobb-Douglas(3) constant returns to scale production technology with two factors of production, labour and capital. Domestic producers are assumed to possess a degree of monopoly power which allows them to behave as price setters subject to the demand function for their output. This yields the standard expression for the profit maximising price level given by

P = |Upsilon~ W(1 + |T.sub.e~)/|Alpha~(Y/L) (1)

where |Upsilon~ is inversely related to the price elasticity of demand, W represents the nominal wage rate, |T.sub.e~ is the rate of tax paid by employers on labour, Y is value added output, L is employment and |Alpha~ is the elasticity of output with respect to labour in the production function.

Equation (1) simply states that the price level will be a mark up, |Upsilon~, on marginal costs. If the elasticity of demand is a constant, it follows that the mark up will also be a constant and prices will change proportionately with marginal costs. Pricing behaviour will be similar in this respect to that followed by a perfectly competitive industry.

However the mark up may vary systematically if the price elasticity of demand is not constant. It is possible that this varies over the business cycle(4) and over time(5). It may also vary systematically with the real exchange rate. For example a higher real exchange rate will encourage domestic producers to reduce their margins in order to remain competitive.(6)

The CED and the RPI are price indices of gross output and therefore include inputs within the production process and imported final goods.

This suggests that they should be modeled as

|P.sup.g~ = h(|Upsilon~ W(1 + |T.sub.e~)/|Alpha~(Y/L), PC, m) (2)

where m represents the cost of inputs and PC refers to overseas competitors' prices.

This simple static stylised model represents the Institute model's long-run pricing structure. It needs to be augmented with a dynamic structure, and this in our model is based on customer search theory. Consumers do not have perfect information at any point in time, which suggests that they obtain price list samples on related products from a variety of sources. However, obtaining comparative price quotes is a time consuming and costly process. Sellers recognise this and have to trade off frequent TABULAR DATA OMITTED changes in the price level, which encourage search behaviour and may hence reduce the demand for their product, against the penalties for charging prices which are not equal to the long-run profit maximising level. The reputational loss model of Rotemberg (1982) incorporates an intertemporal quadratic loss function that penalises both actual price changes and deviations from the desired price level. The period-by-period loss function (L) used in our application is given by

|L.sub.t~ = a|(|p.sub.t~ - |p*.sub.t~).sup.2~ + b|(|p.sub.t~ - |p.sub.t-1~).sup.2~ (3)

where p* is the desired price level and identical to |P.sup.g~ in (2).

The dynamic optimal pricing path for a firm to follow under these circumstances yields an Euler equation decision rule of the form

|Mathematical Expression Omitted~

where linear homogeneity(7) implies |Beta~ = 1 - 2|Alpha~.

This implies that in the long run prices are subject to condition (2) and that prices move in line with marginal costs, input prices and competitors' prices. However, in the short run prices may be away from their desired level due to costs of adjustment and only gradually converge to their long-run desired level. This form of nominal inertia implies a counter cyclical dynamic mark-up since firms are explicitly squeezing contemporaneous profits for their longer-term benefit (see Martin 1992).

The price equations embodied within the Institute model are estimated using the theoretical specification suggested by equation (4) and given in Table 1.

The estimated GDP equation implies that in the medium term desired value added prices are rising in line with unit labour costs. However if intermediate goods prices or competitors' prices start to diverge from the value added price this will cause producers to absorb some of this effect by varying their profit margins. The utilisation variable(10) indicates that the desired mark up on marginal cost rises as demand conditions raise output relative to capacity and implies that profit margins are expanded during periods when demand is rising relative to output growth. Finally a cost of holding stocks term, which is effectively a real interest-rate term, is also included to capture the opportunity cost of maintaining inventories.

The dynamics are best understood by concentrating on the parameter |Mu~ which can be interpreted as measuring the speed of response to the desired price level. If |Mu~ is zero prices are instantly adjusted to their desired level whereas as |Mu~ tends to unity the slower the adjustment process becomes. The price dynamics, although embodied within a forward looking structure, are not necessarily faster than those which could be estimated using a backward-looking specification.

The manufacturing producer price equation and the consumer expenditure deflator excluding oil and private housing consumption can be analysed in a similar manner. However it is noted that they are gross price indices and hence include various input terms as suggested in (2).

Wage formation

Since the early-1980s it has become popular to analyse aggregate wage behaviour within a bargaining type framework (see Nickell and Andrews, 1983). The bargaining process is usually modeled by limiting firms and unions to bargain only over a fixed nominal wage rate to cover a particular period. Given the real wage, the firm is assumed to retain the 'right to manage' and set employment unilaterally according to its labour demand function.(11) The bargaining theory used to solve the competing aims of both the firm and the union over the nominal wage is the Nash Cooperative Solution (Nash 1950). The derivation of the aggregate wage equation implied by this framework is well known and is described in detail in Layard et al. (1991). Equation (4) gives the basic specification

W/P = 1/(1 + Te) Y/N |Iota~|(|Gamma~(1 - RR)).sup.-1~ (4)

where P is the value added deflator, RR is the replacement ratio (B/W), |Gamma~ is the probability of being unemployed and |Iota~ is the relative discount rate of each party in the bargain.

The Nash solution indicates that the bargained real wage will be rising with productivity and the expected opportunity wage a union member can obtain if made unemployed. The solution will also depend on the relative discount rate of each party, i which gives an indication of each side's bargaining strength.

In fact, the estimated model of wage behaviour does depart from the theoretical predictions of this model in some important ways. Table 2 gives the wage equation embodied within the Institute model.

This wage equation assumes that real earnings in the long run rise in line with productivity and fall as the probability of re-employment declines. The re-employment pressure term traditionally used in wage equations is the unemployment rate. However the Institute Model incorporates a term in the 'population not working rate'. This is simply 1 minus the ratio of employees in employment to a measure of the population of working age. In estimation, this measure performed better than the total unemployment rate perhaps due to the nature of the claimant definition of unemployment, see Wren-Lewis (1989) and Gregg (1990). It is modified by an effect from the ratio of long and medium-term unemployed, capturing the fact that the unemployment of these workers may be less likely to affect the re-employment probabilities of those involved in the bargaining process. An industrial mismatch variable is also included, which relates to relative movements in employment in the manufacturing and non-manufacturing sector. This is effectively a measure of industrial turbulence, which Layard et al. (1991) argue affects the aggregate re-employment probability.

Measures of relative union strength are not readily available. Union density, used as a proxy variable, was consistently wrongly signed, as was the benefits to earning ratio.

It should be recalled that the theoretical model underlying the wage bargaining structure does not require the presence of a tax or import price term. In a bargaining framework where effective labour supply is fixed the multiplicative nature of the tax terms causes them to disappear. This is because the theoretical framework essentially concentrates on each party's utility function relative to some fall back level and is hence independent of any scaling parameters such as multiplicative tax rates. This should imply using the value added deflator rather than the consumer expenditure deflator in the empirical specification. Econometrically, however, such an effect from the 'wedge' between these price indices is often significant and necessary, presumably because the relatively short data set (1966q1-1991q4) does not allow a fine distinction to be made between truly long-run effects and highly persistent variables.(13)

Table 2. Factors affecting the determination of wages

Long-run elasticity with respect to Compensation wage
 equation(a)

Value added prices 1.0
Productivity 1.0
Proportion of population not working -0.2
Proportion of long and medium-term unem-
ployed 0.8
Industrial mismatch 3.6
WEDGE(12) 0.3

Notes:
(a) The compensation wage includes employers' national
insurance contributions plus other employee benefits.

The dynamics of this equation are based on the existence of annual wage contracts, see Taylor (1980). Each period, one quarter of all wage settlements are negotiated by agents who will look forward, trying to anticipate prices and other changes, over the forthcoming year for which the contract will apply. However, aggregate earnings indices also reflect past events since they will result from contracts struck in the three previous quarters. In the empirical manifestation, originally described in Moghadam and Wren-Lewis (1989), more complex dynamics are included reflecting the fact that wage contracts will be partly influenced by bargains struck by other wage setters.

Import prices

The system of wage-price equations described so far has comprised three main price equations (for the PGDP deflator, the CED excluding oil and imputed rent and wholesale manufacturing prices) and one equation for average earnings. We are interested in the explanation of these variables for given trajectories of the 'quasi-exogenous' variables. Import prices, however form an intermediate category. In some cases, for many imported intermediate goods for example, these will be set independently of pricing behaviour in the UK. In others, however, importers may price to market thus introducing an effect from UK prices. Similarly, imports which appear as part of final expenditure are likely to be priced by domestic retailers in a way which reflects UK market conditions. Unless stated otherwise, import prices will be treated as endogenous variables in the analysis that follows. For more details of the estimated import price equations in the Institute model, see NIESR (1993).

System properties

In order to understand the mechanics of the wage-price spiral in the Institute model, it is useful to set down a simplified stylised three equation model determining, gross prices, unit labour costs and import prices(14). Equation (5a) determines prices (p) as a weighted average of unit labour costs, import prices (pm) and an exogenous component |X.sub.p~. Equation (5b) determines unit labour costs (w) also as a weighted average of prices, import prices and another exogenous component |X.sub.w~. Equation (5c) sets import prices to grow in line with world prices |p.sub.w~ deflated by the sterling exchange rate (e).

p = |a.sub.1~w + (1 - |a.sub.1~)pm + |X.sub.p~ (5a)

w = |b.sub.1~p + (1 - |b.sub.1~)pm + |X.sub.w~ (5b)

pm = |p.sub.w~ + e (5c)

Despite the simplicity of this system, it captures the key aspect of the standard wage-price system analysed so far; the firm wishes to fix prices subject to input costs and a mark up over labour costs whilst employees wish to mark up their wage over prices. This is the familiar wage-price spiral which continues until specific factors to each side modify their behaviour and reconcile their competing aims. The long-run effect of any of these factors is easily derived by solving the reduced form of the system as follows;

p = pm + S (|X.sub.p~ + |a.sub.1~|X.sub.w~) (5a|prime~)

w = pm + S (|b.sub.1~|X.sub.p~ + |X.sub.w~) (5b|prime~)

where S = 1/(1 - |a.sub.1~|b.sub.1~).

Here, the term S may be interpreted as the wage-price spiral effect, since it indicates the extent to which the ex ante effects of a shock to an exogenous factor will be multiplied up through the wage-price spiral to give the ex post effect. For example, in the case of the Institute model, an ex ante shock of 1 per cent to the average earnings residual will have an ex post effect of around 10 per cent(15).

The reduced form characterisation also illustrates clearly the static homogeneity of the wage-price system with respect to changes in import prices. Hence in this simple system, a devaluation of the exchange rate will feed fully into the price level with no lasting effect on competitiveness. In the Institute model itself, this effect will occur more slowly so that there will be temporary gains in competitiveness (see Westaway (1992) for example). In fact, the speed of return to equilibrium in the Institute model is somewhat quicker than in other large macroeconomic models, mainly because of the forward-looking dynamics already described. Nevertheless, a devaluation still takes some seven years for 99 per cent of the effect to work through to the price level(16).

It is also possible to decompose the explanation of changes in inflation into the different contributions from the exogenous variables. We turn to this analysis in the next section.

Explaining inflation

Given the system of equations determining wages and prices in the Institute model, it is possible to 'explain' the historical profile at a number of different levels. In what follows, attention will be focused on the underlying measure of the CED already described. The first and most simple technique is to examine the one-step ahead forecasts for prices taking everything else as given. Chart 3 illustrates. Clearly, most of the path of prices is captured by the independent and lagged dependent variables in the equations. Of course, this tells us relatively little about our true ability to forecast inflation because of the contemporaneous influence of wages and the other prices which will be simultaneously determined. To remove this dependence, therefore, we can compute the one-step ahead 'system' forecast for prices on the assumption that only lagged values of endogenous prices are known(17).

Since our equations contain a lead in the dependent variable, we carry out this exercise by assuming that expectations are formed with perfect foresight. Chart 3 illustrates the consequent decline in explanatory power relative to the single equation error although the overall fit remains good.

Importantly, however, a large proportion of this 'explanation' is still provided by the contribution of the lagged dependent variables. While this is perfectly acceptable if we are solely interested in the short-run forecasting ability of the wage-price system, it does not explain why inflation arrived at that particular level. We therefore need to 'explain' the lagged dependent variable too. In Rowlatt (1993), this is done by inverting the dynamic reduced form equation to express the price variable purely in terms of 'quasi-exogenous' variables (known there as the 'indirect reduced form' method). Here, we achieve the same 'explanation' using a different route. We use the Institute model itself to compute the diagnostic breakdown into the separate exogenous contributions. Our method measures the contribution of a variable, say unemployment, by comparing actual inflation with what inflation would have been, according to the wage-price system of the model, if unemployment had remained constant throughout the period.

Charts 4a-4c plot the actual level of underlying inflation and the respective contributions of the explanatory variables.

It is convenient to begin with import prices. As we saw from the stylised model, in long-run dynamic equilibrium, UK inflation will be equal to world inflation plus the rate of depreciation of sterling(18).

Chart 4a shows the contribution of these world factors to domestic inflation, first allowing exchange-rate movements to feed into import prices, then holding the exchange-rate trajectory flat in order to isolate the contribution from world price movements alone. Clearly, the overall influence is considerable, suggesting that world inflation was a major contributor to the increasing rate of underlying inflation rate in the early-1970s, and also a major factor behind the reduction in the early-1980s. But despite this strong effect, there is still a large amount of UK inflation to be explained over and above world prices. A depreciating currency added over 5 per cent to the inflation rate both in the mid-1970s and in the early 1980s when the dollar was appreciating strongly.

Charts 4b and 4c analyse the contributions from domestic factors(19). As emphasised above the overall effects of these factors on the domestic inflation rate are not simply the immediate first round consequences, but also include the manner in which they are passed on or 'marked up' in other prices, then in wages and back to prices and so forth. This wage-price spiral is sometimes referred to as 'the battle of the mark ups' between employers and employees.

The equations embody three types of pressure of demand effects in the goods and labour market. The first reflects the willingness and ability of employees to push for higher real wage demands. The wage bargaining framework suggested above implies that workers are attempting to maximise their expected income which depends on their re-employment probability if they become unemployed and the wage rate they receive if they stay in employment. These two factors are inversely related and hence we should expect underlying inflation and labour utilisation to move in opposite directions. The second way demand pressure feeds into the system is via the behaviour of price mark ups with respect to utilisation levels in the goods market, a hotly debated issue. The estimation results quoted in Table 1 indicate that the Institute model incorporates a pro-cyclical mark up.

Chart 4b illustrates the combined effects of labour and goods market demand pressures. Compared to the level of inflation itself, these effects are not large, but inflation is raised by around three percentage points during the boom years of the 1980s, before it declines sharply in the latter years of the decade, taking some three percentage points off inflation during the recession of 1992.

The final demand pressure effect arises from the industrial mismatch term which effectively measures the degree of employment turbulence between sectors. The large shake out in manufacturing employment which occurred around 1979 caused a large number of workers to become unemployed at a time when their skills were obsolescent. This, it may be argued, led to the unemployed pool becoming less effective in reducing wage pressure and hence put upward pressure on underlying inflation. However as unemployment began to spread towards other sectors this effect became less important in the 1980s. Interestingly, Chart 4b illustrates that during the most recent recession this is having a relatively small effect in comparison to 1979/80, because of its more even sectoral impact.

Chart 4c illustrates the contributions to inflation from different tax variables; employers' national insurance contributions, employees' direct tax rates and expenditure taxes. These clearly exerted significant positive inflationary pressures between 1974 and 1983. The combined effects of rising employer and expenditure taxes more than offset the falling average direct income tax burden over this period. The cost of holding stocks term reflects two factors: the ending of stock relief in 1981 and the high level of real interest rates. Chart 4c shows how this variable exerted downward pressure on underlying inflation in the early to mid-1970s, due to the favourable tax relief allowance available on holding stocks and the existence of relatively low and sometimes negative real interest rates. However the opposite was true from 1980 onwards when tax relief was abolished and real interest rates turned sharply positive. Since 1987 the effects arising from this variable have been minimal.

Having calculated each of the individual effects, it is now instructive to combine them. Chart 5a shows all the identified effects together with the dummy variables included(20) in the model, as well as the residual or unexplained category(21); Chart 5b separates out the contribution from domestic and overseas influences. As we would expect, the main characteristics of the profile for underlying inflation over the last twenty years are captured by the model equations. Perhaps the dominant contribution comes from world prices which give the overall trajectory its characteristic feature of high inflation in the 1970s falling to much lower single figure levels in the 1980s. Of course, the average absolute size of the residual category is much larger than the forecast error plotted in Chart 3. (Recall that in Chart 3, the lagged value of inflation was taken as given).

From the late-1980s onwards, the system tends to exaggerate the extent of the inflationary slowdown, suggesting that in recent years the UK economy should have experienced a period of near price stability. This deterioration in explanatory power reflects the single equation residuals in the average earnings equation where problems have emerged. Any improvement in explanation therefore requires a more exhaustive analysis of this individual equation. This will not be attempted here but a number of comments may be relevant.

First, it is worth observing that ERM credibility or the effects of labour market reforms in the 1980s might be expected to cause the model to over predict inflation. Since our equations actually under predict in recent years, we would not expect these factors to improve the explanatory power of our model. Rather, our favoured explanation would focus on the role of domestic utilisation effects, as highlighted in Chart 4b, which according to the equation should be putting downward pressure on inflation during the late-1980s. It seems likely that conventional measures of unemployment which are supposed to be proxying the probability of wage bargainers becoming unemployed may have become increasingly unreliable. This is known to occur as unemployment rises to high levels, although we have attempted to capture the declining influence of the long-term unemployed in reducing wage pressure by including an extra term in short-term unemployment. Nevertheless, some measure of re-employment probability which makes more explicit use of information regarding inflows and outflows from unemployment may yield more robust results in the future.

Concluding remarks

The analysis described in this note has been carried out on the wage-price system of the National Institute model. It parallels and updates a similar analysis carried out on the HM Treasury model which accounted for inflation up to 1986. For the Institute model, it shows a significant role for world inflation and the exchange rate via import prices in explaining the increased levels of inflation in the 1970s and the declining rates in the 1980s. Changes in the rate of utilisation of goods and labour also provided a significant additional influence with direct unemployment effects taking as much as 3 percentage points off the inflation rate at the height of the 1980 recession but adding over 3 percentage points at the peak of the 1980s boom. Interestingly, however, the rate of inflation over the last five years has tended to be higher than can be explained. We have suggested why the conventional explanation for aggregate earnings behaviour may be breaking down but have argued that a deeper analysis of this question is still required.

NOTES

(1) Inflation, as measured by the annual growth rate of the retail price index, fluctuated within the range of 0-5 1/2 per cent over this period.

(2) Household rates were treated equivalently in the two indices. After 1989-90, the community charge was excluded from the CED on the grounds that it was not related to housing consumption. For simplicity, in this note, we adjust our definition of the CED to remove this discontinuity between the two series.

(3) Cobb-Douglas technology is used for simplicity and clarity. Alternative functions may be used but it would not change our qualitative conclusions.

(4) Cyclical variations in the price elasticity of demand have been hypothesised in a number of papers. Unfortunately the debate as to whether the mark up varies pro-cyclically (see Flaig and Steiner, 1990) or contra-cyclically (see Bils 1987 and Rotemberg and Saloner 1986) has not been concluded.

(5) The price elasticity of demand is assumed to reflect the degree of competition within the market for a given product. Therefore Romer (1991) suggests that the increased level of world trade and hence international competition should be reflected in long-term trends in the price mark up.

(6) This effect is emphasised by Young (1989) and Darby and Wren-Lewis (1991).

(7) This assumption is equivalent to having a unit discount factor in the intertemporal cost function.

(8) This is the consumer expenditure deflator (CED) excluding imputed rent on private sector dwellings and including the community charge. The model contains separate equations for imputed rent and community charge components in order to obtain the aggregate deflator.

(9) |Mu~ is the dynamic parameter corresponding to |Mu~ in equation (4). |Mu~ is a speed of response parameter and is obtained by using the lag operator and solving its stable root, such that |Mu~ = {1 |+ or -~ ||1 - 4||Alpha~.sup.2~~.sup.0.5~}/2|Alpha~.

(10) The utilisation variables used are four quarter moving average real growth rates of GDP or consumption designed to proxy demand relative to capacity output rates, for which no data exist outside the manufacturing sector.

(11) Efficient bargains which concentrate on both the wage and employment levels have been shown to yield Pareto superior outcomes (see McDonald and Solow 1981) however the applied literature has mainly focused on the 'right to manage' approach since it is argued to more closely fit the stylised facts.

(12) The wedge is defined as log(ced/pgdp * (1 + ter) * (1 + td)) where ced is the consumer expenditure deflator, pgdp the GDP deflator, ter a measure of employers direct labour costs over and above the wage bill and td is a measure of direct taxation on earnings.

(13) Layard et al (1991) make the same point in justifying the inclusion of an import wedge component in their UK wage equation, see p. 441, table 15.

(14) This is a simplification of the system on the Institute model since it abstracts from the effects of manufacturing wholesale prices.

(15) As |a.sub.1~|b.sub.1~ approaches unity, so the magnitude of the spiral effect will come to be dominated by the endogenous effects of prices on the X variables which are being treated as exogenous in this exercise.

(16) This speed of adjustment refers to the wage-price sub-system with the quasi-exogenous variables fixed.

(17) In Rowlatt (1993), this explanation of inflation was described as the 'direct reduced form method'. The question of how to form expectations did not arise there because of the backward-looking nature of the equations used.

(18) Again, it is worth noting that this would be quite consistent with a monetarist account of the inflationary process if a given rate of domestic monetary growth relative to the rest of the world led to a corresponding rate of depreciation in the exchange rate.

(19) Of course, the factors that we have labelled as domestic may also have been influenced by the exchange rate.

(20) Dummy variables have been included in the dynamics of the wage equation and certain price equations to capture the effects of incomes policies in the mid-1970s and the three-day week. These effects have been included in Chart 5b as a domestic influence.

(21) The residual category also includes the lagged effects of the lagged dependent variables in the initial period. Because of the model's relatively quick dynamics, these effects are negligible after two years.

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