Forward-looking wages and nominal inertia in the ERM.

Anderton, Bob ; Barrell, Ray ; Veld, Jan Willen in't 等

The purpose of this note is to discuss the role of forward-looking behaviour in wage formation in the major economies, and to analyse the implications for policy analysis using the National Institute Global Econometric Model, NIGEM. Our policy analyses are directed at issues relating to the ERM. The first section of the note discusses nominal inertia and staggered contracts (see Taylor, 1980), whilst the second discusses bargaining and wage formation, using the analysis discussed in Layard, Nickell and Jackman (1991). The third section discusses some empirical work on wages undertaken at the Institute, whilst the fourth section analyses the implications of forward-looking wages for our model NIGEM. The final section concludes.

Nominal inertia and staggered contracts

Most economies appear to display a considerable degree of nominal inertia, in that it appears to take some time for wages and prices to adjust in order to "crowd out" a nominal or real demand shock.(2) Early work on wage inertia assumed that expectations were formed adaptively using past information. Although this did produce a considerable degree of inertia in estimated wage-price systems, it can be seen as inconsistent with rational behaviour. Wage bargainers using adaptive expectations would make consistent errors, and the introduction of rational, or consistent, expectations into the bargaining framework appeared to reduce the theoretical justification for observed nominal inertia. In a series of seminal papers Taylor (1979, 1980) demonstrated that the combination of overlapping, or staggered contracts and consistent expectations will result in substantial nominal inertia.

Staggered wage contracts occur when different sections of the workforce negotiate wage contracts at different times. Moghadam and Wren-Lewis (1989) use this notion of staggered contracts to demonstrate how the current wage is an aggregate of the price expectations of different time periods.(3) They assume rational expectations, annual contracts and four negotiating groups of equal size with only one group negotiating in any particular quarter. Consequently, combined with the assumption that each group is entirely forward looking, they show that the aggregate wage in any individual quarter depends upon a symmetric distribution of both past and future price levels.

Define

[W.sub.i] = wage contract negotiated at time i [PJ.sub.i] = expectation of price level J periods ahead held at time i [WA.sub.i] = aggregate wage level at time i [P.sub.i] = price level at time i If settlements last for one year and wage bargainers are totally forward looking after abstracting from other factors, we have:

[W.sub.t] = 0.25([P.sub.t] + [P1.sub.t], + [P2.sub.t] + [P3.sub.t]) (1)

The aggregate wage in period t is made up from bargains struck in four time periods, and hence it is the sum of [W.sub.t], [W.sub.t-1], [W.sub.t-2] and [W.sub.t-3] and we can substitute (1) into this sum and hence write:-

[WA.sub.t] = ([P.sub.t-3] + [2P.sub.t-2] + [3P.sub.t-1] + 4P,

+ 3[P.sub.t+1] + 2[P.sub.t+2] + 3[P.sub.t+1])/16 (2)

This framework gives us a clear idea of the role of forward and backward prices in wage setting. Even in this simple model where agents only look forward the aggregate wage is half forward and half backward looking in terms of prices.

However, the Taylor (1980) model embodies a richer notion of staggered contracts by assuming that the current contract being negotiated is written relative to overlapping contracts in order to preserve the negotiating groups' relative wage. Consequently, wages are set by weighting previous and future rival group wage bargains by the amount of time they overlap the current contract period with some allowance for the extent to which wages adjust to excess demand in the labour market.

In Taylor (1979) the weights on rival group contracts sum to unity and decline linearly into the past and future. Contracts close to the current contract are given most weight, while contracts in the more distant past or future are given less weight. Although the implications of this analysis produce an effect from prices that is symmetric in a forward and backward fashion as in Moghadam and Wren-Lewis, there is a greater degree of inertia as the symmetry is centred around the lagged price level, and also because less weight is given to anticipated contracts the further they lie in the future. Taylor (1980) expands this theme of inertia by analysing wage dynamics under different degrees of forward-looking behaviour.(4) In particular, he demonstrates how the |persistence' of wage inflation is reduced as wage negotiators allocate a greater weight to forward-looking elements relative to backward-looking elements.

It is clear from this discussion of staggered contracts that we would expect that the role of price expectations in the wage bargain would depend upon the bargaining structure of the economy, and in particular upon the frequency with which bargains are struck. The degree to which contracts overlap depends on their duration, and on their distribution over the year. The degree to which one settlement influences another depends upon bargainers' perception of the amount of information that might be contained in a particular settlement, and on the degree of union rivalry and labour mobility. Taylor (1980) and Alogoskoufis (1992) amongst others discuss the degree of persistence in the inflation process. If policy has been non-accommodating then price inflation will have demonstrated little persistence. It is always logical for wages to be forward looking for the period of the contract, but the method of forecasting used will depend upon the persistence of inflation. If inflation is a random walk then changes in it cannot be forecast so it does not make any difference whether bargainers are forward looking or not.

As Lucas (1976) stresses, even the rules of behaviour of the economy may in some sense be endogenous. The frequency with which bargains are struck will depend upon the bargainers' perceptions of the environment within which they find themselves. Re-contracting is an expensive business, and the costs of frequent negotiation have to be offset against the benefits. These will depend in part on the likelihood of expectations being wrong. If bargainers live in a world where inflation is variable and uncertain then they will prefer shorter contract periods than they would if they lived in a world of constant (or no) inflation. The perception of the world that bargainers hold may depend in part on the actions of the authorities and the credibility of their commitments.(5)

We would expect the structure of bargaining to differ between the major economies, in part because their experience of inflation has differed. Some may have wage bargaining institutions with frequent re-contracting, others may have long intervals between bargains. For a given contracting period we should expect that less wage inertia would be observed when wages were more forward looking. Also the shorter the contract period, the less wage inertia we would expect to observe because current information will be fed more quickly into contracts. We would expect countries that have had high and variable inflation, such as Italy, the UK, and to a lesser extent France to have short contracting periods and a significant role for expectations in bargaining. We would expect the low inflation countries, such as Germany and, to a lesser extent, Japan and the US, to have long contracting periods. They may also not need to be particularly forward looking as inflation is not expected to be very persistent, and bargains may only be based around information that is currently available.

There are other reasons why we would expect aggregate wage formation to depend on both backward and forward elements. Some elements of the workforce may not be able to bargain freely over the wage. In the UK, for instance, it is common for public employees to have contracts that allow for backward indexation alone. In France up to 40 per cent of the workforce is covered by minimum wages, and these are set by the State in the light of past wage and price developments. In Japan wage bargains are set up with a very large profit-related bonus element which inevitably reflects past developments. In all these situations it is not necessarily the case that current wage bargains embed only current price expectations.(6)

Bargaining and wage formation

In order to be able to derive estimatable wage equations it is essential that we have a sufficiently well specified theoretical framework. We have adopted that developed by Richard Layard and Stephen Nickell.(7) Unions and employers bargain over the expected real wage, and employers have the |right to manage' in that they are free to choose the level of employment. Workers can be employed by the union firm, work in the secondary sector, or may be unemployed. The bargain can be described by the solution to the one period Nash problem

max [(U([w.sup.*],...) - U).sup.beta] (II(w, ...))

w

where U is the level of union utility and U is the fallback position and II the level of the firm's profit, and [beta] is an indicator of union power. The firm pays w, the real product wage, whilst the worker receives [w.sup.*], the real consumption wage. These differ because the firm's profit depends upon the output price, whilst the worker's utility depends upon the nominal wage net of income tax deflated by consumer prices which are influenced by import prices and by indirect taxes.

The bargain will determine the mark-up of the union over the non-union wage, and it will depend upon factors such as the level of unemployment, the relative power of trade unions and the degree of product market competition.(8) The aggregate wage in the economy will depend, inter alia, on these factors, on the proportion of the population covered by bargaining and by the wage in the non-unionised sector. This in turn will depend upon the level of benefits paid to the unemployed and on the other factors affecting the supply of and demand for labour in the secondary sector.

There has been considerable debate about the factors affecting the bargained wage and we must be careful to include them in our analysis. Of particular interest is the wedge between real producer and consumer wages. Both Hall and Henry (1987) and Moghadam and Wren-Lewis (1989) find a permanent, positive effect of the tax wedge on the producer wage. In a perfectly competitive market with a fixed labour supply the producer wage would be invariant with respect to changes in direct or indirect taxes in the long run, all of which would have to be paid out of the consumption wage. This outcome is not so obvious in a bargaining framework. However, Layard, Nickell and Jackman (1991, see pp 102-109) argue, that as taxes affect both the union wage and the union's fallback position, they should not affect the mark-up, and hence it is possible that in the long run the wedge will not affect the producer wage.(9)

The significance of bargaining with unions will clearly differ both between economies and over time. Around 75 per cent of the workforce is covered by collective bargaining in the major European economies, and coverage has not fallen particularly rapidly. The same cannot be said of the US, where union membership and coverage have both fallen sharply over the last 25 years. Union bargainers can only raise real wages above the competitive level if there is some degree of imperfect competition in product markets. A successful set of bargains will raise the wage above the competitive level, and, as long as the elasticity of substitution between factors in production is not too high, the bargain will raise the share of labour in national income. As a result, part of profit earners' rents have been bargained away. If trade union bargainers gradually lose power, then we would expect the share of labour to decline over time. The situation in the US is particularly interesting. A combination of anti-union legislation, a changing industrial structure, and a gradual drift of industry to non-unionised areas has reduced the power and coverage of trade unions.(10) This, we believe, is an important factor behind the falling share of labour in national income and low real wage growth in the US. The changes in structure and location of industry cannot be seen as independent of the initial existence of a successful union mark-up. Firms in areas with low levels of unionisation were able to make higher levels of profit and to gain market share, and firms in areas with high levels of unionisation would obviously have an incentive to move. It is obviously necessary for us to take these factors into account, both when estimating our wage equations and when analysing the effect of the European single market programme on wages.

Estimation of wage equations with forward-looking

inflation expectations

Our approach has been to estimate wage equations that include both the long-run factors affecting the wage and the bargain and also the factors affecting the dynamics of the wage bargain. We have been particularly interested in testing hypotheses about the presence or absence of variables in our equations, and we have also been interested in testing our equations for structural change. We have therefore avoided using cointegration techniques as they presuppose the absence of structural change. We have estimated error correction equations, and used a general to specific approach. Our producer wage equations were:

[DELATA]log W = a + [b.sub.1] [log W(- 1) - log PP(- 1)]

+ [b.sub.2] log PROD + [b.sub.3] WED + [b.sub.4] U(- 1)

+ [b.sub.5] PE + Dynamics

where W is total compensation per employee hour, PP is our index of the producer price of output, PROD is a measure of average labour productivity in the economy, WED is the wedge between our producer price index and the Consumers' Expenditure Deflator (CED), U is the level of the unemployment rate, and PE is the rate of consumer price inflation expected over the next quarter.(11)

The dynamics on the equation include past terms in the rate of change in the CED and this depends in part on import prices and on indirect taxes. Therefore, even if [b.sub.3] = 0, we have allowed for a short-run tax wedge effect on wages, and this is consistent with the findings in Layard, Nickell and Jackman (1991). The equation determines the real wage in the long run, but the short-run bargain is over the expected real wage. There are a number of propositions to test in this framework. If the supply of labour were fixed, or if all wages were determined by the bargain we would expect real wages to rise in line with productivity in the economy.(12) We would expect the wedge effect to be positive or zero, and in this note we have followed Layard, Nickell and Jackman (1991) and taken our null hypothesis to be that the effect is zero. We have assumed that there should be a role for price expectations, and that the coefficient should be at most equal to one.

We are interested in testing our relationship for structural stability, but our task is made non-standard by the presence of expectation effects. We do not have data on expectations, and hence we have to take as part of our maintained hypothesis the fact that individuals hold expectations that are consistent with the outturn. This does not mean they have to have perfect foresight, but rather that they should not on average be wrong. This allows us to use actual inflation as a proxy for expected inflation. However, we know our proxy measures the actual with error, and hence there can be problems in estimation by ordinary least squares. Even if the errors in the proxy variable are independent of the errors in the equation, the proxy variable will in general have a lower variance (and a different covariance structure) than the true variable, and hence under OLS the estimates of the parameter vector and the variance/covariance matrix of the parameters will be inconsistent. We have estimated our equations by instrumental variables techniques (IV) in order to be able to test hypotheses on individual parameters and on the equation as a whole.(13) We have instrumented price expectations with current and lagged inflation and capacity utilisation. (14) Table 1 reports our results for the major six economies. The results are discussed in detail below, but their overall structure is of some interest. In all cases we could validly accept the restriction that real wages rose in line with productivity in the long run, and generally we found a significant and negative long-run role for unemployment. We tested for wedge effects, and we can only find a role for them in Italy, and then only if we use a narrower definition of the indirect tax rate than that used in the equation in Table 1.(15) All equations have been tested for stability using a Wald deletion test on a set of dummied variables included for half of our sample period. All equations (except that for Italy) pass this test. Further details can be found in Anderton and Barrell (1992).(16)

[TABULAR DATA OMITTED]

The US

Our US equation contains a trade union membership variable. The decline in unionisation in the US has been a major factor behind the fall in labour's share in national income. Our results suggest that the decline in unionisation has reduced the growth in real compensation per person hour by as much as half a per cent a year. Over our sample period we fail to find an adequate equation if this variable is omitted. There is a significant role for unemployment,(17) and that role is stronger if unemployment has been changing recently (and hence the number of short-term unemployed has changed). We have also found a significant role for inflation expectations.

Japan

We could find no significant role for forward-looking expectations in our Japanese wage equation, but there is a role for past inflation. We have used the fourth difference in compensation per employee hour as our dependent variable in order to take account of the pattern of bonus payments in the Japanese economy. We have, therefore, to interpret the coefficients on past Japanese inflation with some care, as we have used the quarterly rate of increase in prices in the equation. If inflation is 1 per cent a quarter for a year, then wages will rise, in the short run at least, by around 2 per cent, and hence the short run dynamic pass-through of prices to wages is around a half.

The European economies

We found no significant role for price expectations in our German wage equation, and it shows no sign of structural instability. Given that wage inflation has been low and steady in Germany over our estimation period we would not, in the light of the discussion in section one, expect a significant role for expected inflation. Past wage bargains and the level of unemployment may contain all the information that bargainers need in the current period. In the long run in Germany real wages rise in line with productivity, but the speed of pass-through of prices to wages is slower in Germany than in any other European economy. This is clearly the result of the low degree of persistence of German inflation. (See Barrell (1990) for a discussion of signal and noise in wage determination). All of our other European wage equations do display a role for forward-looking inflation, and all have a significant role for unemployment (although the evidence is weak for the UK). Only in the case of Italy do we find some structural change, and our Italian equation differs significantly between the pre- and post-1982 periods. Our final equation contains a backward-looking inflation indicator for the period prior to 1982, and over this period there is no role for unemployment. The change in the system of wage bargaining in Italy in the early 1980s(18) is associated with a sharp change in the estimated wage equation. After 1982 we do find a role for forward-looking expectations, and there is a role for unemployment.

The long-run characteristics of our equations are of interest, and they are given in Table 2. The first row gives the sacrifice ratio, which is a widely-used measure of nominal wage rigidity, whilst the second row gives the long-run coefficient on unemployment which is often described as a measure of real wage flexibility. The third and fourth rows gives the mean and median lag of the equation in response to a step change in prices. This reflects the speed of pass-through of wages to prices.

[TABULAR DATA OMITTED]

Forward-looking wages in NIGEM

In this section we analyse the effects of the introduction of this set of forward-looking wage equations into NIGEM. As inflation expectations appear to be significant in four of our countries, we would accept that the previous backward-looking wage equations in the model were misspecified, and hence we would expect model properties to change. The degree of difference between simulations using the old and new models will depend upon the shock we administer and the expectations-generating mechanism we adopt.

There are three alternative ways of specifying expectations in our model. We can adopt the full, or strong version of rational expectations, and assume that individuals act as if they know the true model. This requires that we solve the model in forward-looking mode with model consistent expectations, and that we have terminal conditions on any forward-looking variable.(19) This is the approach we adopt in this note. We have experimented with alternatives elsewhere. In Anderton, Barrell and In't Veld (1992) we analyse problems of European monetary union using forward-looking wages under the assumption of full rational expectations and also using the fixed parameter equation that would be yielded by our instrument set in our IV estimation. This can be seen as an implementation of the weak version of the rational expectations mechanisms with individuals using a fixed parameter inflation predictor. In Barrell, Caporale, Hall and Garrett (1992) we implement a more sophisticated learning mechanism. There we assume that individuals are boundedly rational, and that their expectations are generated in line with a varying parameter Kalman filter on the data set available to them. This approach yields a number of interesting insights into policy, but the essential implications of the introduction of forward-looking wages can be gauged by the simulations presented in this note.

The rest of the model is fully described in the August NIGEM model manual (NIESR(1992)). We have implemented the model with fiscal solvency constraints in place, and we have used either an interest-rate feedback rule for monetary policy when considering realignments, or monetary base targeting when considering a fiscal expansion. The solvency constraint and the feedback rule are described in Barrell and In't Veld (1992). The feedback rule has interest rates reacting to deviations from base in inflation and output, with five times the weight on inflation as on output. In order to avoid instrument instability we use interest rates to target the long run level of the monetary base, and short run target overshoots are permitted. Our inflation and interest rate targetting also involves some instrument damping.

Our simulations are designed to be expository rather than exhaustive, and hence we present a number of policy-related results. The first set models a realignment of the ERM, where Italy, France, and the UK all devalue by 10 per cent against the D-Mark but the overall value of the ECU is unchanged in effective terms. This requires an appreciation of the D-Mark against the Dollar. We assume that monetary policy is run by the Bundesbank, and that as the scenario involves realignments, and therefore changes in relative price levels, it uses the inflation and output based interest rate feedback rule, rather than monetary base targeting, because the former allows step changes in the price level, whilst the latter does not. The second set of simulations involves a fiscal expansion in the US, with the specific intention of overcoming the current prolonged recession in the short run. We are particularly interested in the implications for the European economies. Exchange rates are allowed to jump, and the size of the jump depends on a set of terminal conditions that are designed to return the ratio of net overseas assets to GDP back to its base level.(see Barrell and In't Veld (1992) for a further discussion of the topic).

An ERM realignment

We assume that the realignment is unexpected and therefore cannot influence expected price increases before the event. The internal realignment of the ERM countries helps the Bundesbank deal with inflationary pressures within Germany. The appreciation of the D-Mark lowers output and reduces inflation, and our targetting rule suggests that interest rates will fall by more than 1.3 per cent (see Chart 1). This helps alleviate the slowdown in activity in Germany, and for the rest of the Community it adds to the output gains that follow from a downwards realignment. The change in output relative to base is given in Chart 2. Output rises in the UK, France and Italy, and falls in Germany. In all cases the gains and losses are, as we would expect, transitory. The effect on inflation is also rather transitory, with the effect probably lasting longer in Italy (see Chart 3). Wages move quite quickly in response to the realignment, but they do not jump because the effect of current wages on current prices is limited and hence the forward root in the wage price system is small. (see Chart 4). Employment rises in the UK by 100,000 after two years, and peaks at more than 200,000 above base after four years. The effects on employment in France and Italy are smaller than in the UK, with an increase of around 100,000. This in part reflects these countries' closer trade links with Germany, where output falls and employment is 120,000 below base after two years. The employment effects are also, of course, transitory.

Real exchange rates are pushed away from their base level by the realignment, but relative inflation developments soon push them back to the path to equilibrium represented by the base (see Chart 5). The real depreciation soon disappears in the UK and in France, but the misalignment lasts longer in Italy and in Germany. In the long run if we shock nominal exchange rates real exchange rates will always return to their base levels in this model, and hence the absence or presence of real exchange rate wedges in our wage bargaining equations does not affect the final outcome. However, as is clear from our simulations, the process of adjustment may be protracted. The devaluations in France, Italy and the UK cause producer prices to rise, and they cause aggregate demand to increase. Both of these factors put upward pressure on consumer prices and on wages, and the pressure will continue until the real exchange rate and the real stock of wealth have returned to their equilibrium levels. In the short run the impulse to import prices causes producer prices to rise, and in these simulations the import price wedge persists for some time. The slow pace of adjustment in Italy reflects the changes in the Italian labour market discussed above. If the effects of the reforms of the early 1980s is more transitory than our econometric results suggest, then the consequences of the realignment for the Italian economy could be much worse than our simulations suggest.

There are a number of additional reasons why the outturn for Europe, and especially for Italy, could be less favourable. Previous realignments of the ERM have not been costless. An illustration of the potential implications of an unexpected realignment and the associated loss of credibility is given by the Dutch realignment in 1983, when the guilder was devalued by only 2 per cent against the D-Mark. The credibility of the authorities' stance was brought into question, and the risk of a further realignment raised Dutch short term interest rates by half a per cent for the next two years (see In't Veld (1992) for more details). Realignments have in the past caused inflation expectations to rise, and in those countries where such expectations have a role in wage bargaining we would expect the rate of wage inflation to reflect this. The long run effect on the price level will, however be independent of expectations because it must reflect the necessity of returning to real equilibrium. The simulations reported here reflect this necessity, because they do not include any further realignments, and hence this affects the rate of inflation over the whole of our simulation period.

The model is being operated in fully forward mode, and this is equivalent to individuals believing that the post realignment parities are fully credible. The union stays together after the realignment, and hence there is no need for a risk related rise in interest rates relative to those in Germany because there is no perceived risk of a further devaluation. This assumption is discussed further in Westaway (1992) and in Driffill and Miller (1992). The success of the realignment in this simulation depends crucially on the strong version of the rational expectations hypothesis,and also on the assumption that monetary policy is pursued successfully by the Bundesbank. If Italian inflation expectations are not strongly rational then we would expect a much more marked response to the devaluation.(20)

A US fiscal expansion

A US fiscal expansion is a possible response to the continuing recession. The one per cent of GDP increase in Government spending in our simulation raises output and expected inflation. Both have a significant effect on wages, and they rise sharply in response to the increase in demand (see Chart 6) We have a fiscal solvency constraint in place, but this acts only slowly to reduce the budget deficit and output (Chart 7). The monetary authorities are presumed to be targeting the money stock, and the combination of a higher price level and a higher level of output (albeit temporary) leads them to raise interest rates (Chart 8). This in turn causes the exchange rate to jump upward and then to depreciate along the open arbitrage path (see Chart 9). The appreciation of the exchange rate helps ameliorate the short run inflationary consequences of the fiscal expansion. The rise in interest rates causes US equity prices, which are forward looking, to fall, and this reduces wealth and hence also consumption (see Chart 10).

We have stressed elsewhere (Barrell, Gurney and In't Veld (1992)) that seemingly symmetric shocks to a European Monetary Union may be asymmetric in their short to medium term outcome because of the different speeds of response of wages and prices in the European economies. This simulation involves two shocks: the increase in demand and the appreciation of the dollar. Both should raise output and inflation throughout Europe. Chart 11 plots the responses of wages in each economy, and Chart 12 plots the effect on prices. All effects will eventually be transitory, but inflation reacts more rapidly in France and the UK than in Germany. Our simulations are based on the assumptions that the ERM peg is fully credible in Italy and that the wage bargaining process has changed. Full credibility means that inflation expectations remain low, and policy works. If the inflation expectations formation process is more volatile then the inflationary consequences for the Italian economy could be much worse than we anticipate at least in the short run. This would also be the case if the resulting problems caused the authorities to abandon the policy rule and realign.

The speed of response to a fiscal shock of this sort depends in part on the speed of response of the wage-price system in the US. In the long run outturns are likely to be independent of the fiscal stance, especially if fiscal solvency is a requirement for equilibrium. However, as Barrell and In't Veld (1992) stress, the approach to equilibrium can be rather extended, and our terminal conditions in forward looking mode should be designed to allow the economy described by our model to approach long run equilibrium in such a way that it can actually settle there. As Blake and Westaway (1992) demonstrate, this may be a hard task.

Conclusions

This note has discussed the introduction of forward looking wages into our world model. There are a number of expectations formation processes that could be used when undertaking policy analysis, and it is clear that issues involving the discussion of exchange rate regimes should really address these problems. We now have a model that takes account of expectations and the stockflow equilibrium that comes from the existence of wealth effects, and we feel that it is a useful vehicle for policy analysis. In particular it can be used to throw light on issues concerning the European Monetary System, and we have attempted to do so in this note.

NOTES

(1) Our analysis has been undertaken on our global model NIGEM. It was developed at the Institute and is jointly maintained with the LBS. We would like to thank Mike Artis, Andrew Britton, Stephen Hall, Soterios Soteri and John Whitley for useful comments. This research was funded by the ESRC Macroeconomic consortium. (2) R. Farmer (1991) provides a sound theoretical discussion of these issues. (3) At the moment, for simplicity, we are assuming that expectations in the wage bargain are only concerned with prices. In theory the future values of all factors in the wage bargain should be taken into account. (4) Taylor (1980) makes it clear that the symmetric forward-looking and backward-looking weights are arbitrary and there is no reason why the weights cannot be skewed in one direction or another. (5) Driffill and Miller (1992) develop the continuous time staggered wage contract model of Calvo (1983) to allow for perceptions about the credibility of the authorities, and especially the influence of exchange-rate policy on expectations formation. If a policy of devaluations is anticipated then it becomes more important for wage bargainers to look forward. (6) Some of these issues have been discussed in previous issues of the Review; see Barrell (1990) for instance. (7) For the most recent, and fullest exposition see Layard, Nickell and Jackman (1991). As the framework is well known we will discuss it only briefly here. (8) These issues are extensively discussed in Anderton, Barrell and McHugh (1992) and Anderton, Barrell and In't Veld (1992). We will keep our discussion brief and refer interested readers to these two papers as well as to Layard, Nickell and Jackman (1991). (9) See Anderton, Barrell and In't Veld (1992) for a further discussion. (10) In 1968 some 28-4 per cent of the workforce was unionised. This percentage had fallen to 16-1 by 1991. (11) We tried one-quarter-ahead and one-year-ahead expected inflation, and in all cases the one-quarter-ahead indicator performed better. (12) We have followed Hall and Henry (1987) and used a smoothed moving average for productivity in order to avoid the noise contained in the ratio of one period output to employment. (13) This is the procedure advocated by Pagan (1984). See Cuthbertson, Hall and Taylor (1991) for a discussion of the estimation of RE models. (14) We have also instrumented all other contemporaneous endogenous variables, and the exogeneity of the instrument set has been tested. (15) Further results for the European economies are reported in Anderton and Barrell (1992) where we have undertaken tests on ten countries. Wedge effects appear to be present in only two, Italy and Ireland. (16) If we estimate y = a + bx by IV we cannot use the standard Chow test for stability. However, if we define the variable [alpha] x where [alpha] x is zero before some date and takes the same value as x thereafter, and estimate y = a + bx + [b.sup.*] [alpha] x and undertake a Wald variable deletion test on [b.sup.*], we have a valid IV stability test. See Godfrey (1988), pp.200-203. (17) As we have included current unemployment we have an equation that contains a jointly endogenous variable, and hence we have instrumented it. (18) We have discussed the dismantling of the Scala Mobile at length elsewhere; see Barrell (1990). (19) We use the standard constant rate of growth condition in the terminal period T log CE[D.sub.T] - log CE[D.sub.T-1] = log CE[D.sub.T+1] - log CE[D.sub.T]. (20) These issues are discussed further in Barrell, Caporale, Hall and Garrett (1992)).

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