Swedish Institute for Social Research (SOFI)

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1 Sedish Institute for Social Research SOFI Stockholm University WORKING AER 3/008 WAGE REDISTRIBUTION AND THE LONG RUN HILLIS CURVE by er Lundborg

2 Wage Redistribution and the Long Run hillips Curve* by er Lundborg Sedish Institute for Social Research, Stockholm University ABSTRACT We derive a long-run hillips curve that is negatively sloped at lo inflation rates. Due to exogenous changes, unions ant to redistribute ages across different members also in the long run. Wage stickiness, inflation targeting and union solidarity are central characteristics of our Ne Keynesian model. In the model, high enough inflation becomes the grease of the economy that allos age redistribution across unions ithout causing unemployment to rise above NAIRU. We sho that under nominal age rigidity, long-run unemployment may rise drastically and at zero inflation, unemployment may be trapped at very high levels even if demands for age redistribution tapers off. Under real age rigidity, the economy may get trapped at high unemployment also at positive but lo inflation rates irrespective of demand for age redistribution has vanished or not. Thus, a period of age redistribution may cause an economy of full real age rigidity to get trapped at a high unemployment rate. A policy conclusion is that economies characterized by extensive age rigidity should not target inflation at too lo levels. * This research has been financed by a grant from the Sedish Council for Working Life and Social Research Forskningsrådet för arbetsliv och socialvetenskap, FAS no The paper has benefited greatly from initial discussions ith Hans Sacklén ho, unfortunately, left academic research during the project period. I am also grateful to comments from Steinar Holden, Ragnar Nymoen and Roger Björnstad.

3 Introduction One of the most influential contributions in economics is that the long-run hillips curve LRC is vertical i.e. that unemployment settles at the fixed natural rate at any inflation level. An expression for the influence of this vie is that Central banks target inflation at historically lo levels like to percent. One reason for the forceful influence of the hypothesis of the vertical LRC is the simplicity of the NAIRU model. The model can be understood not only by professional economists but also by policy makers. Many researchers intellectual investments in the model and the fact that inflation targeting rests on credibility of the target makes it unlikely that lo level inflation targeting ill be abandoned. Nevertheless, several studies have questioned the basis of lo inflation targeting, i.e. the notion of the vertical LRC. If the LRC instead implies an inflation-unemployment trade-off at lo inflation, the implication is that lo inflation targeting may give rise to unemployment above the NAIRU level. Akerlof, Dickens and erry 000 presented a model in hich firms age and price setting is different at lo inflation than at high in the sense that inflation tends to be disregarded at lo levels. With these assumptions, the LRC becomes negative at lo enough inflation and an inflation rate exists that minimizes unemployment. When tested empirically, they concluded that US inflation should be somehere beteen.5 and 4.0 percent to minimize unemployment. When basically the same model as applied to a small open economy like the Sedish, Lundborg and Sacklén 006 found similarly strong support for the model. Their preferred regressions imply that inflation should be somehere beteen 3.5 and 4.0 percent, ay above the present to percent inflation target, to minimize unemployment in Seden. Since the vertical LRC is nested in the Akerlof et al model, the empirical results for both the US and Seden reject the notion that the LRC is vertical at lo inflation. Holden 004 constructs a bargaining model based on legal requirements in many European countries that nominal age contracts can only be changed by mutual consent, giving orkers a stronger bargaining position at lo inflation. The key implication of this model is also a long run trade-off beteen unemployment and inflation at lo inflation rates. Friedman 968, helps 970.

4 Researchers have also proposed that donard nominal age rigidity DNWR, a prominent feature of developed economies, may be a credible source of a negatively sloped LRC. The focus on DNWR goes back to Keynes 936 and has been a recurrent theme ever since. In Keynes version, individual orkers or groups of orkers care about relative rather than absolute real ages. They may ithdra labor from the market if their ages fall relative to others but ould not necessarily do so if all real ages fall uniformly. Unless the age bargaining process is fully controlled by the government or by economy-ide bargaining by the social partners so that all ages are reduced uniformly in a slump, inflation is needed to do the job of adjusting relative ages. It has been established that employers as ell as employees are reluctant to accept nominal age cuts. 3 In a model ith optimizing firms and explicit DNWR under all but extreme circumstances, Akerlof, Dickens and erry 996 sho that the effects of DNWR are large in terms of lost employment during lo inflation. Firms that perform poorly and make losses during a slump ith lo inflation cannot loer real ages and firms then need to cut don on employment. Only hen losses are sustained over several years in a ro ill it be possible to loer real ages. In this paper e explore further the consequences of age rigidity. Hoever, e make a quite different analysis than Akerlof et al 996 of the mechanisms that cause age rigidity to generate a negative LRC. One reason for introducing credible lo inflation targeting in highly unionized economies is the expected disciplinary effect on unions age setting. In particular, if some unions demand an extra age increase for their members, other unions need to restrain their age demands correspondingly so that overall age increases are in line ith the inflation target. This setup requires an active union policy for age solidarity. Hoever, there are limits to solidarity. Donard nominal age rigidity and donard real age rigidity DRWR represent such limits and e sho ho demands for age redistribution under DNWR and DRWR matter for the slope of the LRC. The driving force behind the negative slope of the long-run hillips curve is thus the demands for age redistribution. Much of the discussions on changes in relative ages across unions take place publicly and a public support for an extra age increase for some unions may See e.g. Tobin 97, Akerlof, Dickens and erry See Agell and Lundborg , Beley 999, Campbell and Kamlani 997, Akerlof et.al. 996.

5 facilitate the achievement of the age objectives. Our analysis rests on the observations that often before or during age negotiations there are discussions about the needs for extra age hikes for some groups of orkers above the age increases of other groups. This demand from trade unions to redistribute age income across members of different unions may be due to exogenous changes in preferences, technology, ork environment etc. The redistribution of ages is often the result of social needs and is not necessarily the results of union policy per se. While support often can be obtained for a redistribution of ages that is in line ith social objectives, age rigidity, hich becomes a problem particularly in lo inflation periods, may prevent the necessary age adjustments and cause unemployment to rise. Some examples of the type of age redistribution across unions that e ant to capture in the model are the folloing. The most frequent redistribution may be that egalitarian oriented trade unions tend to demand relatively higher age increases in percent for unions organizing the loest paid members. This as particularly common in the 960.s and 970.s among egalitarian oriented unions in the OECD area and particularly so in Seden. To the extent that disciplinary effects are present, this requires some restraint from the unions representing better paid members. The long run effects of these age redistributions shoed up in terms of a highly egalitarian age structure. Another example from Seden concerns teachers ages. After a public discussion about the need to improve schooling results, teacher unions requested a age premium above the increase of other unions so as to raise the quality of teachers. Since the quality of teachers is in the general interest, other unions largely supported the request. Facing a credible lo inflation target they consequently ould need to hold back their on age demands. Another example is the drive to deal ith the gender age gap. Raising the ages of omen implies that unions organizing a majority of omen may find support from other unions for a age premium. This as the case in the recent round of age negotiations in Seden and, after some lengthy discussions among the unions in the blue collar confederation LO, there finally as an agreement that a large union organizing a majority of omen 4 should be given an extra age increase at the expense of other unions. 4 This as the union organizing orkers in local government, Svenska kommunalarbetareförbundet. For a long time the industrial orkers s union in Seden, Svenska metallarbetareförbundet, resisted the demands since it 3

6 Many other age redistributions are motivated in terms of compensated age differentials. Some unions may reveal poor orking conditions for their members and require compensation for exposure to e.g. higher risks of crime, pollution, cigarette smoke, croding etc. The disciplinary effect of inflation target requires solidarity from other unions that in turn may have to restrain their on age demands. Other orkers may be exposed to a demand from foreign employers. Such foreign demand tends to raise also their domestic ages. If their competence is considered crucial to the home country, other unions may find these age increases agreeable and to be in the general interest, since they may prevent emigration of orkers. To prevent a age inflation that is not in compliance ith the inflation target, the other unions may hold back their age demands. The only assumption that is necessary for our macroeconomic model ith union age setting to capture long-run rather than short-run relations is that such demands for age redistribution across members of different trade unions ill not go aay in the long run. 5 Due to technological improvements ork conditions change over time, implying that orkers demand for changing premiums ill persist over time. Groups of orkers that are considered underpaid ill be identified also in the future and demand for redistribution ill continue. references for more or for less equality and the norms for a fair age structure ill also change in the long run leading up to demands for age redistribution. Several results come out of our model based on age rigidity, inflation targeting and union age setting. First, e sho that a sustained need for age redistribution across unions orker categories yields a negatively sloped LRC at sufficiently lo inflation rates, i.e. also ith sustained redistribution the unemployment increase ill come to a halt at some high level. It may be the case, hoever, that also a fairly lo inflation level may be enough to take care of redistributions across unions ithout causing unemployment to rise. Inflation targets under, say, to percent are not likely to be enough, though, to prevent unemployment increases. limited their on age increases. Finally, after long internal discussions they finally agreed to support the extra age increases of Svenska kommunalarbetareförbundet. 5 We sho, hoever, that at zero inflation, the economy may get trapped also if redistribution demands disappear. 4

7 Secondly, e may analyze the effects of a limited period of age redistributions after hich no such redistributions are demanded by unions. We sho that ith a zero inflation target and strict age rigidity the economy ill be in a high unemployment trap, i.e. also ithout any demands for redistribution. With no price increases and donard rigid real or nominal ages there is no room for relative age adjustments. At positive but lo inflation targets, the economy is not trapped but the loer is inflation the larger is the necessary number of contract periods for the economy to return to NAIRU. The higher is the inflation target, the faster is the return to lo unemployment. The model illustrates inflation as grease of age formation. Thirdly, e sho that age redistribution under donard real age rigidity causes unemployment to rise at lo enough levels of inflation but not at high. The unemployment increase ill cease at a high NAIRU at any inflation target. While the economy returns to the NAIRU level under DNWR and any positive inflation, this is not the case under DRWR. Under real age rigidity, the economy gets trapped at this high level also if the demands for age redistribution vanish. With less than full DRWR, the higher is the degree of DRWR the longer time it takes for the economy to return to lo unemployment levels after a period of age redistribution. The basic mechanism of the model can be described ith a simplified example based on nominal age rigidity as follos. Consider a age bargaining economy ith to trade unions, A and B, of identical size and a monetary regime based on targeting inflation at a zero rate. If union A, for instance one dominated by female orkers, demands an extra age increase to contribute to closing the gender age gap, union B ould need to loer its nominal age correspondingly to assure that the overall age increases are compatible ith zero inflation. Hoever, under an efficiency age constraint, a nominal age decrease of union B ould distort output by loering orkers effort yielding an undesired social outcome. To avoid this, union B ill not accept a nominal age drop and if they then agree to age redistribution, the average age costs to the firms ill increase. To avoid higher age costs to raise the price level, the Central Bank loers the money supply, thus loering aggregate demand and causing unemployment to rise. On the other hand, if inflation is high enough, age redistribution occurs ithout a necessary drop in nominal ages yielding constant money supply and unemployment. In this manner, e derive a long run hillips 5

8 curve that is vertical at high inflation but negatively sloped at lo inflation. Thus, a positive inflation rate orks to grease the heels of the economy. The Model. Consumption The point of departure is a Ne Keynesian macroeconomic model 6 into hich e build in inflation targeting and the appropriate age rigidities. We assume to goods, indexed and. Household i i= n maximizes utility that depends positively on aggregate consumption C and real money balances M i / : i g g Ci M i U i = g g. Consumption is a function of the level of consumption of each of the to i i goods, = C C + C, entering the utility function in a symmetric ay. > is the i elasticity of substitution beteen the to goods. The constant g is introduced in to simplify the exposition. M represents the nominal money holdings of the household and + = i is the aggregate price level corresponding to C i. 7 The n identical households on their labor and firms and maximize utility subject to their budget constraint. Labor supply of both types equals. Total factor income are profits Q L and Q L, age income L and L here is the age and L labor demand, plus income hen unemployed B L + L here B are unemployment benefits. Adding yields total factor income as Q + Q + B L but since benefits L are financed by lump-sum taxes of the same amount as total benefits, e get factor income as Q + Q. 6 Cf. for instance Blanchard and Fischer 989 ch In general, introducing real money balances directly in the utility function is gross simplification and a full treatment ould require a considerably more complex dynamic model. Hoever, it is a very useful and innocent simplification that also underlines the importance of monetary policy for the demand. 6

9 For each of the n households, here represented by household i, the budget constraint, equal to income I i, reads as: Ci + Ci + M i = I i [ Q + Q + M ]. n Nominal consumption expenditures and demand for nominal money balances should equal income from market activities, and non-activities plus the household s initial money holdings, M/n. The solution to the utility maximization problem obtains by maximizing subject to and using the aggregation functions of consumption and price. The solution reads: i = C i C 3a i = C i C 3b M = g 4 i I i I i Ci = g 5 Demand for the to goods and for real money is linear in income and is a function of the relative price ith the elasticity -. Using 3a, b, 4 and 5 e can define total demand for the to goods facing firms as real consumption demands, D C andc D, over the n households: and C D = g g M 6a C D = g g M The money supply, M, hich is the decision variable of the Central Bank, is seen to directly affect goods demand. 6b roduction Output, Q, is assumed to be produced using labor in efficiency units as the sole input: Q = 7a el Q = 7b el here e note that labor of type type is used only in production of good good and that 0< <. The term e is effort and ill be determined belo. Workers are organized in 7

10 unions and there is one union connected ith each firm. Firm maximizes profits Π = Q L by setting the price. In maximizing profits, the firm considers that output is determined by demand 6a, the production function 7a and age and the price level are taken as given. Effort equals unity see belo. The solution is: + / gm + / =. 8a g Similarly for Firm that considers 6a and 7a e get + / gm + / =. 8b g Averaging 8a and 8b e get the aggregate price level = g g + = W M 9 / + / + + / + here W is the index of aggregate ages W =. Facing a age increase, e see from 9 that the Central Bank may loer money supply to keep the price level constant. The to firms also maximize profits by determining labour demand, hich, for firm, yields: as and for Firm g M + + L d = g 0a g M + + = L d. 0b g roductivity, ages, and rigidities At this stage the specific assumptions and special features of the model sho up. Inspired by the efficiency age theory e assume that effort of a orker equals unity if the orkers age say type,, is at least as high as last years age,. If less than last year s age, effort is zero. Formally, e have strict donard nominal age rigidity, DNWR, as: e = if a e = 0 if <. b 8

11 Since a zero effort solution is assumed unacceptable to the unions, they ill never set the age belo last year s age if there is DNWR. The same assumptions and similar equations as a and b apply to orkers of type. In some other cases e may assume donard real age rigidity, DRWR, specified as e = if / / c e = 0 if / < /. d for orker type, here is last period s price level. The corresponding equations apply to orkers of type. The age expected by the unions members and leadership is determined as last year s age adjusted for expected inflation hich equals targeted inflation, π, and an extra age adjustment, j, to compensate for some positive or negative exogenous shifts in preferences, ork conditions etc. as discussed above. We can rite the expected age for the to types of orkers as and e + = π V a e + Thus the relative expected price is here V = V /V. e = π V b e e = = / V 3 / Solidarity across the to unions implies that they set the ages in consideration of an expected age redistribution as suggested in 3. Unions consider their members utility plus a term capturing the desired change in relative ages across the to unions. This desired redistribution of ages may be formulated as Ψ V 3b 9

12 0 3b implies that as long as there is a deviation beteen the actual ages / and the desired ages V, there ill be a utility loss imposed on the unions. The term is convex in. Think of this redistribution as representing the type of social goals discussed in the introduction. We can then think of the unions as having a joint maximand that reads:, max arg Ψ = Ω V B u u B u u 4 The first to terms in 4 are the standard expected age of members of union, the third and fourth term the standard expected age of members of union. The fifth term is the added redistribution term, hich due to solidarity beteen the to unions, is desired by both unions. The maximization process obtained by setting 0 = Ω δ δ and 0 = Ω δ δ leads up to the folloing first order conditions: / / V u B u = Ψ + δ δ and / / V u B u = Ψ + δ δ. To solve for the derivative u δ δ e note that the unemployment rate of union members is + + = = M g g L u from hich e obtain L u δ δ + = and similarly e obtain for union L u δ δ + =. When used in the corresponding first order conditions e get: / V u B L = Ψ + + 5a and / V u B L = Ψ + + 5b

13 Monetary olicy: Inflation targeting The Central Bank adjusts the money supply to obtain a price level at time t that equals last period s price level corrected for the inflation target π : = + π. 6 The averages of 8a and 8b should then equal the price level as in 6. Using 6 in the average price level 9 and solving for M e obtain: g M = + π W. 7 g Thus, hen the Central Bank sets the money supply according to 7, the inflation target specified in 6 ill be fulfilled. Firms ill set their prices according to 8a and 8b still complying ith the inflation target 6. roperties and redictions: a The vertical LRC We shall discuss the properties and predictions by means of numerical simulations. With no demand for age redistribution across the to unions, i.e. V=.00, the model ill of course produce a standard vertical LRC. We assume the folloing parameter values: g=.3, =5, =.77, ψ=.0 and B=.548. Assuming no demand for redistribution across unions from last period, V=.0, e obtain the thick LRC as illustrated in Figure. In the no redistribution case the standard result of no relation beteen inflation and unemployment occurs. Unemployment is at its NAIRU level, here.86 percent. Assuming no that there is demand for a period-ise redistribution of percent, i.e. that V=.0. This implies that in period union demands to percent more than union, in period, union demands to percent more than union, in period 3 union again demands to percent more than union and so on. With perfect age flexibility the LRC ill remain fixed at the NAIRU rate of.86 percent. Hoever, every second contract period, union union ill find that unemployment among their members falls rises and every second

14 Inflation target u*=.86 Unemployment Figure. The bolded line shos the long-run hillips curve under no redistribution or under age redistribution ith age flexibility yielding unemployment intervals for to unions. period unemployment rises falls. Thus, over time unemployment among members of the to unions ill vary ithin the shaded area in Figure. Unemployment in the to unions ill vary beteen.4 and 3.4 percent hile the average unemployment rate remains at NAIRU,.86 percent. b Introducing age rigidity In the sections belo, e analyze the effects of age rigidity on the LRC. We first study the effects of the less restrictive case of rigidity, donard nominal age rigidity, i.e. hen a union refuses to set the nominal age belo last years age. This case is represented by applying a and b. We then turn to the more restrictive case hen the union refuses to set the age belo last years age corrected for inflation, as represented in c and d. Of course, at price stability, π = 0, the to are identical phenomena.

15 Nominal age rigidity We shall first sho ho the LRC is affected by the introduction of DNWR at different levels of inflation targeting. Assume that in each contract period five percent age redistribution is required by a union union as before representing half of the union membership. We do not choose this very high level of redistribution because of realism but rather to sho the orkings of the model. The resulting long-run hillips curve is shon in Figure 3. Inflation and unemployment at V=.05 and DNWR Inflation Unemployment Figure 3. The long-run hillips curve under donard nominal age rigidity and V=.05. Of course, at high enough inflation a age cut is not required for real age adjustment and DNWR does not matter. In this case,.5 percent inflation is enough grease for real age adjustment to occur and unemployment remains at the NAIRU level. At loer inflation rates, hoever, DNWR implies a restriction on real age adjustment. At inflation less than around.5 percent, a nominal age cut on behalf of the age restraining union ould have been necessary to avoid unemployment from increasing. Hoever, under DNWR unemployment ill increase and in the long run unemployment settle at a level higher than NAIRU. Consider, for instance, an inflation target at percent. Since V=.05, union demands 5 percent more than union at unchanged unemployment. With DNWR, union ill not 3

16 loer their real ages fully to make up for the age hike of union and the result is an increase in the overall unemployment rate. Still, a one percent inflation rate implies some, but not enough, grease to restrict unemployment increases. 8 For each contract period, unemployment increases as follos:.86 %, 3.5 %, 5.9 %, 5.77 %, 6.60 %, 6.9 %, 7.8 %, 7.64 % and 7.76 %. It thus approaches around 8 percent here it ill remain as long as the age redistribution demand remains. Why does the unemployment increase taper off though demand for age redistribution remains? When in the second contract period, union demands five percent more than union, union cannot adjust real ages fully and unemployment ill go up further. Hoever, hen unemployment increases over time for each contract period, the disutility of increasing unemployment goes up, and less and less age redistribution can be accepted. Thus even if V=.05 remains in the long run, ultimately age redistribution ill come to a halt since the costs in terms of extra unemployment becomes too large to pursue the redistribution. After about nine contract periods, unemployment has settled at its long run rate, here close to 8 percent and there is no further redistribution. rice stability, i.e. zero percent inflation, is an ultimate case to study. Here, under DNWR, no real age adjustment hatsoever on the part of the age restriction union can take place. In this case, at the very high age redistribution rate, e see that unemployment ends up at a very high level: 7.5 percent. Compared to long-run unemployment at percent e see that it makes a large difference hether inflation is targeted at or 0 percent. Reducing redistribution demand under DNWR. The unemployment trap at price stability At the long-run equilibrium, V has been assumed to remain at.05. The high unemployment rate makes unions uninterested in further redistributions since that ould raise unemployment even more. We could ask, though, hat ould happen if unions should become satisfied ith the relative ages, i.e. becomes V=.0 hen e are at the long-run hillips curve and at zero inflation. 8 Note that e start out at equal age levels in the to unions. Therefore, the first step, i.e. unemployment increase, is not as large as it had been had e assumed large age differences also in the initial period. A one percent inflation restricts the initial step. 4

17 Unions ill no find that their relative ages are the optimal ones. Hoever, both ould like to have loer real ages so that unemployment ould come don to the preferred level, i.e. NAIRU. A choice of ages under full age flexibility implies real ages that yield the NAIRU of.86 percent. Hoever, at the high unemployment, and restricted by full DNWR, the unions cannot adjust ages donard and e find that the high unemployment point is a trap from hich the unions cannot escape. With no grease in the machinery e are stuck in a high unemployment trap. Assume instead some grease, say one percent inflation. With a positive inflation rate there is some scope for reducing real ages since if nominal ages are constant, real ages ill fall. At lo inflation, hoever, this adjustment takes time and e may experience unacceptably high unemployment rates for many contract periods. A level of V=.05 appears to be a high demand for age redistribution. Figures 4 and 5 sho the LRC as V=.0 and.04, respectively. Inflation 9 Inflation and unemployment at V=.0 and DNWR Unemployment 5

18 Figure 4. The long-run hillips curve under donard nominal age rigidity and V=.0. Inflation Inflation and unemployment at V=.04 and DNWR Unemployment Figure 5. The long-run hillips curve under donard nominal age rigidity and V=.04. We can note that a fairly lo inflation target seems to do the job of greasing the economy. Note that even hen e assume as high a age redistribution rate as 5 percent, i.e. V=.05 Figure 3, a to percent inflation target prevents unemployment from rising. At a percent age redistribution demand, illustrated in Figure 4, half a percent of inflation is enough to grease the economy. Doubling the age redistribution demand to V=.04, a little more than one percent inflation is enough to keep unemployment at NAIRU. These simulations could perhaps imply that DNWR really is not a major problem as long as Central Banks target the inflation rates at around percent. Hoever, economies are also exposed to real age rigidity to hich e no turn. 6

19 Real age rigidity Introducing real age rigidity implies that a union that under age flexibility had reduced the real age in solidarity ith the age increasing union no ill refuse to do so. Instead it ill raise the nominal age at least as much as the expected targeted inflation rate so as to avoid real ages from falling. With a positive redistribution demand, i.e. V>.00, and ith the age restraining union restricting its nominal age hikes to the targeted inflation rate to keep the real age constant, one might have expected that unemployment ould increase at any inflation target. This is not the case, hoever. At high enough inflation, unemployment remains at the NAIRU level. At zero inflation unemployment becomes identical to the one obtained under DNWR. As noted, at zero inflation, DNWR and DRWR are identical concepts yielding identical solutions. In Figure 6, e sho the derived LRC as V=.05 and the zero inflation solution is seen to be identical to the zero inflation solution in Figure 3. Inflation and unemployment at V=.05 and DRWR Inflation Unemployment 7

20 Figure 6. The long-run hillips curve under donard real age rigidity and V=.05. Why is it that at higher inflation the LRC is negatively sloped and becomes vertical at around 5 percent inflation? Assume a redistribution of ages in favour of union. DRWR like DNWR expresses ho small age increase union is illing to accept to allo union a higher age increase. The DRWR regime implies that union is not very cooperative as union alays raises its age as much as the inflation rate. At lo inflation union raises its age by the lo inflation rate, giving scope for union to raise its age by more than the inflation rate so as to loering the loss term in 3b. Since union raises the age above the inflation rate, real age costs rise and unemployment goes up. At high inflation, on the other hand, union raises its age by the high inflation rate thus giving no scope for union to raise its age above the inflation rate. Thus, like union, union ill also raise its age by the inflation rate and real age costs are unchanged and unemployment remains at NAIRU. Consequently e obtain a LRC that is vertical at high inflation rates, here both unions raise ages by the inflation rate, and negatively sloped at lo inflation rates, here union raises its age above the inflation rate. The crucial equations are 5a and 5b. On the left hand side e find the standard effects of raising the age, i.e. the effects on real ages and employment. On the right hand side e find the effects on the age redistribution. Based on 5a, e sho in Appendix that union ill increase its age by more than the inflation rate at a lo inflation rate. We also sho that the rate of increase of union s age falls as inflation gets higher and that there exists a positive inflation rate at hich union ill select a age increase identical to the inflation rate. This latter inflation rate is the one at hich the LRC changes from being negatively sloped to being vertical. In Figure 6, this occurs at approximately 5 percent inflation. At a lo inflation rate, union finds it rational to accept a higher unemployment rate since their real age increase also implies an increase in their age relative union. Hence, the difference beteen actual relative ages and desired real ages, V, falls. Since the term Ψ V is convex in, see Appendix higher inflation implies that union selects a higher, union finds that at some higher inflation rate it cannot 8

21 efficiently reduce V by choosing a age increase above the inflation rate. 9 Rationally, it opts for a age increase identical to the inflation rate. Comparing Figure 6 to Figure 3, e see that donard real age rigidity has a strong impact on the LRC. Under DNWR Figure 3,.5 percent inflation is enough to keep unemployment at the NAIRU level. Under the more restrictive DRWR, somehat more than four percent is needed to keep unemployment at NAIRU. A V=.05 may seem to imply a high demand for age redistribution. Figure 8 shos the LRC at the considerably loer level of V=.0. The zero inflation solution is of course again identical to the one under DNWR as in Figure 4 and e see here that percent inflation is enough to keep unemployment at the loest level of.86 percent, i.e. at NAIRU. A V=.04 yields the LRC depicted in Figure 9. Here, four percent inflation is needed to keep unemployment don at the minimum level. Reducing redistribution demand under DRWR. Unemployment traps at lo inflation targets. We noted above that in the case hen demand for redistribution falls, i.e. hen V becomes.00 under DNWR, the economy ould be trapped at very high unemployment hen inflation is zero. When inflation is positive, hoever, it moves back to the NAIRU level but very sloly so hen inflation is lo. Do these results carry over to the case of DRWR? No! In this case, the economy is trapped at high unemployment not only at price stability, i.e. at zero inflation, as in the DNWR but also at all other levels of inflation target. If DRWR is a binding restriction on the age formation, there is no ay back to the NAIRU level of unemployment once e have ended up on the negative sections of the long-term hillips curves depicted in Figures 6, 8 and 9. At real age rigidity, no real age adjustment can take place that ould take the economy back to the NAIRU level. 9 The convexity is of course imperative to our results, but it is hard to 9

22 Inflation Inflation and unemployment at V=.0 and DRWR Unemployment Figure 8. The long-run hillips curve under donard real age rigidity and V=.0. Inflation Inflation and unemployment at V=,04 and DRWR Unemployment Figure 9. The long-run hillips curve under donard real age rigidity and V=.04. 0

23 Empirical credibility? So far, e are a long ay from empirical credibility. Not only have e assumed redistributions like V=.05 that seem empirically quite unrealistic but e have also assumed the hole labor force to be characterized by either nominal or real age rigidity. Can empirical research on DNWR and DRWR be of any guidance in putting some realistic figures on our model? The first empirical studies on nominal age rigidity, McLaughlin 994 and Lebo 995, found little evidence of its existence hile Akerlof et al 996, Card and Hyslop 996, Kahn 997 and Altonji and Devereux 999, Lebo et al 999 found quite strong evidence. All these studies are based on US data during relatively high inflation, 3.4 to 7.4 percent, and though DNWR exists under high inflation, one cannot dra any inferences about the existence of DNWR under lo inflation. For nominal age rigidity to have real effects on the economy it is necessary, as amply shon in this paper that it also exists in lo inflation environments. While DNWR exists in high inflation, it has been hypothesized that nominal age rigidity ill not persist in the long run under lo inflation. 0 The argument that DNWR carries over from high inflation to lo inflation situations is subject to the Lucas critique, i.e. the microeconomic behavior ould change as inflation changes, implying that DNWR need not exist under lo inflation. Hoever, the only available evidence on DNWR in a lo inflation environment is provided by Fehr and Goette 005 ho sho, using lo inflation Siss data that DNWR persists also under lo inflation. The most comprehensive evaluation of DNWR and DRWR has been provided by the international age flexibility project reported by Dickens et al 005. They find that the fraction of orkers potentially affected by DNWR range from 9 % Germany to 66 % ortugal hile the fraction exposed to DRWR varies from 3 % Greece to 5 % Seden. Thus, for a country like Seden their results suggest that around half of the ork force is exposed to DRWR. We may interpret this by considering a situation in hich half of membership of the to unions has flexible ages hile the other half is characterized by 0 See Gordon 996 and Manki 996. They conclude: Yet, the results indicate that the lo inflation environment only slightly reduced the reluctance to cut nominal ages. This decrease as far too small to accommodate the greater need for nominal age cuts as inflation approached zero. Instead of a decrease in the quantitative relevance of nominal age rigidity, e actually observe an increase over time. Fehr and Goette 005 p. 78.

24 DRWR. Thus, the age restraining union ill loer the real age to half beteen the flexible age level and the nominal age that implies constant real ages. Thus instead of assuming that the age floor is determined byπ, it ill be determined by * + + π here * is the equilibrium age under fully flexible ages and + is the age set under DRWR. π We have performed simulations under the above assumptions that are likely to take us closer to a real orld situation. Consider Figure 0, shoing the results hen half of membership is restricted by DRWR and V=.05. Inflation Inflation and unemployment at V=.05 and 50% DRWR Unemployment Figure 0. The long-run hillips curve under 50 percent donard real age rigidity and V=.05. V=.05 appears, as already noted, to be a high level of demand for age redistribution. The Sedish Riksbank has a percent inflation target and the results suggest that the economy ould be unable to handle such redistribution demands and at the same time keep This approach may underestimate the rigidity of real ages since e assume that those not characterized by DRWR are illing to go all the ay and accept fully flexible ages. In reality they may accept only a limited real age cut.

25 unemployment at the NAIRU level of.86 percent. Instead, unemployment ould in the long run end up at a level of 5. percent. At a zero rate inflation target, unemployment ould end up at 8.4 percent hich is a combination of inflation and unemployment that the economy experienced in the late 990.s. Figure provides the effects of a more realistic age redistribution demand, V=.0. The simulations yielding this curve suggest that the present percent inflation target could handle the desired age redistributions of V=.0. Inflation and unemployment at V=.0 and 50% DRWR Inflation Unemployment Figure. The long-run hillips curve under 50 percent donard real age rigidity and V=.0. Since inflation targets of to percent are not uncommon, it could be of some interest to explore the unemployment rates that different values of the redistribution factor V generate at this particular level of inflation target. At this target, the economy can handle age redistribution up to 3 percent V=.03 but not more. At 3.5 percent, unemployment rises to 3

26 approximately 3.5 percent, at ends up at 5.4 percent if the redistribution parameter is as high as.05. Conclusions The only assumption needed to accept that the long-run hillips curve has a negatively sloped segment at lo inflation is that there exists, also in the long term, a need to redistribute ages across different types of orkers. In a Ne Keynesian macroeconomic frameork e sho that high redistribution demands produce unemployment rates above the NAIRU level hen inflation is targeted at lo levels and demands for age redistribution are large enough. Wages ill be redistributed more in lo unemployment periods and redistribution ceases if unemployment is high enough. We also sho that inflation targeting may trap the economy at high levels of unemployment. For instance, at zero inflation and donard nominal age rigidity, the economy may get trapped at a high unemployment also in the case hen the demand for age redistribution disappears. The economy ill return to the NAIRU level as long as there is some positive inflation rate, but the loer inflation, the longer time it takes for this to occur. At donard real age rigidity, the situation is even orse as the economy then may get trapped at any level along the long-run hillips curve also hen age redistribution demands are gone. As noted, at high enough unemployment age redistribution ill not occur since that ould raise unemployment to unacceptable levels. This implies that to the extent that the age redistribution had been in the general interest there are not only social losses in terms of unemployment and production foregone, but also a loss in terms of economic efficiency. Lo inflation targeting and age rigidity is not a healthy combination for an economy. Of course, age rigidity is not total and e have approached the real orld situation by relying on previous estimates of real age rigidity. The simulations suggest that in an economy here half the labor force is characterized by real age rigidity, to percent inflation, hich is a common target, may be able to handle fairly large age redistributions ithout unemployment increases. On the other hand, should inflation be loer the risk exists for increasing unemployment that remains also in the long run. At higher inflation there may be periods of large redistributions that take unemployment up to high levels and if folloed 4

27 by periods of no or small redistributions, the return may be slo and unemployment may remain at high levels. Thus, as the paper points to problems involved in combining lo inflation targeting ith age rigidity 5

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