The Costs of Price Stability - Downward Nominal Wage Rigidity in Europe

Holden, Steinar Working Paper The Costs of Price Stability - Downward Nominal Wage Rigidity in Europe Working Paper, No. 2002/8 Provided in Cooperation with: Norges Bank, Oslo Suggested Citation: Holden, Steinar (2002) : The Costs of Price Stability - Downward Nominal Wage Rigidity in Europe, Working Paper, No. 2002/8, ISBN 82-7553-198-5, Norges Bank, Oslo, https://hdl.handle.net/11250/2498654 This Version is available at: https://hdl.handle.net/10419/209807 Standard-Nutzungsbedingungen: Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden. Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen. Sofern die Verfasser die Dokumente unter Open-Content-Lizenzen (insbesondere CC-Lizenzen) zur Verfügung gestellt haben sollten, gelten abweichend von diesen Nutzungsbedingungen die in der dort genannten Lizenz gewährten Nutzungsrechte. Terms of use: Documents in EconStor may be saved and copied for your personal and scholarly purposes. You are not to copy documents for public or commercial purposes, to exhibit the documents publicly, to make them publicly available on the internet, or to distribute or otherwise use the documents in public. If the documents have been made available under an Open Content Licence (especially Creative Commons Licences), you may exercise further usage rights as specified in the indicated licence. https://creativecommons.org/licenses/by-nc-nd/4.0/deed.no ANO 2002/8 Oslo September 25, 2002 Working Paper Research Department The costs of price stability – downward nominal wage rigidity in Europe by Steinar Holden ISSN 0801-2504 ISBN 82-7553-198-5 Working papers from Norges Bank can be ordered by e-mail: [email protected] or from Norges Bank, Subscription service, P.O.Box. 1179 Sentrum N-0107 Oslo, Norway. Tel. +47 22 31 63 83, Fax. +47 22 41 31 05 Working papers from 1999 onwards are available as pdf-files on the bank’s web site: www.norges-bank.no, under "Published". Norges Bank’s working papers present research projects and reports (not usually in their final form) and are intended inter alia to enable the author to benefit from the comments of colleagues and other interested parties. Views and conclusions expressed in working papers are the responsibility of the authors alone. Working papers fra Norges Bank kan bestilles over e-post: [email protected] eller ved henvendelse til: Norges Bank, Abonnementsservice Postboks 1179 Sentrum 0107 Oslo Telefon 22 31 63 83, Telefaks 22 41 31 05 Fra 1999 og senere er publikasjonene tilgjengelige som pdf-filer på www.norges-bank.no, under "Publisert". Working papers inneholder forskningsarbeider og utredninger som vanligvis ikke har fått sin endelige form. Hensikten er blant annet at forfatteren kan motta kommentarer fra kolleger og andre interesserte. Synspunkter og konklusjoner i arbeidene står for forfatternes regning. 1 The costs of price stability - downward nominal wage rigidity in Europe by Steinar Holden University of Oslo and Norges Bank Department of Economics University of Oslo Box 1095 Blindern, 0317 Oslo, Norway email: [email protected] homepage: http://folk.uio.no/sholden/ First version: 15 September 2000 This version: 25 September 2002 Comments are welcome. Abstract In most European countries, the prevailing terms of employment, including the nominal wage, can only be changed by mutual consent. If inflation is so low that nominal wages have to be cut, the workers have strategic advantage in the wage negotiations, which induces higher unemployment in equilibrium. The upshot is a long run tradeoff between inflation and unemployment for low levels of inflation. Specifically, downward nominal wage rigidity, and excess unemployment at zero inflation, are related to three factors: the coverage of collective agreements, the legal framework at contract renewal, and the strictness of the employment protection legislation for non-union workers. Previous versions of the paper have circulated under the title "Monetary policy and nominal rigidities under low inflation". I am grateful John Driscoll, Stein Evju, Daniel Gros, Hans Haller, Kalle Moene, Asbjørn Rødseth, Fredrik Wulfsberg, as well as participants at presentations at CESifo, Harvard University, Virginia Polytechnic and State University, the EEA meeting in Lausanne, University of Essex, Oxford University, FIEF in Stockholm, and the Geilo seminar for useful comments on earlier drafts, to Larry Katz and Greg Mankiw for helpful discussions, and to the NBER for the hospitality when main parts of this paper was written. JEL Classification: J5, J6, E31, E52, K31. Keywords: Nominal wage rigidity, wage contracts, collective bargaining, monetary policy, inflation, equilibrium unemployment. 2 1 Introduction In recent years, a number of countries have adopted explicit inflation targets for monetary policy, reflecting a general agreement that monetary policy must ensure low inflation. Yet several economists have argued that if policy aims at too low inflation, downward rigidity of nominal wages may lead to higher wage pressure, involving higher equilibrium unemployment (eg Tobin, 1972, Holden, 1994, and Akerlof, Dickens and Perry, 1996, 2000).1 Many other economists have been less concerned, arguing that any downward rigidity that may exist is the result of an inflationary environment, and that society will adapt to a zero inflation policy without large and persistent impact on output and employment (Ball and Mankiw, 1994, Gordon, 1996). The debate has inspired a lot of empirical research, and there is now a considerable amount of evidence documenting downward nominal wage rigidity in many OECD countries (see references in section 6). However, far from settling the debate, the different views still exist (see eg the opposing views of William Dickens and Lars Svensson at the ECB conference Why price stability, http://www.ecb.int/). A problem when evaluating the opposing views is that the theoretical foundation for downward nominal wage rigidity is not well explored. The empirical literature has generally appealed to money illusion or fairness considerations, ie that workers view a cut in nominal wages as unfair, referring to documentation for such effects in eg Shafir, Diamond and Tversky (1997) and Bewley (1999). There is also a smaller mainly theoretical literature explaining nominal wage rigidity as the result of nominal wage 1 Low inflation may also limit the scope for expansionary monetary policy as the nominal interest rate cannot be negative, cf Keynes (1936). 3 contracts that can only be changed by mutual consent (MacLeod and Malcomson, 1993, Holden, 1994, 1999). This is the typical form of employment contracts in Europe, and MacLeod and Malcomson show that they are efficient under a large variety of circumstances. However, as yet research on the macroeconomic implications of such contracts has only considered completely unionised economies (Holden, 1994, 1997), severely limiting the applicability for many countries where unionisation is on the return. In this paper I consider a model with both a unionised and a non-unionised sector, with explicit consideration of the institutional features of the wage setting in each sector. As in the models of Holden (1994, 1997), the legal requirement of mutual consent to change a nominal wage contract implies that workers/unions have a strategic advantage in the wage setting when they try to prevent a nominal wage cut. If inflation is so low that employers want to cut nominal wages, this strategic advantage leads to stronger wage pressure and higher unemployment in equilibrium. The upshot is the existence of a long run tradeoff between unemployment and inflation. Incorporating a non-union sector allows for an investigation of the causes of nominal wage rigidity outside the union sector, as well as for comparisons between countries with different degrees of unionisation. I find that the extent of downward nominal wage rigidity, and the unemployment costs associated with very low inflation that this involves, are related to three key factors: the coverage of collective agreements, the legal framework at renegotiations of collective agreements, and the strictness of the employment protection legislation for non-union workers. These are novel empirical predictions that can be tested for in future empirical work. The predictions are consistent 4 empirical studies indicating that downward nominal wage rigidity is stronger in Sweden and Italy than in Switzerland, the UK and the US (see references below). In the formal model I neglect that agents may care about nominal changes. This is done to simplify the formal analysis, as well as making clear that such “money illusion” is not necessary for inflation to have real effects. However, in the concluding remarks, I argue that fairness considerations and the legal effects focused here may in fact reenforce each other. The contract idea of the present paper is very different from the literature on overlapping wage contracts of Taylor (1979), both when it comes to theoretical explanation and empirical implications. In the present model, persistent nominal rigidity linking consecutive contract periods is explained without staggering of wage contracts. Furthermore, the long-run Phillips curve has downward-sloping parts, in contrast to the vertical long run Phillips curve in the overlapping contracts literature. The argument of the present paper has important implications for the inflation target that monetary policy should aim at. In countries with high bargaining coverage and regulated labour markets, aiming at very low inflation may involve considerable costs in the form of higher unemployment and reduced output. In contrast, in countries with low bargaining coverage and weak employment protection legislation, aiming at low inflation is likely to have a much smaller impact on unemployment. This contention is consistent with the empirical findings of Bullard and Keating (1995) for the period 1960-90. They find that a negative and significant long-run response of output to a reduction in inflation in European countries with low inflation (Germany, Austria, Finland and the UK), but they do not find a similar relationship in the US. Note, however, that I do not aim at 5 finding the optimal rate of inflation - inflation clearly also involves important costs, associated with among other things increased uncertainty, reduced money holdings and capital taxation, all of which are neglected in the present paper (see eg Feldstein, 1997). The remainder of the paper is organised as follows. The basic model is provided in sections 2 and 3. Section 4 derives the equilibrium of the model. Numerical simulations are presented in section 5. In section 6, I discuss available empirical evidence. Section 7 concludes. All proofs are in the appendix. 2 The model We consider a standard monopolistic competition economy, consisting of a large number K symmetric firms, each producing a different good (alternatively, firms may be thought of as industries, each consisting of several firms that produce an identical product under Bertrand competition). A share γ of the economy is unionised, with one union in each firm, each with 1/K members. In these firms, the wage is set in a bargain between union and firm. The remaining share (1 – γ) is non-unionised, and the wage is set in an individual bargain between the worker and the firm. The model considers one contract period. However, a key assumption (to be discussed below) is that there is a nominal wage contract from the previous contract period, WU-1 in all unionised firms, and WN-1 in non-unionised firms, and this contract can only be changed by mutual consent (see Gottfries, 1992, for a possible explanation of why wage contracts may be in nominal terms). For modelling purposes related to the wage setting, the contract period is divided into an infinite number of short time spans. In each such time span, a small fraction s of 6 the labour force leaves the work force (“retires”), and is replaced by identical workers entering as unemployed. At the immediate beginning of the contract period, the following events take place. First, the central bank (CB) sets the total money stock M > 0. Second, wages are set simultaneously in each firm. Third, each firm sets the price and employment levels. All agents are fully aware of how the economy works, so they can predict what other agents will do at the same and later stages of the model. As agents are small, they treat the aggregate variables as exogenous. Observe that in contrast to the literature on overlapping nominal contracts, wage and subsequently price setting are simultaneous in each firm, with perfect knowledge about the monetary policy. Thus, the effects of monetary policy in equilibrium should be interpreted as long run effects that are not based on expectational errors. Each firm j has a constant returns to scale production function Yj = Nj, where Yj is output and Nj is employment. In principle, Yj and Nj (as well as the other flow variables) may vary from time span to time span, however, in equilibrium they will be constant, and for notational simplicity I do not index time span. The real profits of the firm are (1) Πj = (PjYj –WjNj)/P, where Pj is the price of output, Wj is the nominal wage in firm j, and (2) η η − − ∑ =1 1 1) 1 ( j j P K P η > 1, is the aggregate price level. The demand function facing each firm is 13 from actually stopping work. Bargaining is undertaken under holdout threats, as discussed in relation to equation (11) above. One way to view this is that the player who wants to renegotiate the contract by use of work stoppage threats has a strategic disadvantage. To raise the wage above the outcome from a holdout, the union must threaten to call a costly strike, and the costs associated with calling a strike weaken the potency of this threat. Correspondingly, the costs that the firm incurs by initiating a lock-out weaken the potency of lock-out threats. As the old contract may affect the bargaining outcome, the parties should ideally take into consideration that the bargaining outcome affects future wage negotiations. This is neglected in the present model. However, in Holden (1997), I analyse an infinitehorizon version of a similar model, where agents take into consideration how the bargaining outcome in one period affects subsequent negotiations. There it is shown that this feature does not affect the qualitative results, only dampens the magnitudes. We then turn to wage setting in the non-unionised firms. Here, wages are set in an individual bargain between worker and firm, and again there is an existing nominal wage contract that can only be changed by mutual consent (MacLeod and Malcomson, 1993, consider a similar model). As this assumption is crucial for the analysis, I’ll take some time to justify it. Most workers in Europe are hired in permanent jobs. The general legal principle is then that the prevailing terms of employment are interpreted as a legal contract, and may as such only be changed by mutual consent. To reduce wages, the employer must persuade the employee to accept the wage cut. One possibility is to threaten to lay off the employee temporarily or permanently unless he accepts a wage cut. In principle, the 14 employer can terminate the employment contract and offer a new contract with lower pay. However, in some countries, courts may interpret a job offer at lower pay as evidence that the initial dismissal was unwarranted, unless the wage reduction could be justified by the economic situation of the firm. In countries with weak employment protection legislation, like the UK, enforcing a cut in nominal wages is likely to be more feasible than in countries with stricter employment protection legislation, like Germany, Italy and Sweden. In the US, the legal situation is different, as the requirement of mutual consent is largely irrelevant: if the employer announces a wage cut, the general principle is that the employee's continuance in service is considered to constitute acceptance (see Malcomson, 1997, for a further discussion). In many cases, the remuneration also consists of more "flexible" parts, like bonus schemes and fringe benefits, which may give the employer some scope for reducing pay even within the existing contract (the effects of this is considered in footnote 7 below). Note, however, that while annual fluctuations in the factors that these forms of remuneration depend on may lead to annual fluctuations in pay, there may still be contractual and labour regulations that severely restrict employers' scope of reducing remuneration at will. Lebow, Saks and Wilson (2000) show that US firms are able to circumvent some, but not all the wage rigidity by varying benefits. Why does the institutional feature preventing employers from unilaterally cutting nominal wages exist? It can be seen as a consequence of the requirement of mutual consent to change contracts that applies in standard contract law. This feature may play an important role in inducing efficient levels of investment, by preventing one player 15 from reaping the return of the investment of the other by demanding a renegotiation of the contract (MacLeod and Malcomson, 1993, and Holden, 1999). Then return to the model: In contrast to the collective bargaining case, it does not seem realistic to allow players to stop work temporarily as a means of enforcing a change in the wage (ie. no strike or lockout). On the other hand, terminating the relationship permanently (quits or layoffs) is more relevant than under collective bargaining. If the firm decides to lay off the worker and recruit a new one, I assume this involves an additional cost Z > 0. These costs include possible severance pay, legal costs, as well as the costs of hiring and training a new worker. Z is clearly increasing in workers' alternative income; for tractability, I assume a proportional relationship, ie Z = zR, where z > 0.5 In addition, I assume that there is a potential shirking problem, á lá Shapiro and Stiglitz (1984) (workers' effort is imperfectly monitored), so that the firm must ensure that the wage is sufficiently high that workers do not shirk. 6 If a shirking worker is discovered and fired, he may expect to obtain workers' alternative income R. However, as the probability that a shirker is caught is less than one, the firm must pay more than the expected payoff if being fired. The analysis of this situation is straightforward but 5 It would be realistic to assume that Z also depends on the situation of the firm, as to whether e.g. the firm wants to increase or reduce employment, but such issues are not well captured in a model, which is essentially static. 6 The shirking problem is incorporated to ensure unemployment in equilibrium – otherwise all workers would be hired in the non-unionised sector. Note also that while the shirking problem and the firing costs also applies to unionised firms, they will not affect the wage setting in these firms on the assumption that the union is sufficient strong to push wages above the levels for which shirking and firing costs are relevant (formally, it is assumed that kS > kE and kL > kZ). For expositional reasons, shirking and firing costs were thus not mentioned under unionised wage setting. 16 cumbersome, and to save space I just postulate a non-shirking constraint à là ShapiroStiglitz (1984) that the wage must satisfy, (12) Rk P WE N ≥ k E > 1. Formally, I consider a Rubinstein-type framework where players alternate in making offers. As long as the players are bargaining, both receive the payoff of the existing contract. However, whenever a player has rejected an offer, the player has the option of terminating the relationship permanently. The game thus constitutes a straightforward application of a standard Rubinstein game with outside options, and it follows directly using standard arguments that the outside option principle of Binmore, Shaked and Sutton (1989) applies: the outside options only affect the bargaining outcome if they are better than the “inside” alternative (in this case the payoff of the existing contract). (MacLeod and Malcomson derive a similar result; however, in their model the old contract can also be changed due to threats of stopping work.) Thus, if the real value of the old contract, WN-1/P, is below kER, firms will agree to raise the wage so as to avoid shirking. If the real value of the old contract is above kZR, where kZ = kE + z, firms may credibly demand a wage reduction, because in this case it would be less costly to lay off the workers and hire a new one, than to pay the old contract. However, the firm will not be able to push the wage down below kZR, because the worker will reject this. Finally, if 17 kER ≤ WN-1/P ≤ kZR, neither of the players can credibly demand a wage change, and the old contract will be prolonged. The result is summarised in the following Proposition7: Proposition 2 The unique SPE outcome to the wage bargaining in a non-union firm j is 1 11 1 () " " , ()" " , ()" " , NN EE NNN EZ NN ZZ WW ie ff icienc y wa g ecase I f kR kR PP WWW ii holdout case If k R k R PPP WW iii la y o ff case I f kR kR PP − −− − <=  ∈=  >= 4 The equilibrium We now turn to the equilibrium of the whole economy. For sake of comparison, we first consider an alternative legal regime, which essentially involves the standard assumptions in the literature. In the union sector, I assume that production cannot take place under the wage negotiations, ruling out the possibility of holdout. In this case the bargaining outcome is given by the Nash bargaining solution where both disagreement points are set to zero, irrespective of the wage of the old contract. As shown in the appendix, the outcome can be written on the form WU/P = kBR, where kL > kB > kS. In the non-union sector, I assume that employment is at-will, so that the firm may essentially unilaterally set the wage. Furthermore, I neglect other possible costs associated with cutting the wage, 7 As under union wage setting, one can show that if both parties can inflict a cost on the opponent without violating the existing contract (eg the firm reduces bonuses, and the employee reduce the quality of his work), the pay changes at a rate κN, ie. WN = (1+κN)WN-1. κN may be positive or negative depending on the institutional framework, like the strictness of employment protection legislation, which provides the worker with scope for reducing effort without being fired. For simplicity, I set κN to zero. 18 like adverse effect on morale etc, in effect setting z = 0. In this case the firm will always ensure that the efficiency wage restriction is binding, implying WN/P = kER. As explained in the Layard, Nickell and Jackman (1991), in wage setting models the equilibrium can be derived by imposing that the real wage that comes out of the wage setting is consistent with the real wage implied by the price setting. Combining (2), (6) and (7), we find that the price setting implies that the aggregate real wage is a constant (because of constant returns to scale and constant elasticity of demand): W/P = 1/ν. As for the wage setting, we substitute out for WU/P = kBR and WN/P = kER in (6). The requirement that wage and price setting be consistent thus implies that (13) () () () () () () 1 11 1 1 11 1 (1 ) 1 (1 ) BE BE BE B E kRP kRP WkR PP where k k k ηη η ηη η γγ ν γγ −− − −− − +− == = ≡+− Substituting out for R using (5), and linearising σ(u) ≡ σu, where σ > 0, to obtain an explicit solution for the equilibrium rate of unemployment, we get (14) B k k uBE BE B − − = ν ν σ / 1 /11 Observe that, here and below, the equilibrium rate of unemployment exhibits standard properties by being increasing in the markup of wages over workers' alternative income (kB and kE), and in the payoff of the unemployed B relative to the average real wage 1/ν, and decreasing in the difficulty of finding a new job given the rate of unemployment (σ). The rest of the model then follows from straightforward substitution in the relevant 19 equations (cf appendix), and the results are summarised in Proposition 3, involving the standard properties in the literature (as in Layard et al, 1991): Proposition 3 In a legal regime where holdout is banned in the union sector, and employment at-will prevails in the non-union sector, the unique equilibrium rate of unemployment is uB, given by (14). All nominal variables are homogenous of degree one in the nominal money stock, so that the size of the nominal money stock does not affect real variables. Then return to the main model of the paper. There are now several different types of equilibria, and as will become apparent below, the size of the nominal money stock relative to the nominal wage of the old contracts determines which type prevails. Consider first an equilibrium where strike threats are used in unionised firms, and the efficiency wage applies in the non-union sector. The equilibrium requirement that price setting is consistent with wage setting gives an equation of the same form as (13), which as above can be used to derive the equilibrium rate of unemployment (15) () () () η ηη γγ ν ν σ − −− −+≡ − − =1 1 11 )1( /1 /11 ESSE SE SE Skkkwhere B k k u Comparing (15) and (14) shows that the only one difference between the standard regime and the strike regime is related to kS < kB, implying that uS < uB; the possibility of holdout actually weakens the potency of strike threats (cf. Proposition 1), thus mitigating wage pressure and reducing equilibrium unemployment. 20 Then consider an equilibrium where lock-out and layoff threats apply in, respectively, union and non-union firms. As above, we can solve for equilibrium unemployment (16) () () () η ηη γγ ν ν σ − −− −+≡ − − =1 1 11 )1( / 1 /11 ZLLZ LZ LZ Lkkkwhere B k k u Comparing (16), (15) and (14) shows that the lock-out equilibrium is associated with higher unemployment than both the strike equilibrium and the standard legal regime, uL > uB > uS. This follows from the fact that kLZ > kBE > kSE. Intuitively, firms are at a strategic disadvantage in a lock-out equilibrium: In the union sector, the costs associated with initiating a lockout imply that unions can demand a high markup on the alternative income (kL > kB); in the non-union sector, the costs of replacing a worker can be exploited by the incumbent worker to obtain a higher wage than would be given to a newcomer (kZ > kE), and both these features imply that a higher rate of unemployment is required in equilibrium. Proposition 4 shows that the monetary policy determines which regime prevails (proof in appendix). Proposition 4 There is a trade-off between unemployment and inflation over a range of equilibrium rates of unemployment [uS, uL], where the outcome depends on the value of the nominal money stock. Specifically, there exist critical values MS and ML, and associated inflation rates πS and πL, where MS > ML, πS > πL, and πS > 0, such that (i) If M > MS, strike threats prevail in the union sector, efficiency wages in the non-union sector, inflation P/P-1 – 1 ≥ πS, and the rate of unemployment, u = uS. 21 (ii) If M ∈ [ML, MS], holdout threats prevail in at least one sector, inflation P/P-1 -1 ∈ [πL, πS], and the rate of unemployment u ∈ [uS, uL]. (iii) If M < ML, lock-out threats prevail in the union sector, and layoff threats in the non-union sector, inflation P/P-1 -1 ≤ πL, and the rate of unemployment, u = uL. Proposition 4 entails important non-linearities between monetary policy, inflation and industrial action. In the low unemployment equilibrium, u = uS, strike threats must prevail in the unionised sector, and efficiency wages in the non-union sector. As all unions can obtain a nominal wage (1+κ)WU-1 by a holdout, strike threats must give at least this wage, and this puts a lower bound on the rate of inflation. Specifically, if money growth is sufficiently high to involve inflation greater than πS, (which is equivalent to M > MS), the economy will be in the “strike” regime. Likewise, the high unemployment equilibrium, u = uL, is associated with lock-out threats in union firms, and the layoff case in non-union firms. Firms can credibly cut wages from the level associated with the old contract, which will happen if money growth is so low that inflation is below πL, ie that M < ML. For intermediate levels of the money stock, M ∈ [ML, MS], inflation is between the critical rates πL and πS, so that nominal rigidity is binding in at least one sector, while unemployment takes an intermediate value, between uS and uL. (McDonald, 1995, surveys other theories of a range of equilibria.) 5 Simulation results Proposition 4 above establishes the existence of the long run trade-off between inflation and unemployment. Moreover, a comparison with Proposition 3 shows that the 22 possibility of holdout threats and the existence of firing costs hold the key to the long run effects of monetary policy. However, the practical importance of these results depends on the quantitative effects; this is the topic of the numerical simulations presented in this section. Here I also allow for additional features that are not included in the theoretical model. First, productivity growth leads to growth in real wages, allowing for growth in nominal wages even at constant nominal prices. I include annual labour productivity growth at a rate α = 0.02. Second, there is heterogeneity at industry/firm level, involving changes in relative wages: I distinguish five groups within each sector, unionised and non-unionised, and add a group-specific stochastic term (standard error 0.01) to the bargaining outcome except in the holdout cases (cf appendix). Figure 2 shows the trade-off between inflation and unemployment in the form of a long-run Phillips curve under the basis simulation (see also Table 1, column 2). Note that the highly stylised nature of the model implies that the position of the Phillips curve, as well as the entries in Table 1, should only be considered as illustrative. Yet the simulations provide a rough indication of the mechanisms that are at work, and of the relative importance of the various effects. According to the basis simulation, inflation can be reduced down to 1.9 percent on annual basis with only a small increase in unemployment, from 6.5 to 6.7 percent. However, a further reduction in inflation involves a larger increase in unemployment, by almost ½ percentage points (to 6.9 percent) at inflation of 1.4 percent, and by 2.5 percentage point (to 9.2 percent) at 1 percent inflation. Absolute price stability - zero inflation - involves in increase in unemployment of more than 3.5 percentage points, up to 10.2 percent. (Incidentally, Lundborg and Sacklèn, 2001, find in a study of Sweden for 29 consequence of this is that additional unemployment may occur for somewhat higher rates of inflation than if the monetary policy could be set specifically for each country. The costs associated with higher unemployment under very low inflation will clearly induce changes in the way labour markets operate. One would expect pay systems to become more flexible, for example by more extensive use of bonus systems (leading to a reduction in the nominal wage increase under holdouts, κ), which would mitigate the inflation bias. One would also expect more use of temporary employments contracts (Holden, 2001), a tendency that has taken place in many European countries over the last decades. However, it is difficult to predict how far-reaching the changes will be. As observed above, the legal rule that contract renegotiations require mutual consent plays an important role in ensuring efficient investments. Furthermore, restrictions on the employer’s right to unilaterally cut nominal wages seem a key ingredient if employment protection legislation is to be effective. Thus, proposals for changes in labour laws are likely to be met by strong resistance by unions and insiders. The key alternative explanation of downward nominal wage rigidity is fairness considerations. In my view, these two explanations should be seen as complementary rather than alternative. In particular, it seems plausible that they may strengthen each other in the sense that the existence of both makes either more persistent: The fact that many labour market participants find nominal wage cuts unfair may also contribute to the continued existence of legal protection of nominal wages. The legal protection of nominal wages makes wage cuts rare even in a low-inflation environment, thus preventing Gordon’s (1996) argument that the fairness considerations will be undermined by wage cuts being “too common”. The extensive downward nominal wage rigidity in 30 Sweden and Switzerland documented by Agell and Lundborg (1999) and Fehr and Goette (2000), even after years of close to zero inflation and high unemployment, also show that rigidities may be highly persistent. Appendix Derivation of (11), the outcome of the wage bargaining during a holdout The real wage outcome under holdout threats is given by (as noted below, the limit case of the Rubinstein model corresponds to the Nash bargaining solution) (17) Wj/P = arg max[Π(Wj/P, M/P)–(1-τ)Π(WU-1/P,M/P)] [U(Wj/P, R, M/P)–(1-ε)U(WU-1/P, R, M/P)] Using linear approximations to the true payoff functions, ie. Π(WU-1/P, M/P) ≈ Πw WU-1/P and U(WU-1/P, R, M/P) ≈ Uw WU-1/P, the Nash bargaining solution (17) reads (omitting subscript indicating firm) Wj/P = arg max[(Wj/P–WU-1/P)Πw +τΠ(WU-1/P, M/P)] [(Wj/P–WU-1/P)UW +εU(WU-1/P, R, M/P)]. The first order condition can be rearranged to 11 1 1 ( /, /) ( /,, /) 2 UU U j ww WW W PM P UW PRM P PP U τε −− −  Π =+ −  Π  which can be reduced to (11) (invoking the same linear approximations). QED 31 Proof of Proposition 1 To find the SPE outcome, we must analyse the game backwards. As of step 3, we have the Rubinstein (1982) bargaining game. Binmore, Rubinstein and Wolinsky (1986) show that in the limit when the time delay between offers converges to zero, the outcome is given by the Nash bargaining solution (assuming for simplicity that players have equal discount factors). If a work stoppage is initiated, the bargaining outcome is given by (18)                 Π= P M R P W U P M P W P Wj U j F j,,,maxarg λλ Substituting out for (9) and (10), the first order condition can be solved for (19) kwhereRk P WBB j1 12 12 ,> −−− −− ≡= ϕηϕη ηϕη Consider now the choice of the parties whether to initiate a work stoppage in step 1 or 2. Clearly, no party will initiate a work stoppage, leading to a costly dispute, if he/she can obtain higher payoff by renegotiation under a holdout. To formalise this intuition, define two critical values ωL and ωS for the real wage outcome by the following equations (20) ()( ) PMRkPM BFL /,/, Π=Π λω (21) ()( ) PMRRkUPMRU BUS /,,/,, λω = 32 The firm can obtain a payoff λFΠ(kBR, M/P) by initiating a work stoppage. If (1+κ)WU-1/P ≤ ωL, the firm obtains at least as high profits by a holdout leading to a new agreement on (1+κ)WU-1/P than by initiating a work stoppage. Likewise, if (1+κ)WU-1/P ≥ ωS, the union obtains at least as high utility from a holdout as from initiating a work stoppage. From the fact that ∂Π/∂(Wj/P) < 0, ∂U/∂(Wj /P) > 0 and λU, λF < 1, it is immediate that ωS < kBR < ωL for all R. Let me then prove that ωL and ωS are linear functions of R, ωL = kLR and ωS = kS R. To show this, note that substituting out for Π using (9), (21) can be solved for (22) BFLLL kkwhereR kR η λω − ≡= 1 1 )()( To verify the same property for ωS, substitute out for (10) in (22) to obtain (ωS-R)(ωS)-η = λS(kBR -R)(kBR)-η. Dividing by R1-η, we obtain ((ωS/R)-1)(ωS/R)-η = λS(kB-1)(kB)-η, which determines a unique value kS = (ωS/R) in the appropriate interval for ωS/R (which is (1, ν)), validating the assumption that ωS is a linear function of R, ωS = kSR. I now complete the proof by sketching the equilibrium path. (It is straightforward to show that a deviation would hurt the deviator.) Case (i), The firm offers kSR, which is immediately accepted by the union. Case (ii), Any offer different from (1+κ)WU-1/P is rejected, with no work stoppage. Case (iii), There are two alternative equilibrium paths, leading to the same outcome. One path is that the firm offers kLR, which the union accepts. The other is that the firm offers less, is rejected by the union, and then the union offers kLR which the firm accepts. QED Proof of Proposition 3 The real wages in the two sectors are found by inserting uB in the expression for R, to obtain WUB/P = kBRB, and WNB/P = kERB, where RB ≡ (1-uB)/ν + uBB. Output levels in the two sectors are YUB = γ(νkBRB)-η(M/P) and YNB = (1-γ)(νkERB)-η(M/P). To find the 33 equilibrium value for the real money stock, we substitute out for sectoral employment in the definition of the rate of unemployment, using that YU = NU and YN = NN, ie (23) uB = 1 – YUB – YNB = 1 - γ(νkBRB)-η(M/P) – (1-γ)(νkERB)-η(M/P). Rearranging, we find the equilibrium real money stock as (24) ηη νγνγ −− −+ − =       ))(1()( 1 RkRk u P M EB B B It follows that the equilibrium price level is homogenous of degree one in the nominal money stock, P = [1/(M/P)B] M, and so are all other nominal variables. The real variables are derived by inserting for (M/P)B in the relevant expressions. Proof of Proposition 4 Part (i): Analogously to the proof of Proposition 3, the equilibrium level of the real money stock associated with equilibrium where strike threats and efficiency wages prevail, is given by (with obvious notation) (25) ηη νγνγ −− −+ − =       ))(1()( 1 RkRk u P M ES S S In an equilibrium where strike threats and efficiency wages prevail, the nominal wages in the two sectors are functions of the nominal money stock (26) M PM RkPRkW S SSSSUS )/( 1 == (27) M PM RkPRkW S SESENS )/( 1 == 34 The critical value MS, given by MS = max[MUS, MNS], where MUS is given by (28) WUS = kSRSMUS/(M/P)S = (1+κU)WU-1 Or, solving for MUS, (29) MUS = (M/P)S(1+κU)WU-1/(kSRS) Likewise, MNS is given by (30) MNS = (M/P)SWN-1/(kERS) From the definitions of MS, MUS and MNS, it is now clear that WUS > (1+κU)WU-1 and WNS > WN-1 for all M > MS. Using the results of Propositions 1 and 2, this implies that strike threats and efficiency wages prevail if M > MS, which again implies (as derived in the main text) that u = uS. The minimum associated rate of inflation, πS, is then given by πS = P/P-1 –1 = [1/(M/P)S] MS/P-1 – 1. This completes the proof of part (i). Part (iii): The proof is analogous to the proof of part (i): just define ML = min[MUL, MNL] and replace superscript S with superscript L, and superscript E with superscript Z, in equations (25) – (30)). We then find that WUL < (1+κU)WU-1 and WNL < WN-1 for all M < ML. πL is given analogously to πS, by πL = [1/(M/P)L] ML/P-1 – 1. Part (ii): As inflation is increasing monotonically in M, it follows that π is in the interval [πL, πS], for all M satisfying ML ≤ M ≤ MS. From the proofs of part (i) and (iii), it also follows that holdout threats prevail in at least one sector. The contention that ],[ LS uuu ∈ follows from the fact that if u < uS, then WUS > (1+κU)WU-1 and WNS > WN-1 so that 35 holdout threats does not apply in either sector; correspondingly, if u > uL, then WUL < (1+κU)WU-1 and WNL < WN-1 so that holdout threats does not apply in either sector. QED Numerical simulations The numerical simulations are done in the Nonlinear application in Gauss, based on the following equations (firms i =1-5 are unionised, 6-10 non-unionised). (31) ()()( ) η ηηηηηηηηηη γγ − −−−−−−−−−− ++++−+++++= 1 1 1 10 1 9 1 8 1 7 1 6 1 5 1 4 1 3 1 2 1 1)1(2.02.0 PPPPPPPPPPP (32) ()()( ) η ηηηηηηηηηη γγ − −−−−−−−−−− ++++−+++++= 1 1 1 10 1 9 1 8 1 7 1 6 1 5 1 4 1 3 1 2 1 1)1(2.02.0 WWWWWWWWWWW (33) (, ) (1 ) WW R Ru u uB PP σσ =≡−+, (34) u = 1 – N = 1 - Σj Nj (35) Pi = νWi, where ν = η/(η-1) > 1. (36) ) ~ 1( i S US idRPkW += i = 1, 2, 3, 4, 5 (37) 1; )1( − += i UU UH iWW κ (38) ) ~ 1( i L UL idRPkW += (39) max min , US UH UL iiii WWWW   =  i = 1, 2, 3, 4, 5 (40) (1 ) NS E ii WkRPd=+ % i = 6,7,8,9,10 (41) 1;− =i N NH iWW (42) ) ~ 1( i Z NL idRPkW += (43) max min , NS NH NL iiii WWWW   =  i = 6, 7, 8, 9, 10 (44) () 1 15 i i P M NPP η γ α −  = + i = 1, 2, 3, 4, 5 (45) () 11 15 i i P M NPP η γ α −−  = + i = 6, 7, 8, 9, 10 (46) )1( 1gMM += − (47) )1( 1, jjj gMM += − (48) )1,0(~,*01.0*67.0 1, Nvvsswheresgg jjjj + =+= − j = 1,..12 36 In the EMU simulation, (47) and (48) replace (46) to give the nominal money stock, and (31)-(45), (46)-(46) are solved for 12 different countries. To ensure that the shock to relative wages, i d ~ , is basically exactly that, I use an auxiliary variable i d ˆ which is independently and normally distributed with zero expectation and variance 0.01. Then, I define the average shock ∑ =ii dd ˆ 10 1, and let ddd ii −= ˆ ~ . To avoid noise arising from stochastic wage setting and initial conditions, I let the economy run for 55 periods, with an exogenous money growth rate g that determines the rate of inflation. The entries in Table 1 are the average rate of unemployment over the last 50 periods. In the EMU simulations, the entry is the average for all 12 countries. To calculate the proportion of nominal wage cuts, I define a dummy variable Di = 1 if W it-1 > Wit, i = 1, 2, 3 .. 10, and then calculate the proportion of wage cuts as (49) ( ) () 12345 678910 Pr 0.2 0.2(1 )opcut D D D D D D D D D D γγ =+++++−++++ 37 References: Agell, J. and H. Bennmarker (2002). Wage policy and endogenous wage rigidity: A representative view from the inside. CESifo WP 751. Agell, J. og P. Lundborg (1999). Survey evidence on wage rigidity and unemployment. IFAU WP 1999:2, Uppsala, Sverige. Akerlof, G.A., W.T. Dickens and W.L. Perry. (1996). The macroeconomics of low inflation. Brookings Papers on Economic Activity 1, 1-75. Akerlof, G.A., W.T. Dickens and W.L. Perry. (2000). Near rational wage and price setting and the long run Phillips curve. Brookings Papers on Economic Activity 1, 1-60. Altonji, J.G. and P.J. Devereux (1999). The extent and consequences of downward nominal wage rigidity. NBER Working Paper 7236. Ball, L. and N. G. Mankiw (1994). Asymmetric price adjustment and economic fluctuations. Economic Journal, 247-261. Beissinger, T. and C. Knoppik (2000). Downward nominal rigidity in West-German earnings 1975-1995. University of Regensburg Discussion Paper No 344. Bewley, T.F. (1999). Why Wages Do Not Fall During a Recession? Harvard University Press. Blanpain, R. (ed) (1994). International Encyclopaedia for Labour Law and Industrial Relations. Deventer: Kluwer Law and Taxation Publishers. Binmore, K., A. Rubinstein, and A. Wolinsky (1986).The Nash bargaining solution in economic modelling. RAND Journal of Economics 17, 176-188. Binmore, K., A.Shaked, and J. Sutton (1989). An outside option experiment. Quarterly Journal of Economics 104, 753-770. Bullard, J. and J.W. Keating (1995). The long-run relationship between inflation and output in postwar economies. Journal of Monetary Economics 36, 477-496. Calmfors, L. A Booth, M. Burda, D Checchi, R Naylor, and J. Visser (2001). The future of collective bargaining in Europe. In T. Boeri, A Brugiavini, and L. Calmfors (eds). The Role of Unions in the Twenty-First Century Oxford: Oxford University Press. Christofides, L.N. and M.T. Leung (1999). Wage adjustment in contract data: Wage rigidity and menu costs. Mimeo, University of Guelph. Cramton, P. and J. Tracy. (1992). Strikes and holdout in wage bargaining. Theory and data. American Economic Review 82, 100-121. 38 Dessy, O. (1999). Wage rigidity in Italy. University of Southampton working paper. Fehr, E. and L. Goette (2000). Robustness and real consequences of nominal wage rigidity. Institute for Empirical Research in Economics, University of Zurich, WP 44. Feldstein, M. (1997). The Costs and Benefits of Going from Low Inflation to Price Stability. In C.D. Romer and D.H. Romer (eds). Reducing Inflation: Motivation and Strategy. The University of Chicago Press. Fortin, P. and K. Dumont (2000). The shape of the long-run Phillips curve: Evidence from Canadian macrodata, 1956-97. Mimeo, Canadian Institute for Advanced Research. Gordon, R. J (1996). Comment on Akerlof, Dickens and Perry, The macroeconomics of low inflation, Brookings Papers on Economic Activity 1, 61-66. Gottfries, N. (1992). Insiders, outsiders, and nominal wage contracts. Journal of Political Economy 100, 252-270. Holden, S. (1989). Wage drift and bargaining. Evidence from Norway. Economica 56, 419-432. Holden, S. (1994). Wage bargaining and nominal rigidities, European Economic Review 38, 1994, 1021-1039. Holden, S. (1997). Wage bargaining, holdout, and inflation. Oxford Economic Papers 49, 235-255. Holden, S. (1999). Renegotiation and the efficiency of investment. Rand Journal of Economics 30, 106-119. Holden, S. (2001). Does price stability exacerbate labour market rigidities in the EMU Empirica 28, 403-418. Keynes, J.M. (1936). The General Theory of Employment, Interest and Money. MacMillan. Kimura, T. and K. Ueda (1997). Downward nominal wage rigidity in Japan: Is price stability costly? Working Paper, Bank of Japan. Kramarz, F. (2001).Rigid Wages: What Have we Learnt from Microeconometric Studies, in Advances in Macroeconomic Theory, J. Drèze ed., 194-216, Oxford University Press, Oxford, UK. Knoppik, C. and T. Beissinger (2001). How rigid are nominal wages? Evidence and implications for Germany. IZA Discussion Paper 357, University of Regensburg.