1 Introduction A monetary union means that national interest rates and nominal exchange rates are no longer available to member countries as adjustmen

Transcription

1 Wage Setting Behaviour, the Monetary Union and the New Keynesian Model Edith Gagnon Bank of Canada Preliminary draft, comments welcome May 1, 25 Abstract Recent research has noted that the loss of adjustment mechanisms resulting from a monetary union membership may affect wage dynamics. In particular, Calmfors and Johanson (22) propose that EMU membership should increase incentives for wage indexation and shorter durations of wage contracts relative to non membership. This paper considers the implication of the EMU structural change on the euro-zone shortrun wage dynamics. The importance of household wage-setting behaviour is highlighted using a standard New Keynesian model with micro foundation. Rolling estimates of the wage indexation New Keynesian Phillips Curve (NKPC) indicate that the degree of wage indexation has increased and contract length has decreased among most EMU members as opposed to non-members such as the United States and the United Kingdom. This evidence is consistent with the Calmfors and Johanson model. JEL classification: E31 Key words: Indexation, wage-phillips curves, monetary union The views in this paper are those of the author and not necessarily those of the Bank of Canada. Edith Gagnon, Tel.: ; fax:

2 1 Introduction A monetary union means that national interest rates and nominal exchange rates are no longer available to member countries as adjustment mechanisms to economic shocks. Hence, the European and Monetary Union (EMU) will probably increase the demand for nominal wage flexibility, because of the need for alternative adjustment mechanisms to offset asymmetric shocks or desequilibrium. 1 In this context, the Calmfors and Johanson (22) model says that if EMU membership increases macroeconomic variability (because of a loss of stabilizing monetary policy), then EMU membership is likely to strengthen the incentives for wage indexation, thus meaning that nominal wages will be more flexible. 2 Similarly, contract length may be shortened. 3 They also point out that wage indexation is more likely if indexation decisions are taken in a decentralized rather than in a centralized fashion. 4 Although EMU as a whole has moved in the direction of more decentralization since the 199's, it has remained relatively centralized compared to the United States and the United Kingdom (OECD, 24). According to the Calmfors and Johanson (22) model, each wage setter chooses indexation to minimize employment and real wage variability arising from both demand and supply shocks. Hence, the gain of indexation is large. Outside EMU, indexation only protects against the employment and real wage instability caused by exchange rate shocks. Because the central bank then does not allow demand and supply shocks to affect the CPI, there is no need to stabilize these shocks, and there is no point in trying to stabilize employment this way. Therefore, indexation outside the EMU gives only a small stabilizing gain. The incentives to indexation are thus stronger inside than outside the EMU. For a contract length, Calmfors and Johanson adapt their model so that the assumption is that uncertainty is increasing over time, so that an optimal contract length reflects 1 According to the theory of the optimum currency area (Mundell 1961, Mc Kinnon 1963, and Kenen 1969), there remain principally three adjustment mechanisms to offset asymmetric shocks or desequilibrium in a monetary union (variation in wages, labour market mobility, and fiscal transfers). 2 It is commonly believed that a monetary union will increase macro economic variability. 3 However, note that lower inflation, which islikely to be associated with lower variability of the inflation rate, works in the direction of longer contract periods. The reason is that there is then less need for frequent revisions of nominal wage levels and the real wage consequences of given nominal wage changes are easier to forecast (Ball et al., 1988; Gottfries, 1992; Calmfors et al., 1997). 4 In the Calmfors and Johanson (22) model, if there is more nominal wage flexibility inside than outside, the EMU is at best an imperfect substitute for a national monetary policy. Increased nominal wage flexibility may even be socially undesirable. Although employment and real wage variability are reduced, the welfare gain from this could be outweighed by the welfare loss from more price variability. Since a socially optimal indexation is always lower than equilibrium indexation in the Calmfors and Johanson (22) model, the more centralized the decisions on indexation are, the less likely they are. 1

3 a trade-off between contract costs on the one hand and employment and real wage variability on the other. The total loss for a wage setter over a contract period is the sum of the contract cost and the squared deviations from the employment, real wage and CPI goals. Each wage setter's objective is then to choose contract length to minimize the total expected loss over a relevant time horizon. With numerical examples Calmfors and Johanson (22) show that wage indexations are larger inside than outside EMU and that wage contracts are shorter inside than outside the EMU. We propose to verify Calmfors and Johanson's (22) predictions with empirical evidence. In this context, the wage New Keynesian Phillips Curve (NPKC) is a useful tool. It allows one to consider the implication of the EMU structural change for wage dynamics. The wage NKPC describes wage dynamics driven by the wage gap which is the marginal rate of substitution between consumption and labour services in deviation from real wages. It is based on micro foundations of optimizing, monopolistically competitive households that receive random wage adjustment signals according to the Calvo (1983) formulation. 5 Following the work of Gali, Gertler, and Lopez-Salido (23), empirical implementations use an observable proxy for the marginal rate of substitution between consumption and labour services. In this paper, we use the wage indexation NKPC framework of Erceg, Henderson, and Levin (2) and examine rolling estimates of the degree of wage indexation and the Calvo wage signal (the wage contract length). These estimations are performed on the EMU (the euro zone), and individual EMU member countries before and after joining the EMU. 6 That should capture the change in wage setting policies due to EMU membership. Also, comparison with non-emu countries such as the United States,the United Kingdom, and Sweden would help bring additional evidence. The e stimations would be used to assess the Calmfors and Johanson (22) proposition, that the EMU will create incentives for an increase in wage indexation and a reduction in wage contract length. The parameters of the wage NKPC are estimated by GMM. 7 5 The structure we assume is analogous to the structure developed by Calvo to model price stickiness. Examples of early contributions to this kind of literature include Roberts (1995), Yun (1996), King and Wolman (1996), Rotemberg and Woodford (1997), and Goodfriend and King (1997). Excellent discussions of the framework are presented in Sbordone (21, and 23), Erceg, Henderson, and Levin (2), and Rabanal and Ramirez (21). 6 Gagnon and Khan (25) have estimated the Calvo price signal (the price contract length) for the euro zone, the United States, and Canada. 7 Sbordone (21,23) and Rabanal and Ramirez (21) use different estimation methodologies for the United States and the euro zone. They found estimates for the duration of wage contracts for certain points in time rather than across time. 2

4 We find evidence that the degree of wage indexation has increased during the period of EMU existence in the euro zone and its member countries. No evidence of change is found among most non-emu countries (the United States and the United Kingdom). In addition, we find evidence that the average duration of wage stickiness has decreased for the euro zone and some of its member states since the EMU years. In comparison, wage contract duration has remained stable in non- EMU countries during the same period. This evidence for the EMU members is in line with the Calmfors and Johanson (22) model. The rest of this paper is organized as follows. In Section 2, we describe the theory behind the wage NKPC. In Section 3, we present the wage indexation NKPC equation and model the wage gap. In Section 4, we present the data, the estimation methodology, and the results. Section 6 concludes. 2 Wage Setting Let us consider a monopolistically competitive market structure with a continuum of households distributed uniformly on a unit interval. 8 Each household, indexed by z 2 [; 1], supplies differentiated labour services, L t (z). A typical household, z, faces a downward-sloping demand curve for its services, ffl Wt (z) L t (z) = L t ; (2.1) The nominal wage charged by the household per unit of services is W t (z). W t The aggregate wage, W t, and labour services demand, L t, are represented as W t =[ R 1 W t(z) 1 ffl dz] 1 1 ffl and Lt = ffl R 1 [ L t(z) ffl 1 ffl dz] ffl 1, respectively.9 The parameter, ffl>, is the constant wage elasticity of demand facing a household, as well as the Dixit-Stiglitz elasticity of substitution between the differentiated labour services. Each household faces a constraint on the frequency of wage adjustment that it can undertake in response to shocks. This constraint reflects sticky-wage and staggered wage decisions across households. A tractable way to capture these aspects is described by Calvo (1983) to model price stickiness. Under the analogy of the Calvo set-up for wages, each household faces 8 The discussion of the theoretical model follows Yun (1996), Rotemberg and Woodford (1997), and Goodfriend and King (1997). 9 Assuming that a representative labour aggregator (or employment agency) combines household labour services in the same proportions as firms would choose. Thus the aggregator's demand for each household's labour is equal to the sum of firms' demands L t. 3

5 a constant probability (1 ) 2 [; 1] of adjusting its wage in any given period, independent of the history of previous wage adjustments. The average duration, D, for which a household's wage can remain unchanged is then 1. Each household chooses labour services to maximize 1 P 1 an expected lifetime utility j= fij E t [U t (z)(c j+j (z);l j+j (z); ο j+j )] subject to an intertemporal h i R t;t+j ;W r t;t+j (z)l tt; t + j(z) + a, where budget constraint P 1 j= E t [R t;t+j ;C t;j+j (z)]» P 1 j= E t R t;t+j is the stochastic discount factor that defines the present value at t of real income at time t + j. fi is the subjective discount factor. ο is a stochastic disturbance to household's preferences, W r t;t+j is the real wage; a is initial wealth. By minimizing the disutility of providing a given level of services, a household determines its desired real wage, which is equal to the marginal rate of substitution between consumption and labour services at a certain level of labour services supply (MRS t+j;t (z) U L U C (C t+j;t (z);l t+j;t (z))). 1 The desired real wage defines the real wage at which the marginal benefit of an increase in real wage is zero. At time t, a fraction, 1, of households are able to reset their wage. The wage-maximization problem for every wage-adjusting household is identical. Therefore, each household chooses the same optimal wage, W Λ t, by maximizing the expected discounted utility given the demand conditions, the budget constraints, and the possibility of wage stickiness in future periods. Formally, max 1X W t(z) j=» j Wt (z) E t R t;t+j P t+j 1 MRS t;t+j(z) L t;t+j (z) ; (2.2) where L t;t+j (z) represents the demand facing the household at time t + j whose wage is set at time t. Similarly, MRSt;t+ j(z) represents the marginal rate of substitution between consumption and providing a unit of labour service at time t + j when the wage of the labour services is set at time t. R t;t+j is the stochastic discount factor that defines the present value at time t of real income at time t + j. Defining the relative wage, X t W Λ t W t, the wage inflation rate Π W t W t+1, and the real wage Wt P t, the log-linear approximation (around a zero-wage-inflation steady state, ie Π W desired real wage steady state) of a household's optimal wage rule is 11 : 1 W t = 1 and a 1 With flexible wages, the usual condition is that real wages equal the desired marginal rate of substitution. 11 Where all variables are in deviation from their steady state. Notation: y t denotes the log deviation of a variable Y t from its steady state level. 4

6 x t =(1 fi) 1X j= ( fi) j E t "mrs t;t+j (z) w r t+j + where fi is the subjective discount factor, mrs t;t+j (z) w r t+j jx k=1 ß w t+k # : (2.3) represents the deviation of the household marginal rate of substitution from real wage. That is, the optimal wage depends on the current and future realizations of the marginal rate of substitution between consumption and labour services. 3 Wage NKPC 3.1 Nominal wage rigidity with wage indexation We use the wage model of Erceg, Henderson, and Levin (2) with wage indexation, which assume that households stipulate wage contracts in nominal terms, and that the wage of households that are not reset in t is indexed to the average price inflation rate of the previous period. 12 At the stipulated wage, households supply as many labour services as are demanded. We suppose that utility is separable into consumption and leisure. In this context, the aggregate wage level evolves according to W t = (1 )(W Λ t ) 1 ffl + (ß pρ t 1 W t 1) 1 fflλ 1 1 ffl the following form: 13 and the wage NKPC specification takes where ß w t ρß p t 1 = fie t(ß w t+1 ρßp t )+ μ t; (3.1) (1 )(1 fi ) ; D 1 (1 + l ffl)) 1 μ t is the wage gap and l depends on the marginal rate of substitution. 3.2 The wage markup As mentioned in Section 2, the equilibrium wage that solves the household optimization problem under flexible wages is equal to the ratio of the marginal disutilityofworking U L, and the marginal 12 Rabanal and Rubio-Ramirez (21) found that this model does a good job of explaining U.S. data. 13 With the objective of allowing for further inertia in inflation and greater persistence in output in a general equilibrium model, this modification was introduced first by Christiano, Eichenbaum and Evens (21)). As per Sbordone (21), we allowe for an intermediate degree of indexation as in the Woodford (21) formulation. Complete derivation of the wage NKPC equation with sticky nominal wages is in the appendix of Sbordone (21). 5

7 utility of consumption U C which in turn equals the marginal rate of substitution between consumption and labour services MRS t. We follow Gali, Gertler, and Lopez-Salido (23) and assume that the (log) marginal rate of substitution can be written as: mrs t = c c t + l l t ο μ t ; (3.2) where the coefficients c and l are the elasticities of the marginal rate of substitution with respect to consumption and labour services ( c is the inverse of the elasticity of intertemporal substitution and l is the inverse of the elasticity of labour supply). ο μ t is a low frequency preference shifter. 14 With flexible wages, the usual condition that real wages equal the desired marginal rate of substitution is met: mrs t = wt r. Hence, the wage markup is given by the difference between the marginal rate of substitution (the disutility ofwork) and the real wage: 15 μ t = mrs t w r t ; (3.3) When the wage markup is different from zero, it means that wages are not fully flexible and in Equation 3.1 indicates the speed by which nominal wage dynamic will adjust to that disequilibrium. Identification of the wage markup requires that we make assumptions on the coefficients c and l and on ο μ t. Following Gali, Gertler, and Lopez-Salido (23), we calibrate l =1 and c = 5. Those values are a reasonable compromise between the values suggested in the micro and macro literature. 16 To identify the low frequency shifter ο μ t, we define ^μ t = c c t + l l t wt r to be the observable component of the wage markup. It follows that: ^μ t = μ t + μ ο t ; (3.4) From this perspective, the wage markup μ t is the cyclical component of ^μ t and μ ο t is the trend component. Then, following Gali, Gertler, and Lopez-Salido (23), we approximate the low frequency movements of ^μ t by fitting a fifth-order polynomial of time to ^μ t. (s and wage 14 This preference shifter over consumption versus leisure can be interpreted broadly to include institutional or demographic changes that affect the labour market, but which are unlikely to be relevant to business cycle frequencies. 15 Notice that the wage markup should be understood in a broad sense, including the wage created by efficiency wages, payroll taxes paid by the firm and labour income taxes paid by the worker, search frictions, and so on. 16 Note that we also experiment with values for c between 3.3 and 1 as Gali, Gertler, and Lopez-Salido (23). 6

8 inflation for the euro zone and its members ' states, the United States, the United Kingdom, and Sweden are represented in Figure 1.) 7

9 Figure 1: (ß w t ) and wage markup (mrs t ) Euro Zone Netherlands Germany Belgium France Sweden Italy United States Spain United Kingdom

10 4 Data, Estimation, and Results 4.1 Data We use quarterly data with the sample periods 197Q1 to 23Q4 for the euro zone, 197Q1 to 24Q2 for Germany, France, the Netherlands, and Sweden, and 196Q1 to 24Q2 for the United States and United Kingdom. Data availability for Italy, Spain, and Begium forces us to use annual frequencies with a sample period 197 to 24 for the three countries. For other EMU members, data restriction does not allow us to estimate the model. German data are adjusted for the reunification of East and West. Hence, prior to 1991, the data are adjusted to reflect the whole country. Before doing any modifications to the series, they are reconstructed from 199 going backward to 197, using growth rates. Conceptually, each German series x t are adjusted as: X t X t+1 1+ X t, starting with t=199 to t=197. The Appendix gives a complete description of the data. 4.2 GMM estimation We estimate by generalized method of moments the parameters and ρ of the wage indexation NKPC of Equation 3.1, and compute values for the duration of wage stickiness D. The wage indexation NKPC orthogonality conditions are: 17 where, E t [(ß w t (1 ρß p t 1 fie t(ß w t+1 ρßp t ) )(1 fi ) μ t )z t ]=; (4.1) (1 + l ffl) D 1 1 and, the instrument set z t consists of four lagged variables t 1tot 4 for wage inflation, real wage, consumption and labour services. 18 The standard errors of the estimated parameters are modified using the Newey-West correction. Next, we test the model's overidentifying restrictions based on the J-statistic. The model restrictions imply that not all parameters can be estimated. We therefore calibrate fi to.9, c to 5. and l to For each GMM estimation that we perform, we apply the F-test to the first-stage regressions, to check the potential weakness of the instruments, as Staiger and Stock (1997) recommend. These tests indicate that the instruments used in the estimation are relevant. Staiger and Stock (1997) point out the importance of examining this statistic, as conventional asymptotic results may break down under the weak correlation between the instruments and the endogenous regressor. 18 Wehave chosen instruments that are correlated to the endogenous variables of the model. 9

11 4.3 Results Table 1 shows the results of the estimations of the wage indexation NKPC for the euro zone, its member countries, and non-emu countries (the United States, the United Kingdom, and Sweden). Estimates for the slope, the degree of wage indexation ρ, and the average duration D of wage contract with their p values are presented. To capture the EMU impact on the wage setting contract, the estimation results are presented for two periods. Recalling that the euro zone changed to the single currency on 1 January 1999, we split the sample accordingly. Hence, one period excludes the EMU's years (countries' first sample year up to 1998) where the other sample includes it (full countries' sample). Figures 2 and 3 plot the estimates for ρ and D with their 5 per cent confidence intervals. These figures' values are obtained by rolling regressions from a couple of years before the EMU's creation, 1997, to the end of each country's sample. We find that all estimates have good signs and are with some exceptions, significant. The euro zone estimates are all significant at the 95 percent for both periods (see Table 1). The average duration of wage stickiness has decreased since the introduction of the single currency. This reduction seems significant asthe point estimates prior to 1999 and after 1999 are not lying in the same confidence intervals (see Figures 2 and 3). In addition, we find some evidence that the degree of wage indexation to the past period inflation rate has increased since the EMU. However, the point estimates prior to 1999 and after 1999 don't seem significantly different since they lie on the same 95 percent confidence intervals. For individual EMU member countries, Figure 2 shows that the average duration of wage stickiness has decreased since 1999 in France, Spain, Belgium, and the Netherlands. However, the estimated values of D for Spain and Belgium prior to 1999 and after 1999 don't seem significantly different. For the degree of wage indexation, evidence for Italy, Spain, and Belgium is in accord with the Calmfors and Johanson assumptions. The estimated values of ρ seem to have increased in these countries since However, for Belgium, while close to one, ρ abnormally overpasses it at the end of the sample estimations. This might be due to the fact that Belgian's estimations are on annual data which significantly reduce the sample size. Counter evidence of the Calmfors and Johanson assumptions is only visible in Germany and, to a lesser extent, the Netherlands. For Germany, D has risen since 1999 while ρ has diminished. In the Netherlands, ρ has decreased to being not different from zero. Among the non-emu members, the United States and the United Kingdom, we find no evidence 1

12 of a change in the values of D or ρ prior to 1999 and after Although these estimates change slightly over time, they remain in the same confidence bands. In Sweden, both ρ and D show statistically significant reductions of their values. Overall, we have found evidence supportive ofthe Calmfors and Johanson assumptions. Nevertheless, although generally in favour, the evidence is not strong for all EMU member countries. Non-EMU countries such as the United States and the United Kingdom, provide further evidence to the Calmfors and Johanson model as they don't show as much change in the estimated coefficient of the wage indexation NKPC. It should be noted that the few years of existence of the EMU might reduce the possibility of capturing the EMU effect on wage contract setting in the estimations. Moreover, it is quite possible that the New Keynesian model captures other factors besides the EMU impact on wage contract setting. 11

13 Table 1: Wage Indexation NKPC estimates Country Period D ρ Period D ρ Euro Zone 197:1-1998: :1-23: (.) (.) (.) (.) (.) (.) Germany 197:1-1998: :1-24: (.1) (.) (.) (.6) (.) (.5) France 197:1-1998: :1-24: (.29) (.) (.) (.4) (.) (.) Italy (.) (.) (.) (.) (.) (.) Spain (.) (.) (.) (.) (.) (.) Netherlands 197:1-1998: :1-24: (.1) (.) (.4) (.7) (.) (.22) Belgium (.) (.) (.) (.) (.) (.) Sweden 197:1-1998: :1-24: (.1) (.) (.4) (.) (.) (.27) United States 196:1-1998: :1-24: (.) (.) (.) (.) (.) (.) United Kingdom 196:1-1998: :1-24: Note: p-values in brackets. (.1) (.) (.) (.1) (.) (.) 12

14 Figure 2: Estimates of the duration of wage stickiness (D) 4.9 Euro Zone 9.5 Netherlands Germany 2.2 Belgium France 9.5 Sweden Italy 3.7 United States Spain 7.25 United Kingdom

15 Figure 3: Estimates of the degree of wage indexation (ρ).8 Euro Zone.55 Netherlands Germany 1.1 Belgium France.25 Sweden Italy 1.2 United States Spain.3 United Kingdom

16 5 Conclusions We have examined the implications of a monetary union on short-run wage dynamics using the New Keynesian framework. The euro zone and individual EMU members are used to model the monetary union. The United States, the United Kingdom, and Sweden are used to compare the EMU membership impact to non-emu membership. Overall, rolling estimates of the wage indexation New Keynesian Phillips Curve (NKPC) for the euro zone and its member countries point to some increase in the degree of wage indexation since the introduction of the single currency. In addition, we find some evidence of decreases of contract length, in the euro zone and its member countries, during the period of EMU existence. In contrast, for non-emu countries, no evidence of a change in the way wage contracts are set has been found. This evidence is consistent with the Calmfors and Johanson (22) model. 15

17 APPENDIX Data Description A. Definition of the variables All the variables are quarterly time series with exception of Italy, Spain and Belgium for which data frequency is annual. All the variable are in log. German series P t, W t, L t, and C t are adjusted for the German reunification (see Data of Section 4). Price inflation is the quarterly growth rate of the total GDP deflator: ß p t = 1(lnP t -lnp t 1 ). is the quarterly growth rate of compensation of employees: ß w t = 1(lnW t - lnw t 1 ). Real wage is the ratio between nominal wage and total GDP deflator: w r t = 1(lnW r t ), where W r t = Wt P t. Labour services is total employment l t = 1(lnL t ). Consumption is aggregate of non-durable and services c t = 1(lnC t ). B. Data sources, series labels, and sample periods The euro zone data are updates from the European Central Bank (see Fagan, Henry, and Mestre (21)). All the other countries data are from the OECD. Country Period P t L t W t C t Euro Zone 197Q1 23Q4 Y ED LN N WIN PCR Germany 197Q1 24Q2 q:deu:pgdp q:deu:et q:deu:wsss q:deu:cpv France 197Q1 24Q2 q:f ra:pgdp q:f ra:et q:f ra:wsss q:f ra:cpv Italy q:ita:pgdp q:ita:et q:ita:wsss q:ita:cpv Spain q:esp:pgdp q:esp:et q:esp:wsss q:esp:cpv Netherlands 197Q1 24Q2 q:nld:pgdp q:nld:et q:nld:wsss q:nld:cpv Belgium q:bel:pgdp q:bel:et q:bel:wsss q:bel:cpv Sweden 197Q1 24Q2 q:swe:pgdp q:swe:et q:swe:wsss q:swe:cpv Unated sates 197Q1 24Q2 q:usa:pgdp q:usa:et q:usa:wsss q:usa:cpv Unated Kingdom 197Q1 24Q2 q:gbr:pgdp q:gbr:et q:gbr:wsss q:gbr:cpv 16

18 Figure 4: Price inflation (ß p t ) 4.5 Euro Zone 3. Netherlands Germany 12 Belgium France 7.5 Sweden Italy 3. United States Spain 7.5 United Kingdom

19 References Calvo, G.A Staggered Prices in a Utility-Maximizing Framework. Journal of Monetary Economics 12: Erceg, C., D. Henderson, and A. Levin. 2. Optimal Monetary Policy with Staggered Wage and Price Contracts. Journal of Monetary Economics 46: Gagnon, E. and H. Khan. 25. New Philips Curve Under Alternative Production Technologies for Canada, the United States, and the euro area. European Economic Review 49: Rabanal, P. and J.F. Rubio-Ramirez. 21. Nominal versus real Wage Rigidities: A Bayesian Approach. Federal Reserve of Atlanta Working paper Sbordone, A An Optimizing Model of U.S. Wage and Price Dynamics. Manuscript, Rutgers University. Economics 49: Staiger, D. and J. Stock Instrumental Variables Regression with Weak Instruments. Econometrica 65: To complete... 18