This note analyses the interaction between nominal wage stickiness and costly employment adjustment in a small closed-economy New Keynesian model with simple rule-based or optimal monetary policy. The results show (1) the costs of nominal and real rigidity to depend on the policy regime, (2) optimal policy to substantially contain the welfare loss, and (3) the absence of quantitatively important second-best interaction, suggesting that reducing rigidity along one dimension alone does not risk reducing overall welfare

Vogel, Lukas

Munich Personal RePEc Archive

MPRA
Munich Personal RePEc Archive
Interacting nominal and real labour
market rigidities
Lukas Vogel
November 2008
Online at http://mpra.ub.uni-muenchen.de/22647/
MPRA Paper No. 22647, posted 11. May 2010 19:09 UTC
1 
Interacting nominal and real labour market rigidities 
 
Lukas Vogel* 
DG Economic and Financial Affairs 
European Commission 
 
First version: November 2008 
This version: May 2010 
 
Abstract:  
This note analyses the interaction between nominal wage stickiness and costly employment adjustment 
in a small closed-economy New Keynesian model with simple rule-based or optimal monetary policy. 
The results show (1) the costs of nominal and real rigidity to depend on the policy regime, (2) optimal 
policy to substantially contain the welfare loss, and (3) the absence of quantitatively important second-
best interaction, suggesting that reducing rigidity along one dimension alone does not risk reducing 
overall welfare. 
 
 
JEL classification: E24, E32, J23, J30 
Keywords: wage stickiness; employment adjustment costs; second best 
 
1. Introduction 
The basic New Keynesian (NK) model emphasises the role of nominal rigidities for business cycles 
and monetary transmission. Real rigidities such as habit persistence on the demand and factor 
adjustment costs on the supply side are added to improve the empirical fit. The focus on real rigidities 
in the NK framework is more recent. Blanchard and Galí (2007) analyse the impact of real wage 
rigidity on the sacrifice ratio and inflation persistence. Ascari and Merkl (2009) investigate the effects 
of monetary policy shifts under real wage rigidity and given degrees of price stickiness. Lechthaler 
and Snower (2008) analyse the impact of labour adjustment costs on output and inflation persistence 
for constant price stickiness. Duval and Vogel (2007) depart from one-dimensional parameter 
variation and look at the interaction between nominal and real rigidities, concluding that price rigidity 
can be second best when real wages are sticky. 
                                                 
* Address: Lukas Vogel, European Commission, DG ECFIN, BU-1 3/129, B-1049 Brussels. Email: 
lukas.vogel@ec.europa.eu. 
2 
This note extends the analysis of the nominal-real rigidity interaction by looking at nominal wage 
stickiness and employment adjustment costs. It shows the welfare consequences of the interaction 
between labour market rigidities to depend on the policy regime and the nature of exogenous shocks. 
The note presents results for a simple interest rate rule and optimal monetary policy. While the former 
may approximate the actual conduct of policy; the latter indicates the smallest possible loss for given 
shocks and rigidity parameters. Results are given for technology, labour supply, consumption and 
monetary policy shocks. The remainder of the note outlines a small model with flexible prices, but 
nominal and real labour market rigidities and illustrates their interaction for simple rule-based versus 
optimal monetary policy. 
2. Model 
The analysis uses a small closed-economy model with labour as the only production factor. Goods and 
labour markets are monopolistically competitive, so that goods prices and wages are set with a mark-
up over marginal costs and the marginal disutility of labour, respectively. Goods prices are fully 
flexible. Nominal wages are sticky and derive from Calvo-staggered wage setting. Adjusting the level 
of employment is subject to quadratic employment adjustment costs. 
Consider a representative household maximising welfare as the discounted stream of period utility: 
(1) ∑∞= + ⎟⎟⎠
⎞⎜⎜⎝
⎛
+−= 0
1
1
ln
t itt
t
i NeCeU
n
t
c
t ϕεε
ϕ
κβ  
where C is consumption, Ni is hours worked by labour of type i, κ is the relative weight of labour 
disutility, β is the discount factor, 1/φ the elasticity of labour supply, εc a consumption and εn a labour 
supply shock. 
The household i faces the budget constraint:  
(2) ( )1 1it it t t t t t t tW N PD PC B r B++ = + − +  
equating labour and dividend income, on the left side, with nominal consumption expenditure and net 
saving in risk-free one-period bonds B on the right. Wi is the nominal wage for labour of type i in a 
labour market with monopolistic competition and Calvo-staggered wage setting.  
Let N be a CES aggregate of the differentiated types of labour: 
(3) 
11 1
0
t itN N di
η
η η
η
− −⎡ ⎤= ⎢ ⎥⎢ ⎥⎣ ⎦∫  
with η as the elasticity of substitution between the differentiated labour inputs Ni. The demand for 
labour of type i is: 
(4) itit t
t
WN N
W
η−⎛ ⎞= ⎜ ⎟⎝ ⎠
. 
3 
Output of firm j derives from the one-factor production function: 
(5) jtjt NeY
a
tε= , 
where εa is a technology shock that is identical across all firms and Nj the labour aggregate employed 
by firm j. 
Households consume a bundle of differentiated goods 
11
0
1 −−
⎥⎦
⎤⎢⎣
⎡= ∫ σ
σ
σ
σ
djCC jtt , where σ is the elasticity of 
substitution between varieties j. For simplicity, adjustment costs are conceived as consuming such 
bundles of varieties too. 
Demand for output j depends on aggregate demand and the relative price: 
(6) t
t
jt
jt YP
P
Y
σ−
⎟⎟⎠
⎞
⎜⎜⎝
⎛=  
With fully flexible prices there is no price dispersion and aggregate production 
1
0 jt t
Y dj Y=∫  equals: 
(7) tt NeY
a
tε= . 
Nominal wage stickiness makes wage setting a dynamic optimisation problem. Wage setters maximise 
(1) under the budget constraint (2), the labour demand function (4) and the production function (7).1 
The optimal nominal wage for the re-optimising households is: 
(8) ( ) ( ) ( )[ ]( )[ ]∑∑ ∞=
∞
=
+++
−=
00
0
11
01*
1
t ttt
t
t tt
t
t
NWE
NWeE
W
n
t
η
ϕηϕεηϕ
λωβ
ωβ
η
ηκ  
where 1-ω is the probability of wage re-adjustment, which corresponds to the share of households 
resetting wages in a given period, and tt Ce
c
t /ελ =  is the marginal utility of consumption. The 
nominal wage level is a weighted average of reset and unadjusted contracts: 
(9) ( )( ) ηηη ωω −−−− +−= 111*1 1 ttt WWW . 
Firms operate in a monopolistically competitive goods market and face quadratic employment 
adjustment costs, providing them with the incentive to smooth employment adjustment over time. 
Maximisation of real firm profits: 
(10) ( ) ⎥⎦
⎤⎢⎣
⎡ −−−= −∞=∑ 21000 2max jtjtjtttjtt
j
t
t
tj
P NNNP
W
Y
P
P
EDj
t
φβ  
under the production and demand functions (5) and (6) yields the profit maximising price. 
Assuming symmetric behaviour and symmetric constraints among firms, the aggregate price level is: 
                                                 
1 Calvo wage setting is derived in detail in, e.g., Canzoneri et al. (2007).  
4 
(11)
( ) 11
11
11 −⎥⎦
⎤⎢⎣
⎡ ⎟⎠
⎞⎜⎝
⎛+++−
=
+−
+−
a
t
a
t
a
t
a
t
e
NE
e
N
e
Ne
WP
t
t
tt
t
t
εεε
ε βφφβφσ
σ
. 
Aggregate demand in the closed economy is the sum of consumption demand and the employment 
adjustment costs: 
(12) ( )212 −−+= tttt NNCY
φ
. 
Intertemporal optimising households that can lend and borrow against future income choose the 
consumption path: 
(13) ⎟⎟⎠
⎞
⎜⎜⎝
⎛
+= +
+
+ 1
1
11
11
t
t
t
t
t
t CP
P
e
eE
r
C c
t
c
t
ε
ε
β . 
The note considers two alternative settings for monetary policy. First, a simple Taylor-type rule: 
(14) ( )1 ˆ1 rt r t r y t t tr r y πβα α α α π εβ−
⎛ ⎞1−= + − + + +⎜ ⎟⎝ ⎠ , 
where fYYy lnlnˆ −≡  is the output gap as the log difference between actual output and output in 
absence of nominal and real stickiness, 1lnln −−≡ ttt PPπ  is inflation and εr is a monetary policy 
shock. Second, optimal monetary policy with full information and credible commitment. The first 
setting, adopted e.g. in Canzoneri et al. (2007), accounts for the fact that monetary policy is rarely 
optimal; the second one shows the loss frontier as the best possible outcome for given structural 
parameters and shocks.2 
The relevant measure of economy-wide welfare under staggered wage setting is: 
(15) ∑∞= + ⎟⎟⎠
⎞⎜⎜⎝
⎛
+−= 0
1
1
ln
t ttt
t
i NDWeCeU
n
t
c
t ϕεε
ϕ
κβ  
where C is per capita consumption and DWN1+φ the average disutility of work. DW measures 
the dispersion of wages: 
(16) ( )
( ) ( )
1
1
1
1*
1 −
+−
−
+−
⎟⎟⎠
⎞
⎜⎜⎝
⎛+⎟⎟⎠
⎞
⎜⎜⎝
⎛−= t
t
t
t
t
t DWW
W
W
WDW
ϕηϕη
ωω . 
Wage dispersion makes firms hire different amounts of work from individual households. If wages are 
flexible (ω=0), firms hire the same amount of labour from each households (3) and individual and 
economy-wide welfare coincide (see Canzoneri et al., 2007). 
To study the interaction of nominal wage stickiness and costly employment adjustment, the model is 
simulated over a grid of rigidity combinations. The Calvo parameter ω varies between 0.1 and 0.9, on 
quarterly basis, and adjustments costs φ  between 0 and 10, comprising the estimates of Hall (2004) or 
                                                 
2 Ramsey optimal policy is computed using the routine of Levin et al. (2005). 
5 
Ratto et al. (2010) for the U.S. economy. The parameter values β=0.99, σ=10, η=5, κ=1, φ=2.5, 
αr=0.9, αy=0.1 and απ=1.5 reflect parameter estimates in Ratto et al. (2010), Sahuc and Smets (2008) 
and Smets and Wouters (2005, 2007). To facilitate comparison, the technology, labour supply and 
consumption shocks εt= ρεt-1+νt have persistence ρ=0.90 and an innovation ν of 0.10 standard errors; 
the monetary shock has ρ=0, because the autoregressive component in the policy rule already implies 
persistence, and a smaller innovation of 0.01 standard errors. The values are within the estimated order 
of magnitude in Sahuc and Smets (2008) and Smets and Wouters (2005, 2007). 
3. Results 
This section describes the interaction between nominal wage stickiness and real employment 
adjustment costs and their impact on economic welfare as defined by equation (15). Figures 1 and 2 
display the welfare loss as percentage of steady-state consumption. A first view shows the magnitude 
of losses to depend on the type of shock; notably, technology shocks imply larger losses than labour 
supply or consumption shocks of the same size and persistence. 
 
[Figure 1] 
 
Figure 1 shows results for the Taylor rule (13) and indicates a substantial impact of nominal wage 
rigidity on the welfare loss. The reason is that with a monetary rule focusing on price level stability, 
higher nominal wage rigidity also increases the stickiness of real wages, which constrains the optimal 
adjustment of real variables. In the frictionless economy, a positive technology shock (A) reduces 
production costs and prices; households consume more but work less, so that the shock does not fully 
translate into higher real wages, output and consumption. The combination of nominal wage stickiness 
with a strong inflation target in the policy rule prevents the gradual rise in the price level deriving from 
declining labour supply and a less than proportionate increase in real wages; activity and consumption 
are higher and leisure lower than in the flexible economy. The welfare loss from real adjustment costs 
is largest for the technology shock which implies the biggest employment adjustment. A positive 
shock to the disutility of labour (B) raises nominal wage claims and lowers activity and consumption 
in the frictionless economy; production costs and prices increase and moderate the rise in real wages. 
Nominal wage stickiness combined anti-inflation policy eliminates the dampening of real wage 
growth. Real wages increase and activity and consumption fall more strongly than under flexible 
adjustment. A positive shock to consumption utility (C) dampens nominal wage claims; activity and 
consumption increase especially in a low inflation environment. In case of zero adjustment frictions, 
lower wage claims translate into less real wages moderation and activity growth. Finally, the interest 
rate shock (4) dampens demand and output. Nominal wage flexibility translates this into falling 
nominal wages and production costs; monetary policy turns expansionary to prevent the fall in the 
price level and offsets the decline in activity and consumption. Nominal wage stickiness prevents a 
6 
swift adjustment of nominal wages and productions costs; short of monetary easing the initial shock 
causes larger contraction. Taken together, the combination of nominal wage rigidity and monetary 
policy with strong focus on price level stability increases the impact of shocks on real variables.  
 
[Figure 2] 
 
Figure 2 displays the welfare losses under optimal monetary policy, i.e. the smallest possible loss for 
given shocks and rigidities. Losses for each shock are substantially below those in Figure 1. In 
addition, the loss frontier has almost identical shape for all three shocks and the impact of nominal 
wage rigidity is practically zero.3 The reason is that optimal policy places less restrictions on price 
level adjustment than the above Taylor rule. Flexible prices allows real wages to adjust freely to limit 
the impact of shocks on consumption and activity. Optimal policy cannot prevent the welfare loss 
from real adjustment costs, however, which remain the only costly dynamic rigidity. 
Figures 1 and 2 do not display any quantitatively relevant interaction between nominal wage rigidity 
and employment adjustment costs in the sense of a second-best solution discussed in Duval and Vogel 
(2007) for the given shocks and rigidity parameter ranges.4 The lack of second-best interaction 
suggests that policy reforms undertaken independently in one of the areas do not risk having 
detrimental impact on economic welfare. 
4. Conclusion 
The results of this note suggest three conclusions on the interaction of nominal and real labour market 
rigidity: (1) Costs of nominal and real inertia depend on the policy regime: nominal wage inertia can 
be costly under non-optimal policy, but under optimal monetary policy only real rigidities matter. (2) 
Compared to a simple Taylor rule, optimal policy can substantially limit the welfare loss from 
exogenous shocks. (3) There is no quantitatively relevant second-best interaction between nominal and 
real stickiness for the selected shocks and parameter spaces; absence of second-best interaction 
implies that structural reforms in one dimension will not incur welfare losses if adjustment frictions in 
the other dimension remain unchanged. 
Acknowledgements 
The views in the paper are solely those of the author and not those of the European Commission. I 
thank an anonymous referee for very helpful comments on an earlier draft. 
                                                 
3 Figure 2 does not include an interest rate shock as the latter is difficult to conceive in the context of optimal 
monetary policy. 
4 Second-best solution here means that, from the welfare perspective, higher might be preferable lower nominal 
(real) rigidity for given real (nominal) adjustment frictions. 
7 
References 
Ascari, G., Merkl, Ch., 2009. Real Wage Rigidities and the Cost of Disinflations. J. Money, Credit, 
Banking 41, 417-435.  
Blanchard, O., Galí, J., 2007. Real Wage Rigidities and the New Keynesian Model. J. Money, Credit, 
Banking 39, 35-65. 
Canzoneri, M., Cumby, R., Diba, B., 2007. The Cost of Nominal Rigidity in NNS Models. J. Money, 
Credit, Banking 39, 1563-1586. 
Duval, R.. Vogel, L., 2007. How Do Nominal and Real Rigidities Interact? A Tale of the Second Best. 
MPRA Papers 7282. 
Hall, R., 2004. Measuring Factor Adjustment Costs. Quart. J. Econ. 119, 899-927.  
Lechthaler, W., Snower, D., 2008. Quadratic Labor Adjustment Costs and the New-Keynesian Model. 
Kiel Working Papers 1453. 
Levin, A., Onatski, A., Williams, J., Williams, N., 2005. Monetary Policy Under Uncertainty in 
Micro-Founded Macroeconometric Models. NBER Working Papers 11523. 
Ratto, M., Roeger, W., In't Veld, J., 2010. Using a DSGE Model to Look at the Recent Boom-Bust 
Cycle in the US. European Economy Economic Papers 397. 
Sahuc, J.-G., Smets, F., 2008. Differences in Interest Rate Policy at the ECB and the Fed: An 
Investigation with a Medium-Scale DSGE Model. J. Money, Credit, Banking 40, 505-521. 
Smets, F., Wouters, R., 2005. Comparing Shocks and Frictions in US and Euro Area Business Cycles: 
A Bayesian DSGE Approach. J. Appl. Econometrics 20, 161-183. 
Smets, F., Wouters, R., 2007. Shocks and Frictions in US Business Cycles: A Bayesian DSGE 
Approach. Amer. Econ. Rev. 97, 586-606. 
 
  
Figure 1: Welfare loss under Taylor rule 
0.1 0.3 0.5 0.7 0.9 2 4
6 8 10
0
2
4
6
8
10
12
14
W
el
fa
re
 lo
ss
 (%
 o
f s
te
ad
y 
st
at
e 
co
ns
um
pt
io
n)
Nominal w age rigidity Employment adjustment 
costs
A. Technology shock
 
0.1 0.3 0.5 0.7 0.9 2
4 6 8
10
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
W
el
fa
re
 lo
ss
 (%
 o
f s
te
ad
y 
st
at
e 
co
ns
um
pt
io
n)
Nominal w age rigidity Employment adjustment 
costs
B. Labour supply shock
 
8 
0.1 0.3 0.5 0.7 0.9 2
4 6 8
10
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
W
el
fa
re
 lo
ss
 (%
 o
f s
te
ad
y 
st
at
e 
co
ns
um
pt
io
n)
Nominal w age rigidity
Employment adjustment 
costs
C. Consumption shock
 
0.1 0.3 0.5 0.7 2 4
6 8 10
0.0
0.5
1.0
1.5
2.0
2.5
W
el
fa
re
 lo
ss
 (%
 o
f s
te
ad
y 
st
at
e 
co
ns
um
pt
io
n)
Nominal w age rigidity
Employment adjustment 
costs
D. Monetary policy shock
 
 
Figure 2: Welfare loss under optimal policy 
0.1 0.3 0.5 0.7 0.9 2
4 6 8
10
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
4.5
W
el
fa
re
 lo
ss
 (%
 o
f s
te
ad
y 
st
at
e 
co
ns
um
pt
io
n)
Nominal w age rigidity Employment adjustment 
costs
A. Technology shock
 
0.1 0.3 0.5 0.7 0.9 2
4 6 8
10
0.00
0.05
0.10
0.15
0.20
0.25
W
el
fa
re
 lo
ss
 (%
 o
f s
te
ad
y 
st
at
e 
co
ns
um
pt
io
n)
Nominal w age rigidity Employment adjustment 
costs
B. Labour supply shock
 
0.1 0.3 0.5 0.7 0.9 2
4 6 8
10
0.00
0.05
0.10
0.15
0.20
0.25
0.30
0.35
W
el
fa
re
 lo
ss
 (%
 o
f s
te
ad
y 
st
at
e 
co
ns
um
pt
io
n)
Nominal w age rigidity Employment adjustment 
costs
C. Consumption shock
 
 
 
 


Interacting nominal and real labour market rigidities

https://mpra.ub.uni-muenchen.de/22647/2/MPRA_paper_22647.pdf

Interacting nominal and real labour market rigidities

Abstract

Similar works

Full text

Available Versions

Munich Personal RePEc Archive