The Cyclical Behavior
of the Price-Cost Markup
By
Christopher J. Nekarda
and
Valerie A. Ramey
Role of Markups in New Keynesian Models
•The key transmission mechanism in the NK model is sticky prices
and variable markups.
•A positive demand shock (e.g. monetary or government spending)
leads output and MC to increase. Prices don’t adjust, so the
markup falls.
•A positive technology shock lowers MC and raises output. Prices
don’t adjust, so the markup rises.
A Contractionary Monetary Shock in the NK Model
•A contractionary monetary shock decreases demand because
prices don’t fall.
•Nominal MC falls with output. Thus, real MC falls.
• Since the markup is the inverse of real MC, the markup is
countercyclical.
From SmetsWouters (2003).
“MC” is real
marginal cost.
Effects of Government Spending
Neoclassical:
↑G → ↑L → ↓ MPL → ↓ W/P
Wt
At FL ( Lt , K t ) 
Pt
New Keynesian
↑G → ↑L, ↓ MPL and ↓ μ→ ↑ W/P
(μ is the markup)
Wt
At FL ( Lt , K t )   t
Pt
Findings of this paper
1. Markups are procyclical
•
observed both in aggregate and industry data
2. Aggregate Evidence
• Markups trough during recessions and peak in the middle of
expansions
• Markups are procyclical in response to monetary shocks
• Not sensitive to average-marginal cost distinction
3. Industry Evidence
• Markups are procyclical in response to government-spending
induced increases in shipments in detailed industries
Outline
1. Theoretical framework for measuring markups
2. Aggregate Evidence
• Data
• Creation of wage factor
• Assessment of unconditional cyclicality
• Monetary VARs
3. Industry Evidence
• Data
• Regressions
Theoretical Framework
Theoretical Markup:
P

MC
Key points for measuring marginal cost MC:
1. A cost-minimizing firm should equalize the marginal cost of
raising output across all possible margins.
2. Inputs with adjustment costs have more complicated marginal cost
structures.
3. Thus, we focus on the input that the empirical evidence suggests
has negligible adjustment costs: average hours per worker, h.
Cost Minimization
Minimize
Cost  h  N  (Ws , h)  other terms not involving h
subject to
Y  F ( A  h  N ,...)
h = average hours per worker
N = number of workers
Ω(Ws,h) = wage function
Y = output
A = labor-augmenting technological progress
Marginal Cost
MC   
N  (WS , h)
A  N  F1 ( A  h  N ,...)
The standard procedure is to use the average wage as the
marginal cost of an extra hour.
Bils (1987) observed that because of overtime hours, the
average wage per hour differs from the marginal wage per hour.
The problem is that we observe the average wage, not the
marginal wage.
Deriving Marginal Hours Costs:
The Wage Function
Consider the following wage function:
Suppose:
(WS , h)  W (h)  h
v
W (h)  W A  WS  [1    ]
h
W A  average wage
WS  straight  time wage
  overtime premium
v  average overtime hours
Linking Average and Marginal Wages
Marginal cost of raising average hours per worker
(Bils’ “marginal wage”)
dv 


WM   (WS , h)  WS  1    
dh 

Thus, the relationship between average wages and
marginal wages is:

1    dv
WM
dh

WA
1   v
h
 

Thus, marginal cost becomes:
WA

1    dv
dh
 

1   v
(WS , h)
h
MC 

A  F1 ( A  h  N ,...) A  F1 ( A  h  N ,...)
WA is available data. I will discuss below how we measure the
factor multiplying WA.
But, first we need to derive a specification for marginal
productivity in the denominator.
Measuring Productivity
 Y 
A  F1 ( A  h  N ,..)   

h N 
 Y 
A  F1 ( A  h  N ,..)   A 

 A h  N 
Cobb-Douglas
1

CES
σ is the elasticity of substitution between capital and labor
Measuring Markups

CD
A
 CD
M 

CES
M
P



W A /[ (Y / hN )] s
P


WM /[ (Y / hN )] s  [WM / W A ]

1
 Y 

s  [WM / W A ]  AhN 
s = labor share =
Average Markup, CobbDouglas
Marginal Markup, CobbDouglas
1
W A hN
PY
Marginal Markup, CES
Aggregate Analysis
•We first construct the marginal-average wage
adjustment factor.
•We then combine that variable with standard
government data to derive series on markups.
•The only other complicating factor is the CES
specification, which requires a measure of technology.
Measuring v/h
•There is readily available CES data on average hours and overtime
hours for manufacturing.
•But manufacturing was only 26 percent of GDP at its post WWII
peak and is now only 11 percent.
•Also, Deleire et al (2002) show that the CES overcounts overtime
hours – implies that those who work overtime hours work 25 hours
per week.
•We construct new series on average hours and overtime hours for
the entire civilian economy using a previously unexploited data
source.
Source of hours data for entire economy
•The BLS Employment and Earnings publication provides
data on persons at work and average hours of persons at
work (Cociuba, Prescott, Ueberfeldt (2009))
•E & E also reports persons at work by ranges of hours of
work, such as 35-39 hours per week, etc.
•We constructed series on the number of hours worked in
excess of 40 hours per week. We call those “overtime
hours,” although they do not necessarily command a
premium.
Average Weekly Hours, Aggregate Economy
Average Weekly Hours per Worker
3.00
4.00
5.00
Average Weekly Overtime Hours per Worker
2.00
37.0 38.0 39.0 40.0 41.0 42.0
CPS
1955 1960 1965 1970 1975 1980 1985 1990 1995 2000 2005
1955 1960 1965 1970 1975 1980 1985 1990 1995 2000 2005
0.10
0.12
Fraction of Overtime Hours
0.04
0.06 0.08
v
h
1955 1960 1965 1970 1975 1980 1985 1990 1995 2000 2005
Average Weekly Hours per Worker
3.00
4.00
5.00
Average Weekly Overtime Hours per Worker
2.00
37.0 38.0 39.0 40.0 41.0 42.0
Average Weekly Hours, Manufacturing
CES
1955 1960 1965 1970 1975 1980 1985 1990 1995 2000 2005
1955 1960 1965 1970 1975 1980 1985 1990 1995 2000 2005
0.10
0.12
Fraction of Overtime Hours
0.04
0.06 0.08
v
h
1955 1960 1965 1970 1975 1980 1985 1990 1995 2000 2005
Estimating
dv
dh
Use difference approximation
vt     t ht   t
Bils allowed ηt to depend on cubics in ht and time trends.
We determined that a state-space model was best for
estimating the time-varying coefficient. Thus, we
estimate the equation above along with the transition
equation:
 t   t 1   t
Estimated dv/dh
0.1
0.2
0.3
0.4
0.5
Aggregate Economy
1955
1960
1965
1970
1975
1980
1985
1990
1995
2000
2005
1990
1995
2000
2005
0.0 0.2 0.4 0.6 0.8
Manufacturing
1955
1960
1965
1970
1975
1980
1985
Overtime Premium, ρ
Statutory overtime premium is 50%.
Mitigating factors:
•Trejo (1991), Hamermesh (2006) – effective rate is
around 25%
•CES overtime hours for manufacturing are defined
as those that command a premium. Our aggregate
economy hours are simply hours worked above 40.
According to May CPS, between 25% and 35% of
worker who work more than 40 hours per week
actually receive overtime pay.

dv
WM 1    dh

WA
1   v
h
Estimated
 

1.02 1.04 1.06 1.08 1.10
Aggregate Economy
25 percent
1955
1960
1965
1970
1975
1980
50 percent
1985
1990
1995
2000
2005
1990
1995
2000
2005
1.00
1.10
1.20
1.30
Manufacturing
1955
1960
1965
1970
1975
1980
1985
1.361.401.441.48
Nonfinancial corporate business (NIPA)
1.50 1.60 1.70
Aggregate Average Markups
Private business (NIPA)
1.50 1.70 1.90 0.94 0.98 1.02
Private business (BLS)
Manufacturing (NIPA)
1950
1960
1970
1980
1990
2000
Marginal Markups, Aggregate Economy
0.85
0.90
0.95
1.00
1.05
Level
Unadjusted
1955
1960
1965
1970
25 percent
1975
1980
1985
1990
50 percent
1995
2000
2005
1995
2000
2005
-0.03-0.02-0.01
0.00 0.01 0.02 0.03
Cyclical Component
1955
1960
1965
1970
1975
1980
1985
1990
Marginal Markups, Manufacturing
1.20 1.40 1.60 1.80 2.00
Level
Unadjusted
50 percent
1955
1960
1965
1970
1975
1980
25 percent
1985
1990
1995
2000
2005
1995
2000
2005
-0.15-0.10-0.05
0.00 0.05 0.10 0.15
Cyclical Component
1955
1960
1965
1970
1975
1980
1985
1990
Cyclicality of Markups
Correlation of HP filtered components with GDP
Avg., nonfinancial corporate, (NIPA)
0.279
Avg., private business (NIPA)
0.434
Avg., private business (BLS)
0.346
Avg., Manufacturing (NIPA)
0.390
Marginal, aggregate business, ρ = 0.25
0.326
Marginal, aggregate business, ρ = 0.50
0.351
Marginal, manufacturing, ρ = 0.25
0.388
Marginal, manufacturing, ρ = 0.50
0.421
Cyclicality of Markups
Dynamic Correl. of HP filtered components with GDP
Aggregate Economy
-1.0 -0.8 -0.6 -0.4 -0.2
-1.0 -0.8 -0.6 -0.4 -0.2
0.0 0.2 0.4 0.6 0.8 1.0
0.0 0.2 0.4 0.6 0.8 1.0
Manufacturing
Unadjusted
25 percent
50 percent
-8
-6
-4
-2
0
2
4
6
8
-8
-6
-4
-2
0
2
4
6
8
CES Production Function



Requires estimate of technology A.
We use 2 approaches
1. Bivariate SVAR
2. HP filter – A is the HP trend
Correlation of markup with cyclical component of
GDP (premium = 25%)
SVAR: 0.040
HP: 0.424
Implications of Procyclical Markups for NK
Models



As discussed above, the NK model predicts
procyclical markups in response to technology
shocks, but countercyclical markups in response
to demand shocks.
Thus, unconditional countercyclical markups are
potentially consistent with the NK model if
technology shocks are the main cyclical force.
Thus, it is important to look at the cyclicality of
the markup conditional on demand shocks in
order to test the NK model.
Effects of Monetary Shocks on Markups



We estimate a standard VAR on quarterly data
from 1960:III – 2008:IV.
Variables: log real GDP, log commodity prices, log
GDP deflator, log markup, federal funds rate.
A shock to the federal funds rate, ordered last, is
the monetary policy shock.
Effect of a Contractionary Monetary Shock
Marginal (25%)
Marginal (50%)
0
4
8 12 16 20
-0.3-0.2-0.1
-0.3-0.2-0.1
-0.3-0.2-0.1
0.0 0.1 0.2
0.0 0.1 0.2
0.0 0.1 0.2
Average
0
4
8 12 16 20
0
4
8 12 16 20
Marginal (50%), manuf.
-1.0 -0.5
-1.0 -0.5
-0.4 -0.2
0
8 12 16 20
0.0 0.5
0.5
0.0
0.0 0.2 0.4
Marginal (25%), w/interest rate Marginal (25%), manuf.
4
0
4
8 12 16 20
0
4
8 12 16 20
Relation to the New Keynesian Phillips’ Curve
Literature
 t    xt  Et ( t 1 )
Xt = output gap
 t   mct  Et ( t 1 )
mc = real marginal cost = labor share = 1/markup
The reason that the output gap enters with the wrong sign but mc
enters with the right sign is that mc and x are negatively
correlated. That means the markup and the output gap are
positively correlated.
Relation to Rotemberg and Woodford (1999)
Recall that labor
share is the
inverse of the
average markup.
Their graph
implies a
procyclical
markup.
Relationship to Bils (1987)
Our adjustments are an extension of Bils’ framework. Why does
he conclude that markups are countercyclical?
The key is the details of implementation
Bils
Nekarda-Ramey
Annual 2-digit mfg industry data,
1956-83
Monthly aggreg mfg data, 19562008, merged to quarterly share data
Parametric specification
Nonparametric specification
Filtered hours as cyclical indicator
Filtered GDP as cyclical indicator
Re-estimation of Bils (1987)
All specifications use 2-digit manufacturing industry data
Time
period
Freq. of
Freq. of markup
data used to and agg. Data
estimate
dv/dh
HP filtered
correlation with
GDP
HP filtered
correlation with
hours
19561983
Monthly
Quarterly
0.249
0.014
19561983
Monthly
Annual
0.157
-0.084
19561983
Annual
Annual
0.052
-0.179
19562003
Annual
Annual
0.041
-0.071
Relation to the Literature

Inventory-Sales Ratios
Why We Also Do an Industry Analysis



It is always useful to see whether aggregate results
hold at a more disaggregated level.
We can construct a highly relevant demand instrument
We can construct markups using gross output. Basu
and Fernald argue value added is not a natural
measure of output, and that it only makes sense when
markups are constant at unity.
Data Construction

NBER-CES Manufacturing Industry Database
Annual data from 1958-1996 on 4-digit SIC manufacturing
industries
Data on hours, employment, payrolls, shipments, capital

Benchmark Input-Output Tables that use SIC codes
1963, 1967 1972, 1977, 1982, 1987, 1992
Traces interindustry linkages, including final
shipments to the government
1.6
1.8
2
2.2
2.4
2.6
Real Defense Spending Per Capita
1960
1970
1980
year
1990
2000
Data Construction (cont.)



Merging and matching industries yields 272 4-digit
industries
Although only the benchmark years are available, their
timing is very fortuitous – they correspond to peaks
and troughs of military spending
Our instrument:
1 Git  Gi ( t 5)
 5 GYit  
5 [Yit  Yi (t 5) ] / 2
Construction of Wage Conversion Factors



The NBER database contains data on total hours of
production workers and the number of production
workers employed.
From this we construct average hours per worker.
We use estimates of the relationship between
overtime hours and average hours in CES 2-digit data
to construct these for the associated 4-digit data.
Estimated equation
Let μ = ln(Markup), s = labor share
Average Markup
 5  Ait   5 ln( sit )
 WMit 

  5 ln( sit )   5 ln 
 W Ait 
Marginal Markup
 5  Mit
Estimating Equation
5 it   0it   15 ln( Yit )   it
First-Stage Regressions using Government Demand
 5 ln( Yit )  industry and time fixed effects  0.949   5GYit
(0.061)
Number of observations = 1,631
R-squared = 0.495
F-statistic on Δ5GY = 239.7
Regression of Markup on Gross Shipments
(Coefficient on Gross Shipments)
Specification Average
Markup
Marg. mkup
(ρ = 0.25)
Marg. mkup
(ρ = 0.5)
Production
0.119***
workers OLS (0.013)
0.115***
(0.013)
0.112***
(0.014)
Production
workers IV
0.119***
(0.032)
0.123***
(0.034)
0.126***
(0.036)
All workers
OLS
0.155***
(0.012)
0.155***
(0.030)
0.150***
(0.012)
0.156***
(0.032)
0.145***
(0.013)
0.157***
(0.035)
All workers
IV
Specifications with industry and time fixed effects.
Regression of Markup on Value Added
(Coefficient on Value Added)
Specification Average
Markup
Marg. mkup
(ρ = 0.25)
Marg. mkup
(ρ = 0.5)
Production
0.063***
workers OLS (0.006)
0.064***
(0.006)
0.065***
(0.006)
Production
workers IV
-0.010
(0.037)
-0.008
(0.037)
-0.006
(0.038)
All workers
OLS
0.067***
(0.006)
0.011
(0.035)
0.068***
(0.006)
0.012
(0.036)
0.069***
(0.006)
0.012
(0.036)
All workers
IV
Specifications with industry and time fixed effects.
Robustness



Concern about technological change
We tried excluding computer industries, using only
direct government demand, and using only lagged Y in
the denominator of the demand instrument.
All of the coefficient estimates were similar.
Conclusions

We find no evidence of countercyclical markups, for
the entire economy, for aggregate manufacturing, or
for detailed industries.

Our results are robust to adjustments of average
wages to marginal wages.

Our results hold unconditionally as well as conditional
on demand shocks.

More research is needed to see whether basic
mechanism of the New Keynesian model actually holds.