The Cyclical BehaviorThe Cyclical Behavior

of the Price-Cost Markupof the Price-Cost Markup

ByBy

Christopher J. NekardaChristopher J. Nekarda

andand

Valerie A. RameyValerie 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 Smets-Wouters (2003).

“MC” is real marginal cost.

Effects of Government Spending

Neoclassical:

↑G → ↑L → ↓ MPL → ↓ W/P

New Keynesian

↑G → ↑L, ↓ MPL and ↓ μ→ ↑ W/P

(μ is the markup)

t

tttLt P

WKLFA ),(

t

ttttLt P

WKLFA ),(

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:MC

P

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

h = average hours per worker

N = number of workers

Ω(Ws,h) = wage function

Y = output

A = labor-augmenting technological progress

subject to ,...)( NhAFY

Minimize

hhWNhCost s involvingnottermsother),(

Marginal Cost

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.

,...)(

),(

1 NhAFNA

hWNMC S

Deriving Marginal Hours Costs:The Wage Function

Consider the following wage function:

Suppose:]1[)(h

vWWhW SA

hoursovertimeaveragev

premiumovertime

wagetimestraightW

wageaverageW

S

A

hhWhWS )(),(

Linking Average and Marginal Wages

Thus, the relationship between average wages and marginal wages is:

Marginal cost of raising average hours per worker

(Bils’ “marginal wage”)

hvdh

dv

W

W

A

M

1

1

dh

dvWhWW SSM 1),(

Thus, marginal cost becomes:

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.

,...)(

1

1

,...)(

),(

11 NhAFAhvdh

dvW

NhAFA

hWMC

A

S

Measuring Productivity

Nh

YNhAFA ,..)(1

1

1 ,..)(

NhA

YANhAFA

Cobb-Douglas

CES

σ is the elasticity of substitution between capital and labor

Measuring Markups

Average Markup, Cobb-Douglas

Marginal Markup, Cobb-Douglas

Marginal Markup, CES

shNYW

P

A

CDA

)]/(/[

]/[)]/(/[ AMM

CDM WWshNYW

P

11

]/[

AhN

Y

WWs AM

CESM

s = labor share = PY

hNWA

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 EconomyCPS

37.0

38.0

39.0

40.0

41.0

42.0

1955 1960 1965 1970 1975 1980 1985 1990 1995 2000 2005

Average Weekly Hours per Worker

2.00

3.00

4.00

5.00

1955 1960 1965 1970 1975 1980 1985 1990 1995 2000 2005

Average Weekly Overtime Hours per Worker

0.04

0.06

0.08

0.10

0.12

1955 1960 1965 1970 1975 1980 1985 1990 1995 2000 2005

Fraction of Overtime Hours

h

v

Average Weekly Hours, ManufacturingCES

37.0

38.0

39.0

40.0

41.0

42.0

1955 1960 1965 1970 1975 1980 1985 1990 1995 2000 2005

Average Weekly Hours per Worker

2.00

3.00

4.00

5.00

1955 1960 1965 1970 1975 1980 1985 1990 1995 2000 2005

Average Weekly Overtime Hours per Worker

0.04

0.06

0.08

0.10

0.12

1955 1960 1965 1970 1975 1980 1985 1990 1995 2000 2005

Fraction of Overtime Hours

h

v

Estimating

Use difference approximation

dh

dv

tttt hv

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:

ttt 1

Estimated dv/dh0.

10.

20.

30.

40.

5

1955 1960 1965 1970 1975 1980 1985 1990 1995 2000 2005

Aggregate Economy0.

00.

20.

40.

60.

8

1955 1960 1965 1970 1975 1980 1985 1990 1995 2000 2005

Manufacturing

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.

Estimated

1.02

1.04

1.06

1.08

1.10

1955 1960 1965 1970 1975 1980 1985 1990 1995 2000 2005

25 percent 50 percent

Aggregate Economy1.

001.

101.

201.

30

1955 1960 1965 1970 1975 1980 1985 1990 1995 2000 2005

Manufacturing

hvdh

dv

W

W

A

M

1

1

1.36

1.40

1.44

1.48 Nonfinancial corporate business (NIPA)

1.50

1.60

1.70 Private business (NIPA)

0.94

0.98

1.02

Private business (BLS)

1.50

1.70

1.90

1950 1960 1970 1980 1990 2000

Manufacturing (NIPA)

Aggregate Average Markups

Marginal Markups, Aggregate Economy

0.85

0.90

0.95

1.00

1.05

1955 1960 1965 1970 1975 1980 1985 1990 1995 2000 2005

Unadjusted 25 percent 50 percent

Level-0

.03-

0.02

-0.0

10.

000.

010.

020.

03

1955 1960 1965 1970 1975 1980 1985 1990 1995 2000 2005

Cyclical Component

Marginal Markups, Manufacturing

1.20

1.40

1.60

1.80

2.00

1955 1960 1965 1970 1975 1980 1985 1990 1995 2000 2005

Unadjusted 25 percent

50 percent

Level

-0.1

5-0.

10-0

.05

0.00

0.05

0.10

0.15

1955 1960 1965 1970 1975 1980 1985 1990 1995 2000 2005

Cyclical Component

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

-1.0

-0.8

-0.6

-0.4

-0.2

0.0

0.2

0.4

0.6

0.8

1.0

-8 -6 -4 -2 0 2 4 6 8

Unadjusted25 percent50 percent

Aggregate Economy

-1.0

-0.8

-0.6

-0.4

-0.2

0.0

0.2

0.4

0.6

0.8

1.0

-8 -6 -4 -2 0 2 4 6 8

Manufacturing

CES Production Function

Requires estimate of technology A.

We use 2 approaches1. Bivariate SVAR2. 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-0

.3-0

.2-0

.10.

00.

10.

2

0 4 8 12 16 20

Average

-0.3

-0.2

-0.1

0.0

0.1

0.2

0 4 8 12 16 20

Marginal (25%)

-0.3

-0.2

-0.1

0.0

0.1

0.2

0 4 8 12 16 20

Marginal (50%)

-0.4

-0.2

0.0

0.2

0.4

0 4 8 12 16 20

Marginal (25%), w/interest rate

-1.0

-0.5

0.0

0.5

0 4 8 12 16 20

Marginal (25%), manuf.

-1.0

-0.5

0.0

0.5

0 4 8 12 16 20

Marginal (50%), manuf.

Relation to the New Keynesian Phillips’ Curve Literature

)( 1 tttt Ex

)( 1 tttt Emc

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.

Xt = output gap

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, 1956-2008, 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 data used to estimate dv/dh

Freq. of markup and agg. Data

HP filtered correlation with GDP

HP filtered correlation with hours

1956-1983

Monthly Quarterly 0.249 0.014

1956-1983

Monthly Annual 0.157 -0.084

1956-1983

Annual Annual 0.052 -0.179

1956-2003

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 DatabaseAnnual data from 1958-1996 on 4-digit SIC manufacturing industries

Data on hours, employment, payrolls, shipments, capital

Benchmark Input-Output Tables that use SIC codes1963, 1967 1972, 1977, 1982, 1987, 1992Traces interindustry linkages, including final shipments to the government

1.6

1.8

22

.22

.42

.6

1960 1970 1980 1990 2000year

Real Defense Spending Per Capita

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:

2/][5

1

)5(

)5(5

tiit

tiitit YY

GGGY

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

)ln(55 itAit s

Ait

MititMit W

Ws ln)ln( 555

itititit Y )ln(5105

Average Markup

Marginal Markup

Estimating Equation

First-Stage Regressions using Government Demand

)061.0(

949.0effectsfixedtimeandindustry)ln( 55 itit GYY

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 workers OLS

0.119***

(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)

0.150***

(0.012)

0.145***

(0.013)

All workers IV

0.155***

(0.030)

0.156***

(0.032)

0.157***

(0.035)

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 workers OLS

0.063***

(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)

0.068***

(0.006)

0.069***

(0.006)

All workers IV

0.011

(0.035)

0.012

(0.036)

0.012

(0.036)

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.