Consumers’ preferences, number of firm dynamics and the factor

shares evolution

Alexander Osharin and Valery Verbus

NRU HSE – Nizhny Novgorod

The motivation

To investigate the capabilities of the extended two-factor ZKT model in explaining some observations concerning factor shares dynamics, markup movements and asymmetry of the business cycle.

Some papers on factor shares

1. Bentolila (2003): Explaining Movements in the Labor Share. 2. Jalava, Pohjola, Ripatti and Vilmunen (2005): Biased Technical Change and Capital-Labor Substitution in Finland, 1902-2003.3. Матвеенко (2008): Ресурсы, институты, инновации и экономический рост: двойственный подход.4. Ripatti , Vilmunen (2010): Declining labor share – Evidence of a change in the underlying production technology?5. Tipper (2011): One for all? The capital-labor substitution elasticity in New Zealand.6. Raurich, Sala, Sorolla (2011): Factor shares, the Price Markup, and the elasticity of Substitution between Capital and Labor.

Empirical evidence on factor shares dynamics

Decline of labor share since the mid-1980s in most of the OECD countries.

Empirical evidence on labor share short and medium run movements (1)

Empirical evidence on labor share short and medium run movements (2)

Empirical evidence on labor share short and medium run movements (3)

Empirical evidence on labor share short and medium run movements (4)

Empirical evidence on labor share short and medium run movements (5)

Labor share Real wage

Levels (%) Changes (%) Changes (%)1970 1980 1990 1970-1990 1970-1990

United States 69.7 68.3 66.5 -3.3 0.4Canada 66.9 62.0 64.9 -2.0 1.3Japan 57.5 69.1 68.0 10.5 3.5Germany 64.1 68.7 62.1 -2.0 2.0France 67.6 71.7 62.4 -5.2 2.2Italy 67.1 64.0 62.6 -4.5 2.1Australia 64.8 65.9 62.9 -1.9 1.2Netherlands 68.0 69.5 59.2 -8.8 1.8Belgium 61.6 71.6 64.0 2.4 2.9Norway 68.4 66.4 63.9 -4.5 2.2Sweden 69.7 73.6 72.6 2.9 1.6Finland 68.6 69.6 72.3 3.7 3.5Mean 66.2 68.4 65.1 -1.1 2.1Standard deviation 3.6 3.3 4.1 5.2 0.9

Source: OECD Economic Outlook Statistics on Microcomputer Diskette.

The Labor Share and Real Wages in 12 OECD countries

Raurich, Sala, and Sorolla (2011) findings: 1. The elasticity of substitution between capital and labor is larger than one in Spain and smaller than one in the U.S.

2. In Spain the labor income share (LIS) has decreased while the ratio of capital to GDP has increased.

3. In contrast, both the ratio of capital to GDP and the LIS have decreased in the U.S., which implies an elasticity of substitution lower than one.

4. Consideration of the price markup drives the value of the elasticity of substitution away from one and, therefore, provides a further cause of rejection of the Cobb-Douglas (CD) specification. This result holds both for Spain and the U.S. but goes in opposite direction: it yields an upward bias in Spain and a downward bias in the U.S.

5. Price markup accounts for 63% of the LIS evolution in Spain and 57% in the US, whereas the elasticity of substitution explains, respectively, 27% and 39% of its variation.

6. Price markup time series in both countries is countercyclical.

Mark-ups and return to capital in Spain

Mark-ups and return to capital in the USA

How markups move, in response to what, and why, is however nearly terra incognita for macro. . . . We are a long way from having either a clear picture or convincing theories, and this is clearly an area where research is urgently needed.

Blanchard (2008)

Markups and firm entry and exit decisions literature

1. Jaimovichz (2003): Firm Dynamics, Markup Variation and the Business Cycle.

2. Jovanovic (2005): Asymmetric Cycles.

3. Jaimovichz, Floetotto (2008): Firm dynamics, markup variations, and the business cycle.

4. Floetotto, Jaimovichz, Pruitt (2009): Markup Variation and Endogenous Fluctuations in the Price of Investment Goods.

5. Li, Mehkari (2009): Expectation Driven Firm Dynamics and Business Cycles.

6. Nekarda, Ramey (2010): The Cyclical Behavior of the Price-Cost Markup.

7. Cheremukhin, Tutino (2012): Asymmetric Firm Dynamics under Rational Inattention.

Empirical evidence on asymmetry of business cycle, markups and firm entry and exit decisions

1. Business cycle is asymmetric. The economy tends to alternate between long periods of slow expansion and short periods of sharp contraction.

2. Markups lag the business cycle. Lagged markups are countercyclical.

3. Firm exit is at list 30% more volatile than firm entry.

4. Firm exit is strongly countercyclical and asymmetric.

5. Firm entry is procyclical and symmetric.

Empirical evidence on firm entry and exit rates (Nekarda and Ramey, 2010)

Two-factor model of monopolistic competition

Preferences of consumers are additively separable (as in ZKT) and utility maximization has the form:

where is the demand of a consumer, is the variety price vector and is the individual expenditure, which is supposed to be constant, is the mass of varieties.

edixptsdixuUN

iix

N

ii

00

..,max)(

ix ipe

N

L

Goods market

Each firm produces a unique variety and solves the following profit maximization problem:

where is the output of a firm, and are the marginal and constant production cost, which are identical across firms.

iqiiii fmqqpq max)(

ii Lxq m f

Goods market SR equilibrium

Since all firms are identical, there exist a continuum of the symmetric short-run equilibriums with

where is the relative love for variety, and are the equilibrium levels of price and output of a firm.

fmqpqq )(

Lxq p

Npe

rm

p

u1

1Np

ex

)(ur

Capital and labor markets

To get an equilibrium on capital and labor markets each firm solves the following profit maximization problems:

where and are the nominal wage and interest rate of capital, and are capital and employment of a firm.

ii lkiiiiiiii fWlRklkqplk

,max),(),(

W Rik il

Capital and labor market SR equilibrium

SR - equilibrium profit as a function of labor and capital cost:

where is a markup of a firm, is a

production function of a firm.

m

p

Wl

qp

Rk

qp

fWlRkpqq )(

),( lkqq

Capital and labor shares (1)For the Cobb-Douglas (CD) production function

the capital and labor shares equal to

Where is a constant.

1),( lklkq

constss

pq

Wls

pq

Rks

lk

lk

,1

1,

10

Capital and labor shares (2)For the CES production function

where is a parameter, related with capital-

labor substitution by , ,

the capital and labor shares equal to

where is a constant.

/1])1([),( lklkq

1/

11,1/

/1)1/()1/(

)1/(

RWs

RW

RWs lk

)1/(1]1/([

1 )1/(1 klkl kl0

Substitution between capital and labor

When is negative, , then

and

In this case capital and labor are technical compliments and labor share will increase with increasing relation.

When is positive, , then and

In this case capital and labor are technical substitutes and labor share will decrease with increasing relation.

0 0)1/(

10 kl

10 0)1/(

kl0

RW /

RW /

Constant absolute risk aversion (CARA) utility function

The following constant absolute risk aversion (CARA) utility function

has the relative love for variety (RLV)

with . The more is the more risk aversive is the consumers.

))exp(1()( axxu

axxru )(

10 a a

SR equilibrium price and mark-up as a function of the mass of the firms

Price level for CARA utility function and mark-up in the SR-equilibrium are inversely dependent on the mass of the firms:

which corresponds to the pro-competitive behavior of the equilibrium price.

N

aemp

*

mN

ae

m

p *

1

Mark-ups counter-cyclical behavior (1)

Since real aggregate income equals to and

, where is the total nominal expenditure level (assumed to be constant in the model), we have

It means that mark-ups are countercyclical (at list towards the shocks changing the number of the firms).

The key question for us: whether the real GDP is increased or decreased in the period when labor share decreased?

NqY *ENpq *E

m

E

p

ENqY

Mark-ups counter-cyclical behavior (2)

Let

and is shocked, and is increased, then for mark-ups

while for the total real income

It means that mark-up is countercyclical.

0,11**

m

aec

N

с

mN

ae

012

N

c

N

c

NN

011

22

*

2

***

N

c

m

E

Nm

E

m

E

Np

E

NN

Y

N N

De-trended GDP for the USA (1950-2005)

De-trended GDP for France (1950-2005)

De-trended GDP for Germany (1970-2005)

De-trended GDP for the United Kingdom (1950-2005)

The key question for us: what is going with the number of firms ?

If the number of monopolistically competitive firms on the market increase, then the mark-ups fall and labor income share increases.

If the number of monopolistically competitive firms on the market decrease, then the mark-ups rise and labor income share decreases.

LR equilibrium price and mark-up as functions of the exogenous parameters

Price level for CARA utility function in the LR equilibrium

Mark-up level for CARA utility function in the LR equilibrium

1

21

21

2*

mL

af

mL

afmp

12

12

12

*

mL

af

mL

af

m

p

Profit as a function of the number of firms

mxrp

fLmxLpxN

u )(1

)(

fxLpxrN u )()(

2

)(/)()(

N

xrdNxNdrLe

dN

Nd uu

Profit as a function of the number of firms

Since (as it is stated in ZKT), the right hand

side sign depends on the sign of the RLV derivative

N

xr

dN

dxxr

N

Le

dN

Nd uu

)()(

)(

0dN

dx

)(xru

Profit as a function of the number of firms

In the price-decreasing (pro-competitive) case:

In the price-increasing (anti-competitive) case:

The sign of the initial value of the profit:

0)(

0)( dN

Ndxru

0

0)(0)(

dN

Ndxru

0)( Le

Nfxru 0)(

Le

Nfxru

Profit as a function of the number of firms in the pro-competitive case

137000

137500138000

138500139000

139500140000

140500141000

141500

142000142500

143000143500

144000144500

145000

0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40

t(quarters)

Y R

8

9

10

11

12

13

14

15

0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40

t(quarters)

Mark-up, %

26,0

26,2

26,4

26,6

26,8

27,0

27,2

27,4

27,6

0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40

t(quarters)

Labor share, %

137000

137500138000

138500139000

139500140000

140500141000

141500

142000142500

143000143500

144000144500

145000

0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40

t(quarters)

Y R

Thank you for rational attention!