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Title: Consumers

1
Consumers preferences, number of firm dynamics
and the factor shares evolution

Alexander Osharin and Valery Verbus
NRU HSE Nizhny Novgorod

2
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.

3
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. ????????? (2008) ???????, ?????????,
????????? ? ????????????? ???? ????????????
??????.
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.

4
Empirical evidence on factor shares dynamics

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

5
Empirical evidence on labor share short and
medium run movements (1)
6
Empirical evidence on labor share short and
medium run movements (2)
7
Empirical evidence on labor share short and
medium run movements (3)
8
Empirical evidence on labor share short and
medium run movements (4)
9
Empirical evidence on labor share short and
medium run movements (5)
10
The Labor Share and Real Wages in 12 OECD
countries
Labor share Labor share Labor share Labor share Real wage
Levels () Levels () Levels () Changes () Changes ()
1970 1980 1990 1970-1990 1970-1990
United States 69.7 68.3 66.5 -3.3 0.4
Canada 66.9 62.0 64.9 -2.0 1.3
Japan 57.5 69.1 68.0 10.5 3.5
Germany 64.1 68.7 62.1 -2.0 2.0
France 67.6 71.7 62.4 -5.2 2.2
Italy 67.1 64.0 62.6 -4.5 2.1
Australia 64.8 65.9 62.9 -1.9 1.2
Netherlands 68.0 69.5 59.2 -8.8 1.8
Belgium 61.6 71.6 64.0 2.4 2.9
Norway 68.4 66.4 63.9 -4.5 2.2
Sweden 69.7 73.6 72.6 2.9 1.6
Finland 68.6 69.6 72.3 3.7 3.5
Mean 66.2 68.4 65.1 -1.1 2.1
Standard deviation 3.6 3.3 4.1 5.2 0.9
Source OECD Economic Outlook Statistics on Microcomputer Diskette. OECD Economic Outlook Statistics on Microcomputer Diskette. OECD Economic Outlook Statistics on Microcomputer Diskette. OECD Economic Outlook Statistics on Microcomputer Diskette. OECD Economic Outlook Statistics on Microcomputer Diskette.
11
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.

12
Mark-ups and return to capital in Spain
13
Mark-ups and return to capital in the USA
14
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)
15
Markups and firm entry and exit decisions
literature

Jaimovichz (2003) Firm Dynamics, Markup
Variation and the Business Cycle.
Jovanovic (2005) Asymmetric Cycles.
Jaimovichz, Floetotto (2008) Firm dynamics,
markup variations, and the business cycle.
Floetotto, Jaimovichz, Pruitt (2009) Markup
Variation and Endogenous Fluctuations in the
Price of Investment Goods.
Li, Mehkari (2009) Expectation Driven Firm
Dynamics and Business Cycles.
Nekarda, Ramey (2010) The Cyclical Behavior of
the Price-Cost Markup.
Cheremukhin, Tutino (2012) Asymmetric Firm
Dynamics under Rational Inattention.

16
Empirical evidence on asymmetry of business
cycle, markups and firm entry and exit decisions

Business cycle is asymmetric. The economy tends
to alternate between long periods of slow
expansion and short periods of sharp contraction.
Markups lag the business cycle. Lagged markups
are countercyclical.
Firm exit is at list 30 more volatile than firm
entry.
Firm exit is strongly countercyclical and
asymmetric.
Firm entry is procyclical and symmetric.

17
Empirical evidence on firm entry and exit rates
(Nekarda and Ramey, 2010)
18
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.

19
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.

20
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.

21
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.

22
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.

23
Capital and labor shares (1)

For the Cobb-Douglas (CD) production function
the capital and labor shares equal to
Where is a constant.

24
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.

25
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.

26
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.

27
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.

28
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?

29
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.

30
De-trended GDP for the USA (1950-2005)
31
De-trended GDP for France (1950-2005)
32
De-trended GDP for Germany (1970-2005)
33
De-trended GDP for the United Kingdom (1950-2005)
34
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.

35
LR equilibrium price and mark-up as functions of
the exogenous parameters