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Growth and Redistribution with a Taste for Status
Lewis Davis Union College
Presented at NYU, May 4, 2012
Overview
• I develop a model of growth and distribution with productive public goods in which agents have a preference for status.
• Status preferences mean that agents care about both absolute and relative consumption levels.
• The model suggest that societies can be divided into three types depending on their preferences and the distributions of economic and political power.
• These societies have different outcomes regarding tax policy, economic growth and redistribution
• They also respond differently to preference and democracy shocks.
Motivation
• Why did some countries adopt policies “that protected the privileges of the elites and restricted opportunities for the broad mass of the population?” SE (2000, p. 221).
• General Answer: Policies affect level and distribution of output look to distributional consequences. – Olson (1982): special interest politics distort relative prices – Easterly and Levine (1997): Ethnic politics favor growth-retarding
redistributional policies – Acemoglu and others (various) and Bourguignon and Verdier
(2000): Economic development threatens political power. (No political Coase theorem.)
Why look at preferences?• Criticism: Any outcome can be justified by appealing to arbitrary
preferences: “People in poor countries just happen to like poverty, disease, war, etc.”
• Response: • Not an arbitrary preference structure. Large lit documenting
existence of status preferences: Heffetz and Frank (2011), Clark et al. (JEL, 2008)
• Status interesting b/c reject otherwise Pareto improving policies • Davis and Wu (in process): find the taste for status differs
systematically across countries as a function of national culture. • Does this matter for policy outcomes? Need a theory to provide
testable hypotheses.
Davis and Wu: Status and CultureControlling for age, age squared, sex, marital status, children, educational
attainment, employment status, wave of WVS, income category, and Hofstede’s power distance index
Note: coef. biased b/c happiness increasing in national income.
life satisfaction Coefficient Std. Err. t-statmean_income 0.377895 0.026232 14.41pdi*mean_income -0.00662 0.000376 -17.59number of obs 127125Adj. R-squared 0.0876
Coef. evaluated at: mean pdi +1 sd pdi -1 sd pdimean income -0.01023 -0.15614 0.135687
Model Overview
• Model: Positive theory of growth and redistribution with a taste for status
• Status Preferences: utility is decreasing in the level of average consumption
• Production: Alesina and Rodrik (1994) productive public goods financed by a tax on capital
• Politics: Preferred tax of the pivotal voter depends on level of democracy and wealth inequality
Production
• Output:
• Public goods:
• Relative labor endowment:
1 1
1 1
( ) ( ) ( )
( ) ( )
( ) ( )
// (0, )
/
i i
i i
ii i
i
q t Ak t z t l
z t k t
q t A k t l
k kk k
Factor Incomes and Returns
• Labor Income:
• Capital Income:
• Individual income:
1
1
1
( )
( ) (1 )
'( ) 0 "( ) 0
( ) ( )
( )
'( ) 0 "( ) 0
( ) ( )
li i i
ki i i
i i i
y k
A
y A k r k
r A
r r
y r k
Preferences• Lifetime Utility:
• Instantaneous U:
• Roles of Absolute and Relative Consumption:
0
( ) ( )
(1 ) ( ) ( / )
ti it
it it t
it it it t
V e u dt
u ln c ln c
u ln c ln c c
Consumer’s Problem
0( )
0
max ( ( )) ( ( ))
. .,
( ) ( ) ( ) ( ) ( ) ( )
(0)
( ) (0)
( ) (0)
i
ti i
c t
i i i
i i
gt
gt
V e ln c t ln c t dt
s t
k t k t r k t c t
k k
c t e c
k t e k
Solution
• Growth:
• Consumption:
• Average C:
• Lifetime U:
0 0
0 0
20 0
( )
( )
( )
( ) ( ) (1 )
c
i i i
i i
g r
c k
c k
V ln c ln c g
Status and Lifetime Utility
• Egoistic:
• Pure status:
• Status shock:
20 0 0
10 0 0 0
0 : , ,
1: , , /
/0
/0
g c
c c
V g c c g ln c
V g c c ln c c
d V V c
d
d V V c
d c
Preferred Tax Rate
• A max exists for large enough sigma-i• F is C1, so the max obeys FOC and SOC.
2
0
( ; , ) (1 ) '( ) '( )( ) ( )
lim ( ; , ) (1 ) 0
( )lim ( ; , ) , where ( )
( ) 1
ii
i
i
ii
i
F V r
F
F
Note: if = 0, then ( )i i
Special Cases
• Sigma-i = 1:
– distribution doesn’t matter
• Gamma = 1:
– only distribution matters
'( )(1 ) '( )
( )
1
F r
'( ) 1; ,1
( ) ( )i
ii
F
Proposition 1: The existence of a preferred tax rate
1. Given ( , ) 0,1i x such that ( )1i
, there exists a positive tax rate
*( , ) 0i such that *( , )i maximizes ( ; , )iV over . Furthermore, at the
preferred tax rate, we have *( ( , ); , ) 0i iV and *( ( , ); , ) 0i iV .
2. Given ( , ) 0,1i x such that ( )1i
, individual i’s preferred tax rate is
*( , ) 0i .
3. Taking the limit as 1 , *
0, 1
( , ) , 1
, 1
i
i i
i
, for some 0 .
Intuition and comparative statics
2
2
2
( , , ) 0 ; , '( ) ; , '( )
'( ) 10
( )
0, 11'( ) 10, 1(1 ) ( ) ( )
i g i i
i
i i
iii
ii
V V g V
d
d V
d
d V
Distributions of wealth and political power
Let : 0,1nF , with 0( )n iF i k for 0,1i and '( ) 0nF i ; let
( )k nG F be the Gini coefficient of capital associated with the
distribution nF ; and let nF F , be a family of distribution
functions with 1,2,...n , and non-intersecting the Lorenz curves.
In a political system 0,1D , an individual i may vote if 0,i D .
The pivotal voter is: / 2p D .
Proposition 3: Democracy, Inequality and the Pivotal Voter
Given wealth inequality and democracy, kG and D, as defined above, the relative labor
endowment of the pivotal voter is a function of the levels of wealth inequality and democracy:
( , )p p D G . Moreover, the relative labor endowment of the pivotal voter is
1. is increasing in wealth inequality: ( , ) 0pG D G ,
2. is increasing in level of democracy: ( , ) 0pD D G ,
3. equals the median voter in a pure democracy: (1, )p mG , and
4. equals one in an egalitarian society: ( ,0) 1p D .
Does the preferred tax rate max growth?
• Preferred tax rate• Growth-max tax rate:
(..) '( ) (..) '( )
ˆ'( ) 0
p prV r V
r
( ) ( )( ; , ) 0
( ) ( )
ˆ ˆ ˆ ˆ( ) (0) 0 (1) 1 '( ) 0ˆ(1 ) ( )
'( )ˆ ( ) '( ) (..) 0
(..)
p p pp p
p p p
p
pp p
r
V
r VV
Figure 1 Equilibrium Growth and Wages in a Status-Oriented Society at the
Preferred Tax Rates of Agents with 1 2 0 3ˆ ( ) and 00 1 .
2 0( , )V
( )g
*0(0, ) *
2 0( , ) *3 0( , )
ˆg
*1 0
*3 0
( , )
( , )
g
g
growth
1 0( , )V
3 0( , )V
Proposition 4: The pivotal voter and the rate of economic growth
Let p be the relative labor endowment of the pivotal agent. Given 0,1 , there exists a
threshold level of the relative labor endowment, ˆ ( ) 0ˆ(1 ) ( )
such that:
1. If ˆ ( )p , then the pivotal voter prefers the growth maximizing tax rate and the
economy grows at its maximum rate: * ˆ( , )p and * ˆ( , )pg g .
2. If ˆ ( )p , then the pivotal voter’s preferred tax rate is less than the growth
maximizing rate and the growth rate is increasing in the tax rate: * ˆ( , )p and
*' ( , ) 0pg .
3. If ˆ ( )p , then the pivotal voter’s preferred tax rate is greater than the growth
maximizing rate and the growth rate is decreasing in the tax rate * ˆ( , )p and
*' ( , ) 0pg .
Income and Consumption Ginis
1
2
2
( )( , )
( ) ( )
,( )
( , ) (1 )0
( ) ( )
( , ) '( )0
( )
y k k
kc k
y kk
c kk
rG G G
r
GG G
dG GG
d r
dG GG
d
Proposition 5: The Comparative Statics of Inequality
Given ( , ) 0,1i x such that ( )1i
, it follows that:
0
0
0, 1
0, 1
0, 1
0, 1
py y
p p
pc cp p
ppy y
p
ppc c
p
dG dG d
d d d
dG dG d
d d d
dG dG d
d d d
dG dG d
d d d
• Tax rates increase going to the right • t = 0: above t = 0 locus • dg/dt > 0: left of t-hat locus • dt/dg < 0: left of t-bar locus
Figure 2: Iso-Tax Lines by Status Orientation and the Relative Labor Endowment of the Pivotal Voter
Status Orientation
Relative Labor Endowment
1
1p
Region I
Region IV
Region II
Region III
* 0
* ˆ * locus
Societies
• A society is defined by an ordered triple involving preferences, the political system and the resource endowment:
• These map into an ordered pair:
• which determines a society’s location in one of four regions of Figure 2.
, ,
, ( , )
k
pk
D G
D G
Types of Societies• Region I: Above the t* = 0 locus. “Non-Developmental Society”
• Region II: B/w t* = 0 and t-hat loci – Unequal political power and high taste for status – “Status-Oriented Oligarchy”
• Region III: B/w t-hat and t-bar loci– Includes Egoistic societies. Pivotal voter is rich – “Plutocratic Democracy“
• Region IV: to the right of the t-bar locus. – Includes Egoistic societies. Pivotal voter is poor – “Proletarian Democracy”
Figure 3: Growth and Wages in Three Societies: Status Oriented Oligarchy (SOO), a Plutocratic Democracy (PLD) and a Proletarian
Democracy (PRD)
SOO PLDg g
PRDg
( )g
0SOO ˆ( )
0PLD
( )
0PRD
growth
0PLDV
0SOOV
0PRDV
Figure 4: Status Shock
( )g
1SOO 0
SOO 1
PLD 0PLD
( )
0PRD 1
PRD
ˆg
*1 0
*3 0
( , )
( , )
g
g
growth
1PLDV 0
PLDV
1SOOV
0SOOV
1PRDV
0PRDV
Preference Shocks: gamma rises• Status Oriented Society:
– Rich Pivotal Voter: tax rate falls – Under Supply of Public Goods: dg/dt > 0– Growth falls, Inequality rises
• Plutocratic Democracy: – Rich Pivotal Voter: tax rate falls – Over Supply of Public Goods: dg/dt > 0– Growth rises, Inequality rises
• Proletarian Democracy: (A+R case) – Poor Pivotal Voter: tax rate rises– Over Supply of Public Goods: dg/dt > 0– Growth falls, Inequality falls
Figure 5: Democracy Shock
( )g
0SOO
1SOO
0PLD
1PLD
( )
0PRD 1
PRD
ˆg
*1 0
*3 0
( , )
( , )
g
g
growth
1PLDV 0
PLDV
0SOOV
1SOOV
1PRDV
0PRDV
Democracy Shocks: Sigma-i rises • All Societies:
– equilibrium tax rate rises Inequality falls
• Status Oriented Society: Under Supply of Public Goods: dg/dt > 0– Growth rises
• Plutocratic and Proletarian Democracy: – Over Supply of Public Goods: dg/dt > 0– Growth falls
• Growth is an inverted U-shaped in democracy, e.g. Barro (1996)
• Inequality is monotonically increasing in Democracy:
Democratization, Growth and Redistribution
*
*
Let ( , ) ( , )
ˆ ˆ ˆˆ ˆ( ( ), ) ( , ),
ˆ ˆ0 0 and 0
(1, ) ( , ),
0
p pk k
pk k
pk k
D D G F D G
D D G D G
D D
D D G D G
D
Figure 5 Democracy and Growth in Egoistic and Status-Oriented Societies
( | 0)g D
0ˆ( ( ), )kD G D Democracy
ˆg
g
*0(0, )g
Growth
0( | 0)g D
Summary of Comparative Statics
Societies and Thresholds dg
d ydG
d
dg
dD ydG
dD
Non-Developmental Oligarchy 0 0 0 0
Status-Oriented Oligarchy - + + -
Plutocratic Democracy + + - -
Proletarian Democracy - - - -
Growth-Maximizing Tax Rate 0 + 0 -
Egalitarian Tax Rate 0 - 0 -
Conclusions• Status effects interact with economic and political inequality in non-
trivial ways to generate equilibrium policies that influence growth and redistribution
• The model suggest societies fall into three categories based on the taste for status and the relative labor endowment of the pivotal voter.
• As democracy rise, growth rises and falls, (Barro, 1996) , while inequality falls (Li, Squire and Zou, 1998).
• An stock to the taste for status may either increase or decrease growth and increase or decrease inequality.
Extensions
• Alternative policies and political environments: e.g. Alesina and Drazen’s (1991) delayed adjustment model.
• Endogenize democratization, e.g. Bourguignon and Verdier (2000) or Acemoglu et al. (2xxx).
• Empirical testing