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