The Redistributive Consequences of Segregation Lisa Windsteiger Max - - PowerPoint PPT Presentation

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The Redistributive Consequences of Segregation Lisa Windsteiger Max Planck Institute for Tax Law and Public Finance First WID World Conference, December 2017 Lisa Windsteiger (MPI) Segregation and Redistribution December 2017 Introduction

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The Redistributive Consequences of Segregation

Lisa Windsteiger

Max Planck Institute for Tax Law and Public Finance

First WID World Conference, December 2017

Lisa Windsteiger (MPI) Segregation and Redistribution December 2017

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SLIDE 2

Introduction

Why do we in general observe a non-monotone relationship between income inequality and support for redistributive policies in society? Income inequality has increased in many (industrialized) countries

  • ver the last 35-40 years

In general, demand for redistribution in society has not exhibited the same trend (see Ashok et al. (2015))

Lisa Windsteiger (MPI) Segregation and Redistribution December 2017

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Introduction

Socio-economic segregation has increased, especially where inequality is high (Reardon and Bischo¤ (2011), Chetty et al. (2014)). Misperceptions of the income distribution (own survey, Norton and Ariely (2011), Cruces et al. (2013))

Lisa Windsteiger (MPI) Segregation and Redistribution December 2017

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Putting the pieces together

People are segregated according to income. They are biased about the overall income distribution. This a¤ects people’s support for redistributive policies.

Lisa Windsteiger (MPI) Segregation and Redistribution December 2017

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Preview of Results

Demand for redistribution is lower than without segregation and misperceptions. An increase in inequality always leads to a smaller increase in demand for redistribution and can even lead to a decrease in demand for redistribution.

Lisa Windsteiger (MPI) Segregation and Redistribution December 2017

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A Model of Segregation and Misperceptions

= )

Beliefs Social Segregation

( =

Lisa Windsteiger (MPI) Segregation and Redistribution December 2017

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Today’s presentation

Introduce model of group formation with misperceptions Apply it to the question of income inequality and support for redistribution

I non-monotone relationship between inequality and demand for

redistribution

Lisa Windsteiger (MPI) Segregation and Redistribution December 2017

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Sorting with Misperceptions

Lisa Windsteiger (MPI) Segregation and Redistribution December 2017

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Sorting according to income

Income y is distributed on Y = [0, ymax] with cdf F(y)

I F(y) 2 C([0, ymax]) and strictly monotonic

Person with income yj can pay b > 0 to join group Sb and get yjE[y 2 Sb] b

  • r pay nothing and get

yjE[y 2 S0]

general Lisa Windsteiger (MPI) Segregation and Redistribution December 2017

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Possible partitions

Any monotone partition f[0, ˆ y), [ˆ y, ymax]g of Y and corresponding sorting fee b is possible y ¯ E(ˆ y) b < yE(ˆ y) 8y 2 [0, ˆ y) y ¯ E(ˆ y) b

  • yE(ˆ

y) 8y 2 [ˆ y, ymax]

Lisa Windsteiger (MPI) Segregation and Redistribution December 2017

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Sorting with Misperceptions

Add exogenous belief function People’s belief about average income in the other group is a continuous function of ˆ y Poor group’s belief about average income in the rich group: ¯ Ep(ˆ y) 6= ¯ E(ˆ y) Rich group’s belief about average income in the poor group: E r(ˆ y) 6= E(ˆ y) People are correct about average income in their own group: E p(ˆ y) = E(ˆ y) and ¯ Er(ˆ y) = ¯ E(ˆ y)

Lisa Windsteiger (MPI) Segregation and Redistribution December 2017

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Sorting with Misperceptions

A person with income yi in the rich group gets utility yi ¯ E(ˆ y) b thinks she would get yiE r(ˆ y) in the poor group

Lisa Windsteiger (MPI) Segregation and Redistribution December 2017

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Biased sorting equilibrium

De…nition

A partition of Y and a sorting fee b constitute a biased sorting equilibrium i¤ y ¯ Ep(ˆ y) b < yE(ˆ y) 8y 2 [0, ˆ y) (IC1) y ¯ E(ˆ y) b

  • yE r(ˆ

y) 8y 2 [ˆ y, ymax] (IC2)

Lisa Windsteiger (MPI) Segregation and Redistribution December 2017

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Consistency requirement

De…nition

A partition of Y with corresponding sorting fee b satis…es consistency i¤ y ¯ E(ˆ y) b < yE r(ˆ y) 8y 2 [0, ˆ y) (CR1) y ¯ Ep(ˆ y) b

  • yE(ˆ

y) 8y 2 [ˆ y, ymax] (CR2)

Lisa Windsteiger (MPI) Segregation and Redistribution December 2017

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Corollary

In a biased sorting equilibrium with consistency any equilibrium cuto¤ ˆ y must satisfy ˆ y ¯ E(ˆ y ) ˆ y E r(ˆ y ) = ˆ y ¯ Ep(ˆ y ) ˆ y E(ˆ y ) = b

Lisa Windsteiger (MPI) Segregation and Redistribution December 2017

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Underestimating inequality

Poor underestimate rich, rich overestimate poor: ¯ Ep(ˆ y) < ¯ E(ˆ y) 8ˆ y 2 (0, ymax) E r(ˆ y) > E(ˆ y) 8ˆ y 2 (0, ymax) See e.g. Kiatpongsan and Norton (2014), Norton and Ariely (2011), Norton et al. (2014) and my own survey

more Lisa Windsteiger (MPI) Segregation and Redistribution December 2017

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Proportional biased beliefs

Poor’s belief about rich group: ¯ Ep(ˆ y) = β(1 F(ˆ y))ˆ y + (1 β(1 F(ˆ y)) ¯ E(ˆ y) Rich’s belief about poor group: E r(ˆ y) = βF(ˆ y)ˆ y + (1 βF(ˆ y))E(ˆ y)

I β 2 (0, 1) Lisa Windsteiger (MPI) Segregation and Redistribution December 2017

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Existence and uniqueness of equilibrium

Equilibrium cuto¤: ˆ y [ ¯ E(ˆ y ) E r(ˆ y )] = ˆ y [ ¯ Ep(ˆ y ) E(ˆ y )] Unique equilibrium cuto¤ > 0 exists ˆ y = E

Consistency Lisa Windsteiger (MPI) Segregation and Redistribution December 2017

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Inequality and the Demand for Redistribution

Lisa Windsteiger (MPI) Segregation and Redistribution December 2017

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Voting for redistribution

Meltzer Richard Model: people vote for linear tax rate Without misperceptions:

I high inequality =

) high demand for redistribution

I increase in inequality =

) increase in demand for redistribution

With misperceptions:

I lower perceived inequality =

) lower demand for redistribution

I increase in inequality can lead to decrease in perceived inequality

= ) decrease in demand for redistribution

Lisa Windsteiger (MPI) Segregation and Redistribution December 2017

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Redistribution without misperceptions

Linear taxation and redistribution: person with income yj has post-redistribution income (1 t)yj + τ(t)E Preferences are single-peaked = ) median voter theorem holds The tax rate determined by majority voting will be the median earner’s optimal tax rate given by τ0(t) = yM E if y M

E < 1 and t = 0 otherwise

Tax rate is decreasing in "equality ratio" y M

E

Lisa Windsteiger (MPI) Segregation and Redistribution December 2017

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Redistribution with misperceptions

If people knew the average income in the other group they could calculate overall average income correctly: E = F(ˆ y)E(ˆ y) + (1 F(ˆ y)) ¯ E(ˆ y) With segregation and misperception, poor people underestimate average income Ep(ˆ y) = F(ˆ y)E(ˆ y) + (1 F(ˆ y)) ¯ Ep(ˆ y) < E Rich people overestimate average income Er(ˆ y) = F(ˆ y)E r(ˆ y) + (1 F(ˆ y)) ¯ E(ˆ y) > E

Lisa Windsteiger (MPI) Segregation and Redistribution December 2017

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Redistribution with misperceptions

ˆ y = E The median earner is in the poor group and her preferred tax rate is given by τ0(˜ t) = yM Ep yM Ep > yM E

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Proposition (Segregation =

) Low taxes)

The median voter’ s preferred tax rate is lower in the presence of economic segregation.

Lisa Windsteiger (MPI) Segregation and Redistribution December 2017

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Increasing inequality and redistribution

Without misperceptions

E¤ects of a mean-preserving spread of the income distribution:

I Equality ratio y M

E

decreases ∆ yM E ! = ∆yM E = ∆yM yM yM E

I Demand for redistribution t increases Lisa Windsteiger (MPI) Segregation and Redistribution December 2017

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Increasing inequality and redistribution

With misperceptions

Equilibrium cuto¤ stays at ˆ y = E Ep decreases because ∆ ¯ Ep < ∆ ¯ E Perceived equality ratio: ∆ yM Ep

  • = ∆yMEp yM ∆Ep

(Ep)2 = ∆yM yM ∆Ep Ep yM Ep Percentage decrease in perceived equality is less than in the absence

  • f segregation

Lisa Windsteiger (MPI) Segregation and Redistribution December 2017

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Proposition (Inequality % =

) Redistribution &)

There always exists a mean-preserving spread that leads to a decrease in the median voter’s demand for redistribution.

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Conclusion

Model of sorting with misperceptions, interaction of beliefs and segregation Application to inequality and redistribution

I Non-monotone relationship between inequality and demand for

redistribution

Outlook:

I Empirical analysis, especially in European countries I Supply side Lisa Windsteiger (MPI) Segregation and Redistribution December 2017

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Consistency

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Positional bias

Poor people tend to overestimate and rich people tend to underestimate their relative position (Bias1 = Perceived income percentile - True income percentile)

  • 100
  • 50

50 100 20 40 60 80 100 Income percentile Fitted values Bias1

Lisa Windsteiger (MPI) Segregation and Redistribution December 2017

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Inequality and the supply side of segregation I

Suppose a pro…t-maximizing monopolist can decide whether or not to

  • ¤er segregation

Pro…t: ˆ y ( ¯ E E r)(1 F(ˆ y )) c = E(E E)[1 γF(E)(1 F(E))] c

Lisa Windsteiger (MPI) Segregation and Redistribution December 2017

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Inequality and the supply side of segregation II

An increase in inequality can make it pro…table for the monopolist to become active Median voter’s demand for redistribution changes from T 01 yM E

  • to

T 01 ˆ yM Ep

  • where

Ep = E β(1 F)2( ¯ E + ∆ ¯ E E) there always exists a mean-preserving spread that leads to a decrease in demand for redistribution

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The median earner is the decisive voter if E Er(E) yM Ep(E) A su¢cient condition for this inequality to hold is E yM β ¯ E(E) E(E) 4 which is satis…ed (for a given β) if the income distribution is su¢ciently positively skewed with not too much mass in the upper and lower tails of the distribution as long as E yM > 0 then even if 4(E yM) ¯ E(E) E(E) this inequality can always be satis…ed if β is small enough

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20 40 60 80 Frequency 50000 100000 150000 200000 250000 Income

Figure: Sample household income distribution

Lisa Windsteiger (MPI) Segregation and Redistribution December 2017

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4.00% 5.00% 6.00%

Figure: US household income distribution

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Secretary, Nurse, Teacher, Cleaner, University lecturer, Artist, Electrician, O¢ce manager, Solicitor, Farm worker, Chief executive, Software designer, Call center worker, Postal worker, Scientist, Lorry driver, Accountant, Shop assistant

back Lisa Windsteiger (MPI) Segregation and Redistribution December 2017

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Positional bias

Poor people tend to overestimate and rich people tend to underestimate their relative position (Bias1 = Perceived income percentile - True income percentile)

  • 100
  • 50

50 100 20 40 60 80 100 Income percentile Fitted values Bias1

Lisa Windsteiger (MPI) Segregation and Redistribution December 2017

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Sorting according to income

Income y is distributed on Y = [0, ymax] with cdf F(y)

I F(y) 2 C([0, ymax]) and strictly monotonic

Person with income yj can pay b > 0 to join group Sb and get U(yj, E[y 2 Sb]) b

  • r get

U(yj, E[y 2 S0]) U(., .) is continuous, strictly increasing in both arguments and strictly supermodular

back Lisa Windsteiger (MPI) Segregation and Redistribution December 2017

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Uniqueness in Case 1 with general utility

Uniqueness is guaranteed if additionally it holds that at any ˆ y for which U(ˆ y , ¯ E(ˆ y )) U(ˆ y , E r(ˆ y )) = U(ˆ y , ¯ Ep(ˆ y )) U(ˆ y , E(ˆ y )) we have that U1(ˆ y , ¯ E(ˆ y )) U1(ˆ y , E r(ˆ y )) U1(ˆ y , ¯ Ep(ˆ y )) U1(ˆ y , E(ˆ y )) U2(ˆ y , E r(ˆ y )) U2(ˆ y , E(ˆ y )) and U2(ˆ y , ¯ E(ˆ y )) U2(ˆ y , ¯ Ep(ˆ y ))

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Biased sorting equilibria

Four possible combinations of biases:

1

Poor underestimate rich, rich overestimate poor

2

Poor overestimate rich, rich underestimate poor

3

Poor overestimate rich, rich overestimate poor

4

Poor underestimate rich, rich underestimate poor

Lisa Windsteiger (MPI) Segregation and Redistribution December 2017

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Existence of sorting equilibria

Proposition

Biased sorting equilibria with consistency always exist in Case 1 and Case 2 and can never exist in Case 3 and Case 4. The perceived di¤erences between groups must be equal at the equilibrium cuto¤: ¯ E(ˆ y ) E r(ˆ y ) = ¯ Ep(ˆ y ) E(ˆ y )

Lisa Windsteiger (MPI) Segregation and Redistribution December 2017

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Uniqueness of equilibrium

Proposition

If d j ¯ E(ˆ y) ¯ Ep(ˆ y)j d ˆ y < 0 and d jE r(ˆ y) E(ˆ y)j d ˆ y > 0 then there exists a unique biased sorting equilibrium with consistency in Case 1 and Case 2.

general back Lisa Windsteiger (MPI) Segregation and Redistribution December 2017

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Assumptions

1

Range: ¯ Ep(ˆ y) 2 [ˆ y, ymax] and E r(ˆ y) 2 [0, ˆ y]

2

Constant direction of bias: ¯ Ep(ˆ y) < (>) ¯ E(ˆ y) 8ˆ y 2 (0, ymax) E r(ˆ y) < (>)E(ˆ y) 8ˆ y 2 (0, ymax)

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estates tax: https://www.irs.gov/pub/irs-soi/ninetyestate.pdf

Lisa Windsteiger (MPI) Segregation and Redistribution December 2017

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Evidence from Household Surveys

look at support for redistribution over time (GSS and ANES)

3 3.5 4 4.5 5 Inverse of ANES variable VCF0809 1970 1980 1990 2000 2010 ANES Year Fitted values Fitted values Bottom 16% Rest of the income distribution

Bottom 16% vs rest of the income distribution

Preferences for Redistribution

Figure: ANES variable VCF0809: Should the government see to it that everybody has a job and a good standard of living? Average preferences of the bottom 16% and the rest of the income distribution

Lisa Windsteiger (MPI) Segregation and Redistribution December 2017

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Bias2

dev_av 603 .403361 .3184763 .0272741 6.704556 Variable Obs Mean Std. Dev. Min Max . summarize dev_av

Lisa Windsteiger (MPI) Segregation and Redistribution December 2017

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Bias

dev_av2 603 -.3555657 .3711611 -.9998074 6.704556 Variable Obs Mean Std. Dev. Min Max . summarize dev_av2

Lisa Windsteiger (MPI) Segregation and Redistribution December 2017

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Camsd (Social circle diversity)

camsd 603 7.319444 3.590801 0 19.09188 Variable Obs Mean Std. Dev. Min Max . summarize camsd

Lisa Windsteiger (MPI) Segregation and Redistribution December 2017

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Factor (Social Segregation)

f7 509 3.88e-11 .6054928 -1.673802 1.848242 Variable Obs Mean Std. Dev. Min Max . summarize f7

Lisa Windsteiger (MPI) Segregation and Redistribution December 2017