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 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 over 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
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
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
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
A Model of Segregation and Misperceptions = ) Beliefs Social Segregation ( = Lisa Windsteiger (MPI) Segregation and Redistribution December 2017
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
Sorting with Misperceptions Lisa Windsteiger (MPI) Segregation and Redistribution December 2017
Sorting according to income Income y is distributed on Y = [ 0 , y max ] with cdf F ( y ) I F ( y ) 2 C ([ 0 , y max ]) and strictly monotonic Person with income y j can pay b > 0 to join group S b and get y j E [ y 2 S b ] � b or pay nothing and get y j E [ y 2 S 0 ] general Lisa Windsteiger (MPI) Segregation and Redistribution December 2017
Possible partitions Any monotone partition f [ 0 , ˆ y ) , [ ˆ y , y max ] g of Y and corresponding sorting fee b is possible y ¯ E ( ˆ y ) � b < yE ( ˆ y ) 8 y 2 [ 0 , ˆ y ) y ¯ E ( ˆ y ) � b � yE ( ˆ y ) 8 y 2 [ ˆ y , y max ] Lisa Windsteiger (MPI) Segregation and Redistribution December 2017
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: ¯ y ) 6 = ¯ E p ( ˆ 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: y ) and ¯ y ) = ¯ E p ( ˆ y ) = E ( ˆ E r ( ˆ E ( ˆ y ) Lisa Windsteiger (MPI) Segregation and Redistribution December 2017
Sorting with Misperceptions A person with income y i in the rich group gets utility y i ¯ E ( ˆ y ) � b thinks she would get y i E r ( ˆ y ) in the poor group Lisa Windsteiger (MPI) Segregation and Redistribution December 2017
Biased sorting equilibrium De…nition A partition of Y and a sorting fee b constitute a biased sorting equilibrium i¤ y ¯ E p ( ˆ y ) � b < yE ( ˆ y ) 8 y 2 [ 0 , ˆ y ) (IC1) y ¯ E ( ˆ y ) � b � yE r ( ˆ y ) 8 y 2 [ ˆ y , y max ] (IC2) Lisa Windsteiger (MPI) Segregation and Redistribution December 2017
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 ) 8 y 2 [ 0 , ˆ y ) (CR1) y ¯ E p ( ˆ y ) � b � yE ( ˆ y ) 8 y 2 [ ˆ y , y max ] (CR2) Lisa Windsteiger (MPI) Segregation and Redistribution December 2017
Corollary y � In a biased sorting equilibrium with consistency any equilibrium cuto¤ ˆ must satisfy y � ¯ y � ) � ˆ y � E r ( ˆ y � ) ˆ E ( ˆ y � ¯ y � ) � ˆ y � E ( ˆ y � ) = ˆ E p ( ˆ = b Lisa Windsteiger (MPI) Segregation and Redistribution December 2017
Underestimating inequality Poor underestimate rich, rich overestimate poor: ¯ ¯ E p ( ˆ y ) < E ( ˆ y ) 8 ˆ y 2 ( 0 , y max ) E r ( ˆ y ) > E ( ˆ y ) 8 ˆ y 2 ( 0 , y max ) 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
Proportional biased beliefs Poor’s belief about rich group: ¯ y )) ¯ E p ( ˆ y ) = β ( 1 � F ( ˆ y )) ˆ y + ( 1 � β ( 1 � F ( ˆ E ( ˆ y ) Rich’s belief about poor group: E r ( ˆ y ) = β F ( ˆ y ) ˆ y + ( 1 � β F ( ˆ y )) E ( ˆ y ) I β 2 ( 0 , 1 ) Lisa Windsteiger (MPI) Segregation and Redistribution December 2017
Existence and uniqueness of equilibrium Equilibrium cuto¤: y � [ ¯ y � ) � E r ( ˆ y � )] = ˆ y � [ ¯ y � ) � E ( ˆ y � )] E ( ˆ E p ( ˆ ˆ Unique equilibrium cuto¤ > 0 exists y � = E ˆ Consistency Lisa Windsteiger (MPI) Segregation and Redistribution December 2017
Inequality and the Demand for Redistribution Lisa Windsteiger (MPI) Segregation and Redistribution December 2017
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
Redistribution without misperceptions Linear taxation and redistribution: person with income y j has post-redistribution income ( 1 � t ) y j + 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 τ 0 ( t � ) = y M 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
Redistribution with misperceptions If people knew the average income in the other group they could calculate overall average income correctly: y )) ¯ E = F ( ˆ y ) E ( ˆ y ) + ( 1 � F ( ˆ E ( ˆ y ) With segregation and misperception, poor people underestimate average income y )) ¯ E p ( ˆ y ) = F ( ˆ y ) E ( ˆ y ) + ( 1 � F ( ˆ E p ( ˆ y ) < E Rich people overestimate average income y )) ¯ E r ( ˆ y ) = F ( ˆ y ) E r ( ˆ y ) + ( 1 � F ( ˆ E ( ˆ y ) > E Lisa Windsteiger (MPI) Segregation and Redistribution December 2017
Redistribution with misperceptions y � = E ˆ The median earner is in the poor group and her preferred tax rate is given by t � ) = y M τ 0 ( ˜ E p y M > y M E p E more Lisa Windsteiger (MPI) Segregation and Redistribution December 2017
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
Increasing inequality and redistribution Without misperceptions E¤ects of a mean-preserving spread of the income distribution: I Equality ratio y M decreases E ! y M = ∆ y M = ∆ y M y M ∆ y M E E E I Demand for redistribution t � increases Lisa Windsteiger (MPI) Segregation and Redistribution December 2017
Increasing inequality and redistribution With misperceptions y � = E Equilibrium cuto¤ stays at ˆ E p decreases because ∆ ¯ E p < ∆ ¯ E Perceived equality ratio: � y M � � ∆ y M � y M = ∆ y M E p � y M ∆ E p y M � ∆ E p ∆ = ( E p ) 2 E p E p E p Percentage decrease in perceived equality is less than in the absence of segregation Lisa Windsteiger (MPI) Segregation and Redistribution December 2017
Proposition (Inequality % = ) Redistribution & ) There always exists a mean-preserving spread that leads to a decrease in the median voter’s demand for redistribution. more Lisa Windsteiger (MPI) Segregation and Redistribution December 2017
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
Consistency back Lisa Windsteiger (MPI) Segregation and Redistribution December 2017
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 0 -50 -100 0 20 40 60 80 100 Income percentile Fitted values Bias1 Lisa Windsteiger (MPI) Segregation and Redistribution December 2017
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