Status-seeking behavior, the evolution of income inequality, and growth

1. Status-seeking behavior, the evolution of income inequality, and growth Presented by Miyoung Oh 602Macro_ Spring2009

2. Introduction Main idea Status-seeking behavior affects the evolution of income inequality • Status preferences: the higher relative income, the higher utility • When average income rises • Case 1: marginal utility of own income increases (KUJ) • Case 2: marginal utility of own income decreases(RAJ) • Income inequality shrinks over time in case1, it expands in case2.

3. Introduction Status seeking preferences (past studies VS this paper) KUJ : keeping up with the Joneses RAJ : Running away from the Joneses Status desire(envy) negative externality Dynamic inefficiency KUJ: Income inequality decreases RAJ: Income inequality increases Initial ineuality?

4. Step1 The model Basic structure • two periods OG model (continuum of HHs, no pop growth) • two groups of Households (type i=1,2) with proportion • : according to the levels of income(human capital holding) of adult agents in the initial period • Young agents are endowed with one unit of time :They allocate a fraction of it to learning and a fraction to leisure - Adult agents supply their human capital ,inelastically, and allocate their wage income to consumption, and educational expenditure, • final goods are produced under a CRS (human capital is the only input) # Learning technology

5. Step1 The model Preferences and the external effects on marginal utility * Preferences Where where the function Vi (·) represents preferences for social status * the external effects on marginal utility  the sign of determines KUJ or RAJ

6. Step1 The model Individual’s behavior and solution of UMP(from FOC) : constant fraction of income on educational expenditure The solution for this UMP is characterized by the following conditions:

7. Step1 The model States of the economy Given state variables at t, the levels of learning efforts of young agents, determine the state variables in the next period * the mean of relative income, * Let σt denote the measure of inequality * average level of human capital in period t + 1(from (4)) * Relative positions evolve (from (4), (8))

8. Step2 Equilibrium conditions Ump condition +states equation + technology * equations to determine lt, given the income distn(from (5c), (8)) From (9), (10) implies (11) * The learning technology (from (4))

9. Step2 Equilibrium conditions Lemma 1

10. Step2 Equilibrium conditions Lemma 2

11. Step2 Equilibrium conditions Lemma 3

12. Step3 Equilibrium with symmetric preferences Proposition 1

13. Step3 Equilibrium with symmetric preferences Proposition 1 • Proposition 1 Suppose that there exists income inequality in the initial period of the economy, that is, • When the status preference function exhibits “keeping up with the Joneses”, • income inequality in the economy is diminishing over time. • (b) When the status preference function exhibits “running away from the Joneses”, • income inequality in the economy is expanding over time.

14. Step4 Equilibrium with asymmetric preferences When the strengths of status preferences are identical ( ) • We refer to the parameter Bi as the strength of status preferences of the type i agents, which is equal to V i (1), that is the marginal utility of relative income when the agent’s income is equal to the average. (2) The parameters α and β are the elasticities of marginal utility of relative income. If the elasticity is larger (less) than unity, then Vi exhibits KUJ (RAJ).We restrict our attention to the case where the preferences of type 1 agents exhibit RAJ (0 < α < 1), and the preferences of type 2 agents exhibit KUJ (β > 1).

15. Step4 Equilibrium with asymmetric preferences Proposition 2

16. Step4 Equilibrium with asymmetric preferences Proposition 2 In an economy where preferences are heterogeneous across two types of agents but strengths of status preferences are identical, there exists a steady state with perfectly equal income distribution. Such a steady state is locally stable when [(1−π)α + πβ] is larger than unity, whereas it is locally unstable when [(1−π)α + πβ] is less than unity.