Income and Wealth Heterogeneity in the Macroeconomy

Per Krusell and Tony Smith (JPE 1998)

Georgetown Macro Reading Group

Presentation by Jinhui Bai

Krusell and Smith (Georgetown Macro Reading Group) Heterogeneity Presentation by Jinhui Bai 1 / 9

Quick Summary

Questions

What determines wealth inequality in the economy?How does heterogeneity a¤ect evolution of aggregate variables?

Answers

Evaluate two hypothesis of wealth inequality

Inequality from accumulated labor market shock: noIneqaulity from both labor market luck and heterogeneous thrift: yes

Heterogeneity on aggregate variables

In all models evaluated, small e¤ect on capital, investment and GDPIn most models evaluated, small e¤ect on consumptionBut in heterogeneous thrift model, a large e¤ect on consumption

Methodological Contribution

Develop a method to compute models with heterogeneity

Krusell and Smith (Georgetown Macro Reading Group) Heterogeneity Presentation by Jinhui Bai 2 / 9

Model

A Recursive Competitive Equilibrium Formulation:

v (k, ε; Γ, z) = maxfc ,k 0g

�u (c) + βE

�v�k 0, ε0; Γ0, z 0jz , ε

��s.t.

c + k 0 = r�k, l , z

�k + w

�k, l , z

�lε+ (1� δ) k,

Γ0 = H�Γ, z , z 0

�,

k 0 � 0,

where Γ is the joint distribution on (k, ε) and

r�k, l , z

�= αz

�k

l

�α�1, w

�k, l , z

�= (1� α) z

�k

l

�α

.

Q: How to approximate Γ, an in�nite-dimensional object?

Krusell and Smith (Georgetown Macro Reading Group) Heterogeneity Presentation by Jinhui Bai 3 / 9

Solution Method

Some possible approximation

Parameterize Γ, say normal, Pareto, etcUse other distributional statistics: e.g., percentileUse moments of distribution: e.g., mean and variance

Solution Procedure

Replace Γ with moments, say k and var (k)Conjecture a functional form for H (Γ, z , z 0): say, log-linearSolve the household problemSimulate the economy and get a time series of momentsUse simulated data to estimate parameters in HIterate until convergence

Krusell and Smith (Georgetown Macro Reading Group) Heterogeneity Presentation by Jinhui Bai 4 / 9

Approximate Aggregation

Approximate aggregation results:

log k0= 0.095+ 0.962 log k, R2 = 0.999998,

log k0= 0.085+ 0.965 log k, R2 = 0.999998.

Economic Intuition

Rich people hold most of capital stockRich people has a close to linear saving function (due to good selfinsurance)

Interpretation: Inequality and aggregate variables

Changing wealth inequality and aggregate variables

Interpretation: Heterogeneity and aggregate variables

The economy may behave close to some representative-agent economyBut not necessarily the representative-agent economy with the sameutility and constraint

Krusell and Smith (Georgetown Macro Reading Group) Heterogeneity Presentation by Jinhui Bai 5 / 9

Preference Shock and Inequality

Can benchmark model match inequality?

No: the model generates a Gini Coe¢ cent of 0.25

Introduce heterogeneity of discount rate (β)

Interpretation: imperfect transmission of genes across generationsGenerates a realistic wealth inequality compared to the data

Krusell and Smith (Georgetown Macro Reading Group) Heterogeneity Presentation by Jinhui Bai 6 / 9

Heterogeneity and Macroeconomy

E¤ect of heterogeneity on macro aggregates

small for capital stock, investment and GDPFor most of cases, small for consumptionBut in stochastic β model, the consumption behavior is quite di¤erent

Why is consumption behavior quite di¤erent?

Poor people take a big fraction in consumptionPoor people are not well insured, hence consume di¤erently comparedwith complete market economy

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Discussion

Economic Question: Determination of inequality?

Methodology: Other numerical tools?

JEDC Special Issue on computation

Krusell and Smith (Georgetown Macro Reading Group) Heterogeneity Presentation by Jinhui Bai 8 / 9

Heterogeneity and macro economy

Firm Heterogeneity and Aggregate Dynamics

The interaction of heterogeneity and economic policy

Distributional E¤ects of economic policy:Economic Policy Determination:

Optimal Policy DeterminationPolitical process

Examples: Fiscal Policy, Monetary Policy, Labor Policy, Immigration,etc

Question: how di¢ cult on the technical side?

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