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
Krusell and Smith (Georgetown Macro Reading Group) Heterogeneity Presentation by Jinhui Bai 7 / 9
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?
Krusell and Smith (Georgetown Macro Reading Group) Heterogeneity Presentation by Jinhui Bai 9 / 9