Introduction
Facts
Model Overview
Intergenerational Links
Entrepreneurship
Earnings Risk
Models of Wealth Inequality, an Overview
Mariacristina De Nardi1
1 UCL,
Federal Reserve Bank of Chicago, IFS, CfM, and NBER
March 3, 2015
Conclusions and Discussion
Introduction
Facts
Model Overview
Intergenerational Links
Entrepreneurship
Earnings Risk
Conclusions and Discussion
Wealth Inequality, a Macroeconomist view
• Macroeconomics: no longer just representative agent models.
• There is a lot of inequality (in human capital, consumption, earnings, wealth...).
• There is a lot of redistribution.
• Inequality might affect responses to tax reform (even if we are not interested in
focusing on redistribution by itself).
• Incomplete markets models as a laboratory to study these questions.
Introduction
Facts
Model Overview
Intergenerational Links
Entrepreneurship
Talk roadmap
• Summary of some facts.
• Some models.
• Intergenerational links.
• Entrepreneurship.
• Earnings risk.
• What we have learned so far.
• What are the questions that are still open?
Earnings Risk
Conclusions and Discussion
Introduction
Facts
Model Overview
Intergenerational Links
Entrepreneurship
Earnings Risk
Facts: U.S. earnings, income and wealth
• Davies and Shorrocks (2000)
• Diaz-Gimenez, Quadrini, and Rios-Rull (1997) + updates.
• Heathcote, Perri, Violante (2009)
• Guvenen, Ozcan, Song (2013)
• Saez (various papers), Piketty (various papers).
Conclusions and Discussion
Introduction
Facts
Model Overview
Intergenerational Links
Entrepreneurship
Earnings Risk
Conclusions and Discussion
Some facts
• Labor earnings, income and wealth are unequally distributed.
• Distributions are skewed, with fat lower tail and thin upper tail.
• Wealth is more concentrated than labor earnings and income.
• Wealth is positively correlated with earnings and income, but not strongly.
Introduction
Facts
Model Overview
Intergenerational Links
Entrepreneurship
Earnings Risk
Conclusions and Discussion
Some facts
• Rich people (with high lifetime income) keep lots of assets as they age.
• A large fraction of aggregate wealth is transferred across generations, rather than
accumulated out of life cycle savings.
Introduction
Facts
Model Overview
Intergenerational Links
Entrepreneurship
Earnings Risk
Conclusions and Discussion
Transfer wealth and life-cycle savings
How much of wealth is saved and how much is inherited?
• Kotlikoff and Summers: 81% inheritance, 19% life cycle.
• Modigliani: 20% inheritance component, 80% life cycle.
Where does the 61% difference come from?
• 31.5%: capitalization of inheritances.
• 14% : expenditures on durables, consumption or saving? If consumption, this
reduces lc saving and inflates inheritance.
• 15.5%: classification of parental support for children above 18. K-S: bequest
(since it is investment in their hc).
Introduction
Facts
Model Overview
Intergenerational Links
Entrepreneurship
Earnings Risk
Conclusions and Discussion
Gale and Scholz’s computations
• Intervivos transfers and bequests account for at least 51% of US wealth
• Adding college expenses, at last 64% of wealth is transferred across generations
rather
Introduction
Facts
Model Overview
Intergenerational Links
Entrepreneurship
Earnings Risk
Entrepreneurship, some data
Fraction of entrepreneurs
Wealth percentile, top
1%
5%
Business owners or self-employed
81% 68%
Active business owners
65% 51%
Self-employed
62% 47%
Self-employed business owners
54% 39%
10%
20%
54%
39%
42%
30%
38%
26%
32%
22%
Conclusions and Discussion
Introduction
Facts
Model Overview
Intergenerational Links
Entrepreneurship
Earnings Risk
Conclusions and Discussion
Quantitative models to study inequality
• Bewley models.
• Ex-ante identical households get hit by idiosyncratic shocks (earnings).
• Households are ex-post heterogeneous because they face different histories of
shocks.
• There is a (constant) distribution of people over states (assets, age), but
individuals face a lot of uncertainty.
Introduction
Facts
Model Overview
Intergenerational Links
Entrepreneurship
Related Literature
Dynasty models
• Krusell and Smith (1997).
• Castañeda, Dı́az–Giménez and Rı́os–Rull (1998)
• Quadrini (1997).
OLG models
• Huggett (1996).
• Gokhale et al. (1998)
• Heer (1999)
Earnings Risk
Conclusions and Discussion
Introduction
Facts
Model Overview
Intergenerational Links
Entrepreneurship
Earnings Risk
De Nardi, Review of Economic Studies 2004
• OLG;
• lifetime and income uncertainty;
• parents are altruistic;
• children partially inherit parents’ productivity.
Why?
• Age structure generates inequality;
• Motives to save: precautionary, life cycle, bequests.
poor people: life–cycle component of savings;
rich: inheritance.
• Also differences due to different family backgrounds.
Conclusions and Discussion
Introduction
Facts
Model Overview
Intergenerational Links
Entrepreneurship
Earnings Risk
Conclusions and Discussion
Other key model elements
Simplified model of the household: 1 parent and children.
• 20 year old people start consuming, working and paying taxes
• 25 year old people procreate
• exogenous number of children
• inherit once in a lifetime, at a random date
• after retirement the agent does not work and receives social security benefits
Introduction
Facts
Model Overview
Intergenerational Links
Entrepreneurship
Earnings Risk
Preferences
• Period utility from consumption:
u(ct ) =
ct1−σ
1−σ
• Bequest motive: ”Warm glow altruism”
φ(b + k)
Notice The larger is k, the more bequests are luxury goods
Conclusions and Discussion
Introduction
Facts
Model Overview
Intergenerational Links
Entrepreneurship
Earnings Risk
Conclusions and Discussion
Technology
• Observe parental productivity when one’s parent is 40 and use it to infer expected
bequest distribution.
• Workers experience productivity shocks.
• After age 20 it evolves stochastically according.
• Initial level at 20 is inherited from parent’s productivity (at 40).
• One asset: capital.
• The household faces a borrowing constraint.
Introduction
Facts
Model Overview
Intergenerational Links
Entrepreneurship
Experiments
Add sequentially key elements to model economies:
• Age structure and income uncertainty
OLG, no intergenerational links.
Accidental bequests:
• redistributed equally to people alive
• given to the deceased’s children
• Add bequest motive:
OLG + bequest motive
• Add productivity link:
OLG + bequest motive + productivity inheritance
Earnings Risk
Conclusions and Discussion
Introduction
Facts
Model Overview
Intergenerational Links
Entrepreneurship
Earnings Risk
Beq/Wealth Wealth
Percentage wealth in the top
%≤0
Ratio
Gini
1% 5% 20% 40% 60% Wealth
U.S. data
.60
.78
29
53
80
93
98
5.8-15.0
No intergenerational links, equal bequests to all
.67
.67
7
27
69
90
98
17
No intergenerational links, unequal bequests to children
.38
.68
7
27
69
91
99
17
One link: productivity inheritance
.38
.69
8
29
70
92
99
17
One link: parent’s bequest motive
.55
.74
14
37
76
95
100
19
Both links: parent’s bequest motive and productivity inheritance
.60
.76
18
42
79
95
100
19
Conclusions and Discussion
Introduction
Facts
Model Overview
Intergenerational Links
Entrepreneurship
Earnings Risk
Conclusions and Discussion
Wealth .1, .3, .5, .7, .9, .95 quantiles. No links, equal bequests to all.
7
6
Wealth
5
4
3
2
1
0
20
30
40
50
60
Age
70
80
90
Facts
Model Overview
Intergenerational Links
Entrepreneurship
Earnings Risk
Conclusions and Discussion
Wealth .1, .3, .5, .7, .9, .95 quantiles. Bequest motive.
7
6
5
Wealth
Introduction
4
3
2
1
0
20
30
40
50
60
Age
70
80
90
Introduction
Facts
Model Overview
Intergenerational Links
Entrepreneurship
Earnings Risk
Conclusions and Discussion
Int’s links: summary of the main results
• Accidental bequests do not help explain the concentration in the upper tail of the
wealth distribution.
Voluntary bequests do.
• Transmission of productivity across generations increases concentration in the
upper tail but voluntary bequests are quantitatively more important.
• Bequest motive → life–cycle accumulation profile more consistent with the U.S.
data.
• Still, they do not generate enough really rich people. There is still something
missing.
Introduction
Facts
Model Overview
Intergenerational Links
Entrepreneurship
Earnings Risk
Conclusions and Discussion
Cagetti and De Nardi, 2006 JPE
• Altruistic agents care about their children.
• Every period agents decide whether to run a business.
• High ability entrepreneurs are borrowing constrained and have a large desired firm
size. Thus, they keep saving even when rich.
f (k) = θk ν + (1 − δ)k
k = a + b(a)
• Borrowing constraints.
• This model can generate the wealth concentration observed in the data.
Introduction
Facts
Model Overview
Intergenerational Links
Entrepreneurship
Earnings Risk
Cagetti and De Nardi, 2006 JPE
Percentage wealth in the top
Gini entrepreneurs
1% 5% 20%
U.S. data
0.8
7.55%
30
54
81
Baseline with entrepreneurs and altruism
0.8
7.50%
31
60
83
40%
94
94
Conclusions and Discussion
Introduction
Facts
Model Overview
Intergenerational Links
Entrepreneurship
Earnings Risk
Conclusions and Discussion
Wealth Distribution in population, Data: dashed line and Model: solid line.
0.08
0.07
Fraction of people
0.06
0.05
0.04
0.03
0.02
0.01
0
0
1000
2000
3000
4000
Positive wealth, in thousands of dollars
5000
Introduction
Facts
Model Overview
Intergenerational Links
Entrepreneurship
Earnings Risk
Conclusions and Discussion
Wealth Distribution entrepreneurs, Data: dashed line and Model: solid
line.
Fraction of people
0.08
0.06
0.04
0.02
0
0
1000 2000 3000 4000 5000
Positive wealth, in thousands of dollars
Introduction
Facts
Model Overview
Intergenerational Links
Entrepreneurship
Earnings Risk
Conclusions and Discussion
Earnings risk, Castaneda et al. JPE 2003.
• Consider an altruistic agent.
• This agent can, every period, faces very large earnings risk. Use this risk to match
both earnings and wealth inequality.
• This model can generate the wealth concentration observed in the data.
Introduction
Facts
Model Overview
Intergenerational Links
Entrepreneurship
Earnings Risk
Conclusions and Discussion
Earnings risk, the rock stars
Earnings level
Fraction at inv distr.
1.0
61.11%
3.0
22.25%
10.0
16.50%
1060
0.04%
The earnings rich have a 20% probability of turning into working poor every year.
Introduction
Facts
Model Overview
Intergenerational Links
Entrepreneurship
Earnings Risk
Conclusions and Discussion
Earnings risk or high returns to capital
• Entrepreneurship and earnings risk generate a lot of wealth inequality.
• But have very different tax policy prescriptions (Kitao, 2008 and Kindermann and
Krueger 2014).
Introduction
Facts
Model Overview
Intergenerational Links
Entrepreneurship
Earnings Risk
Conclusions and Discussion
Conclusions and Discussion
• The rich have very high saving rates.
• Bequest motives, entrepreneurship, and specific forms of income risk help match
these saving rates.
• More work is needed to better quantify the various explanations and this is
important to do because these saving motives have different policy implications.
Introduction
Facts
Model Overview
Intergenerational Links
Entrepreneurship
Earnings Risk
Conclusions and Discussion
Some ideas for future research
• More work is needed to understand why the rich keep saving. This is key for
policy evaluation.
• Where does earnings inequality come from? Modeling labor supply and human
capital decisions.
• Empirical evidence seems to indicate heterogeneity in bequest motives. Think
more about how to model bequests and how to discipline modeling choices using
data.
• What else is the model missing that could be important?
• Capturing changes in inequality over time.