Sources of Lifetime Inequality

TLDR: For example, this paper found that differences in initial conditions account for more of the variation in lifetime earnings, lifetime wealth, and lifetime utility than do differences in shocks received over the working lifetime.

Abstract: Is lifetime inequality mainly due to differences across people established early in life or to differences in luck experienced over the working lifetime? We answer this question within a model that features idiosyncratic shocks to human capital , estimated directly from data, as well as heterogeneity in ability to learn, initial human capital, and initial wealth. We find that, as of age 23, differences in initial conditions account for more of the variation in lifetime earnings, lifetime wealth, and lifetime utility than do differences in shocks received over the working lifetime. ( JEL D31, D91, J24, J31) To what degree is lifetime inequality due to differences across people established early in life as opposed to differences in luck experienced over the working lifetime? Among the individual differences established early in life, which ones are the most important? A convincing answer to these questions is of fundamental importance. First, and most simply, an answer serves to contrast the potential importance of the myriad policies directed at modifying or at providing insurance for initial conditions (e.g., public education) against those directed at shocks over the working lifetime (e.g., unemployment insurance). Second, a discussion of lifetime inequality cannot go too far before discussing which specific type of initial condition is the most critical for determining how one fares in life. Third, a useful framework for answering these questions should also be central in the analysis of a wide range of policies considered in macroeconomics, public finance, and labor economics. We view lifetime inequality through the lens of a risky human capital model. Agents differ in terms of three initial conditions: initial human capital, learning ability, and financial wealth. Initial human capital can be viewed as controlling the intercept of an agent's mean earnings profile, whereas learning ability acts to rotate

Figures

Table 1: Estimation of Human Capital Shocks

Figure 4. Mean Time in Human Capital Accumulation

Figure 5. Earnings Dispersion: Learning Ability versus Shocks

Table 6: Importance of Changes in Initial Conditions: Model with Initial Wealth

Table 4: Sources of Lifetime Inequality: Benchmark Model

Table 5: Sources of Lifetime Inequality: Model with Initial Wealth Differences

Full text

NBER WORKING PAPER SERIES
SOURCES OF LIFETIME INEQUALITY
Mark Huggett
Gustavo Ventura
Amir Yaron
Working Paper 13224
http://www.nber.org/papers/w13224
NATIONAL BUREAU OF ECONOMIC RESEARCH
1050 Massachusetts Avenue
Cambridge, MA 02138
July 2007
We thank seminar participants at the SED, Minnesota Workshop in Macroeconomic Theory, NBER
Summer Institute, Productivity over the Life Cycle Conference (Bank of Canada), Macroeconomics
of Imperfect Risk Sharing (UC-Santa Barbara), PSU-Cornell Macro Theory Conference, Georgetown,
NYU, Oslo, Penn, UCLA, Wharton, Wisconsin and Yale. We thank the National Science Foundation
Grant SES-0550867 for research support. Ventura thanks the Research and Graduate Studies Office
from The Pennsylvania State University for support. Yaron thanks the Rodney White Center at the
The Wharton School for research support. The views expressed herein are those of the author(s) and
do not necessarily reflect the views of the National Bureau of Economic Research.
© 2007 by Mark Huggett, Gustavo Ventura, and Amir Yaron. All rights reserved. Short sections of
text, not to exceed two paragraphs, may be quoted without explicit permission provided that full credit,
including © notice, is given to the source.

Sources of Lifetime Inequality
Mark Huggett, Gustavo Ventura, and Amir Yaron
NBER Working Paper No. 13224
July 2007
JEL No. D31,D91,E21
ABSTRACT
Is lifetime inequality mainly due to differences across people established early in life or to differences
in luck experienced over the working lifetime? We answer this question within a model that features
idiosyncratic shocks to human capital, estimated directly from data, as well as heterogeneity in ability
to learn, initial human capital, and initial wealth -- features which are chosen to match observed properties
of earnings dynamics by cohorts. We find that as of age 20, differences in initial conditions account
for more of the variation in lifetime utility, lifetime earnings and lifetime wealth than do differences
in shocks received over the lifetime. Among initial conditions, variation in initial human capital is
substantially more important than variation in learning ability or initial wealth for determining how
an agent fares in life. An increase in an agent's human capital affects expected lifetime utility by raising
an agent's expected earnings profile, whereas an increase in learning ability affects expected utility
by producing a steeper expected earnings profile.
Mark Huggett
Georgetown University
mh5@georgetown.edu
Gustavo Ventura
Department of Economics
University of Iowa
W358 PBB
Iowa City, IA 52242
gventura1967@gmail.com
Amir Yaron
The Wharton School
University of Pennsylvania
2256 Steinberg-Dietrich Hall
Philadelphia, PA 19104-6367
and NBER
yaron@wharton.upenn.edu

1 Introduction
To what degree is lifetime inequality due to differences across people established early in
life as opposed to differences in luck experienced over the lifetime? Among initial conditions,
individual differences established early in life, which ones are the most important?
A convincing answer to these questions is of fundamental importance. First, and most
simply, an answer serves to contrast the potential importance of the myriad policies directed
at modifying or at providing insurance for initial conditions (e.g. public education) against
those directed at shocks over the lifetime (e.g., unemployment insurance programs). Second,
a discussion of lifetime inequality cannot go too far before discussing which type of initial
condition is the most critical for determining how one fares in life. Third, a useful framework
for answering these questions should also be central in the analysis of a wide range of policies
considered in macroeconomics, public finance and labor economics.
We view lifetime inequality through the lens of a risky human capital model. Agents
differ in terms of three initial conditions: initial human capital, learning ability and financial
wealth. As agents age, they accumulate human capital by optimally dividing their available
time between market work and human capital accumulation. Human capital and labor
earnings are risky as human capital is subject to uninsured, idiosyncratic shocks each period.
We ask the model to account for key features of the earnings distribution dynamics by
cohorts. To this end, we document how mean earnings and measures of earnings dispersion
and skewness evolve for U.S. males. We find that mean earnings are hump shaped and that
earnings dispersion and skewness increase with age over most of the working lifetime.
1
Our model produces a hump-shaped mean earnings profile by a standard human capital
channel. Early in life earnings are low as agents allocate time to accumulating human capital.
Earnings rise as human capital accumulates and as a greater fraction of time is devoted to
market work. Earnings fall later in life because human capital depreciates and little time is
put into producing new human capital.
Two forces within the model account for the increase in earnings dispersion. One force is
that agents differ in learning ability. Agents with higher learning ability have steeper mean
1
Mincer (1974) documents related patterns in U.S. cross-section data. Deaton and Paxson (1994),
Storesletten, Telmer and Yaron (2004), Heathcote, Storesletten and Violante (2005) and Huggett, Ventura
and Yaron (2006) examine cohort patterns in U.S. repeated cross section or panel data.
2

earnings profiles than low ability agents, other things equal.
2
The other force is that agents
differ in idiosyncratic human capital shocks received over the lifetime.
To identify the contribution of each of these forces, we exploit the fact that the model
implies that late in life little or no new human capital is produced. As a result, moments of
the change in wage rates for these agents are almost entirely determined by shocks, rather
than by shocks and the endogenous response of investment in human capital to shocks
and initial conditions. We estimate the shock process from U.S. data using precisely these
moments. Given an estimate of the shock process and other model parameters, we choose
the initial distribution of financial wealth, human capital and learning ability across agents
to best match the earnings facts described above.
3
We find that learning ability differences
are important in that they produce much of the rise in earnings dispersion over the lifetime,
given our estimates of the magnitude of human capital risk.
We use our estimates of shocks and initial conditions to quantify the importance of differ-
ent proximate sources of lifetime inequality. We find that as of a real-life age of 20 differences
in initial conditions are more important than are shocks received over the remaining lifetime
as a source of variation in realized lifetime utility, lifetime earnings and lifetime wealth.
4
We
find that between 62 to 73 percent of the variation in lifetime utility and between 60 to 71
percent of the variation in lifetime earnings is due to variation in initial conditions. The
higher estimate for each statistic applies when the magnitude of shocks is set to our lowest
point estimate, whereas the lower estimate applies when the magnitude of shocks is set to
our highest point estimate. Intuitively, the greater the shock variance the smaller is the role
for initial conditions in accounting for the pattern of increasing earnings dispersion over the
lifetime.
Among initial conditions, we find that, as of age 20, variation in initial human capital is
substantially more important than variation in either learning ability or initial wealth for how
an agent fares in life. This analysis is conducted for an agent with the median value of each
initial condition. We find that a one standard deviation increase in initial wealth increases
2
This mechanism is supported by the literature (see Card (1999)) on the shape of the mean age-earnings
profiles by years of education. It is also supported by the work of Lillard and Weiss (1979), Baker (1997) and
Guvenen (2006). They estimate a statistical model of earnings and find important permanent differences in
individual earnings growth rates.
3
Since a measure of financial wealth is observable, we choose the tri-variate initial distribution to be
consistent with features of the distribution of wealth for young households.
4
Lifetime earnings equals the present value of earnings, whereas lifetime wealth equals lifetime earnings
plus initial wealth.
3

expected lifetime wealth by 3 to 4 percent. In contrast, a one standard deviation increase in
learning ability or initial human capital increases expected lifetime wealth by 9 to 10 percent
and 30 to 34 percent, respectively. We also analyze how an agent in the model values these
changes in initial conditions. Specifically, we ask what is the permanent percentage change
in consumption which is equivalent for an agent in expected utility terms to these changes
in initial conditions. We find that the equivalent percentage changes in consumption are
roughly in line with how a change in initial condition impacts, in percentage terms, expected
lifetime wealth.
A leading and alternative view of lifetime inequality to the one analyzed in this paper is
presented in Storesletten et. al. (2004). The model analyzed in that paper is a standard,
incomplete-markets model in which labor earnings over the lifetime is exogenous.
5
These
authors estimate an earnings process from U.S. panel data to match features of earnings over
the lifetime. Within their model, slightly less than half of the variation in realized lifetime
utility is due to differences in initial conditions.
6
We note three difficulties related to this alternative incomplete-markets view. First, the
importance of idiosyncratic earnings risk may be overstated. The reason is that all of the
rise in earnings dispersion with age is attributed to shocks and none to initial conditions. In
our model learning ability differences lead to systematic differences in earnings growth rates
across agents. Lillard and Weiss (1979), Baker (1997) and Guvenen (2006) provide evidence
for such differences in permanent earnings growth rates in male earnings data. Second,
although the incomplete-markets model with exogenous earnings produces the rise in U.S.
within cohort consumption dispersion over the period 1980-90 documented by Deaton and
Paxson (1994), the rise in consumption dispersion is substantially smaller in U.S. data over
a longer time period. Our model produces less of a rise in consumption dispersion than the
exogenous-earnings model. A key reason for this is that part of the rise in earnings dispersion
is due to initial conditions. This component is anticipated by agents and therefore reflected
in consumption dispersion early in life. Finally, the standard incomplete-market, life-cycle
model is not useful for some purposes. Specifically, since earnings are exogenous, the model
gives up on theorizing about the underlying sources of earnings inequality. Thus, the model
5
Similar models have been used in the macroeconomic literature on economic inequality. Recent papers
in this literature include Huggett (1996), Casta˜neda, Diaz-Jimenez and Rios-Rull (2003), Krueger and Perri
(2006), Guvenen (2006) and Heathcote, Storesletten and Violante (2006), among many others.
6
In the context of a career-choice model, Keane and Wolpin (1997) find a more important role for initial
conditions. They find that unobserved heterogeneity realized at age 16 accounts for about 90 percent of the
variance in lifetime utility.
4

Frequently asked questions

Q1. What are the contributions in this paper?

The views expressed herein are those of the author ( s ) and do not necessarily reflect the views of the National Bureau of Economic Research. 

Q2. What are the future works in this paper?

For example, on the policy side, the framework is ideal to study tax policy. All these reasons suggest that future work should investigate this framework in more detail. 

Q3. What is important for determining the rise in consumption dispersion within the model?

What is important for determining the rise in consumption dispersion within the model is the magnitude of residual risk that remains after taxation and any insurance opportunities rather than the rise in earnings dispersion. 

Q4. What is the reason why ability dispersion falls as human capital risk increases?

The intuition for why ability dispersion falls as human capital risk increases is that human capital risk is itself a source of increased earnings dispersion. 

Q5. What is the implication of Figure 3?

The implication is that average earnings in Figure 3 fall late in life because growth in the rental rate of human capital is not enough to offset the mean fall in human capital. 

Q6. What is the potential of the incomplete-markets model?

It has the potential to replace the standard incomplete-markets model with exogenous earnings or exogenous wages for both positive and normative analysis. 

Q7. What are the forces that account for the rise in earnings as a cohort ages?

since individual human capital is repeatedly hit by shocks, these shocks are a source of increasing dispersion in human capital and earnings as a cohort ages. 

Q8. What is the proportional earnings tax rate in the US social security system?

The model social security system features a proportional earnings tax of 10.6 percent, which is the old-age and survivors insurance benefit tax rate in the US social security system. 

Q9. What is the mechanism for the increase in earnings of high ability individuals?

This mechanism implies that earnings of high ability individuals are relatively low early in life and relatively high late in life compared to agents with lower learning ability, holding initial human capital equal. 

Q10. What is the important factor in determining how one fares in life?

a discussion of lifetime inequality cannot go too far before discussing which type of initial condition is the most critical for determining how one fares in life. 

Q11. What is the impact of a change in initial conditions on the expected lifetime wealth of an agent?

with incomplete insurance markets, a risk-averse agent values such an increase in expected lifetime wealth at less than the equivalent change in current wealth.