Risk and Career Choice?
Raven E. Saksyand Stephen H. Shorez
June 8, 2004
Choosing a type of education is one of the largest …nancial de-
cisions we make. Educational investment di¤ers from other types
of investment in that it is indivisible and non-tradable.
di¤erences lead agents to demand a premium to enter careers
with more idiosyncratic risk.Since the required premium will
be smaller for wealthier agents, they will tend to enter careers
with more idiosyncratic risk.
After developing a model of career choice, we use data from
the Panel Study of Income Dynamics (PSID) to estimate the risk
associated with di¤erent careers. We …nd education, health care,
and engineering careers to have relatively safe streams of labor
income; business, sales, and entertainment careers are more risky.
By choosing a college major, many students make a costly hu-
man capital investment that allows them to enter a speci…c career.
To examine the link between wealth and college major choice im-
plied by the model, we use data on choice of college major from
the National Postsecondary Student Aid Survey (NPSAS). Con-
trolling for observable measures of ability and background, we
…nd evidence that wealthier students tend to choose riskier ca-
reers, particularly business.
?We thank John Campbell, Caroline Hoxby, Lawrence Katz, Howard Stone, and
Joshua White. We also thank seminar participants at Harvard, Oxford, NYU,
Northwestern, the University of Chicago, the Federal Reserve Board, and the Federal
Reserve Bank of New York for helpful comments.
excellent research assistance.
yHarvard University. Cambridge, MA.
zUniversity of Pennsylvania, Wharton School of Business, 3012 Steinberg
Hall-Dietrich Hall, 3620 Locust Walk, Philadelphia, PA 19104, (215) 898-7770,
We thank David De Remer for
This paper explores educational investment as a portfolio choice deci-
sion. Educational investment is one of the largest investments a person
makes in his lifetime. This investment allows him to earn a stream of
labor income whose properties depend on the career he has chosen. In
this way, educational investment is similar to investment in many other
…nancial assets, where purchasing the asset today gives its owner the
right to receive a stream of risky dividend payments in the future. Tra-
ditional asset pricing and portfolio choice models assume that assets are
tradable and divisible. By contrast, educational investment is lumpy
and not tradable. An agent can attend law school precisely once, can-
not sell his diploma if he decides to switch careers, and cannot practice
medicine and law at the same time. This lack of divisibility and trad-
ability makes human capital correlated with marginal utility. Therefore,
unlike traditional asset pricing models, idiosyncratic labor income risk
This paper examines how the …nancial risks associated with di¤erent
careers in‡uence who goes into which careers.
choose a type of education given the risk and return attributes of educa-
tional opportunities? How should di¤erences in wealth and risk aversion
impact who enters which profession? In this setting, agents demand a
premium to enter careers with more idiosyncratic risk.
required size of that premium depends on wealth. Controlling for ability
and preferences, wealthier agents should demand smaller risk premiums
and consequently be more willing to choose riskier careers.
ition for this result is that by investing a larger fraction of his wealth to
obtain an education, a poor agent is putting all of his eggs in one basket.
If he ends up with a low paying job, he has nothing else to fall back on.
By contrast, a wealthier agent will be able to rely on other sources of
income and is therefore less worried about labor income risk.
After developing a model of risk and career choice, we look for evi-
dence that its predictions are consistent with observed behavior. Ceteris
paribus, are wealthier agents more likely to enter riskier careers? Since
the theory predicts that risk is important to career choice, our …rst step
is to measure the riskiness of di¤erent careers. Using the Panel Study
of Income Dynamics (PSID), we measure the exposure of individuals in
di¤erent careers to career-wide and individual-level shocks.
that teaching, health care, and engineering professionals have less risky
labor income streams than sales, management, and entertainment pro-
fessionals.Most of the risk we observe in the PSID is idiosyncratic.
Conditioning on background and ability, these di¤erences in risk should
be more important to poor agents than rich ones.
How should an agent
Next, using the
National Postsecondary Student Aid Survey (NPSAS), we examine how
the riskiness of di¤erent careers might impact who goes into which …elds.
The analysis centers on estimating how di¤erent personal attributes in-
‡uence the likelihood of going into di¤erent careers. Consistent with our
theory, we …nd evidence that wealthier agents are more likely to go into
riskier …elds. This …nding is driven primarily by the fact that business
…elds tend to be high-risk and also tend to be chosen by richer students.
For example, we …nd that doubling a student’s family wealth increases
by roughly 20% his likelihood of studying business.
2 Related Literature
This paper is part of a large literature that analyzes education as an
investment. Education is seen as an investment because it has an up-
front cost, but allows an individual to receive a stream of labor income
in the future.
There are many empirical papers which try to measure the returns
to educational investment. A standard approach to measuring these
returns is associated with Mincer (1974), who regresses income on years
of education, age, and a variety of control variables. The focus of this
literature has been on obtaining an unbiased estimate of the coe¢cient
on schooling despite problems stemming from individual heterogeneity
and selection bias. Prominent examples are Ashenfelter and Krueger
(1994) and Angrist and Krueger (1991).
for example Card and Krueger (1992) addresses quality as well as quan-
tity of education. In addition to estimating the expected returns to
education, a few papers have tried to estimate the risks of di¤erent
types of occupations. For example, Topel (1984) estimates the proba-
bility of becoming unemployed as well as compensating wage di¤eren-
tials. Palacios-Huerta (2003) estimates the impact of human capital on
the mean-variance frontier of assets.
follow, Carroll and Samwick (1997) estimate the wage risks associated
with di¤erent industries.
Rather than examining the reduced form relationship between educa-
tion and income, another strand of the literature examines the problem of
choosing the optimal quantity of educational investment. Becker (1964)
notes that since human capital is both risky and illiquid, it should de-
mand a premium over safer assets. Williams (1978), Levhari and Weiss
(1974), Levhari and Weiss (1974), Williams (1979), and Judd (2000)
model the decision about what quantity of education to receive when
investment in education is risky.Our paper di¤ers from these models
of education choice in two respects: …rst, we focus on the type of ed-
ucation people choose instead of just the quantity; second, we test the
A related body of literature,
Also, using a technique that we
predictions of our model by looking at how the probability of entering
risky careers varies with initial wealth.
Previous research estimating the career decision as an unordered
choice has focused on the e¤ects of the level of income.
Boskin (1974) …nds that an occupation with higher lifetime earnings and
lower training costs is more likely to be chosen. Relating occupational
choice to college major, Berger (1988) …nds that predicted future earn-
ings in‡uence the choice of college major of young men. Neither of these
papers analyzes the di¤erential impact of initial income on di¤erent ca-
reers. Another framework often used in the career choice literature is
a cobweb model. For example, Freeman (1976) shows how current and
expected wages impact the supply and demand for speci…c classes of
engineers. Again, he focuses on the e¤ects of the level of income rather
than variance or risk.
The impact of risk on career choice could also be compared to the
decision about whether to become an entrepreneur. Just as this paper
predicts that richer agents are more likely to enter riskier careers, richer
agents may also be more likely to become entrepreneurs, an occupation
that carries large non-diversi…able risks.
Gentry and Hubbard (2002) document that entrepreneurs tend to have
larger …nancial wealth than other agents. However, Rosen and Willen
(2002) argue that the wage premium associated with self-employment is
too large to be explained by risk.
Finally, recent research in …nancial economics has looked at how tra-
ditional portfolio choice theory should be modi…ed by the introduction
of risky labor income. This literature takes labor income risk as ex-
ogenous and determines the optimal …nancial portfolio given this risk.
Merton (1971) has a HARA model of portfolio choice with non-tradable
labor income and stochastic raises. Viceira (2001), Koo (1998), Bertaut
and Haliassos (1997), Cocco, Gomes, and Maenhout (1998), Gakidis
(1997), Heaton and Lucas (1997), and Storesletten, Telmer, and Yaron
(1998) have also explored the impact of labor income on …nancial port-
folio choice. Davis and Willen (2000b) estimate the covariance of the
occupation-level component of income using CPS and use these as inputs
to compute the optimal portfolio of …nancial wealth for a given occupa-
tion. Davis and Willen (2000a) also compute the gains to risk-sharing
across professions and …nd that it is large. The goal of this paper is to
endogenize the career choice that these papers take as exogenous. While
endogenizing career choice is new in …nance models, endogenizing other
parts of the labor decision is not. Bodie et al. (1992) endogenizes the
decision about the quantity of labor supplied jointly with the …nancial
Consistent with this theory,
While there is a great deal of literature about risk, career choice, and
educational investment, this is the …rst paper to tie them together by
looking at the impact of career risk on type of educational investment.
3 A Simple Model of Career Choice
We begin by presenting a stylized model to illustrate why di¤erent agents
might have di¤erent preferences over risky careers.
agent has initial …nancial wealth, W0. Initially, the agent must choose
a career c, which will generate risky labor income,~Yc.
period, the agent merely consumes initial wealth plus labor income, so
his problem is to maximize expected utility:
Labor income depends on the agent’s career and can be decomposed
into risky and deterministic components, ~ "cand ?c:
Imagine that an
In the next
U = Eu
~Yc? ?c+ ~ "c;
E [~ "c] = 0:
We consider career c to be safer than career c0if ~ "csecond order stochas-
tically dominates ~ "c0.
We assume the agent has decreasing absolute risk aversion (DARA),
which implies that he becomes less concerned about any speci…c amount
of risk as he gets richer. The impact of this type of utility function
on career choice is relatively straightforward. Wealthier agents will be
more comfortable undertaking risky careers than poorer agents. While
this assumption is common and quite realistic, it is critical in driving
our results. An agent with constant absolute risk aversion utility would
demand the same-risk premium for undertaking a speci…c risk regardless
Formally, the use of DARA utility means that absolute risk aversion,
A ? ?u00=u0, is decreasing in consumption. Therefore, A0< 0 implies
The key result of the model is that if the agent gets richer, he will not
choose a career that is safer.
Proposition 1 Assume that an agent with DARA preferences over con-
sumption prefers career c over all others when his initial wealth is W.
If that agent’s wealth increases to W0> W, the agent chooses a career
c0. Then, career c0cannot be strictly safer than career c.
Proof. See Appendix A.
This proposition shows that agents become (weakly) more likely to
enter risky careers as they become wealthier.
premium to enter a risky career over a safe one.1However, if agents have
DARA utility, the demanded wage premium falls with wealth. Thus, ca-
reers with wage premiums that are insu¢cient at a given wealth become
su¢cient as an agent gets richer. Since an analytic solution describing
the consumption and career choice of an agent with DARA utility does
not exist, it is di¢cult to quantify the importance of wealth for career
choice. Therefore, we perform a simple calibration exercise to explore
the magnitude of the impact of wealth on career choice.
We consider the stylized career choice problem of two agents, one with
a greater initial wealth than the other. We assume that the wealthier
agent has $100,000 of initial wealth and that the poorer agent has $10 of
initial wealth. Each considers the choice between two careers, one riskier
than the other. The proposition above implies that the richer agent
would be more likely than the poorer agent to choose the riskier career
over the safer one. To illustrate this point, we assume a simple, discrete-
time model and calibrate numerically the impact of risk on career choice.
First, we assume that labor income follows a simple process:
Agents demand a wage
where the lognormal shocks, ", are identically and independently dis-
tributed with mean, ?", and standard deviation, ?".
common choice of simple stochastic process, any process for " will gen-
erate the similar results. The annual standard deviations for the safe
and risky career are set to 10% and 20%, respectively.
correspond roughly to the estimates of permanent time-series variability
of wages for safe and risky careers that we will estimate below in Section
4. For simplicity, we set ?"= 0 and do not allow agents to buy risky
assets. These assumptions can be loosened without changing the results
substantially. If the expected wages of the two careers were equal, all
agents would prefer the safer career. To show the impact of di¤erences
in risk on di¤erences in choice, we must assign a wage premium to the
risky career. We set the initial annual wages to $20,000 for the safe
career and $30,000 for the risky career, so that the expected wages are
50% higher for the risky career.
Similar to Viceira (2001), we assume that agents have power utility,
which exhibits decreasing absolute risk aversion, over lifetime consump-
While this is a
1The equilibrium wage is set by the wage premium demanded by the marginal
worker. The existence of this wage premium is con…rmed by Topel (1984), who
shows that jobs with higher unemployment risk demand wage premiums.
U (W;Y;t) = Et
1 ? ?
Wt+1= (1 + r)(Wt? Ct) + Yt+1
We set the parameters to the following plausible values: interest rate,
r = 0:05; discount rate, ? = 0:9; and risk aversion parameter, ? = 5.
We assume the agent works for 40 years.
optimization and numerical procedures used to estimate this problem.
Table 1 shows the certainty equivalent of a safe and a risky career
for both a rich and a poor agent. Given the parameters assumed, the
richer agent prefers the risky career while the poorer agent prefers the
safe career. For the richer agent, the 50% wage premium of the high-
risk career outweighs its increased risk. For the poorer agent, the higher
wages associated with the high-risk career are insu¢cient to make that
career attractive. This example emphasizes the role of risk because the
agents have a high degree of risk aversion and social insurance is not
included. In practice, social insurance prevents incomes from falling
too low and increases consumption in very bad states of the world. The
absence of social insurance from this calibration makes the risky career
look even more unappealing. This example demonstrates that, even for
individuals facing the same set of choices, initial wealth can cause people
to make substantially di¤erent decisions regarding the risk-reward trade-
Appendix B describes the
4 Estimating Career Risk
4.1 Cross-sectional Dispersion of Wages
In the remaining sections, we use several data sources to look for evidence
that wealthier people choose riskier careers.
the impact of risk on career choice, we must …rst determine the risk
associated with di¤erent careers.The simplest way to measure career
risk would be to look at the cross-sectional dispersion of wages. Within
an occupation, di¤erences in wages are likely to re‡ect heterogeneity in
ability. If people did not know their ability before entering a career, then
the cross-sectional dispersion of wages in that career would provide one
measure of the labor income risk they face. However, to the degree that
agents do know their ability before choosing a career, the cross-sectional
dispersion of wages will overstate the degree of risk.
While cross-sectional measures of wage dispersion are far from per-
fect as a measure of risk, we begin with these estimates because they are
Before we can measure
straight-forward. For this analysis, we use data from the Baccalaureate
and Beyond (B&B) Longitudinal Study, which will be described in more
detail in Section 5. The B&B collects data on education and work expe-
riences for a sample of undergraduate students one year after graduation.
The survey includes information on college major, post-college employ-
ment, scholastic test scores, and school attributes. If college is a time
when people make career-speci…c human capital investments, students
may look at the cross-sectional dispersion of wages as a measure of their
major’s labor income risk. While the problem of heterogeneous ability
should be taken seriously, we believe it is less severe in this context as
the individuals in this sample have recently entered the work force and
so are less likely to know their abilities.
this survey is that we can control for observable measures of ability.
Table 2 presents the unconditional mean and standard deviation of
annual salary one year after graduation by college major. To measure
cross-sectional wage dispersion conditioning on observables, we regress
annual salary on SAT scores and demographics and report the standard
deviation of residuals for each major. By controlling for test scores, we
hope to remove at least part of the component of wage dispersion that
is attributable to ability. Unconditionally, the table shows that business
majors have the most disperse wages after graduation, while education
majors have the least disperse wages. Conditioning on observables does
not change the dispersion of these major’s wages substantially.
provides suggestive evidence that majoring in business is riskier than
majoring in education. While health care and computers have a moder-
ate level of wage dispersion, we suspect this result re‡ects a larger degree
of heterogeneity in these …elds and may not be related to risk. Consis-
tent with this hypothesis, the dispersion of wages falls substantially in
these …elds after conditioning on observable measures of ability.
A second advantage of using
4.2 Panel Data on Wage Changes
Because of concerns about heterogeneous ability, we next use the Panel
Study of Income Dynamics (PSID), a data set that allows us to observe
the wages of individuals over time. We will estimate career risk by look-
ing at the time-series variability of wages. Ideally, career risk would best
be measured by looking at the time-series variability of consumption, not
wages. A career with a variable labor income stream might not be risky
in a utility sense if workers in that …eld were able to borrow and save so
that the variability of their consumption was low. Risky careers are those
that require people in them to have more variable consumption streams.
Measuring career risk using consumption variability poses several prob-
lems. The most obvious of these is that careers are held by individuals
while consumption is made by households. Factors that in‡uence what
career a person chooses also in‡uence whether and with whom they form
households. Therefore, using household consumption to measure career
risk may simply measure the degree of ‘assortative mating’ by career.
Also, panel data with information on both consumption and occupation
Therefore, we approximate the riskiness of careers with the
variability of labor income. To the extent that households are liquidity
constrained and simply consume what they earn, wage variability will
be a good proxy for consumption variability.
Using observed changes in wages, we estimate the variance of shocks
to an individual’s income and compare these variances for di¤erent ca-
reers. We interpret these shocks as unexpected, involuntary changes.
Therefore, we consider these wage changes to re‡ect labor-income risk.
We consider risky careers to be those with a high variance of unexpected
income shocks. While we will try to …lter out voluntary or expected
shocks, these are di¢cult to di¤erentiate from unexpected and involun-
The PSID is a nationally representative longitudinal household sur-
vey in the US. The data are collected annually and spans the years
Using information on household heads and “wives”4, we
de…ne the wage for each person as total real labor income5divided by
annual hours worked.6Since we will focus on careers that require some
form of human capital investment, we restrict the analysis to individuals
who report sixteen or more years of education. Another reason to restrict
the sample is that people with di¤erent amounts of schooling are likely
to be working in di¤erent kinds of jobs with di¤erent career opportuni-
ties open to them, even if they report similar occupation classi…cations.
Table 3 shows the average and standard deviation of hourly wages in
our sample for each career. Not surprisingly, teachers and entertainers
have relatively low wages while technical workers have relatively high
wages. The self-employed also tend to have very high wages. People in
entertainment, health care, management and sales careers tend to have
wages with higher cross-sectional dispersion than workers in technical
2The PSID, which contains information on food expenditures, is the only U.S.
dataset of which we are aware which …ts these criteria.
3Starting in 1998, the PSID began collecting data biannually.
focus on year-to-year changes, we exclude data after 1997 from our analysis.
4The PSID uses the term “wife” to mean a long-term female cohabiter.
5Nominal wages are de‡ated by the price index for personal consumption expen-
ditures from the National Income and Product Accounts.
6For the years before labor income was reported separately from total income, we
use only those observations where labor income is reported to be the sole source of
Because of our
and educational careers. As we discussed above, it is impossible to tell
from this cross-sectional analysis whether di¤erences in dispersion across
careers are the result of risk or dispersion in ability.
A signi…cant component of labor income-risk is the chance of becom-
ing unemployed, which is di¤erent for di¤erent careers.
unemployment rate in our sample is 2.9%7, which corresponds to esti-
mates obtained for college graduates reported by the Bureau of Labor
Statistics. Table 3 shows the average unemployment rate for each career.
Entertainers have the highest unemployment rate, followed by salesmen.
When estimating the time-series properties of labor income, we will use
hourly wages instead of total annual earnings. This understates unem-
ployment risk if unemployment causes an involuntary reduction in hours
but no change in hourly wages. However, estimating career risk using
total annual wages yields similar estimates of risk and similar ordinal
ranking of careers by risk.8
In order to estimate the risk of various careers, we …rst need to de…ne
the career groups we will examine.
Census code for each individual’s occupation, a measure that is too dis-
aggregated for our purpose.9
For example, we would like to treat a
person who reports being an “electrical engineer” and another who re-
ports being a “mechanical engineer” as having made the same choice
from a risk perspective. In other words, we believe that the variance of
shocks in these two occupations is similar. People evaluating potential
careers based on the riskiness of labor income streams should treat these
two occupations as the same. Broadening occupation categories in-
creases the number of observations within each group, and consequently
the precision of our estimates. On the other hand, the career de…ni-
tions should be narrow enough that the choice between one category and
another is meaningful.
An empirical test of the relevance of our de…nitions is to look at the
number of people who move between groups. If the groups are de…ned
The PSID reports the three-digit
7In this sample, the mean length of an unemployment spell is 1.3 years. This is
potentially a large overestimate since data is only collected annually. We consider an
agent who was unemployed in only one data point as having a one year unemployment
8While using annual wages instead of hourly wages allows us to better measure
unemployment risk, it also misidenti…es voluntary changes in hours worked as risk.
Estimating career risk using annual wages increases the measured risks somewhat in
technology …elds and to a larger degree in health care …elds. Because it is di¢cult
to identify voluntary vs involuntary changes in hours, we choose to focus our analyis
on hourly wages.
9Since individuals in the PSID often report an occupation for some years and
not others, we impute missing values by assigning the previously or subsequently
well, the people in each career group will have made a di¤erent set of de-
cisions regarding human capital investment, meaning that those in one
career group cannot easily switch to another. Columns 4 and 5 of Table
3 show the fraction of individuals who switch into or out of each of our
career groups. The average number of switches may be biased upward
by the existence of a few people who switch careers frequently. Misre-
porting of occupation codes could compound this problem. Therefore,
we also compare the median number of career switches for an individual
with the median number of years an individual appears in the sample.
Both columns show the incidence of career-switching to be fairly low,
lending credibility to our de…ned career groups. In the rest of the analy-
sis, we restrict the sample to wage changes where the individual reports
the same career in both periods. By looking only at people who stay in a
career, we are ignoring career change as an avenue through which people
may respond to shocks. If people leave a profession when they get a bad
shock, true risk may be higher than we observe.
since switching careers entails a loss of human capital and is therefore
costly, people should only switch careers in response to the worst shocks.
We test the sensitivity of our results to this issue by classifying people
by their initial career, as opposed to their current career. The resulting
variances we calculate are similar and the ordinal ranking of careers by
risk remains unchanged.
On the other hand,
4.3 Estimating Career Risk using Wage Changes
Next, we develop a relatively simple model that will allow us to create
an ordinal ranking of careers by risk. Following a methodology similar
to Carroll and Samwick (1997), we decompose the variance of observed
shocks into permanent and transitory components. The framework we
present below is more general than theirs in that it allows for career-
speci…c age pro…les and a career-wide component to the variance.
see how we back out the variances of each of the di¤erent types of shocks,
consider the following decomposition of log labor income,
ln(Yit) = git+ ai+ pit+ "ct+ "it;
where gitis a deterministic career-speci…c age pro…le which gives an esti-
mate of an individual’s expected wage given his age and career, aiis an
individual-speci…c, time-invariant ability measure, "ctand "itare career-
wide and individual-speci…c transitory shocks, and pit is a permanent
shock with a unit root that has both career-wide and individual-speci…c
pit= pit?1+ !ct+ !it:
Note that this structure makes the unrealistic assumption that all wage
shocks that are not immediately reversed will remain forever. Because
data on a given person is collected for an average of only 13 years, our
panel is not long enough to estimate models that allow a variety of shocks
to persist for intermediate lengths of time and dampen at di¤erent rates.
However, since our goal is to generate an ordinal ranking of careers by
risk, this simple model will be su¢cient unless careers vary greatly in
the relative importance of medium-term and permanent shocks.10
We assume that each of the four shocks (!ct;!it;"ct;"it) have inde-
pendent distributions with zero mean and constant variance.
shocks are uncorrelated with one another. The age pro…le git is esti-
mated with a quartic polynomial in age.
deviations from this career-speci…c age pro…le, this method controls for
di¤erences in the level of income for di¤erent careers. As made clear by
equation 6, any estimates obtained using the level of wages may be bi-
ased if we do not adequately control for the heterogeneity of individuals’
abilities. Instead, we assume that the impact of ability on log wages, ai,
remains constant over time. Therefore, we use a …rst-di¤erenced form
of equation 6:
Since we measure risk using
ln(Yit)?ln(Yit?1) = f(ageit)+!ct+!it+("ct?"ct?1)+("it?"it?1): (8)
Estimating equation 8 separately for each career by ordinary least
squares (OLS), the individual and career-wide residuals can be written
as functions of the underlying shocks:
b eit= !ct+ !it+ ("ct? "ct?1) + ("it? "t?1)
Pb eit= !ct+
+ ("ct? "ct?1) +
where Nctis the number of individuals in occupation c at time t. A slight
complication to the equations above is that a signi…cant fraction of the
individuals in our sample disappear from the sample and reappear two
or more years later. Rather than throwing out all of the wage changes
that span more than one year, we modify the framework to allow for d
years between observations.Under the assumptions stated above, we
obtain the following expressions for the variances and covariances of the
10Ordinal rankings will be unchanged unless careers with large shocks of medium
duration have small permanent shocks.
expect measures of higher order serial correlation to be more negative for high-risk
careers than for low ones. Empirically, we do not …nd this to be the case.
If this problem was important, we would
V ar(b eit) = d?2
V ar(b ect) = d?2
Cov(b ect;b ect?d) = ??2
Cov(b eit;b eit?d) = ??2
where Nct;t?dis the number of individuals who are in the sample in both
time periods t and t?d. For each occupation and each value of d from
1 to 5, we solve the four equations above for each of the parameters
of interest (?2
i"). We then form a weighted-average of
these results over the di¤erent values of d to obtain our estimates of the
The results are shown in Table 4.11
sults is that career-wide shocks account for only a small fraction of the
total variance.We interpret this …nding to mean that our de…nitions
of career categories are too broad to capture true career-wide ‡uctua-
tions. Since the career-wide component of the shock should be largely
a re‡ection of changes in the demand and supply of workers for a given
occupation, we will only detect the shock if there are demand or supply
shocks that a¤ect all of the people in a group. Instead, if the demand
or supply of more narrowly de…ned occupations within the career group
are not positively correlated with one another other, then the estimated
common component to the wages in the group would be zero.
sample sizes prevent us from looking at more detailed de…nitions of ca-
reers. Another reason why our estimates of the career-wide component
may be imprecise is that once we aggregate over all of the people in a
given year, we have only one data point per year, giving less than 30
observations per occupation. This small sample makes inference even
Turning to the individual-speci…c shocks, the variance of permanent
shocks is highest for sales workers and managers. The permanent com-
ponent of the individual shocks for these …elds is approximately 0.05,
corresponding to an annual standard deviation of wages of 23%.
relatively high for entertainers and low for engineers, computer profes-
sionals, and scientists.12
The pattern of transitory variances is similar
One of the most noticeable re-
11The negative variance estimates are generated by positive serial correlation in
the errors, which violates one of the assumptions of our model.
these results re‡ect the fact that the career-wide component of transitory shocks is
nearly zero but measured with noise.
12Carroll and Samwick (1997) report a similar variance of transitory shocks for
We believe that
to that of permanent variances, with sales, management, and entertain-
ment being higher than the others.
are moderate for teachers and health care workers.13
individual permanent component of wage shocks is approximately 0.033,
corresponding to an annual standard deviation of wages of 18% While
substantially lower than the risks for sales and management …elds, we
believe these estimates may be upward-biased. Unlike the other occupa-
tions, the majority of the teachers and nurses in our sample are women
and not the primary earners in their households.
likely to have a weaker attachment to the labor force than household
heads. As a secondary earner’s family responsibilities change over time,
she may change the intensity of her work, leading to large ‡uctuations
in her wage. Since we consider these wage changes to be the result
of decisions made voluntarily, we do not want to attribute the variance
associated with these changes in income as risk.
mate of career risk for teachers and health care workers are likely to
be upward-biased. To address this concern, we estimate labor-income
risk limiting the sample to household heads. Although the sample size
for certain careers, particularly in health care and education, is greatly
reduced, the ordinal ranking of careers by wage variability is similar.
Although these results allow us to rank careers by labor income risk,
it is the riskiness of consumption that impacts an individual’s utility.
Therefore, as a robustness check we investigate the relationship between
careers and consumption risk using the volatility of food expenditures
in the PSID. We associate household consumption with the career of
the household head and calculate the volatility of total consumption
and consumption per person for each career. Using the same method
as described above for changes in income, we decompose the variance
of consumption into career-wide and idiosyncratic permanent and tran-
sitory shocks. In contrast to our …ndings about income, we …nd no
substantial di¤erences in the variance of consumption shocks across ca-
reers. One interpretation of this …nding is that individuals in di¤erent
occupations are equally able to smooth consumption, so that people
The individual-speci…c variances
For example, the
These workers are
Therefore, our esti-
individuals with a college or advanced degree.
however, is somewhat lower. We attribute this di¤erence to the fact that they use
only three- to …ve-year changes in income to calculate their estimates, while our
estimates rely heavily on one- and two-year changes.
their occupational categories to ours, they also …nd lower variances for professional
and technical workers, and …nd higher variances for self-employed and sales workers.
Using a di¤erent strategy, Davis and Willen (2001), also …nd lower variances for
teachers, engineers and nurses using the CPS.
13The category of health care workers includes college-educated nurses, health
technicians and health administrators as well as doctors and physicians.
Their measure of permanent shocks,
Although it is di¢cult to map
with riskier labor income streams o¤set the additional risk. However,
the evidence for consumption smoothing in the PSID is weak because
the estimated variances (both transitory and permanent) are higher for
consumption expenditures than for income. More likely, measurement
error in food consumption makes food expenditures look more variable
than they actually are. Consequently, we believe that wage variability,
not consumption variability, is the most appropriate measure of career
In summary, we …nd that labor income risk is high for entertainers,
sales workers, and managers. Teachers, health care workers and engi-
neers have relatively safe occupations.
care workers may have particularly safe occupations since our estimate
of their career risk may be upward-biased.
Of these, teachers and health
5 Estimating Career Choice
5.1 College Major Choice as Career Choice
Having established the riskiness of various occupations, we now examine
the relationship between wealth and career choice. The theory developed
in Section 3 suggests that wealthier agents are better able to tolerate a
speci…c amount of risk. Therefore, giving an agent additional wealth
should make him more likely to enter a risky career.14
educated individuals, the time spent during college is often a period
when the choice among various occupations is considered.
reer has been chosen, students study a …eld in-depth, making human
capital investments that are speci…c to the chosen career.
this behavior, we take students’ choice of an undergraduate major as an
indication of career choice.To evaluate the hypothesis that students
from wealthier families will tend to enter riskier majors, we use data from
the National Postsecondary Student Aid Survey (NPSAS) and estimate
which college majors are more likely to be chosen by richer individuals.
Before estimating a model of college-major choice, we …rst present
some evidence that college majors are indeed linked to future careers.
To explore this link, we look at the Baccalaureate and Beyond (B&B)
Longitudinal Study. The B&B collects data on education and work
experience after graduation for a subset of students in the NPSAS. This
survey includes data on college major, post-college employment and the
Once a ca-
In view of
14Feelings about other career attributes may also change with wealth. For example,
as an agent gets richer, a labor-leisure trade-o¤ leads enjoyable careers to seem more
appealing as income increases. Our estimation procedure does not allow us to
determine whether wealth impacts career choice through risk, enjoyment of career,
or another channel.
student’s evaluation of the relationship between their major and their
job. Using this data, we can see if graduates take jobs in …elds close to
their majors. If so, their majors may have been investments enabling
them to get their jobs. However, we will not be able to explicitly rule
out the possibility that students choose majors close to their careers out
of interest in the …eld and not as an investment.
Table 5 shows the type of job taken by graduates a year after gradu-
ation in a variety of majors. Each row in the table represents a di¤erent
college major, while each column represents a di¤erent type of job. The
values in the table are the fraction of students in each major who choose
each career, with cells in bold indicating majors and careers that are sim-
ilar. The table shows that students who study engineering, education,
health care, and computers are very likely to enter careers corresponding
to their majors. Business majors overwhelmingly enter business, sales,
and clerical jobs. While science majors seldom enter science …elds, a
high fraction of these majors are listed as “not in the labor force.” Many
of these individuals are in graduate school, and we suspect that these
students chose science majors as undergraduates in preparation for more
advanced scienti…c study later. Not surprisingly, humanities majors en-
ter a wide variety of …elds, suggesting that majoring in the humanities
is unlikely to be an investment in a particular career. Interestingly, arts
majors are not very likely to take arts jobs after college. In fact, while
arts majors go into arts jobs slightly more frequently than humanities
majors, the employment patterns of these two majors are quite similar.
This …nding suggests that the choice to major in art, like the humani-
ties, is not undertaken as an investment in preparation for a particular
While Table 5 documents a correlation between the jobs students
take and their major, this does not necessarily mean that their major
and job are related. For example, a …nance major who takes a job in
marketing has both a job and a major in business, despite the fact that
he may not have received any training in marketing.
problematic, we suspect that many jobs held by recent graduates are
entry-level positions and are thus classi…ed as clerical occupations even
though they may be related to another occupation.
be in a wide variety of …elds and it is di¢cult to determine how closely
related they are to the students’ majors.
examine the graduates’ self-reported relationship between their major
and their occupation. The B&B asks students to characterize the rela-
tionship between their degree and their occupation as “closely related”,
“somewhat related”, or “not related.” The results, by major, are shown
in Table 6. Consistent with the results in Table 5, humanities and arts
These jobs could
To address this concern, we
majors are most likely to report no relationship between their jobs and
their majors. Computer, engineering, business, health, and education
majors are the least likely to report no relationship between their oc-
cupation and their major.Taking both sets of evidence together, we
conclude that business, engineering, health care, and education majors
are more closely linked to particular careers. Arts and humanities ma-
jors do not seem closely linked to particular careers.
5.2 NPSAS Data
Now that we have shown how the choice of a college major can re‡ect a
particular investment, we analyze the relationship between wealth and
college major choice. Although our theory concerns the marginal e¤ect
of wealth on one individual’s career decision, our use of cross-sectional
data requires comparison of decisions made by di¤erent individuals.
Consequently, in order interpret our estimates as the e¤ect of additional
wealth on a single individual’s choice, it will be important to control for
personal attributes that may be correlated with both career choice and
wealth. We use the NPSAS, which compiles information on student loan
applicants at various educational institutions including public, private,
non-pro…t, for-pro…t, two-year and four-year institutions. Since the sur-
vey was designed to focus on …nancial aid considerations, it has detailed
information on scholarships, loans and income, as well as some data on
family wealth. Other background data were also collected on scholastic
performance, student characteristics and parent characteristics.
Our sample contains three cohorts of undergraduate students from
the academic years 1986-7, 1992-3 and 1995-6.15In contrast to our focus
on undergraduates, it might be natural to consider the choices made in
graduate school as a better indication of a future career plans. However,
we exclude graduate students because we are concerned that their re-
ported wealth or income are endogenous. Many graduate students are
likely to have worked in their respective …elds before entering graduate
school. As such, their income and wealth may re‡ect the career they
have chosen and their success in this chosen …eld.
not be a problem if we used data on parental income and wealth, this
information is not available for students who are independent from their
parents. Since our ultimate goal is to estimate the e¤ect of income on
career choice, we choose to focus on undergraduates to avoid this endo-
geneity problem. Furthermore, we want to rule out credit constraints
as a reason why wealth and career choice might be linked.
may be harder to borrow in some graduate schools than others, …nancial
While this would
15Since we use only data on undergraduate students, we implicitly take the decision
to attend college and the amount of education chosen as given.
aid within an undergraduate institution should be the same regardless
of major. In order to increase the likelihood that an undergraduate’s
college major represents a meaningful choice, we limit our sample to
students who are either juniors or seniors at a four-year institution, and
students in their second year of a two-year program. In order to con-
trol for ability, we limit the sample to schools that require applicants
to report standardized test scores.
groups of majors corresponding to di¤erent occupations.
the following major categories: humanities, arts/entertainment, physical
science, computers, engineering, education, business, and health.
Because the NPSAS is based on federal …nancial aid applications,
the data on income is quite complete and we believe it to be fairly
reliable. The NPSAS also asks for information on several types of
wealth including savings and home equity, but this data is missing for
…fty percent of the sample and we are more concerned about the accuracy
of this information. Our theory is about the e¤ect of total wealth on
career choice. However, one year of income or current reported …nancial
wealth may be imperfect proxies for total wealth. Therefore, we create
a measure of total lifetime wealth that incorporates information about
both …nancial wealth and the net present value of wages.
observations where wealth data is missing, we use income and parental
occupation to predict …nancial wealth.
constant and continued forever, the net present value of this stream of
income would be annual income divided by the discount rate. Making
this simplifying assumption and using a discount rate of 0.1 implies that
the net present value of wages is ten times current annual income. Then,
we de…ne total lifetime wealth as the sum of …nancial wealth16and the
net present value of wages. For both income and wealth measures, we
use parents’ information if the student is a dependent and the student’s
own information if he or she is not a dependent.
The distribution of majors in our NPSAS sample is shown in Table 7.
The table shows that humanities, physical science, art/entertainment,
and business majors have higher family incomes than other students.
Since di¤erences in income and background are correlated, income vari-
ation across college majors may re‡ect di¤erences in background and not
the marginal impact of wealth on career choice. For example, a student
with parents in white-collar occupations and a family income of $75,000
is likely to be considering a di¤erent set of careers than a student from a
blue-collar background whose total family income is only $30,000. Al-
though some di¤erences in student choice may be due to wealth, many
We categorize these students into
If current annual income were
16We use actual …nancial wealth when reported and predicted …nancial wealth
when …nancial wealth is missing.
other factors such as race, quality of prior education, family expecta-
tions, and type of school may also play a signi…cant role.
of these factors, we include measures of race, sex and other observable
student, parent, and school characteristics in all regressions.
School quality and student ability are two important factors that
are likely correlated with both income and college major choice. As a
measure of ability, we show students’ SAT scores in Table 7.17
dents studying science and engineering have higher scores, while the
scores of education majors are relatively low. We measure the quality
of a student’s school with a rating generated by Barron’s Guide. This
rating, which goes from 1 to 9, is meant to re‡ect school quality and
Schools of higher quality have a lower score, so the table
shows that people studying engineering and science tend to attend bet-
ter schools. Since school quality, student ability and other observable
student attributes are clearly correlated with major choice and income,
we control for these variables in the regressions that follow.
5.3 Career Choice Results
We use a multinomial logit model to examine the impact of wealth on
college major choice. In this framework, the utility that student i
receives from choosing major c is a random function of his characteristics:
Uic= ?0xic+ "ic:
Students choose a major from the set ? if they prefer it to all others. As-
suming that errors are i.i.d. with Weibull distributions, the probability
that the student will choose career c is:
Pr(c?= c) =
Using maximum likelihood, we …nd the^?s that best …t the data on
student attributes and career choices. Since each student must pick one
17A student’s raw SAT score, the sum of his math and verbal scores, is translated
into a percentile. If the student took the ACT but not the SAT, we translate
the ACT score into a comparable SAT score using a mapping available from ACT.
For students whose test scores are missing but who attend a school that requires a
standardized test, we use the average reported score of that school.
whom we use this imputed test score comprise 52% of our sample. Since the same
score is assigned to all students in a school regardless of major, this imputation has
the e¤ect of narrowing the distribution of scores across majors. It does not, however,
change the ranking of the average test scores of the majors. The results are similar
when the sample is restricted to only students who report actual test scores.
18For the 16% of students at institutions not selective enough to be rated by
Barron’s, we assign a rating of 10. These schools are mostly community colleges
and vocational or technical institutes.
of the career options, the probabilities will sum to one. This restriction
requires us to impose a normalization, a “base” choice c0for which ? is
set to zero. We choose the education major as our base choice. In this
setting, the coe¢cients can be best understood in terms of their impact
on odds ratios:
c0 re‡ects the impact of an incremental change in the independent
variable on the log odds ratio, the log of the probability of choosing c0
As mentioned above, in order to estimate the marginal impact of
total lifetime wealth on career choice we want to compare students of
similar backgrounds. To control for di¤erences in background, we use
information about gender, race, parent’s education, school quality, and
test scores. We control for parents’ education using a dummy variable if
the highest education attained by either parent is high school, a dummy
variable if either parent has a college education, and a dummy variable
if either parent has an advanced degree. To control for type of school,
we try two di¤erent strategies. First, we include the Barron’s rating
in our regression.As an alternative, we also include institution …xed-
e¤ects, which allow us to identify the coe¢cients using only within-
school variations in wealth. The advantage of controlling for school
quality is that students with similar backgrounds are likely to attend
similar types of institutions. A disadvantage, however, is that income
may have an impact on major choice through choice of school.
possible that giving a student more wealth would lead him to attend
a di¤erent institution that o¤ers di¤erent majors.
channel through which wealth impacts major choice in a regression with
The …rst column of Table 8 shows the estimated coe¢cients on total
lifetime wealth for the sub-sample of students who are dependents at
four-year colleges and are under age 25. About half of the students in the
sample fall into this group. Individuals in this sub-sample should come
from more similar backgrounds and be facing more similar choices than
two students picked randomly from the entire sample.
the income and wealth of these students are less likely to be the result
of previous career decisions. In this speci…cation, we control for school
characteristics using Barron’s codes and dummy variables for institution
attributes. The second column of Table 8 uses institution …xed-e¤ects
to examine variation in major choice within a school.19
We will miss this
Both sets of
19To avoid small-sample bias and reduce computation time, we restrict the sample
to institutions with enough students to identify meaningful coe¢cients. This restric-
results indicate that richer students choose business majors, while all
other choices are insigni…cantly di¤erent from education. The coe¢cient
on business is approximately 0.2. This magnitude indicates that a 10%
increase in total lifetime wealth leads to a 2% increase in the odds ratio,
the probability of majoring in business relative to the probability of
majoring in education.
Another interesting result in this table is that once we control for
student characteristics, increasing wealth does not signi…cantly increase
the probability of studying arts and entertainment. To the degree that
majoring in art leads to a career in art and artistic careers are relatively
risky, our theory predicts that students majoring in art should be richer.
In addition, studying artistic subjects is often considered to be more
pleasant than learning the skills taught in other “more useful” …elds, so
we also might have expected to see richer students studying art as a form
of consumption. One step towards resolving this puzzle can be found
in Section 5.1, where we found that the link between arts majors and
arts careers is very weak. The career patterns of art majors resemble
those of humanities majors and do not show a strong leaning towards
arts careers. Therefore, while it is puzzling that arts majors are not
chosen by richer students due to a labor-leisure trade-o¤, this …nding
does not seem to be problematic for our theory about risk and career
In addition to the factors mentioned above, a parent’s occupation
may also in‡uence a student’s college major.
result from students following in their parents’ footsteps and choosing
to study something related to a parent’s occupation.
be an indirect relationship if parent’s occupation is correlated with the
student’s socioeconomic background. Since parent’s occupation is also
correlated with wealth, omitting this factor may potentially bias our
coe¢cient estimates. To address this concern, we look at the sub-
sample of students for which the NPSAS reports parents’ occupations20
and add a dummy variable indicating whether the major chosen by the
This correlation may
There may also
tion limits the sample to schools with at least 3 students majoring in education and
at least 15 students overall. Including smaller schools would dramatically increase
the amount of time needed to run the regression without adding power to the esti-
mation. Also, to reduce computing time, we exclude humanities majors from the
20Limiting the sample to students who provide data on parent’s occupation re-
duces the sample size by approximately one quarter. First, we estimate the original
regression restricting the sample to students with non-missing values for a parent’s
occupation. The coe¢cients on total lifetime wealth are similar to those for the
whole sample, so we conclude that the results are not being driven by changes in the
student is similar to a parent’s occupation.21
dummy variables are of the expected sign and signi…cantly di¤erent from
zero. The coe¢cients on wealth are reported in column 3, and show
a similar pattern to the previous results.
a parent’s occupation will in‡uence his or her child’s choice of career
only if the parent has been successful.
a measure of success, this hypothesis implies that interactions of the
parent occupation dummy variables with wealth should impact college
major choice. We estimate the model including interactions of wealth
and parent occupation, but we …nd these interactions to be insigni…cant
while the wealth coe¢cients remain unchanged.
Finally, column 4 reports estimated coe¢cients the entire NPSAS
sample. This includes many non-traditional students such as older
students, students at two-year institutions, and students who are not
dependents. In this speci…cation, we control for age, dependency sta-
tus, marital status, and two- versus four-year institution status.
coe¢cient on wealth for business remains approximately 0.2. Interest-
ingly, the coe¢cients are somewhat higher than before for computer and
health care majors. These results show that non-traditional students
studying these …elds tend to have high incomes prior to college.
may re‡ect the fact that computer and health care jobs, the kinds of
jobs held by computer and health care majors before college, tend to be
high paying. This hypothesis is consistent with Table 2, which shows
that for college graduates, health care and computer jobs are relatively
lucrative. This problem demonstrates the endogeneity of a student’s
wealth when the student has worked prior to making a human capital
In summary, we …nd that increasing wealth raises the likelihood of
studying business relative to other …elds.
The coe¢cients on these
A related concern is that
Using total lifetime wealth as
5.4Linking Risk and Career Choice
In the preceding sections, we have investigated separately the labor-
income risk of di¤erent careers and the relationship between wealth and
college major choice. In this section, we combine these results to show
the link between risk and career choice.
Figure 1 plots the relationship between wealth and risk for di¤erent
careers. We associate each career in the PSID with the major from
the NPSAS that we think is most appropriate.
coe¢cient on log lifetime wealth from the regression in column 1 of Table
The x-axis shows the
21Since the regression results are all relative to the probability of choosing edu-
cation, in equations for all majors we also include a variable that is equal to one if
either parent is a teacher.
reported in Table 8 re‡ect log odds ratios.
can be interpreted as the impact of a one percent change in wealth on the
percent change in the odds ratio. The y-axis shows the total labor income
risk from permanent shocks, which is the sum of the individual-speci…c
and career-wide variances reported in Table 4.
risks since intertemporal optimization predicts that these shocks will be
relatively unimportant. The graph shows an upward trend: careers with
more labor income risk are more likely to be chosen as an individual’s
wealth increases. This correlation is exactly what our model would
predict. However, this result is driven primarily by business, which is
both high risk and chosen by richer students.
Since the income coe¢cients may also re‡ect a variety of omitted
factors, there may be other explanations for this …nding. For example,
individuals with higher ability may choose risky careers because their
ability insulates them from some career risk.
correlated with unobserved ability, we would still see a positive correla-
tion between risk and the coe¢cients on wealth, but not for the reason
given by our model. Another possible explanation for our results is
that people derive more satisfaction from careers that happen to be
risky. Consequently, richer agents may choose these careers as a form
of consumption. However, we think it is unlikely that people consider
business to be more fun than the arts or humanities.
bility is that credit constraints make careers with low initial wages but
high wage growth relatively unappealing to poorer students.
careers have this wage pro…le, it would also generate a link between
risk and career choice. However, the wage pro…les we estimate in the
PSID for risky careers are not substantially di¤erent from safer careers.
Also, since tuition is the same for all students in the same institution,
credit constraints cannot explain why richer students are more likely to
choose business majors when we control for institution …xed-e¤ects. Yet
another possibility is that agents from wealthier families have a higher
preference for consumption relative to leisure.
enter business …elds because they have higher average wages. However,
this story would also suggest that wealthy students would be more likely
to enter technical …elds, which unconditionally have the highest wages.
This does not seem to be the case.
relationship between risk and wealth that our theory would predict, it is
di¢cult to completely rule out other explanations of the same …nding.
On the other hand, it is di¢cult to reconcile many of these alternative
stories with an informal examination of the data.
Recall from the logit formula in equation 15 that the coe¢cients
Therefore, the coe¢cients
We neglect transitory
If wealth or income is
In this case, they may
In short, while we document the
The goal of this paper is to understand the impact of risk on career
choice. Unlike traditional asset pricing models, idiosyncratic risk mat-
ters in career choice since career risk is not divisible or tradable. Con-
sequently, agents dislike risky careers.
should be more pronounced for poorer agents, for whom a given labor in-
come risk constitutes a larger fraction of wealth. Therefore, holding all
else …xed, we should expect to see richer agents entering riskier careers.
To investigate this hypothesis, we use the PSID to measure the riski-
ness of di¤erent careers. Looking at the time-series variability of wages,
we …nd that business careers are riskier than health, education, and
technical careers. Next, we use the NPSAS to examine which factors
in‡uence college major choice. We view college major choice as a sim-
ple and early way to observe career choice, and estimate the impact of
lifetime wealth on career choice. Controlling for other student charac-
teristics, we …nd that students with more family wealth are more likely
to choose business majors. Since these …elds have relatively high labor
income risk, this …nding is consistent with our theory that richer agents
will choose riskier careers.
This distaste for risky careers
A Appendix: Proof of Proposition 1
While the agent faces a variety of careers, only two, c and c0, are optimal
at wealth levels W and W0. Consequently, we need only compare these
two. The following is a proof by contradiction. We assume that career
c0is safer than c, and then show that this leads to a contradiction. If c0is
safer than c, then it will have a lower mean income, ?c0 < ?c: Otherwise,
no risk averse agent would ever prefer c to c0.
W, the agent prefers career c to career c0:
When initial wealth is
E [u(W + ?c+ ~ "c)] ? E [u(W + ?c0 + ~ "c0)]:
There is an equalizing wage di¤erential, D(W), that is the maximum
the agent is willing to pay to undertake career c instead of career c0.
E [u(W ? D(W) + ?c+ ~ "c)] ? E [u(W + ?c0 + ~ "c0)]:
D(W) ? 0: To …nd D0(W), we di¤erentiate 18 with respect to W and
solve for D0:
D0= 1 ?
E [u0(W ? D + ?c+ ~ "c)]
To determine the sign of D0, we must determine the relationship between
the denominator and numerator in equation 19.
function v ? ?u0.
satis…es v0> 0, v00< 0. Since u satis…es equation 3, the coe¢cient of
absolute risk aversion is higher everywhere for v than for u :
E [u0(W + ?c0 + ~ "c0)]
De…ne a new utility
Since u is a DARA function, v is continuous and
Therefore, an agent with utility function v requires a higher compensat-
ing wage di¤erential to undertake risky career c.
E [u(W ? D + ?c+ ~ "c)] = E [u(W + ?c0 + ~ "c0)];
E [v (W ? Dv+ ?c+ ~ "c)] = E [v (W + ?c0 + ~ "c0)];
Plugging equation 22 into equation 21 yields:
E [v (W ? D + ?c+ ~ "c)] > E [v (W + ?c0 + ~ "c0)]:
Plugging equation 23 into equation 19 shows that:
D0= 1 ?
E [u0(W + ?c0 + ~ "c0)]
E [u0(W ? D + ?c+ ~ "c)]> 0:
Since D(W) ? 0 and D0> 0 for all W, D(W0) > 0.
career c must be preferred to c0when wealth is W0.
our original assumption that c0was preferred to c when wealth was W0.
As a result,
B Appendix: Numerical Calibration of DARA prob-
We assume that labor income follows:
where the lognormal shocks, " are identically and independently dis-
tributed with mean, ?", and standard deviation, ?".
numerical exercise, we use quarterly binomial shocks to approximate an-
nual lognormal shocks. We do not allow agents to buy risky assets; the
agents’ only decision concerns how much to consume. We assume that
an agent in career c has power utility over lifetime consumption:
Wt+1= (1 + r)(Wt? Ct) + Yt+1
We assume that the agent makes a decision about how much to consume
four times per year. If the agent consumes and works for 40 years (from
25 to 65), then the agent makes a consumption decision in each of the
160 periods. The utility at the end of life is trivially:
To speed up our
U (Wt;Yt;t) = Et
1 ? ?
U (WT;YT;T) =W1??
1 ? ?:
We solve this problem through backward induction, since we know that:
To speed up our calculations, we transform the problem to reduce the
number of state variables from three (W, Y, t) to two (Y/W, t). De…ning:
U (Wt;Yt;t) = max
1 ? ?+ ??tEt[U (Wt+1;Yt+1;t + 1)]
Jt= (1 ? ?)W??1
the problem becomes:
Wt+1;t + 1
WT;T = 1
We can solve this problem numerically using backward induction on a
grid of possible values of the state variable, Yt=Wt. We set a grid with
1000 values of the state variable from zero to one. Since shocks will lead
the state variable to take on values in between the points on the grid,
we use a linear interpolation algorithm to estimate the value of these
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Career Choice and Initial Wealth Calibration
Of Two Agents in Two Careers
Parameters: γ=5 for both agents, δ=0.9 for both agents, r=0.05, σ=0.1 or 0.2 for the low and high risk careers respectively,
µ=0 for both careers. All parameters are expressed in annual terms, but the model is generated using quarterly shocks.
Both agents live for 40 years, T=40 years*4 periods/year=160 periods. The rich agent has an initial wealth of $100,000;
the poor agent has an initial wealth of $10. The safer career, with σ=0.1, has an initial quarterly salary, Y=$5,000 ($20,000
annualized). The riskier career, with σ=0.2, has an initial quarterly salary, Y=$7,500 ($30,000 annualized). The number in
each quadrant represents the certainty equivalent of the agent’s labor income, how much money the agent would require to
forego that career and receive no labor income.
Distribution of Annual Salaries by College Major
1. Distribution of residuals from a regression of annual salary on SAT scores, sex, race, age at graduation, a private-school dummy,
and a dummy for schools granting advanced degrees.
Career Group Summary Statistics
Median # career
switches / median
# years in sample1
1 / 17
1 / 14
1 / 11
1 / 10
2 / 10
1 / 11
2 / 11
1 / 10
2 / 13
Number of obs.
in final sample
1. The first number in column 6 is the median number of career switches for an individual during their time in the sample. The
second number is the median number of years an individual appears in the sample.
2. Includes individuals of all education levels.
3. Includes all individuals with a college degree or greater who report being self-employed. These individuals are also included in other career categories.
All dollar values are stated in inflation-adjusted 1996 dollars.
Estimated Variances of Shocks to Wages
Note. Numbers in parentheses are standard deviations calculated by Monte Carlo simulation. See Section 4 for
details. Includes data with between 1 and 5 years between observations, estimating variances for each skip length
and calculating a weighted average.
1. Includes individuals of all education levels.
2. Includes individuals in any college-educated occupation.
Percentage of Graduates in Each Major
Taking a Given Job After Graduation
Source: Baccalaureate and Beyond Longitudinal Study. Each row represents a college major. Majors are grouped based on the Baccalaureate and Beyond major categories. Each column
represents a type of job held one year after graduation. These jobs are grouped based on 2-digit SIC codes. The column reports the percentage of graduates from a given major who
entered each type of job. Cells are in bold when the major and job closely correspond.
Arts Sciences Computers Engineering Education Business Health Clerical Sales Other Unemployed Not in Labor Force Total % Total #
25.19% 6.23% 12.57%
25.11% 5.45% 21.90%
18.72% 5.66% 10.82% 100.00%
453 1193 875 8089
Graduate’s Self-Reported Link Between College Major
and First Job After Graduation
Source: Baccalaureate and Beyond Longitudinal Study. Each row represents
a college major. Majors are grouped based on the Baccalaureate and Beyond
major . Each column represents the link that a recent graduate reports
between their major and their first job after graduation. Each cell refers to the
percentage of graduates in a given major who identify a given amount of
connection between their major and work.
Distribution of College Majors in the NPSAS
Data is from the NPSAS. Each row refers to a category of major as grouped in the NPSAS. Income is defined as parent's income if
the student is a dependent and own income if he files his taxes as an independent. Lifetime wealth = wealth+10*annual income. The
Barron’s rating takes as a student’s rating the rating of their school, and averages over students. Schools without a Barron’s rating
are given a rating of 10. Lower numbers indicate more selective schools. Test scores are the average percentile of the student’s
ACT or SAT score. The score is reported as the student’s school’s average score when the student’s score is missing.
Coefficient on ln(lifetime wealth) from Multinomial Logit Regressions
Arts/entertainment - .086
Control for institution
Control for SAT score?
Only dependents under 25?
Control for parent occupation?
Number of observations
Note. Standard errors in parentheses. Lifetime wealth = wealth+10*income. See text for details. All
regressions include dummy variables for race, sex, age, and parents’ education. All coefficients represent
the impact of a change in log wealth on the log odds ratio of choosing a given major over education.
Humanities are excluded from the fixed-effects regression to save processing time. Fixed effects
regression excludes all schools with fewer than 15 students in the sample and fewer than 3 education
majors in the sample.
Estimated variance of
permanent shock to labor wealth
Percent change in odds ratio given a 1% increase in wealth
0 .05.1 .15.2
The x-axis shows the coefficients on ln(lifetime wealth) from column 1 of Table 8, the impact of a change in log income on the log
odds ratio. Since the base choice in each regression is the education major, these results indicate how the likelihood of choosing a
given major over education changes with wealth. See Section 5.4 for details.