Estimating the Effect of Unearned Income on
Labor Earnings, Savings, and Consumption:
Evidence from a Survey of Lottery Players
Written By: Guido W. Imbens, Donald B.
Rubin, and Bruce I. Sacerdote
Presented By: Sara Walcott
The Current Study
Original survey of lottery players in
Massachusetts in the mid-1980s
 Analyze the effects of lottery prizes on
earnings, consumption, and savings
 Critical Assumption: Among the people
who win the lottery, the amount that a
person wins is randomly assigned

The Main Issue: Income Effects

It is extremely important for welfare policy
makers to understand the effects of income on
economic behavior, particularly upon labor
supply.

Would the receipt of welfare payments
(additional unearned income) to certain groups
of individuals cause them to work less or, in
some cases, stop working completely?
Income Effect Estimation Issues

Estimating the effects of unearned income is
difficult because instances of randomly
assigned and exogenous changes in
meaningful amounts of income are quite rare
and hard to identify.

Researchers often end up assuming either
spousal income or property income is
exogenous and try to use that to estimate the
effects of unearned income - obviously a
problematic assumption.
Literature on Income Effects

Model A: Use data from large, representative
surveys




i.e. the Panel Study of Income Dynamics (PSID), the
National Longitudinal Survey (NLS), or the Current
Population Survey (CPS)
Run into problems with finding exogenous
measurements of unearned income in data
Often must use capital income or spousal income as
previously mentioned
See John Pencavel (1986), Richard Blundell and
Thomas MaCurdy (2000) and Mark Killingsworth and
James Heckman (1986)
Literature Continued…

Model B: Analyze experimental data with clearly
exogenous sources of unearned income


1970s Negative Income Tax experiments - selected
population received randomly assigned tax
schedules
Limitations due to the duration of the supplement (35 years), the modest size of the amounts of income
assigned, and problems with attrition in the sample
over time.
Literature Continued…


Model C: “Natural experiments” where large
amounts of money are allocated without regard
for preferences and other determinants of
economic behavior
Examples:



Mordechai Kreinin (1961) and Michael Landsberger
(1963) - One-time war reparations payments to
Israeli citizens
Ronald Bodkin (1959) - One-time payments from US
government to selected service men post-WWII
Douglas Holtz-Eakin et al. (1993) - Inheritances and
their effect on employment
Most Similar Previous Study

H. Roy Kaplan (1985) analyzed a survey
of lottery winners, much like the authors
of this study

Shortcomings of Kaplan (1985): The data
collected only reflected changes in economic
behavior immediately prior to and
immediately after the subjects won the lottery
and there were only limited controls
introduced.
How This Study Addresses the
Issues in the Previous Studies


The randomization of the lottery provides an
exogenous source of unearned income, which
is missing in the Model A literature and weaker
in much of the Model C literature
The authors have six years of accurate postlottery earnings data from the Social Security
Administration, and the winners are on average
10 years into their 20 years of payments. This
addresses the time constraint issues of the
Model B studies and the Kaplan (1985) lottery
study.
The Data

Two Samples - “Winners” and “Non-Winners”

Winners population: People playing the Mass.
Megabucks lottery in 1984 through 1988 and winning
a major prize that is paid out in yearly installments
over 20 years
• Total prizes in this sample range from $22,000 to
$9,696,000 with a sample mean of $1,104,000 and a
sample median of $635,000.

Non-Winners population: Mass. Megabucks lottery
season ticket holders between 1984 and 1988 who
have won at least one small, one-time prize ranging
from $100 to $5,000.
Data Continued…

The survey questionnaire included three sets of
questions
Outcomes at the time of the survey
 Economic behavior and background characteristics
at the time of winning
 Earnings - the release of Social Security earnings
records for at least six years preceeding and six
years following the time of winning
Authors analyzed the data of individuals who gave
complete answers to questions relating to certain prelottery conditions and who authorized their earnings to
be released. The sample consists of 259 non-winners
and 237 winners.


Summary Statistics
Summary Stats Continued…
Specifications of Analysis

Given a population of individuals with
Stone-Geary preferences who are
maximizing utility over consumption and
leisure, subject to an intertemporal budget
constraint…

Can write an expression for labor earnings as
a linear function of the yearly lottery prize
Specifications Continued…


The above equation REQUIRES that within the
sample, the amount of money won is
independent of all the other inputs to the
economic decision-making process (i.e. wages,
other unearned income, life span, and lifetime
discounted discretionary income without the
lottery winnings.
If this is true, then the error term is uncorrelated
with the independent variable, and a leastsquares estimator of the coefficient will be
unbiased.
Specifications Continued…

The authors also estimate regression
functions with additional covariates such
as…

As long as the added covariates are
independent of the given lottery prize, they
can be included without introducing a bias
into the equation, and their inclusion may
correct some of the non-response bias.
Results: Coefficient Estimates
Notes on the Previous Table
For Average Post-Lottery Earnings…
 In specifications I-IV, the estimates do not
change very much, although they do become
more precise.
 In specification V, it is shown that the skewed
distribution of prizes means that the few very
large observations disproportionately affect the
linear regression estimates.
 Note that the winners only specification VI
results are similar to those in I-IV and results
from the specifications that exclude the big
winners (VII and VIII) are closer to those in V.
Interactions With MPE Results
Notes on the Previous Table



Estimate of MPE of .085 for those with zero
earnings in the year prior to winning the lottery
is not significantly different from zero, but at
least suggests no evidence of negative effects
of the lottery payments on the labor supply of
low earners.
Surprising to find no significant differences
between MPE of men and women, even though
in this sample men and women have
substantially different labor market experiences.
Being close to retirement age (but not above)
seems to have an effect on the MPE
Effects on Consumption & Savings
Notes on the Previous Table



For car values, total or net, there is a small but
highly significant effect of lottery prize
After winning the lottery, people appear to be
buying more expensive houses, especially the
big winners, but they also finance them through
correspondingly larger mortgages.
The authors’ preferred estimate of the marginal
propensity to save out of unearned income is
based on the sample without non-winners and
big winners and is equal to 15.8% (5.6%).
Interactions with Savings Results
Notes on the Previous Table



Men appear to be saving more out of their
winnings than women do.
Surprising that there is no evidence to support
the idea that older people save less out of
unearned income.
The closer someone is to the end of their lottery
payments, the larger the marginal propensity to
save.

This pattern seems to be consistent with consumptions
smoothing - people make large expenditures when
they first start receiving lottery payments and then
save more as they get towards the end
The Authors’ Conclusions

Find that for annual unearned income between
zero and $100,000, the MPE out of unearned
income is around -11%.


Robust against a variety of specifications and does
not differ much between men and women; however,
the effect is stronger for those close to retirement
age
Savings rate for unearned income is estimated
at 16% and increases as a greater proportion of
the prize has been received.
Critical Comments

Greatest Issue: Although the authors present
the research as being fundamental to
answering policy questions related to the effect
of unearned income on labor supply, they never
return to the discussion after presenting their
data and results.


Make no efforts to relate their results to policy issues
whatsoever after their introduction
The only part of the paper that at all ties back to the
policy issue is one sentence that states that they
found no evidence of negative effects of the lottery
payments on the labor supply of low earners.
Critical Comments Continued…

The sample is significantly different from
the CPS and may not be representative of
the population policy makers are
concerned with.
Critical Comments Continued…

The authors do not actually measure hours of
labor and measurement earnings may not
necessarily accurately reflect labor market
participation.


No way to know whether changes in earnings are
due to changes in number of hours worked or
changes in wage or some combination of the two.
Earnings may not be able to really address the
question of how unearned income affects labor
market participation as it would relate to welfare
policy issues and whether welfare payments
discourage workforce participation.
Final Comments

Although there is no direct evidence concerning the
difference in responses to lottery winnings versus other
sources of unearned income (such as welfare), lottery
winnings do provide the exogenous source of unearned
income that researchers need in order to estimate the
effects of unearned income on labor.

However, future studies need to be able to measure
labor force participation directly and need to be focused
on relating their studies more closely to welfare policy
issues.