Department of Economics
University of California
Berkeley
Psychology and Economics
Spring 2007
Botond K˝oszegi
Problem Set 2 – Solutions
(please address any questions regarding the grading of this problem set and these solutions to
Matt Levy)
1.
(a) Neither of these facts are consistent with a model of exponential discounting. Choosing
to get the EITC payment as a single payment at the end of the tax year is strictly
worse from a (purely) financial standpoint than getting the payments over the course
of the year. Getting it as a single large payment is essentially like saving it in a zero
interest bearing account. One could do strictly better by taking the monthly payments
and putting them in a (positive interest bearing) bank account. At the end of the year,
one would have the EITC payment, plus a nontrivial amount of accrued interest.
The “refund anticipation” loan is also not consistent with a model of dynamic consis
tency. If the family foresaw needing the EITC payment a few weeks before their income
tax refund would arrive, they should have chosen the monthly payments. It is highly
unlikely that so many families would have unexpected shocks right at tax season, and
even less likely that EITC recipients are so borrowingconstrained that paying over 100%
interest on a $2,000 loan makes sense (remember, one has to be substantially employed
to receive the EITC).
(b) A
sophisticated
hyperbolic discounter could make these decisions.
Knowing that his
future selves have a taste for immediate gratification, such a taxpayer correctly predicts
that he would squander the small monthly payments if he chose the first option. Even
though it is financially inferior to the monthly payments, he chooses the lumpsum as
a selfcontrol device against his future selves’ impatience. When he gets the large tax
refund, he can spend the EITC payment on some larger purchase that his current self
(may) find more beneficial.
Note that choosing the lump sum payment is not consistent with a
na¨
ıve
hyperbolic
discounter. A na¨
ıf believes that he will not be impatient in the future, so a selfcontrol
device is unwarranted.
A na¨
ıf would behave much like an exponential discounter and
choose the monthly payments.
The sort of extreme impatience demonstrated by the “refund anticipation loan” is exactly
what is predicted by hyperbolic discounting. Because the future is heavily discounted
relative to the present, a shortterm, highinterest loan is appealing to someone with a
sufficiently small
β
.
(This doesn’t mean they’d take any bad loan – consider how he
might feel about a loan with a similarly high interest rate, but over a much longer time
frame)
(c) Part of the puzzle here is why someone would accrue debt (on which she has to pay
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 Spring '08
 K
 Economics, monthly payments, Refrain, Refrain Refrain

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