ps2sol - Department of Economics University of California...

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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 non-trivial 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 borrowing-constrained 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 lump-sum as a self-control 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 self-control 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 short-term, high-interest 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 interest) and wait to receive the EITC payment (on which she earns no interest), when she could just opt for the monthly payments and pay off the debt as she goes along. We’ve already established in part
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This homework help was uploaded on 04/20/2008 for the course ECON 119 taught by Professor K during the Spring '08 term at University of California, Berkeley.

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ps2sol - Department of Economics University of California...

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