Unformatted text preview: HYPERBOLIC DISCOUNTING
Another example of an anomaly is the phenomenon known as hyperbolic discounting. The economic theory of inter-temporal choice forces the use of a constant market based rate of discount for all decision-making. The reasons are that: Any other choice loses money Any other choice causes regret and inconsistency in choices over time.
Professor Schulze Lecture 6 AEM 414 Economic Theory In this example the interest rate is 10%. U(N,F) = utility of N and F. So, given that she earns 10k this year and 10k next year she could borrow all of her future (F=0) income and spend 19.091k this year (N=19.091) or save all her income this year and spend 21k in the future (F). She maximizes her utility by choosing to consume 3.82k this year and spending 16.61k next year! Obviously she lives at home this year and is going away to college next year! Note, her opportunity cost of money over time is the interest rate, r. AEM 414 Professor Schulze Lecture 6 Lets look at your experiment. You were given four choices: Decision 1: Offer to sell $10 asset, payable to you on Nov. 30th for cash paid to you today_________. Decision 2: Offer to accept $10 liability due on Nov. 30th for cash paid to you today____________. Decision 3: Bid to buy $10 asset payable to you on Nov. 30th for cash paid by you today___________. Decision 4: Bid to pay off $10 liability due on Nov. 30th for cash paid by you today____________.
AEM 414 Professor Schulze Lecture 6 Formula Economic theory says that if your credit card has a 10% discount rate, that for any decision the value today of a gain or loss in two months is: ($10) e**-.10(2/12)= $9.83 AEM 414 Professor Schulze Lecture 6 Hyperbolic Discounting In contrast, the theory of Hyperbolic Discounting derived from experimentation argues that if you are buying a bond, discount rates over the near future are huge, often in the 100's of percent, and that over the longer run they become very small approaching 0%. Larger amounts are discounted less. In addition, loss aversion (framing) strongly affects inter-temporal preferences and can produce negative rates of time preference! AEM 414 Professor Schulze Lecture 6 Lets see what you did! So much for inter-temporal choice theory! People do so badly at this that it is a wonder that the economy functions at all. No wonder that credit cards are such a great money maker for banks! Mean Standard Deviation $3.47 $4.61 Interest Rate + 11% - 41% Compensation to give up a bond. Compensation to accept a future liability Payment to buy a bond Payment to eliminate a future liability
AEM 414 Decision 1 Decision 2 Decision 3 Decision 4 $9.81 $10.71 $8.43 $9.09 $5.02 $3.95 + 102% + 57% Professor Schulze Lecture 6 Question? If you could buy a bond today that would pay interest at an annual rate of 70% over the next two months, how many would buy it? (please raise your hand) Yes _____ No _____ AEM 414 Professor Schulze Lecture 6 Tests of Time Preference. Hominid ancestors faced immediate survival pressures and no banks paying interest! One of the first challenges to discounted utility theory was:
Jerry A. Hausman, 1979. "Individual Discount Rates and the Purchase and Utilization of Energy-Using Durables," Bell Journal of Economics, RAND, vol. 10(1), pages 33-54. The voluminous literature on anomalies in time preferences is surveyed in:
Shane Frederick,George Loewenstein, and Ted O'Donoghue, 2002. "Time Discounting and Time Preference: A Critical Review," Journal of Economic Literature, vol. 40, issue 2, pages 351-401 (FLO)
AEM 414 Professor Schulze Lecture 6 Temporal choice anomalies When the size of the money outcome is varied, larger outcomes are discounted less than smaller outcomes, the magnitude effect. Hyperbolic discounting implies a high discount rate over the near term followed by lower discount rates over the long term. Thus, the longer the period, the lower the discount rate observed. Many show a preference for improving sequences and wanting to get pain over with rather suffering anxiety. The sign effect implies that gains are discounted more than losses (compare Decisions 3 and 4). So the asset is discounted more than the liability. The delay/speedup asymmetry is illustrated by the following example: On average, subjects who expected a VCR in a year would pay $54 to get it today but subjects who expected it today demanded $126 to delay it a year. The preference for spread occurs when the best meal out is placed in the middle of the week if it is the only fancy meal in a week but placed first if there are two fancy meals in a week. Not irrational but a violation of the assumption utility independence over time.
Professor Schulze Lecture 6 AEM 414 Some other strange results can be seen in the following figure: AEM 414 Professor Schulze Lecture 6 What have we learned?
People have difficulty making tradeoffs. People have difficulty with probability. People have difficulty with time. People care about efficiency and equity. People reciprocate. People have difficulty if they don't have sufficient cognitive resources. All people are irrational some of the time, some people are irrational all of the time, but not all of the people are irrational all of the time. AEM 414 Professor Schulze Lecture 6 ...
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