Behavioral economics
Mohammad Amin Zandi
Abstract
The precise measurement of individual time preferences in assessing the economic plans that individuals are involved in, in the estimation of social time preferences, in the assessment of environmental and health plans is very crucial. The purpose of this research is to estimate and also describe the ...
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The precise measurement of individual time preferences in assessing the economic plans that individuals are involved in, in the estimation of social time preferences, in the assessment of environmental and health plans is very crucial. The purpose of this research is to estimate and also describe the method of estimating individual intertemporal preferences. The sample is 70 students of Allameh Tabataba'i (A.S) and Payam Noor Universities. For this purpose, the experimental method, which allows controlling the confounding variables, is used. In order to estimate the discount function among various functions, the hyperbolic function had a better fit on the data. In this type of function, the discount does not take place at a fixed rate, but with the extension of the selection period, the discount decreases. The fitting of data using the hyperbolic function showed that this kind of discounting is consistent with past research. The average individual discount rate obtained was 0.0615 with a standard deviation of 0.796.1.IntroductionDecisions with varying consequences across different time periods are referred to as intertemporal choices. The scope of these decision types is extensive in human life, encompassing economic considerations like saving for retirement, investing in stocks, choosing between mortgage and renting, buying insurance, planning for student loan repayments, initiating a business, budgeting, planning for financial issues, buying energy-efficient equipment, purchasing a car, planning for estate, and deciding on the retirement withdrawal strategy. Moreover, decisions extend to non-economic realms, including investing in education, practicing delayed gratification in daily life, making choices regarding health and wellness, selecting a career path, deciding on healthcare options, engaging in environmental protection, and establishing education budgets for children. In essence, a myriad of intertemporal decisions shape the course of an individual’s life.In Samuelson’s framework for intertemporal choices, the total utility is determined as the weighted sum of utility across each time period. (1) The weight in each period is determined by the discount function. (2) represents the total utility from the perspective of the current period (i.e., t). T is the final period of life. signifies the instantaneous utility in the period t+k. is the discount function. k denotes the time delay from the present moment, and ρ is the instantaneous discount rate reflecting time preferences. The discount function, as incorporated in this model, takes the form of an exponential function. When computing the growth rate of the discount function, we have: (3) The growth rate of the discount function is independent of the delay in receiving goods (or rewards) postponed from the present time (i.e., k). This implies that altering the delay period for receiving delayed goods does not lead to a change in a person’s intertemporal preferences. For instance, if an individual favors receiving one apple today over receiving two apples tomorrow, this preference should extend to preferring one apple in one year over receiving two apples in one year and one day. This is the example introduced by Strotz (1955) to illustrate temporal consistency.Experimental research based on the discounted utility model has highlighted its limitations. First, extensive studies indicate that the discount rate tends to decrease as the delay in receiving the reward increases (Chapman, 1996; Heller & Pender, 1996; Redelmeier, 1993; Thaler, 1981). In other words, the growth rate of the discount function should also be contingent on the delay in receiving the goods (or reward). The second observed shortcoming in these investigations is termed inverse utility. This occurs when an individual prefers $1000 today to $1100 tomorrow but favors $1100 one year and one day later over $1000 one year later. Consequently, the behaviors noted in these studies lack time consistency. Additional research has identified instances of reverse preferences in individuals (Elster, 1979; Laibson, 1997; O'Donoghue & Rabin, 1999). The exponential discount function employed in the discounted utility model falls short in explaining such phenomena, as it conducts discounting at a fixed rate, irrespective of whether the delay in receiving the bonus increases or decreases.To address this issue, Mazur (1987) made modifications to the discount function originally proposed by Bam and Rachlin (1969) by incorporating k into the denominator. The adjustment resulted in a discount function that overcame the shortcomings of the exponential function. This hyperbolic function found extensive application in subsequent research and demonstrated a better alignment with the data acquired from experiments. The hyperbolic function is expressed as follows:(4) Here, k represents the discount rate, and D signifies the delay in receiving the reward from the present time. The discount rate in the hyperbolic discount function is given by: (5) In this rate, there is an inherent consideration for the delay in receiving goods (or rewards) from the present time. Consequently, the discount rate will undergo changes corresponding to alterations in this interval. This adjustment serves to rectify the deficiencies noted in this functional form.The findings of the meta-analysis on discount rates, encompassing both experimental and empirical methods, reveal that the variance of discount rates obtained from experimental approaches is lower than that observed in empirical methods. This discrepancy can be attributed to several factors. First, the limited availability of field data for determining time preferences contributes to the higher variance in empirical results. In addition, there is no available field data in which individuals make comparative choices. Third, the complexity arises from the numerous intervening variables influencing real-world data, making it challenging to isolate and analyze specific factors. The estimates obtained from experimental methods demonstrate greater predictability of intertemporal behaviors in the real world.Despite the significant importance of individual time preferences and the consistent data yielded by the experimental method, this approach has been underutilized for measuring individual time preferences in Iran. In this respect, the present research aimed to estimate and describe a methodology for calculating individual intertemporal preferences through the experimental method.2.Materials and MethodsThere are four experimental methods for measuring time preferences. The first method is the choice task, where subjects are prompted to select between a smaller reward in the present or near future and a larger reward in the distant future. Some studies implement this experiment using actual rewards, while others use hypothetical or non-financial rewards, such as a hypothetical job offer. The second method is known as matching tasks, in which subjects are asked to answer a question and fill in the blank. A common structure for this method is exemplified by questions like: 20,000 dollars now or … dollars one year later. Experiments use both real and hypothetical currencies. The third method is termed rating task. Here, subjects are exposed to the rewards provided at specific time intervals. They are tasked with rating the (un)attractiveness of these proposals. The fourth method is called pricing task, where subjects are requested to specify their willingness to pay for a hypothetical reward at a certain time (Feredrick et al., 2002).The present study used the method of choice task, and the task design was based on validated designs (Calluso et al., 2015a, 2015b, 2017, 2020). Each subject was exposed to a series of intertemporal choices, including receiving a fixed amount of money (14500 Tomans) immediately or a variable amount (22000, 36500, 44000, 59000, 66000, 80000, 88000 Tomans) across six time intervals (i.e., 7, 15, 30, 60, 90, and 180 days later). Consequently, the subjects were presented with 42 intertemporal choices, and each question was repeated 10 times. The subjects thus answered a total of 420 questions in a randomly distributed order. To determine the monetary values in intertemporal choices, the study converted the previously-researched valid monetary values into Iranian currency based on the purchasing power parity (PPP) index, utilizing the Central Bank data. The PPP index can be defined as the number of currency units a country needs to purchase the same quantity of goods and services in the domestic market that can be bought with US dollars.3.Results and DiscussionThe hyperbolic function, prevalent in most recent studies and previously discussed, was employed to estimate the discount rate. In this function, as the delay increases, the discount rate concurrently decreases. To obtain this rate for each tested individual, the research relied on conventional process from past research studies (Calluso et al., 2015a, 2015b, 2017, 2020; Iodice et al., 2017; Kable & Glimcher, 2007; Li et al., 2013). Concerning each delay period (7, 15, 30, 60, 90, and 180 days), a ratio of responses was obtained, where subjects expressed a preference for the future over the present, taking into account the delayed reward amounts. Subsequently, the Points of Subjective Equivalence (PSE) was calculated, representing the amount at which subjects chose an equal number of future and present options. To achieve this, the study estimated a logistic function that regressed the preference ratio of future-to-present responses on the reward amounts. Using this function, the research determined the amount equivalent to fifty percent of the frequency of the ratio of future-to-present preferences (i.e., PSE). Then the following formula was used to calculate the subjective value for each delay period: (6) The immediate reward was set at 14,500 Tomans. The subjective value was then normalized to the immediate reward. Subsequently, the discount rate for each subject was determined by fitting a hyperbolic function (Grossbard & Mazur, 1986; Laibson, 1997) to the relationship between the subjective value and the delay time in receiving the delayed reward.(7) Below is the scatter diagram depicting delays by day and the PSE for the aforementioned three subjects. Figure 1.The scatter diagram of delays by day and the PSE Source: Research resultsThe graphs illustrate that individuals with lower discount rates exhibit a lower PSE in delays, whereas those with higher discount rates demonstrate correspondingly higher PSE.Table 1 presents the results of estimating the individual discount rates for the three subjects.Table 1. Discount rate for the three subjectsR SquareSignificanceDiscount rateSubject0.8071significant0.0182patient0.7965significant0.0484average0.8028significant0.1173hastySource: Research results4.ConclusionThe estimation of the individual discount rate derived from this research confirmed the hyperbolic nature of the individual discount function, yielding a rate of 0.0615. In the evaluation of economic plans, the calculation involves determining the benefits and costs associated with the plan. A comparison of the benefits and costs is used to determine whether the plan is economical or not. Yet this proves challenging due to the presence of time preferences and the time value of money, the occurrence of benefits and costs at different points in times, and the varying weight of these factors in economic plans over time. Therefore, it seems less feasible to judge whether the plan is economical or not simply by adding benefits and costs.
