1 The impact of hyperbolic preferences on savings Jouke Thomas Houtsma 1554999
JEL classification: D91, G21
Keywords: time preference, hyperbolic discounting, saving, microcredit
Hyperbolic discount functions can constrain an agent his own future choices. This paper analyzes the impact of hyperbolic preferences on savings behavior on women who applied for a microcredit loan, using data from a survey from Professor Lensink from the University of Groningen. The sample consists of 3781 clients or former members of the TYM fund, which provides microcredit loans for women in Vietnam. The respondents answered hypothetical discount questions in order to distinguish their hyperbolic time preferences. There is no significant statistical relationship between hyperbolic preferences and lifetime savings. Moreover, there is no significant relationship between hyperbolic preferences and savings in the past six months. The results are in stark contrast with theoretical literature, which all predict a lower savings rate on agents with hyperbolic preferences.
Women with strong household decision power have significantly higher total savings.
1. Introduction
There are severe limits to what the human mind is able to do. It is does not always make rational and consistent choices. Human decision making is vastly different to the decision making of the homo economicus. The field of behavioral economics studies the anomalies that the human brain produces when facing economic decision making. The focus of this paper is on one of these irrationalities, namely preference reversal. The following example illustrates the preference reversal phenomenon.
‘When presented with the options of a receipt of $50 now or $100 in two years, a majority of decision makers prefer the immediate $50. Shifting this choice into the future, however, causes a reversal of preferences; when given the choice between $50 in four years and $100 in six years, the majority chooses $100 in the later time period.’(Ainslie, 1991)
The “majority” in this example exhibits hyperbolic preferences. The existence of hyperbolic preferences can play a major part in the decision making process, in loan repayment and savings behavior. The process could be self-defeating, where a person wants to be prudent but is unable to do exhibit prudent behavior in the present.
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Microcredit can be an effective policy tool to alleviate poverty in third World countries. The goal of most microcredit enterprises is to correct the market failure to deliver credit to the rural poor population. It allows people to attain skills to run their own businesses which in turn improve their standards of living. Small or informal businesses make up almost half of the labor force in developing countries (De Mel, McKenzie, & Woodruff, 2008). Moreover, microcredit loans are more cost effective than other poverty alleviation instruments (Khandker, 2005).
Not every microcredit institution has been successful. The biggest risk of providing any loan is the inability to repay a loan. Will the loan provide substantial income growth for the recipient, or will the loan just provide a source of income for low productivity individuals who are otherwise unable to find work? Several financial institutions had to file for bankruptcy due to customers failing to meet interest payments.
Reneging on loan repayment is not the only reason many microcredit institutions had to file for bankruptcy. In the advent of the economic crisis of 2008, microcredit institutions were unable to obtain credit on the global market. Most of the credit provision froze entirely and this severely hindered the banks in providing credit to the poorest people in the world. A microcredit institution can operate more independently if it is able to generate savings from its own clients. Furthermore, the bank will be better protected from interest volatility risk and currency risk that is associated with external financing (Atkinson, de Janvry, McIntosh, & Sadoulet, 2013).
Having hyperbolic time preferences signals an innate lack of self-control. Being constantly tempted to splurge now and save later can have a negative effect on savings. Microcredit institutions might benefit from knowing the time preferences of the individuals and providing commitment devices (Ashraf, Karlan, & Yin, 2006b) or by closer monitoring.
The impact of having hyperbolic preferences on savings has not yet been tested empirically. This paper will test whether clients of the TYM fund in Vietnam have accrued less lifetime savings than people who do not exhibit hyperbolic preferences. Additionally, it will test whether people with hyperbolic preferences have saved less in the past six months.
The paper is structured as follows. Section two will give a brief explanation of the difference between hyperbolic discounting and exponential discounting. Section three discusses the literature. Section four explains the underlying methodology and Section five describes the data. Section six shows the empirical results. Section seven concludes.
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2. The difference between hyperbolic and exponential discounting
When we talk about time preferences, we refer to one decision maker who has to choose between two points in time and two different rewards. The choice he makes is defined as the intertemporal choice. Samuelson (1937) introduces the concept of discounted utility in timed decision making in his Discounted Utility (DU) model. The DU model uses exponential discounting. In the DU model, people are considered completely rational. When comparing the value of two rewards, people want to be rewarded for being patient. When an agent compares two rewards at two different points in time, he values future payoffs less than present payoffs. The discounted amount is called the discount factor.
Two payments with different timing and equal value must obey the equation (1).
(1)
The discount factor is smaller than 1, since agents value future payoffs less than immediate ones.
Agents do not like to wait. The main difference between exponential discounting and hyperbolic discounting lies in the formulation of the discount factor. The hyperbolic discount factor is mathematically described by:
(2)
Where f(D) is the discount factor that multiplies the value of the reward. D is the delay in the reward and k is a parameter governing the degree of discounting.
In the exponential case the discount function is mathematically defined by:
(3)
f(D) is the discount factor, where k discounting degree parameter and e is the mathematical constant equal to approximately 2.71828.
Hyperbolic discount functions are characterized by a high discount rate in near future payoffs, but a relative lower discount functions in the future. Having hyperbolic preferences creates a conflict within oneself. Your current-self has a strong distaste of savings, while your future-self does prefer waiting. Graph 1 provides a useful illustration of the several discount functions. Note that the discount function declines steeply between the year 0 and the year 3 for hyperbolic discount functions, while the exponential discount declines more gradually.
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Graph 1. Source: (Liabson, 1997)
3. Literature review
The notion of hyperbolic discounting is not new. Most of the literature brings forth theoretical models. Strotz (1955) was the first one to formalize time inconsistent consumption paths when discount functions are not exponential. When perfect rational consumers make a consumption plan, they often cheat on their plans when the future becomes the present. They might decide to devise an aggressive savings plan which will start next year. When next year comes around, however, they decide they rather postpone their sacrifices for next year. The consumer will reevaluate his plan each year and will decide to save less then he originally sought out to do, resulting in under saving. Strotz (1955) coined the phrase time-inconsistency. He had two strategies to combat this time consistency, namely pre-commitment devices and strategy of consistent planning. Pre-commitment devices are external forces which punish you when you decided to deviate from not committing to your original plan. Examples include promises, fines, pension plans and physical constraints like locked savings boxes. The strategy of consistent planning is simply rejecting all saving plans where the agent knows he will cheat anyway.
Phelps and Polak (1968) adopted a macro-economic approach and predicted that democratic elected governments will adopt a national savings rate that favors the current generation and the electorate.
This savings rate can be either higher or lower depending on the preposition if the present generation can make the future generation commit to a certain savings rate or if it can successfully predict the future generation’s savings rate. In most common cases, the present bias of generations will cause national under saving.
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The papers of Strotz (1955) and Phelps and Polak (1968) theorize how present biased preferences leads to under saving. Common causes of the present time preference bias are a lack of self-control and temptation. Ainslie (1992) graphs the present biased preferences and maps the hyperbolic nature of the discount curve. He was the first to coin the phrase hyperbolic time preference in his book Piconomics (1992). Research human behavior has led psychologist, biologists and economists to conclude that a significant portion of the human race has hyperbolic time preferences (Ainslie, 1992).
Saving can really help poor people achieve greater long term wealth. However, people find it difficult to postpone immediate gratification. Rationally, they know they should save more in order to maximize their rewards. However, they have difficulties not spending their wealth to gratify their present needs (Ainslie, 1992). There are plenty of humans who persist in self-defeating behavior, while they know they should change their behavior in order to achieve results. There is an obvious split between rationality and human nature going on within agents who show this ambivalence. The discount curves of the Samuelson DU model cannot explain this ambivalence. The most logical explanation as to why organisms fail to maximize their expected rewards is that they discount the value of future rewards. The agent fails to make a stable decision between saving for later and spending now. When a choice-maker fails to make a stable decision between two familiar alternatives, he is called ambivalent.
The real life observation of this ambivalence tells us something of the shape of the discount curve. It should include two real life human traits. Firstly, there should be regular changes of preference in the absence of new information. There is no consistent preference of one choice over the other.
Secondly, there is a motivational conflict within the choice-maker. One part of the choice maker heavily prefers the present choice, while the other part, the future self, wants to save and be prudent. Part one is effectively undermining the other part of oneself. Discount curves must cross in order to produce ambivalence. They must generate curves that lie so close together that one choice shall not dominate the other. If the savings decision would be postponed due the simple fact that humans exhibit a high discount rate, it would never create the motivational conflict we see in daily life. In certain situations, a total carelessness about the future might even endanger an organism his chance of survival.
An ambivalent discount curve must differ in steepness and in shape. It has to be more concave than an exponential curve. The discount function must have steeper discount rates at small delays and it must flatten out at the tail. In conclusion, the discount function must have the shape of a hyperbola.
This is why they are called hyperbolic preferences. The steep discounting of the near future and the less discounting on the far future makes the discount rate have a hyperbolic shape. Exponential
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curves decline by a constant proportion of the remaining balance per unit of time elapsed. Unless different events are discounted at different rates, this kind of curve will never predict vacillations in their relative values.
Ainslie (1992) acknowledged that in order to escape the present bias trap, the choice-maker has to precommit himself to future behavior or use other tricks to resist temptations. He showed methods of defeating inherent present biased preferences. The first method is committing through extraphysic mechanisms. They are devices that involve arranging for either physical or social interaction upon a person’s motivational state. A classic example of an extraphysic mechanism is the Ulysses pact. Odysseus wants to hear the Siren song when they pass their island although he is fully aware that doing so will render him incapable of any rational thoughts. He put wax into the ears of his men so they would be deaf to the sirens call. Then he orders his men to tie him to the mast so he cannot jump into the sea when he would hear the Siren song (Ainslie, 1992). Modern day examples include removing temptations within range or contracts which impose fines. Physical mechanism like piggy banks or black boxes are commonly used to enforce commitment. The second form of resisting temptation is by control of attention. In this method people try to distract away from the earlier reward. It is easier to not choose the earlier rewards when you are not thinking about the two choices at all.
The third method is preparation of emotion. A person can prevent themselves from experiencing emotions that will lead to self-defeating behavior. Certain emotions are acknowledged to cause vicious circles. Once a certain emotion in underway, the threshold to engage in the self-defeating behavior is lowered. Avoiding such emotions can assure your behavior stays sound. The final method is using personal rules. This method amounts to using your willpower to resist the urges. One can map the willpower segment with hyperbolic curves if we assume that curves from multiple rewards combine in an additive fashion. Choosing rewards in aggregates rather than individually gives later rewards an advantage over smaller earlier ones. This would require a certain degree of sophistication of the borrower. He needs to be fully aware of what kind of path he will travel in the future.
Liabson (1997) labels the lack of self-control as a virtue that someone seemingly cannot get enough of. He expands the general notion of commitment by adding another commitment mechanism in his golden eggs model. A Golden egg is an investment to an illiquid asset which will provide a steady stream of benefits and is difficult to sell due to large transactional costs, fines for withdrawal, incomplete markets or informational problems. These assets provide a similarity into investing into the goose who laid the golden eggs. The asset class can be seen as an extraphysic mechanism as
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described in Piconomics (Ainslie, 1992). Prime examples of these investments are pension plans, buying a house and savings bonds. These assets provide substantial benefits. They are impossible to attain immediately without incurring a serious loss in wealth. The Liabson (1997) model shows how investing in these golden eggs in the first period will cause the agent to be liquidity constrained in future periods, which prevents the future self from cheating on his original plan. By lowering the maximum consumption that future self can make, he effectively prevents the future self from diverting from the original plan. Committing increases consumer welfare.
The only paper which provides empirical evidence on the effect of hyperbolic discounting and savings is the “Tying Odysseus To The Mast” (Ashraf et al., 2006b) . It tests the effect of a savings product, a physical black box, on savings behavior in the Philippines. They tested the presence of hyperbolic time preferences in the following manner. Respondents were asked whether they preferred 200 pesos now or 250 pesos in one month. If they did not accept the 250 pesos in one month, they were asked whether they prefer 200 pesos now or 300 pesos in one month. If they did not accept the 300 pesos, they had to fill in the number of pesos they would accept after waiting a month. Table 1 shows the tabulation of the responses to these hypothetical time preferences questions.
Table 1. Responses from hyperbolic time preference. Source: Ashraf et al. (2011)
Indifferent between 200 pesos in 6 months and x in 7 months Patient
X<250
Little impatient 250<X<300
Impatient 300<X
Patient X<250
606 (34,4%) 126 (7,2%) 73(4,1%)
Indifferent between 200 pesos now and X in one month
Little impatient 250<X<300
206(11,7%) 146 (8,3%) 59 (3,3%)
Impatient 300<X
154(8,7%) 93(5,3%) 299(17%)
Total 966 (54,8%) 365(20,7%) 431(24,5%)
The light gray boxes are respondents with hyperbolic time preferences. The dark-grey box from the bottom right corner shows a group who might have hyperbolic preferences. It depends on the
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quantities they filled in the questions of the questionnaire. The percentage of respondents with hyperbolic preference ranges between 25,7% and 42,7%. 19,8% were more patient now than they were in future payoffs, which mean that they exhibited the opposite of hyperbolic preferences.
The research yielded several important conclusions. Firstly, the researchers found an increased desire for commitment products for female respondents with hyperbolic preferences. Secondly, the implementation of the commitment product was wildly successful. A year after offering a savings constraint package, savings went up with over 81% compared to the control group. The commitment device empowered women and increased their household decision making power. This resulted in increased expenditure in education, food and durable goods. (Ashraf, Karlan, & Yin, 2006a)
In conclusion, a plethora of theoretical models exist in which hyperbolic preferences lead to under saving and suboptimal implementations of saving plans. However, the literature describes a lot of mechanisms which agents can use to resist their present-biased urges. The question is how difficult it is to overcome their own hyperbolic preferences when it comes to savings. Are savers sophisticated enough to acknowledge their tendencies to splurge in the present and use the commitment devices effectively, or is there a significant negative impact of hyperbolic time preferences on savings?
Empirically, there is only indirect proof effect of hyperbolic preferences on savings. People who exhibit hyperbolic preferences have an increased demand for commitment devices (Ashraf et al., 2006b). The literature proves the success of extraphysic commitment products. It does not prove, however, that the previously low savings rate was due to having hyperbolic preferences.
4. Data and descriptive statistics
Data is collected through an extensive questionnaire, taken by professor Lensink of the University of Groningen. The main objective of the questionnaire is to measure the impact of business development training for female clients in microfinance institutions in Vietnam. Respondents had to fill in a questionnaire at 20 November 2012 and had to fill in a follow-up questionnaire in September 2013. The data from the follow up questionnaire was unavailable to me. The initial questionnaire of 20 November 2012 provides the necessary data for this research. All respondents are clients of the TYM fund, a microfinance institution who operates in Vietnam. The mission of the TYM fund is to improve the quality of life of poor women by providing credit and savings, creating favorable conditions for their participation in socio-economic activities and enhancing their role in society. The TYM Fund was founded in 1992 by the Vietnam Women’s union in order to help implement the poverty alleviation program of the Government. As of date, it has 28000 women members in 8 North Vietnamese provinces. 4042 clients answered the questionnaire. 261 observations are ineligible for
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study due to the fact the clients not fill in the questions about time preferences properly or incompletely.
4.1 Hyperbolic preferences
The questionnaire contains a small section about intertemporal decisions. The questions were divided in two parts, each containing 3 questions. At part 1, respondents were given the following question;
“Suppose you have a chance to get a specific amount of money, would you prefer
90.000 VND now or 110.000 VND in one month? ” (question 1a)
90.000 VND is an equivalent of 3,60 euros in the currency markets. 110.000 VND equals 4,40 euro.
Table 2 shows the distribution of the respondents between the two answers.
Table 2. Frequency of answers to question 1
Decision Frequency Percent
90.000 VND now 2168 57,3%
110.000 VND later 1613 42,7%
Total 3781 100%
57,3% of the respondents were impatient and chose the 90,000 VND. 42,7% of the respondents preferred to wait one month and can thus be qualified as patient. The patient respondents did not answer any more questions in this block. If the respondent chose 90,000 VND, they were asked the following question;
“Would you prefer 90,000 VND now or 135,000 VND in one month?” (question 1b)
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Table 3 depicts the distribution of the respondents between the two answers.
Table 3. Frequencies of question 1b
Decision Frequency Percent
90.000 VND now 1553 71,6%
135.000 VND later 615 28,4%
Total 2168 100%
71,6% were still not persuaded to wait one month, even though they would be rewarded with a 50%
monthly interest rate. If the respondent chose 90.000 VND again, they were asked the final question:
“How much would we have to give you in one month for you to choose to wait?”(question 1c)
On average, respondents require 451.735 VND for waiting one month, which corresponds to a 501,9% monthly interest rate.
In the second block of time preference questions, respondents were asked similar questions as the ones described above. The following questions were asked;
“Suppose you have a chance to get a specific amount of money, would you prefer 90.000 VND in 6
months or 110.000 VND in 7 months” (question 2a)
“Would you prefer 90.000 VND in 6 months or 135.000 VND in seven months?” (question 2b)
“How much would we have to give you in one month for you to choose to wait?” (question 2c)
Note that the questions are almost completely similar, with one big exception: the time frame.
Respondents do now have to choose between waiting 6 months and waiting 7 months. Table 3 depicts the distribution of the first questions.
Table 4. Frequencies of question 2a
Decision Frequency Percent
90.000 VND in 6 months 2051 54,2%
110.000 VND in 7 months 1730 45,8%
Total 3781 100%
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There is not much change between patient and impatient respondents when comparing table 2 and table 4. The amount of patient respondents increases by 140. Table 5 shows the distribution between the two choices in the second question.
Table 5. Frequencies of question 2a
Decision Frequency Percent
90.000 VND in 6 months 1492 72,7%
135.000 VND in 7 months 559 27,3%
Total 2051 100%
When comparing table 2 and table 4, the percentage of applicants choosing to be patient is surprisingly lower in the 7 month timeframe. One of the probable conclusions is that the group who chose 135.000 VND in the 1 month time frame chose 110.000 in the 7 month time frame. The remainder is a persistent group of impatient loan applicants.
Surprisingly, the impatient group requires 568.724 VND on average in order to wait one month. This is 100.000 VND higher than in the one month timeframe and it corresponds to a 626.3% monthly interest rate.
When do these loan applicants exhibit hyperbolic preferences? They have hyperbolic preferences if we have to pay them more in the first section than in the second one. In practice this means they have hyperbolic preferences when one of the following three conditions is met. Firstly, they are impatient at question 1a, and patient at 2a. Alternatively, they are impatient at question 1a and 1b and patient at 2b. Finally, they require more money at question 1c than at question 2c. In total, 573 observations exhibit hyperbolic preferences, which correspond to 15.15% of the total population.
4.2 Savings
The clients were asked whether they had accrued savings from various sources, namely the TYM bank account, other bank accounts, cash at home, from precious metals, crops in storage and/or other sources. The reported statistics are measured in Vietnamese dông (VND). One euro is worth 25.000 VND. Additionally, they were asked what amount they deposited in the past 6 months, what
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amount they withdrew in the past 6 months and what the savings balance is as of today. I decided to add all the deposits and create new variables called total deposits, total withdrawals and total savings. Table 5 shows the summary statistics of the dependent variables. As expected, the total balances are a lot higher than the total withdrawal and deposit amount in the past six months. On average, clients deposit more funds than they withdraw.
Table 6.Summary statistics of dependent variables
Variable Mean Standard
deviation
Maximum
Total Savings 11556,94 157748,3 7547000
Total withdrawals 1276,1 25239,22 1500000
Total deposits 2088,76 22648,36 720000
4.3 Control variables
Table 7 depicts the summary statistics of the control variables. Average debt is 14695 VND, which is considerably higher than the total savings balance. Average income is 6300. Consequently, the average respondent has around 2,5 years of income in debt. Both variables have a high standard deviation. The average household bargaining score is 13,34. Women control more than half of the financial decisions in the household.
Table 7.Summary statistics of control variables
Variable Mean Standard
deviation
Minimum Maximum
Debt 14695,00 27692,00 0 352015
Household bargaining 13,34 3,48 0 20
Unemployment 1,70%
Age (Years) 43,80 10,27 20 72
Income 6301,13 3163,67 0 50000
Cognitive abilities 8,27 2,70 0 30
Health 2,07 0,87 1 4
13 5. Methodology
I will test whether present-biased humans save less by running an ordinary least squares (OLS) regression in order to measure the effects of hyperbolic preferences on total savings and on savings of the past six months. I will estimate the relationships (4) and (5) using the Stata econometric package.
(4)
is total savings, α is the constant, Dh is the hyperbolic preference dummy. The other terms are the control variables education, age, employment status dummy, household income, health status, cognitive abilities and household decision making. I expect the Dh variable to be negative, because a person with hyperbolic preferences will save less. In the same fashion, I would like to estimate total net deposits ,which is the savings of the past six months minus withdrawals of the past six months.
(5) 5.1 Hyperbolic preferences
The respondents answered questions about hypothetical rewards, in order to discover their tendency towards hyperbolic discounting. Section 5.1 explains the procedure in detail. The
hyperbolic preference variable is a dummy. If a respondent has hyperbolic preferences, it is labeled with a one. Otherwise, the variable coefficient is zero.
5.2 Control variables
The control variables were picked on the basis of literature examination and economic arguments.
They should allow a correct approximation of savings behavior.
5.2.1 Age
Increasing age both gives more stimuli and opportunity to save. The most common reasons to save is to provide for oneself during old age. The total number of lifetime savings should increase with age.
Respondents had to fill in their birth year.
14 5.2.2 Employment status
Unemployment is positively correlated with impatience (Ashraf et al., 2006b). This is explained by the sudden reduction of income when one becomes unemployed. People need time to reduce their consumption pattern when they become unemployed or in order to raise their income levels by finding a job again. The employment statistic is a dummy variable. Unemployed respondents are marked with the number 1 and employed people are marked with a zero. The variable is expected to be negative.
5.2.3 Household income
Households with more income have more resources and opportunities to save. Keynes (1936) asserted a fundamental psychological rule of any modern community that, when its real income is increased, it will not increase its consumption by an equal absolute amount," and stated somewhat less definitely that "as a rule, . . . a greater proportion of income. . . (is) saved as real income increases." Increased income should definitely yield an increase in savings as well. Even though this assertion seemed to make a lot of sense intuitively, empirical studies showed that the savings rate in the US did not increase a lot even though real incomes rose in the postwar period(Friedman, 1957).
The marginal propensity to save did not increase a lot. However, the absolute amount of savings increases when income increases.
5.2.4 Health
It is much harder to generate income when persons are ill and unable to work full time. Moreover, people with health problems will have a lower life expectancy and therefore less motivation to save.
Respondents had to rate whether they could work half a day easily. They rated it from 1(easily) to 4 (not at all). The health coefficient should have a negative impact on savings.
5.2.5 Cognitive abilities
The ability to understand and carry out tasks can be an important indicator for savings behavior. In order to persuade a person to save, he must have the sophistication to understand the choices he is able to make. Being able to learn and remember the choices can also determine the shortsightedness of the respondent. Respondents with higher cognitive ability should have higher savings.
Respondents named as many animals as they could think of in one minute. This number they name translates to a cognitive ability score.
15 5.2.6 Intrahousehold bargaining power
A lack of savings can come from disagreements about money in the household. Males often prefer to spend their funds in a different manner than women. When women gains a larger income share, she often gets more decision making power in the allocation of resources in the household. This in turn leads to increased investment in education, housing and nutrition for children. The more bargaining power the males have, the more problematic saving poses (Ashraf et al., 2006a). Respondents, all of them female, were asked the following questions:
Who makes the most decisions about asking for a loan
Who makes the most decisions about food items to purchase?
Who makes the most decisions about educational expenditures to make?
Who makes the most decisions about clothing items to purchase?
Who makes the most decisions about consumer durable items?
Who makes the most decisions about saving for business and for households?
Who makes the most decisions about expenses for home purchase, improvement or repair?
Who makes the most decisions about where to invest surplus money?
Who makes the most decisions about how to assist family members?
The respondents had to enter a 0 when the husband had control about the decision. If the couple both had some say in the matter, they had to enter a 1. Finally, when the respondents had full control about the decision, they would enter a 2. The scores add up to a decision making score variable
5.2.7 Debt
Debt has a close relationship with savings. It is often more beneficial to pay off debt, than to start saving as the interest on the savings account is lower than the interest on the debt. There are, however, sophisticated models which justify savings even though the interest rate on savings is lower than debt interest rate (Atkinson et al., 2013). Respondents had to fill in how many loans they had from various institutions. All these loans were added to a total loan amount score. The debt level should have a negative impact on savings rates, due to a reduction of available wealth caused by interest payments.
16 6. Results
In this section, the analysis of the impact of hyperbolic preferences on lifetime saving and net savings for the past 6 months is presented. The OLS regression had an issue with heteroskedasticity.
Robust standard errors were used to correct the problem. The regression outcome is shown in table 8.
Table 8.Robust standard errors. Dependent variable: Savings.
Variable Coëfficient Standard
deviation
p-value
Hyperbolic time preferences -489,00 659,33 0,46
Debt 0,00 0,01 0,88
Household bargaining 245,29 107,98 0,02
Unemployment -711.74 1555,25 0,65
Age 150,02 75,52 0,05
Income 0,36 0,11 0,001
Cognitive abilities 504,65 119,78 0,00
Health -398,74 434,50 0,36
R-squared 0,02
F-test statistic 0,00
The hyperbolic time preference coefficient is negative. The p-value is above the critical 0,1 threshold, which leads us to reject the null hypothesis that hyperbolic time preferences have an impact on lifetime savings. Having hyperbolic preferences is not a determinant on accrued lifetime wealth. This result is in contrast with most literature written on the subject.
The household bargaining score has significant positive effects of on lifetime savings. This confirms the findings of Ashraf et al. (2006a) who found similar results. When women have more decision making power, more lifetime savings will be accrued through their lifetimes. It is important that microcredit institutions like the TYM women’s fund are actively providing loans to women.
Generating a steady income by entrepreneurship will shift their bargaining power and will lead to a higher savings rate in the household. Accrued debt has no significant effect on savings, which is peculiar. Apparently, respondents map debts and savings differently. Their savings rate is the same as their peers who do not have large loans to repay, despite having lower consumable income caused by interest payments. Health has no significant effect on saving behavior. Being in poor health does
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not increase shortsightedness, nor will it increase savings. As expected, age and cognitive abilities are positively correlated to lifetime wealth. The size of the coefficient on cognitive abilities is high. Being an adept learner is very beneficial to developing prudent savings behavior. Unemployment is not an indicator of lifetime savings. Unemployment is often a temporary state, which should have more impact on temporary savings than on lifetime savings.
Table 9.Robust standard errors. Dependent variable: Net Saving (past 6 months)
Variable Coëfficient Standard deviation p-value
Hyperbolic time preferences -498,00 659,33 0,46
Debt 0,00 0,00 0,25
Household bargaining 34,24 57,39 0,55
Unemployment -654,73 1072,79 0,54
Age 87,02 75,14 0,24
Income 0,01 0,08 0,91
Cognitive abilities 26,22 85,76 0,76
Health -576,09 241,23 0,36
R2 0,00
F-test statistic 0,26
The coefficients of the net savings regression are all insignificant. Debt, household bargaining, unemployment, age, income, cognitive abilities and health are not good indicators in prediction saving behavior in the past 6 months. The p-value in the F-statistic is higher than the critical value of 0,1. Therefore, the hypothesis that all coefficients are equal to zero cannot be rejected. The regression produces noise only. Hyperbolic time preferences produce an insignificant result in this regression as well. Savings behavior is not affected by hyperbolic time preferences both in the long run and in the short run. The results contrast everything which has been written on this subject.
6. Conclusion
Using data from the borrowers of the TYM fund in Vietnam, I researched the impact of hyperbolic preferences on lifetime savings and savings from the past six months. Saving requires a delay in an immediate reward in order to obtain a greater reward, which would theoretically be very difficult for people with hyperbolic preferences. Using hypothetical questions, the survey was able to distinguish clients who showed impatience in near future tradeoff and patience in future tradeoffs. There is no
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significant relationship between the existence of hyperbolic preferences and savings behavior in both time frames. This finding is in contrast of the theoretical literature, which predicted that the presence of hyperbolic preference would provide a major hindrance to follow through on a savings plan made in the past. To this date, any empirical evidence which directly links hyperbolic time preferences and savings behavior does not exist.
The results can be explained in several ways. People who have hyperbolic preferences have the sophistication to acknowledge their flaws when it comes to discounting values in the present and have found ways commitment in order to combat. The second explanation is that hyperbolic preferences are not as big of a deal as originally thought. Motives for saving are more dominant than the immediate temptation to splurge.
Alternatively, respondents might treat hypothetical rewards differently than real money. When being posed with an immediate hypothetical reward, people start thinking about how they would spend that money. They might fantasize about fulfilling a lifelong dream or strong desire. When the respondents actually would actually receive the money, they might produce more prudent behavior.
A third explanation why the results are insignificant is can be found in the way questions on time preferences are asked. Persons might answer prefer the immediate rewards because they perceive the latter rewards as risky, even though the question itself does not mention risk. When discussing the possibility between these choices with family and friends, they would often mention the fact that the immediate reward is guaranteed, while you never know whether you will receive the latter reward. Rewards from six months in the future are often perceived to be equally risky as a reward of seven months in the future. Respondents who are defined hyperbolic in the questionnaire might not suffer from hyperbolic discounting in real life.
7.1 Discussion
The study does suffer from limitations. The findings from the net savings data are not very useful, since there was not a single variable on the regression with a significant coefficient. The total savings variable is rather low on average, which makes it difficult to measure any impact on variables.
Unfortunately, the results of the follow-up questionnaire were not available to me when the thesis was written. It would have enabled me to study the effects of hyperbolic preferences on loan repayment, and see whether the savings behavior of the respondents would change due to business training exercises that the respondents received after filling in the initial questionnaire. Business training could be a major control variable which is now omitted from the model. The definition of total savings is debatable. Perhaps I should have included the amount of housing and livestock the test subjects own. The survey does include saved harvest as savings.
19 References
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20
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Appendix
The appendix is a list of robustness checks. The stata econometrics package produces the data output.
1. Heteroskedasticity
Breusch-Pagan / Cook-Weisberg test for heteroskedasticity Ho: Constant variance
Variables: fitted values of totalsavings chi2(1) = 5492.95
Prob > chi2 = 0.0000
We reject the Ho hypothesis of homoskedasticity. The result justified an approach by using robust standard errors.
2. Omitted variable bias
Ramsey RESET test using powers of the fitted values of totalsavings Ho: model has no omitted variables
F(3, 3767) = 2.44 Prob > F = 0.0630
I fail to reject the Ho. At the 0.05 level. Therefore, the model does not need more variables.
21 3. Multicollinearity
Table 1: Value of inflation (VIF) test
Variable Value of Inflation 1/Value of Inflation
Hyperbolic time preferences 1.01 0.99
Debt 1.03 0.97
Household bargaining 1.07 0.93
Unemployment 1.05 0.95
Age 1.05 0.95
Income 1.03 0.97
Cognitive abilities 1.03 0.97
Health 1.07 0.93
Mean VIF 1.04 0.96
The variance of inflation (VIF) is higher than 0.1 and lower than 10. Therefore, there is no problem of multicollinearity.
