Self-­‐Control and Awareness: Evidence from a Homeless Shelter Elif Incekara-­‐Hafalir Tepper School of Business Carnegie Mellon University Sera Linardi Graduate School of Public and International Affairs University of Pittsburgh Abstract: Resource-­‐constrained organizations that aim to help populations with self-­‐control problems face several challenges. First, though one’s awareness of his or her self-­‐control problem determines the benefit of commitment devices, measures of self-­‐control are generally silent about awareness. Second, the economics literature focuses almost exclusively on eliciting self-­‐
control through incentivized choice experiments, which may not fit the organizations’ needs for a method that is task specific, low cost, and easy to administer at a large scale. In this paper, we take the first step to fill this dual gap by investigating the potential of Ameriks et al.’s (2007) survey measure to provide information on both awareness and self-­‐control. This measure asks individuals what they consider to be their ideal action in a particular situation and their prediction of which action they will actually take. The difference between the two is expected deviation (ED). We first expand the range of empirical evidence for ED from the financially and academically very successful (Ameriks et al. 2007; Wong 2008) to the very impoverished by testing if ED predicts the savings of residents at a homeless shelter. We then provide a simple theoretical interpretation of ED survey responses, derive predictions for the correlation of ED and outcomes with and without commitment devices, and organize existing empirical evidence within this framework. 1. Introduction Recent studies document the importance of self-­‐control for outcomes ranging from financial well-­‐being and health to law obedience (Tangney et al. 2004; Meier and Sprenger 2010; Moffitt et al. 2011).1 Previous literature also shows that the implications of self-­‐control might differ substantially depending on whether or not people are aware of their self-­‐control problems (Strotz 1956; O’Donoghue and Rabin 2001). If people are aware of their self-­‐control problems, simply providing commitment devices could help them overcome these problems and achieve their goals. However, if people are largely unaware of these problems, policies providing commitment devices alone might not work since people do not realize their need for them. If these policies are supplemented with educational programs aiming to make people aware of their self-­‐control problems, then these policies are more likely to be successful (Frederick et al. 2002). 1
Meier and Sprenger (2010) find that present-­‐biased preferences correlate with credit card borrowing. Moffit et al. (2011) provide an evidence for the importance of self-­‐control for health, wealth, and public safety. Tangney et al. (2004) discuss personal and academic achievements. Imagine a social service organization that wants to investigate the value of offering a commitment device in order to help its clients. This organization is likely to weigh the information about self-­‐control and awareness provided by available elicitation methods against its limited budget, its minimal manpower, and its need to report information focused on behavior in a specific program. Despite the plethora of self-­‐control measures, this organization has limited options. First, there is only very limited research on measuring awareness (Frederick et al. 2002).2 The commonly used method of eliciting time preferences either implicitly assumes a complete lack of awareness or remains silent about awareness (Meier and Sprenger 2010; Tanaka et al. 2007; Fang and Silverman 2009; Brown et al. 2009).3 Second, the few available elicitation methods that do measure awareness (Auguenblick et al. 2013) may be prohibitively complex for these institutions. In general, although incentivized choice experiments have obvious strengths in eliciting preferences (such as incentive compatibility), in practice organizations are much more likely to adopt the survey method because of its intuitive design and ease of large-­‐scale deployment.4,5 For these reasons, we focus on the self-­‐control survey measure developed by Ameriks, Caplin, Leahy, and Tyler (2007), which we will refer to as the Expected Deviation (ED) elicitation method. The ED method is unique in that it directly asks respondents to formulate what all self-­‐
control measures are attempting to capture: the temptation to deviate from one’s ideal course of action. In the ED elicitation method, individuals are asked what they consider their ideal action in a particular situation and are then asked to predict which action they will actually take. The difference between the two is expected deviation (ED). Because of its construction, this measure is likely to be informative about self-­‐control in populations that are sophisticated about their self-­‐control problems. Empirical evidence backs this assertion: Ameriks et al. (2007) 2
Although demand for commitment devices in real market settings indicates some consumer awareness about their self-­‐control problems (Ariely and Wertenbroch 2002), this demand reflects both sophistication and self-­‐
control and is therefore not informative of the level of awareness. 3
For example, a time-­‐discounting experiment may ask subjects to choose between a smaller, sooner reward and larger, later reward for time periods both near and far in the future. The experimenter can elicit long-­‐run and short-­‐run time discounting with these types of intertemporal choice questions. If the subject prefers the larger, later reward for the far future but prefers the smaller, sooner reward for the near future, this may imply time-­‐
inconsistency but does not tell us about the subject’s awareness. 4
The issue of future payments, which is a clearly identified confound in a self-­‐control measure (Frederick et al. 2002), can be particularly difficult to overcome. For example, future payments for the homeless population can neither be delivered at a future date (since there are no reliable future address or contact information) nor delivered immediately and cashed later (money orders cannot be post-­‐dated, and since many homeless individuals do not have bank accounts, the shelter would have to cover check-­‐cashing fees). Paying out cash payments at the shelter on a future date may introduce a confound, since those who want to leave the shelter may early opt for earlier payments in order to not have to return to the shelter later to pick up the payment (Linardi and Tanaka 2013). 5
Duckworth and Kern (2011) published an extensive survey of self-­‐control measures and found “dramatically stronger evidence for convergent validity among questionnaire measures” (compared to task measures), and hence concluded that “researchers facing time and budget constraints may be advised to choose questionnaire over any single executive function or delay of gratification task measure.” Similarly, we argue that economists should continue to explore elicitation through survey methods while recognizing its limitations, if the choice, in some real-­‐world setting, may be one of surveys or no elicitation at all. We do not, however, in any way suggest that incentivized elicitation should be replaced with unincentivized methods. found that ED in luxury goods consumption is negatively correlated with liquid assets of high-­‐
net-­‐worth TIAA CREF mutual fund holders. Wong (2008) found that ED in midterm preparation dates is negatively correlated with final grades for National University of Singapore students. However, when we cannot assume that the subjects are sophisticated, ED (and other self-­‐
reports) may confound awareness and self-­‐control. Instead of seeing this feature as a disadvantage, this paper sees it as an opportunity. We will attempt to explore whether, by complementing ED with observations of actual behavior, we can learn some basic information about the self-­‐control and awareness of a population. This paper does two things. First, we test whether ED predicts savings among the working homeless. This fills an important gap in the literature. With all the empirical data on ED coming from individuals on the high end of financial and academic success, our work with the homeless population provides some bounds on the extent to which the predictive validity of this survey measure depends on the financial and academic background of the subject pool. Second, we provide an interpretation of ED that lends itself to a simple theoretical model. Using this theoretical model, we predict the relationship between ED and actual outcomes for various populations, classified in terms of self-­‐control and awareness. We then use our mapping of the mediating influence of types on the correlation between ED and outcomes to organize existing empirical results. Results from the model provide some suggestions about the limitations and possibilities of the ED survey method. We study whether ED is correlated with the amount saved by recently employed homeless individuals in a commitment savings account during their stay at a shelter in Arizona. We administer a survey consisting of several parts: (1) questions about what portion of their income they would ideally save in the upcoming month and the amount they expect to actually save; (2) questions about the cause and extent of the individuals’ homelessness; and (3) standard demographic questions. We find that ED is positively correlated with the proportion of income saved in a commitment savings account. This is surprising in light of previous studies that have found a negative correlation between ED and the outcome of interest. Our results can be explained by allowing heterogeneity in awareness of self-­‐control problems within a population to dominate heterogeneity in the self-­‐control problem itself. We then provide a theoretical interpretation of ED based on the beta delta model (Laibson 1997; O’Donoghue and Rabin 2001) and derive the correlation between ED and outcomes with and without commitment devices for various combinations of time-­‐inconsistency and self-­‐awareness. We start with the standard types: time-­‐
consistent, sophisticated, naïve, and partially naïve, and then explore further distinctions of partially naïve populations: (1) populations where differences across individuals in the population are mainly due to differences in self-­‐control problems (Partially naïve with Heterogeneity in self-­‐Control/Partial HC) and (2) populations where differences across individuals in the population are mainly due to differences in awareness of self-­‐control problems (Partially naïve with Heterogeneity in Awareness/Partial HA). We then organize existing empirical results around these theoretical predictions. Awareness in itself has important implications for public policy (Frederick et al. 2002; Ashraf et al. 2006). This study makes several contributions. First, it provides empirical evidence that in some populations, heterogeneity in awareness of a self-­‐control problem can be more dominant than heterogeneity in self-­‐control itself. We refer to this type of population as Partial HA, to distinguish it from the more commonly discussed partially naïve types who implicitly assume that the main difference is one of self-­‐control. Second, our study provides one possible theoretical interpretation of a self-­‐control survey measure that has appealing qualities for practitioners. We then show that this interpretation can explain previous empirical results, which suggests that the ED measure does behave in theoretically predictable ways across very different populations. Even though further theoretical and empirical research still needs to be done, our findings that population type mediates the relationship between expected deviation and outcomes suggests a unique way forward. An organization interested in a long-­‐term outcome can use a combination of survey responses and observations on a short-­‐term outcome to assess potential interventions to improve longer-­‐term outcomes.6 Take, for example, the setting in Wong (2008): conducting the ED survey on midterm study plans and comparing survey responses to actual midterm study dates may provide instructors with information about students’ awareness and self-­‐control that can be used to consider interventions to improve final grades. The rest of the paper will be organized as follows. In section 2, we provide the setting of the homeless shelter where our study took place (2.1), discuss our main dependent and independent variables (2.2), and test whether ED predicts savings (2.3). We find that ED is positively correlated with savings when a commitment device is offered, suggesting that the variation in ED came from variations in awareness about self-­‐control problems. In section 3, we provide a theoretical model of ED and show how the prediction organizes existing empirical studies. Section 4 concludes the paper. 2. Empirical Evidence When studying TIAA CREF mutual fund owners, Ameriks et al. (2007) assumed individuals to be highly aware of their self-­‐control problems and interpreted larger ED as indicating less self-­‐control. They found that positive ED on a consumption plan is negatively correlated with non-­‐commitment savings (liquid net worth) and uncorrelated with commitment savings (retirement savings), confirming their assumptions. Wong (2008) asked students at the National University of Singapore about their ideal and expected study plan for a microeconomics midterm, and, as did Ameriks et al. (2007), found that ED has a negative effect 6
Ly et al. (2013) emphasize the importance of identifying the factors that prevent people from achieving their long-­‐term goals, namely bottlenecks, in designing successful nudges. Similarly, one needs to identify bottlenecks to come up with effective policies. on final outcome (final grade) when no commitment devices are offered. In this paper, we investigate the predictive power of the ED measure for an entirely different population: the working homeless. We surveyed 95 homeless individuals who have recently become employed about their ideal and expected savings for the upcoming month and compared it to their actual savings within that month. 2.1 Setting We conducted our study at a large transitional homeless shelter in Arizona in conjunction with a randomized experiment on a savings competition (Linardi and Tanaka 2013, henceforth LT). The shelter covers almost all of its residents’ living expenses (such as room and board, bus passes, limited toiletries, and clothing) and also provides supportive services to help them regain the ability to sustain permanent housing. In exchange, shelter residents agree to complete programs to advance through various “levels” at the shelter. When they provide proof of employment, individuals are promoted to Level III, the highest level at the shelter before transitioning to permanent housing.7 Note, however, that residents are often employed in unstable, lower-­‐quality jobs in sales, temporary staffing, or seasonal events. Level III residents who lose their jobs or fail to earn an income are given time to obtain another job before being moved back to Level II. Upon entering Level III, individuals are expected to participate in a commitment savings program where savings cannot be withdrawn until exit from the shelter.8 Clients are required to report their financial standing, including their income, expenditure, and savings, to their case managers. Reports must be accompanied by evidence such as paystubs and ATM receipts. Since many have no bank account, the shelter provides an option to save by directly depositing cash to a shelter-­‐managed lockbox service. All Level III shelter residents from April 2009 to April 2010 were sent an invitation to participate in the study. Participation involved completing a survey questionnaire through an in-­‐person interview and permission to access their financial behavior at the shelter for the duration of the study.9 More than 90% of the residents (N = 110) agreed to participate. Eleven subjects could not provide subsequent proof of having been formally admitted to Level III and another four did not complete the ideal/expected questionnaire, resulting in 95 survey respondents.10 The data were collected in three non-­‐overlapping waves: June-­‐July 2009 (N=23), 7
This group is particularly policy relevant because the working homeless represents the most upwardly mobile segment of a population, which has been an intractable policy problem. 8
The formal requirement of the shelter is that Level III clients must save 70% of their income; this requirement is quite possible given that almost all expenses are paid for, but it is rarely followed in practice. Before the arrival of researchers to the shelter, residents were saving only 28% of their income; see LT for details. 9
A $5 fast food gift certificate was given for survey completion. 10
Neither the computer system nor the shelter management was able to indicate when these subjects were promoted to Level III. February-­‐March 2010 (N=44), and April-­‐May 2010 (N=28).11 The standard survey included questions about ideal/predicted savings, demographics, and the subject’s experience of homelessness. In the first and last waves, a more extensive survey was administered that included the subjects’ income expectations.12 Adopting Ameriks et al.’s (2007) survey question for this setting, we asked participants to state the ideal amount they would like to save and to predict the amount that they would actually save over the next four weeks. The exact statements of the questions were: “How much would you ideally like to save in the next 4 weeks?” and “How much do you think you will actually save in the next 4 weeks?” We construct our main dependent variable, Expected Deviation (ED), by subtracting predicted savings from ideal savings for each individual. After the survey, we tracked participants’ actual savings for the four weeks through their financial reports. This period coincided with LT’s randomized savings competition.13 In their analysis, LT checked closely for unintended effects of the competition, including manipulation of financial reporting and discouragement of those in the baseline group. They found that competition induced a temporary increase in savings rate without affecting behavior in any other dimension.14 Their findings, in addition to the fact that competition is widely used in other environments as a commitment device, motivated us to proceed with the assumption that the subjects in the baseline and competition group are different only in that the competition group has the additional incentive to use the commitment device.15 2.2 Summary Statistics Table 1 provides a summary statistics of the survey responses of the 95 subjects. In our sample, 16% are female, 38% are black, and 59% are single. The average age is 41.66, and participants have on average one child and have completed high school. They have been homeless for nearly a year. Of the sample, 44% are homeless for the first time in their life; 20% self-­‐reported being homeless due to incarnation and 16% due to addiction. On average, the 95 participants report that they would ideally save $776.15 in the next four weeks but would only 11
Residents interviewed in one data collection wave have left the shelter by the time residents in the next wave entered Level III. LT also collected data in fall 2009 but the ideal/expected survey was not administered then. 12
The self-­‐control scale (SCS) questionnaire was also administered to this subset of our population. See results in footnote 23. 13
After taking the survey, 70 of the subjects in our sample were randomly assigned to a competition group where they would win $100 in cash if they saved the most. The two groups are regressed separately in Appendix Table 3. 14
For example, there was no evidence of strategic behavior such as underreporting income to inflate savings rate or deferring savings from one month to another. There were also no positive or negative spillovers: competition did not change the likelihood of submitting a financial report or earning an income. 15
Brocas and Carrillo (2001) theoretically modeled the mitigating effect of competition on self-­‐control problems. Wong’s NUS students faced a competitive environment where only 10% receive an A or better. See http://blog.nus.edu.sg/provost/2012/01/20/the-­‐bell-­‐curve/comment-­‐page-­‐2/. be able to save $660.48.16 The average ED for the population is $115.66, which represents 15% of ideal savings. Table 1: Summary Statistics Variable N Mean Std. Err. age 95 41.66 1.08 female 95 0.16 0.04 single 95 0.59 0.05 children 95 0.90 0.15 education 95 12.01 0.23 black 95 0.38 0.05 first time homeless 95 0.44 0.05 months homeless 95 11.68 1.30 homeless due to incarceration 95 0.20 0.04 homeless due to drug/alc. addiction 95 0.16 0.04 days employed 95 28.67 3.39 ideal savings 95 776.15 71.11 expected savings 95 660.48 73.20 expected deviation 95 115.66 29.34 submitted financial report 95 0.76 0.04 actual income 72 289.28 42.95 actual savings 72 184.34 27.37 The general disadvantage of survey measures is that respondents may interpret the measure in ways not intended by the researcher. This issue is also present with our survey questions. We checked two alternative interpretations of the ED questions in this setting. First, while their answer to the second question (“How much will you actually save”) is reflective of their current financial standing, the first question (“How much would you ideally save”) may have cued subjects to imagine saving in an “ideal world” unbounded by reality. Using data from another set of survey questions, we find that 76% of the subjects stated ideal savings and predicted savings that are well within their expected income.17 Ideal savings, predicted savings, and expected deviation represent on average 65% (SE: 0.039), 58% (SE: 0.046), and 8% (SE: 0.041) of expected income, respectively. This indicates that the majority of subjects interpreted the savings questions with a particular expected income in mind. Second, shelter residents know that being at Level III entails participation in a commitment savings account. This 16
Subjects appeared highly motivated to save: 88% of subjects indicated that in order to overcome homelessness they would need to increase savings. 17
Monthly income information was collected in a separate survey that included participants in the first and last wave of data collection (N=49). The question simply stated “Income: ________/ month.” On average, stated income was $1016.23 (SE: 86.63) per month. However, note that the length of the study coincided with the height of the economic crisis; compounded with the fact that most Level III residents were relatively new at their jobs and held jobs with sporadic work hours and commissions based pay, these responses are closer to representing subjects’ income expectation than actual income. introduces the possibility that instead of interpreting the questions as one about their ideal and expected savings more generally, subjects were responding to: “Given that there is a commitment device, how much would you ideally save?” and “Given that there is a commitment device, how much will you actually save?” On this interpretation, ideal savings would be identical to predicted savings, resulting in ED of 0. However, only 34% of subjects reported an ED of $0; average ED is positive and significant (Table 1), suggesting that subjects did not fully consider the effect of the commitment device in their responses. How much does subjects’ background determine their ideal and predicted savings? In Appendix Table 1 we regress ideal savings (Model 1), predicted savings (Model 2), and ED (Model 3) against demographic variables as well as the individuals’ experience of homelessness. Women state lower ideal savings and expect to save less. Interestingly, both individuals who are homeless for the first time and those who have been on the street longer state higher ideal savings and expect to save more. These differences are netted out in ED. Apart from a slight decrease in ED for older individuals, neither demographic variables nor reasons for homelessness are significant predictors of ED. We now focus on subjects’ actual actions during the four weeks after the survey. During those four weeks, 72 clients (76%) submitted financial reports with income averaging $289.28 and savings averaging $184.34, and 23 clients (24%) did not submit any financial reports. Shelter management suspects that these clients have lost their jobs and coded their income and savings as $0; however, we cannot rule out the possibility that these individuals are different in important yet unmeasured ways from those who submitted financial reports. To deal with the potential selection problem, we will use both the Heckman selection model and the OLS in our empirical analysis. 2.3 Relationship between outcome and predicted deviation In this section we investigate whether ED predicts how much an individual will actually save when a commitment device is present. The relationship that we expect to see depends on our assumptions about the population; we briefly discuss them here but will show later how they can be theoretically derived (Section 3). As a starting point, suppose we follow the (implicit) common assumption in the literature: a population can be sophisticated, naïve, or partially naïve, but within a population, awareness is relatively similar while self-­‐control varies. If subjects are fully sophisticated, those with more self-­‐control problems will report higher ED, but the actual outcome will not depend on self-­‐control due to the commitment device. If subjects are completely naïve, ED will be around zero. There will be no demand for the commitment device and outcomes will depend solely on self-­‐control. In both cases, ED will not be correlated with outcomes. On the other hand, if all subjects are partially naïve with a fixed level of awareness, they will all equally underestimate their self-­‐control problem and under-­‐use the commitment device. The outcome lies between the sophisticates and the naïves: though their awareness helps the sophisticates save more than the naïves, they are not aware enough to completely overcome their self-­‐control problem, and hence ED and outcome will be negatively correlated: those with the highest self-­‐control will report the smallest ED and save the most. In Appendix Table 2, we ran a Heckman selection model to check whether unobservables causing individuals not to submit a financial report are correlated with unobservables affecting the savings. We use the number of days the person has been in Level III as the exclusion restriction: being newly admitted to Level III may affect the likelihood that an individual will submit any financial reports due to their relative unfamiliarity with the case manager. However, the number of days an individual have been in Level III should not affect the rate at which they save. The likelihood ratio test indicates that the correlation between error terms in the selection and outcome equations is not significant for both dependent variables (chi2(1)=0.23 prob>chi2=.62), and therefore we proceed with the standard linear regression for the rest of our analysis. Table 2: Expected deviation is positively correlated with outcome (1) (2) (3) (4) (5) VARIABLES Report Income Saving Saving Saving ED $100 -­‐0.0114 -­‐2.232 8.004 9.275** 8.243* (0.0134) (15.02) (9.524) (4.223) (4.758) Income 0.569*** 0.544*** (0.0343) (0.0409) Competition 0.0735 118.1 132.2** 64.93** 61.68* (0.0880) (99.41) (63.03) (28.24) (30.12) Constant 0.310*** 481.3*** 190.1* -­‐84.00* -­‐117.12 (0.109) (160.5) (101.7) (48.05) (114.29) Demographic N N N N Y Project FE Y Y Y Y Y Observations 95 72 72 72 71 R-­‐squared 0.308 0.111 0.120 0.830 0.835 Standard errors in parentheses *** p<0.01, ** p<0.05, * p<0.1 Table 2 summarizes our regression results. In all models we include controls for data collection waves (project FE) and include a dummy variable to control for the effect of the savings competition. We first check if ED affects subjects’ likelihood to submit financial reports or income earned. The insignificant coefficients on ED in both Model (1) and Model (2) suggest that it does not. We then turn to our main variable of interest, the amount saved in the four weeks following the survey. ED has no effect on savings when we regress savings against ED without controlling for income, but it becomes highly significant when income controls are included. Income is the main predictor of savings: note how R2 jumped from 0.12 from 0.83 from Model (3) to (4). The coefficient on competition is always positive and often significant, confirming LT’s finding that competition has a positive effect on savings rate.18 Subjects save 56 cents out of every $1 earned; in addition to this, for every $100 in ED, subjects saved another $9.3. Since average ED is about $115, this translates to $10.70 in extra savings. Though it appears to be a small number, it represents a 6% increase in savings in this environment where the average savings come to about $184. Our finding that ED positively predicts the savings rate of the homeless in a shelter commitment savings program is robust when controlling for extensive demographic variables (Model 5).19 When we take all the existing empirical evidence of the ED survey measure together, we get what first seems to be a mixed bag. Ameriks et al. (2007) found that ED in luxury goods consumption is negatively correlated with liquid assets of high-­‐net-­‐worth TIAA CREF mutual fund holders; however, it is uncorrelated with assets in retirement savings. Wong (2008) found that ED in midterm preparation dates is negatively correlated with final grades for National University of Singapore students. And in this paper, we find that ED in savings is positively correlated with actual savings of the working homeless in a homeless shelter commitment savings program. This positive correlation is surprising if we think of variation in the survey responses as capturing variations in self-­‐control. However, this result is not surprising if we allow for the possibility that in some populations, heterogeneity in awareness can be more dominant than heterogeneity in self-­‐control. In the next section, we provide one theoretical interpretation of what ED is measuring, predict the relationship between ED and outcomes, and evaluate whether all these disparate results can be consistent with this interpretation. 3. Theory 3.1 Expected Deviation as a function of self-­‐control and awareness We use an individual's savings decision to illustrate our theoretical interpretation of subjects’ responses to the survey questions. To model an individual's time-­‐inconsistency and awareness, we use the β-­‐δ model (Strotz (1956), Laibson 1997). The literature on time-­‐
inconsistency divides individuals into those who are time consistent and those with self-­‐control problems. In our model, δ captures exponential discounting and β captures having a self-­‐control problem, where β=1 denotes time consistency and β<1 denotes a self-­‐control problem (time-­‐
inconsistency). 18
When Model (3) is run on the baseline (N=25) and competition group (N=70) separately, the coefficient on expected deviation is positive for both groups; as we would expect, it is statistically significant and larger for competition group (7.78 (pval=0.033) for competition and 2.53 (pval=0.70) for baseline). 19
Appendix Table 1 Model 4-­‐7 includes regressions with the same set of dependent variables as Table 2 Model 1-­‐5 with the addition of extensive demographic variables. Among those with self-­‐control problems, the literature identifies three levels of awareness: sophisticated, naïve, and partially naïve (Strotz 1956; O'Donoghue and Rabin 2001). An individual’s perception of his level of self-­‐control is denoted as β′, where 𝛽 ′ = 1 − 𝛼 1 − 𝛽 𝑤𝑖𝑡ℎ 0 ≤ 𝛼 ≤ 1 For a time-­‐inconsistent individual, 𝛼 =0 (β′=1) indicates complete naïveté (unawareness) about his self-­‐control problem, 𝛼 =1 (β′=β) denotes complete sophistication (awareness), and 0 < 𝛼 < 1 (β<β′<1) denotes partial naïveté (or partial awareness). As in standard β-­‐δ models, we look only at the cases in which 0<β≤β′≤1, which captures present bias. To focus the analysis on the effect of self-­‐control and awareness, we make the simplifying assumption that δ can be treated as a constant. We also assume that per period utility function u(.) exhibits constant absolute risk aversion (CARA).20 There are three periods in our model. At the initial period (period zero), the consumer reports his ideal savings and his expected savings. In period one, the consumer makes actual savings decisions. In period two, the consumer consumes his savings. The consumer's problem according to period-­‐zero self is: 𝐦𝐚𝐱 𝜷𝜹 𝒖 𝑰 − 𝒔 + 𝜹𝒖 𝒔 (1) The subject's ideal savings (𝑠 ∗ ) will be the solution to Eq (1): 𝑠 ∗ = 𝑎𝑟𝑔𝑚𝑎𝑥 [𝑢 𝐼 − 𝑠 + 𝛿𝑢(𝑠)] (2) When the consumer actually arrives at period one, which is the actual decision period, his maximization problem according to period-­‐one-­‐self is: max 𝑢 𝐼 − 𝑠 + 𝛽𝛿𝑢(𝑠) (3) However, the consumer may not be aware of 𝛽 and instead believes that he will discount all future periods with the discount factor β′=1 − 𝛼(1 − 𝛽). Henceforth at period zero the consumer thinks that at period one he will be solving a maximization problem of: (4) max 𝑢 𝐼 − 𝑠 + 1 − 𝛼 1 − 𝛽 𝛿𝑢(𝑠) The subject’s expected savings 𝑠 ! will therefore be the solution to Eq. (4). Note that the period-­‐zero self's prediction on how much he will save when he arrives at period one is equal to the amount he will actually end up saving (Eq. 1) only when 𝛼 =1 (when the consumer is 20
This assumption is only necessary for Lemma 3. completely aware of his self-­‐control problem). If 𝛼 <1, the consumer overpredicts how much he will end up saving. Lemma 1. Define Expected Deviation (ED) as ED ≡ s* -­‐𝑠 ! . • 𝐸𝐷 = 0 𝑖𝑓 𝛼 = 0 𝑜𝑟 𝛽 = 1 ! !"
•
< 0 𝑖𝑓 𝛼 > 0, !"
•
! !"
!"
< 0 𝑖𝑓 𝛽 < 1. Proof. See the proof in the appendix. Lemma 1 demonstrates that ED is driven by both self-­‐control and awareness. Consumers who are completely naïve and those who are fully time consistent expect to reach their ideal savings and consequently report no expected deviation. Observations of actual savings, which we will discuss below, will distinguish the two types. For a given level of awareness, partially naïve and sophisticated individuals with more self-­‐control will report predicted savings that are closer to ideal savings than those reported by individuals with less self-­‐control. On the other hand, for a given level of self-­‐control, individuals with more self-­‐
awareness will report predicted savings that are further from ideal savings than those reported by individuals with less self-­‐control. 3.2 Actual outcomes without and with commitment devices The relationship between ideal, expected, and actual behavior will depend on whether a commitment device is present. When there is no commitment device, consumers are unable to take advantage of their self-­‐awareness by making precommitments that allow them to resist foreseeable temptations. Therefore, the actual savings are driven by period-­‐one self's problem (Eq. 3) and depend on self-­‐control (β) but not awareness (α). Defining temptation savings (𝑠 ! ) as the actual savings without a commitment device, we can write: 𝑠 ! = argmax[ 𝑢 𝐼 − 𝑠 + 𝛽𝛿𝑢(𝑠)] (5) Lemma 2. With no commitment device, actual savings depend only on self-­‐control. !! !
!! !
Specifically, !" > 0 𝑎𝑛𝑑 !" = 0. Proof. See appendix. Lemma 2 demonstrates that ceteris paribus, without commitment devices, the actual savings of individuals with more self-­‐control will be larger than those with less self-­‐control. However, for a fixed level of self-­‐control, the savings of individuals with more awareness of their self-­‐control problems will be no different from the savings of individuals who are less aware about them, since they cannot make use of their awareness by making precommitments that allow them to resist foreseeable temptations. On the other hand, awareness changes the outcome when commitment devices are available. For simplicity, assume that the commitment device is perfect. The consumer's problem according to period-­‐one self would change from (2) to: max 𝑢 𝐼 − 𝑠 + 𝛽𝛿𝑢(𝑠) (6) s.t. !
∗
!
𝑠 ≥ 𝑠 + 𝑠 − 𝑠 (7) The constraint (7) says that consumers can now save at least as much as they would without the commitment device, plus the extent to which they expect to deviate from their ideal savings (ED). This ensures that with the commitment device, a fully sophisticated consumer will be able to achieve his ideal savings while a completely naïve consumer’s savings remain unchanged. Defining commitment savings (𝑠 ! ) as the solution of the above maximization problem, we get: 𝑠 ! = 𝑠 ! + 𝑠 ∗ − 𝑠 ! (8) Lemma 3. With commitment devices, actual savings depend on self-­‐control and awareness. Specifically, !! !
• !" > 0𝑖𝑓 𝛽 < 1, •
!! !
!"
> 0 𝑖𝑓 𝛼 > 0. Proof. See the proof in the appendix. Lemma 3 describes the influence of self-­‐control and self-­‐awareness on outcomes when commitment devices are available. For a given level of awareness, the actual savings of individuals with more self-­‐control will be larger than those with less self-­‐control. The similarity to the case of no commitment device arises from the fact that with the same (imperfect) awareness, all individuals equally discount their self-­‐control problems, and hence, all under-­‐
demand commitment devices. Commitment savings will be better than temptation savings, but individuals with the smallest self-­‐control problem will still have the largest commitment savings. On the other hand, for a fixed level of self-­‐control, individuals who are more aware of their self-­‐control problems will demand a greater commitment device than those who are less aware. As a result, the amount of commitment savings will increase as awareness increases. 3.3 Organizing empirical evidence by theoretical results Simplifying away from future-­‐biased individuals, the time-­‐inconsistency literature categorizes individuals as those who have perfect self-­‐control (β=1) and those with self-­‐control problems (β<1). Existing studies often assume a particular fixed α since the subject of interest is usually β: individuals are usually either sophisticated (α=1), naïve (α=0), or partially naïve (0<α<1). Figure 1 illustrates these types in a two-­‐dimensional map with β on the X axis and α on the Y axis. The time-­‐consistent occupy the northwest point of the map (black dots), while the sophisticated occupy the top horizontal region (‘+’) and the naïve the bottom horizontal region (‘x’). This leaves most of the area to be classified as partially naïve. The concept of partial naïveté (0<α<1, β<1), however, does not provide a meaningful classification, since both parameters can vary. We therefore propose to distinguish this group further into two types depending on which parameter best explains the variation within the population. The first partial type we will refer to as Partial HC (partially naïve with heterogeneity in self-­‐control) that spreads horizontally as shown in blue (0<α<1, β varies). The second partial type we will refer to as Partial HA (time-­‐inconsistent with heterogeneity in awareness) that spreads vertically as shown in green (0< β <1, α varies). Figure 1: Types mapped on self-­‐control (x axis) and awareness (y axis) Table 3 below provides predictions about the correlation between ED and outcomes with and without commitment device for each of these types. First, in column 1, we use Lemma 1 to determine if ED will be positive, negative, or zero for each type in Figure 1 above. Since we interpret the ED survey question as asking about participants’ general behavior, not their behavior given commitment devices, ED should be the same with or without commitment devices. Columns (2-­‐3) predict the relationship between ED and actual outcome when there is no commitment device. Column 2 compares actual outcome to expected outcome, while column 3 predicts the correlation between ED and actual outcome. Columns (4-­‐5) predict the relationship between ED and actual outcome with the aid of commitment devices. Since commitment devices are available, self-­‐awareness now allows individuals to modify their actual behavior so that it is closer to their ideal behavior. The relevant comparison in column 4 is therefore no longer between expected and actual but between actual and ideal. Column 5 predicts the correlation between actual outcome and ED, as in column 3. Let us discuss each type and relate them to the empirical findings. The time-­‐consistent individuals (TC) are unique in that the ideal, expected, and actual outcomes are the same for them with or without commitment devices. The naïve will expect to match their ideal savings but will fall short. Since they are completely unaware of their self-­‐control problem, they will achieve the same outcome with or without commitment devices. The sophisticated types, on the other hand, have self-­‐control problems but are aware of it. Because of this they will (1) correctly predict the action they will actually take when there are no commitment devices, and (2) when a commitment device is available, use it to fully overcome their self-­‐control problem and take the ideal action. As a result, the correlation between ED and actual outcome without commitment device is negative, while the correlation between ED and actual outcome with commitment device is zero. This is the same result as that of Ameriks et al. (2007): ED (referred to as expected-­‐ideal (EI) gap) in luxury goods consumption is negatively correlated with liquid assets of high-­‐net-­‐worth TIAA CREF mutual fund holders; however, it is uncorrelated with assets in retirement savings. On the other hand, in a Partial HCs population all individuals similarly underestimate the extent of their self-­‐control problem. Because of this, they end up achieving less than their expectations when there are no commitment devices, and demanding too little commitment when the commitment devices are available. As a result, outcomes will still be a decreasing function of self-­‐control regardless of the availability of commitment devices. Since ED is increasing in their self-­‐control problem, actual outcome will be negatively correlated with ED. This fits the Wong (2008) data of students at an elite university. He finds that students on average predict that they will delay studying for an exam but will underestimate the magnitude of this delay. He also finds a negative correlation between delay and midterm exam scores in line with the prediction for Partial HCs. Partial HAs underestimate their self-­‐control problem just like Partial HCs, and therefore they achieve less than their expectations. Unlike Partial HCs, individuals across the population may be roughly similar in their self-­‐control problem but differ substantially in their awareness of it. The more aware subjects report a higher ED and demand more commitment devices, which results in a more positive outcome. This drives the positive correlation between ED and actual outcome. Our homeless shelter residents appear to resemble Partial HA, for several reasons. 21 First, mean ED is positive, suggesting that subjects were at least partially aware of their self-­‐control problem. Second, subjects do not appear to be able to reach their ideal 21
Self-­‐control parameters have been estimated for this population using other measures — unfortunately the number of subjects for whom there is an overlap between these various measures is small. It is interesting to note, however, that the mean SCS elicited for this population using Tangey et al. (2004) measure was on the high end of previous estimates while beta elicited through time discounting is at the low end of other studies. The mean SCS for this population was 3.5 (SE: 0.104), while SCS of 3.3 (SD: 0.48) was estimated from college students (Gailliot et al. 2007) and employees of a firm (Bechtoldt et al. 2007). On the other hand, Linardi and Tanaka (2013) estimated beta to be 0.40 while Tanaka et al. (2010) study with other population have found a beta of 0.64. savings rate even with the commitment device.22 Third, there is a positive correlation between ED and actual savings. Table 3: Summary of theoretical prediction and empirical evidence Self-­‐
No With Type Awareness control ED Commitment Commitment Empirical Evidence Cor Cor Exp-­‐ (ED, Ideal-­‐ (ED, Α Β Act Act) Act Act) (1) (2) (3) (4) (5) TC 1 1 0 0 0 0 0 Ameriks et al. (2008), Sophisticated 1 Vary + 0 -­‐ 0 0 mutual fund owners Wong (2008), students Partial HC 0<α<1 Vary + + -­‐ + -­‐ at an elite university Naïve 0 Vary 0 + 0 + 0 Incekara-­‐Hafalir and Linardi (2014), the Partial HA vary 0<β<1 + + 0 + + homeless 4. DISCUSSION Both self-­‐control and awareness about self-­‐control have important implications for public policy (Frederick et al. 2002; Ashraf et al. 2006). However, with the exception of Augenblick et al. (2013), the literature focuses on measures of self-­‐control and either remains silent about awareness or assumes it to be at a certain level. In addition, since many of these measures require complex incentivized elicitation, organizations that would greatly benefit from understanding self-­‐control and awareness among their clients have yet to integrate these measures in their operations. Given their need for measures that are task specific, intuitive to design, and easy to administer, organizations are much more likely to integrate information about self-­‐control and awareness if such information can be elicited in the form of survey questions. This paper fills this gap by focusing on the ideal/predicted survey (Ameriks et al. 2007), one the few survey methods developed in economics to elicit self-­‐control, and by 22
We cannot say very much due to the sparseness of our data, but among the 49 subjects for whom we have income expectation, there are 17 subjects for whom income expectation is collected and who earned a positive income. They would ideally save 66% and would predict they will save 62%. In reality, with the commitment device they saved 60%. providing a simple theoretical interpretation of the survey responses and its correlation with observed outcome. Ameriks et al. (2007) found that ED in luxury goods consumption is negatively correlated with liquid assets of high-­‐net-­‐worth TIAA CREF mutual fund holders; however, it is uncorrelated with assets in retirement savings. Wong (2008) found that ED in midterm preparation dates is negatively correlated with final grades for National University of Singapore students. We run the ED survey on a population that is the polar opposite of these two highly successful populations: the working homeless at a homeless shelter in Arizona. With previous literature showing a correlation between financial well-­‐being and many behavioral attributes (self-­‐
control, cognitive ability, numeracy, etc.), we expect to see some differences in outcome between our study and previous studies (Tangney et al. 2004). We find that ED in savings is positively correlated with actual savings in the shelter commitment savings program. This positive correlation is surprising if we assume that variation in responses is capturing variation in self-­‐control. However, this result is not surprising if we allow for the possibility that heterogeneity in awareness can be so strong as to swamp differences in self-­‐control in some populations. We then provide a theoretical interpretation of ED and derive results from it. As opposed to previous studies, we did not assume that expected deviation from the ideal is driven by self-­‐control or awareness alone; rather, we allowed it to be affected by both. Relaxing this assumption, the ED method no longer identifies individuals in terms of their self-­‐control problem, but identifies populations in terms of the relative variation of self-­‐control and awareness. Our derivation shows that Ameriks et al.’s (2007) results are predicted by our model under the assumption that the Ameriks et al. population is sophisticated; Wong’s results are predicted under the assumption of Partial HC (partially naïve population with heterogeneity in self-­‐control). Our results are predicted under the assumption that the population is Partial HA (partially naïve population with heterogeneity in awareness). This suggests that (1) there are further distinctions that can be made within the partial naïve population; (2) in some populations, heterogeneity in awareness can swamp heterogeneity in self-­‐control; and (3) ED behaves in a predictable way with very different populations and in very different situations. We hope these early results encourage other researchers to explore ways to utilize the subjectivity of survey responses in combination with objective data to inform organizations about awareness and self-­‐control in their population of interest. 5. APPENDIX TABLE 1: (1) VARIABLES Ideal ED $100 Income Competition Age -­‐1.009 (6.835) female -­‐453.9** (216.4) children 17.25 (54.96) education 6.345 (33.27) black -­‐248.7 (150.5) # of days in Level III 1.853 (2.225) first time homeless 486.9*** (165.7) month homeless 16.39*** (6.209) addiction -­‐177.5 (211.4) incarceration -­‐118.6 (193.3) Project 2 -­‐331.9* (188.0) Project 3 -­‐236.8 (204.5) Constant 709.8 (550.7) Observations 94 R-­‐squared 0.260 (2) (3) (4) (5) Predicted ED Report Income -­‐0.0128 2.838 (0.0130) (15.53) 0.0797 88.02 (0.0864) (97.59) 4.750 -­‐5.759* 0.00218 9.190** (7.183) (3.140) (0.00374) (4.147) -­‐442.1* -­‐11.84 -­‐0.0161 -­‐1.200 (227.4) (99.40) (0.116) (133.2) 39.10 -­‐21.85 0.0120 -­‐25.95 (57.76) (25.25) (0.0296) (34.54) -­‐0.304 6.650 0.0281 -­‐5.214 (34.96) (15.28) (0.0178) (18.80) -­‐223.4 -­‐25.25 -­‐0.136* -­‐90.82 (158.1) (69.12) (0.0808) (94.76) 1.845 0.00845 -­‐0.00197 0.246 (2.338) (1.022) (0.00121) (1.486) 503.2*** -­‐16.38 0.208** 32.33 (174.2) (76.13) (0.0889) (114.7) 18.54*** -­‐2.152 -­‐0.00354 2.764 (6.525) (2.852) (0.00335) (5.229) -­‐193.0 15.47 -­‐0.121 -­‐33.43 (222.2) (97.13) (0.114) (134.6) -­‐89.33 -­‐29.30 -­‐0.124 162.4 (203.1) (88.79) (0.104) (124.2) -­‐212.7 -­‐119.1 0.608*** -­‐420.7** (197.6) (86.36) (0.102) (162.7) -­‐127.4 -­‐109.4 0.666*** -­‐357.9** (214.9) (93.93) (0.114) (173.5) 281.3 428.5* -­‐0.0975 210.2 (578.7) (252.9) (0.308) (371.9) 94 94 94 71 0.229 0.081 0.462 0.285 Standard errors in parentheses *** p<0.01, ** p<0.05, * p<0.1 (6) (7) Savings Savings 9.786 8.243* (9.668) (4.758) 0.544*** (0.0409) 109.5* 61.68** (60.77) (30.12) 4.536* -­‐0.459 (2.582) (1.325) -­‐16.73 -­‐16.08 (82.95) (40.82) -­‐15.48 -­‐1.370 (21.50) (10.63) 2.876 5.711 (11.71) (5.764) -­‐76.23 -­‐26.85 (59.00) (29.27) 0.322 0.188 (0.925) (0.455) 12.25 -­‐5.322 (71.42) (35.17) 2.928 1.425 (3.256) (1.606) -­‐33.42 -­‐15.25 (83.83) (41.27) 120.3 31.97 (77.33) (38.63) -­‐203.4** 25.27 (101.3) (52.76) -­‐146.5 48.03 (108.0) (55.15) -­‐2.855 -­‐117.1 (231.6) (114.3) 71 71 0.304 0.835 TABLE 2: Heckman Selection Model OLS Heckman Outcome Equation ED $100 8.407* 7.956* (4.707) (4.311) Income 0.544*** 0.542*** (0.0406) (0.0364) Competition 60.48** 62.30** (29.75) (26.81) Age -­‐0.430 -­‐0.394 (1.314) (1.171) Female -­‐18.66 -­‐17.45 (40.03) (35.70) Children -­‐1.019 -­‐1.077 (10.52) (9.365) Education 6.123 6.706 (5.635) (5.165) Black -­‐26.70 -­‐29.92 (29.05) (26.87) first time homeless -­‐3.362 0.177 (34.59) (31.79) months homeless 1.463 1.384 (1.592) (1.423) homeless due to addiction -­‐14.84 -­‐16.49 (40.95) (36.58) homeless due to incarceration 29.32 26.91 (37.81) (34.08) Project 3 29.73 38.79 (51.26) (49.68) Project 4 49.18 60.14 (54.67) (54.20) Number of days in Level III -­‐ -­‐ Constant -­‐121.4 -­‐141.7 (113.0) (109.5) Correlation Parameter ρ -­‐ 0.177 Observations 71 94 Standard errors in parentheses *** p<0.01, ** p<0.05, * p<0.1 OLS Heckman Selection Equation -­‐ -­‐0.0307 (0.0628) -­‐ -­‐ 0.459 (0.469) -­‐ 0.0236 (0.0253) -­‐ 0.406 (0.688) -­‐ -­‐0.00273 (0.160) -­‐ 0.202* (0.105) -­‐ -­‐0.695 (0.455) -­‐ 1.529** (0.630) -­‐ -­‐0.0139 (0.0165) -­‐ -­‐0.497 (0.578) -­‐ -­‐0.602 (0.545) -­‐ 2.570*** (0.670) -­‐ 3.041*** (0.734) -­‐ -­‐0.00730 (0.00599) -­‐ -­‐4.527** (1.977) TABLE 3: Individuals in the competition group regressed separately from individuals not in the competition group. Competition Not in competition VARIABLES Savings Savings ED $100 2.53 7.78** (5.37) (3.57) Income 0.392*** 0.621*** (0.0356) (0.0319) Project 3 11.54 45.40* (33.11) (26.22) Project 4 21.28 49.49 (31.70) (31.09) Constant -­‐7.919 -­‐30.36 (30.12) (23.34) Observations 25 70 R-­‐squared 0.869 0.860 Standard errors in parentheses *** p<0.01, ** p<0.05, * p<0.1 6. REFERENCES Ameriks, J., Caplin, A., Leahy, J., Tyler, T., 2007. Measuring self-­‐control problems. American Economic Review 97(3), 966-­‐972. Ariely, D., Wertenbroch, K., 2002. Procrastination, deadlines, and performance: Self-­‐control by precommitment. Psychological Science 13(3), 219-­‐224. Ashraf, N. Karlan, D., Yin, W., 2006. Tying Odysseus to the mast: Evidence from a commitment savings product in the Philippines. The Quarterly Journal of Economics 121(2), 635-­‐672. Augenblick, N., Niederle, M., Sprenger, C., 2013. Working over time: Dynamic inconsistency in real effort tasks. NBER Working Paper No. 18734. Bauer, M., Chytilová, J., Morduch, J., 2012. Behavioral foundations of microcredit: Experimental and survey evidence from rural India. American Economic Review 102(2), 1118-­‐1139. Bechtoldt, M. N., Welk, C., Zapf, D., Hartig, P. C., 2007. Main and moderating effects if self-­‐
control, organizational justice, and emotional labour on counterproductive behavior at work. European Journal of Work and Organizational Psychology 16(4). Brocass, I., Carrillo, J., 2001. Rush and procrastination under hyperbolic discounting and interdependent activities. The Journal of Risk and Uncertainty 22(2), 141-­‐164. Brown, A., Dhua, Z. E., Camerer, C., 2009. Learning and visceral temptation in dynamic saving experiments. The Quarterly Journal of Economics 124(1), 197-­‐231. Duckworth, A. L., and Kern, M. L., 2011. A meta-­‐analysis of the convergent validity of self-­‐
control measures. Journal of Research in Personality 45(3), 259-­‐268. Fang, H., Silverman, D., 2009. Time-­‐inconsistency and welfare program participation: Evidence from the NLSY. International Economic Review 50(4), 1043-­‐1077. Frederick, S., Loewenstein, G., O’Donoghue, T., 2002. Time discounting and time preference: A critical review. Journal of Economic Literature 40(2), 351-­‐401. Gailliot, M. T., Schmeichel, B. J., Maner, J. K., 2007. Differentiating the effects of self-­‐control and self-­‐esteem on reactions to mortality salience. Journal of Experimental Social Psychology 43(6), 894-­‐901. Laibson, D., 1997. Golden eggs and hyperbolic discounting. The Quarterly Journal of Economics 112(2), 443-­‐478. Linardi, S., and Tanaka, T., 2013. Competition as a savings incentive: A field experiment at a homeless shelter. Journal of Economic Behavior and Organization 95, 240-­‐251. Ly, K., Mazar, N., Zhao, M., Soman, D., 2013. A practitioner’s guide to nudging. Rotman School of Management: Behavioral Economics in Action Report Series 2013. Meier, S., Sprenger, C., 2010. Present-­‐biased preferences and credit card borrowing. American Economic Journal: Applied Economics 2(1), 193-­‐210. Moffitt, T. E., Arseneault, L., Belsky, D., Dickson, N., Hancox, R. J., Harrington, H., Houts, R., Poulton, R., Roberts, B. W., Ross, S., Sears, M. R., Thomson, W. M., and Capsi, A., 2011. A gradient of childhood self-­‐control predicts health, wealth, and public safety. PNAS 108(7), 2693-­‐
2698. O’Donoghue, T., and Rabin, Matthew, 2001. Choice and procrastination. The Quarterly Journal of Economics 116(1), 121-­‐160. Strotz, R. H., 1956. Myopia and inconsistency in dynamic utility maximization. The Review of Economic Studies 23(3), 165-­‐180. Tanaka, T., Camerer, C., Nguyen, Q., 2010. Risk and time preferences: Linking experimental and household survey data from Vietnam. The American Economic Review 100(1), 557-­‐571. Tangney, J. P., Baumeister, R. F., and Boone, A. L., 2004. High self-­‐control predicts good adjustment, less pathology, better grades, and interpersonal success. Journal of Personality 72(2), 271-­‐324. Wong, W., 2008. How much time-­‐inconsistency is there and does it matter? Evidence on Self-­‐
Awareness, Size, and Effects. Journal of Economic Behavior and Organization 68, 645-­‐656.