An Under-Shooting Bias in Asymmetric Resource Problems

ASSOCIATION FOR CONSUMER RESEARCH

Association for Consumer Research, University of Minnesota Duluth, 115 Chester Park, 31 West College Street Duluth, MN 55812

An Under-Shooting Bias in Asymmetric Resource Problems Christopher Hsee, University of Chicago, USA Xilin Li, University of Chicago, USA Ying Zeng, University of Chicago, USA Alex Imas, Carnegie Mellon University, USA

People are often faced with choices between accounts or options with more and fewer resources. We introduce a Two-Account Game to study asymmetric resource-competition problems and discover a systematic under-shooting bias. People tend to choose fewer- resource options, partly because they incorrectly assume others will choose the option with more resources.

[to cite]: Christopher Hsee, Xilin Li, Ying Zeng, and Alex Imas (2019) ,"An Under-Shooting Bias in Asymmetric Resource Problems", in NA - Advances in Consumer Research Volume 47, eds. Rajesh Bagchi, Lauren Block, and Leonard Lee, Duluth, MN : Association for Consumer Research, Pages: 232-236.

[url]: http://www.acrwebsite.org/volumes/2551957/volumes/v47/NA-47

[copyright notice]: This work is copyrighted by The Association for Consumer Research. For permission to copy or use this work in whole or in part, please contact the Copyright Clearance Center at http://www.copyright.com/. Wise and Foolish Consumer Financial Decisions Chair: Kellen Mrkva, Columbia University, USA

Paper #1: A Structural Test of Mental Accounting and Consumer which causes them to choose cards that accumulate higher fees. Fi- Fungibility From Credit Card Expenditures nally, Hsee, Li, Zeng, and Imas examine how people allocate money Nicholas Pretnar, Carnegie Mellon University, USA when there are multiple accounts, some with more resources than Christopher Olivola, Carnegie Mellon University, USA others. They find that people allocate too much toward smaller ac- Alan Montgomery, Carnegie Mellon University, USA counts. The potential audience for this session is broad. Though the Paper #2: Minimum Payments Alter Debt Repayment Strategies talks focus on consumer financial decision making and credit cards, Across Multiple Credit Cards it will be interesting to many. For example, three of the papers cover Abigail Sussman, University of Chicago, USA a novel heuristic or bias in decision making, several are rooted in be- Samuel Hirshman, University of Chicago, USA havioral economics, several use big data, some focus partly on time Paper #3: Searching, Fast and Slow: How Time Preferences preferences and intertemporal choice, two have clear policy implica- Influence Credit Card Search and Choice tions, one examines consumer search and information processing, Kellen Mrkva, Columbia University, USA and one has direct relevance for researchers who study perspective- Elizabeth C Webb, Columbia University, USA taking and economic games. Eric J Johnson, Columbia University, USA All talks are based on papers in the late stages of development. Paper #4: An Under-Shooting Bias in Asymmetric Resource All four papers are either currently being prepared or will soon be Problems prepared for submission to A journals. Christopher Hsee, University of Chicago, USA Xilin Li, University of Chicago, USA A Structural Test of Mental Accounting and Consumer Ying Zeng, University of Chicago, USA Fungibility from Credit Card Expenditures Alex Imas, Carnegie Mellon University, USA EXTENDED ABSTRACT SESSION OVERVIEW The theory of mental accounting suggests that consumers treat Americans hold over $800 billion in credit card debt. The aver- different sources of money and different expenditures differently age cardholder owns four credit cards, often with high interest rates (Thaler 1999). One implication of mental accounting is that consum- that can cause debt to spiral out of control. Some people even hold ers may be more likely to spend with credit cards than with cash or high-interest credit card debt and savings simultaneously, a tendency debit (e.g., Prelec and Simester 2001), particularly for durable goods called “the credit card debt puzzle,” which can be extremely harm- purchases (Prelec and Loewenstein 1998). Under this theory, in- ful. Understanding how consumers use credit cards and the processes creasing the credit limit on a consumer’s credit card should increase that lead consumers to accumulate excessive debt is of paramount his/her consumption, regardless of whether his/her income or wealth importance. The difference between wise and foolish decision mak- also increased. ing in this high-stakes domain can be the difference between finan- We test this prediction using a unique dataset of linked credit cial security and financial turmoil. and debit card users. Our analysis adds to the literature on mental How do consumers pick among the many credit cards available accounting theoretically, by deriving a measure of fungibility with to them? How do people determine which debts to pay off first? What regards to credit and debit card usage directly from a consumer’s factors make people more likely to pay off debt? structural consumption/savings problem. It also adds to previous The papers in this session will help answer these questions. In theorizing empirically by using linked household credit/debit card so doing, they will advance the field’s understanding of consumer field data from a large North American bank to show that consumers financial decision making, as well as our understanding of the heu- behave in ways consistent with mental accounting. ristics, biases, and strategies people use more generally. Though the We construct a theoretical, economic utility maximization talks focus on consumer financial decision making and credit card model that allows different consumers to exhibit different degrees decisions in particular, there is also a diversity of topics that will of fungibility. Specifically, we incorporate the mental accounting make this symposium interesting to a broad audience. concept of partitioned ex-ante and ex-post budgeting by splitting the In the first paper, Olivola, Pretnar, and Montgomery use data household budget constraint into separate constraints for each liquid- from a large North American bank with over 3 million observations ity category and then allowing consumers to choose shares of con- to examine factors that help or harm consumers’ ability to make debt sumption for different commodities out of different liquidity sources. repayments. They show that some factors, including whether con- Specifically, we focus on credit card verses debit card expenditure, sumers buy a durable rather than non-durable good, impact debt bal- though the model is general enough to admit many more liquidity ances long-term. sources by simply adding a new constraint. Among other things, the In the second paper, Hirshman and Sussman demonstrate that model reconciles a heretofore unsolved problem in mainstream eco- minimum payments can interfere with people’s ability to make wise nomics known as “the credit card debt puzzle,” wherein consumers debt repayment decisions. Minimum payments make people less simultaneously save and carry interest-bearing credit card debt (see likely to choose the optimal strategy of paying off debt from higher- Telyukova 2013; Telyukova and Wright 2008). Depending on indi- interest credit cards first, even though most people are aware that vidual consumers’ innate aversion to holding debt, an individual may paying off high-interest debt first is the best strategy. or may not simultaneously save and carry interest-bearing debt. This In the third paper, Mrkva, Webb, and Johnson focus on how preference-based explanation allows us both to solve the puzzle and people choose a credit card. They find that impatient, present-biased reconcile the vast degree of heterogeneity observed in the data with individuals are less willing to search for the optimal credit card, regards to savings and debt-accumulating behavior.

Using the equilibrium fungibility condition, we empirically test We draw on lab and field data to provide evidence that people whether the median consumer unit (i.e., household) in our sample are knowledgeable that they should repay their highest interest rate exhibits perfect fungibility with respect to credit and debit card ex- debts first. Furthermore, borrowers do prioritize these debts to some penditure. We find that the median consumer behaves as if receiving degree. In addition, we document a dispersion effect of minimum $1 in additional credit is equivalent to receiving $2.03 in additional payments. That is, minimum payments reduce participants likeli- cash in terms of marginal consumption value. A statistical test shows hood of repaying optimally by leading them to spread their discre- that the median consumer is thus significantly non-fungible with re- tionary repayments (i.e., payments above the minimum) across more gards credit verses debit card expenditure. However, the distribution accounts than those without minimum payments. We find that this of this trait varies substantially across consumers: 59% of our sample strategy change persists after accounting for the tendency to target behave as if the consumption value of credit is higher than that of minimum payment amounts (Stewart 2009), and we do not find cash, whereas the other 41% behave in the opposite manner. evidence supporting widespread use of heuristics based on balance Our structural model of fungibility can be used to better un- amount. derstand how consumers across the joint income, wealth, and debt Data from the lab and field suggest consumers are sensitive to distribution respond to exogenous credit and income shocks. For the importance of interest rates in debt repayment. Our field data example, in counterfactual simulations, we can quantify how con- comes from a budgeting app and has 39,626 months of repayment sumers who exhibit a pronounced aversion to accumulating credit data for 1,956 unique consumers. We find that consumers repay card debt respond to unexpected, adverse income shocks. Being about $132 more (t(37,789)=3.14, p=.0017, equivalent to 4% of the more sensitive to debt accumulation, the model predicts that such average balance) to their highest interest rate debt in a month, con- consumers will adjust their overall consumption downward to avoid trolling for the size of their balance. These data are consistent with accumulating too much debt. On the other hand, a consumer unit that self-reported strategies from Mturk experiments. Many participants is not debt averse may excessively smooth their consumption in re- (47%) report repaying high interest debt is the most important ele- sponse to a negative income shock by taking on more debt to ensure ment in their decision, significantly more than the second highest that their level of consumption, and thus standard of living, remains strategy, splitting evenly across cards (14.5%, χ2(1)=43.68, p<.001). fairly consistent over multiple periods. However, of the group focused on high interest, 38.5% report want- Additionally, we affirm the theory of Prelec and Loewenstein ing to pay most, rather than all, of their repayments toward their (1998), that consumers are more apt to use credit cards for durable highest interest rate debt, thus insufficiently weighting interest. goods purchases than non-durable goods purchases, because the pain We next examine minimum payments as one structural factor of continually paying down accrued interest on debt is offset by the that may alter repayment strategies away from paying the highest stream of utility they continue to enjoy from using durable goods. interest rate cards first, further interfering with the ability to repay Specifically, we find that the median consumer unit in our sample optimally. In study two, participants responded to a three round debt (of over 10,000 households) responds to a $1 increase in credit by repayment scenario. Each participant had 6 credit cards to repay, spending $0.32 more on durable goods than if s/he received the same with outstanding balances and interest rates stated for all cards. Par- $1 increase in available cash. For non-durables, by comparison, this ticipants (N=375) were randomly assigned either to have a minimum effect is less pronounced in magnitude (only $0.05 more), though payment associated with each debt or not. In the minimum payment still significantly greater than zero. Our empirical results are con- condition, participants faced a $25 fee per account paid below the sistent with a similar analysis on U.K. credit card users (Quispe- minimum. Participants made allocations to all debts in the same Torreblanca et al. 2019). Altogether, our results both bolster previous table. We find that participants in the minimum payment condition theorizing on mental accounting and build on this theory. Our results were less likely to repay optimally (t(373)=2.91, p<.01). This sub- provide a clearer picture of how people mentally represent increases optimal allocation in the minimum payment condition was driven in credit, cash, and debit, and how people mentally represent their by overdispersion. Participants made payments towards more cards, expenditures across different categories. Our data also afford a pow- over and above the minimums payments themselves (t(373)=3.624, erful tests of mental accounting using a large and unique dataset of p<.01). We did not find evidence of substantial portions of partici- credit and debit card usage from a large North American bank. pants paying off the smallest debt first, contrary to prior literature. We also replicated these effects in a setting where participants made Minimum Payments Alter Debt Repayment Strategies one allocation per screen. Across Multiple Credit Cards In study three, we replicated these findings utilizing a within subject design over 3 weeks. Participants (n=189) completed the EXTENDED ABSTRACT self-report measures discussed previously and were then randomly Americans hold an increasing amount of revolving credit card assigned to one of two orders of our minimum payment and no debt, currently estimated at $808 billion (Federal Reserve Bank of minimum control conditions. Within-subjects, we find a marginally New York 2017), on an average of four cards per cardholder (CFPB significant decrease in optimal play in the minimum payment ver- 2015). A growing body of literature suggests people do not repay sion of our task (t(188)=1.698, p=.091) and a significant increase in their debt in the cheapest possible way (e.g., Ponce et al. 2017). the proportion of accounts paid above the minimum (t(188)=4.513, Prior work explains suboptimal repayment through lack of interest p<.00001). The within-subject version suggests that knowledge and rate knowledge (Seira et al.2017) or through a variety of heuristic individual differences are unlikely the key driver of the strategic ef- strategies inconsistent with the optimal repayment (Gathergood et fects. al. 2017). In particular, a laboratory examination of borrowers with In study four, we allow participants (N=366) to save money in multiple cards shows that they prioritize paying off smaller debts addition to repaying debt. Participants in the minimum payment con- rather than high interest rate debts (Amar et al., 2011). By contrast, dition are significantly more likely to save than those without mini- data from the field suggests that credit card holders use a balance mums (t(364)=3.20, p<.01), leading to higher interest costs incurred. matching heuristic, paying more to their largest debts (Gathergood In addition to repaying less, they continued to repay less optimally et al. 2017). than those without minimums (t(364)=3.46, p<.01). Among partici- 234 / Wise and Foolish Consumer Financial Decisions pants who made any excess repayment, participants in the minimum fees), with monetary incentives to choose correctly ($2.00 per cor- payment condition allocated to more accounts above the minimum rect answer). To assess time preferences, we used an adaptive mea- (t(360)=1.97, p<.05). These results suggest that impacts of minimum sure (DEEP; Toubia et al. 2013) that uses a series of choices between payments on strategy remain important even after allowing for the smaller-sooner and larger-later amounts to assess discounting. effects of targeting. Finally, in experiment five we introduce a default As predicted, present-biased individuals searched substantially minimum payment condition in which minimum payments are auto- less, opening fewer attribute boxes (t = 7.06, p < .001). This effect filled for the participants (i.e., the default is to pay the minimum held when we added covariates to control for individual differences amount on all cards; N=258). Since the optimal strategy in the de- in participants’ credit scores and debt literacy (t = 3.65, p < .001). fault and the minimum payment conditions are the same, differences Additionally, the effect was not driven by reduced engagement in between these conditions are unlikely to be driven by decision com- the survey; even when we controlled for how long participants spent plexity. We find that the default condition attenuates the strategic dif- on the survey as a whole, the effect of present bias on less search ferences between the minimum payment and no minimum payment remained (t = 7.26, p < .001). condition. Like the no minimum condition (t(167)=3.52, p<.01), par- Present bias also had a significant negative effect on choice ac- ticipants in the default condition are more likely to use the optimal curacy (t = 1.95, p < .05). A mediation model (Preacher and Hayes strategy (t(171)=2.16, p<.05). As a result, it is unlikely that the com- 2008) was consistent with our hypothesis that present-biased con- plexity of the optimal rule is responsible for the changes induced by sumers choose credit cards with higher fees because they search minimum payments. Additionally, the increase in optimal repayment less extensively. Finally, process evidence suggests the difference in above the minimum payment condition provides evidence that ac- search is driven by the amount of search, not which attributes are tively selecting an allocation amount for each debt contributes to the searched. Accordingly, present-biased participants searched less for strategic differences we observe induced by the minimum payments. every piece of information, even for low introductory rates and back- We provide new evidence on the strategies that lead people loaded fees that might be most appealing to them. Present-biased to repay their debts sub-optimally. Contrary to prior literature, we individuals also were not significantly more likely to choose cards find people are aware of the importance of prioritizing payments to with low introductory rates. This suggests that present bias affects higher interest rate debts. They are sensitive to interest rates, but the process through which individuals make credit card decisions, insufficiently so. We document a novel cost of minimum payments: not the weights they place on different attributes. minimums induce participants to spread money more evenly across In Study 2, we demonstrated that the effect is not caused by the accounts. Our results suggest that mandating salient presentations unfamiliar display of Mouselabweb, in which information is hidden of interest rates could reduce the costs of borrowing for consumers. behind boxes. Neither was it confined to the online Mechanical Turk sample. We sought a sample of 300 participants, some of whom were Searching, Fast and Slow: How Time Preferences university students who searched credit cards in the laboratory while Influence Credit Card Search and Choice they were monitored using a Tobii eye-tracker (n = 52). Others were online participants monitored using Mouselabweb with closed boxes EXTENDED ABSTRACT as in Study 1 (n = 248, from Prolific Academic). The rest of the pro- When we think about present bias, we usually think about the cedure was the same as in Study 1. We coded search as the number choices that people make. We expect people who are present biased of boxes opened for Mouselabweb participants (as in Study 1) and to eat the one marshmallow now, take the smaller immediate pay- as the number of boxes fixated for eye-tracking participants. Present ment, and choose the credit card with a teaser rate (Chabris et al. bias again predicted less search (t = 2.05, p = .041). There was no 2009; Reimers et al. 2009; Shoda et al. 1990). present bias x sample interaction (t = 0.91, p = .326), suggesting that Across four studies and four field surveys (total N = 18,405), the relationship was not moderated by the type of search monitoring we show that present-biased individuals are not any more likely to or sample. In Study 3, we replicated Study 1 with a group of MBA choose credit cards with teaser rates nor do they focus attention on or students (n = 185), who scored considerably higher on measures of give more weight to up-front costs. Instead, they simply search less financial literacy and numeracy, and in many cases had experience overall, terminating search much more quickly than patient individu- working in the financial sector. The results mirrored those in Study 1. als. They search less for all pieces of information about credit cards, In Studies 4A–4D, we measured the association between time which leads them to choose cards that accrue higher total costs. This preferences and search in large field surveys of American households was consistent with our hypothesis that present-biased individuals (SBI’s MacroMonitor field survey). In each of the four field surveys, would search less, being unwilling to engage in unpleasant search there were over 4,000 American households participating. Respon- that could reduce future costs. dents reported how many resources they searched in the past year In Study 1 (pre-registered, MTurk, 300 recruited, n = 273 when choosing financial products. They also responded to a series completes, Mage = 35.6 years, 57% male), participants were asked of intertemporal choices between smaller-sooner and larger-later to imagine they are choosing a credit card from four options. They amounts. From these choices, we calculated present bias for each were told they would hold the card for two years, with an average participant. We then analyzed whether present bias predicted less unpaid balance of $5,000 (excluding fees), which is the average un- search. There was a significant negative correlation between pres- paid balance on credit cards in the US. After testing comprehension ent bias and search, such that present-biased respondents searched of the set-up, participants were shown eight credit cards (two trials significantly less than more patient respondents (r = –0.18, p < .05). with four credit cards each). The cards varied in introductory interest Though the effect size was fairly small, these results suggest that rate, introductory period, standard interest rate, annual fee, and ap- present biased consumers search less. pearance. Participants viewed the credit cards with attribute informa- Every choice depends upon the selection of a decision strategy, tion in Mouselabweb; to track search, we hid attribute information which involves the expenditure of effort now for better outcomes behind boxes, revealing it only when participants moved their mouse later. Our results suggest that time preferences do not lead people over the box. They were asked to choose the credit card that would to search different pieces of information nor does it influence the accumulate the lowest total costs (considering all interest rates and Advances in Consumer Research (Volume 47) / 235 weight given to each attribute. Rather, they lead to less extensive all conditions, fewer participants went to the large event than the search, causing people to terminate search more quickly. proportion of customers in the large event. Study 4 explored a boundary condition of the under-shooting An Under-Shooting Bias in Asymmetric Resource bias. One potential mechanism for the bias is mistaken beliefs about Problems the strategies of others. If that were indeed the case, then manipula- tions that increase participants’ understandings of how others form EXTENDED ABSTRACT strategies could potentially mitigate the bias. Based on prior work Suppose that you are one of many competitors choosing be- showing that making others more vivid leads to improved perspec- tween two options. One option has more resources than the other, tive-taking, we manipulated the vividness of other players to exam- and the resources from each option will be divided equally among ine whether this manipulation would mitigate the under-shooting everyone who chooses it. Which option would you choose? A myriad bias. Thus, Study 4 had two between-subjects conditions: control of important decisions involve these basic characteristics: one option and vividness. All participants were asked to imagine that they were contains more resources than the other (e.g., more customers, more playing the two-account game with 19 acquaintances. In the vivid- jobs, etc.), and the greater the number of competitors choosing that ness condition, participants were asked to write down the first names option, the fewer the resources available to each. In order to maxi- of the 19 acquaintances and then choose the account. In the control mize your own outcome, you have to think about the strategies of condition, participants were not asked to do so. The results showed others. that the under-shooting bias appeared in the control condition but We refer to such decision problems as asymmetric resource disappeared in the vividness condition, suggesting that vividness problems. To mimic this type of problem, we have developed a Two- manipulation mitigated under-shooting and led participants to make Account Game. In the game, N players choose between a large ac- choices consistent with the equilibrium prediction. count containing $L and a small account containing $S (<$L). Play- Resources are limited, and competition is an important part of ers know that everyone must choose independently and cannot swap life; people apply for a limited number of jobs and compete for a money afterward, and that the money in each account will be divided limited number of customers. While extensive research has studied equally among those who choose it. resource-competition problems in which the allocation of resources If everyone followed the Nash equilibrium mixed strategy, on is either symmetric or unknown, little work has been done on the average approximately L/(L+S)*N players should choose account general class of problems that involve asymmetric allocations. This L. This proportion is an equilibrium because, regardless of account research fills this gap by developing a simple yet versatile Two-Ac- choice, each competitor stands to earn $(L+S)/N, and no competitor count Game to study the asymmetric resource problem. We found has an incentive to deviate and choose a different account. the asymmetry to be critical for behavior—while extant work has Behaviorally, however, people may not adopt equilibrium strat- yielded little evidence of systematic deviations from equilibrium egies. If the proportion of players choosing the large account exceeds strategies, we found a significant under-shooting bias across differ- L/(L+S), then those who chose the large account will stand to earn ent populations, different domains, and different levels of resource less than those who chose the small account; we term this outcome asymmetries. Additionally, we show that this bias vanishes if the over-shooting. 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