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Clocks on Wall

Logistic Regression

Using a large data set of randomly sampled U.S. households (n = 17,360), I analyzed the relationship between impatience (present bias or beta in a quasi-hyperbolic discounting model) and financial search. Financial search is proxied using a variable measuring financial sources consulted by a household. Impatience is measured via a titration task commonly used in behavioral economics research. The analysis demonstrates that individuals who are more patient (less present-biased) perform more financial search than those who are less patient.

01

Mean Values (per HH)

$96,962 gross income
$4,168 outstanding credit balance
4.3 credit card accounts

Data Description

The data covers consumer financial behavior for 17,360 U.S. households over four years. This data was provided by a third-party entity and selected via random sampling to be representative of the U.S. population. The panel was also oversampled on affluent households (those with household incomes of at least $100K or investable assets of at least $500K).

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Each household provided responses to 117 questions, bringing the total number of records to over 2.03 million.

02

Data Selection

Given the large number of variables per household (117), selecting the correct variables for the DV, IV, and controls was essential. I was interested in the relationship between time preferences/patience (IV) and financial search (DV), so I had first to identify the most representative variables for each. Next, I had to select variables I thought necessary to include as controls, given that they could be related to the IV of interest.

Independent Variable (IV)

The data included a measure for time preferences, making the identification of the IV straightforward. This measure is a titration task asking respondents to select between varying amounts (a smaller-sooner amount and a larger-later amount). The task included six questions, each asking participants whether they would prefer receiving $100 today or various (larger) amounts in twelve months. The six larger-later amounts were $110, $125, $150, $175, $200, and $225, respectively.

 

From the titration task, I computed two time preference variables. The first variable, present bias, primarily reflects beta (in a beta-delta model), according to the reasoning of O’Donoghue and Rabin (2015). This variable uses responses to the choice between $100 now vs. $225 in 12 months and infers that those who prefer $100 now are present biased (coded as 1, else 0) and those who prefer $225 in 12 months are less present biased.

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The second variable was the discount factor (delta), computed as the largest discount factor consistent with a respondent’s choices. For example, respondents who chose $225 in 1 year (over $100 today) but chose $100 today over $200 in 1 year (and all smaller amounts) would be given a value of 100/200 = 0.5. Non-monotonic responses were excluded from the primary analyses, though I tested that the results were robust when including these responses. For this measure, I exclude people with discount factors less than .7 because research has shown that discount factors of that magnitude primarily reflect present bias (see . However, the results from the primary analyses are robust to higher and lower discount rate cut-offs and when a single measure of discounting is used (vs. separate variables for beta and delta).

Controls

From the variables included in the survey, I selected the following as controls: subjective feelings of confidence regarding financial decisions, education level, gross income, current outstanding credit card balance, total number of financial transactions, total number of credit card transactions, percentage of transactions that are credit card transactions, number of credit card accounts, SES, life stage, whether the respondent is employed or not, whether the respondent is Caucasian or not, respondent gender, respondent age, year of data. These variables have been included because they have a potentially confounding relationship to the IV, DV, or both (identified in the data directly via correlational analysis or in prior research on intertemporal preferences).

Dependent Variable (IV)

The DV needs to operationalize financial information search effort. I explored the relationship between search effort and patience, believing that a more extensive information search leads to better financial choices (in this case, credit card choices). Note that this data analysis focuses solely on the relationship between patience and search effort. 

 

Multiple variables in the data could serve as a proxy for financial search efforts. Since I could not observe search directly, I had to select a variable that best represented a respondent's likelihood to gather information for important financial decisions. Two variables in the data met these criteria: (1) "Which of the following did your household use in the last 12 months for information about financial products or services or financial decisions? (select all answers that apply)" (22 response options were provided, including "None of These"), and (2) "How completely do you or someone in your household typically read or listen to financial services advertisements, solicitations, bill inserts, or calls from each source?" The first variable seemed more representative of search- specifically, gathering information from different sources of the respondent's choosing. In contrast, the latter seemed more related to interest in information delivered directly to them (though thorough reading does imply a more significant effort).

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Ultimately, I chose the first variable as it allowed for greater flexibility than the second. Specifically, I could create a variable for any search at all (if at least one box other than "None of These" was selected search variable equal to 1; 0 otherwise) and proxy search effort by adding up the total number of sources considered (under the assumption that gathering information from more sources requires more effort) (amount of search variable equals sum of sources considered, conditional on search being equal to 1). I also concluded that this variable represents intrinsic motivation to search, whereas the second variable indicates extrinsic motivation since rewards are directly or indirectly provided with information. Further, for the second variable, it is hard to distinguish between individuals who receive information but choose not to read it and those who do not receive information at all (e.g., because they have opted out of spam mail) but would read it if they did.

03

Data Cleaning

Since the IVs (intertemporal preferences captured by beta and delta) were based on a titration task, two potential scale misuse issues are possible: responses that show dominated choices (e.g., an individual choosing $110 in twelve months over $100 today but then choosing $100 today over $200 in twelve months), and incomplete responses within the task (individuals only responding to some of the tradeoffs). Below, I describe how I dealt with both of these issues in the primary analyses.

Dominated Choices

Approximately 0.5% of the sample showed some form of dominated choice. This suggested that the overall results were unlikely to be significantly affected by dominated choices. For the primary analyses, I included a dominated flag dummy (equal to 1 if the responses showed a dominated choice pattern, 0 otherwise). In one version of the analyses, I included the dominated responses when calculating beta and delta and then included the dominated dummy variable in the model. For a second version, I dropped any observations with dominated choice patterns. Excluding (vs. including) dominated choices did not change the significance of any effects and effect sizes for the IVs were not significantly different from each other.

Calculating the IVs

I used the titration task to calculate both beta and delta. 

 

For delta (discount rate), I first calculated the indifference point between receiving $100 today and $X in twelve months for each respondent. This amount was calculated as the midpoint value for the individual’s switchover point from the sooner to the later amount. For example, if an individual chose the $100 today option until offered $200 in twelve months, their indifference amount was $188 (I rounded the amounts to the nearest whole integer). A respondent who always chose $100 today had an indifference amount of $238 (the midpoint between the highest offered value, $225, and the hypothetical following greatest amount, $250). From this amount, I then calculated each individual’s annual discount rate as [(indifference amount/ 100)-1/1]. The average discount rate across the sample is 0.78 (SD = 0.47). Higher discount rates correspond to greater impatience.

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For beta (present bias), I used a simple dummy-coded variable equal to one if every tradeoff response showed a preference for the smaller, sooner payment and equal to zero otherwise. While less precise, this coding is a more conservative estimate of the effect of beta on financial search effort.

Incomplete Responses

In the data, approximately 37% of the sample had at least one missing response within the titration task. To deal with missing responses, I wanted to create rules that would retain as much data as possible while remaining conservative in how the retained data was coded.

 

For example, if participants had a response for the last tradeoff but none of the tradeoffs before that, I coded the missing responses in one of two ways, dependent on the choice for the last tradeoff. If the choice for the last tradeoff was the today (sooner) amount, I coded all of the previous tradeoffs as a preference for the today amount; if the choice for the last tradeoff was the amount in twelve months (the later amount), I coded all previous tradeoffs as a preference for the year amount.

 

Sometimes, participants only responded to one of the tradeoffs, and it wasn’t the first or last tradeoff, which makes filling assumptions easier. Whenever a participant who responded in this manner indicated a preference for the larger, later reward, I filled all previous tradeoffs as a preference for the today amount and all subsequent tradeoffs as a preference for the year amount. In other words, I assumed the single response was the switching point for the respondent (where they switched from preferring the sooner amount to the later amount).

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Ultimately, I ran two versions of the model-one with the modified responses included in the calculation of beta and delta and one with any incomplete responses dropped. The results held regardless of the version used.

04

Results

While I ran several robustness checks (some of which are described above), I am only reporting results from two models-one with search (equal to 1 if the respondent performed any search, 0 otherwise), and one with the amount of search performed (equal to the count of financial resources indicated). The latter is conditional on the respondent performing any search at all. These analyses were run separately because the search variable is inflated at 0. While not reported below, all control variables listed above were included in both models.

Model 1: The Effect of Intertemporal Preferences on Financial Search

For this model, I used a weighted logistic regression using the sample weights provided in the survey data (since the data was oversampled on affluent households). A logistic regression was selected because the DV is binary (1 = any search at all is conducted, 0 otherwise). The model includes both beta and delta as IVs.

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In the model (with coefficients reported as odds ratios), I find that beta has a significant negative effect on the likelihood of conducting any financial search (β = 0.67, SE = 0.07, p < .001). A marginal effects analysis shows that present-biased individuals are 8.8% less likely to conduct any financial search than more patient individuals. Similarly, for discount rate, I find that higher discount rates have a significant negative effect on the likelihood of conducting any financial search at all (β = 0.65, SE = 0.05, p < .001). This means that individuals who are more impatient are less likely to conduct any financial search than those who are more patient. Specifically, a marginal effects analysis shows that when the average discount rate increases, individuals are 34.9% less likely to conduct financial search.

Model 2: The Effect of Intertemporal Preferences on the Level of Financial Search Effort

For this model, I used a weighted ordered logistic regression using the sample weights provided in the survey data (since the data was oversampled on affluent households). An ordered logistic regression was selected because the DV is ordinal (count), but the difference between values is not necessarily known (i.e., is an increase from 1 to 2 sources the same as an increase from 5 to 6?). Other specifications for the model were tested, but the ordered logistic offered the greatest fit. The model includes both beta and delta as IVs. Note that the data included in the model is observations for respondents who reported some level of financial search only.

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The model (with coefficients reported as odds ratios), shows a significant negative effect for discount rate (β = 0.77, SE = 0.06, p = .001) and a non-significant effect for beta (β = 1.01, SE = 0.14, p = .94). This suggests that as average discount rates increase, individuals are 23.5% less likely to increase their search for financial information. The non-significant effect of beta could be due to the fact that only 9.39% of the individuals who did any search at all were present-biased.

References

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