5.1 Sample Profile
The profile of the respondents presents the following demographic characteristics: average age of 26.50 years, with more women (85) than men (57). The women in the sample are, on average, older than the men (28 versus 24 years). The majority of participants are gainfully employed (62.7%), while 37.3% of them do not carry out paid work. Based on self-declared color/race, 53.5% of participants declared themselves as white, 38.7% as brown or black, 2.8% as yellow, and 4.9% preferred not to declare.
Regarding the level of education, the majority of participants have at least high school education (67.6%), 21 (14.8%) have higher education, 16 (11.3%) with technical course, 4.2% with specialization or MBA, 2 participants (1.4%) have a master's degree (highest level of education in the questionnaire) and 1 respondent (0.7%) had only elementary education. 99.3% of the individuals in the sample finished high school.
In relation to the income level, the majority of individuals have an average monthly income of up to 1 minimum wage (53.5%), and 28.2% between 1 to 2 Brazilian minimum wage (BRL 1,045). Whereas, the majority of individuals have an average monthly family income between 5 to 10 minimum wages (31%), 25.4% between 2 to 5 minimum wages, 23.2% between 10 to 30 minimum wages, and 14.8% between 1 to 2 minimum wages.
In addition to these socioeconomic characteristics, two sessions of questions were added: financial literacy and saving habits. Regarding the financial literacy of the respondents, a scoring criterion was used based on the scale of Lusardi and Mitchell (2014). The participants’ score is the result of the sum of their correct answers, its maximum is 3, when all three questions are answered correctly, and its minimum is 0, when none of the answers is correct. Half of the participants (71 out of 142) got all three questions right, 45 participants (31.7%) got two questions right, 17 participants (12%) got only one question right and 9 participants (6.3%) got all the questions wrong. The best performance was observed in the question about the interest rate, where 83.1% answered correctly, and in the others the success rate is 76.76% and 73.24%, in the questions about inflation and risk diversification, respectively.
As for saving habits, 55 respondents (38.7%) do not make any kind of financial application, 51 respondents (35.9%) claim to have some money saved for emergencies, 36 respondents (25.4%) claim to have more resources saved than just for emergencies. Still, when the participants were asked about what kind of saver they were, 24 participants (16.9%) claim they cannot save money, whereas, among savers, the majority of the survey participants (54.9%) claim to save irregularly, and 28.2% claim to save regularly.
5.2 Results of the conditions for the implicit annual interest rates
To make relevant comparisons between anchoring conditions, horizons, and saved amounts, it was necessary to determine the implicit annual rates with a two-step process. In the first step, the points at which a participant is indifferent between consuming today or saving money for the future were determined, thus capturing the average of the upper and lower limits of the future values chosen by the participants, the indifference points. In the second step, the indifference points are used to calculate the corresponding implicit annual interest rates, as proposed in Thaler (1981) and Corneille et al. (2021).
In Panel A of Table 3, the average indifference points are presented depending on both the anchoring condition and the amount saved. Panel B of Table 3 presents the average implicit annual interest rates based on the indifference points reported in Panel A in each scenario (High and Low).
Table 3 - Average indifference points and implied interest rates
|
|
Time horizon
|
Condition
|
1 year
|
10 years
|
Panel A: Midpoints of Indifference
|
|
|
Ascendant (High - BRL 20,000)
|
BRL 20.045.33
|
BRL 20.949.69
|
Ascending (Low - BRL 500)
|
BRL 501.13
|
BRL 527.24
|
Descending (High - BRL 20,000)
|
BRL 20.054.55
|
BRL 20.573.98
|
Descending (Low - BRL 500)
|
BRL 502.27
|
BRL 524.48
|
Panel B: Implicit Interest Rates
|
|
|
Ascendant (High - BRL 20,000)
|
0.23%
|
0.46%
|
Ascending (Low - BRL 500)
|
0.23%
|
0.52%
|
Descending (High - BRL 20,000)
|
0.28%
|
0.28%
|
Descending (Low - BRL 500)
|
0.46%
|
0.47%
|
Source: experimental results.
The first hypothesis of this study postulates that participants should demand lower annual interest rates for a higher saved value (BRL 20,000) than for a low value (BRL 500) (hypothesis 1a), and it is expected that the implicit annual interest rates will decrease as the time horizon increases, as NRRs are associated with the loss in purchasing power of the invested capital. Thus, participants should be more likely to tolerate NRRs for the low savings value (BRL 500) than for the high value (BRL 20,000). We performed the Mann Whitney U test, two-tailed, to compare the difference in the means of the implicit annual interest rates between the low and high values for each time horizon, and also between the time horizons of 1 and 10 years.
Between time horizons, the difference between the implicit annual interest rates is negative and significant both for the low value (U=864.5; p<0.05, Panel A of Table 4), and for the high value (U=793; p<0.05, Panel B of Table 4). This evidence supports our first hypothesis (1b), namely, that implicit annual interest rates decrease as the time horizon increases (Table 4).
Table 4 - Differences in Average Annual Implicit Interest Rates – Hyperbolic Discounting
|
|
Time Horizon
|
Annual Implied Interest Rates
|
|
|
Panel A: Time horizons (Low - BRL 500)
|
|
Differences(1 ano - 10 anos)
|
0.237%
|
|
U
|
864.5
|
|
p-value
|
0.013**
|
|
Panel B: Time horizons (High - R$ 20,000)
|
|
Differences (1 year - 10 years)
|
-0.237%
|
|
U
|
793
|
|
p-value
|
0.03**
|
|
Note. This table shows the differences between the implied average annual interest rates for the time horizons, the differences between the average annual interest rates related to the highest and lowest amounts, and the corresponding U and p-values conducted with the two-tailed Mann-Whitney U test, ** and * indicate significance at 1%, 5% and 10%, respectively.
|
|
|
|
|
For the ascending rate condition, the difference between the implicit annual interest rates between high and low values is negative and significant only at the 1-year horizon, and only at the 10% level (Panel A of Table 5). The difference between the 1 and 10 year horizons is negative and significant (Panel B of Table 5). In the descending rate condition, the difference between the implicit annual interest rates between high and low values is negative and significant for both the short horizon (U=117; p<0.05) and the long horizon (U=87; p<0.05, Panel B of Table 5).
These findings reveal a magnitude effect in the descending condition for both time horizons and in the ascending condition only for the shorter horizon, of 1 year. The average implicit annual interest rates are significantly lower for the high savings value. This evidence partially supports our first hypothesis (1a).
Table 5 - Differences in annual average implicit interest rates – magnitude effect
|
|
Time horizon
|
Condition
|
1 year
|
10 years
|
Panel A: Ascending Condition
|
|
|
Differences (High - Low)
|
0.00%
|
-0.395%
|
U
|
195
|
115.50
|
p-value
|
0.07*
|
0.15
|
|
|
|
Panel B: Descendant Condition
|
|
|
Differences (High - Low)
|
-0.459%
|
0.00%
|
U
|
117
|
87
|
p-value
|
0.048**
|
0.045**
|
Note. This table presents the implied average annual interest rates for both anchoring conditions over all time horizons, the differences between the average annual interest rates related to the highest and lowest amounts, and the corresponding U and p-values conducted with the two-tailed Mann-Whitney U test. Panel A focuses on the differences in the Ascending condition, while Panel B refers to the Descending condition, ** and * indicate significance at 1%, 5% and 10%, respectively.
|
Due to the anchoring bias, it is expected that the average implicit annual interest rates will be lower in the Ascending condition than in the Descending condition (Kahneman et al., 1986). Table 6 presents the results of the Mann Whitney U test, two-tailed, evaluating the differences in the average implicit annual interest rates between the two anchoring conditions. Only for the high amount at the 10-year horizon, is the implicit annual interest rate significantly lower than the Descending condition (U=209.5; p<0.01, Panel A of Table 6). These findings partially support hypothesis 3, that ascending real rates lead to a greater tolerance of NRRs.
Table 6 - Differences in annual average implicit interest rates – anchoring bias
|
|
Time Horizon
|
Condition
|
1 years
|
10 years
|
Panel A: High ammount
|
|
|
Differences (Descending - Ascending)
|
0.009%
|
0.024%
|
U
|
217
|
209.5
|
p-value
|
0.143
|
0.007**
|
Panel B: Low ammount
|
|
|
Differences (Descending - Ascending)
|
-0.45%
|
0.418%
|
U
|
171
|
221
|
p-value
|
0.546
|
0.115
|
Note: This table presents the annual average implicit interest rates for both anchoring conditions over all time horizons, the differences between the annual average implicit interest rates for the maximum and minimum amounts separately, and the corresponding U and p-values conducted with the two-tailed Mann-Whitney U test. Panel A focuses on differences in annual implied interest rates for the high value of savings, while Panel B refers to those for the low value of savings. , ** and * indicate significance at 1%, 5% and 10%, respectively.
|
In order to test hypothesis 2 that participants exposed to an inflation scenario (without going through the explanation about real interest rates), should be more likely to tolerate NRRs in their savings, we performed the same analyses as above, but now inserting the control variable about the provision of information about the real interest rate. Significant differences were found in the average annual implicit interest rates between the treatment group and the control group, but only in the ascending condition at the 10-year horizon for the high value (U=65; p<0.05, Panel B of Table 7), and descending condition for low value (U=48; p<0.048, Panel D of Table 7). These findings partially support the second hypothesis (Table 7).
Table 7 - Differences in the annual mean implicit interest rates of the treatment and control groups
|
|
|
Time horizon
|
|
Condition
|
1 year
|
10 years
|
|
Panel A: Ascending Condition for High Amount
|
|
|
|
Differences (Treatment - Control)
|
0.00%
|
0.395%
|
|
U
|
38.5
|
29
|
|
p-value
|
0.836
|
0.952
|
|
Panel B: Upward Condition for Low Amount
|
|
|
|
Differences (Treatment - Control)
|
0.00%
|
0.789%
|
|
In the
|
19.0
|
65.0
|
|
p-value
|
0.186
|
0.045*
|
|
Panel C: Descending Condition for High Amount
|
|
|
|
Differences (Treatment - Control)
|
0.917%
|
0.00%
|
|
U
|
63.0
|
41.0
|
|
p-value
|
0.214
|
0.57
|
|
Panel D: Descending Condition for Low Amount
|
|
|
|
Differences (Treatment - Control)
|
0.00%
|
0.772%
|
|
U
|
36.0
|
48.0
|
|
p-value
|
1
|
0.048*
|
|
Note. This table presents the implicit average annual interest rates of the treatment and control groups, for both anchoring conditions over all time horizons, the differences between the average annual interest rates related to the highest and lowest amounts, and the corresponding U and p-values conducted with the Mann-Whitney U test, two-tailed. Panel A focuses on the differences in the Ascending condition for high values, Panel B refers to the differences in the Ascending condition for lower values, and nhow much Panels C and D refer to the Descending condition. , ** and * indicate significance at 1%, 5% and 10%, respectively.
|
|
|
In addition, in order to test hypotheses 4 and 5, the Kruskal-Wallis test and the non-parametric one-way ANOVA test were performed. Both indicate that there are effects of the saving habit on the annual implicit interest rates (X2 (2) = 6.035; p< 0.05) and of the level of financial literacy on the annual implicit interest rates (X2 (2) = 16.309; p< 0.001). Pairwise comparisons (or post-hoc) showed significant differences, between saving regularly and not saving, and between the “low” level of financial literacy and the “high” and “higher” levels. In addition, the Spearman correlation coefficient indicated a positive correlation (0.169; p< 0.05) between the participant being a regular saver and their annual implicit interest rates, and a negative correlation (-0.264; p< 0.01) between the low level of financial literacy and the annual implicit interest rates.
5.3 Variables that influence the tolerance of NRRs
To evaluate the tolerance of NRRs, we estimated a binary Logit model. Initially, the possible presence of multicollinearity was analyzed using the Variance Inflation Factor (VIF), setting the cut-off for the VIF value at 5.3 corresponding to adjusted R-squared of 0.90.
The dependent variable Tolerance to NRRs (TNRR,d), takes a value equal to 1 when the annual interest rate associated with a certain decision d made by participant i is negative, and zero otherwise. To represent the non-metric independent variables (whether ordinal or nominal), they were transformed into dichotomous variables, using the fact that any ordinal or nominal variable with k categories can be represented by k – 1 dichotomous variables (Hair et al.,2019). The procedure was performed for all variables (Table 8).
Table 8 - Representation and coding of non-metric variables with dichotomous variables
|
Non-metric variable
|
Dichotomous variables
|
Non-metric variable
|
Dichotomous variables
|
Framing group
|
Sex
|
X1
|
Treatment group
|
1
|
X17
|
Male
|
0
|
X2
|
Control group
|
0
|
X18
|
Female
|
1
|
|
|
|
|
|
|
Non-metric variable
|
Dichotomous variables
|
Non-metric variable
|
Dichotomous variables
|
Anchoring conditions
|
Self-declaration of color
|
X3
|
Descendant
|
0
|
X19
|
White
|
1
|
X4
|
Ascending
|
1
|
X20
|
Non-White
|
0
|
Non-metric variable
|
Dichotomous variables
|
Non-metric variable
|
Dichotomous variables
|
Amounts saved
|
Level of Education
|
X5
|
High (BRL 20.000)
|
1
|
X21
|
< Higher Education
|
0
|
X6
|
Low (BRL 500)
|
0
|
X22
|
≥ Higher Education
|
1
|
Non-metric variable
|
Dichotomous variables
|
Non-metric variable
|
Dichotomous variables
|
Time horizon
|
Engages in gainful employment
|
X7
|
10 years
|
1
|
X23
|
Yes
|
1
|
X8
|
1 year
|
0
|
X24
|
No
|
0
|
Non-metric variable
|
Dichotomous variables
|
Non-metric variable
|
Dichotomous variables
|
Level of financial literacy
|
Monthly family income
|
X9
|
Lowest level
|
0 0 0
|
X25
|
if < $1,212
|
0
|
X10
|
Low level
|
1 0 0
|
X26
|
if ≥ $1,212 & < $2,424
|
1
|
X11
|
High level
|
0 1 0
|
|
|
|
X12
|
Highest level
|
0 0 1
|
Non-metric variable
|
Dichotomous variables
|
|
|
|
Own monthly income
|
Non-metric variable
|
Dichotomous variables
|
X27
|
if < $2,424
|
0
|
Saving habit
|
X28
|
if ≥ $2,424
|
1
|
X13
|
Non-saver
|
0
|
|
|
|
X14
|
Saver
|
1
|
|
|
|
|
|
|
Metric Variable
|
|
Non-metric variable
|
Dichotomous variables
|
Age
|
Saving habit
|
X29
|
Age (in years)
|
|
X15
|
It has no financial application.
|
0
|
|
|
|
X1 6
|
It has financial application.
|
1
|
|
|
|
This encoding can be synthesized in the following general specification of the differences investigated in the following Logit model:
where Xk represents each group of dichotomous variables in the regressor matrix. Table 9 presents the results of three estimated models, and Table 10 their fit statistics.
Table 9 - Model Coefficients - Acceptance of Negative Interest Rates
|
|
Model 1
|
Model 2
|
Model 3
|
Predictor
|
B
|
Exp(b)
|
B
|
Exp(b)
|
B
|
Exp(b)
|
Intercept
|
-0,05
|
|
0.951
|
-0.175
|
|
0.84
|
1.259
|
|
0.284
|
X1
|
-0.665
|
*
|
0.514
|
-0.676
|
*
|
0.509
|
-0.663
|
*
|
0.512
|
X4
|
0.210
|
|
0.810
|
0.229
|
|
0.796
|
-0.205
|
|
0.814
|
X5
|
0.745
|
**
|
2.106
|
0.754
|
**
|
2.126
|
0.65
|
*
|
1.916
|
X7
|
-0.404
|
|
0.668
|
-0.412
|
|
0.662
|
-0.507
|
|
0.602
|
X10
|
|
|
|
0.531
|
|
1.701
|
0.718
|
|
2,051
|
X11
|
|
|
|
-0.221
|
|
0.802
|
-0.182
|
|
0.934
|
X12
|
|
|
|
0.016
|
|
1.016
|
0.107
|
|
1.113
|
X14
|
|
|
|
-0.423
|
|
0.655
|
-0.106
|
|
0.899
|
X1 6
|
|
|
|
0.787
|
*
|
2.196
|
0.767
|
|
2.152
|
X18
|
|
|
|
|
|
|
0.176
|
|
0.838
|
X20
|
|
|
|
|
|
|
-0.230
|
|
0.795
|
X22
|
|
|
|
|
|
|
-0.152
|
|
0.838
|
X23
|
|
|
|
|
|
|
0.345
|
|
1.378
|
X26
|
|
|
|
|
|
|
-0.273
|
|
0.761
|
X28
|
|
|
|
|
|
|
0.353
|
|
1.404
|
X29
|
|
|
|
|
|
|
-0.025
|
|
1.025
|
Note: The estimates represent the Log of the Chances of Tolerating Negative Interest Rates, ** and * indicate significance at 1%, 5% and 10%, respectively. β = logistic coefficient, Exp(β) = exponential coefficient.
|
Table 10 - Model Adjustment Measures
|
Model
|
McFadden’s R²
|
Cox & Snell’s R²
|
R² by Nagelkerke
|
–2 Log-likelihood
|
d.f.
|
p
|
1
|
0,055
|
0,072
|
0,097
|
10,626
|
3
|
0,031
|
2
|
0,076
|
0,099
|
0,132
|
14,746
|
9
|
0,098
|
3
|
0,093
|
0,120
|
0,160
|
18,115
|
16
|
0,323
|
The estimates of the logit models indicate that the tolerance to NRRs is higher when the amount saved is high (result associated with the positive and significant coefficient of the variable X5) and this result is robust in the alternative specifications in models 2 and 3 that include the control variables, related to the socioeconomic characteristics of the respondents. That is, participants who made decisions in the condition of a high savings value (BRL 20,000.00) are more likely to tolerate NRRs than participants in the low value condition (BRL 500.00), a result that is consistent with the magnitude effect postulated in hypothesis 1a. A possible reason for this effect is that individuals tend to evaluate this difference in nominal terms, so the interest to be paid seems lower in absolute terms for the small amount of savings than for the corresponding interest on the large amount of savings.
For participants exposed to an inflation scenario, but who receive an explanation about real interest rates (i.e., from the treatment group, represented by the coefficient X1), the chances of a decision to tolerate NRRs in their savings decrease by approximately 48.75%, a result that is also robust in the alternative specifications of models 2 and 3. And, therefore, in line with the second hypothesis (expressed in sub-hypotheses 2a and 2b), in which the presence, respectively, of monetary illusion, in line with previous studies by Wilcox (1990), Diamond et al. (1997), Hordijk (2020) and Darriet et al. (2020) and loss aversion, in line with the studies by Ganzach and Wohl (2018), Lian et al. (2018) and Corneille et al. (2021), were tested.
However, the estimated model does not show significant differences with respect to the variation in the time horizon, represented by the coefficient of the dichotomous variable X7 and associated with hypothesis 1b, nor for the anchoring condition (coefficient for X4, referring to hypothesis 3). That is, of the initial hypotheses of the study, represented in model 1, there is no contribution of the effects of anchoring in ascending interest rates - a result that may be related to the magnitude of the variation in rates - and neither to the time horizon, which was fixed at 2 periods only and without a longitudinal follow-up of the participants' choices.
Finally, no effects were found of saving habits (coef.X14, referring to hypothesis 4), and financial literacy (coefficients for variables X10; X10; X12, referring to hypothesis 5) in models 2 and 3, and neither do they affect the significance of the results of hypotheses 1 and 2. This result may be associated with the fact that, for hypotheses 4 and 5, the absence of experimental manipulation of these components - saving habits and financial literacy - as well as the characteristics of the sample - mostly composed of university students - may be influencing these results.