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2016 | OriginalPaper | Buchkapitel

12. Hyperbolic Discounting, the Sign Effect, and the Body Mass Index

verfasst von : Shinsuke Ikeda, Myong-Il Kang, Fumio Ohtake

Erschienen in: Behavioral Economics of Preferences, Choices, and Happiness

Verlag: Springer Japan

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Abstract

Analysis of a broad survey of Japanese adults confirms that time discounting relates to body weight, not only via impatience, but also via hyperbolic discounting, proxied by inclination toward procrastination, and the sign effect, where future negative payoffs are discounted at a lower rate than future positive payoffs. Body mass index is positively associated with survey responses indicative of impatience and hyperbolic discounting, and negatively associated with those indicative of the sign effect. A one-unit increase in the degree of procrastination is associated with a 2.81 percentage-point increase in the probability of being obese. Subjects exhibiting the sign effect show a 3.69 percentage-point lower probability of being obese and a 4.02 percentage-point higher probability of being underweight than those without the sign effect. These effects are substantial compared with the prevalence rates of the corresponding body mass status. Obesity and underweight thus result in part from the temporal decision biases.

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Note, however, that associations between discount rates and body mass status do not necessarily imply “rational” obesity. People’s time preferences may be controlled by external pressures from corporations. For example, fast food companies do not want people to wait until tomorrow to consume and will coerce them into having a high discount rate by using various advertisements.

Shapiro (2005) shows that participants in low-income families who were provided food stamps by the U.S. government displayed less smoothed time profiles of caloric intake that are consistent with hyperbolic discounting. There are studies reporting that participations in the food stamp program is related to obesity (e.g., Chen et al. 2005). Combining these results implies that hyperbolic discounting may relate to the incidence of obesity. By showing empirically that obese people likely fail to use information and commitment devices to protect long-term heath, Scharff (2009) provides indirect evidences to the association between hyperbolic discounting and body mass formation.

For the English-language version of the report, see Examination Committee (2002).

The use of the WHO criterion for Asian populations has been criticized since Asian populations have a high body fat deposit at a lower BMI than Caucasians, and type 2 diabetes mellitus and cardiovascular diseases are prevalent even with a BMI lower than 25 in Asian countries. For detailed discussions, see Low et al. (2009).

The same obesity criterion as that of JSSO was provided for Asian populations by the International Association for the Study of Obesity and the International Obesity Task Force (2000). See also WHO Expert Consultation (2004), which advised further study on appropriate ethnic-specific BMI cut-off points.

The JSSO criteria for underweight (BMI < 18.5) and ideal weight (BMI = 22), which are the same as the corresponding WHO criteria, are based on the research by Tokunaga et al. (1991). By using the sample of the Japanese adults, they estimated quadratic regression curves relating BMI to morbidity, thereby showing that (i) the BMI value associated with the lowest morbidity was 22.2 for males and 21.9 for females, and (ii) the morbidity rates at a BMI of 18.5 are as high as those at a BMI of 25.

For detailed comparison between the body mass distributions of JHS05 and NSHN04, see Tables 12.15 through 12.18 in Appendix A.2.

Following Cawley (2004), Chou et al. (2004) corrected for the underreporting biases in the original self-reported data by (1) estimating the quadratic relations between actual and self-reported values of weight and height using the Third National Health and Nutrition Examination Survey (NHANES III), U.S.A., and (2) applying the estimated relations to their American self-reported data (the BRFSS) pertaining to weight and height to obtain bias-corrected data and to compute bias-corrected BMI. Michaud et al. (2007) applied the quadratic correction function estimated by Burkhauser and Cawley (2008) to their European self-reported data. In Japan, we have no data set that, like NHANES III, is composed of self-reported as well as actually measured data of the same subjects. Furthermore, it might be questionable to directly apply Burkhauser and Cawley’s (2008) estimated correction function to the Japanese data because the BMI distribution in Japan and the definition of obesity therein both differ from those in Western countries.

Some respondents switched their choices between “A” and “B” more than once. As in the literature (e.g., Harrison et al. 2002), we removed those data from the sample.

Although the standardized average DISCRATE of the elicited discount rates should theoretically satisfy \( E\left(\mathrm{DISCRATE}\right) = 0 \) and \( \upsigma \left(\mathrm{DISCRATE}\right)=1 \), neither of the equalities is fulfilled, as seen in Table 12.5. This is due to the fact that the number of effective responses differs in the five discount rate questions.

Instead of DISCRATE, we also tried for an alternative impatience index factor scores to the first factor that was extracted by factor analysis from the discount rate data. Although our main results did not change qualitatively, the significance levels were slightly weakened compared with the case in which DISCRATE is used for the impatience variable.

In addition, although we have not included the results of the t test in Table 12.4, DR₃, the discount rate for JPY 10,000 is significantly higher than DR₄, applied for JPY 1 million, implying that people are more patient in the case of larger amounts than in the case of smaller amounts. This tendency is called the magnitude effect (e.g., Benzion et al. 1989; Frederick et al. 2002).

Although the means of DR₁ and DR₂ do not differ greatly, the mean of HYPERBOL is high (61.1 %). This is because, even when in the corresponding two choice tables like Table 12.3, a respondent’s choice switches from “A” to “B” at the same step, say, when the implied interest rate moves from 20 to 50 %, the estimate of DR₁, obtained by the method of Kimball et al. (2005), is larger than that of DR₂, reflecting the fact that the average respondents switch from “A” to “B” at a higher interest rate.

In Japanese elementary and high schools, students are usually given many homework assignments during vacations.

This is probably because of multicollinearity between DISCRATE and PROCR.

We also conducted the same analysis by using the money amount data of debt, instead of the debt holding dummy DEBT. The results including those of body mass regressions below were very similar to the case of DEBT, except that the negative correlation between debt and the sign effect was insignificant, unlike in Table 12.6, when the debt amount was used.

For example, Chapman (1995) reports that monetary discount rates do not have a strong explanatory power for intertemporal choices regarding health investments. In fact, in Borghans and Golsteyn (2006), monetary discount rates elicited from hypothetical pecuniary choices do not display as strong correlations with BMI as do other impatience proxies that are constructed from responses to behavioral and/or psychological questions.

Smoking suppresses appetite and reduces BMI (e.g., Michaud et al. 2007). As is often stressed in the literature (e.g., Becker and Murphy 1988; Khwaja et al. 2007), less patient people are likely to smoke more since the future loss caused by smoking is likely to be discounted more intensely. Unless the smoking habit is controlled for, true positive correlation between BMI and impatience, if present, might be underestimated due to the confounding negative correlation via smoking. The same logic is also true for the correlations of BMI with hyperbolic discounting and the sign effect. By reporting the regression results for BMI when smoking is not controlled for, Appendix A.3 shows that these predictions hold fairly valid.

Even when the effects of the regional and occupational differences are controlled for by adding the prefecture and occupation dummies to the set of the explanatory variables, the main results do not change substantially. See Ikeda et al. (2009).

Our data of time discounting variables contain measurement errors due to decision errors (see, e.g., the special issue of Experimental Economics, introduced by Starmer and Bardsley 2005). Especially the measurement errors of HYPERBOL and SIGN might be magnified as they are constructed based on the differences of two discount rates. The weakness of the results regarding HYPERBOL may be partially attributable to underestimation bias due to measurement errors.

The accuracy of BMI in diagnosing obesity is known to be limited especially for males because muscular persons can have large BMI even when they are not really fat (see, e.g., Burkhauser and Cawley 2008; and Romero-Corral et al. 2008). The poor performance for the male sample may be partially attributable to this property of BMI. If exercise habits need patience, patient men are likely to be muscular and hence have a high BMI, which makes true positive correlations between obesity and impatience underestimated unless the exercise habits are controlled for.

As for associations of BMI with the control variables, Table 12.8 shows that (i) males have significantly greater BMI than females, and (ii) BMI depends non-monotonically on age, per capita household income, and work hours. Finding (i) contrasts to the tendency in Western countries (e.g., Komlos et al. 2004; Borghans and Golsteyn 2006). The U-shaped relation between BMI and income in finding (ii) is in contrast with monotonic, negative correlations between the two which are observed in Western countries (e.g., Chou et al. 2004; Zagorsky 2005). For detailed discussions, see Ikeda et al. (2009).

These results remain unchanged even when the probabilities of being obese, severely obese, and underweight are jointly estimated by estimating multivariate probit models with correlated error terms. For the results of the multivariate probit regression, see Ikeda et al. (2009).

Taiwan’s Bureau of Health Promotion is drafting a bill to levy the special tax on unhealthy food leading to obesity.

As another example, Japan’s Ministry of Health, Labour and Welfare started in 2008 the Specific Health Check-Up System, which aimed at an early detection of metabolic syndrome and obesity. In the system, the insurers of health insurances are required to check up every year the body mass status of the people insured, and give practical advice for healthier life to the insured who are diagnosed with metabolic syndrome, or in danger of developing metabolic syndrome. Because receiving compulsory consultation takes time and psychological costs, the system raises the present costs of being obese for incipiently obese people.

As for the information-oriented policy, the Nutrition Labeling and Education Act, which took effect in 1994 in U.S., made labeling mandatory for most processed food. Varyam and Cawley (2006) report a negative association between implementation of the new labels and body weight among non-Hispanic white women.

For the degrees of obesity in the JSSO criterion, see Table 12.1.

The significance levels in the multinomial probit regressions are much lower than in the binary probit regressions in the text because the number of parameters to be estimated is much larger than in the binary probit regressions.

To check the possibilities that underweight respondents are more likely to manifest high discount rates, hyperbolic discounting, and/or to be without the sign effect than those of normal body mass, we also conducted BMI regressions by using (1) the sample of non-obese respondents of BMI < 25 and (2) the sample of those with BMI ≤ 22. For either sample, however, we could find no significant correlations that are opposite in signs to those obtained in the text.

Because the NSHN04 survey was conducted in November 2004, and the JHS05 survey was conducted in February 2005, possible differences in the two BMI data sets due to time difference can be regarded as negligible.

Our procedure is a modified version of what is proposed in the literature (e.g., Cawley 2004; Chou et al. 2004; Burkhauser and Cawley 2008; and Michaud et al. 2007). See also footnote 9.

See Table 12.1 and the related discussions in Sect. 3.1.

However, the corrections of the downward bias in the SDs remain insufficient for males in their 20s and 30s and for females in their 30s and 40s.

In fact, for the subsample of the respondents who self-reported not to be obese, i.e., those with an uncorrected BMI < 25, the implied magnitude of underreporting, computed as corrected BMI minus uncorrected BMI, displays significant positive correlations with DISCRATE and SIGN after individual attributes including self-reported BMI are adjusted for.

This addendum has been newly written for this book chapter.

The robustness of these tendencies is confirmed for the JHS data of each annual wave from 2005 to 2010.

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Titel: Hyperbolic Discounting, the Sign Effect, and the Body Mass Index
verfasst von: Shinsuke Ikeda
Myong-Il Kang
Fumio Ohtake
Verlag: Springer Japan
Buch: Behavioral Economics of Preferences, Choices, and Happiness
Print ISBN: 978-4-431-55401-1

Electronic ISBN: 978-4-431-55402-8

Copyright-Jahr: 2016
DOI: https://doi.org/10.1007/978-4-431-55402-8_12