The prevalence of hyperbolic discounting: some European evidence

Abstract

Experimental matching data are used from the 2000 Bank of Italy Survey of Household Income and Wealth (SHIW) and the 2000 wave of the Center for Economic Research (CentER) Savings Survey at Tilburg University to compare the relative frequencies of hyperbolic and exponential discounters. Among 3200 Italian respondents and 1400 Dutch respondents, less than a quarter exhibited hyperbolic discounting. This finding is both statistically significant and robust with respect to various assumptions regarding utility; moreover, it holds across a wide variety of economic, social and demographic characteristics. The youngest, poorest, most urban and least educated individuals are the most likely to be hyperbolic discounters. In addition, it is found that hyperbolic discounters accumulate less wealth and are somewhat less likely than exponential discounters to utilize commitment devices to constrain their future choices.

Acknowledgements

This study uses data from the CentER Savings Survey at Tilburg University in the Netherlands; we are grateful to Marcel Das for providing us with access to these data. We also thank the Bank of Italy for access to the Survey of Household Income and Wealth data.

Notes

¹ Regarding preference reversals, Deaton (1992, p. 15) contends, ‘This is not only dynamic inconsistency, it is irrationality’. Acharya and Balvers (2004) likewise find time inconsistent behaviour to be irrational in a model of lifetime maximization.

² Because each household in the survey is represented by a single respondent taken to be the head of the household, the terms ‘household’, ‘respondent’, and ‘individual’ are used interchangeably.

³ The 2000 SHIW was conducted before Italy converted to the Euro. At the time of the survey, 10 million lire were worth approximately US$5000.

⁴ Notice that for any positive reservation price q ₁, positive marginal utility implies that U(y + w + 10 000 000 − q ₁) < U(y + w + 10 000 000); however, if the index of cardinal utility is negative, then U(y + w + 10 000 000)/U(y + w + 10 000 000 − q ₁) < 1, which implies p ₁ < 0. Though a negative rate of time preference is certainly possible (see, for example, Loewenstein and Prelec (1991)), such an outcome makes little sense if one is willing to pay a positive fee to obtain a sum of money now rather than later. Of course, a negative utility index can be made positive by the addition of a constant, but this complicates the empirical analysis substantially without yielding new insights. Thus, for ease of interpretation, one assumes positive utility indices throughout the study.

⁵ Ideally, one would like to take opportunity cost into account by assuming that individuals incorporate the interest rates available on bank deposits into their decision-making. In that case, the one-period discount rate (p ₁) would be defined by

and p ₂ would be defined analogously by

where b ₁ and b ₂ are the annualized, inflation-adjusted, after tax bank rates. Such a formulation would allow one to disentangle truly personal rates of time preference from exogenous market forces. Unfortunately, the data on bank rates in the SHIW are incomplete and somewhat unreliable: the survey asks for an ‘average rate’ without defining the time period, and many respondents failed to answer the question, creating missing values. Thus, like most studies in this genre (see, for example, Benzion et al. (1989)), the study proceeds without market rates, recognizing that the resulting discount rates are thereby distorted. However, the extent of the bias appears to be quite small, and provided that it is consistent across time, it should not affect the relative magnitudes of p ₁ and p ₂. For further discussion of market censoring, see Coller and Williams (1999) or Harrison et al. (2002).

⁶ The logarithmic utility function also displays other convenient properties, including strongly decreasing absolute prudence, as proposed by Kimball (1990). The empirical results below concerning the proportions of hyperbolic discounters are not substantially changed if we assume either a more general form of constant relative risk aversion, U(c) = c ^{1 − R} /(1 − R), where R denotes relative risk aversion, or the constant absolute risk aversion (CARA) function, U(c) = (− e ^{− cA} )/A, where A denotes the degree of absolute risk aversion. (In the latter case, however, the cardinal utility index is negative, and this may create the interpretation difficulty described in note 4.) Nor are the results regarding the prevalence of hyperbolic discounting altered if continuous compounding is assumed.

⁷ To avoid confusion, it is useful to emphasize that in the present notation, subscripts measure temporal distance to the payoff. Thus, p ₁ is the discount rate applied in the final period before payoff, and p ₂ is the rate applied in the preceding period.

⁸ More recently, Ventura (2003) estimated utility discounts assuming constant rates of time preference.

⁹ Inflationary expectations would not appear to play an important role in the context of the 2000 SHIW. The Italian inflation rate (computed from the consumer price index) was extremely low in the period leading up to the survey: 1.88% in 1998, 1.66% in 1999, and 2.5% in 2000.

¹⁰ This aggregation problem also highlights the danger of replacing missing survey responses with means as some prior work, such as Chapman's (1996) study, has done.

¹¹ At the time, 100 000 guilders, or Dutch florin (Dfl.) were worth about US$40 000.

¹² See for example Frederick et al. (2002). Harrison et al. (2002) also found higher discount rates over 6 months than 12 months, but essentially constant rates over 12, 24, and 36-month horizons. In contrast, Benzion et al. (2004) found that for periods up to 12 years and inflation rates up to 7%, students without calculators priced past and future goods in a manner consistent with exponential discounting, whereas for a 20-year horizon and higher inflation rates, students priced goods in a manner more consistent with hyperbolic discounting.

¹³ Missing values for some socio-demographic variables reduced the sample size slightly.

¹⁴ DellaVigna and Malmendier (2003) provide additional evidence that hyperbolic discounters may be naïve in this sense.