Abstract
Environmental goods such as carbon abatement or green space development often generate benefit streams that may not occur until far into the future. How individual consumers value such amenities, therefore, depends critically on the discount rate. The usual assumption is that agents discount future values using constant, exponential rate, but there is some evidence from the lab suggesting that discount functions are more likely quasi-hyperbolic. We compare estimates of subjects’ rate of intertemporal time preference for financial rewards and environmental goods using multiple price-list and a new matrix multiple price list approaches. Our objective is to determine if discount functions for environmental and monetary goods differ, and to estimate the structure of discounting in both contexts. We find that financial discount functions are not hyperbolic, but those for environmental goods are. Discount rates for environmental goods are generally lower than for financial rewards, but are still above zero. Consumers, therefore, value long-lived environmental goods differently than financial goods.
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Notes
As Cropper and Laibson (1999) and Karp (2005) explain, observed consumption paths of individuals with hyperbolic preferences can be explained by allowing them to play games with each of their “intertemporal selves.” The resulting consumption path for a finite-lived individual can be shown to be a unique, sub-game perfect equilibrium of these games and is observationally equivalent to the consumption path for an individual with exponential time preferences (Cropper and Laibson 1999).
Weikard and Zhu (2005) argue for “dual discounting” or the application of different discount rates for environmental and consumption goods, and provide a theoretical rationale for why dual discounting is appropriate.
It is important to note that students may graduate and some may move from the region before the green space is restored making it highly unlikely that they would benefit from the improvements. That said, the majority of the student-subjects are local and intend to stay in the Puget Sound area.
Previous research shows that 24 months is sufficient to identify the hypothesized curvature in the discount function. Benhabib et al. (2010), for example, use a maximum horizon of 6 months. Any longer than 24 months and the incentive-compatibility of our experimental design would no longer be credible.
Note that these interest rate calculations were not shown to subjects on their choice screen, but are revealed in Table 1 to show the exact discount rates implied by each choice.
Ideally, or maximum delay would be longer than 24 months to identify truly long-term discount rates. However, decisions regarding rewards more than 2-years out are no longer plausibly incentive compatible as subjects are not likely to expect payment after a 2-year delay.
Similar to the MPL, subjects may also exhibit “multiple switch points” (Andersen et al. 2006a) by moving among columns as they move down. However, as Andersen et al. (2006a) explain, such behavior may be due to the subject being indifferent between the options presented, and that the only requirement is that the responses exhibit consistency on average over the responses. Viewed from the perspective of utility theory, “...preferences are only required to be weakly convex rather than strictly convex...” (Andersen et al. 2006a).
The three charitable organizations are: Seattle Parks Foundation for park restoration, Puget Soundkeeper Alliance for storm water quality, and Bonneville Environmental Foundation for reductions of carbon emissions. Each non-profit was detailed at the beginning of the appropriate section of the survey.
This development is based on Benhabib et al. (2010).
Benhabib et al. (2010) specify and estimate perhaps the most general empirical model, but find that their nesting parameter is estimated imprecisely in nearly all specifications with individual-level models. It is not clear from their data how their data are able to identify the separate fixed- and variable-cost effects that they report.
Using the decreasing impatience (DI) criteria for a discount function to capture hyperbolic discounting, it is straightforward to show that the function we choose exhibits DI for \(\alpha >1\), but not for \(\alpha <1.\) Specifically, the second derivative of the log-discount function in our case is \(d^{2}\ln D/dt^{2}=-\alpha (\alpha -1)\delta _{h}t^{\alpha -2},\) which is only negative when \(\alpha >1.\)
This factor is also akin to the “...additive constant...” of Becker and Mulligan (1997).
A reviewer points out that these behaviors are well-known to be addictive, so may be out of the subject’s control. However, according to the rational addiction model of Becker and Murphy (1988), addictive behaviors are fully consistent with individuals who maximize utility, have stable preferences, and discount the future in a rational way. Our including these variables in the model rests on this assumption.
The first-stage function, estimated with non-linear least squares, also consists of a constant term and discount-rate estimate. These parameters, each of which are statistically significant, are available upon request.
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Richards, T.J., Green, G.P. Environmental Choices and Hyperbolic Discounting: An Experimental Analysis. Environ Resource Econ 62, 83–103 (2015). https://doi.org/10.1007/s10640-014-9816-6
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DOI: https://doi.org/10.1007/s10640-014-9816-6