Many of the most important decisions we make involve trade-offs between the present and future. How much of my income should I save today for my retirement? What costs should governments incur today to reduce the risk of catastrophic climate change in the (hopefully) distant future? How should businesses allocate investments that pay off in the short run (advertising) and those with riskier, long-run benefits (R&D)?
The finance profession has used the concept of net present value to answer such questions for more than a century. It’s a mathematical formula that allows us to compare and decide between present and future cash flows. The standard (“exponential”) version entails discounting future cash flows on by a fixed percentage each year: A dollar in one year is worth 93 cents today. And a dollar in two years is worth 0.93 multiplied by 0.93 = 0.86 today. One of the consequences of this approach is that events in the distant future have little relevance today. One dollar of cost or benefit in fifty years is worth less than three cents today. So, the benefits of addressing long-term climate change, for example, seem to have little weight today. See the orange line, below.
Researchers in behavioral economics and cognitive psychology have determined that humans make trade-offs differently (no surprise). We tend to discount the earlier years much faster than the later years (blue line, above). For example, we’ll choose $50 today over $100 next year, but prefer $100 in six years to $50 in five years, a logically inconsistent result. This can be described by hyperbolic discounting. One result is that our future selves may regret the inconsistent decisions we’ve made in the past. We’ll overweight the value of the one marshmallow today versus two in fifteen minutes.
Hyperbolic discounting reflects how we like to defer costs and accelerate short term gains, also known as present-bias. It may also reflect brain structure. Decisions about short-term trade-offs are affected by the limbic system, which controls the most basic human emotions (greed, fear) and drives (approach, avoid). Longer-term trade-offs are mediated by the pre-frontal cortex, which handles executive functions that require logical reasoning. In this sense, the hyperbolic discount curve seems to model our brain’s different physical handling of problems with different time frames.
As we used to say in philosophy class: you can’t get an ‘ought’ from an ‘is‘. Just because people tend to use a process that resembles hyperbolic discounting to make trade-offs between the present and the future doesn’t mean that they should. We’ve already seen that it can be logically inconsistent. Pragmatically, it is associated with a lack of willpower, procrastination and drug addictions. It can also reflect a lack of empathy for our future selves. On the other hand, exponential discounting seems to undervalue distant future and both models suffer from challenges in choosing the right parameters.
I believe that neither formula is inherently better or more rational: they both reflect value judgements. A society or individual who values highly the experiences of our future selves or future generations will choose a discount curve that slopes gently in later years (gray line). A politician or CEO whose interests are more short-term will use a curve with a sharp decline in the early years. Decision-makers must pro-actively design the discount function that describes the present/future trade-offs they will accept.
Decision-makers must design the discount function that describes the present/future trade-offs they will accept.
How do you make trade-offs between the present and the future?
Interesting examples. I don’t know how the math is impacted, but it feels to me that talking about saving for retirement is a different animal from climate change. The former is almost certainly an individual or familial necessity for most people. The latter is could potentially effect everyone, some for the better and some for the worse; it’s not clear whether the proposed actions (reducing carbon emissions) will have the desired outcome; and even if some nations take action, other nations could choose not to do the same. Not to mention that the science isn’t as unanimous as proponents of global warming would like everyone to believe. Anyway, if you introduce uncertainty into the equation, it feels to me that the decision making and the willingness to make trade-offs must be impacted. Perhaps the decisions around a hypothetical comet that definitely will hit the Earth in 100 years would make for an interesting comparison with climate change.
Thank you for your comment, LK. I agree the questions are different, each with a unique set of uncertainties and risks. However, causality is clear in both cases. We invest for retirement because we know mathematically that this will improve our personal welfare later on. We ought to invest to address climate change because we know scientifically* that this is very likely to improve social welfare later on.
*http://climate.nasa.gov/scientific-consensus/
Regarding your recent posts on discounting and college, I propose that real option analysis can serve as a fruitful alternative to NPV.
— From Wikipedia
Real options analysis, as a discipline, extends from its application in corporate finance, to decision making under uncertainty in general, adapting the techniques developed for financial options to “real-life” decisions.
For example, R&D managers can use real options valuation to help them allocate their R&D budget among diverse projects; a non-business example might be the decision to join the work force, or rather, to forgo several years of income to attend graduate school.
It, thus, forces decision makers to be explicit about the assumptions underlying their projections, and for this reason ROV is increasingly employed as a tool in business strategy formulation.
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I took a class on real options analysis in undergrad and used this framework help inform my decision to go to grad school, specifically to undertake a 1-year MSc in the UK, opposed to a 2-year MBA in the US.
While you might already be familiar with this method, I figured I would mention it since it is relatively obscure.
For your reference, Investment and Uncertainty by Dixit and Pindyck is the pioneering text on the topic.
Best,
Scott
Excellent point. Thanks, Scott.
Another important distinction is between discounting consequences which are durable or can be traded within a market (which are the often hidden underlying assumptions of the discounting concept) versus consequences which are not and therefore must be consumed or experienced in the current time. The latter are many times discounted at a null or even negative discount rate.
Ricardo, thank you for your comment. Perhaps you could offer an example?