Discount Rates and Academic Mau-Mauing
Will Wilkinson ably takes on the idea that economists have a whole lot to say about what discount rates should be used in comparing costs and benefits in the debate over global warming. I have a more aggressive take: I dispute that we should care about discount rates, per se, at all.
Let me start with a stylized example to illustrate why. Suppose you were presented with two alternative policies to deal with global warming, A & B. A is roughly speaking, do nothing, and B is roughly speaking, a stiff global carbon tax. Let’s further assume that scientists, agronomists and so forth have constructed a good estimate for the GDP of the planet for each year 2010, 20011, and so on out to, say, 2260 (i.e., 250 years from now). That is, you have for policy A a list of 250 numbers, each of which is the projected global GDP for each year; and you have an analogous list for policy B. Let’s further assume that global GDP over the next 250 years is all you care about, and that these are the only two options. You are emperor of the world. How would you decide which policy to pursue?
One way to do this would be to create a “discounting function”, of greater or lower complexity, that can be applied to any list of GDP estimates by year to generate one number, the present value of this list. You could apply this discounting function to the list of projected GDPs for options A and B, and then choose the policy that has the higher present value. Alternatively, you could simply look at the two lists of GDP projections for policy A and policy B side-by-side, and choose the one that you think is better. In the example given, I would always employ the second method.
Why should I believe that there is any discounting function relevant to global warming that exists in closed form? I have a set of preferences for comparing current to future scenarios of projected costs vs. benefits. Much of the knowledge that informs this set of preferences is tacit and/or contingent on elements of the scenarios that I didn’t list comprehensively in advance, but react to as I am presented with specific scenarios. This is of particular practical importance in a case like global warming which operates across a scope – centuries of time across the globe – in which many of the embedded assumptions that I use when making discounting assumptions in day-to-day life will likely be violated. If an economist can’t find a function that encompasses these, I’m not necessarily irrational; the economist just can’t model my beliefs in a way that he finds convenient. The discounting function is merely a heuristic, not some straightjacket that I have agreed to be bound by just because I haven’t disputed its assumptions.
The primary practical use for these discounting functions in global warming analysis is to have a function that allows integrated environment-economics models to search a wide space of possible policies automatically with a commonly-applied set of explicit assumptions without requiring human intervention to consider each model run. When it comes time to look at the policies that the model says are best, I would always want to see the actual data by time period for a variety of “good” scenarios to determine what policy I think makes sense.
Think of these models as being like a Google search. With infinite time and patience, I could review every document on the Web, but I have only finite time. The Google PageRank algorithm imperfectly, but usefully, narrows down the number of documents I need to review; usually, however, I don’t use the “I Feel Lucky” button, and certainly would not in a case where my life depended on it.
Discount rates are not just a means of creating present value calculations, they reflect the opportunity cost of spending money now to address costs in the future. For simplicity assume that all the costs of global warming (or any policy) occur fifty years from now, and all the costs of abatement are incurred now. We can do two things, invest money into abatement now, which will yield returns in the form of reduced costs in the future, or we can invest that money in something else (Bonds, stocks another project, whatever) If we could get a rate of return of say 3% than foregoing this return is a cost of the project and must be taken into account by discounting. Whether or not you believe that a $500 return on a traditional investment is comparable with an estimated $500 return on abatement is a quibble with the monetization of costs and benefits, not the discount rate.
— Kailer · Jun 5, 08:55 PM · #
Kailer:
I don’t follow your argument at all.
Under the hypothetical, we have projected forward the actual economic production of planet Earth under two alternative policies. The projection for each will embody the results of any deployments of resources of any kind and their effects. All the costs created by global warming, as one example, are already embodied in the projections. Unless I’m missing something, what remains to be done is to decide which of these streams of outcomes I prefer.
— Jim Manzi · Jun 5, 09:16 PM · #
Yes, but costs this year are not the same as costs next year. If I am to incur a cost this year in exchange for a benefit next year, I would not agree to it unless I get more tomorrow than I do today, with one minus the ratio of benefits tomorrow to costs today being my personal discount rate. Now you’re right that each of us will have our own time preference, but each of us prefer apples and oranges differently too, yet the cost of an apple and an orange is the price of an apple plus the price of an orange. These prices are set by the market, just as interest rates are. Obviously there are many different interest rates, and the hypothetical social discount rate is immeasurable, but one can be reasonably sure it lies between zero and ten percent based on the rates of return for various investment goods. Any proper CBA ought to report net present benefits for a range of discount rates. I don’t understand why you don’t object to monetize costs using market prices within time periods, but not accross them.
— Kailer · Jun 5, 11:03 PM · #
I’m having a hard time understanding the argument (in particular, what do you mean by “closed form?”—are you using it in a technical sense, or is roughly equivalent to “simple form”? Ditto for “embedded assumptions”).
The crux of things seems to be that fourth paragraph. Are you just supposing that if you were to consider various scenarios, you would be moved to prefer some to others, without the intermediary of a discounting function, and that whatever those preferences might be, they would be just as valuable as your preferences based on a discounting function?
— Justin · Jun 6, 04:35 AM · #
Justin:
I’m having a hard time understanding the argument (in particular, what do you mean by “closed form?”—are you using it in a technical sense, or is roughly equivalent to “simple form”? Ditto for “embedded assumptions”).
I mean a function that can be expressed as an equation integrable over the reals. For all practical purposes, what is meant in plain English as “an equation”.
The crux of things seems to be that fourth paragraph. Are you just supposing that if you were to consider various scenarios, you would be moved to prefer some to others, without the intermediary of a discounting function, and that whatever those preferences might be, they would be just as valuable as your preferences based on a discounting function?
Yes. Even stronger, as a practical matter, as I said in the post, I think the reaction to actual scenarios is far more relaible as an indicator of actual preference than agreement to an abstract discount rate.
— Jim Manzi · Jun 6, 01:24 PM · #
Kailer:
Obviously there are many different interest rates, and the hypothetical social discount rate is immeasurable, but one can be reasonably sure it lies between zero and ten percent based on the rates of return for various investment goods.
As you indicate, there is no one abstract “rate”. I may use one (implicit or explicit) rate for determing how much I demand from my bank for a 6-month CD and a very diffferent one for 250 years of warming damage reduction. Economists may believe that they can decompose the differences into “duration”, “risk” and so forth, but I don’t have to be bound by this structure: my preferences in any given choice are what they are. The preferences themselves are the atomic units of analysis.
I agree with you that as a practical matter, it is unlikly that a rational person would apply an (implicit) dicosunt rate below 0% or above 10% in th case of AGW. But the real debate (taking, say Stern and Nordhaus as end-points) is between something like 1% and 6%. I think, for reasons indicatd in the post, that it is far more reliable to simply assess preference between projections of effect by year (or even grouped by decade) when comparing alternative policies, than it is to try to execute a syllogism of getting agreement to an abstract rate, and then showing that “now that you’ve agreed to this discunt rate, you must accept my conclusion that you prefer policy A to policy B”.
— Jim Manzi · Jun 6, 01:37 PM · #
I’m not sure I see the huge difference between (a) looking at a list of future GDP’s (or whatever) and “choos[ing] the one that you think is better”; and (b) applying a discounting function of some sort. Obviously if you did (b), you’d end up doing (a). But it’s also true that in doing (a) you are implicitly doing (b), or at least, revealing certain things about the sort of discounting you favor, if not the entirety of your personal discount curve.
Also not sure what “closed-form” or “equation integrable over the reals” for a discounting function has to do with anything. Nowhere is it written that discount rates have to come from “equations”; this is a straw-man, who ever said they did?
Moreover, by dismissing them you miss discounting rates’s usefulness in precisely the task you (otherwise correctly) cite as important: “usefully…narrowing down” one’s preferences. In these discussions the precise value of the discounting (let alone whether it’s “integrable over the reals”) is usually far less important than the form – and this is what people are getting at, because for some questions it can be determined what one’s preference ought to be not merely for this or that discounting function, but across a broad range of discounting functions that have the same general shape.
In other words, one can say: ‘if your discounting function is like such-and-such, you’d prefer A and B to C and D.’ In other words you’d get some sorting utility out of the exercise, as you claim to want. This is why it can be important and useful to discuss (rather than poo-poo) discount rates.
— Sonic Charmer · Jun 7, 02:57 AM · #