DISCOUNTING CLIMATE CHANGE

DISCOUNTING CLIMATE CHANGE: PLANNING FOR AN UNCERTAIN FUTURE
Kenneth J. Arrow,
24 April 1995

All serious economic decisions, public or private, require consideration ofthe future. Typically, a decision is made today, which requires some costs todayor in the near future, In the hope of returns in the future. This pattern ischaracteristic of investments, ... All serious economic decisions, public or private, require consideration ofthe future. Typically, a decision is made today, which requires some costs todayor in the near future, In the hope of returns in the future. This pattern ischaracteristic of investments, ...

The key characteristics of these returns are that they occur in the futureand that they are, usually, uncertain. ... How does the investor decide whether it is worthwhile to invest?He or she is making a comparison between two unlike magnitudes, expendituresand incomes that differ in date and usually in the degree of uncertainty. ... the choice between present and future incomes, even though both seem to bemeasured in the same units, is reflected in the prices paid for these incomes.These are in fact essentially interest rates or discount rates. Incomes of varyingdegrees of uncertainty will also be valued differently. ...

II Thinking About Appropriate Rates of Interest

There are basically two different strands of thought which have to be drawn together to give some judgment as to appropriate rates for discounting benefits.One may be termed valuation of the future; it asks questions about our judgments, how much do we care about future generations, how much do we care about our future selves. Since it will concern benefits to others, valuation of the future is at least in part an ethical judgment. The second strand is the notion of opportunity costs. There are alternative ways of providing for the future. Given that we are going to make an investment, we could, instead of spending resources on abatement of pollution, save andinvest in the production of private goods. This will not prevent global warming, but it will make future generations better off than they would otherwise be and possibly compensate them fully. Suppose, for example, there is a high rate ofreturn in the private sector. This implies that drawing resources from privateinvestment to finance abatement of carbon dioxide production will involve thesacrifice of a large amount of private goods in the future. This diversion implies a high price for avoiding climate change.

Let us examine the opportunity cost argument in more detail. Basic to the existence of alternative investment possibilities is the clearly established fact that production over time generally yields more output than input, although the output emerges later. In principle, whatever amount we desire to put aside for the future can bespent on either abatement or on private investment. (Actually, as we shall see, this proposition may not in fact be true, but, for the moment, let us follow itsimplications.) Both abatement and private investment benefit the future, one by minimizing climate effects, one by producing more ordinary goods. We should, itwould appear invest at the higher rate of return. If in fact we both save and abate,the rates of return in the two activities should be equal. The apparent implication of the opportunity cost argument is that the rate of return on private investment is the appropriate rate to be used for discounting the future in evaluating public investment. Since pretax real rates of return in the corporate sector are estimated at 10% or more, this policy would imply little regard for the future relevant to abatement policies for meeting climate change. The argument, I will claim, is flawed, but it has been officially accepted by theUnited States Office of Management and the Budget. However, probably very little public investment has in fact been stopped by this policy.

Let me return to the more fundamental approach, based on valuation of the future. On what basis do we form judgments about the value of future benefits and costs? One way of posing this question is to ask why the interest rate is not zero. Afterall, the future is basically like the present. If we consider the problem as an ethical issue, we have to ask why these future individuals should not be treated just as we are. Why does the mere displacement in time change one's values?

Two reasons have been given in the economic literature for discounting the future, originally by the Austrian economist, Eugen von Böhm-Bawerk about 1887. The first, which we may term the wealth effect, is that we expect the future generations to be better off than we are. After all, in the advanced world, at least, we have experienced several centuries of steady growth in income per head. We expect that an additional unit of goods to be valued less in the richer societies of the future. Therefore, an investment which gives one unit of goods in the futurein exchange for one unit of goods in the present would not be acceptable. Hence, future goods have to be discounted.

What is the discount rate implied by the wealth effect? A little analysis suggests that it is the product of two numbers, the growth rate in per capita income and the responsiveness of valuation to changes in income. Some rather thin evidence suggests that this responsiveness is of the order of 1.5 or 2. The growth rate of per capita income in most countries has been of the order of 2% per year over a long period. This would yield the conclusion that the interest rate due to the wealth effect alone would be about 3% to 4%. Of course, we do not know that the growth rate will continue to be 2%. Those who emphasize the effects of natural resource scarcity will see lower growth rates in the future. But others will argue that the effects of the enormous improvements in information technology have yet to be realized in productivity, and the world faces a period of more rapid growth. My view is that 2% is a fairly conservative estimate of the per capita growth rate.

The wealth effect is relatively uncontroversial as to principle, though the quantitative magnitudes are in dispute. A second reason advanced for discounting the future may be termed, pure time preference. Suppose there were no growth in per capita income. Would it still be reasonable to discount the future? The point has been very much disputed by economists and philosophers. Even for an individual contemplating his or her own future, it has frequently been held that it is at best a deficiency to value future benefits less than present ones, "faulty telescopic vision," in the words of A. C. Pigou. These words were strongly endorsed by his brilliant younger colleague, Frank Ramsey, in his major paper on the theory of saving, in 1928. But elsewhere, in a less formal, mode, Ramsey remarked that he was not depressed by the fact that life would eventually be extinguished by the cooling of the Sun, for that event would have little present value at even modest rates of interest. The ethical and even descriptive argumentis that future individuals are very much like those now living and that an individual will think of his or her own future as equally worthy of support withthe present.

Other economists. have tended to doubt the thesis of zero pure timepreference. I find an argument first advanced by the Dutch-American economist,Tjalling Koopmans, in 1960 to be very persuasive. Put simply, it observes that a zero time preference makes investment and savings decisions insensitive to the needs of any one generation. Concretely, as we shall see, zero time preference implies unacceptably large savings rates.

To understand this, it must be recognized that the two approaches to discounting the future, opportunity cost and valuation of the future are not independent of each other. Suppose we value the future highly, that is, theinterest rate implied by our values is low. Then we should be willing to invest alot in each way of benefiting the future. This will be observed as a high saving rate. Put another way, the higher the value put on the future, the more anyg eneration should sacrifice for the future.

We can perform a thought-experiment: how much saving would be impliedif we assumed no time preference? Consider Koopmans's original argument.Imagine that we are in a stationary economy. In each period, there is a steadyflow of goods which can only be consumed in that period. The present generationis presented with an investment opportunity which will not recur. For each dollarinvested, it will yield a fixed positive income throughout the future. This incomemay be very small compared with the initial investment, but it will last forever. Ifthere is no time preference, how much should the present generation invest? Itshould invest its entire income, leaving it completely destitute; at least it should reduce itself to the lowest level compatible with sheer survival. Any loss in welfareto the present generation, no matter how small, will be made up by the benefits toan indefinitely large number of generations, no matter how small the gain to each may be.

The reference to lasting forever may sound fanciful; after all the Earth willnot be habitable for ever. But the underlying argument is only slightly changed ifwe consider a long but finite future. If we assume that the investment will yieldonly 1% return per year, then the present generation should sacrifice 90% of income if the investment continues to pay off for 3,000 years or so.

I do not believe most of us will find these conclusions acceptable. We do not believe that any one generation should be called upon to make such sacrifices, nomatter how long the period which receives some benefit. It is true that theKoopmans argument is biased in one way; only the present generation has theopportunity to make an investment. We cannot call on future generations to help, because the assumptions preclude that. Nevertheless, it seems to me to, bea compelling argument. An ethical argument that all generations should betreated equally should, if valid, yield reasonable results for cases which are conceivable, even if not realistic.

To supplement this argument, I have considered growth models of a more reasonable nature, those in which the future also has opportunities for investment. There is no one agreed-on model which gives good clue as to therelation between investment in one period and subsequent returns, so I tried several. The results are different for different models, but they agree that in theabsence of pure time preference, the savings rates are much higher than those observed and much higher than I think most people would judge reasonable.

I conclude therefore that our ethical and empirical conclusions strongly lead to the existence of a pure time preference which is greater than zero, perhaps about 1%. I therefore that a reasonable figure for total time preference, taking account both the wealth effect and pure time preference, is between 4% and 5%. This is a higher figure than some analysts are willing to concede, but nearly as high as the figures based on opportunity costs.

III. Risk and the Discounting of Public-Goods

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