Wednesday, February 9, 2011

Discount rates, relative prices and climate economics

Yesterday I wrote a bit about the "relative prices" argument for swift and decisive action against climate change. Some additional comments to provide context:

For economists engaged in the climate change debate, one of the most important –  yet difficult –  things to find agreement on is a suitable discount rate. This may seem a strange issue to fixate on from the perspective of non-economists, but the point here is that climate change is an intergenerational problem that will potentially affect many people over time. The question then is how to measure future costs and benefits against those of the present?

As with any investment which involves cost-benefit analysis over time, the favoured approach in climate change economics is to use a discount rate.[*] This allows us to assess things in present value (PV) terms. Thus, and while it may seem somewhat trivial against the wider scientific uncertainties of climate change, the discount rate actually proves a critical factor in determining the economically efficient level of abatement. Here's a simple example to illustrate the importance of choosing a particular rate of discount:
If we discount $100 a hundred years from now at a rate of 1 percent, we obtain a present value of around $37. However, if we feel slightly more impatient and raise the discount rate to 3 percent, then the present value falls to only $5! 
Importantly, the effect of compound interest means means that we see an exponential impact from the difference in discount rates, as well as the length of time that we are discounting. In other words, we're dealing with a distinctly non-linear process.The central message to take away is that – when it comes to estimating economic costs and benefits of the future – seemingly innocuous changes in your a priori assumptions over the discount rate can lead to substantial differences in cumulative terms. (Use this calculator to see for yourself.)

So, the choice of discount rate has a potentially massive impact on the perceived efficiency and timing of climate policy. Again, it is worth emphasising the intergenerational nature of climate change, where present (and future) sacrifices will have to be made in order to protect future incomes and utilities. The corollary of this is that acting too slowly may harm future generations in the form of rising climate costs, whilst acting too quickly may be equally as harmful by unnecessarily limiting economic growth.

Against this background, it probably won't be surprising to hear that the chief criticisms for the much-feted Stern Review –  from an economics perspective at least –  were reserved for his choice of discount rate. By drawing on the famous Ramsey Equation[**], Stern used largely ethical arguments in deriving a final discount rate of 1.4%. This, his critics argued, was much too low in comparison with observed market rates, which are closer to 3-4%. Moreover, since Stern's major findings hang on a "low" discount rate, the same critics say that his central policy recommendation of "act fast, act now" does not hold. (Indeed, a belief in higher discount rates is what underpins a lot of economic rationalisation on the benefits of delayed action against climate change; e.g. focus on growing our economies as fast as possible now so that we will be in a better, wealthier position to deal with the effects of climate change in the future.)

At the same time, however, numerous other economists have come out strongly in support of Stern, while he also has vigorously defended his methodology in the period since. In the interest of keeping this post as short as possible, I won't go into much further detail on this debate between supporters of Stern and their opponents (or those in between). I highly encourage you to look over the Sterner and Persson paper that I recommended previously for a very readable summary of the various elements involved in determining the discount rate, as well as the different schools of thought on what the appropriate level really is.

What I did want to get to today was this: One of the most interesting insights of the "relative prices" argument from my perspective is that strong, early emissions reductions can be economically justified even in the presence of high discount rates. Prior to this, opponents to early abatement paths such as those proposed by Stern have argued that such plans can only be sustained in the presence of what they perceive to be unacceptably/unrealistically low discount rates. And yet, we now see compelling economic reasons to follow an aggressive emissions path even when using high rates of interest.[***]

In other words, the relative price argument allows us to partly abstract from the intrinsic subjectivity of the discount debate, which currently clouds the timing of climate policy. It does this by demonstrating the extent to which a loss in natural assets (clean water, predictable seasons, etc) could affect our ability to generate, or even enjoy, man-made assets (such as cars, computers, restaurants and so on) in the future. In this way, we are able to formalise the intuitive concerns that many people have regarding the destabilisation of natural systems that we are intimately dependent on.

THOUGHT FOR THE DAY: The choice of discount rate is crucial to determining an "economically efficient" response to climate change. Unfortunately, there is widespread disagreement among economists as to what the correct discount rate is. However, by incorporating the impact of relative prices into our analysis, we can still conclude that it is better to act sooner, rather than later... even if we assume a discount rate that is relatively high. And that is a critical first step to reach agreement on.

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[*] There are people who question the validity of even using the "standard" cost-benefit analysis (CBA) approach to climate change, but that remains another subject for another day.

[**] The Ramsey Rule is: r = δ + η * g 
        Which says that the discount rate (r), is equal to the sum of the pure rate of time preference (δ) and the product of the elasticity of the marginal utility for money (η) and the per capita growth rate of the economy (g). To simplify, we interpret the first component of the equation, δ, as the tendency to discount future utility simply because it is in the future. The second component, η * g, implies that we value future consumption less than consumption today, because our wealth should increase over time as the result of economic growth. This latter notion rests on the assumption that a rich person gains less welfare than a poor person for a given quantity of money.

[***] This is a bit of a simplification. The choice of discount rate will always have an impact on how aggressively we approach the issue of climate change. However, we are left with a central message that – regardless of differing opinions on what the discount rate should be – it is still in humanity’s best interest to decisively cut emissions sooner rather than later.

1 comment:

  1. Frank Ramsey, for which the above equation is named, was a pretty incredible guy. He was only 26 when he died, but had already made seminal contributions in numerous fields by that time, including mathematics, economics, philosophy and logic.
    http://en.wikipedia.org/wiki/Frank_P._Ramsey

    As an interesting aside, Ramsey was strongly against pure time rate discounting (δ in the above Ramsey Rule) and, in a famous passage, decried it as “ethically indefensible”, saying that the assumed preference for current enjoyments over future ones “arises merely from the weakness of the imagination”.

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