### Discount Rates and Middle-Class Stagnation

Discount rates are how economists measure the importance of the future versus the present. If the discount rate is low, we care a lot about the future; the reverse is true if the rate is high. It turns out that one of the key factors driving the discount rate — maybe *the* key factor — is whether we expect to get richer in the future.* Small changes in discounts are important in carcinogens due to the 20-30 year latency period between exposure and illness. They are even more important for climate change, which will have effects far into the future.

Suppose, just for the sake of argument, that we have a hypothetical country where part of the population (call them the “elite” just for convenience) will experience rapid income growth and part of the population (call them the 47%) will have stagnant income. That’s a fairly accurate picture of America since for the past 30-40 years. Given these entirely hypothetical facts, the elite will have a high discount rate, while the 47% will have a low discount rate, so climate change will matter more to them.

Now think of climate change mitigation as an investment. This is an investment that would have high value for the 47% because they have a low discount rate, and almost no value to the elite because their discount rate is so high. It would seem like society should add these two values in order to decide on the value of the investment. Current approaches to discounting use the GDP per capita, essentially pretending that society consists of a single “average” income earner, but this could be quite misleading if there’s major and growing inequality.**

—————-

*For the nerds among you, growth is the *g* factor in the Ramsey formula, r = ρ + θ g. ρ is an impatience factor, which is relatively small, θ tell us how much personal welfare results from the growth.

**For example, I *think* that using the growth per capita GDP rate to set the discount rate fails to correct this problem. Here’s a heuristic argument, which is the best I can do. Suppose that the elite are half the population and that they will have essentially infinite wealth by the end of the time period and thus a zero discount rate. If we look at per capita income at the end of the period, it will be half of infinity and therefore the discount rate will still be zero. So when we discount the environmental harm, using per capita GDP growth gives us the same result as only looking at the elite, leaving the interests of the 47% completely out of consideration. That seems wrong. Of course, “infinite” here is just a heuristic, but “extremely large” would work just as well.

And yes, I do know that it’s ridiculous to have footnotes in a blog post. I just couldn’t resist.

#### Reader Comments

## 8 Replies to “Discount Rates and Middle-Class Stagnation”

Comments are closed.

Dan,

Check out Weitzmann’s recent paper on a related issue: how well do we really know the growth rate in the future?

http://www.nber.org/papers/w18157

Weitzmann points out that if we work within the Ramsey Growth Model and assume increasing uncertainty about future rates of growth, discount rates fall to negative infinity at the limit. From a climate change CBA perspective, the take home is that if we assume the economic future MIGHT be different than the past (or we assume that we don’t actually know what or why current growth rates are what they are), we should use a lower discount rate for climate change related investment.

Interesting to muddle over.

Best,

MW

Michael– Yes, very interesting indeed.

Dan

> New comment on your post “Discount Rates and Middle-Class Stagnation” > Author : Michael Wara (IP: 171.66.37.92 , 171.66.37.92) > E-mail : [email protected] > URL : http://stanfordlaweei.wordpress.com > Whois : http://whois.arin.net/rest/ip/171.66.37.92

Dan,

Check out Weitzmann’s recent paper on a related issue: how well do we really know the growth rate in the future?

http://www.nber.org/papers/w18157

Weitzmann points out that if we work within the Ramsey Growth Model and assume increasing uncertainty about future rates of growth, discount rates fall to negative infinity at the limit. From a climate change CBA perspective, the take home is that if we assume the economic future MIGHT be different than the past (or we assume that we don’t actually know what or why current growth rates are what they are), we should use a lower discount rate for climate change related investment.

Interesting to muddle over.

Best,

MW

Michael– Yes, very interesting indeed.

Dan

> New comment on your post “Discount Rates and Middle-Class Stagnation” > Author : Michael Wara (IP: 171.66.37.92 , 171.66.37.92) > E-mail : [email protected] > URL : http://stanfordlaweei.wordpress.com > Whois : http://whois.arin.net/rest/ip/171.66.37.92

If you are evaluating an investment with the power to alter the course of world history, shouldn’t the number you use for growth be based more on the effect of the investment than on observations of past growth? Maybe the climate cahnge cost benefit analyses already take this into account, but it seems like sub-optimal investment in climate change mitigation should lead you to expect low growth, which would lead you to use a small discount factor, which would lead you to prefer a greater level of mitigation. If you formalized this idea into an “endogenous growth Ramsey model”, it might turn out that the rational actor would prefer to invest in climate change mitigation up to the point at which the investment of $1 more would cause expectations about growth to improve by enough to make the discount rate high enough that the rational actor values the future harm at less than the present cost of losing that marginal $1 today.

Tyler,

You raise an interesting point. The effect of climate change on growth rates should certainly be taken into account and in economic terms is more significant than the effect on any single year. But the standard models are really evaluating the effect of a marginal ton of carbon, not of climate change as a whole. It’s unclear to me how to evaluate non-marginal changes, such as the overall effect of climate change on future history, especially since this also impacts the size of the population (always a tricky issue for utilitarians).

Dan

On Tue, 14 May 2013 00:35:15 +0000, “Legal Planet: Environmental Law and

If you are evaluating an investment with the power to alter the course of world history, shouldn’t the number you use for growth be based more on the effect of the investment than on observations of past growth? Maybe the climate cahnge cost benefit analyses already take this into account, but it seems like sub-optimal investment in climate change mitigation should lead you to expect low growth, which would lead you to use a small discount factor, which would lead you to prefer a greater level of mitigation. If you formalized this idea into an “endogenous growth Ramsey model”, it might turn out that the rational actor would prefer to invest in climate change mitigation up to the point at which the investment of $1 more would cause expectations about growth to improve by enough to make the discount rate high enough that the rational actor values the future harm at less than the present cost of losing that marginal $1 today.

Tyler,

You raise an interesting point. The effect of climate change on growth rates should certainly be taken into account and in economic terms is more significant than the effect on any single year. But the standard models are really evaluating the effect of a marginal ton of carbon, not of climate change as a whole. It’s unclear to me how to evaluate non-marginal changes, such as the overall effect of climate change on future history, especially since this also impacts the size of the population (always a tricky issue for utilitarians).

Dan

On Tue, 14 May 2013 00:35:15 +0000, “Legal Planet: Environmental Law and