Friday, June 26, 2009

More on Climate Change (nerdy; skip if you don't like numbers)

. Friday, June 26, 2009

My erstwhile co-blogger Sarah raised some questions about the costs of climate change in comments to my previous post:

Question - is the 2% total per year inflation adjusted? Because a 3% real loss in GDP by 2100 translates into a much higher nominal GDP loss.

Additionally, I'm very skeptical at this assessment. Temperature changes will have overarching economic and non-economic effects. Food and water supplies will shift and could decrease. Maybe the better way to look at the 2% of Global GDP cost of C02 reduction is like an insurance premium. If we have a pretty good idea of what it costs to protect us but a not-so-fail-proof idea of what it would cost if we did nothing, than buying insurance is a rational choice.

Dealing with the last part first, buying insurance is only rational if the expected NPV is greater than or equal to the cost of the insurance. Further, insurance is never geared at prevention; only mitigating the effects of something after it happens. In this discussion, "buying insurance" would be closer to doing nothing to stop climate change and instead using the economic gains to deal with the situation then.

But I want to focus on the crux of my first point: the costs of prevention are much, much greater than people tend to think. After all, when people say that we can mitigate the costs of global warming by spending one or two percent of GDP, it doesn't sound like very much. But it is actually quite a bit when you compound those costs over time. In my previous post, I presented an obviously unrealistic model in which there is no economic growth. Let's flesh it out a little more with some more realistic assumptions. First, let's assume that the U.S. economy will grow at its trend rate (roughly 3%/year) from now until 2100. If we do nothing about climate change, then our economy will grow from $14tn to over $200tn by 2100. According to the CBO report, we will lose 3% of that, or $6tn, due to the effects of climate change. Let's look at two scenarios where we combat climate change to look at the costs:

1. If we sacrifice just 1% of GDP growth per year (not actual GDP) over that time to combat climate change, so we grow at 2% instead of 3%, then what have we given up? In 2100 our GDP will be $83tn, or $117tn less than it would have been otherwise. In other words, our standard of living in 2100 would be halved. Of course, our standard of living from years 2011 - 2099 would also be lower at greater and greater rates. This is quite a lot to give up.

2. But maybe we can spend more now and less later, as Nicholas Stern suggests. If we follow his recommendation and sacrifice 2% of GDP from 2010-2020 and then (presumably) nothing after that, then where are we? From 2010-2020 our economy grows at 1% per year instead of 3% per year and in 2020 our GDP would be $15.46tn, After that, growth returns to 3% per year until 2100 when our GDP would be $165.5tn, or $35tn less than it would have been if we'd done nothing. This represents roughly 17% of potential 2100 GDP, and also does not include the lower standard of living in years 2010-2099.

In both of the above the scenarios, the costs are actually much, much higher. For example, if we do nothing and have GDP of $200tn in 2100 and stay at the same trend rate of growth (3%), in 2200 our GDP would be roughly $3,844tn. If we follow scenario #1, but stop spending on climate change in 2100 and return to 3% growth, then our 2200 GDP would be $1,595tn, or roughly 40% of what it could have been. If we follow scenario #2, then our 2200 GDP would be $3,180. In both cases, the divergence between actual and potential GDP will increase over time with an upper bound of infinity. We never get that lost growth back, and in fact we lose more and more the further out into time we go.

All of this, of course, assumes that we can actually slow or stop climate change by spending this money. In practice, that will be very difficult to do without getting major concessions from the BRICs, the oil-exporting states, and the rest of the developed and developing world. Such concessions are not likely achievable. But even if we lived in a perfect world where international cooperation was easily achievable and our actions to slow climate change were effective, it still might not be worth it. A very high bar must be cleared before it makes sense to give up even a little bit of economic growth. That's why looking at compounding rates of growth is so important.

Now, the CBO report could be completely wrong; maybe climate change will cost the economy much more than 3% in 2100. Some people certainly think it will, and they may be right: there is a lot of uncertainty built into the climate models. But in order for it to be economically productive, the difference would have to be extreme; even in the less-costly Stern model (scenario #2), the CBO would have to be wrong by 600% in order for it to make sense to follow Stern's recommendations. I find that to be unlikely.

And I still haven't mentioned discount rates.


Alex Parets said...

I'd be really interested to see the comparative statics on GDP growth in 2100 if we do nothing compared to GDP growth in 2100 if something is done now.

You make an assumption that doing nothing will not hurt economic growth in 2100. You assume that the economy will grow at its trend rate for the next 200 years if nothing is done. I think you are overlooking the potential negative economic effects of climate change.

It still may not be worth it to invest so much money now and sacrifice that much compounded growth to attempt to fix something that may be unfixable. But, I think your analysis and your numbers are missing a big chunk. You aren't taking into account the potential downsides of climate change on the steady state rate of growth.

Kindred Winecoff said...

you're right. to be consistent, i should have subtracted the 3% of 2100 GDP as the CBO suggests. if i do that, then 2200 GDP in the "do-nothing" scenario is $3,728tn rather than $3,844tn. i don't think it affects the substantive point, but it does make a little difference in the actual numbers.

i should stress a few caveats again:

1. the output depends on the inputs. if growth isn't 3%/year, or if climate change costs more than 3% of 2100 GDP, then we haven't sacrificed as much, and in fact could be in the black. of course the reverse is true: if growth is more than 3%/year or if climate change is less than the CBO's estimate, then we've sacrificed much more. but the point of the CBO estimate is that the US is pretty insulated from the effects of climate change; our economy does not depend much on highly local farming or fishing to drive the economy. so yes, the Aspen skiing industry will weaken or maybe disappear, but that's not that big of a deal for the broader economy.

2. these estimates are for the U.S., and other countries may face a radically different calculus. that brings up another normative question: how much should we be willing to spend to make others better off? this obviously has implications for all sorts of other aspects of public policy besides global warming. but it is also true that if we limit our economic growth, we will also be limiting opportunities for developing countries to sell into our market and increase their growth. so a pro-growth strategy could actually benefit even the countries hit much harder by climate change.

i have not seen a rigorous non-partisan discussion of how much climate change will decrease global GDP. if you know of something like that, please point it out to me. but also keep in mind that global GDP is projected to be much higher than 3% over the next century, and slowing China's pollution would require much more than 1% of their GDP growth, so we'd be cutting into a much bigger pie.

More on Climate Change (nerdy; skip if you don't like numbers)
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