Thursday, November 6, 2008


The Optimal Savings Rate

Some people think that although people make efficient decisions about how much to save personally, the social discount rate we use is too low. The market gets it right, but government does not. I think the opposite is true.

Individuals are too eager to consume in the present instead of the future. Think of a person as a sequence of selves over time. Most people are selfish and favor the present self over the future self. They save too little.

On the other hand, when it comes to decisions across generations, we have to remember that future generations will be richer than we are. Thus, we should not incur too much cost now in exchange for benefits for them later.

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Friday, August 8, 2008


Stern's Ely Lecture on Climate Change and DIscounting

I just finished reading Prof. Stern's Ely Lecture ( Stern, Nicholas. 2008. "The Economics of Climate Change", American Economic Review 98(2), pp. 1-37.). He is in favor of drastic measures to reduce CO2 emissions. Concentrations are now 430 ppm and he wants to stabilize them at 550 ppm. He is fearful of a 5 degree Centigrade temperature increase otherwise. Here are my notes.

1. He says the most recent warm period was around 3 million years ago. Really? There have been lots of ice ages and warmings.

2. He dismisses geoengineering in one paragraph with weak arguments.

3. His Figure 4 from McKinsey has lots of *negative* abatement costs-- things such as insulation improvement, fuel-efficient commercial vehicles, water heating, etc. We can't believe any of that. If it saves money, why isn't it done already? Liquidity constraints?

4. (p. 13). He cites 1.5% as the indexed bonds rate of return on longterm government bonds, and 6-7 percent for private investments:

In the United Kingdom and United States, we find (relatively) “riskless,” indexed lending rates on government bonds centered around 1.5 percent over very long periods. For private very long-run rates of return on equities, we find rates centered around 6 or 7 percent (Rajnish Mehra and Edward C. Prescott 2003, 892; Kenneth J. Arrow et al. 2004, 156; Sree Kochugovindan and Roland Nilsson 2007a, 64; 2007b, 71).
He has a puzzling sentence about what discount rate to use:
Given that it is social discount rates that are at issue, and also that actions to reduce carbon are likely to be financed via the diversion of resources from consumption (via pricing) rather than from investment, it is the long-run riskless rates associated with consumer decisions that have more relevance than those for the investment-related equities.
This is a good question, but what is the implication? Consumers are willing to borrow at rates on the order of 10%, so is that the appropriate social discount rate?

He makes the point that environmental goods' prices will change (though he does not point out that those goods are a tiny part of the consumption basket):

Suppose, however, that we persisted with the argument that it is better to invest at 6-7 percent and then spend money on overcoming the problems of climate change later rather than spending money now on these problems. The multi-good nature of the problem, together with the irreversibilities from GHG accumulation and climate change, tell us that we would be making an additional mistake. The price of environmental goods will likely have gone up very sharply, so that our returns from the standard types of investment will buy us much less in reducing environmental damage than resources allocated now (see also Section I on the costs of delay).12 This reflects the result that if environmental services are declining as stocks of the environment are depleted, then the SDR with that good as numeraire will be negative. On this, see the interesting work by Michael Hoel and Thomas Sterner (2007), Sterner and U. Martin Persson (2007) and Roger Guesnerie (2004), and also the Stern Review (Stern 2007, 60). Environmental services are also likely to be income elastic, which will further reduce the implied SDR.
He has some useful sources on the appropriate rate of pure utility time preference:
Indeed, the ethical proposition that delta should be very small or zero has appealed to a long line of illustrious economists including Frank P. Ramsey (1928, 543), Arthur Cecil Pigou (1932, 24–5), Roy F. Harrod (1948, 37–40), Robert M. Solow (1974, 9), James A. Mirrlees (Mirrlees and Stern 1972), and Amartya Sen (Sudhir Anand and Sen 2000). I have heard only one ethical argument for positive delta (Wilfred Beckerman and Hepburn 2007; Simon Dietz, Hepburn, and Stern 2008) that has some traction—namely a temporal interpretation of the idea that one will have stronger fellow feelings for those closer to us (such as family or clan) relative to those more distant.
When it came to choosing a social discount rate, Stern is opposed to using market interest rates. Later, though, when it comes to choosing the appropriate amount of equality and income redistribution, he slyly switches to favoring observed amounts:
Value judgements are, of course, precisely that and there will be many different positions. They will inevitably be important in this context— they must be discussed explicitly and the implications of different values should be examined. Examples follow of what we find when we turn to empirical evidence and try to obtain implied values (the “inverse optimum” approach). Empirical evidence can inform, but not settle, discussions about value judgements... The upshot is that empirical estimates of implied welfare weights can give a wide range of eta, including h below one and even as little as zero.
Here he is trying to squirm out of the powerful growing-income argument against a low social discount rate. The argument goes like this. Suppose we are considering taking $1,000 away from someone earning $40,000/year so we can give $1,600 to someone else earning $107,000/year. Should we do it? Despite the increase in social wealth, it seems unfair and not calculated to increase total happiness. Yet that is what happens when we require $1,000 in abatement costs in in 2008 because it has a 1%/year return in benefits obtained in 50 years, if incomes grow at 2%/year in the meantime. This argument is particularly powerful against liberals, though it works for conservatives too, and lays out starkly the forced transfers that libertarians hate.

There is a lot of posturing going on:

Costa Rica, New Zealand, and Norway, declared targets of 100 percent reductions by 2050, i.e., “going carbon-neutral.” ... California has a target of 80 percent reductions by 2050. France has its “Facteur Quatre”: dividing by 4, or 75 percent reductions, by 2050 (Stern 2007, 516). The United Kingdom has a 60 percent target but the Prime Minister Gordon Brown indicated in November 2007 that this could be raised to 80 percent (Brown 2007). Australia, under the new government elected at the end of November 2007, has now signed Kyoto and has a target of 60 percent...
Costa Rica doesn't matter of course, any more than the United Kingdom does, or anybody else but China and India:
Even with fairly conservative estimates, it is likely that, under BAU, China will reach current European per capita emissions levels within 20-25 years. With its very large population, over this time China under BAU will emit cumulatively more than the USA and Europe combined over the last 100 years.
"BAU" means "business as usual".

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Friday, June 6, 2008


Weitzman's Gamma Discounting

I was just thinking about the article "Gamma Discounting", Martin L. Weitzman The American Economic Review, Vol. 91, No. 1 (Mar., 2001), pp. 260-271. Weitzman has a model in which you are unsure of the proper discount rate, and concludes that your discount rate should become small in far future periods. He says the intuition has to do with compound interest. He uses the gamma function for your prior. I think a numerical example works better, though I'm not sure if this is what he's getting at-- he says that using continuous compounding you don't get his result.

Anyway, here's the simple idea. Suppose we don't know whether the interest rate will be 2% or 4%, and these have equal probability. We will get a benefit of $1 in 100 years. What is it worth in present value?

If the interest rate is 2%, the value is about $.13. If the interest rate is 4% the value is about $.02. The expected value is therefore about $.07. But if the interest rate were a known 3%, the expected value would be about $.05. Thus, our ignorance results in less discounting.

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