## But innovation is endogenous, too

Risk aversion usually makes investments look less attractive. In the standard story, then, as risk aversion goes up, we would spend less money today to avert future catastrophes. Martin Weitzman argues, however, this relationship reverses when we’re uncertain about future productivity levels. For if it turns out that productivity is low in the future (e.g. because of a climate catastrophe) then consumption will be low. Low consumption means high marginal utility and so low discount rates.

My purpose here is to focus sharply on clarifying the long-run discounting issue by using a

super-simple super-crisp formulation… There is no good substitute for seeing clearly before ones eyes the basic structure of a model laid bare.

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Suppose [there's uncertainty about discount rates in the future and] that discount rate ri > 0 will occur with probability-like weight wi > 0, where sum wi = 1… The [expected] discount rates … decline over time starting from their average value and going down over time to approach their lowest possible value. Over time, the impact of the higher discount rates … diminishes because the higher rates effectively discount themselves exponentially out of existence, leaving the field to the lower discount rates (and, eventually, to the lowest).

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[A]ny given value of [future productivity level] subsequently determines the endogenous future growth rate … and endogenous consumption level … as the solution to a Ramsey optimal growth problem (given that value of [productivity]). The paper shows that when future productivity … is uncertain, then higher values of [risk aversion] are associated with lower future discount rates, thereby reversing the conventional wisdom.

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[An example using standard parameter values] indicate[s] that the risk-aversion effects of uncertain future productivity on lowering distant-future discount rates might be quite powerful. The driving force is a ”fear factor” associated with the possibility of low-probability but catastrophically-high permanent damages to future productivity.

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I personally would be inclined toward a much lower climate-change discount rate than 6% per annum, but the ultimate goal of this paper … will be to show that under uncertainty, even with expected discount rates as high as 6%, the effective discount rate, which ought to be used, can be much lower than 6%.

The results in the example he gives depend very much on the distribution of future productivity, especially on its variance. Here’s his assumed distribution:

In his model, this distribution should be interpreted as the distribution of the average productivity over a very long time (i.e. the next century or so). To me, his assumed uncertainty about productivity is too high (i.e. the variance of the distribution is too wide). Is it even remotely possible that the capital-output ratio will average 50 or 100 for the next century? Even if there’s a sudden, cliff diving catastrophe, I can’t imagine people won’t invent their way around it thus increasing the productivity of capital in the long run. And if catastrophe happens in slow motion, certainly people will be adjust fast enough to keep returns on capital high on average.

The most striking stylized fact about growth is its constancy. For whatever reason, people route around the particular circumstances of their time and space and invent their way to 2% growth. Why would climate change pose fundamentally different obstacles to innovation than what has been seen over the last 200 years? Do the open systems studied in Diamond’s Collapse tell us anything about the closed global system?

I thought this point was obvious. Think of dealing with climate change as deciding what level of insurance to buy or how much hedging to do. The more risk averse you are, the more insurance you will buy or the more hedging you will do.

The important feature is not that we are discussing “levels of productivity”, but that climate change policies are designed to mitigate bad events, where “investments” are normally designed to make good events more likely. You’d pay more now to decrease the chance of losing $100k than to increase the chance of gaining $100k. The higher the probability, the higher the discrepancy. The same goes for climate change.

Its the observation that mitigating climate change is like insurance that wasn’t obvious (at least to all the critics of the Stern report). We don’t expect high returns (i.e. high discount rates) from insurance.

A standard result in finance is that we buy insurance because it pays off when marginal utility is high (i.e. when consumption is low b/c, for example, your house just burned down). I think Weitzman’s results are new because he contemplates uncertain but permanent decreases in payoffs. I wonder what financial economists have to say about the paper.