Friday, July 29, 2011

"Paying for Long-Term Storage" Revisited

In this comment to my post onPaying for Long-Term Storage I linked to this speech by Andrew Haldane and Richard Davies of the Bank of England. They used historical data from 624 UK and US companies to estimate the extent to which short-term thinking is reflected in the prices of their stock. In theory, the price of each company's stock should reflect the net present value of the stream of future dividends. They find that:
First, there is statistically significant evidence of short-termism in the pricing of companies’ equities. This is true across all industrial sectors. Moreover, there is evidence of short-termism having increased over the recent past. Myopia is mounting. Second, estimates of short-termism are economically as well as statistically significant. Empirical evidence points to excess discounting of between 5% and 10% per year.
In other words, the interest rate being charged when using standard discounted cash flow computations to justify current investments is systematically 5-10% too high, resulting in investments that would be profitable not being made.

This is obviously a serious problem for all efforts to preserve content for future readers; the value the content eventually delivers to the future readers has to be enormous to justify even minimal investment now in preserving it. Below the fold I describe how even this analysis fails to capture the scale of the problem of short-termism.

In this comment to the same post I had an insight which, thanks to Yves Smith and Mark Buchanan, I now realize was a pale shadow of something truly important.

Yves and Mark discuss a 2009 paper by Doyne Farmer of the Santa Fe Institute and John Geanakoplos of Yale entitled Hyperbolic Discounting is Rational: Valuing the Far Future With Uncertain Discount Rates that shows things are far worse than the Bank of England paper suggests. For non-mathematicians, Mark Buchanan provides two blog posts that are far more accessible than the paper itself.

Farmer and Geanakoplos examine the assumption underlying standard discounted cash flow computations that the discount rate is a constant, i.e. that the value of future income decreases exponentially. I did the same when discussing the possibility that Kryder's Law, the exponential decrease in cost-per-byte of disk storage, might suffer some fluctuation. They replaced the assumption of a constant discount rate by one varying as a geometric random walk, which is a reasonable match for the observed behavior of interest rates. Their results have implications far more serious than archiving; they point out:

What this analysis makes clear, however, is that the long term behavior of valuations depends extremely sensitively on the interest rate model. The fact that the present value of actions that affect the far future can shift from a few percent to infinity when we move from a constant interest rate to a geometric random walk calls seriously into question many well regarded analyses of the economic consequences of global warming. ... no fixed discount rate is really adequate – as our analysis makes abundantly clear, the proper discounting function is not an exponential.
The flawed mathematical model used to think about the costs and benefits of mitigating or ignoring long-term climate change is massively biased to ignoring it.

Returning to long-term archiving, we see that even if the investors in the Bank of England study had used the values generated by standard discounted cash flow computations instead of adding 5-10%, they would still have been massively undervaluing the stream of future dividends. Even the limited thinking that I and others have been doing about the economics of long-term preservation has been using a mathematical model that systematically undervalues the long-term future. Most thinking about the problem doesn't even get that far; it is noteworthy that the chapter in the Blue Ribbon Task Force Report called The Economic Perspective on Digital Preservation doesn't even use the concept of discounting. Given that: the future for our digital heritage looks even bleaker than it used to.

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