Smoothly runs the Don

Earlier, I wrote something about changing distributions. More recently a couple of examples of this phenomena have come up, so let's make things concrete.

Suppose x(t) is randomly distributed according to N(0,s(t)) [normal distribution with mean zero and standard deviation s(t)] where s(t) is a continuous, bounded and slow function of t. Suppose we sample x(t) discretely. (Take s(t) = 2 + sin(t) with t in years and daily sampling, for instance.)

The variables x(t) are not iid, but (under a bunch of smoothness conditions) they are locally iid: we can think of the distribution being fibred over time and a small change in time inducing a small change in the distribution. One might hope that one could import a lot of non parametric statistics into this setting, where we were trying to gain information about the variation of s(t) by sampling the xs.

Note that this is not a stochastic volatility model or a GARCH model: volatilities are not random, but rather determined by an initially unknown function.

Is this sort of thing well known I wonder? It's similar to local volatility models, but there we have a situation where we can deduce s(t) with certainty as we know the prices of all vanilla options, whereas I'm more interested in a situation where we can only observe s(t) by sampling x(t).

One of the applic- ations, as in this picture of a large piece of metal hanging from a crane a hundred feet above a busy junction, is operational risk, but there are others which may be even more slippery.

What is rational?

Someone might not have read their Wittgenstein, let alone their Bakhtin. At Overcoming Bias, we find:

[People give] views on risks of nanotechnology even when [...they] know that they do not know much about the subject and these views become strengthened along ideological lines by more facts. Facts do not matter as much as values: people appear to make a quick gut feeling decision (probably by looking at the word "technology"), which is then shaped by their ideological outlook.

[...]

This does not bode well for public deliberations on new technologies (or political decisions on them), since it seems to suggest that the only thing that will be achieved in the deliberations is a fuller understanding of how to express already decided cultural/ideological identities in regards to the technology. It does suggest that storytelling around technologies, in particular stories about how they will fit various social projects, will have much more impact than commonly believed. Not very good for a rational discussion or decision-making, unless we can find ways of removing the cultural/ideological assumptions of participants, which is probably pretty hard work in deliberations and impossible in public decision making.

Does the author believe that the 'rational' decision is something other than the average community decision? What does 'rational' mean, when we are talking about language, if it isn't 'what most people agree follows'? Is there a manual on correct deductions in English? Is the only person without 'cultural/ideological assumptions' the author? Or is the assumption that a certain mode of discourse is the only rational one itself just possibly a cultural/ideological assumption?

American Asymmetry

Foreign Nations Can Be Sued on Property Taxes, U.S. Court Says yet The US embassy owes more than £1m in unpaid congestion charges and fines, according to the London mayor's office. Pot, kettle anyone?

Keeping with the iron mongery theme, the flatiron building, New York.

Errors in Cost Benefit Analysis

A recent Bloomberg article referring to the AEI-Brookings Institute paper Has Economic Analysis Improved Regulatory Decisions? made me think again about cost benefit analysis.

The paper condemns both the quality of cost benefit analysis used in determining the impact of regulation and the `tenuous' use made by policy makers of that analysis. Undoubtedly that is partly for political or hegemonic reasons - cost benefit analysis sometimes comes to the `wrong' conclusions - but I suspect it is also partly because the conclusions of a cost benefit analysis are sometimes not believed. The analyst may be at fault here for not stating the margin of error?

Error bars are common in experimental science: the fine structure constant, for instance, is known to roughly one part in a billion, and in any precise discussion we would state not 1/alpha = 137.035999710 but rather 1/alpha = 137.035999710(96) meaning that the reciprocal of alpha could be as high as 137.035999796 or as low as 137.035999624.

In cost benefit analysis this could be a very useful tool, especially as the error bars are much larger. To take the first example that google coughed up, an amusing cost benefit analysis of different law schools (where the cost is the fees and the benefit is the increase in expected salary after going to the school), the problem is that while the costs are fixed, the benefits aren't. Not only do different individuals earn different amounts despite having the same education, speciality counts so that (in the perverse world in which we live) a tax lawyer earns more than a criminal defender. Moreover the reputation of various law schools will change over time effecting not just the earnings of current graduate but also those of past ones.

An even better example is one of the next hits, a discussion of the cost benefit analysis of rebuilding New Orleans after Katrina given its obvious hurricane risk. Here not only is the benefit uncertain, but so too is the cost. Any analysis with error bars would suggest at best 'case not proven': that, rather than 'cost > benefit' or 'cost < benefit' is often the best that we can conclude since it will often be the case that the intervals [cost - possible error in cost, cost + possible error in cost] and [benefit - possible
error in benefit, benefit + possible error in benefit] intersect.

Spread thin can be tasty

Just as pressure groups can sometimes be effective because they are passionately concerned about one view that most people oppose but don't care much about, so one of the problems with the tax system is that it is easy to see how much an individual would benefit from lower tax, but harder to see who would suffer from the change - that money is spread over so many school children, sick people, public servants and so on. We hear so much about the competitiveness implications of higher tax: surely balance suggests we should hear as much about what those tax pounds do.

Servicer-related convexity in RMBS

An aban- doned shoe and a banana skin on Old Street to begin a post on the willingness of ABS servicers to abandon their trades if things go badly. Specifically, Tanta on Calculated Risk makes a good point about rising defaults in RMBS:

Foreclosure waves create additional losses just by being foreclosure waves. You can try to rush for the exits all you want; it takes too long to get out of this door if there are too many people in line [...] when declining home values [...] get to a certain point, the foreclosure volume gets to a point such that the operational risk explodes, which drives those loss severities even deeper.

So when house prices go down not only do you have rising losses in RMBS, these losses increase costs dramatically at the servicer. Therefore you also have massive pressure on servicing fees because if you don't agree to let the servicer raise them to cover these costs, they default, and the back up servicer will demand higher fees anyway. There is not sufficient liquidity for all holders to be able to get out at anything like the marked price once this starts happening. As Tanta puts it:

"Look, bondholders, you'll either approve some modifications or your servicer will fold beneath you and any substitute servicer will be able to name its price because you need them waaay more than they need you,"

In most ABS the holder is short a (real) option for the servicer to demand a change in fees, and this option is really worth something. Moreover its moneyness is highly correlated with default levels. If you hold, say, non Agency AAA, are you getting paid for being short this option?

Three things to reflect on

Private equity executives are "paying less tax than a cleaning lady".

A study of 25,000 travellers shows that only 40% believe they are getting good value for money from the railway system. (Maybe you would be better off going by barge?)

Britain's energy policy fails to stack up, says expert panel.

Just possibly, might it be that the reason the UK has crumbling infrastructure and a lack of a credible energy policy is that a lot of people, private equity included, are not being charged enough tax to pay for it?

How long does it take a good idea to triumph?

There's a provocative post on Econlog which raises an interesting question. Suppose someone has a good academic idea. How long does it take to be become part of the canon of accepted wisdom?

Clearly some ideas hit quickly: many of these are simple technical improvements which are obviously correct. Some never hit because, although correct, they are too boring and marginal to make a difference. Indeed some ideas enter the canon then leave it again as subject areas die: a great example here are many of the techniques used to speed tedious calculations from the days before digital computers.

As Kuhn pointed out, however, some ideas are so radical that they cannot be incorporated into the mainstream without effecting it: the paradigm must change. These ideas tend to take longer to be accepted.

I'm interested in mid-sized ideas: theories which are somewhat disruptive, but which are not big enough to qualify as paradigm changes. My suspicion is that these are slow to be accepted too, perhaps even slower than paradigm changing ideas because there is less payoff from including them, yet they still challenge the current academic hegemony. I'd love to see a careful sociological study on this. Could it be that the average time to acceptance of a such an idea is a significant fraction of a career?