Political comic strips around the Mississippi Bubble of the 1710s

I wish that I had time to read this paper by David Levy and Sandra Peart.

It’s about political comics (cartoons) drawn to depict John Law and the Mississippi Bubble of the early 1700s.  It also speaks to subtlely different meanings of the words “alchemy” and “occult” than we are used to today. Here is an early paragraph in the paper:

Non-transparency induces a hierarchy of knowledge. The most extreme form of that sort of hierarchy might be called the cult of expertise in which expertise is said to be accompanied by godlike powers, the ability to unbind scarcity of matter and time. The earliest debates over hierarchy focused on whether such claims are credible or not.

Here is the abstract:

Economists have occasionally noticed the appearance of economists in cartoons produced for public amusement during crises. Yet the message behind such images has been less than fully appreciated. This paper provides evidence of such inattention in the context of the eighteenth century speculation known as the Mississippi Bubble. A cartoon in The Great Mirror of Folly imagines John Law in a cart that flies through the air drawn by a pair of beasts, reportedly chickens. The cart is not drawn by chickens, however, but by a Biblical beast whose forefather spoke to Eve about the consequences of eating from the tree of the knowledge. The religious image signifies the danger associated with knowledge. The paper thus demonstrates how images of the Mississippi Bubble focused on the hierarchy of knowledge induced by non-transparency. Many of the images show madness caused by alchemy, the hidden or “occult.”

Hat tip: Tyler Cowen.

Double-yolk eggs, clustering and the financial crisis

I happened to be listening when Radio 4’s “Today Show” had a little debate about the probability of getting a pack of six double-yolk eggs.  Tim Harford, who they called to help them sort it out, relates the story here.

So there are two thinking styles here. One is to solve the probability problem as posed. The other is to apply some common sense to figure out whether the probability problem makes any sense. We need both. Common sense can be misleading, but so can precise-sounding misspecifications of real world problems.

There are lessons here for the credit crunch. When the quants calculate that Goldman Sachs had seen 25 standard deviation events, several days in a row, we must conclude not that Goldman Sachs was unlucky, but that the models weren’t accurate depictions of reality.

One listener later solved the two-yolk problem. Apparently workers in egg-packing plants sort out twin-yolk eggs for themselves. If there are too many, they pack the leftovers into cartons. In other words, twin-yolk eggs cluster together. No wonder so many Today listeners have experienced bountiful cartons.

Mortgage backed securities experienced clustered losses in much the same unexpected way. If only more bankers had pondered the fable of the eggs.

The link Tim gives in the middle of my quote is to this piece, also by Tim, at the FT.  Here’s the bit that Tim is referring to (emphasis at the end is mine):

What really screws up a forecast is a “structural break”, which means that some underlying parameter has changed in a way that wasn’t anticipated in the forecaster’s model.

These breaks happen with alarming frequency, but the real problem is that conventional forecasting approaches do not recognise them even after they have happened. [Snip some examples]

In all these cases, the forecasts were wrong because they had an inbuilt view of the “equilibrium” … In each case, the equilibrium changed to something new, and in each case, the forecasters wrongly predicted a return to business as usual, again and again. The lesson is that a forecasting technique that cannot deal with structural breaks is a forecasting technique that can misfire almost indefinitely.

Hendry’s ultimate goal is to forecast structural breaks. That is almost impossible: it requires a parallel model (or models) of external forces – anything from a technological breakthrough to a legislative change to a war.

Some of these structural breaks will never be predictable, although Hendry believes forecasters can and should do more to try to anticipate them.

But even if structural breaks cannot be predicted, that is no excuse for nihilism. Hendry’s methodology has already produced something worth having: the ability to spot structural breaks as they are happening. Even if Hendry cannot predict when the world will change, his computer-automated techniques can quickly spot the change after the fact.

That might sound pointless.

In fact, given that traditional economic forecasts miss structural breaks all the time, it is both difficult to achieve and useful.

Talking to Hendry, I was reminded of one of the most famous laments to be heard when the credit crisis broke in the summer. “We were seeing things that were 25-standard deviation moves, several days in a row,” said Goldman Sachs’ chief financial officer. One day should have been enough to realise that the world had changed.

That’s pretty hard-core.  Imagine if under your maintained hypothesis, what just happened was a 25-standard deviation event.  That’s a “holy fuck” moment.  David Viniar, the GS CFO, then suggests that they occurred for several days in a row.  A variety of people (for example, Brad DeLong, Felix Salmon and Chris Dillow) have pointed out that a 25-standard deviation event is so staggeringly unlikely that the universe isn’t old enough for us to seriously believe that one has ever occurred.  It is therefore absurd to propose that even a single such event occurred.   The idea that several of them happened in the space of a few days is beyond imagining.

Which is why Tim Harford pointed out that even after the first day where, according to their models, it appeared as though a 25-standard deviation event had just occurred, it should have been obvious to anyone with the slightest understanding of probability and statistics that they were staring at a structural break.

In particular, as we now know, asset returns have thicker tails than previously thought and, possibly more importantly, the correlation of asset returns varies with the magnitude of that return.  For exceptionally bad outcomes, asset returns are significantly correlated.

Epistemology in the social sciences (economics included)

I’m not sure how I came across it, but Daniel Little has a post summarising a 2006 article by Gabriel Abend:  “Styles of Sociological Thought: Sociologies, Epistemologies, and the Mexican and U.S. Quests for Truth“.  Daniel writes:

Abend attempts to take the measure of a particularly profound form of difference that might be postulated within the domain of world sociology: the idea that different national traditions of sociology may embody different epistemological frameworks that make their results genuinely incommensurable.

[…]

Consider this tabulation of results on the question of the role of evidence and theory taken by the two sets of articles:

[…]

Here is a striking tabulation of epistemic differences between the two samples:

Abend believes that these basic epistemological differences between U.S. and Mexican sociology imply a fundamental incommensurability of results:

To consider the epistemological thesis, let us pose the following thought experiment. Suppose a Mexican sociologist claims p and a U.S. sociologist claims not-p.  Carnap’s or Popper’s epistemology would have the empirical world arbitrate between these two theoretical claims. But, as we have seen, sociologists in Mexico and the United States hold different stances regarding what a theory should be, what an explanation should look like, what rules of inference and standards of proof should be stipulated, what role evidence should play, and so on. The empirical world could only adjudicate the dispute if an agreement on these epistemological presuppositions could be reached (and there are good reasons to expect that in such a situation neither side would be willing to give up its epistemology). Furthermore, it seems to me that my thought experiment to some degree misses the point. For it imagines a situation in which a Mexican sociologist claims p and a U.S. sociologist claims not-p, failing to realize that that would only be possible if the problem were articulated in similar terms. However, we have seen that Mexican and U.S. sociologies also differ in how problems are articulated—rather than p and not-p, one should probably speak of p and q.  I believe that Mexican and U.S. sociologies are perceptually and semantically incommensurable as well. (27)

Though Abend’s analysis is comparative, I find his analysis of the epistemological assumptions underlying the U.S. cases to be highly insightful all by itself.  In just a few pages he captures what seem to me to be the core epistemological assumptions of the conduct of sociological research in the U.S.  These include:

  • the assumption of “general regular reality” (the assumption that social phenomena are “really” governed by underlying regularities)
  • deductivism
  • epistemic objectivity
  • a preference for quantification and abstract vocabulary
  • separation of fact and value; value neutrality

There is a clear (?) parallel dispute in the study of economics as well, made all the more complicated by the allegations leveled at economics as a discipline as a result of the global financial crisis.

Nassim Taleb takes bat, ball; goes home

The author of The Black Swan doesn’t approve of the looming reappointment of Ben Bernanke as chairman of the US Federal Reserve.  Writing in the Huffington Post, he says:

What I am seeing and hearing on the news — the reappointment of Bernanke — is too hard for me to bear. I cannot believe that we, in the 21st century, can accept living in such a society. I am not blaming Bernanke (he doesn’t even know he doesn’t understand how things work or that the tools he uses are not empirical); it is the Senators appointing him who are totally irresponsible — as if we promoted every doctor who caused malpractice. The world has never, never been as fragile. Economics make[sic] homeopath and alternative healers look empirical and scientific.

No news, no press, no Davos, no suit-and-tie fraudsters, no fools. I need to withdraw as immediately as possible into the Platonic quiet of my library, work on my next book, find solace in science and philosophy, and mull the next step. I will also structure trades with my Universa friends to bet on the next mistake by Bernanke, Summers, and Geithner. I will only (briefly) emerge from my hiatus when the publishers force me to do so upon the publication of the paperback edition of The Black Swan.

Bye,
Nassim

That’s quite a god complex Taleb’s got going on there (“he doesn’t even know he doesn’t understand how things work”).

The likelihood-ratio threshold is the shadow price of statistical power

Cosma Shalizi, an associate professor in statistics at Carnegie Mellon University, gives an interpretation of the likelihood-ratio threshold in an LR test: It’s the shadow price of statistical power:

[…]

Suppose we know the probability density of the noise p and that of the signal is q. The Neyman-Pearson lemma, as many though not all schoolchildren know, says that then, among all tests off a given size s, the one with the smallest miss probability, or highest power, has the form “say ‘signal’ if q(x)/p(x) > t(s), otherwise say ‘noise’,” and that the threshold t varies inversely with s. The quantity q(x)/p(x) is the likelihood ratio; the Neyman-Pearson lemma says that to maximize power, we should say “signal” if its sufficiently more likely than noise.

The likelihood ratio indicates how different the two distributions — the two hypotheses — are at x, the data-point we observed. It makes sense that the outcome of the hypothesis test should depend on this sort of discrepancy between the hypotheses. But why the ratio, rather than, say, the difference q(x) – p(x), or a signed squared difference, etc.? Can we make this intuitive?

Start with the fact that we have an optimization problem under a constraint. Call the region where we proclaim “signal” R. We want to maximize its probability when we are seeing a signal, Q(R), while constraining the false-alarm probability, P(R) = s. Lagrange tells us that the way to do this is to minimize Q(R) – t[P(R) – s] over R and t jointly. So far the usual story; the next turn is usually “as you remember from the calculus of variations…”

Rather than actually doing math, let’s think like economists. Picking the set R gives us a certain benefit, in the form of the power Q(R), and a cost, tP(R). (The ts term is the same for all R.) Economists, of course, tell us to equate marginal costs and benefits. What is the marginal benefit of expanding R to include a small neighborhood around the point x? Just, by the definition of “probability density”, q(x). The marginal cost is likewise tp(x). We should include x in R if q(x) > tp(x), or q(x)/p(x) > t. The boundary of R is where marginal benefit equals marginal cost, and that is why we need the likelihood ratio and not the likelihood difference, or anything else. (Except for a monotone transformation of the ratio, e.g. the log ratio.) The likelihood ratio threshold t is, in fact, the shadow price of statistical power.

It seems sensible to me.

Characterising the conservative/progressive divide

I’ve been thinking a little about the underlying differences between progressives/liberals and conservatives in the American (US) setting.  I’m not really thinking of opinions on economics or the ideal size of government, but views on economics and government would clearly be affected by what I describe.  Instead, I’m trying to imagine underlying bases for the competing social and political ideologies.

I’m not claiming any great insight, but it’s helped me clarify my thinking to imagine three overlapping areas of contention.  Each area helps inform the topic that follows in a manner that ought to be fairly clear:

  1. On epistemology and metaphysics.  Conservatives contend that there exist absolute truths which we can sometimes know, or even – at least in principle – always know.  In contrast, progressives embrace the postmodern view that there may not be any absolute truths and that, even if absolute truths do exist, our understanding of them is always relative and fallible.
  2. On the comparison of cultures[by “cultures”, I here include all traditions, ways of life, interactional mannerisms and social institutions in the broadest possible sense].  Conservatives contend that it is both possible and reasonable to compare and judge the relative worthiness of two cultures.  At an extreme, they suggest that this is plausible in an objective, universal sense.  A little more towards the centre, they alternately suggest that individuals may legitimately perform such a comparison to form private opinions.  Centrist progressives instead argue that while it might be possible to declare one culture superior to another, it is not reasonable to do so (e.g. because of the relative nature of truth).  At their own extreme, progressives argue that it is not possible to make a coherent comparison between two cultures.
  3. On changing one’s culture.  Conservatives suggest that change, in and of itself, is a (slightly) bad thing that must be justified with materially better conditions as a result of the change.  Progressives argue that change itself is neutral (or even a slightly good thing).  This leads to conflict when the material results of the change are in doubt and the agents are risk averse.  To the conservative mind, certain loss (from the act of changing) is being weighed against uncertain gain.  To the progressive mind, the act of change is a positive act of exploration which partially offsets the risks of an uncertain outcome.

Regulation should set information free

Imagine that you’re a manager for a large investment fund and you’ve recently been contemplating your position on Citigroup.  How would this press release from Citi affect your opinion of their prospects?:

New York – Citi today announced the sale of its entire ownership interest of three North American partner credit card portfolios representing approximately $1.3 billion in managed assets. The cards portfolios were part of Citi Holdings. Terms of the deals were not disclosed. Citi will continue to service the portfolios through the first half of 2010 at which time the acquirer will assume all customer servicing aspects of the portfolios.

The sale of these card portfolios is consistent with Citi’s strategy to optimize the assets and businesses within Citi Holdings while working to generate long-term profitability and growth from Citicorp, which comprises its core franchise. Citi continues to make progress on its strategy and will continue to pursue opportunities within Citi Holdings that create the most value for stakeholders.

The answer should be “not much, or perhaps a little negatively” because the press release contains close to no information at all.  Here is Floyd Norris:

A few unanswered questions:

1. Who is the buyer?
2. Which card portfolios are being sold?
3. What is the price?
4. Is there a profit or loss?

A check of Citi’s last set of disclosures shows that Citi Holdings had $67.6 billion in such credit card portfolios in the second quarter, so this is a small part of that. Still, I can’t remember a deal announcement when a company said it had sold undisclosed assets to an undisclosed buyer for an undisclosed price, resulting in an undisclosed profit or loss.

Chris Kaufman at Reuters noted the same.

Now, to be fair, there is some information in the release if you have some context.  In January 2009 Citigroup separated “into Citicorp, housing its key banking business, and Citi Holdings, which included its brokerage, consumer finance, and troubled assets.”  In other words, Citi Holdings is the bucket holding “assets that Citigroup is trying to sell or wind down.”  The press release is a signal to the market that Citi has been able to offload some of those assets – it’s an attempt to speak of improved market conditions.  But the refusal to release any details suggests that they sold the portfolios at a deep discount to face value, which implies either that Citi was desperate for the cash (a negative signal) or that they think the portfolios were worth even less than they got for them, which doesn’t bode well for the rest of their credit card holdings (also a negative signal).  It’s unsurprising, then, that Citi were down 4.1% in afternoon trading after the release.

Some more information did emerge later on.  American Banker, citing “industry members with knowledge of the transaction,” reported:

The buyer was U.S. Bancorp, according to industry members with knowledge of the transaction, who identified the assets as the card portfolios for KeyCorp and Associated Banc-Corp, which Citi issues as an agent bank, and the affinity card for the American Dental Association.

But a spokeswoman for Citi, which only identified the portfolios as “North American partner credit card portfolios” in a press release, would not comment, identify the buyer, or elaborate on the release. U.S. Bancorp, Associated Bank and the American Dental Association did not return calls by press time; a spokesman for KeyCorp would not discuss the matter.

It’s tremendously frustrating that even this titbit of information needed to be extracted via a leak.  Did Maria Aspan — the author of the piece at American Banker — take somebody out for a beer?  Did the information come from somebody at Citigroup, Bancorp or one of the law firms that represent them?

In what seems perfectly designed to turn that furstration into anger, we then have other media outlets reporting this extra information unattributedHere‘s the Wall Street Journal:

Citigroup Inc. sold its interest in three North American credit-card portfolios to U.S. Bancorp of Minneapolis, continuing the New York bank’s effort to unload assets that aren’t considered to be a core part of its business, according to people familiar with the situation.

[…]

Citigroup announced the sale, but it didn’t identify the buyer or type of portfolio that was being sold. Representatives of U.S. Bancorp couldn’t be reached for comment.

That’s it.  There’s no mention of where they got Bancorp from at all.

It’s all whispers and rumours, friendships and acquaintences.  It’s no way for the market to get their information.

Here’s my it’ll-never-happen suggestion for improving banking regulation:

Any purchase or sale of assets representing more than 1% of a bank’s previous holdings in that asset class [in this case the sale represented 1.9% of Citi’s credit card holdings] must be accompanied by the immediate public release of information uniquely identifing the assets bought or sold and the agreed terms of the deal, including the price.  Identities of all parties involved must be publicly disclosed within 6 months of the transaction.

Article Summary: Noisy Directional Learning and the Logit Equilibrium

The paper is here (ungated).  The ideas.repec entry is here.  I believe that this (1999) was an early version of the same.  The authors are Simon P. Anderson [Ideas, Virginia] , Jacob K. Goeree [Ideas, CalTech] and Charles A. Holt [Ideas, Virginia].  The full reference is:

Anderson, Simon P.; Goeree, Jacob K. and Holt, Charles A., “Noisy Directional Learning and the Logit Equilibrium.” Scandinavian Journal of Economics, Special Issue in Honor of Reinhard Selten, 2004, 106(3), pp. 581-602, September 2004

The abstract:

We specify a dynamic model in which agents adjust their decisions toward higher payoffs, subject to normal error. This process generates a probability distribution of players’ decisions that evolves over time according to the Fokker–Planck equation. The dynamic process is stable for all potential games, a class of payoff structures that includes several widely studied games. In equilibrium, the distributions that determine expected payoffs correspond to the distributions that arise from the logit function applied to those expected payoffs. This ‘‘logit equilibrium’’ forms a stochastic generalization of the Nash equilibrium and provides a possible explanation of anomalous laboratory data.

This is a model of bounded rationality inspired, in part, by experimental results.  It provides a stochastic equilibrium (i.e. a distribution over choices) that need not coincide with, nor even be centred around, the Nash equilibrium.  The summary is below the fold.

Continue reading “Article Summary: Noisy Directional Learning and the Logit Equilibrium”