Wednesday, April 29, 2009

Induction, deduction, and a model is only as good as its interpretation

View, understand, and then predict the behavior of the macro environment, rather than attempting to go from assumptions about micro to predictions about macro. – Robert Haugen, Emeritus Professor of Finance, University of California, Irvine. From his 2004 book, "The New Finance", 3rd Edition, page 123.

...as we travel from left to right, we go from order to complexity and finally into chaos.

At the extreme left, where there is order, mathematical models predict and explain well [as in much of physics].

As we move to the right, induction and statistical estimation dominate deduction and mathematical modeling in their ability to explain and predict... –"The New Finance", page 131.

Financial economists, both rational and behavioral, dazzle themselves with sophisticated mathematics. They gain much comfort in the intellectual rigor of their methodologies.

It makes no difference if their assumptions are completely unrealistic, so long as they parallel those made by their peers.

To them elegance [advanced, complete, and impressive mathematics] is all that matters. They look with disdain on studies of psychologists, sociologists, and anthropologists because their work seems so mushy in comparison to their own. They dismiss as unimportant forces that may actually be crucial but impossible to treat with mathematical rigor. –"The New Finance", page 132.

Reading London School economist John Kay's recent Financial Times article, "How Economics Lost Sight of the Real World", reminded me of Robert Haugen. Haugen is a maverick (let's not let John McCain and Sarah Palin ruin an important word), who fought very hard, and caustically, for decades against grossly unrealistic literal, or relatively literal, interpretation of models that show tremendous efficiency by making assumptions like, for example:

– Everyone in the world has perfect, or near perfect, rationality.

– Everyone in the world has advanced and specialized expertise in finance, economics, law, government, science, etc., that takes years or even decades of education and training to acquire. Or, they are able to perfectly know who has that expertise and can also be trusted to give it honestly, and at relatively little or no cost.

– Gathering information relevant to financial asset valuation (information, not just data) takes no time and is costless – even massive information gathering.

– Analysis of information relevant to financial asset valuation – even massive amounts of very complicated and difficult to interpret information – takes no time and is costless.

– Unlimited liquidity for all assets, and all buyers and short sellers.

– All assets can be sold short, and this short selling can be done instantly and at zero transactions cost.

– Even a relatively tiny number of savvy investors will have enough wealth, or access to enough wealth, that they can always buy assets up to their efficient price (Note: Even if they actually did have enough wealth to do this if they wanted to, a big problem that I pointed out in a 2006 letter in the Economist's Voice, which I have not seen elsewhere in the literature at least explicitly, is that they would be constrained by how undiversified their portfolio could become. As I wrote:
...suppose IBM is currently selling for $100, but its efficient, or rational informed, price is $110. It must be remembered that the rational informed price is what the stock is worth to the investor when added in the appropriate proportion to his properly diversified portfolio of other assets. Such a savvy investor will purchase more IBM as it only costs $100, but as soon as he purchases more IBM, IBM becomes worth less to him per share, because it becomes increasingly risky to put so much of his money in the IBM basket. By the time this investor has purchased enough IBM that it constitutes 20 percent of his portfolio, the stock may have become so risky that it’s worth less than $100 to him for an additional share. At that point he may have only purchased enough IBM stock to push the price to $100.02, far short of its efficient market price of $110. Thus, if the rational and informed investors do not hold or control enough—a large enough proportion of the wealth invested in the market—they may not be able to come close to pushing prices to the efficient level.
– The global equilibrium of the model is reached before any of the exogenous factors change, rather than those exogenous factors regularly changing before the economy can get anywhere close to that equilibrium (oh, and heaven forbid that a model should ever not have an equilibrium, that some key things should just always move, on average, in one direction. That never happens in reality over any time period of important length – except for trivial things like GDP growth, accumulation of knowledge, and advancement of technology)

– All asset returns have a normal data generating process (DGP), or some other DGP which is simple enough to write mathematically on a single line, or maybe a few, (The real DGP, depending on the level of precision you desire, can take thousands of pages to describe, or more), and has at least relatively thin, well behaved tails.

– Quick simple local numerical optimization techniques will find the global optimum even in highly complicated, high dimensional problems (and any cherry picking the starting point to get a more publishable result is fine, especially since you're almost never asked to provide the computer programs and a large class of important assumptions and details you used by the academic finance journals, including by and large the top ones)

– Accuracy and stability of numerical algorithms is never a problem, so you can use whatever techniques you know, whichever are the easiest, or give you the most publishable results. (And, you learn how to do numerical accuracy and stability well and then spend the time to do it well at your own peril. Because it's given little if any consideration at the academic finance journals, and it takes a lot of time, which will substantially lower your publication production and therefore your advancement.)

Of course, not all models in economics and finance that conclude great efficiency make all of these assumptions, but they all make assumptions like these, that as a group are extremely unrealistic. Does that mean that you can't still learn some valuable lessons from models like these? No. Often you can. But you have to interpret the model intelligently, using high level, not mechanical, intelligence. You certainly don't unthinkingly automatically interpret these models literally, as if the real world behaves exactly, or even qualitatively exactly, like the model. And the same goes for econometric models and techniques utilizing empirical data.

Now let's get back to Haugen. In his 2004 book, "The New Finance", 3rd edition (the 4th is being released May 2nd), he makes many of the same points Kay does, as well as important related ones. I think this book can convey some very important insights that are seldom or never heard in the academic finance literature, but like models, and like most writing today, you should be careful about interpreting it too literally. There's hyperbolic or very hyperbolic writing throughout the book, and many of the statements are literally exaggerated, or falsely absolute.

Does Haugen understand that these statements are exaggerated and falsely absolute? I've read a lot of his work, and he's extremely intelligent. I think he does understand this, at least in most cases. In part, though, like almost everyone, he succumbs at least to a substantial extent to the great pressure to write with what's considered "good style", and that means smooth and simple, (as well as, depending on the venue, profound-sounding, "professional", entertaining, etc.) even if it results in a false simplicity, saying things that are literally false and/or likely to mislead a substantial percentage of the readers in important ways (for more on this, see my very first blog post).

In large part, though, Haugen is just shouting because he's angry, and because it's so hard to get through with the grip the unrealistic efficient market people have (and especially had) on academic finance, with their great control of the journals and departments, and therefore advancement, prestige and money.

That said, let's get to some of the statements in Haugen's book that are similar to, or related to, statements in Kay's article. I think they can add valuable insight; there's a lot of truth to them. But again, I recommend that you be careful not to take Haugen's exaggerated and absolutist statements completely literally:

KAY: Since the 1970s economists have been engaged in a grand project. The project’s objective is that macroeconomics should have microeconomic foundations...

Most economists would claim that the project has been a success. But the criteria are the self-referential criteria of modern academic life. The greatest compliment you can now pay an economic argument is to say it is rigorous. Today’s macroeconomic models are certainly that...

But policymakers and the public at large are, rightly, not interested in whether models are rigorous. They are interested in whether the models are useful and illuminating – and these rigorous models do not score well here...There is not, and never will be, an economic theory of everything. Physics may, or may not, be different. But the knowledge we can hope to have in economics is piecemeal and provisional, and different theories will illuminate different but particular situations. We should observe empirical regularities and – as in other applied subjects such as medicine and engineering – we will often find pragmatic solutions that work even though our understanding of why they work is incomplete.

HAUGEN: Chaos aficionados sometimes use the example of smoke from a cigarette rising from an ashtray. The smoke rises in an orderly and predictable fashion in the first few inches. Then the individual particles, each unique, begin to interact. The interactions become important. Order turns to complexity. Complexity turns to chaotic turbulence...(page 122)

How then to understand and predict the behavior of an interactive system of traders and their agents?

Not by taking a micro approach, where you focus on the behaviors of individual agents, assume uniformity in their behaviors, and mathematically calculate the collective outcome of these behaviors.

Aggregation will take you nowhere.

Instead take a macro approach. Observe the outcomes of the interaction – market-pricing behaviors. Search for tendencies after the dynamics of the interactions play themselves out.

View, understand, and then predict the behavior of the macro environment, rather than attempting to go from assumptions about micro to predictions about macro...(page 123)

...as we travel from left to right [in figure 10-5 above], we go from order to complexity and finally into chaos.

At the extreme left, where there is order, mathematical models predict and explain well [as in much of physics].

As we move to the right, induction and statistical estimation dominate deduction and mathematical modeling in their ability to explain and predict...

Induction dominates deduction in its predictive power... (page 131)

Financial economists, both rational and behavioral, dazzle themselves with sophisticated mathematics. They gain much comfort in the intellectual rigor of their methodologies.

It makes no difference if their assumptions are completely unrealistic, so long as they parallel those made by their peers.

To them elegance [advanced, complete, and impressive looking mathematics] is all that matters. They look with disdain on studies of psychologists, sociologists, and anthropologists because their work seems so mushy in comparison to their own. They dismiss, as unimportant forces that may actually be crucial but impossible to treat with mathematical rigor. (page 132)

I largely agree with Haugen, but a key point of disagreement, at least with what he often writes literally, is that deduction is useless, or near useless, in highly complex situations. Deduction can still be extremely valuable.

Although in such situations deduction alone is not very good at very precise forecasts:

a) It can still give you very valuable qualitative understanding and ideas, like if you do X, or follow X policy, you will become much wealthier, at least 50% wealthier. You don't know the amount very precisely, but you do know that it's in a big range, and so the policy or idea is well worth doing. For example, the Capital Asset Pricing Model (CAPM) may not be very good (used alone) at precise forecasts of stock prices, but it does make clear that I can get a far lower risk level, not just a little lower, but far lower, for a given mean return, if I buy stocks in a large, highly diversified portfolio, than if I buy them singly, if I'm a layperson with no special information or analysis.

b) The understanding we get from deduction can help us improve our inductive research and models. It can give us a much better idea of where to look and what to look at in the inductive process of studying end results and situations. But we only get good and valuable understanding from deductive models if we interpret them intelligently, not automatically literally, or automatically qualitatively literally. It's worth repeating: A model is only as good as its interpretation.

c) Deductive understanding can be combined with inductive models and econometrics to substantially – often greatly – improve the forecasts. It can tell us when the inductive model's forecast based on the past will be much too low, or much too high, because of important recent changes from the past.

The problem isn't that deduction, and deductive models, are useless, or near-useless, in highly complex situations. It's that especially fresh water economists have been making ridiculously overly-literal interpretations and claims from deductive models. This is partly due to a focus on mathematics rather than economic intuition and other high level thinking. And it's partly due to the fact that many of these economists are extremely Libertarian, and are very willing to intentionally mislead in making conclusions from these models to support Libertarian economic policies.

In addition, there is a very strong incentive to make untrue big claims about an academic's models, or the models in an academic's area, so that they are more likely to be published in top journals, which is overwhelmingly what determines employment, promotion, power, prestige, and earnings. Academics especially feel freer to make these claims when they use advanced mathematics so little known that not only the general public can't read the papers to see how overblown and downright false they are, even the vast majority of fellow economists can't; even for them these paper are like written in Greek. They may even speak some Greek, but to decipher Greek this elaborate and advanced would take a lot more time than they have, especially since the vast majority of economists are not in this area and don't get paid to spend time in this area.

Eventually we reached a point where academics making grandiose, but ridiculous claims from highly mathematical models with efficient equalibria exerted great control at the top journals. And they used their gatekeeper ability to fight very hard to allow in papers that agreed with them, and to keep out papers that didn't. Sadly, they have been very successful at this, and they did it largely because if their research became a lot less prestigious and publishable, it would mean a huge decrease in personal prestige, positions, prizes, and earnings.

Likewise, their students, future economists, had a huge incentive to push these ridiculous claims and conclusions, because they had spent years learning these models and the associated mathematics, and if the claims of these models were exposed, their ability to publish in top journals, and from that to get high paying, high prestige jobs at top universities, would decrease dramatically. Since Economics Ph.D. students at schools like Chicago are largely type A, ultra-ambitious from childhood, work-a-holics, the thought of ending up making $80,000 per year as a professor at Penn State, rather than hundreds of thousands, or millions per year, including royalties, consulting, etc., at Chicago, is a huge incentive to support the party line.

So there are serious problems in economics and finance academia that stem pivotally from enormous asymmetric information, the fact that those predominantly paying for the research, the tax payers, have almost no ability to understand the highly mathematical and technical papers, and discern which are of great societal value, which are of little, and which have extremely unrealistic and harmful overly-literal conclusions from models to the real world.

We talk about market problems in finance justifying greater regulation, but the same may be true of finance academia, and economics academia. We really need to think about having a federal government department to monitor, study, and regulate, at least to some extent, how academia uses it's human and other resources, whether they are being spent in proportion to their risk-adjusted expected societal value over the short, medium, long, and extremely long run. The journals and departments right now, and for some time, award publications, grants, jobs, promotions, and prizes grossly out of line with the social NPV of the research work.

We really need to seriously study the idea, and specifics, of a large federal government department staffed by academics in economics, finance and other fields to study whether their academic fields, their departments and journals, are rewarding, and spending resources, in line with societal NPV (which does, of course, consider all benefits, including very long term, and unlikely but potentially huge), rather than largely in line with the enjoyment, prestige, and enrichment of those in control. And if things are way out of line, the government department has strong and wide ranging powers to do something about it.

Such a government department will, of course, need to develop a culture of loyalty to the public good, and not one's academic field. And there will need to be transparency and watchdogs, and in general the systems, techniques, and procedures which have greatly improved the efficiency and professionalness of civil service over the last century (especially when we have a party in power that tries to make government succeed, rather than one which tries to make it fail, and uses it extensively to enrich cronies).

Certainly there are problems with this idea; any implementation would require a lot of fine tuning, checks and balances and safeguards, with some portion of funds earmarked to be spent completely at academic department disgression, but too many economists forget a cornerstone of economics, that analyses should be cost-benefit, not cost alone. Yes, there are costs and problems with this idea, but the benefits could be enormous, and the costs of doing nothing could be far larger. If academic economics and finance had been tightly focused on honest research to maximize societal NPV over the last generation, we could easily have generated trillions of dollars more in wealth and total societal utility. A great place to start in increasing economics' societal NPV would be stopping the gatekeepers from ignoring the pink elephant of economics, positional/context/prestige externalities.