LARS P. SYLL

Sherlock Holmes inference and econometric testing

Sherlock Holmes stated that ‘It is a capital mistake to theorize before one has data. Insensibly one begins to twist facts to suit theories, instead of theories to suit facts.’ True this may be in the circumstance of crime investigation, the principle does not apply to testing. In a crime investigation one wants to know what actually happened: who did what, when and how. Testing is somewhat different.

With testing, not only what happened is interesting, but what could have happened, and what would have happened were the circumstances to repeat itself. The particular events under study are considered draws from a larger population. It is the distribution of this population one is primarily interested in, and not so much the particular realizations of that distribution. So not the particular sequence of head and tails in coin flipping is of interest, but whether that says something about a coin being biased or not. Not (only) whether inflation and unemployment went together in the sixties is interesting, but what that tells about the true trade-off between these two economic variables. In short, one wants to test.

The tested hypothesis has to come from somewhere and to base it, like Holmes, on data is valid procedure … The theory should however not be tested on the same data they were derived from. To use significance as a selection criterion in a regression equation constitutes a violation of this principle …

Consider for example time series econometrics … It may not be clear a priori which lags matter, while it is clear that some definitely do … The Box-Jenkins framework models the auto-correlation structure of a series as good as possible first, postponing inference to the next stage. In this next stage other variables or their lagged values may be related to the time series under study. While this justifies why time series uses data mining, it leaves unaddressed the issue of the true level of significance …

This is sometimes recommended in a general-to-specific approach where the most general model is estimated and insignificant variables are subsequently discarded. As superfluous variables increase the variance of estimators, omitting irrelevant variables this way may increase efficiency. Problematic is that variables were included in the first place because they were thought to be (potentially) relevant. If then for example twenty variables, believed to be potentially relevant a priori, are included, then one or more will bound to be insignificant (depending on the power, which cannot be trusted to be high). Omitting relevant variables, whether they are insignificant or not, generally biases all other estimates as well due to the well-known omitted variable bias. The data are thus used both to specify the model and test the model; this is the problem of estimation. Without further notice this double use of the data is bound to be misleading if not incorrect. The tautological nature of this procedure is apparent; as significance is the selection criterion it is not very surprising selected variables are significant.

D. A. Hollanders Five methodological fallacies in applied econometrics

Econometric disillusionment

Because I was there when the economics department of my university got an IBM 360, I was very much caught up in the excitement of combining powerful computers with economic research. Unfortunately, I lost interest in econometrics almost as soon as I understood how it was done. My thinking went through four stages:

1.Holy shit! Do you see what you can do with a computer’s help.
2.Learning computer modeling puts you in a small class where only other members of the caste can truly understand you. This opens up huge avenues for fraud:
3.The main reason to learn stats is to prevent someone else from committing fraud against you.
4.More and more people will gain access to the power of statistical analysis. When that happens, the stratification of importance within the profession should be a matter of who asks the best questions.

Disillusionment began to set in. I began to suspect that all the really interesting economic questions were FAR beyond the ability to reduce them to mathematical formulas. Watching computers being applied to other pursuits than academic economic investigations over time only confirmed those suspicions.

1.Precision manufacture is an obvious application for computing. And for many applications, this worked magnificently. Any design that combined straight line and circles could be easily described for computerized manufacture. Unfortunately, the really interesting design problems can NOT be reduced to formulas. A car’s fender, for example, can not be describe using formulas—it can only be described by specifying an assemblage of multiple points. If math formulas cannot describe something as common and uncomplicated as a car fender, how can it hope to describe human behavior?
2.When people started using computers for animation, it soon became apparent that human motion was almost impossible to model correctly. After a great deal of effort, the animators eventually put tracing balls on real humans and recorded that motion before transferring it to the the animated character. Formulas failed to describe simple human behavior—like a toddler trying to walk.

Lately, I have discovered a Swedish economist who did NOT give up econometrics merely because it sounded so impossible. In fact, he still teaches the stuff. But for the rest of us, he systematically destroys the pretensions of those who think they can describe human behavior with some basic Formulas.

Jonathan Larson

Wonder who that Swedish guy is …

Data mining and the meaning of the Econometric Scripture

Some variants of ‘data mining’ can be classified as the greatest of the basement sins, but other variants of ‘data mining’ can be viewed as important ingredients in data analysis. Unfortunately, these two variants usually are not mutually exclusive and so frequently conflict in the sense that to gain the benefits of the latter, one runs the risk of incurring the costs of the former.

Hoover and Perez (2000, p. 196) offer a general definition of data mining as referring to “a broad class of activities that have in common a search over different ways to process or package data statistically or econometrically with the purpose of making the final presentation meet certain design criteria.” Two markedly different views of data mining lie within the scope of this general definition. One view of ‘data mining’ is that it refers to experimenting with (or ‘fishing through’) the data to produce a specification … The problem with this, and why it is viewed as a sin, is that such a procedure is almost guaranteed to produce a specification tailored to the peculiarities of that particular data set, and consequently will be misleading in terms of what it says about the underlying process generating the data. Furthermore, traditional testing procedures used to ‘sanctify’ the specification are no longer legitimate, because these data, since they have been used to generate the specification, cannot be judged impartial if used to test that specification …

An alternative view of ‘data mining’ is that it refers to experimenting with (or ‘fishing through’) the data to discover empirical regularities that can inform economic theory … Hand et al (2000) describe data mining as the process of seeking interesting or valuable information in large data sets. Its greatest virtue is that it can uncover empirical regularities that point to errors/omissions in theoretical specifications …

In summary, this second type of ‘data mining’ identifies regularities in or characteristics of the data that should be accounted for and understood in the context of the underlying theory. This may suggest the need to rethink the theory behind one’s model, resulting in a new specification founded on a more broad-based understanding. This is to be distinguished from a new specification created by mechanically remolding the old specification to fit the data; this would risk incurring the costs described earlier when discussing the first variant of ‘data mining.’

The issue here is how should the model specification be chosen? As usual, Leamer (1996, p. 189) has an amusing view: “As you wander through the thicket of models, you may come to question the meaning of the Econometric Scripture that presumes the model is given to you at birth by a wise and beneficent Holy Spirit.”

In practice, model specifications come from both theory and data, and given the absence of Leamer’s Holy Spirit, properly so.

Peter Kennedy

Watch out for econometric sinning in the basement!

Brad DeLong wonders why Cliff Asness is clinging to a theoretical model that has clearly been rejected by the data …

 
There’s a version of this in econometrics, i.e. you know the model is correct, you are just having trouble finding evidence for it. It goes as follows. You are testing a theory you came up with, but the data are uncooperative and say you are wrong. But instead of accepting that, you tell yourself “My theory is right, I just haven’t found the right econometric specification yet. I need to add variables, remove variables, take a log, add an interaction, square a term, do a different correction for misspecification, try a different sample period, etc., etc., etc.” Then, after finally digging out that one specification of the econometric model that confirms your hypothesis, you declare victory, write it up, and send it off (somehow never mentioning the intense specification mining that produced the result).

Too much econometric work proceeds along these lines. Not quite this blatantly, but that is, in effect, what happens in too many cases. I think it is often best to think of econometric results as the best case the researcher could make for a particular theory rather than a true test of the model.

Mark Thoma

Mark touches the spot — and for the sake of balancing the overly rosy picture of econometric achievements given in the usual econometrics textbooks today, it may also be interesting to see how Trygve Haavelmo, with the completion (in 1958) of the twenty-fifth volume of Econometrica, assessed the the role of econometrics in the advancement of economics. Although mainly positive of the “repair work” and “clearing-up work” done, Haavelmo also found some grounds for despair:

We have found certain general principles which would seem to make good sense. Essentially, these principles are based on the reasonable idea that, if an economic model is in fact “correct” or “true,” we can say something a priori about the way in which the data emerging from it must behave. We can say something, a priori, about whether it is theoretically possible to estimate the parameters involved. And we can decide, a priori, what the proper estimation procedure should be … But the concrete results of these efforts have often been a seemingly lower degree of accuracy of the would-be economic laws (i.e., larger residuals), or coefficients that seem a priori less reasonable than those obtained by using cruder or clearly inconsistent methods.

There is the possibility that the more stringent methods we have been striving to develop have actually opened our eyes to recognize a plain fact: viz., that the “laws” of economics are not very accurate in the sense of a close fit, and that we have been living in a dream-world of large but somewhat superficial or spurious correlations.

And as the quote below shows, Frisch also shared some of Haavelmo’s — and Keynes’s — doubts on the applicability of econometrics:

I have personally always been skeptical of the possibility of making macroeconomic predictions about the development that will follow on the basis of given initial conditions … I have believed that the analytical work will give higher yields – now and in the near future – if they become applied in macroeconomic decision models where the line of thought is the following: “If this or that policy is made, and these conditions are met in the period under consideration, probably a tendency to go in this or that direction is created”.

Ragnar Frisch