PKT message, Statistical Method And Economics [Was: Re: Piorot on Madrick

As one, whose formal study of statistical method comprised a couple of courses at Manchester University some 40 years ago, I had occasion a few days ago to check out some of the work of the late Edwin T. Jaynes, whose 'Probability Theory - The Logic of Science' - summarizing his life-long cutting-edge work in the field - is now in the final pre-publication stage.

If, as someone put it, Jaynes was the "real McCoy" in the field, then the extract below from an early 1980s paper of his on 'The Intuitive Inadequacy Of Classical Statistics' would seem to raise important questions with respect to the logical coherence of the modus operandi of modern theoretical economists as reflected, inter alia, in the underlined parts of the following:

PAUL: Fundamentals in the long run-- are you assuming that the P/E ratios in the future are drawn from the same universe as the P/E ratios of past and current samples? If you are you are assuming the future is predetermined; if you are not then the future is uncertain and there is NO information regarding P/E ratios over the life of long-lived capital assets. You must choose which side of the street you are working Chip.

Here is Jaynes on related issues:

In any approach, the reasoning format one can use is determined by the techniques used to make these connections between the mathematics and the real world. In principle, orthodox theory recognizes such a connection only when it consists of empirically observable frequencies. But one can work in statistics for a long time without ever encountering a real problem in which the data actually consist of frequencies. Therefore, to maintain this viewpoint, if frequencies are not already inherent in the nature of the problem and the data, they must be implanted by artificial means.

The technique for doing this is well known. Given some data D1, we imbed it in a "sample space" (D1, D2...., Dn) containing other data that one postulates might have been observed, but were not. Then one introduces a "sampling distribution" consisting of the probabilities [such and such] that the data set Di would be observed if some hypothesis H were true. The frequency connection is then made by asserting that, for example, [such and such] is the frequency with which the unobserved data set D2 would have been obtained in the long run if the experiment were repeated indefinitely with H constantly true. Ususally, such sampling distributions are the only probabilities one is allowed to use for inference, because a probability is not considered respectable until a frequency interpretation is bestowed upon it; and this special blessing is reserved for sampling distributions.

But where does the orthodox statistician obtain all this knowledge? What determines the "true" sample space and the "true" sampling distribution? How can one know what the actual frequencies would be? Surely, when one asserts that the long-run results of an arbitrarily long sequence of experiments that have not been performed, he is drawing upon a vivid imagination; and not on any fund of actual knowledge of the phenomenon. How is it possible that for decades claims of great "scientific objectivity" for this approach have not been effectively challenged? It cannot have been only physicists and Bayesians who perceive the lack of substance in such pretensions.

The answer must be that for decades workers have been cowed by the oppressive weight of authority in this field. Indeed, Jimmie Savage [1962a] used just this term in recalling his own early experiences. The path of least resistance - also the one safest for one's worldly career - is to put up a public front, giving lip service to things which we believe to be false, remaining silent on what we see as truth, our of fear of the "clamor of the Boeotians". We know that Newton, Gauss, and von Neumann delayed publication of some of their most original ideas for this reason.

It is not only in science that this false public front is expedient. At the turn of the century, Jules Massenet enjoyed enormous public success with his religious and operatic music; but he said privately to Vincent d'Indy, "I don't believe in all that creeping Jesus stuff, but the public likes it, and we must always agree with the public."

Illusions of objectivity are preserved, not so much by authority imposed from above, but by the ring of authority in an official language that encourages them. "It is a gaussian random process" sounds very much like a statement of physical fact; i.e., something that is true or false independently of anybody's state of knowledge. The notions of sample space, population from which we draw, and sampling frequencies, are almost always represented as if they were physical facts. Like religion, this gives a certain feeling of security that the statistical "public" likes.

Yet almost everyone has lucid moments in which he recognizes that these representations cannot be really true....

But these lucid moments are rare, and the illusions of authority artificially created by our language continue to dominate the way we formulate, and think about, problems of inference. In the case of a time series, that language almost forces us to believe that there exists a "true but unknown" frequency distribution, mean, covariance, power spectrum, etc. which we are to estimate by various means. In occasional lucid moments we must recognize that these things are only figments of our imagination. What does it mean to "estimate" a figment?.... (Epistemologia VII (1984), Fascicolo Speciale - Special Issue. Probability, Statistics, and Inductive Logic, pp. 43-74)

On the basis of my own personal experience with the Harvard Department of Economics triggered by 'unorthodox' ideas back in the mid-1970s, it would not surprise me to learn that these bothersome issues of logic, coherence, and relevance insofar as the statistical methods of modern academic economists are concerned have been brushed aside and ignored.

If it is otherwise, I stand to be corrected.

Gunnar

----- Original Message -----

From: Paul Davidson

To: pkt@xxxxxxxxxxxxxxxx

Sent: Saturday, September 07, 2002 2:01 PM

Subject: Piorot on Madrick

Poirot has written a thoughtful response to the Jeff Madrick article in the New York Times.

Here are some comments of mine on Poirot'