The UKIP Councillor for Henley on Thames in Oxfordshire has written an odd, homophobic letter to a local newspaper.
David Silvester, who resigned from the Conservative Party over David Cameron’s same-sex marriage policy, has said gay marriage is to blame for Britain’s recent spell of bad weather in a letter to The Henley Standard.
He wrote: “Since the passage of the Marriage (Same Sex Couples) Act, the nation has been beset by serious storms and floods.”
Wooh! Who would have thought anything like that.
Impressive indeed …
Isn’t it just splendid with all these intelligent and unprejudiced conservative politicians …
Photo by barnilsson
During my first ten years traveling back and forth between Lund and Berlin it was still there, even when this photo of yours truly — leisurely reading taz — was taken at Café Einstein back in the summer of 1988.
Had anyone told me then that the wall would soon come tumbling down, I would probably just have shaken my head and laughed. At the time everyone thought it was there for good.
For twenty-five years now I’ve been happy we were all so wrong, so wrong.
Having mastered all the technicalities of regression analysis and econometrics, students often feel as though they are the masters of universe. I usually cool them down with a required reading of Christopher Achen‘s modern classic Interpreting and Using Regression. It usually get them back on track again, and they understand that
no increase in methodological sophistication … alter the fundamental nature of the subject. It remains a wondrous mixture of rigorous theory, experienced judgment, and inspired guesswork. And that, finally, is its charm.
Giving an introductory econometrics course, yours truly usually — at the exam — asks students to explain how one should correctly interpret p-values. Although the correct definition is p(data|null hypothesis), a majority of the students either misinterpreted the p-value as being the likelihood of a sampling error (which of course is wrong, since the very computation of the p-value is based on the assumption that sampling errors are what causes the sample statistics not coinciding with the null hypothesis) or that the p-value is the probability of the null hypothesis being true, given the data (which of course also is wrong, since it is p(null hypothesis|data) rather than the correct p(data|null hypothesis)).
This is not to blame on students’ ignorance, but rather on significance testing not being particularly transparent – conditional probability inference is difficult even to those of us who teach and practice it. A lot of researchers fall pray to the same mistakes. So – given that it anyway is very unlikely than any population parameter is exactly zero, and that contrary to assumption most samples in social science and economics are not random or having the right distributional shape – why continue to press students and researchers to do null hypothesis significance testing, testing that relies on weird backward logic that students and researchers usually don’t understand? As Achen writes:
Significance testing as a search for specification errors substitutes calculations for substantive thinking. Worse, it channels energy toward the hopeless search for functionally correct specifications and divert attention from the real tasks, which are to formulate a manageable description of the data and to exclude competing ones.
The techniques we use affect our thinking in deep and not always conscious ways. This was very much the case in macroeconomics in the decades preceding the crisis. The techniques were best suited to a worldview in which economic fluctuations occurred but were regular, and essentially self correcting. The problem is that we came to believe that this was indeed the way the world worked.
To understand how that view emerged, one has to go back to the so-called rational expectations revolution of the 1970s … These techniques however made sense only under a vision in which economic fluctuations were regular enough so that, by looking at the past, people and firms (and the econometricians who apply statistics to economics) could understand their nature and form expectations of the future, and simple enough so that small shocks had small effects and a shock twice as big as another had twice the effect on economic activity. The reason for this assumption, called linearity, was technical: models with nonlinearities—those in which a small shock, such as a decrease in housing prices, can sometimes have large effects, or in which the effect of a shock depends on the rest of the economic environment—were difficult, if not impossible, to solve under rational expectations.
Thinking about macroeconomics was largely shaped by those assumptions. We in the field did think of the economy as roughly linear, constantly subject to different shocks, constantly fluctuating, but naturally returning to its steady state over time …
From the early 1980s on, most advanced economies experienced what has been dubbed the “Great Moderation,” a steady decrease in the variability of output and its major components—such as consumption and investment … Whatever caused the Great Moderation, for a quarter Century the benign, linear view of fluctuations looked fine.
Blanchard’s piece is a confirmation of what I argued in my paper Capturing causality in economics and the limits of statistical inference — since “modern” macroeconom(etr)ics doesn’t content itself with only making “optimal” predictions,” but also aspires to explain things in terms of causes and effects, macroeconomists and econometricians need loads of assumptions — and one of the more important of these is linearity.
So bear with me when I take the opportunity to elaborate a little more on why I — and Olivier Blanchard — find that assumption of such paramount importance and ought to be much more argued for — on both epistemological and ontological grounds — if at all being used.
Limiting model assumptions in economic science always have to be closely examined since if we are going to be able to show that the mechanisms or causes that we isolate and handle in our models are stable in the sense that they do not change when we “export” them to our “target systems”, we have to be able to show that they do not only hold under ceteris paribus conditions and a fortiori only are of limited value to our understanding, explanations or predictions of real economic systems. As the always eminently quotable Keynes wrote (emphasis added) in Treatise on Probability (1921):
The kind of fundamental assumption about the character of material laws, on which scientists appear commonly to act, seems to me to be [that] the system of the material universe must consist of bodies … such that each of them exercises its own separate, independent, and invariable effect, a change of the total state being compounded of a number of separate changes each of which is solely due to a separate portion of the preceding state … Yet there might well be quite different laws for wholes of different degrees of complexity, and laws of connection between complexes which could not be stated in terms of laws connecting individual parts … If different wholes were subject to different laws qua wholes and not simply on account of and in proportion to the differences of their parts, knowledge of a part could not lead, it would seem, even to presumptive or probable knowledge as to its association with other parts … These considerations do not show us a way by which we can justify induction … /427 No one supposes that a good induction can be arrived at merely by counting cases. The business of strengthening the argument chiefly consists in determining whether the alleged association is stable, when accompanying conditions are varied … /468 In my judgment, the practical usefulness of those modes of inference … on which the boasted knowledge of modern science depends, can only exist … if the universe of phenomena does in fact present those peculiar characteristics of atomism and limited variety which appears more and more clearly as the ultimate result to which material science is tending.
Econometrics may be an informative tool for research. But if its practitioners do not investigate and make an effort of providing a justification for the credibility of the assumptions on which they erect their building, it will not fulfill its tasks. There is a gap between its aspirations and its accomplishments, and without more supportive evidence to substantiate its claims, critics will continue to consider its ultimate argument as a mixture of rather unhelpful metaphors and metaphysics. Maintaining that economics is a science in the “true knowledge” business, yours truly remains a skeptic of the pretences and aspirations of econometrics. So far, I cannot really see that it has yielded very much in terms of relevant, interesting economic knowledge.
The marginal return on its ever higher technical sophistication in no way makes up for the lack of serious under-labouring of its deeper philosophical and methodological foundations that already Keynes complained about. The rather one-sided emphasis of usefulness and its concomitant instrumentalist justification cannot hide that neither Haavelmo, nor the legions of probabilistic econometricians following in his footsteps, give supportive evidence for their considering it “fruitful to believe” in the possibility of treating unique economic data as the observable results of random drawings from an imaginary sampling of an imaginary population. After having analyzed some of its ontological and epistemological foundations, I cannot but conclude that econometrics on the whole has not delivered “truth”. And I doubt if it has ever been the intention of its main protagonists.
Our admiration for technical virtuosity should not blind us to the fact that we have to have a cautious attitude towards probabilistic inferences in economic contexts. Science should help us penetrate to “the true process of causation lying behind current events” and disclose “the causal forces behind the apparent facts” [Keynes 1971-89 vol XVII:427]. We should look out for causal relations, but econometrics can never be more than a starting point in that endeavour, since econometric (statistical) explanations are not explanations in terms of mechanisms, powers, capacities or causes. Firmly stuck in an empiricist tradition, econometrics is only concerned with the measurable aspects of reality, But there is always the possibility that there are other variables – of vital importance and although perhaps unobservable and non-linear, not necessarily epistemologically inaccessible – that were not considered for the model. Those who were can hence never be guaranteed to be more than potential causes, and not real causes. A rigorous application of econometric methods in economics really presupposes that the phenomena of our real world economies are ruled by stable causal relations between variables. A perusal of the leading econom(etr)ic journals shows that most econometricians still concentrate on fixed parameter models and that parameter-values estimated in specific spatio-temporal contexts are presupposed to be exportable to totally different contexts. To warrant this assumption one, however, has to convincingly establish that the targeted acting causes are stable and invariant so that they maintain their parametric status after the bridging. The endemic lack of predictive success of the econometric project indicates that this hope of finding fixed parameters is a hope for which there really is no other ground than hope itself.
Real world social systems are not governed by stable causal mechanisms or capacities. As Keynes wrote in his critique of econometrics and inferential statistics already in the 1920s (emphasis added):
The atomic hypothesis which has worked so splendidly in Physics breaks down in Psychics. We are faced at every turn with the problems of Organic Unity, of Discreteness, of Discontinuity – the whole is not equal to the sum of the parts, comparisons of quantity fails us, small changes produce large effects, the assumptions of a uniform and homogeneous continuum are not satisfied. Thus the results of Mathematical Psychics turn out to be derivative, not fundamental, indexes, not measurements, first approximations at the best; and fallible indexes, dubious approximations at that, with much doubt added as to what, if anything, they are indexes or approximations of.
The kinds of “laws” and relations that mainstream econ(ometr)ics has established, are laws and relations about entities in models that presuppose causal mechanisms being atomistic and linear (additive). When causal mechanisms operate in real world social target systems they only do it in ever-changing and unstable combinations where the whole is more than a mechanical sum of parts. If economic regularities obtain they do it (as a rule) only because we engineered them for that purpose. Outside man-made “nomological machines” they are rare, or even non-existant. Unfortunately that also makes most of the achievements of econometrics — as most of contemporary endeavours of mainstream economic theoretical modeling — rather useless.
Unfortunately, in case it needs restating, freshwater economics turned out to be based on two ideas that aren’t true. The first (Fama) is that financial markets are efficient. The second (Lucas/Sargent/Wallace) is that the economy as a whole is a stable and self-correcting mechanism. The rational-expectations theorists didn’t refute Keynesianism: they assumed away the reason for its existence. Their models were based not just on rational expectations but on the additional assertion that markets clear more or less instantaneously. But were that true, there wouldn’t be any such thing as involuntary unemployment, or any need for counter-cyclical monetary policy.
It should be emphasized that the equality between savings and investment … will be valid under all circumstances. In particular, it will be independent of the level of the rate of interest which was customarily considered in economic theory to be the factor equilibrating the demand for and supply of new capital. In the present conception investment, once carried out, automatically provides the savings necessary to finance it. Indeed, in our simplified model, profits in a given period are the direct outcome of capitalists’ consumption and investment in that period. If investment increases by a certain amount, savings out of profits are pro tanto higher …
One important consequence of the above is that the rate of interest cannot be determined by the demand for and supply of new capital because investment ‘finances itself.’
One story that can be told about today’s announcement is the Royal Swedish Academy of Sciences’ own explanation: that French economist Jean Tirole has been awarded the The Sveriges Riksbank Prize in Economic Sciences in Memory of Alfred Nobel for 2014 because he “has clarified how to understand and regulate industries with a few powerful firms.”
The other story is: Tirole has shown how much the real world of capitalism—industries that are dominated by a few firms that have extensive market power, which can charge prices much higher than costs and block the entry of other firms—differs from the fantasy taught in countless introductory courses in economics: a world of perfectly competitive firms, which have no negative effects on society and which therefore don’t need to be regulated …
Last year, the Academy tried to have it both ways, offering the Prize to both Eugene Fama and Robert Schiller. This year, the message is both clearer and yet unspoken: the neoclassical model of perfect competition and individual incentives bears no relation to the kinds of capitalism that exist anywhere in the world.
The most expedient population and data generation model to adopt is one in which the population is regarded as a realization of an infinite superpopulation. This setup is the standard perspective in mathematical statistics, in which random variables are assumed to exist with fixed moments for an uncountable and unspecified universe of events …
This perspective is tantamount to assuming a population machine that spawns individuals forever (i.e., the analog to a coin that can be flipped forever). Each individual is born as a set of random draws from the distributions of Y¹, Y°, and additional variables collectively denoted by S …
Because of its expediency, we will usually write with the superpopulation model in the background, even though the notions of infinite superpopulations and sequences of sample sizes approaching infinity are manifestly unrealistic.
In econometrics one often gets the feeling that many of its practitioners think of it as a kind of automatic inferential machine: input data and out comes casual knowledge. This is like pulling a rabbit from a hat. Great — but first you have to put the rabbit in the hat. And this is where assumptions come in to the picture.
The assumption of imaginary “superpopulations” is one of the many dubious assumptions used in modern econometrics.
As social scientists — and economists — we have to confront the all-important question of how to handle uncertainty and randomness. Should we define randomness with probability? If we do, we have to accept that to speak of randomness we also have to presuppose the existence of nomological probability machines, since probabilities cannot be spoken of – and actually, to be strict, do not at all exist – without specifying such system-contexts. Accepting a domain of probability theory and sample space of infinite populations also implies that judgments are made on the basis of observations that are actually never made!
Infinitely repeated trials or samplings never take place in the real world. So that cannot be a sound inductive basis for a science with aspirations of explaining real-world socio-economic processes, structures or events. It’s not tenable.
In his great book Statistical Models and Causal Inference: A Dialogue with the Social Sciences David Freedman also touched on this fundamental problem, arising when you try to apply statistical models outside overly simple nomological machines like coin tossing and roulette wheels:
Lurking behind the typical regression model will be found a host of such assumptions; without them, legitimate inferences cannot be drawn from the model. There are statistical procedures for testing some of these assumptions. However, the tests often lack the power to detect substantial failures. Furthermore, model testing may become circular; breakdowns in assumptions are detected, and the model is redefined to accommodate. In short, hiding the problems can become a major goal of model building.
Using models to make predictions of the future, or the results of interventions, would be a valuable corrective. Testing the model on a variety of data sets – rather than fitting refinements over and over again to the same data set – might be a good second-best … Built into the equation is a model for non-discriminatory behavior: the coefficient d vanishes. If the company discriminates, that part of the model cannot be validated at all.
Regression models are widely used by social scientists to make causal inferences; such models are now almost a routine way of demonstrating counterfactuals. However, the “demonstrations” generally turn out to depend on a series of untested, even unarticulated, technical assumptions. Under the circumstances, reliance on model outputs may be quite unjustified. Making the ideas of validation somewhat more precise is a serious problem in the philosophy of science. That models should correspond to reality is, after all, a useful but not totally straightforward idea – with some history to it. Developing appropriate models is a serious problem in statistics; testing the connection to the phenomena is even more serious …
In our days, serious arguments have been made from data. Beautiful, delicate theorems have been proved, although the connection with data analysis often remains to be established. And an enormous amount of fiction has been produced, masquerading as rigorous science.
And as if this wasn’t enough, one could — as we’ve seen — also seriously wonder what kind of “populations” these statistical and econometric models ultimately are based on. Why should we as social scientists — and not as pure mathematicians working with formal-axiomatic systems without the urge to confront our models with real target systems — unquestioningly accept models based on concepts like the “infinite superpopulations” used in e.g. the potential outcome framework that has become so popular lately in social sciences?
Of course one could treat observational or experimental data as random samples from real populations. I have no problem with that. But probabilistic econometrics does not content itself with that kind of populations. Instead it creates imaginary populations of “parallel universes” and assume that our data are random samples from that kind of “infinite superpopulations.”
But this is actually nothing else but hand-waving! And it is inadequate for real science. As David Freedman writes:
With this approach, the investigator does not explicitly define a population that could in principle be studied, with unlimited resources of time and money. The investigator merely assumes that such a population exists in some ill-defined sense. And there is a further assumption, that the data set being analyzed can be treated as if it were based on a random sample from the assumed population. These are convenient fictions … Nevertheless, reliance on imaginary populations is widespread. Indeed regression models are commonly used to analyze convenience samples … The rhetoric of imaginary populations is seductive because it seems to free the investigator from the necessity of understanding how data were generated.
In social sciences — including economics — it’s always wise to ponder C. S. Peirce’s remark that universes are not as common as peanuts …