## Peter Dorman on economists’ obsession with homogeneity and average effects

19 July, 2014 at 20:41 | Posted in Economics | 6 Comments

Peter Dorman is one of those rare economists that it is always a pleasure to read. Here his critical eye is focussed on economists’ infatuation with homogeneity and averages:

You may feel a gnawing discomfort with the way economists use statistical techniques. Ostensibly they focus on the difference between people, countries or whatever the units of observation happen to be, but they nevertheless seem to treat the population of cases as interchangeable—as homogenous on some fundamental level. As if people were replicants.

You are right, and this brief talk is about why and how you’re right, and what this implies for the questions people bring to statistical analysis and the methods they use.

Our point of departure will be a simple multiple regression model of the form

y = β0 + β1 x1 + β2 x2 + …. + ε

where y is an outcome variable, x1 is an explanatory variable of interest, the other x’s are control variables, the β’s are coefficients on these variables (or a constant term, in the case of β0), and ε is a vector of residuals. We could apply the same analysis to more complex functional forms, and we would see the same things, so let’s stay simple.

What question does this model answer? It tells us the average effect that variations in x1 have on the outcome y, controlling for the effects of other explanatory variables. Repeat: it’s the average effect of x1 on y.

This model is applied to a sample of observations. What is assumed to be the same for these observations? (1) The outcome variable y is meaningful for all of them. (2) The list of potential explanatory factors, the x’s, is the same for all. (3) The effects these factors have on the outcome, the β’s, are the same for all. (4) The proper functional form that best explains the outcome is the same for all. In these four respects all units of observation are regarded as essentially the same.

Now what is permitted to differ across these observations? Simply the values of the x’s and therefore the values of y and ε. That’s it.

Thus measures of the difference between individual people or other objects of study are purchased at the cost of immense assumptions of sameness. It is these assumptions that both reflect and justify the search for average effects …

In the end, statistical analysis is about imposing a common structure on observations in order to understand differentiation. Any structure requires assuming some kinds of sameness, but some approaches make much more sweeping assumptions than others. An unfortunate symbiosis has arisen in economics between statistical methods that excessively rule out diversity and statistical questions that center on average (non-diverse) effects. This is damaging in many contexts, including hypothesis testing, program evaluation, forecasting—you name it …

The first step toward recovery is admitting you have a problem. Every statistical analyst should come clean about what assumptions of homogeneity are being made, in light of their plausibility and the opportunities that exist for relaxing them.

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 writes (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 causal process lying behind events and disclose the causal forces behind what appears to be simple facts. 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-additive, 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. The kinds of “laws” and relations that econometrics has established, are laws and relations about entities in models that presuppose causal mechanisms being atomistic and 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.

Remember that a model is not the truth. It is a lie to help you get your point across. And in the case of modeling economic risk, your model is a lie about others, who are probably lying themselves. And what’s worse than a simple lie? A complicated lie.

Sam L. Savage The Flaw of Averages

1. FYI The value of search-and-matching models for the labor market

By Marshall Steinbaum

2. This was a good post. He shared some of these reflections on Andrew Gelman’s blog.

• Thanks for the tip! I’ll have a look. Andrew’s blog is one of my absolute favourites among statistics blogs!

3. Weird. I thought you post-Keynesians were all fall understanding the economy “top-down”, and model the aggregates directly. But now you don’t want to estimate the aggregates directly?

It seems like Dorman doesn’t appreciate the idea that you tailor your model to be appropriate for the question you’re asking. If you’re interested in average effects you estimate a model that has as much power as possible to pick up that average effect efficiently (If you’re interested in the mean of a dice, you don’t estimate the distribution of possible outcomes …). If you’re interested in individual behavior, you include interaction terms, individual fixed effects, stochastic parameters and so on. I don’t think we should pretend that this isn’t done in economics. It is.

4. To an extent I agree with punctilious above. Economists and their models have moved beyond simple linear functions. There are issues about assumptions but it is not as if the literature is unaware of this!

5. Lynn Margulis have a very intersting approach in Biology called symbiogenesis, eg, evolution for groups of individuals to form complexes individuals. Atomistic behavior is being expelled from biology also.