## Econometric inconsistencies

from **Lars Syll**

In plain terms, it is evident that if what is really the same factor is appearing in several places under various disguises, a free choice of regression coefficients can lead to strange results. It becomes like those puzzles for children where you write down your age, multiply, add this and that, subtract something else, and eventually end up with the number of the Beast in Revelation.

Prof. Tinbergen explains that, generally speaking, he assumes that the correlations under investigation are

linear… One would have liked to be told emphatically what is involved in the assumption of linearity. It means that the quantitative effect of any causal factor on the phenomenon under investigation is directly proportional to the factor’s own magnitude … But it is a very drastic and usually improbable postulate to suppose that all economic forces are of this character, producing independent changes in the phenomenon under investigation which are directly proportional to the changes in themselves ; indeed, it is ridiculous. Yet this is what Prof. Tinbergen is throughout assuming …

Keynes’ comprehensive critique of econometrics and the assumptions it is built around — completeness, measurability, independence, homogeneity, and linearity — is still valid today.

Most work in econometrics is made on the assumption that the researcher has a theoretical model that is ‘true.’ But — to think that we are being able to construct a model where all relevant variables are included and correctly specify the functional relationships that exist between them, is not only a belief without support, it is a belief *impossible* to support.

The theories we work with when building our econometric regression models are insufficient. No matter what we study, there are always some variables missing, and we don’t know the correct way to functionally specify the relationships between the variables.

*Every* econometric model constructed is misspecified. There is always an endless list of possible variables to include, and endless possible ways to specify the relationships between them. So every applied econometrician comes up with his own specification and ‘parameter’ estimates. The econometric Holy Grail of consistent and stable parameter-values is nothing but a dream.

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. 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.

The theoretical conditions that have to be fulfilled for econometrics to really work are nowhere even closely met in reality. Making outlandish statistical assumptions do not provide a solid ground for doing relevant social science and economics. Although econometrics has become the most used quantitative methods in economics today, it’s still a fact that the inferences made from them are as a rule invalid.

Econometrics is basically a deductive method. Given the assumptions, it delivers deductive inferences. The problem, of course, is that we will never completely know when the assumptions are right. Conclusions can only be as certain as their premises — and that also applies to econometrics.

A theory that has no predictive powers is not worth the paper it is written on.

Econometrics is the biggest culprit amongst non-analytical, brain-washing, conscience-diluting subjects that cannot even describe the “what” let alone the “how” and the “why”. Funnily enough, it is still a compulsory unit in some renowned academic institutions and provides a role model for the rest of the world. As you say, the result is always inclusive leading to more of the same.

At times, linear relationships are relevant, but integrated relationships are not linear. Failure to understand this simple truth appears to be rife among economists. In production theory, there is no example of this in conventional analysis.

Fitted relationships are valid as interpolating-capable functions. They have no other validity whatsoever. Any claims that they are, per se, is a category error. Functional relationships derived from first principles will have a real theoretical basis. When these are fitted to empirical data, they will demonstrate the capability to be extrapolated. It is theoretical justification which is the critical difference.

The final paragraph starting “Econometrics is basically a deductive method …” does not provide a convincing explanation of why curve fitting is required. Simply drawing the graph is likely to provide a much deeper understanding.

Very interesting first sentence, Frank. Likewise in your second paragraph. Taking Newton’s theory about gravitational forces as an example, I understand better what you are trying to say about fundamental relationships. However, my theory is that “Econometrics is basically NOT a deductive method”, it is an inductive one, which is indeed not about proving but justifying the relevant theory, i.e. establishing the reliability of the theory, and in the first instance, that there is one. But take the simpler case of throwing a dice. The fundamental relationship is that it has six sides, so by symmetry the probability of any is 1/6. The point of throwing it is not so much to establish the 1/6 as to check out the symmetry. But now consider the case where you don’t know the fundamental facts. The curve-fitting comes into play here in a different way: the empirical probabilities may actually suggest the dice is six-sided; but it might not be. It might not even be a cubical dice: it could be trapezoidal or a roulette wheel.

Helen elsewhere ask that all this abstruse mathematics be expressed in proverbial form. The obvious suggestion is “There are two sides to every coin”, but my favourite (capturing my reaction to Mrs Thatcher and her neoliberal economics) is “There is no point in being strong if you are wrong”. Frank here being much more right than wrong!

Helen, re your initial comment, I am not sure any theory reliably gives us the power to predict happenings in the future (the sampling rate of the [econometric] observations comes into this). But what Frank says about interpolating is spot on: the predictions enable us to predict happenings in the theory.

Thank you Frank. I could not have explained it better myself if I tried.

“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. Parameter-values estimated in specific spatio-temporal contexts are presupposedto be exportable to totally different contexts”

Another way of putting it is: If the economic system is non ergodic, the necessary condition to do econometrics can never be satisfied.

So, perhaps one can say that extremes of growing “negativisms” are impossible to explain adequately , let alone trusted to predict anything meaningful and therefore of any practical use. A bit like ultra abstract mathematical formulae that circulate in the hands and brains of a handful of specialists who could easily explain it all by quoting a simple proverb in any language or culture or profession to the curious non-specialist and get on with the job at hand more professionally.