Econometrics and the axiom of correct specification
from Lars Syll
Most work in econometrics and regression analysis is — still — made on the assumption that the researcher has a theoretical model that is ‘true.’ Based on this belief of having a correct specification for an econometric model or running a regression, one proceeds as if the only problem remaining to solve have to do with measurement and observation.
When things sound to good to be true, they usually aren’t. And that goes for econometric wet dreams too. The snag is, of course, that there is pretty little to support the perfect specification assumption. Looking around in social science and economics we don’t find a single regression or econometric model that lives up to the standards set by the ‘true’ theoretical model — and there is pretty little that gives us reason to believe things will be different in the future.
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, but 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 regression model constructed is misspecified. There are 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.
In order to draw inferences from data as described by econometric texts, it is necessary to make whimsical assumptions. The professional audience consequently and properly withholds belief until an inference is shown to be adequately insensitive to the choice of assumptions. The haphazard way we individually and collectively study the fragility of inferences leaves most of us unconvinced that any inference is believable. If we are to make effective use of our scarce data resource, it is therefore important that we study fragility in a much more systematic way. If it turns out that almost all inferences from economic data are fragile, I suppose we shall have to revert to our old methods …
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. 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.
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.
The theoretical conditions that have to be fulfilled for regression analysis and econometrics to really work are nowhere even closely met in reality. Making outlandish statistical assumptions does not provide a solid ground for doing relevant social science and economics. Although regression analysis and econometrics have become the most used quantitative methods in social sciences and economics today, it’s still a fact that the inferences made from them are invalid.
Regression models have some serious weaknesses. Their ease of estimation tends to suppress attention to features of the data that matching techniques force researchers to consider, such as the potential heterogeneity of the causal effect and the alternative distributions of covariates across those exposed to different levels of the cause. Moreover, the traditional exogeneity assumption of regression … often befuddles applied researchers … As a result, regression practitioners can too easily accept their hope that the specification of plausible control variables generates as-if randomized experiment.
Econometrics — and regression analysis — is basically a deductive method. Given the assumptions (such as manipulability, transitivity, separability, additivity, linearity, etc) 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 and regression analysis.