Econometrics and the challenge of regression 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 too 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 presupposed to be exportable to totally different contexts. To warrant this assumption one, however, has convincingly to 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.