Uncovering where the econometric skeletons are buried
from Lars Syll
A rigorous application of econometric methods in economics 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.
Invariance assumptions need to be made in order to draw causal conclusions from non-experimental data: parameters are invariant to interventions, and so are errors or their distributions. Exogeneity is another concern. In a real example, as opposed to a hypothetical, real questions would have to be asked about these assumptions. Why are the equations ‘structural,’ in the sense that the required invariance assumptions hold true? Applied papers seldom address such assumptions, or the narrower statistical assumptions: for instance, why are errors IID?
The tension here is worth considering. We want to use regression to draw causal inferences from non-experimental data. To do that, we need to know that certain parameters and certain distributions would remain invariant if we were to intervene. Invariance can seldom be demonstrated experimentally. If it could, we probably wouldn’t be discussing invariance assumptions. What then is the source of the knowledge?
‘Economic theory’ seems like a natural answer, but an incomplete one. Theory has to be anchored in reality. Sooner or later, invariance needs empirical demonstration, which is easier said than done.
David Freedman: Statistical Models – Theory and Practice (CUP 2009:187)
Since econometrics aspires to explain things in terms of causes and effects it needs loads of assumptions. Invariance is not the only limiting assumption that has to be made. Equally important are the ‘atomistic’ assumptions of additivity and linearity. read more