Econometric assumptions matter (wonkish)27 February, 2013 at 18:13 | Posted in Statistics & Econometrics | Leave a comment
[T]he authors take as their text a principle of Haavelmo that every testable economic theory should provide a precise formulation of the joint probability distribution of all observable variables to which it refers. It can be argued, however, that Haavelmo’s principle is sounder than the program for realizing it worked out in this book. For, as noted above, what we are asked to assume is that the precept can be carried out in economics by tech- niques which are established for linear systems, serially independent disturbances, error-free observations, and samples of a size not generally obtainable in economic time series today. In view of such limitations, anyone using these techniques must find himself appealing at every stage less to what theory is saying to him than to what solvability requirements demand of him. Certain it is that the empirical work of this school yields numerous instances in which open questions of economics are resolved in a way that saves a mathematical theorem.
Still, there are doubtless many who will be prepared to make the assumptions required by this theory on pragmatic grounds. We cannot know in advance how well or badly they will work, and they commend themselves on the practical test of convenience. Moreover, as the authors point out, a great many models are compatible with what we know in economics-that is to say, do not violate any matters on which economists are agreed. Attractive as this view is, it fails to draw a necessary distinction between what is assumed and what is merely proposed as hypothesis. This distinction is forced upon us by an obvious but neglected fact of statistical theory: the matters “assumed” are put wholly beyond test, and the entire edifice of conclusions (e.g., about identifiability, optimum properties of the estimates, their sampling distributions, etc.) depends absolutely on the validity of these assumptions. The great merit of modern statistical inference is that it makes exact and efficient use of what we know about reality to forge new tools of discovery, but it teaches us painfully little about the efficacy of these tools when their basis of assumptions is not satisfied. It may be that the approximations involved in the present theory are tolerable ones; only repeated attempts to use them can decide that issue. Evidence exists that trials in this empirical spirit are finding a place in the work of the econometric school, and one may look forward to substantial changes in the methodological presumptions that have dominated this field until now.