MODEL DISCOVERY AND TRYGVE HAAVELMO’S LEGACY

What is it about?

Trygve Haavelmo’s `Probability Approach' aimed to implement economic theories, but he later recognized they were incomplete. Although he did not explicitly consider model selection, we apply it when theory-relevant variables are retained without selection while selecting from other candidate variables. Under the null hypothesis that the additional candidates are irrelevant, by orthogonalizing them with respect to the variables of interest, the estimator distributions of the latter's parameters are unaffected by selection even when there are more variables than observations and for endogenous variables. Under the alternative, so some of the additional candidates are in fact relevant, when the joint model nests the data generating process, an improved outcome results from selection. This implements Haavelmo’s program relatively costlessly: no loss if the theory is complete and correct, and a gain if the theory is incomplete or incorrect and some of the additional variables actually matter.

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Why is it important?

This is a surprising new approach that completely overturns conventional wisdom about model selection: it never harms and almost always helps unless the initial theory is perfectly correct.