Model Discovery and Trygve Haavelmo's Legacy. - Hendry, D; Johansen, S (Department of Economics (University of Oxford), 2012)

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Trygve Haavelmo’s Probability Approach aimed to implement economic theories, but he later recognized their incompleteness. Although he did not explicitly consider model selection, we apply it when theory-relevant variables, {xt}, are retained without selection while selecting other candidate variables, {wt}. Under the null that the {wt} are irrelevant, by orthogonalizing with respect to the {xt}, the estimator distributions of the xt‘s parameters are unaffected by selection even for more variables than observations and for endogenous variables. Under the alternative, when the joint model nests the generating process, an improved outcome results from selection. This implements Haavelmo’s program relatively costlessly.