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Empirical Model Discovery and Theory EvaluationAutomatic Selection Methods in Econometrics$
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David F. Hendry and Jurgen A. Doornik

Print publication date: 2014

Print ISBN-13: 9780262028356

Published to MIT Press Scholarship Online: January 2015

DOI: 10.7551/mitpress/9780262028356.001.0001

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The Theory of Reduction

The Theory of Reduction

(p.85) 6 The Theory of Reduction
Empirical Model Discovery and Theory Evaluation

David F. Hendry

The MIT Press

A well-defined sequence of reduction operations leads from thedata-generating process (DGP) of the economy under analysisto the local DGP (LDGP), which is the generating process inthe space of the variables under analysis. The resulting LDGPmay be complex, non-linear and non-constant from aggregation,marginalization, and sequential factorization, depending on thechoice of the set of variables under analysis. A good choice—one where there are no, or only small, losses of information fromthe reductions—is crucial if the DGP is to be viably captured byany empirical modeling exercise. In practice, the LDGP is alsoapproximated by a further series of reductions, designed so thereare again no (or small) losses of information, but nowif the LDGPdoes not satisfy those reductions, evidence of departures can beascertained by appropriate tests, so they need not be undertaken.The resulting (operational) LDGP is then nested within a generalunrestricted model (GUM), which becomes the initial specificationfor the ensuing selection search.

Keywords:   Theory of reduction, Marginalizing, sequential factorization, conditioning, local data generation process

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