Abstract
This paper shows that a qualitative analysis, i.e., an assessment of the consistency of a hypothesized sign pattern for structural arrays with the sign pattern of the estimated reduced form, can always provide decisive insight into a model’s validity both in general and compared to other models. Qualitative analysis can show that it is impossible for some models to have generated the data used to estimate the reduced form, even though standard specification tests might show the model to be adequate. A partially specified structural hypothesis can be falsified by estimating as few as one reduced form equation. Zero restrictions in the structure can themselves be falsified. It is further shown how the information content of the hypothesized structural sign patterns can be measured using a commonly applied concept of statistical entropy. The lower the hypothesized structural sign pattern’s entropy, the more a priori information it proposes about the sign pattern of the estimated reduced form. As an hypothesized structural sign pattern has a lower entropy, it is more subject to type 1 error and less subject to type 2 error. Three cases illustrate the approach taken here.
Highlights
A demonstration that economics is a science would be comprised of showing that economics organizes its subject matter in some fashion that limits the configurations that may be taken on by the data
Economics as a science should produce meaningful theorems that when true limit the range of data outcomes
The purpose of this paper is to demonstrate the potential of a qualitative analysis in evaluating models when confronted with data
Summary
A demonstration that economics is a science would be comprised of showing that economics organizes its subject matter in some fashion that limits the configurations that may be taken on by the data. Zero restrictions in the structure can themselves be falsified; and, when so, current practice proposes estimated structural arrays that are impossible It is further shown how the information content of the hypothesized structural sign patterns can be measured using Shannon’s [7]. In the realm of the present paper, if the specified model is TRUE in its assigned zero restrictions and sign patterns in expectation the reduced form coefficients estimators mathematically cannot take the wrong signs. We show that a qualitative analysis can always be successfully conducted and that it provides important insight into the “scientific” content of an economic model and can always enumerate outcomes for sgn π that would falsify hypothesized sign patterns for the structural arrays. An appendix provides additional detail about our method of analysis
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