The Epistemological Status of Structural Assumptions

There are four possible methodical functions that motivate maintaining structural assumpti-ons, all of which play a role in this study. First, structural assumptions save estimation parame-ters and thus degrees of freedom, so that statistical significance is enhanced and, at the margin, a model is made estimable in spite of scarce data. This is e.g. always true for the separability assumption implied by data aggregation. Secondly, some effects (like the allocation of compo-nents on compound feeds) can only be calculated if a specific functional structure is assumed (here outputs being nonjoint in input quantities).¹⁰⁰ Thirdly, some models (like the ones in this study) cannot be estimated at all without some structural assumptions (here separability) due to asymmetric data availability.¹⁰¹ Fourthly, examining the adequacy of a structural assumption may be an end in itself in order to gain general knowledge that can be presupposed in future studies. Another distinction can be made with regard to the justification of a structural assump-tion. In some cases, a structural assumption is valid a priori. Consider the following example:

given that inefficiency can be excluded,¹⁰² the assumptions of constant returns to scale in com-ponent composition and nonjointness in comcom-ponents maintained in the present models are true by logical necessity; the constitution of a compound feed as a mixture of components implies their validity, and neither is an empirical test required to establish this result, nor can it be sta-tistically rejected.

But in most cases, structural assumptions are, like economic theory as a whole and thus all deduced hypotheses, of empirical nature. In contrast to conceptually necessary structural as-sumptions which are true whatever purpose they serve, the methodical function of a structural assumption which cannot be validated without empiry – or, formulated properly within the deductionist approach, a structural assumption that is falsifiable¹⁰³ – has important implications on its epistemological status.¹⁰⁴ In some cases, it is possible to conduct a statistical test on the adequacy of the assumption, in other cases not. If a test is successfully passed, the assumption

100 See section 3.2.2 above.

101 See section 3.2.1 above.

102 See section 3.1 above.

103 See POPPER 1961: 40-41

104 For a general treatment of epistemologial aspects of economics and social sciences, respectively, see WALLACE 1971.

is justified as well as the whole model. Ironically, an assumption thus justified is superfluous if the first or third methodical function is the motive; testability indicates that there is no need to introduce it. But a statistical test is principally impossible if the model is inestimable without the assumption, which would, in case of a successful modeling, e.g. be the case with the sepa-rability assumptions in this study allowing the neglection of non-component price variables.

Such assumptions exhibit a queer in-between status: on the one hand, they do not follow from economic theory like the homogeneity or curvature property of dual behavioral functions, i.e. are not premises of the model that, in conjunction, are the object of the epistemological test implied by any application of a theory, and, on the other hand, they are not part of the empiri-cal hypothesis that is tested with statistiempiri-cal means. They are empiriempiri-cal hypotheses, but stay u-nexamined. Rather, justification is sought outside the model. In the best case, justification is provided by other scientific studies, ideally significantly more than one, that all unambigiously support the adequacy of the respective assumption, i.e. that satisfy the fourth methodical func-tion of maintaining structural assumpfunc-tions, and there are no arguments against the adequacy of maintaining the analogy with the model in question. But in many instances, this justification is not available because a test of the respective assumption is generally excluded, if, for example, relevant data is never available.¹⁰⁵ Then, plausibility considerations and pre-theoretical expe-rience with the object of the model are commonly drawn upon. Of course, this is neither theory proper nor empiry proper.

The implied epistemological problem is implied by the influential Duhem-Quine-thesis: if a hypothesis is rejected, it is impossible to infer which premise is responsible for failure.¹⁰⁶ Ac-cording to this holism of justification, a model can only be rejected as a whole. Thus, if, as in the present study, a, strictly speaking, unjustified structural assumption enters the model, neither any other empirical hypothesis nor the underlying behavioral theory can in fact be tested. It follows that, in order to falsify a hypothesis or a theory, the model must at first be made falsifiable by reducing the number of open questions to unity, namely the question of whether the theoretically consistent model is capable of fitting the data.¹⁰⁷ Since this is impos-sible in the present study, all posimpos-sible statistical inferences drawn move on thin epistemological ice.

105 See above.

106 See QUINE 1981.

107 See section 6.2 below for another instance where falsifiability of the maintained hypotheses is considered.

The situation that all structural assumptions utilized in a model can be maintained relying on other – proper – scientific studies where in doubtlessly analogous cases the respective assump-tion was empirically accepted, can be expected to be encountered extremely rarely. The practi-ce, and also the practice of the study at hand, is to be content with less, namely the epistemo-logically "soft" stage of justification of structural assumptions which correspond to "experien-ce" with the object of the theory, i.e. pre-theoretical knowledge. In the framework of a scienti-fic theory like e.g. neoclassical economic theory, any "knowledge" emanating from a source different from the respective scientific theory has to be considered non-theoretic or pre-theoretic, whatever sophistication of the human mind has brought it about, and in whatever number of cases it has turned out to fit the phenomena.

With respect to a proper scientific practice, the classification of information as pre-theoretic implies that it is irrelevant. But since this kind of knowledge often proves to be quite close to knowledge gained scientifically, such a pragmatic maintainance can be seen as a good proxy.

Of course, the proxy use of soft knowledge is only justifiable in an applied context where a test of an empirical hypothesis is not considered, not to talk of an epistemological test of the under-lying theory.¹⁰⁸ For applied purposes, structural assumptions which are maintained only relying on pre-theoretic knowledge can be expected to increase the precision of forecasts and are thus adequate since a theory or hypothesis, even if not truly justified, contains information that is, on average, more likely to be true than the null hypothesis of white noise, i.e. the absence of directed causal relationships which could be detected and modeled for use as a basis for fore-cast. However, even if a theory is closer to the truth than assuming white noise, the introducti-on of theory or structural assumptiintroducti-ons need not necessarily result in an increasing forecast pre-cision.¹⁰⁹

Applied economic practice takes even one step more: pre-theoretic knowledge is commonly used as a posterior credibility benchmark for statistically accepted models, i.e. somehow rated higher than scientific knowledge – because pre-theoretic experience shows that in many cases reliability of pre-theoretic knowledge is at least as high as the reliability of scientifically genera-ted knowledge. One had better refrain from estimating weakly founded models for forecast

108 This must not be interchanged with the use of pre-theoretic knowledge in inventing theories or models: the genesis of a scientific theory or an empirical hypothesis is not exposed to any criteria; it is only the validity of a theory or hypothesis that is the object of epistemological criticism.

109 See section 6.2.4 below.

purposes in order to avoid the hypocritical acceptance of an estimation result which matches intuition where a result contradicting intuition would be rejected. If pre-theoretic knowledge is rated this highly, which may be perfectly appropriate with regard to the ends pursued, a scienti-fic study is useles – except maybe to take advantage of scientiscienti-fic devoutness. In contrast, the benchmark use of pre-theoretic knowledge during the construction process of a scientific mo-del, noting the crucial difference between genesis and validity of a theory or hypothesis with respect to justification, needs no defense.