1.3.1 A Behavioral Model of the German Compound Feed Industry
What is frustrating for the applied researcher may be a thrilling result from a theoretical perspective, namely the failure of the enterprise to establish a consistent model of an industry which is estimable given a certain data availability situation. And this is exactly what happens in this study: three cost modeling approaches and two profit function accounts fail to be both consistent with economic theory and maintained structural assumptions and estimable with regard to the unavailability of sufficient non-component price and quantity data.
19 See section 1.3.2 below and chapters 5 and 6.
Reflecting the practice of all other available studies on the compound feed sector, a desired cost model is presented which allows for complete neglection of non-component data but is immediately shown to be much more restrictive than the maintained separability assumptions imply. An estimation in spite of this renders depiction of existing effects impossible and is thus inadequate both with regard to a test of the empirical hypothesis expressed by the model and forecast purposes. Then, two cost models are proposed which account for relationships where no separability can be reasonably claimed. The first alternative assumes weak separabi-lity of non-component demand shares from output quantities, which is arguable. Nevertheless, this neither leads to a system of estimable demand and marginal cost equations nor to a sys-tem of estimable demand and marginal cost share equations because thus maintained structu-ral assumptions in conjunction imply constant returns to scale for the ovestructu-rall cost function, which renders measurement of marginal cost and marginal cost shares by the product price impossible. As second alternative, a cost structure which, more realistically, accounts for an inseparability of the non-component sector from output quantities, is proposed. While this specification is inarguably consistent, it is still not estimable because both the derived demand and marginal cost functions and the resepective share equations are not independent on non-component prices, which are not available. With the profit function approach, the problem is more general: both alternatives, which are analogous to the two cost function approaches, are not defined since, in the former case, the whole profit function or, in the latter case, the micro-profit function corresponding to the component combination to compound feed, respectively, exhibit constant returns to scale so that the profit maximization problem is unbounded. Thus, either progress in consistently modeling the profit maximizing behavior of the compound feed industry has to be achieved, or, given that the non-component data availability situation does not improve in future, pragmatic cost function approach solutions relying on generated non-component data or instrumental variables for total non-non-component cost data must be favored.
1.3.2 Functional Forms, Flexibility, and Regularity
The three chapters on flexible functional forms, chapters 5, 6, and 7, include an extensive presentation of the theory of flexible functional forms and of commonly used specifications, i.e. cover a wide range of known results. Apart from some remarks on these and some episte-mological conclusions, there is a twofold central result which is new: by means of a concep-tual analysis20 it is shown that, first, requiring a functional form to be locally flexible is
20 See section 1.2.2 above.
lete if it is estimated semi-nonparametrically, i.e. as a globally flexible functional form with a large depth of parameterization determined by the inferential potential of the data, aiming at good approximation of the true data-generating process in its whole course. Secondly, it is shown that this relaxation, coming into effect in a semi-nonparametric estimation function and using a Bayesian estimation technique with an informative prior, allows one to take ac-count of the theoretical consistency requirement much more successfully than within the local flexibility framework.
The neglectability of the local flexibility criterion in a globally flexible framework follows from two arguments in conjunction: First, the local approximation view of flexible functional forms runs empty because there is no way to locate the point of approximation in a statistical context. The analogy to the approximation of a known algebraic function is not available if the approximated structure is merely present through a random sample to which the function is fitted in its whole course. Secondly, if it is possible to find a representation of economic behavior that goes beyond the limited complexity of a local second order approximation, in-sertion of variable values into this representation is by far superior with regard to forecast precision. Level, first and second order effects only restricted by economic theory by no means provide an exhaustive characterization of a technology, as an axiom of the theory of locally flexible functional forms claims. It must be concluded that local flexibility is irrelevant if the approximation function fits the true function as well as possible at any data point rather than locally.
If it is, according to Lau's incompatibility theorem, impossible to make a locally flexible functional form intrinsically consistent with all postulates of economic theory, i.e. a second order flexible functional form approximating function value and first and second order deriva-tives of the underlying function at merely one point, this is all the more so with a globally flexible functional form, i.e. with a more complex specification capable of approximating the underlying function as a whole. But a Bayesian estimation technique with an informative pri-or recently proposed by Barnett, Geweke, and Wolfe provides a solution: drawing samples from the whole sample, estimation results being theoretically inconsistent inside the defined regular region are rejected while all consistent parameter estimates are gathered in a theoreti-cally consistent posterior distribution from which the final parameter estimates are derived.
This is, a set of parameters is estimated that incorporates a regular region in the course of the function, independently of the estimated functional form being intrinsically regular.
In contrast to all studies applying this Bayesian technique with an informative prior which lament that enlarging the regular region of a globally flexible functional form severely harms
the local flexibility property and follow that estimation results must therefore be rejected, this study yields the following: a globally flexible parameter estimation with a Bayesian estimati-on technique with an informative prior yields a parameter set subject to a regular regiestimati-on where any violation of the local flexibility condition is caused by the data alone. The only presuppo-sition for this is that the functional form which is used as estimation function (as opposed to the concrete parameterization subject to the implemented regular region obtained in the esti-mation) satisfies the local flexibility property, i.e. only those consistency properties are incor-porated by construction or by parametric restrictions that do not a priori restrict the ability of the function to depict any theoretically consistent behavior locally. Otherwise, the possibility to depict an arbitrary economic behavior would not only be restricted by economic theory, i.e.
by the regular region, but in addition by the intrinsic incapability of the used functional form.
This implies that, in a proper globally flexible estimation, the extension of the regular regi-on is a decisiregi-on exclusively based regi-on the trade-off between an unlimited forecast regiregi-on and the best available fit. The increasing local flexiblity violations with a growing regular region are irrelevant again, and thus, accounting for maintained theory is freed from the burden of accounting for local flexibility simultaneously – Lau’s incompatibility theorem is no longer effective.
Part I: A Behavioral Model of the German Compound Feed Industry
2 Data
Since the reason for the ultimate failure of all modeling efforts undertaken in this study lies in an insufficient data availability, the data will be presented prior to the models of chapters 3 and 4. As an estimation is impossible in the current state of affairs, considerations are distinued after a description of the asymmetric data availability situation to preserve the con-sistency of the study: on the one hand, there is quite good data on feed components and com-pound feed, which will be presented to emphasize how regrettable the inavailability of other essential data is and, on on the other hand, the desired but inavailable data is discussed. This is, the questions of how to appropriately edit the data, which aggregation technique to favor, which commodities to aggregate due to which criteria, et c., that is the questions normally completing an exposition of the data material, are not treated.