The question naturally arises whether an FLS residual efficiency frontier (REF) or cost-efficient frontier (CEF) of estimated models determined on the basis of K distinct goodness-of-fit criteria for K distinct types of discrepancy terms (K > 1) can be further reduced, ideally to a single "best" estimated model.
As will now be argued, this is akin to asking for the further reduction of budget lines (iso-cost curves) in standard economic analysis. Of course a single point can always be selected along a budget line by the introduction of a scalar-valued utility function inducing a specific preferential weighting across conceptually distinct types of goods and services. The key question, however, is whether this specific weighting can be done in a scientifically objective manner, assented to by others, or whether it simply represents the personal preferences of the researcher doing the weighting.
The argument can be made as follows:
-
Any model estimation procedure conducted for a given postulated model conditional on a given data set is essentially a method for distributing the irreducible incompatibility between the model and data across conceptually distinct types of discrepancy terms.
-
This irreducible incompatibility distributed across discrepancy terms can be compared to an "income" distributed across the purchase of goods and services. Deciding on the precise representation for discrepancy terms (with corresponding costs) is akin to deciding on the precise representation for goods and services (with corresponding prices) on which an income is to be spent. However these representation issues are resolved, they do not affect the objective existence of an irreducible theory-data incompatibility (income).
-
The choice of a particular estimated model along a REF/CEF, conditional on a given model, given data, and a given representation of discrepancy terms (with corresponding costs), is analogous to the selection of a consumption bundle along a budget line conditional on a given income and a given representation for goods and services (with corresponding prices).
Starting at any estimated model along the REF/CEF, a decision to lower the cost associated with any one type of discrepancy by moving to a different estimated model must necessarily result in an increase in the cost associated with at least one other type of discrepancy. Similarly, starting at any point along the budget line, a decision to increase expenditures on any one type of good or service must necessarily result in a decrease in expenditures on at least one other type of good or service.
-
Objective agreement can reasonably be sought for the construction of a REF/CEF, just as it can reasonably be sought for the construction of a budget line.
-
However, the selection of any one "best" estimated model along a REF/CEF is akin to a consumer bringing a utility function to bear in order to select one "best" consumption bundle along a budget line. Any such unique selection must necessarily involve the personal preferences of the selector for one particular cost-efficient choice over another on the basis of some additional personally-introduced criterion.
-
To the extent that a group of researchers can agree on the relative importance of various types of discrepancies for an application at hand, they might be able to construct a "social welfare function" for selecting a unique estimated model from among the family of cost-efficient estimated models constituting a REF/CEF. But this does not change the fact that any such unique selection will rely on the subjective judgements of the researchers concerning which cost-efficient distribution of discrepancies is "best" for this application.
Overview
