by On the use of mathematics in empirical modeling I have argued that in order for a mathematical modeling exercise to illuminate its target the following two conditions must be met:(1*) the objects under investigation must plausibly be stable, modular, and quantitative, with no qualitative differences among instantiations of each type; and (2*) the relations between them must be fixed and law-like throughout the context under study in the modeling exercise … If we have not established that (1*) and (2*) are satisfied, then the most we could claim is that the analysis could be a test of a theory about the proto-model form of the delimited social phenomena. By definition, proto-model entities possess the characteristics needed to be legitimate inputs into
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On the use of mathematics in empirical modeling
I have argued that in order for a mathematical modeling exercise to illuminate its target the following two conditions must be met:(1*) the objects under investigation must plausibly be stable, modular, and quantitative, with no qualitative differences among instantiations of each type; and (2*) the relations between them must be fixed and law-like throughout the context under study in the modeling exercise …
If we have not established that (1*) and (2*) are satisfied, then the most we could claim is that the analysis could be a test of a theory about the proto-model form of the delimited social phenomena. By definition, proto-model entities possess the characteristics needed to be legitimate inputs into the theoretical model, but as discussed above their connection to the actual data-generating process is purely conjectural unless the economist explicitly explores whether (1*) and (2*) hold. Put briefly, without establishing that (1*) and (2*) are fulfilled, a mathematical modeling exercise answers only the question of what would be true of the relevant social phenomena if they possessed only the same kind of complexity as their mathematical analogues. But, surely, one of the most vexing aspects of social behavior is that we generally do not know what kind of complexity underlies it. The question of the stability, modularity, and law-like relations of the social phenomena of interest, then, is lexicographically prior to any questions about the legitimacy of the econometric specification and the appropriateness of the data. Unless and until this prior question is addressed, we can have no idea what the econometric results imply about the social phenomena in which we are interested.