3 - The use of mathematics in empirical modeling

Summary

The last chapter analyzed the use of mathematics in theoretical economic modeling exercises, paying close attention to a single paper, Shapiro and Stiglitz (1984). It concluded that further work would need to be done in order to establish that the social phenomena modeled by Shapiro and Stiglitz are essentially compatible with the authors' model. This chapter will extend that analysis by considering the use of mathematics in empirical economic modeling exercises, again by engaging carefully with a single paper: Sushil Wadhwani and Martin Wall's “A Direct Test of the Efficiency Wage Model Using UK Micro-Data” (1991).

By empirical modeling exercises, I mean those that confront the inferences drawn from a mathematical model with empirical data, whether gathered through passive observation or actively generated in laboratory or field experiments. This process represents an important test of the argument made in the last chapter, because empirical modeling exercises are sometimes thought to prove their own adequacy in the extent to which they successfully predict or retrodict the data they seek to represent. Nonetheless, I will argue that the “testing” process within empirical modeling is insufficient to overcome the limitations of mathematical modeling as already outlined in relation to theoretical modeling exercises. Exactly the same kind of objections apply to both. Showing this, however, requires addressing a set of significant additional complications. Specifically, the question of what is meant by “model” and “target,” and the related question of what things are representing and what things being represented, are less straightforward in the case of empirical modeling than in the case of theoretical modeling. In the latter case, the representational process includes only two subjects: the model and the target. In empirical modeling exercises, however, additional subjects come into play, each with a key role in the process. In total, we will have to account for at least three and sometimes four separate entities: namely, the underlying phenomena of interest (i.e. the delimited social phenomena), the data, the empirical model used to analyze the data, and often (though not always) a theoretical model from which the empirical model is derived in some manner.

Understanding the use of mathematics in empirical economic modeling exercises requires that we are first clear on the respective roles and relations of all these entities. This is the goal of Section 3.1.