Empirical and formal models are just models

One of the most stupid divides in the social sciences is that between those who put emphasis on empirical issues and those who put emphasis on theory. I know, I know that this is a discussion that has largely been overcome, that’ big data’, causal identification and formal modeling are to be seen as complementary, and so on.

However, it is a division that can be found in seminars, classrooms and, to some extent, fields: some people are more inclined toward elegant formal models and theories, while others emphasize data and empirical work. I tend to believe this is due to decisions to acquire one set of skills over another. After all, you may decide to take your classes in the computer science, the stats or the econ department and, to the extent to which your time is limited and you may like one over another, your appreciation of one over another is likely to depend on your skill endowment.

As I said, I believe this is a false dilemma, of course. But the most stupid instance of it is that of critics of the ‘unrealistic’ assumptions of formal models alone. I learned to live in peace with the lack of realism of assumptions long ago, when I understood that I had learned most from models that were ‘toy models‘: extreme simplifications of reality, yet, simplifications that can teach you something to the extent to which that something is not directly dependent on the lack of realism.

I’ve always found incredibly hard to understand how harsh people tend to be on the assumptions of, say, rationality, while they seem to be perfectly ok with most standard linear models. I saw the light about this the day I understood that everything that can be said about formal models can be said about empirical  models. Both are simplifications. Both are about making things tractable. If anything, regression models, to the extent to which they assume exogeneity, linearity, and so on, are even harder to believe!

What is a formal model after all, if not a tractable way of keeping track of how parameters (typically, behavioral parameters) related to each other?  As such, I liked Thomas Sargent definition of a model as a restriction on the data generating model. A model tells you how variables are related. Is the relation linear? Is one variable affected by another but not the other way around? A totally unrestricted model would if anything, be gigantic correlation matrix that would be extremely limited.

No one disputes this, of course. People regularly use the Stata command to run regressions with their right hand while they use their left hand to manifest outrage against the lack of realism of behaviorally grounded models to look at how one variable affects another. For some reason, they are often happy to use higher order polynomials as a functional form, but extremely averse to give any behavioral meaning to their parameters.

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Empirical and formal models are just models

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