Some recent papers in formal theory have tried to develop a new link between theory and empirics. These works seek to go beyond generating comparative statics, i.e. predictions, and so diverge from the traditional Empirical Implication of Theoretical Model (EITM) approach. These studies (re)assess in various context what empirical estimates actually measure. These papers start with models of real-world interactions and use formal reasoning to rethink empirical counterfactuals. They are fundamentally distinct from works that use empirical estimates as their starting point and elucubrate on what researchers can do with it.

This recently developed link between formal theory and empirics is best referred as Theoretical Implications of Empirical Model or TIEM. I see two promising uses of the TIEM approach. The first application studies whether empirical estimates measure what authors claim they do. That is, these formal works evaluate whether empirical evidence are sufficient to warrant some causal claims. Examples of this reasoning include Ashworth and Bueno de Mesquita (2014) and Ashworth, Bueno de Mesquita, and Amanda Friedenberg (2018). In these two works, the authors consider whether current political outcomes are evidence of voters’ irrationality as some argue. They show that (i) we cannot conclude based on evidence that voters are irrational (i.e., irrationality is not necessary to explain observed empirical patterns) and (ii) we cannot assert that a democracy with rational voters outperform a democracy with imperfect voters.

The second application of the TIEM approach examines whether a particular empirical strategy induces unbiased estimates. That is, these formal works evaluate the internal validity of a research design. Examples of this reasoning include Eggers (2016) and Fowler (2018). Both evaluate the claim that regression discontinuity designs (RDD) using close elections recover the incumbency status advantage (the electoral benefit of the mere fact of being incumbent). This form of RDD has been widely used because it is often believed that such design keeps everything constant, but the incumbency status. Both papers show that this all else equal claim is not correct. Both show, among other results, that RDD using closed election do not properly control for incumbent’s quality. RDD can be useful to control for many unobservable factors (e.g., district characteristics), but are not sufficient to control for politicians’ underlying ability.

I also use the TIEM approach in the following papers: