discretize: Command to convert a continuous instrument into a dummy variable for instrumental-variable estimation

The Instrumental Variable (IV) method is a standard econometric approach to address endogeneity issues (for example, when an explanatory variable is correlated with the error term). It relies on finding an instrument, excluded from the outcome equation (second stage), but which is a determinant of the endogenous variable of interest (first stage). Many instruments rely on cross-sectional variation produced by a dummy variable, which is discretized from a continuous variable. There might be several reasons for converting a continuous variable into a binary instrument. First, continuous instruments recoded as dummies have been shown to provide a parsimonious nonparametric model for the underlying first-stage relation (Angrist and Pischke 2009). Second, it provides a simple tool to evaluate the IV strategy and the identification assumptions. Unfortunately, the construction of the binary instrument often appears to be arbitrary, which may raise concerns about the robustness of the second-stage results. I propose a data-driven procedure to build this discrete instrument, implemented in a command called discretize. The boundaries of the discrete variable are chosen to maximize the F-statistic in the first stage. This procedure has two main advantages. First, it minimizes the weak instrument problem, which can arise in case of incorrect functional specification in the first stage. Second, it offers a transparent, data-driven, procedure to select an instrument that does not depend on arbitrary decisions made by the researcher. Several options are available with the command to check graphically the robustness of the first- and second-stage parameters. The presentation includes an explanation of the functioning of the discretize command, and an illustration of its usefulness with an example that relates the raise of violent crime in city centers and the process of suburbanization. The endogenous relation is solved using lead poisoning as instrument.