Threshold crossing models are a standard framework for analyzing binary data in microeconomics, medicine, and elsewhere. For example, analysts often model mortality by imagining latent health status falling below a threshold. A common problem arises when one of the regressors is a dummy endogenous variable, such as a medical procedure that is performed on individuals with the worst unobserved health. Standard methodologies for recovering the average effect of the endogenous variable either depend on the validity of parametric distributional assumptions or require strong properties on an instrument. Instrumental variables analysis recovers the 'Local Average Treatment Effect' but not the average effect.
The PIs propose developing a new non-parametric methodology for evaluating the average effect of a dummy endogenous variable in a threshold crossing model where there is an instrument. Using an early version of this methodology, the PI's have constructed sharp bounds. When all regressors are discrete, the PI's have developed confidence sets that asymptotically contain each point in the bounds with a given specified probability. The PI's will extend their procedures for inference, including to allow for continuous regressors and to consider confidence sets that asymptotically contain the entire identified set with the desired probability. The PI's will develop bounds for other classes of threshold crossing models and limited dependent variable models beyond binary choice models, for example, ordered choice models. The PI's will extend their analysis to consider dummy endogenous regressors in discrete-time, dynamic outcome models.
The analysis is applied to an important medical problem. The placement of Swan-Ganz catheters is an extremely common procedure with over 2 million patients in North America catheterized each year. Doctors debate whether the greater observed mortality of patients receiving Swan-Ganz catheterization can be attributed to catheterization itself, or are due to the unobserved worse health of catheterized patients. In preliminary analysis, the PI's have considered the effect of Swan-Ganz catheterization on later mortality. The proposed theoretical work will allow the PI's to apply statistical inference procedures to account for the dynamic nature of the outcome variable to this situation.
The project is of broad intellectual significance because it advances the theoretical literature on endogenous variables in nonparametric, nonseparable models. Previous approaches require a continuous endogenous regressor, a continuous outcome variable, or particularly strong statistical identification requirements. The research introduces a new approach without the need for any of these objects, which are often not available in empirical settings.
This research program will also have broader impacts outside of theoretical econometrics. The empirical project proposed is important in its own right, and the results will provide doctors with guidance on thorny patient care decisions. The analysis of the effect of binary endogenous variables on limited dependent variables is a common problem in empirical economics, sociology, political science, and medicine; hence, the theoretical work will have wide applicablity.
