Simulation-based robust IV inference for lifetime data

Endogeneity or unmeasured confounding is a nontrivial complication in duration data models, for which there are relatively few existing methods. I develop two related, but methodologically distinct, identification-robust instrumental variable estimators to address the complications of endogeneity in an accelerated life regression model. The two unique methods generalize the Anderson-Rubin statistic to (1) lifetime data distributions in the case of the least squares estimator and (2) distribution-free censored models in the case of the rank estimator. Valid confidence sets, based on inverting the pivotal least-squares statistic and the linear rank statistic, form the basis for identification-robust inference using the Mata programming language via exact simulation-based methods. The finite sample performance of the proposed statistics is evaluated using the built-in features of Stata combined with the original Mata code. I provide an empirical analysis, utilizing an original prospectively collected clinical patient dataset in which the trauma status of a pediatric critical care patient instruments a possibly confounded illness severity index in a length of stay regression for a specific pediatric intensive care population. Results suggest a clinically relevant bias correction for routinely collected patient risk indices that is meaningful for informing policy in the healthcare setting.