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I develop the theory around using control functions to instrument hazardmodels, allowing the inclusion of endogenous (e.g., mismeasured) regressors.Simple discrete-data hazard models can be expressed as binary choice panel datamodels, and the widespread Prentice and Gloeckler (1978) discrete-dataproportional hazards model can specifically be expressed as a complementarylog-log model with time fixed effects. This allows me to recast it as GMMestimation and its instrumented version as sequential GMM estimation in aZ-estimation (non-classical GMM) framework; this framework can then beleveraged to establish asymptotic properties and sufficient conditions. Whilstthis paper focuses on the Prentice and Gloeckler (1978) model, the methods anddiscussion developed here can be applied more generally to other hazard modelsand binary choice models. I also introduce my Stata command for estimating acomplementary log-log model instrumented via control functions (available asivcloglog on SSC), which allows practitioners to easily instrument the Prenticeand Gloeckler (1978) model.

A Theory Guide to Using Control Functions to Instrument Hazard Models