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