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HazardModels

A Short Introduction to Hazard Models.

Short Summary

This course is an introduction to modelling transitions into a state of interest (such as the transition into employment from unemployment) and durations (such as unemployment, survival of patients after medical treatment or firms after a financial crash, time-to-default of loans, or time-to-purchase, criminal recidivism). Time-to-event or survival analysis are alternative labels. We start with the basic building blocks (Poisson processes, Markovian transitions, Markov chains, hazard models). Since duration data might be censored (individuals might still be in the state of interest at the end of the observation window), classic ordinary least squares (OLS) is invalid, and we develop appropriate methods for estimation. Unobserved heterogeneity introduces fundamental identification challenges (duration dependence v. dynamic sorting) that are discussed in detail. Finally, we consider how recent machine learning methods have been adapted for such censored duration data (such as Random Survival Forests).

Throughout this course, all methods will be illustrated using examples in R and python, and we will replicate several papers from the established empirical literature (such as Lalive et al. (2006, Restud) and Chetty (2008, JPE) on unemployment durations).

Topics

  • Survival functions: The Kaplan-Meier estimator, the log-rank test
  • Hazards, and the Proportional Hazard (PH) model
    • maximum likelihood estimation (flow and stock samples)
  • The Mixed Proportional Hazard (MPH) model, identification challenges
  • The PH model and grouped data
  • Cox’s Partial Likelihood
  • Machine Learning and Survival Analysis
    • Training a PH model
    • Random Survival Forests

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