1. Event History Modeling, aka Survival Analysis, aka Duration Models, aka Hazard Analysis

2. How Long Until …? Given a strike, how long will it last?
How long will a military intervention or war last?
How likely is a war or intervention?
What determines the length of a Prime Minister’s stay in office?
When will a government liberalize capital controls?

3. Origins Medical Science
Wanted to know the time of survival
0 = ALIVE
1 = DEAD
Model slightly peculiar – once you transition, there is no going back.
Many analogs in Social Sciences

4. Disadvantages of Alternatives (Cross Sections)
Assumes steady state equilibrium
Individuals may vary but overall probability is stable
Not dynamic
Can’t detect causation.

5. Disadvantages of Alternatives (Panel)
Measurement Effects
Attrition
Shape not clear
Arbitrary lags
Time periods may miss transitions

6. Event History Data Know the transition moment
Allows for greater cohort and temporal flexibility
Takes full advantage of data

7. Data Collection Strategy (Retrospective Surveys)
Ask Respondent for Recollections
Benefit: Can “cheaply” collect life history data with single-shot survey
Disadvantages:
Only measure survivors
Retrospective views may be incorrect
Factors may be unknown to respondent

8. Logic of Model T = Duration Time t = elapsed time
Survival Function = S(t) = P(T≥t)

9. Logic of Model (2) Probability an event occurs at time t
Cumulative Distribution function of f(t)
Note: S(t) = 1 – F(t)=

10. Logic of Model (3)
Hazard Rate
Cumulative Hazard Rate

11. Logic of Model (4) Interrelationships
so knowing h(t) allows us to derive survival and probability densities.

12. Censoring and Truncation
Right truncation
Don’t know when the event will end
Left truncation
Don’t know when the event began

13. Censoring and Truncation (2)

14. Discrete vs. Continuous Time
Texts draw sharp distinction
Not clear it makes a difference
Estimates rarely differ
Need to measure time in some increment
Big problem comes for Cox Proportional Hazard Model – it doesn’t like ties

15. How to Set up Data (Single Record)
Prime Minister
Took Office
Left Office
Days
Event
Henry Sewell
7 May 1856
20 May 1856 13 1
William Fox
2 June 1856
Edward Stafford
12 July 1861
1866
6 August 1862
390
Alfred Domett
30 October 1863
450
Frederick Whitaker
24 November 1864
391
Frederick Weld
16 October 1865
326
28 June 1869
1351
10 September 1872
1170
11 October 1872 31

16. Choices / Distributions
Need to assume a distribution for h(t).
Decision matters
Exponential
Weibull
Cox
Many others, but these are most common

17. Distributions (Exponential)
Constant Hazard Rate
Can be made to accommodate coefficients

18. Distributions (Weibull)
Allows for time dependent hazard rates

19. Weibull Survival Functions

20. Weibull Hazard Rates

22. Distributions (Cox) Useful when
Unsure of shape of time dependence
Have weak theory supporting model
Only interested in magnitude and direction
Parameterizing the base-line hazard rate

23. Distributions (Cox – 2) Baseline function of “t” not “X”
Involves “X” but not “t”

24. Distributions (Cox –3)
Why is it called proportional?

25. How to Interpret Output
Positive coefficients mean observation is at increased risk of event.
Negative coefficients mean observation is at decreased risk of event.
Graphs helpful.

26. Unobserved heterogeneity and time dependency
Thought experiment on with groups
Each group has a constant hazard rate
The group with higher hazard rate experience event sooner (out of dataset)
Only people left have lower hazard rate
Appears hazard drops over time
“Solution” akin to random effects

27. Extensions Time Varying Coefficients Multiple Events
Competing Risk Models