[Topic 11-Duration Models] 1/ Duration Modeling

[Topic 11-Duration Models] 2/35 Modeling Duration Time until retirement Time until business failure Time until exercise of a warranty Length of an unemployment spell Length of time between children Time between business cycles Time between wars or civil insurrections Time between policy changes Etc.

[Topic 11-Duration Models] 3/35 The Hazard Function

[Topic 11-Duration Models] 4/35 Hazard Function

[Topic 11-Duration Models] 5/35 A Simple Hazard Function

[Topic 11-Duration Models] 6/35 Duration Dependence

[Topic 11-Duration Models] 7/35 Parametric Models of Duration

[Topic 11-Duration Models] 8/35 Censoring

[Topic 11-Duration Models] 9/35 Accelerated Failure Time Models

[Topic 11-Duration Models] 10/35 Proportional Hazards Models

[Topic 11-Duration Models] 11/35 ML Estimation of Parametric Models

[Topic 11-Duration Models] 12/35 Time Varying Covariates

[Topic 11-Duration Models] 13/35 Unobserved Heterogeneity

[Topic 11-Duration Models] 14/35 Interpretation What are the coefficients? Are there ‘marginal effects?’ What quantities are of interest in the study?

[Topic 11-Duration Models] 15/35 Cox’s Semiparametric Model

[Topic 11-Duration Models] 16/35 Nonparametric Approach Based simply on counting observations K spells = ending times 1,…,K d j = # spells ending at time t j m j = # spells censored in interval [t j, t j+1 ) r j = # spells in the risk set at time t j = Σ (d j +m j ) Estimated hazard, h(t j ) = d j /r j Estimated survival = Π j [1 – h(t j )] (Kaplan-Meier “product limit” estimator)

[Topic 11-Duration Models] 17/35 Kennan’s Strike Duration Data

[Topic 11-Duration Models] 18/35 Kaplan Meier Survival Function

[Topic 11-Duration Models] 19/35 Hazard Rates

[Topic 11-Duration Models] 20/35 Kaplan Meier Hazard Function

[Topic 11-Duration Models] 21/35 Weibull Accelerated Proportional Hazard Model | Loglinear survival model: WEIBULL | | Log likelihood function | | Number of parameters 3 | | Akaike IC= Bayes IC= | |Variable | Coefficient | Standard Error |b/St.Er.|P[|Z|>z] | Mean of X| RHS of hazard model Constant PROD Ancillary parameters for survival Sigma

[Topic 11-Duration Models] 22/35 Weibull Model | Parameters of underlying density at data means: | | Parameter Estimate Std. Error Confidence Interval | | | | Lambda to.0314 | | P to | | Median to | | Percentiles of survival distribution: | | Survival | | Time |

[Topic 11-Duration Models] 23/35 Survival Function

[Topic 11-Duration Models] 24/35 Hazard Function with Positive Duration Dependence for All t

[Topic 11-Duration Models] 25/35 Loglogistic Model | Loglinear survival model: LOGISTIC | | Dependent variable LOGCT | | Log likelihood function | |Variable | Coefficient | Standard Error |b/St.Er.|P[|Z|>z] | Mean of X| RHS of hazard model Constant PROD Ancillary parameters for survival Sigma | Loglinear survival model: WEIBULL | | Log likelihood function | |Variable | Coefficient | Standard Error |b/St.Er.|P[|Z|>z] | Mean of X| RHS of hazard model Constant PROD Ancillary parameters for survival Sigma

[Topic 11-Duration Models] 26/35 Loglogistic Hazard Model

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[Topic 11-Duration Models] 34/35 Log Baseline Hazards

[Topic 11-Duration Models] 35/35 Log Baseline Hazards - Heterogeneity