1、Econometric Analysis of Panel Data,William GreeneDepartment of EconomicsStern School of Business,Econometric Analysis of Panel Data,20A. Hazard and Duration Models,Modeling Duration,Time until business failureTime until exercise of a warrantyLength of an unemployment spellLength of time between chil
2、drenTime between business cyclesTime between wars or civil insurrectionsTime between policy changesEtc.,Hazard Models for Duration,Basic hazard rate modelParametric modelsDuration dependenceCensoringTime varying covariatesSample selection,The Hazard Function,Hazard Function,A Simple Hazard Function,
3、Duration Dependence,Parametric Models of Duration,Censoring,Accelerated Failure Time Models,Proportional Hazards Models,Estimation,Time Varying Covariates,Unobserved Heterogeneity,Interpretation,What are the coefficients?Are there marginal effects?What is of interest in the study?,A Semiparametric M
4、odel,Nonparametric Approach,Based simply on counting observationsK spells = ending times 1,Kdj = # spells ending at time tjmj = # spells censored in interval tj , tj+1)rj = # spells in the risk set at time tj = (dj+mj)Estimated hazard, h(tj) = dj/rjEstimated survival = 1 h(tj) (Kaplan-Meier “product
5、 limit” estimator,Kennans Strike Duration Data,Kaplan Meier Survival Function,Hazard Rates,Hazard Function,Weibull Model,+-+| Loglinear survival model: WEIBULL | Log likelihood function -97.39018 | Number of parameters 3 | Akaike IC= 200.780 Bayes IC= 207.162 |+-+-+-+-+-+-+-+|Variable | Coefficient
6、| Standard Error |b/St.Er.|P|Z|z | Mean of X|+-+-+-+-+-+-+ RHS of hazard model Constant 3.82757279 .15286595 25.039 .0000 PROD -10.4301961 3.26398911 -3.196 .0014 .01102306 Ancillary parameters for survival Sigma 1.05191710 .14062354 7.480 .0000,Weibull Model,+-+ | Parameters of underlying density a
7、t data means: | | Parameter Estimate Std. Error Confidence Interval | | - | | Lambda .02441 .00358 .0174 to .0314 | | P .95065 .12709 .7016 to 1.1997 | | Median 27.85629 4.09007 19.8398 to 35.8728 | | Percentiles of survival distribution: | | Survival .25 .50 .75 .95 | | Time 57.75 27.86 11.05 1.80
8、| +-+,Survival Function,Hazard Function,Loglogistic Model,+-+| Loglinear survival model: LOGISTIC | Dependent variable LOGCT | Log likelihood function -97.53461 | Censoring status variable is C |+-+-+-+-+-+-+-+|Variable | Coefficient | Standard Error |b/St.Er.|P|Z|z | Mean of X|+-+-+-+-+-+-+ RHS of
9、hazard model Constant 3.33044203 .17629909 18.891 .0000 PROD -10.2462322 3.46610670 -2.956 .0031 .01102306 Ancillary parameters for survival Sigma .78385188 .10475829 7.482 .0000+-+| Loglinear survival model: WEIBULL | Log likelihood function -97.39018 | Number of parameters 3 |Variable | Coefficien
10、t | Standard Error |b/St.Er.|P|Z|z | Mean of X|+-+-+-+-+-+-+ RHS of hazard model Constant 3.82757279 .15286595 25.039 .0000 PROD -10.4301961 3.26398911 -3.196 .0014 .01102306 Ancillary parameters for survival Sigma 1.05191710 .14062354 7.480 .0000,Loglogistic Hazard Model,Sample Selection,Building a
11、 Likelihood for a Weibull Duration Model with Selection,Building the Likelihood,Conditional Likelihood,Weibull Model with Selection,Strategy: Hermite quadrature or maximum simulated likelihood. Not by throwing a lambda into the likelihoodCould this be done without joint normality?How robust is the model?Is there any other approach available?,
