In this dissertation I study different versions of the semiparametric proportional hazard duration model and their practical applications under both frequentist and Bayesian econometrics frameworks. I use the unemployment spell data set that is created from the Panel Study of Income Dynamics (PSID).In Chapter 1 I study the effects of unemployment compensation and other important sociodemographic factors on unemployment duration. Whether duration dependence follows a particular function form is also examined. Discrete, semiparametric, proportional hazard models are used and compared among different specifications. I allow for nonparametric estimation of the effect of time on the unemployment exit rate. Because unobserved individual heterogeneity has the potential to bias the estimation results, we also consider gamma heterogeneity as an additional source of error in the hazard model (i.e., the so called mixed proportional hazard model, MPH). I find that the nonparametric baseline hazard estimations capture very well the shape of the empirical duration, which often does not belong to a specific parametric family; and unemployment insurance and socio-demographic aspects have significant impacts on the unemployment spell.In the second chapter I test whether different ways to resume work, such as new job and recall, have different duration behaviors. Hence a semiparametric dependent competing risks proportional hazard model is specified. Identifiability of such model is also discussed. By assuming linearity on the baseline hazard at each time interval, I allow for unrestricted correlation between the competing risks. My model guarantees that the unobserved failure occurs later than the observed failure at any possible time point, and censored observations are accommodated explicitly in the model specification. The estimated correlation coefficient suggests that recall duration and new job duration have a positive relationship that may not be negligible. We also find that there is significant difference in the hazard structure of returning to the same employer and a different employer.Different from the first two chapters, in the third chapter I investigate the ordered probit duration model semiparametrically using the Bayesian Markov Chain Monte Carlo (MCMC) methods. I develop and estimate the model without considering unobserved heterogeneity, and noninformative priors are assumed for both the baseline hazard and regressor parameters. Hybrid Metropolis-Hastings/Gibbs sampler is employed to speed up chain mixture. Convergence of the chains is assessed by the Gelman-Rubin scale reduction factor. Applications on the PSID unemployment duration data demonstrate that the proposed model and estimation method perform well.