Essays on econometric methods for duration data analysis

Resumo

In economic analysis is usual to find that the outcome of interest represents the duration until an event occurs, e.g. the duration until getting a job, the firms lifetime, among others. The major challenge to analyze duration or survival data is the presence of censoring. The most of the existing survival models usually assume a parametric or semiparametric conditional hazard function. This thesis is formed by three chapters regarding alternative semiparametric estimation methods suitable for survival times observed under random censoring that do not require assumptions on the underlying duration distribution. These methods are motivated and applied in the context of unemployment duration studies. Chapter 1 studies counterfactual decomposition methods. Existing inference procedures applicable when data is fully observed, might produce missleading conclussions. This may explain the lack of decomposition exercises for variables related to duration outcomes, typically observed under right censoring. We propose two decomposition methods that consider the presence of this kind of censoring. First, under suitable restrictions on the censoring mechanism, we provide an Oaxaca-Blinder type decomposition method of the mean in a nonparametric context. Consistent estimation of the decomposition components is based on a prior estimator of the joint distribution of duration and covariates. Secondly, we consider a method that makes possible to decompose other distributional features, such as the median or the Gini coefficient. To do so, weaker assumptions on the censoring nature are needed, but it is required to introduce restrictions on the functional form of the conditional distribution of duration given covariates. We provide formal justification for asymptotic inference and study the finite sample performance through Monte Carlo experiments. Finally, we apply the proposed methodology to the analysis of unemployment duration gaps in Spain. This study suggests that factors beyond the workers' socioeconomic characteristics play a relevant role in explaining the difference between several unemployment duration distribution features such as the mean, the probability of being long term unemployed and the Gini coeficient. Chapter 2 proposes inference procedures on distributional regression models in the context of survival analysis. These models generalize classical survival models to a situation where slope coeficients depend on duration time. We formally justify asymptotic inferences on the varying coeficients under weak regularity conditions, similar to those needed when data is not censored. Finite sample properties of the proposed inference procedures are studied by means of Monte Carlo experiments. Finally, proposed method is implemented in two empirical exercises using US data. First, we study the effect of unemployment benefits on unemployment duration; and secondly we perform a counterfactual decomposition in the context of the recent Great Recession using US data. Chapter 3 adapts the generalized method of moments (GMM) to estimating parameters identified by moment restrictions involving survival time observed under right random censoring. When the underlying nonparametric joint distribution of survival time and the rest varibles can be identified under random censoring, the moment restrictions can be consistently estimated by weighting averages, which form a basis for the proposed GMM. Under classical assumptions in GMM estimation, we show consistency and asymptotic normality, and provide the optimal weighting matrix that maximizes relative efficiency. Finite sample properties are studied using a Monte Carlo expertiment of a linear in parameter structural model.