Duration Models with Stochastic Unobserved Heterogeneity

Individuals differ. Not only do they differ among themselves, but also across time periods. To account for both intra- and inter-individual differences, this dissertation considers hazard models in which individual unobserved heterogeneity evolves stochastically during the duration of a spell. For example, skill accumulation during the spell of employment, human capital depreciation during the spell of unemployment, or aging processes relevant to retirement decision problems can all be modeled as stochastic processes, whose effects accumulate in time.;The first chapter of the dissertation introduces and identifies two different classes of hazard functions with stochastic heterogeneity. Unobserved heterogeneity can be allowed to either be independent from observed covariates or be generated by the latter. The identification strategy is based on solving a nonlinear Volterra integral equation of the first kind with an unknown kernel. Assuming the distribution of the process is unknown, both the mean of the distribution and the function of time invariant covariates are identified for both classes of hazard functions. In order to identify the remaining parameters of interest, stronger assumptions are needed. Under the assumption that the distribution of the process is known up to a its mean, the function weighting the stochastic process is identified. When observed covariates vary with time, the function of observed covariates is identified under the assumption that the distribution of the process is known entirely.;The second chapter considers the estimation of one of the frameworks introduced in the first chapter. The estimation strategy is semi-nonparametric sieve maximum likelihood. The estimators are shown to be consistent and their rate of convergence is derived under a certain metric.;The third chapter presents a model of unemployment duration in which individuals exit the unemployment spell when their perceived monetary and non-monetary losses due to unemployment are greater than a threshold level. The threshold combines both the individuals' perceived wage offer distribution and their self-imposed limits on the amount of losses they are willing to sustain during the spell. The model is applied to data from the NLSY79. The empirical application finds that for some groups of individuals, the sunk cost effect weakens over time, while for others, it does not. For some groups, differences in transition rates are driven by differences in initial net wealth, while for others, by differences in sensitivity to losses.;The models introduced and analyzed in this dissertation are of interest whenever individual unobserved heterogeneity is believed to be driven by a random process. Applications abound in biology and reliability studies.