This paper builds on the Empirical Monte Carlo simulation approach developed by Huber et al. (2013) to study the estimation of Timing-of-Events (ToE) models. We exploit rich Swedish data of unemployed job-seekers with information on participation in a training program to simulate placebo treatment durations. We first use these simulations to examine which covariates are key confounders to be included in selection models. The joint inclusion of specific short-term employment history indicators (notably, the share of time spent in employment), together with baseline socio-economic characteristics, regional and inflow timing information, is important to deal with selection bias. Next, we omit subsets of explanatory variables and estimate ToE models with discrete distributions for the ensuing systematic unobserved heterogeneity. In many cases the ToE approach provides accurate effect estimates, especially if time-varying variation in the unemployment rate of the local labor market is taken into account. However, assuming too many or too few support points for unobserved heterogeneity may lead to large biases. Information criteria, in particular those penalizing parameter abundance, are useful to select the number of support points.