A Duration Model with Dynamic Unobserved Heterogeneity

The paper considers a new class of duration models in which unobserved heterogeneity changes with\ud time. The class addresses two main questions: How does the exit probability from a state vary when\ud unobserved heterogeneity evolves through time? And do changes in unobserved heterogeneity have a\ud timing effect? We show the non- and semi-parametric identification of the new class by solving a nonlinear\ud integral equation with unknown kernel. Both the function of observed covariates and the mean of the\ud distribution of unobserved heterogeneity are nonparametrically identified. Identifying timing effects and\ud the distribution of unobserved heterogeneity requires stronger assumptions on either one of the two.\ud An extension to the case when unobserved heterogeneity is a function of observed covariates is also\ud identified. We show that sieve maximum likelihood estimators are consistent and present Monte Carlo\ud simulations for both correct specification and misspecification. The paper also presents an empirical\ud model of unemployment duration in which individuals exit unemployment when total accumulated losses\ud due to unemployment cross over a self-imposed spending limit

Forecasted Treatment Effects

We consider estimation and inference of the effects of a policy in the absence of a control group. We obtain unbiased estimators of individual (heterogeneous) treatment effects and a consistent and asymptotically normal estimator of the average treatment effects, based on forecasting counterfactuals using a short time series of pre-treatment data. We show that the focus should be on forecast unbiasedness rather than accuracy. Correct specification of the forecasting model is not necessary to obtain unbiased estimates of individual treatment effects. Instead, simple basis function (e.g., polynomial time trends) regressions deliver unbiasedness under a broad class of data-generating processes for the individual counterfactuals. Basing the forecasts on a model can introduce misspecification bias and does not necessarily improve performance even under correct specification. Consistency and asymptotic normality of our Forecasted Average Treatment effects (FAT) estimator are attained under an additional assumption that rules out common and unforecastable shocks occurring between the treatment date and the date at which the effect is calculated

On the Role of Covariates in the Synthetic Control Method

We derive conditions under which the original result of Abadie et al (2010) regarding the bias of the Synthetic Control (SC) estimator remains valid when we relax the assumption of a perfect match on observed covariates. We then show that, even when the conditions for the first result are valid, a perfect match on pre-treatment outcomes does not generally imply an approximate match for all covariates. Taken together, our results show that a perfect match on covariates should not be required for the SC method, as long as there is a perfect match on a long set of pre-treatment outcomes