## Causal inference for duration models. An alternative to hazard regression

Stefano Mazzuco, *Università di Padova*

This paper considers possible approaches to study the impact of an event (treatment) on the duration of an episode. Bivariate regression models with normal random intercepts are usually applied to these problems though they usually rely on strong assumptions which violation can heavily influence the final results. The missspecification of functional form of random effects, for example, is a possible source of bias. Moreover identification of such models is conditional to a set of exclusion-restrction hypotheses, which validity is sometimes questionable. An alternative procedure uses a matching method where survival functions are computed conditional on a function of observed variables thus eliminating the selection based on these variables. However also the matching solution relies on a strong assumption, namely the conditional independence assumption, but there is no assumption on the functional form of unobservables. Therefore we can depict two situations: if we are reasonably confident that the effect of the unobserved factors is negligible, then we can use a matching estimator. If our data is not reach enough and we suspect that the effect of the unobserved factors is relevant, but we observe a valid instrument we can apply the same approach to a IV estimator. This works uses a NLSY79 subsample of marriages as a case study, investigating the effect of premarital cohabitation on subsequent divorce. Firstly a hazard model for divorce and a probit model for cohabitation with correlated normal frailties is estimated. The same model will be estimated using different distributions for the frailties (e.g. skew normal, this part of the study is still in progress). Next the model using matching methods is proposed with a comparison of results provided by different models.

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Presented in Session 40: Mortality and duration models, a touch of philosophy