title: On the estimation of a binary response model in a selected population.
abstract: A generalization of the Probit model is presented, with the extended skew-normal cumulative distribution as a link function, which can be used for modelling a binary response variable in the presence of selectivity bias. The estimate of the parameters via ML is addressed, and inference on the parameters expressing the degree of selection is discussed. The assumption underlying the model is that the selection mechanism influences the unmeasured factors and does not affect the explanatory variables. When this assumption is violated, but other conditional independencies hold, then the model proposed here is derived. In particular, the instrumental variable formula still applies and the model results at the second stage of the estimating procedure.
authors.affiliation: Dipartimento di Statistica "G. Parenti", Università di Firenze, Viale Morgagni, 59, 50134, Firenze, Italy.
authors.forename: Francesco Claudio
authors.initials: FC
authors.lastname: Stingo
authors.affiliation: Dipartimento di Economia, Finanza e Statistica, Università di Perugia, Via Pascoli, 1, 06100, Perugia, Italy.
authors.forename: Elena
authors.initials: E
authors.lastname: Stanghellini
authors.affiliation: Dipartimento PE.ME.IS., Università del Sannio, P.zza Arechi, 2, 82100, Benevento, Italy.
authors.forename: Rosa
authors.initials: R
authors.lastname: Capobianco
keywords: directed acyclic graph; extended skew-normal distribution; hidden truncation; instrumental variables; self-selection; unobserved confounder