On the estimation of a binary response model in a selected population |
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Authors: | Francesco Claudio StingoElena Stanghellini Rosa Capobianco |
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Affiliation: | a Department of Statistics, Rice University, 6100 Main St. MS-138, 77005 Houston, USA b Dipartimento di Economia, Finanza e Statistica, Università di Perugia, Via Pascoli, 1, 06100 Perugia, Italy c Dipartimento di Studi dei Processi Formativi e Culturali, Universitá di Roma Tre, Via Manin 53, 00153 Roma, Italy |
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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. |
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Keywords: | Directed acyclic graph Extended skew-normal distribution Hidden truncation Instrumental variables Self-selection Unobserved confounder |
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