Bivariate Probit and Logit Models PDF

Bivariate Probit and Logit Models Ani Katchova © 2013 by Ani Katchova. All rights reserved. 2 Bivariate Probit and Logit Models Overview  Bivariate probit and logit models equations  Coefficients and marginal effects 3 Bivariate probit model Bivariate outcome exam...

Bivariate Probit and Logit Models Ani Katchova © 2013 by Ani Katchova. All rights reserved. 2 Bivariate Probit and Logit Models Overview  Bivariate probit and logit models equations  Coefficients and marginal effects 3 Bivariate probit model Bivariate outcome examples  Individual decision whether to work or not and whether to have children or not.  Farmer decision of whether to use marketing contracts or not and whether to use environmental contracts or not.  The bivariate models estimates decisions that are interrelated as opposed to independent. Bivariate probit model specification  The bivariate probit model is a joint model for two binary outcomes.  These outcomes may be correlated, with correlation ?.  If the correlation turns out insignificant, then we can estimate two separate probit models, otherwise we have to use a bivariate probit model.  The unobserved latent variables are presented as: y 5∗ L 5′?5 EA 5 y 6∗ L 6′?6 EA 6 4  The bivariate probit model specifies the outcomes as: U 5 L \1 EB y 5∗ P0 0 EB y 5∗ Q0 U 6 L \1 EB y 6∗ P0 0 EB y 6∗ Q0  Marginal effects and predicted values can be estimated similarly to those for the binary probit models. Marginal effects for the joint probability, say P(y 1=1 and y 2=1) are also available.