josef-pkt
commented
1 year ago Marra and Radice have R packages with copulas for bivariate binary and copula sample selection models
Marra, Giampiero, and Rosalba Radice. “A Joint Regression Modeling Framework for Analyzing Bivariate Binary Data in R:” Dependence Modeling 5, no. 1 (December 20, 2017): 268–94. https://doi.org/10.1515/demo-2017-0016.
similar to #8765 but when "treatment" and outcome are binary.
recursive, triangular y1 = 1(α y2 + x1 β + ε1 ≥ 0) y2 = 1(x2 β2 + ε2 ≥ 0) ε1, ε2 are correlated
full, parametric MLE but with copulas, so we have flexibility in correlation and CDF-link
bivariate Probit is in Greene
two articles for using copulas
Hasebe, Takuya. “Marginal Effects of a Bivariate Binary Choice Model.” Economics Letters 121, no. 2 (November 1, 2013): 298–301. https://doi.org/10.1016/j.econlet.2013.08.028.
Winkelmann, Rainer. “Copula Bivariate Probit Models: With an Application to Medical Expenditures.” Health Economics 21, no. 12 (2012): 1444–55. https://doi.org/10.1002/hec.1801.
This looks like the simplest case to get started with copulas for discrete random variables, especially in the regression model context.
update
an article that shows identification in this model
Han, Sukjin, and Edward J. Vytlacil. “Identification in a Generalization of Bivariate Probit Models with Dummy Endogenous Regressors.” Journal of Econometrics 199, no. 1 (July 1, 2017): 63–73. https://doi.org/10.1016/j.jeconom.2017.04.001.