Testing Exogeneity in the Bivariate Probit Model: A Monte Carlo Study

Fringe benefits and job satisfaction

“…Estimation of the recursive bivariate probit model explained above and endogeneity testing follows from Monfardini and Radice (2008). The authors explain that, unless there is a very large sample, the likelihood ratio test of the cross-equation correlation coefficient is the best test for endogeneity of the fringe benefit dummy variable.…”

Testing for the Endogenous Nature between Women’s Empowerment and Antenatal Health Care Utilization: Evidence from a Cross-Sectional Study in Egypt

“…The recursive structure builds on a first reduced form equation for the potentially endogenous dummy and a second structural form equation determining the outcome of interest: $\begin{array}{c}{Y}_{\mathrm{1}i}^{\ast }={\tilde{\beta }}_{\mathrm{1}}{X}_{\mathrm{1}i}+u_{\mathrm{1}i}\\ Y_{2i}^{\ast }={\tilde{\beta }}_{\mathrm{2}}{X}_{2i}+u_{2i}={\delta }_1{Y}_{1i}+{\tilde{\delta }}_2{Z}_{2i}+u_{2i},\end{array}$ where Y 1 i * and Y 2 i * are latent variables, and Y 1 i and Y 2 i are binary variables following the rule $\begin{array}{c}{Y}_{Li}=false\{\begin{array}{cc}\mathrm{normal1}\hfill & \text{if}\hspace{0.17em}\hspace{0.17em}{Y}^{\ast }>\mathrm{normal0}\hfill \\ \mathrm{normal0}\hfill & \text{if}\hspace{0.17em}\hspace{0.17em}{Y}^{\ast }\le \mathrm{normal0};\hfill \end{array}\hspace{1em}L=\mathrm{1,2}.\end{array}$ X 1 i and Z 2 i are vectors of exogenous variables, β 1 and δ 2 are parameter vectors, δ 1 is a scalar parameter, and ${\tilde{\beta }}_2=false({\delta }_1{\tilde{\delta }}_2\widetilde{false)}$. In the second specification, the error terms are assumed to be independently and identically distributed as bivariate normal [17]. …”

The Impact of Private Long-Term Care Insurance on the Use of Long-Term Care

“…Upon estimating the model, we formally test for the endogeneity of s9. In the recursive bivariate probit model, the best test for the endogeneity of s9 is a likelihood ratio test that compares a model in which r is assumed to be zero (resulting in two univariate probit equations) to a model where r is allowed to take on its estimated value (Monfardini and Radice 2008). Rejection of the hypothesis, H 0 : r 5 0, indicates that s9 should be treated as endogenous, whereas failure to reject the hypothesis suggests that s9 can safely be treated as exogenous.…”

“…For each LTC measure, Table 3 reports the Chi-squared statistic associated with a test of the hypothesis, Ho: r 5 0, which is the relevant test (Monfardini and Radice 2008). The test results suggest that FIML bivariate probit estimation is appropriate for modeling nursing home use, whereas single-equation ML methods are best for modeling paid home care and informal care.…”