Hi
1) You need to estimate the biprobit to test the exogeneity. But if the exogeneity is rejected then you have to use the biprobit or said differently you cannot rely on the probit. That the coefficent on VC is insignificant in the probit but significant in the biprobit could be due to endogeneity. I would be cautious though . All this relies on your instrument and it has a very high positive effect on VC-dummy (but it is significant which is good), which results in a big difference between the estimate of VC-dummy fo the two models. It is strange. I would check in the data if the instrument doesn't show some strange patterns or if it is set-up correctly.
2) (I think) there's something wrong with the hausman test. By looking at the output, it should be the other way round. The probit is efficient under H0 but inconsistent under Ha. There are some problem with computing the difference between the covariance matrices, which explains why you have a lot of missing values. This a general problem with the test, that is the difference between the two covariance matrices is not necessairly positive definite. Stata actually tells you that in your case. Then you cannot really use the test. Try to run the test the other way round if you get some weird output try the exogeneity test with the residuals we have discussed for a while.
3) I can see that by looking at the z-value of /athrho which is a transformation of the correlation coefficient. When using Maximum likelihood some parameters are not estimated directly but a transformation of these parameters in order to avoid numerical problems. That is what Stata does when it tries to estimate the coefficient correlation of a bivariates normal distribution. By extension if the estimate of this transformation is statistically significant then it will also be the case for the original parameter. But yes, you should actually rely on the p-value of the chi-square test at at the bottom of the output which tests where the correlation coefficient is equal to zero.
4) I think the core of your analysis should be the biprobit and testing the exogeneity with the control function approach. The Hausman test seems to give trouble. Now you have to make sure that your instrument is convincing, which you have to find theoretical arguments for. The effect of your instrument on VC_dummy is also important in your analysis. Does it have the "right" sign. Does the magnitude of the estimate make sense? Is it strongly correlated with the endogenous variable?
The biprobit allows you to get consistent estimate of your model (and VC-dummy in particular) when VC-dummy is endogenous. You can test the exogeneity of the VC_dummy and use probit if it is not rejected.
1) You need to estimate the biprobit to test the exogeneity. But if the exogeneity is rejected then you have to use the biprobit or said differently you cannot rely on the probit. That the coefficent on VC is insignificant in the probit but significant in the biprobit could be due to endogeneity. I would be cautious though . All this relies on your instrument and it has a very high positive effect on VC-dummy (but it is significant which is good), which results in a big difference between the estimate of VC-dummy fo the two models. It is strange. I would check in the data if the instrument doesn't show some strange patterns or if it is set-up correctly.
2) (I think) there's something wrong with the hausman test. By looking at the output, it should be the other way round. The probit is efficient under H0 but inconsistent under Ha. There are some problem with computing the difference between the covariance matrices, which explains why you have a lot of missing values. This a general problem with the test, that is the difference between the two covariance matrices is not necessairly positive definite. Stata actually tells you that in your case. Then you cannot really use the test. Try to run the test the other way round if you get some weird output try the exogeneity test with the residuals we have discussed for a while.
3) I can see that by looking at the z-value of /athrho which is a transformation of the correlation coefficient. When using Maximum likelihood some parameters are not estimated directly but a transformation of these parameters in order to avoid numerical problems. That is what Stata does when it tries to estimate the coefficient correlation of a bivariates normal distribution. By extension if the estimate of this transformation is statistically significant then it will also be the case for the original parameter. But yes, you should actually rely on the p-value of the chi-square test at at the bottom of the output which tests where the correlation coefficient is equal to zero.
4) I think the core of your analysis should be the biprobit and testing the exogeneity with the control function approach. The Hausman test seems to give trouble. Now you have to make sure that your instrument is convincing, which you have to find theoretical arguments for. The effect of your instrument on VC_dummy is also important in your analysis. Does it have the "right" sign. Does the magnitude of the estimate make sense? Is it strongly correlated with the endogenous variable?
The biprobit allows you to get consistent estimate of your model (and VC-dummy in particular) when VC-dummy is endogenous. You can test the exogeneity of the VC_dummy and use probit if it is not rejected.
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