How to conduct IV diagnostic tests after recursive bivariate probit

[hussein bataineh]

HI

I am estimating a recursive bivariate probit model in which CSO_PRESENCE is treated as an endogenous binary explanatory variable in the HARD_FREEZE equation. My excluded instrument for CSO_PRESENCE is CSO_Percentage.

The model is estimated as follows:

asdoc biprobit (HARD_FREEZE  = CSO_PRESENCE  SIZE  ROA  LEV   MB   OCF  SD_OCF BOARD_SIZE GENDER_RATIO   BOARD_IND SUS_COMM   FUND_STATUS  FUND_RATIO  PLAN_SIZE       i.year  i.ff_12 ) (CSO_PRESENCE  = CSO_Percentage SIZE  ROA  LEV   MB   OCF  SD_OCF BOARD_SIZE GENDER_RATIO   BOARD_IND SUS_COMM   FUND_STATUS  FUND_RATIO  PLAN_SIZE       i.year  i.ff_12), vce(cluster id) dec(4) tzok

I would like to know how to conduct and report the following post-estimation diagnostic tests after biprobit:

1. Endogeneity test
   For example, testing whether CSO_PRESENCE is endogenous in the HARD_FREEZE equation.
2. Underidentification test
   For example, a Kleibergen-Paap rk LM-type test.
3. Weak identification test
   For example, a Kleibergen-Paap rk Wald-type test.
4. Stock-Yogo critical values
   For assessing whether the instrument is weak.
5. Anderson-Rubin Wald test
   For weak-instrument robust inference.
6. Instrument relevance test
   For testing whether CSO_Percentage significantly predicts CSO_PRESENCE.

I initially tried the following command for the endogeneity test:

test [athrho]_cons = 0
but Stata returned:

equation [athrho] not found r(303);
Should the endogeneity test after biprobit be conducted using:

test /athrho = 0
or is there another recommended command?

For the instrument relevance test, is it appropriate to test whether CSO_Percentage is statistically significant in the CSO_PRESENCE equation, for example:

test [CSO_PRESENCE]CSO_Percentage = 0
More generally, I would be grateful for advice on how to perform the endogeneity, underidentification, weak identification, Stock-Yogo, Anderson-Rubin, and instrument relevance tests after a recursive biprobit model with clustered standard errors.

Best regards,
Hussein

[George Ford]

athrho test is provided in the result. that's the test of exogeneity. (or nlcom /athrho).

the rest of the stuff is for linear models. they have no comparison in biprobit.

In biprobit, identification comes from both the exclusion restriction and the nonlinearity of the normal CDF (even without an instrument, the model is technically identified).

you can look at z on the exclusion to test it's relevance.

[Jeff Wooldridge]

As George said, you don't have overidentification so those tests are irrelevant. The test on rho equaling zero tests the null of endogeneity. I would use a linear model for both equations and use the effective F statistic to check for weak IVs, using vce(robust). It's not perfect, but it's something.