Test for exogeneity and validity in an ordered probit setting with -cmp-

[Anna Mogilevskaja]

Hi,

I estimated an IV 2sls and IV ordered probit model. For the IV 2sls model I found easily a command to test for the exogeneity of the instrumented variable and the validity of the instruments. However, for the IV ordered probit model I could not find anything so far. I use the cmp command to estimate the model:

cmp (PlannedDurables = inflexp income_exp~d i.growth $controls) (inflexp = devinfpoint inflexppoint_long_a income_exp~d i.growth $controls), ind($cmp_oprobit $cmp_cont) vce(robust) qui

Does anyone have an idea how I can test whether inflexp is exogenous and whether devinfpoint and inflexppoint_long_a are valid instruments?

Thanks in advance for the help.

[Jeff Wooldridge]

Probably the simplest way is to use the estimated correlation coefficient provided with the output. The null of exogeneity is that the correlation is zero. You can look at the 95% confidence interval.

Or, you can use a two-step control function approach (which also works as an estimation method):

regress inflexp = devinfpoint inflexppoint_long_a income_exp~d i.growth $controls
predict vhat, resid
oprobit PlannedDurables inflexp income_exp~d i.growth $controls vhat

Use the t statistic on vhat.

[David Roodman]

What Jeff said.

The output will show you the 95% confidence interval for the arc hyperbolic tangent of the correlation, which is 0 when the correlation is 0 since atanh(0)=0. You can look at whether that CI contains 0. If you apply the tanh() function to its bounds, you'll get a 95% CI for the actually correlation. This wouldn't change the analysis, but could help you understand the output better.