Significance of -ivprobit- analysis interpreting

[Grace Wan]

Hello, I was doing instrumental variable analysis by -ivprobit- syntax, because the dependent variable in my research was coded 0 and 1
Here's a little problem for interpreting the result when I use logistic regression for OLS estimation, and use instrumental variable analysis for IV estimation
The dependent variable is "CVD_incident", the independent variable is "Triglyceride_15", and the IV I used is "rs157580_genotype"

This is the result done by logistic regression

 logistic CVD_incident Triglyceride_15

Logistic regression                             Number of obs     =      1,956
                                                LR chi2(1)        =       2.68
                                                Prob > chi2       =     0.1013
Log likelihood = -249.29997                     Pseudo R2         =     0.0054

---------------------------------------------------------------------------------
   CVD_incident | Odds Ratio   Std. Err.      z    P>|z|     [95% Conf. Interval]
----------------+----------------------------------------------------------------
Triglyceride_15 |   1.002383   .0012998     1.84   0.066     .9998386    1.004934
          _cons |   .0218643   .0046799   -17.86   0.000     .0143728    .0332606
---------------------------------------------------------------------------------

As you can see, the significance is 0.066

Meanwhile, I also do an analysis by instrumental variable analysis by using -ivpbrobit-

ivprobit CVD_incident (Triglyceride_15=rs157580_genotype)

Fitting exogenous probit model

Iteration 0:   log likelihood = -250.64219  
Iteration 1:   log likelihood = -248.87869  
Iteration 2:   log likelihood =  -248.7919  
Iteration 3:   log likelihood = -248.79177  
Iteration 4:   log likelihood = -248.79177  

Fitting full model

Iteration 0:   log likelihood =  -11453.09  
Iteration 1:   log likelihood = -11453.089  

Probit model with endogenous regressors         Number of obs     =      1,956
                                                Wald chi2(1)      =      16.64
Log likelihood = -11453.089                     Prob > chi2       =     0.0000

-----------------------------------------------------------------------------------------
                        |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
------------------------+----------------------------------------------------------------
        Triglyceride_15 |  -.0122655   .0030065    -4.08   0.000     -.018158   -.0063729
                  _cons |    .704075   1.292322     0.54   0.586    -1.828829    3.236979
------------------------+----------------------------------------------------------------
 corr(e.Triglyceride_15,|
         e.CVD_incident)|   .9417286   .1792415                      -.874467    .9998794
   sd(e.Triglyceride_15)|   74.38316   1.189254                      72.08841    76.75096
-----------------------------------------------------------------------------------------
Instrumented:  Triglyceride_15
Instruments:   rs157580_genotype
-----------------------------------------------------------------------------------------
Wald test of exogeneity (corr = 0): chi2(1) = 1.22        Prob > chi2 = 0.2684

But the significance is <0.001...

How could I interpret this result, is there anything wrong?
Because the p-value of IV estimation should seems to be larger then using OLS estimation

Wish there's some expert could help me~ thanks a lot

[Long Hong]

From an econometric point of view, the results do not seem to cast a confusion. If you trust your instrument, then it means the plain result without IV is downward biased, and the true parameter value should be the one from IV regression. However, as I mentioned, if you trust your instrument. Also, I would not emphasize the focus on the p-value, which is technically not comparable. Hope it helps!

[Grace Wan]

Long Hong,

Yes, I trust my instrument, but the result of Wald test of exogeneity seems to conclude that the OLS estimation was not biased, so we only need to estimate the effect by OLS estimation
I also wonder why the p-value is not comparable?

Thank you in advance~