Doing instrumental variable analysis

[Grace Wan]

Hello, I'm new on Statalist.
I have some questions about the process of doing instrumental variable analysis, and the data interpretation to the result.
I just read the Stata documentation about “ivprobit”.

As an Epidemiologist, the most important thing I want to know is the odds ratio (OR) of an exposure variable(X) to the disease outcome(Y).
When I saw an example in the documentation, it shows “coef.” In the result table.

And my question is: how can I transfer the coefficient into the odds ratio?
I just search for the command in some website, and I got this: "dis exp(Coef.)"
Does it have an alternative way to show the odds ratio directly in the table? Or I just need to type the command that I found, and transfer them into odds ratio by myself?


My second question is: unlike the process in the command “ivregress”, which can report first-stage regression statistics by typing “estat first” or just adding “first” after the ivregress command, how can I get the first-stage regression statistics in “ivprobit”? Does it have some commands to type?
Because the strength of the instrumental variable is also very important when I conduct the analysis by using binary dependent variables (eg. having disease or not)

I just want to say thank you in advance, to people who give me some advice.

Sincerely,
Grace

[Carlo Lazzaro]

Grace:
-as far as your first question is concerned, I'm not aware on any Stata built-in option that gives back OR under -ivprobit-;
- you can easily obtain the first-stage statistics under -ivprobit- by adding the -first- option after the comma at the end of you code, as you can see from the following toy-example:

. webuse laborsup

. ivprobit fem_work fem_educ kids (other_inc = male_educ), first

Fitting exogenous probit model

Iteration 0:   log likelihood = -344.63508
Iteration 1:   log likelihood = -252.10819
Iteration 2:   log likelihood = -252.04529
Iteration 3:   log likelihood = -252.04529

Fitting full model

Iteration 0:   log likelihood = -2368.2142
Iteration 1:   log likelihood = -2368.2062
Iteration 2:   log likelihood = -2368.2062

Probit model with endogenous regressors         Number of obs     =        500
                                                Wald chi2(3)      =     163.88
Log likelihood = -2368.2062                     Prob > chi2       =     0.0000

----------------------------------------------------------------------------------------------
                             |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-----------------------------+----------------------------------------------------------------
fem_work                     |
                   other_inc |  -.0542756   .0060854    -8.92   0.000    -.0662028   -.0423485
                    fem_educ |    .211111   .0268648     7.86   0.000     .1584569    .2637651
                        kids |  -.1820929   .0478267    -3.81   0.000    -.2758315   -.0883542
                       _cons |   .3672086   .4480724     0.82   0.412    -.5109971    1.245414
-----------------------------+----------------------------------------------------------------
other_inc                    |
                    fem_educ |   .3351866   .2825972     1.19   0.236    -.2186937     .889067
                        kids |   .8329056   .5475666     1.52   0.128    -.2403052    1.906116
                   male_educ |   2.845253    .282746    10.06   0.000     2.291081    3.399425
                       _cons |   9.872562   5.029193     1.96   0.050     .0155242     19.7296
-----------------------------+----------------------------------------------------------------
                  /athrho2_1 |   .3907859   .1509443     2.59   0.010     .0949404    .6866313
                   /lnsigma2 |   2.813383   .0316228    88.97   0.000     2.751404    2.875363
-----------------------------+----------------------------------------------------------------
 corr(e.other_inc,e.fem_work)|   .3720375   .1300518                      .0946562    .5958136
              sd(e.other_inc)|   16.66621   .5270318                      15.66461    17.73186
----------------------------------------------------------------------------------------------
Instrumented:  other_inc
Instruments:   fem_educ kids male_educ
----------------------------------------------------------------------------------------------
Wald test of exogeneity (corr = 0): chi2(1) = 6.70        Prob > chi2 = 0.0096

[Grace Wan]

Carlo:
I just have a question is that: does this result shows F-statistics, which meanss the strength of the instrumental variable?
Or does it have another statistics representing the strength of the instrumental variable?

Thanks a lot.

[Carlo Lazzaro]

Grace:
as in -ivregress-, -first- option allows the results of the first-stage regression to be displayed.

[Grace Wan]

Carlo, I've tried your example code above, and I've typed -first- after the -ivprobit- syntax
and I got the same result of yours (because it's a online data, it shall have the same result of course )

But I still can not see anything about F-statistics or r-square...
It just showed the "first stage regression" of X and IV (eg. in the example above X should be other_inc while IV should be male_educ)

Hope you can help me~ thanks a lot

[Carlo Lazzaro]

Grace:
you may want to try:

. webuse laborsup
. ivprobit fem_work fem_educ kids (other_inc = male_educ), twostep first
Checking reduced-form model...
first-stage regression

      Source |       SS           df       MS      Number of obs   =       500
-------------+----------------------------------   F(3, 496)       =     34.36
       Model |  28864.2732         3  9621.42439   Prob > F        =    0.0000
    Residual |  138881.269       496  280.002558   R-squared       =    0.1721
-------------+----------------------------------   Adj R-squared   =    0.1671
       Total |  167745.542       499  336.163411   Root MSE        =    16.733

------------------------------------------------------------------------------
   other_inc |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
   male_educ |   2.845253   .2838838    10.02   0.000      2.28749    3.403016
    fem_educ |   .3351866   .2837344     1.18   0.238    -.2222829    .8926562
        kids |   .8329056   .5497701     1.52   0.130    -.2472597    1.913071
       _cons |   9.872562   5.049432     1.96   0.051    -.0483506    19.79347
------------------------------------------------------------------------------

Two-step probit with endogenous regressors        Number of obs   =        500
                                                  Wald chi2(3)    =      93.97
                                                  Prob > chi2     =     0.0000

------------------------------------------------------------------------------
             |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
   other_inc |   -.058473   .0093364    -6.26   0.000    -.0767719    -.040174
    fem_educ |    .227437   .0281628     8.08   0.000     .1722389     .282635
        kids |  -.1961748   .0496323    -3.95   0.000    -.2934522   -.0988973
       _cons |   .3956061   .4982649     0.79   0.427    -.5809752    1.372187
------------------------------------------------------------------------------
Instrumented:  other_inc
Instruments:   fem_educ kids male_educ
------------------------------------------------------------------------------
Wald test of exogeneity: chi2(1) = 6.50                   Prob > chi2 = 0.0108

.

[Grace Wan]

Carlo, thank you for helping me~~~
Although I'm still learning about the syntax, the interpretation...but your reply is very important for me to understand the procedure of doing IV-analysis, and conduct in the Epi field.

I'll try again later, using the same example and using the syntax that you typed above
If I had some problems afterwards, hoping you can help me again (though I wish that I could solve this problem from the time I finish my trying :P)

Anyway, thank you so much~ Wish you have a good day