Interpretation of analysis after ivprobit

[Grace Wan]

Hi, I've done an instrumental variable analysis by using the syntax "ivprobit", which represents that the outcome variable is a binary outcome(yes=1, no=0).
In addition to the main analysis, I also report the result of first stage regression.
Here's the result:

 ivprobit Heart_disease Height (Weight=rs578776_genotype), twostep first
Checking reduced-form model...
first-stage regression

      Source |       SS           df       MS      Number of obs   =     3,509
-------------+----------------------------------   F(2, 3506)      =   1071.14
       Model |  213791.893         2  106895.947   Prob > F        =    0.0000
    Residual |  349887.519     3,506  99.7967823   R-squared       =    0.3793
-------------+----------------------------------   Adj R-squared   =    0.3789
       Total |  563679.412     3,508  160.683983   Root MSE        =    9.9898

-----------------------------------------------------------------------------------
           Weight |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
------------------+----------------------------------------------------------------
rs578776_genotype |   .3987121   .2926412     1.36   0.173    -.1750522    .9724765
           Height |   .9997172   .0216051    46.27   0.000     .9573573    1.042077
            _cons |  -99.16142   3.661257   -27.08   0.000    -106.3398   -91.98301
-----------------------------------------------------------------------------------

Two-step probit with endogenous regressors        Number of obs   =      3,509
                                                  Wald chi2(2)    =       2.84
                                                  Prob > chi2     =     0.2414

------------------------------------------------------------------------------
             |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
      Weight |   .2141107   .2000621     1.07   0.285    -.1780039    .6062253
      Height |  -.2218302   .2000962    -1.11   0.268    -.6140115    .1703511
       _cons |   20.92252   19.74899     1.06   0.289    -17.78478    59.62983
------------------------------------------------------------------------------
Instrumented:  Weight
Instruments:   Height rs578776_genotype
------------------------------------------------------------------------------
Wald test of exogeneity: chi2(1) = 2.03                   Prob > chi2 = 0.1538

According to the result above, I have 2 questions:
(1) Based on the Rule of Thumb by Staiger and Stock(1997), the F-statistics must >10, in order not to be a weak instrument in the analysis. Does the "F-statistics 1071.14" represent the instrumental variable I choose in the analysis a "good instrument" ?
(2) Does the "R-squared 0.3793" represent the explanatory power of the instrumental variable to the endogenous variable?

Thank you in advance!!!

[FernandoRios]

Hi Grace,
As far as i know, the "F-stat" you should be referring would be the F of the instrument only. Since you have only one instrument, your "F" is 1.07^2=1.1449, which is simply too low, indicating your Instrument is a very weak instrument.
HTH

[Grace Wan]

Fernando:
So under this circumstance, the F-statistics should obtained by the square of Z-statistics?!
Rather than the F-statistics showed above?

Because when doing an "ivregress" procedure, which means the dependent variable is continuous, the first stage regression result will show F-statistics and R-square, adjusted R-square, and also partial R-square, just that the example I post below:

 ivregress 2sls Height (Weight=BMI), first

First-stage regressions
-----------------------

                                                Number of obs     =      4,217
                                                F(   1,   4215)   =    1640.74
                                                Prob > F          =     0.0000
                                                R-squared         =     0.2802
                                                Adj R-squared     =     0.2800
                                                Root MSE          =    16.1861

------------------------------------------------------------------------------
      Weight |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
         BMI |   2.829184   .0698459    40.51   0.000      2.69225    2.966119
       _cons |   .6094178   1.730501     0.35   0.725    -2.783277    4.002112
------------------------------------------------------------------------------


Instrumental variables (2SLS) regression          Number of obs   =      4,217
                                                  Wald chi2(1)    =       2.33
                                                  Prob > chi2     =     0.1270
                                                  R-squared       =     0.0709
                                                  Root MSE        =     14.348

------------------------------------------------------------------------------
      Height |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
      Weight |   .0333926   .0218834     1.53   0.127    -.0094982    .0762833
       _cons |   166.1845   1.547135   107.41   0.000     163.1522    169.2169
------------------------------------------------------------------------------
Instrumented:  Weight
Instruments:   BMI

. estat first

  First-stage regression summary statistics
  --------------------------------------------------------------------------
               |            Adjusted      Partial
      Variable |   R-sq.       R-sq.        R-sq.     F(1,4215)   Prob > F
  -------------+------------------------------------------------------------
        Weight |  0.2802      0.2800       0.2802       1640.74    0.0000
  --------------------------------------------------------------------------


  Minimum eigenvalue statistic = 1640.74    

  Critical Values                      # of endogenous regressors:    1
  Ho: Instruments are weak             # of excluded instruments:     1
  ---------------------------------------------------------------------
                                     |    5%     10%     20%     30%
  2SLS relative bias                 |         (not available)
  -----------------------------------+---------------------------------
                                     |   10%     15%     20%     25%
  2SLS Size of nominal 5% Wald test  |  16.38    8.96    6.66    5.53
  LIML Size of nominal 5% Wald test  |  16.38    8.96    6.66    5.53
  ---------------------------------------------------------------------

As the result showed, whenever I type "first" after ivregress syntax, or when I type "estat first" after the main analysis, the F-statistics has consistent result, and F-statistics doesn't need to obtain by the square of Z-statistics...

That's what I know, but however, ivgress and ivprobit have different way to interpret the result

Hope there's somebody can help me lol

[Atiqa Rehman]

I have a question about the Wald test.

We get the statistics for Wald test in three ways in stata.

1. with iv probit, first and two steps that is the Wald test of exogeneity
2. with ivreg2 that is Anderson-Rubin Wald-test
3. weakiv command that is Wald test

My question is, are all of these the same and tell us about the exogeneity of instruments? means the p value should be less than 0.05 so accept the null hypothesis, indicating that the instruments are exogenous.

or the wald test after the ivprobit gives the different interpretation and tells about the regressors endogeneity and if the null hypothesis is rejected it supports the ivprobit in comparison to simple linear regressions.

Any help is highly appreciated

Kind regards,
Atiqa