st: question on ivreg2, ivendog and "good" instruments

[Masha Zakharova <mzakharo@sfu.ca>]

Dear Statalist,

I have a question regarding ivreg2 and ivendog, and I would really appreciate some help, since it seems to me that I am stuck in a vicious circle here...

My model looks like this: My dependent variable is party valence - i.e., how much one likes the party/leader; my instrumented variable is one's subjective distance to that party, which is an absolute distance between respondent's self-placement on the left-right scale and his/her party placement. The instrument is objective distance, which is an absolute distance between one's corrected self-placement and non-subjective party position in that election that are both calculated using a scaling procedure in R (Aldrich-Mcalvey scaling). So theoretically objective distance (instrument) should not be related to valence (main DV).

I ran an instrumental variable regression using ivreg2, and it gave me a p-value of Sargan statistic as 0.000. (see the output below)

. ivreg2 valence (subj=OBJ) if election==13

Instrumental variables (2SLS) regression
----------------------------------------

                                                      Number of obs =    10121
                                                      F(  1, 10119) =  3317.93
                                                      Prob > F      =   0.0000
Total (centered) SS     =  11632.76136                Centered R2   =   0.3139
Total (uncentered) SS   =  11633.38803                Uncentered R2 =   0.3139
Residual SS             =  7981.436867                Root MSE      =      .89

------------------------------------------------------------------------------
     valence |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
        subj |  -.2325729   .0040372   -57.61   0.000    -.2404858   -.2246601
       _cons |   .8629297   .0175047    49.30   0.000     .8286211    .8972384
------------------------------------------------------------------------------
Sargan statistic (overidentification test of all instruments):           0.000
                                                 (equation exactly identified)
------------------------------------------------------------------------------
Instrumented:  subj
Instruments:   OBJ
------------------------------------------------------------------------------



My understanding is that it means that my instruments are not valid (i.e., they correlate with the error term of main dependent variable). My question is, should I try and find an instrument that is not correlated at all with main dependent variable? I understand that technically it should not be correlated with the error term in the main DV, but so far only things that are completely unrelated to my main DV gave me an insignificant Hansen J statistic. Everything that was even a little bit correlated with valence had p=0.000.


Then I decided to see if there is an endogeneity problem in the first place, so I ran ivendog command:

. ivendog

Tests of endogeneity of: subj
H0: Regressor is exogenous
    Wu-Hausman F test:                 48.77272  F(1,10118)  P-value = 0.00000
    Durbin-Wu-Hausman chi-sq test:     48.55314  Chi-sq(1)   P-value = 0.00000


 However, my question is, whether I can trust its results, because somewhere in the Statalist archives I came across advice that DWH test should be done when one has good instruments. So if my instruments are supposedly bad, should I trust DWH test results? Is there any way to check endogeneity between two variables, if I do not have good instruments?


Finally, here is my last question. I decided to see if individual's self-placement and party valence are endogenous, so I ran ivreg2 using valence as DV, subjective self-placement as instrumented variable and corrected self-placement as an instrument. The model explained VERY VERY little variance in valence (less than .0001). And yet, if I ran ivendog test, for some cases it would show that self-placement is endogenous to valence (in some cases, the relationship was stat. significant, but in the other cases it was not). So the results looked very strange. My question is, can I trust the results of DWH test here? I don't understand how self-placement can be endogenous to valence, if it explains such a tiny amount of its variance.

ivreg2 valence (self=idealpt) if election==13

Instrumental variables (2SLS) regression
----------------------------------------

                                                      Number of obs =    10297
                                                      F(  1, 10295) =   279.45
                                                      Prob > F      =   0.0000
Total (centered) SS     =  11755.73554                Centered R2   =  -7.1385
Total (uncentered) SS   =  11758.43573                Uncentered R2 =  -7.1367
Residual SS             =  95674.55873                Root MSE      =        3

------------------------------------------------------------------------------
     valence |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
        self |  -1.037726   .0620715   -16.72   0.000    -1.159384   -.9160684
       _cons |   5.810372   .3498078    16.61   0.000     5.124762    6.495983
------------------------------------------------------------------------------
Sargan statistic (overidentification test of all instruments):           0.000
                                                 (equation exactly identified)
------------------------------------------------------------------------------
Instrumented:  self
Instruments:   OBJ
------------------------------------------------------------------------------

.ivendog

Tests of endogeneity of: self
H0: Regressor is exogenous
    Wu-Hausman F test:                 2.87e+03  F(1,10294)  P-value = 0.00000
    Durbin-Wu-Hausman chi-sq test:     2.24e+03  Chi-sq(1)   P-value = 0.00000






***(By the way, I did all my analyses clustered by individuals [since the data is shaped long, with every individual having their valence judgments/party placements/etc for every party], so I originally ran DWH test using these commands instead of ivendog, since it does not run on clustered data):
reg subj OBJ if election==13, cluster(id)
predict subj_res13 if election==13, res 
reg valence subj subj_res13 if election==13, cluster(id)
The results were the same as ivendog on un-clustered data, so I am using its output as my example, so that I don't overload you with my outputs.


Thank you so much for your time,
Masha
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