st: Re: Tests of endogeneity by ivreg2

[Kit Baum <baum@bc.edu>]

Dear Torunn

The ivendog command performs the same function as the endog() option  
and the orthog() option in ivreg2, as the ivreg2 help file illustrates:

(Equivalence of DWH endogeneity test when regressor is endogenous...)

        . ivreg2 lwage exper expersq (educ=age kidslt6 kidsge6)

        . ivendog educ

(... endogeneity test using the endog option)

        . ivreg2 lwage exper expersq educ (educ=age kidslt6  
kidsge6), endog(educ)

(...and C-test of exogeneity when regressor is exogenous, using the  
orthog option)

        . ivreg2 lwage exper expersq educ (=age kidslt6 kidsge6),  
orthog(educ)


The hypothesis being tested is that the variable(s) being challenged  
(educ in the above example) could be treated as exogenous in order to  
derive consistent estimates. In the first and second examples above,  
it is treated as endogenous, and the estimated model is contrasted  
with one in which educ is treated as exogenous. The Durbin-Wu-Hausman  
test (see our 2003 Stata Journal paper) compares the IV and OLS  
estimates to determine whether they are 'close enough'. If they are,  
there is insufficient evidence to reject the null. In the third  
example, we estimate the model treating the variable as exogenous,  
and contrast it with a model in which it is endogenous--the same test  
from the opposite perspective, yielding the same test statistic.

This is not the same as the test of overidentifying restrictions  
("Sargan - Hansen"), as you have noted.

The statistics differ with different specifications of instruments  
because the model being estimated takes account of y, X and Z (the  
matrix of instruments). If you vary Z in IV regression you get a  
different set of estimates, and any test statistics based on those  
estimates will differ.

Kit

Kit Baum, Boston College Economics and DIW Berlin
http://ideas.repec.org/e/pba1.html
An Introduction to Modern Econometrics Using Stata:
http://www.stata-press.com/books/imeus.html



> Hello,
>
> Could you please tell me more about the Ivendog test in ivreg2?  
> This test
> statstic differs with different instruments used, see below. Does a  
> high
> significance level mean that the variable is correctly  
> instrumented? I thought
> this was a test of the possible endogeinity of a regressor (whether  
> the
> regressor is correlated with the error term) and don't understand  
> why the
> statistics differ with different instruments.
>
> When the equation is exactly identified, the Sargan statistic does  
> not tell
> anything about the validity of the instrument used, i.e. whether the
> instrument is uncorrelated with the error term.
>
> Sincerly,
> Torunn Kvinge
>
> . ivreg2 dbrutto dvar dkap (naceand  =  bruttolag2 h_2) if  
> bnrlag2==bnr&major==0,noco
>
> Instrumental variables (2SLS) regression
> ----------------------------------------
>
>                                                       Number of obs  
> =    27336
>                                                       F(  3, 27333)  
> = 28008.10
>                                                       Prob > F       
> =   0.0000
> Total (centered) SS     =  79149.00578                Centered R2    
> =   0.7542
> Total (uncentered) SS   =  79240.13053                Uncentered R2  
> =   0.7545
> Residual SS             =  19453.73944                Root MSE       
> =      .84
>
> ---------------------------------------------------------------------- 
> --------
>      dbrutto |      Coef.   Std. Err.      z    P>|z|     [95%  
> Conf. Interval]
> ------------- 
> +----------------------------------------------------------------
>      naceand |  -.7821335   .4831546    -1.62   0.105     
> -1.729099    .1648322
>        dvar1 |   1.102227   .0041356   266.52   0.000      
> 1.094121    1.110332
>         dkap |   1.100465   .0054046   203.62   0.000      
> 1.089872    1.111057
> ---------------------------------------------------------------------- 
> --------
> Sargan statistic (overidentification test of all  
> instruments):           3.604
>                                                    Chi-sq(1) P-val  
> =   0.05764
> ---------------------------------------------------------------------- 
> --------
> Instrumented:  naceand
> Instruments:   bruttolag2 h_2 dvar1 dkap
> ---------------------------------------------------------------------- 
> --------
>
> . ivendog naceand
>
> Tests of endogeneity of: naceand
> H0: Regressor is exogenous
>     Wu-Hausman F test:                  1.43488  F(1,27332)  P- 
> value = 0.23098
>     Durbin-Wu-Hausman chi-sq test:      1.43502  Chi-sq(1)   P- 
> value = 0.23095
>
> . ivreg2 dbrutto dvar dkap (naceand  =  bruttolag2 ) if  
> bnrlag2==bnr&major==0,noco
>
> Instrumental variables (2SLS) regression
> ----------------------------------------
>
>                                                       Number of obs  
> =    32422
>                                                       F(  3, 32419)  
> = 32376.15
>                                                       Prob > F       
> =   0.0000
> Total (centered) SS     =  95034.69372                Centered R2    
> =   0.7475
> Total (uncentered) SS   =  95234.76917                Uncentered R2  
> =   0.7481
> Residual SS             =  23991.92712                Root MSE       
> =      .86
>
> ---------------------------------------------------------------------- 
> --------
>      dbrutto |      Coef.   Std. Err.      z    P>|z|     [95%  
> Conf. Interval]
> ------------- 
> +----------------------------------------------------------------
>      naceand |   -3.34325   .5468789    -6.11   0.000     
> -4.415113   -2.271388
>        dvar1 |   1.100445   .0038692   284.41   0.000      
> 1.092862    1.108029
>         dkap |    1.10401    .005045   218.83   0.000      
> 1.094122    1.113898
> ---------------------------------------------------------------------- 
> --------
> Sargan statistic (overidentification test of all  
> instruments):           0.000
>                                                  (equation exactly  
> identified)
> ---------------------------------------------------------------------- 
> --------
> Instrumented:  naceand
> Instruments:   bruttolag2 dvar1 dkap
> ---------------------------------------------------------------------- 
> --------
>
> . ivendog naceand
>
> Tests of endogeneity of: naceand
> H0: Regressor is exogenous
>     Wu-Hausman F test:                 34.48155  F(1,32418)  P- 
> value = 0.00000
>     Durbin-Wu-Hausman chi-sq test:     34.44916  Chi-sq(1)   P- 
> value = 0.00000
>
> . ivreg2 dbrutto dvar dkap (naceand  =  h_2 ) if  
> bnrlag2==bnr&major==0,noco
>
> Instrumental variables (2SLS) regression
> ----------------------------------------
>
>                                                       Number of obs  
> =    27336
>                                                       F(  3, 27333)  
> = 28031.26
>                                                       Prob > F       
> =   0.0000
> Total (centered) SS     =  79149.00578                Centered R2    
> =   0.7544
> Total (uncentered) SS   =  79240.13053                Uncentered R2  
> =   0.7547
> Residual SS             =  19437.07382                Root MSE       
> =      .84
>
> ---------------------------------------------------------------------- 
> --------
>      dbrutto |      Coef.   Std. Err.      z    P>|z|     [95%  
> Conf. Interval]
> ------------- 
> +----------------------------------------------------------------
>      naceand |    -.13545   .5909122    -0.23   0.819     
> -1.293617    1.022717
>        dvar1 |   1.102789   .0041444   266.09   0.000      
> 1.094666    1.110911
>         dkap |   1.099174   .0054448   201.87   0.000      
> 1.088502    1.109845
> ---------------------------------------------------------------------- 
> --------
> Sargan statistic (overidentification test of all  
> instruments):           0.000
>                                                  (equation exactly  
> identified)
> ---------------------------------------------------------------------- 
> --------
> Instrumented:  naceand
> Instruments:   h_2 dvar1 dkap
> ---------------------------------------------------------------------- 
> --------
>
> . ivendog naceand
>
> Tests of endogeneity of: naceand
> H0: Regressor is exogenous
>     Wu-Hausman F test:                  0.02136  F(1,27332)  P- 
> value = 0.88380
>     Durbin-Wu-Hausman chi-sq test:      0.02136  Chi-sq(1)   P- 
> value = 0.88379
>
> -----End Original Message-----
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