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st: RE: First-stage F from -xtivreg- versus AP F


From   "Schaffer, Mark E" <[email protected]>
To   "[email protected]" <[email protected]>
Subject   st: RE: First-stage F from -xtivreg- versus AP F
Date   Tue, 21 Jan 2014 14:54:51 +0000

Diego,

In your case you have a single endogenous regressor, which means the standard diagnostic first-stage F and the Angrist-Pischke first-stage F are the same number.

So if you wade through the output of -xtoverid,noi-, you'll find this under the first-stage estimation:

> F test of excluded instruments:
>   F(  2, 27825) =  3528.57
>   Prob> F      =   0.0000
> Angrist-Pischke multivariate F test of excluded instruments:
>   F(  2, 27825) =  3528.57
>   Prob> F      =   0.0000

And then in the main regression output of -xtoverid,noi-, where the -xtivreg- results are replicated, you'll find this:

> Weak identification test
> Ho: equation is weakly identified
> Cragg-Donald Wald F statistic                                    3528.57

and this:

> Weak identification test (Cragg-Donald Wald F statistic):             3528.573

So your first-stage F stat is 3528.57.  Looks a bit large to me, but that's the number you are looking for.

HTH,
Mark

> -----Original Message-----
> From: [email protected] [mailto:owner-
> [email protected]] On Behalf Of David Torres
> Sent: 21 January 2014 14:29
> To: [email protected]
> Subject: st: First-stage F from -xtivreg- versus AP F
> 
> Statalisters,
> 
> I'm using -xtivreg- to estimate a 2SLS random effects model in Stata 13.0.  I'm
> needing help getting the first stage F statistic in addition to the Angrist-
> Pischke F I can get from the postestimation command -xtoverid- (more on
> this below).
> 
> . which xtivreg
> /Applications/Stata/ado/base/x/xtivreg.ado
> *! version 1.6.2  14apr2011
> 
> . which xtoverid
> /Users/diego/Library/Application Support/Stata/ado/plus/x/xtoverid.ado
> *! xtoverid version 2.1.6   2Nov2011
> *! Authors Mark Schaffer and Steve Stillman
> *! Derived from overidxt and overid
> 
> 
> Here is the most basic conditional model in which I am regressing vertically
> scaled reading scores on year and year-squared.  The endogenous regressor,
> diffsch, denotes whether a student attended an out-of-zone magnet school.
> It is instrumented with the log difference in distance between the zoned
> school and the nearest magnet school and the log distance to the enrolled
> school:
> 
> . xtivreg srsc year yearsq (diffsch=diffdist dist_enrld), re first
> 
> 
> First-stage G2SLS regression
>                                                  Number of obs    =      27830
>                                                  Wald chi(4)      =       7182
>                                                  Prob> chi2      =     0.0000
> ------------------------------------------------------------------------------
>      diffsch |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
> -------------+----------------------------------------------------------------
>         year |   .0010897   .0023365     0.47   0.641    -.0034898    .0056692
>       yearsq |   .0009441   .0005764     1.64   0.101    -.0001858    .0020739
>     diffdist |    .004433    .001686     2.63   0.009     .0011284    .0077376
>   dist_enrld |    .162999   .0019443    83.84   0.000     .1591883    .1668097
>        _cons |   .1364031   .0035329    38.61   0.000     .1294787    .1433274
> ------------------------------------------------------------------------------
> 
> G2SLS random-effects IV regression              Number of obs      =     27830
> Group variable: short_id                        Number of groups   =      6168
> 
> R-sq:  within  = 0.8770                         Obs per group: min =         3
>        between = 0.2215                                        avg =       4.5
>        overall = 0.6533                                        max =         5
> 
>                                                 Wald chi2(3)       = 154192.94
> corr(u_i, X)       = 0 (assumed)                Prob> chi2        =    0.0000
> 
> ------------------------------------------------------------------------------
>         srsc |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
> -------------+----------------------------------------------------------------
>      diffsch |   9.999284   1.941415     5.15   0.000      6.19418    13.80439
>         year |   74.19692   .3811099   194.69   0.000     73.44996    74.94389
>       yearsq |  -7.926549   .0940278   -84.30   0.000     -8.11084   -7.742258
>        _cons |   475.1334   .6555358   724.80   0.000     473.8486    476.4182
> -------------+----------------------------------------------------------------
>      sigma_u |  37.264026
>      sigma_e |  25.567877
>          rho |  .67991546   (fraction of variance due to u_i)
> ------------------------------------------------------------------------------
> Instrumented:   diffsch
> Instruments:    year yearsq diffdist dist_enrld
> ------------------------------------------------------------------------------
> 
> 
> Now I would like to get the first stage F-statistic, but the first option above
> does not appear to give it.  If I use the postestimation command -xtoverid-
> with the noisily option, as shown below, I do get the Angrist-Pischke F, but in
> my write-up I'd like to show the regular F-stat to test joint significance of the
> instruments.
> 
> .  xtoverid, nois
> 
> First-stage regressions
> -----------------------
> 
> First-stage regression of __00000I:
> 
> OLS estimation
> --------------
> 
> Estimates efficient for homoskedasticity only
> Statistics consistent for homoskedasticity only
> 
>                                                       Number of obs =    27830
>                                                       F(  5, 27825) =  2097.56
>                                                       Prob> F      =   0.0000
> Total (centered) SS     =  875.5555503                Centered R2   =   0.2037
> Total (uncentered) SS   =  960.0415225                Uncentered R2 =   0.2737
> Residual SS             =  697.2383726                Root MSE      =    .1583
> 
> ------------------------------------------------------------------------------
>     __00000I |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
> -------------+----------------------------------------------------------------
>     __00000R |   .0010897   .0023365     0.47   0.641      -.00349    .0056694
>     __00000U |   .0009441   .0005764     1.64   0.101    -.0001858    .0020739
>     __00000E |   .1364031   .0035329    38.61   0.000     .1294784    .1433277
>     __00000L |    .004433    .001686     2.63   0.009     .0011283    .0077377
>     __00000O |    .162999   .0019443    83.84   0.000     .1591881    .1668098
> ------------------------------------------------------------------------------
> Included instruments: __00000R __00000U __00000E __00000L __00000O
> ------------------------------------------------------------------------------
> F test of excluded instruments:
>   F(  2, 27825) =  3528.57
>   Prob> F      =   0.0000
> Angrist-Pischke multivariate F test of excluded instruments:
>   F(  2, 27825) =  3528.57
>   Prob> F      =   0.0000
> 
> 
> 
> Summary results for first-stage regressions
> -------------------------------------------
> 
>                                            (Underid)            (Weak id)
> Variable     | F(  2, 27825)  P-val | AP Chi-sq(  2) P-val | AP F(  2, 27825)
> __00000I     |    3528.57    0.0000 |     7058.41   0.0000 |     3528.57
> 
> Stock-Yogo weak ID test critical values for single endogenous regressor:
>                                    10% maximal IV size             19.93
>                                    15% maximal IV size             11.59
>                                    20% maximal IV size              8.75
>                                    25% maximal IV size              7.25
> Source: Stock-Yogo (2005).  Reproduced by permission.
> 
> Underidentification test
> Ho: matrix of reduced form coefficients has rank=K1-1 (underidentified)
> Ha: matrix has rank=K1 (identified)
> Anderson canon. corr. LM statistic       Chi-sq(2)=5630.40  P-val=0.0000
> 
> Weak identification test
> Ho: equation is weakly identified
> Cragg-Donald Wald F statistic                                    3528.57
> 
> Stock-Yogo weak ID test critical values for K1=1 and L1=2:
>                                    10% maximal IV size             19.93
>                                    15% maximal IV size             11.59
>                                    20% maximal IV size              8.75
>                                    25% maximal IV size              7.25
> Source: Stock-Yogo (2005).  Reproduced by permission.
> 
> Weak-instrument-robust inference
> Tests of joint significance of endogenous regressors B1 in main equation
> Ho: B1=0 and orthogonality conditions are valid
> Anderson-Rubin Wald test           F(2,27825)=    13.53     P-val=0.0000
> Anderson-Rubin Wald test           Chi-sq(2)=     27.06     P-val=0.0000
> Stock-Wright LM S statistic        Chi-sq(2)=     27.03     P-val=0.0000
> 
> Number of observations               N  =      27830
> Number of regressors                 K  =          4
> Number of endogenous regressors      K1 =          1
> Number of instruments                L  =          5
> Number of excluded instruments       L1 =          2
> 
> IV (2SLS) estimation
> --------------------
> 
> Estimates efficient for homoskedasticity only
> Statistics consistent for homoskedasticity only
> 
>                                                       Number of obs =    27830
>                                                       F(  4, 27826) =  3.6e+05
>                                                       Prob> F      =   0.0000
> Total (centered) SS     =  122387579.2                Centered R2   =   0.8485
> Total (uncentered) SS   =  976762125.4                Uncentered R2 =   0.9810
> Residual SS             =  18546537.84                Root MSE      =    25.82
> 
> ------------------------------------------------------------------------------
>     __00000G |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
> -------------+----------------------------------------------------------------
>     __00000I |   9.999284   1.941276     5.15   0.000     6.194454    13.80412
>     __00000R |   74.19692   .3810826   194.70   0.000     73.45002    74.94383
>     __00000U |  -7.926549    .094021   -84.31   0.000    -8.110827   -7.742271
>     __00000E |   475.1334   .6554887   724.85   0.000     473.8487    476.4181
> ------------------------------------------------------------------------------
> Underidentification test (Anderson canon. corr. LM statistic):        5630.398
>                                                    Chi-sq(2) P-val =    0.0000
> ------------------------------------------------------------------------------
> Weak identification test (Cragg-Donald Wald F statistic):             3528.573
> Stock-Yogo weak ID test critical values: 10% maximal IV size             19.93
>                                          15% maximal IV size             11.59
>                                          20% maximal IV size              8.75
>                                          25% maximal IV size              7.25
> Source: Stock-Yogo (2005).  Reproduced by permission.
> ------------------------------------------------------------------------------
> Sargan statistic (overidentification test of all instruments):           0.577
>                                                    Chi-sq(1) P-val =    0.4474
> ------------------------------------------------------------------------------
> Instrumented:         __00000I
> Included instruments: __00000R __00000U __00000E
> Excluded instruments: __00000L __00000O
> ------------------------------------------------------------------------------
> 
> Test of overidentifying restrictions:
> Cross-section time-series model: xtivreg g2sls
> Sargan-Hansen statistic   0.577  Chi-sq(1)    P-value = 0.4474
> 
> 
> Can anyone tell me how to get what I want, the regular first stage F-stat,
> from all this?  I'd very much appreciate your help.
> 
> Thanks for your consideration, folks,
> Diego Torres
> *
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