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# Re: st: RE: IVREG2 with two endogenous variables: CD/KP F-stat vs. APF-stat

 From Miguel Àngel García López To statalist@hsphsun2.harvard.edu Subject Re: st: RE: IVREG2 with two endogenous variables: CD/KP F-stat vs. APF-stat Date Fri, 01 Feb 2013 22:16:47 +0100

```Hi Mark,

You're right, the Kleibergen-Paap rk LM statistic indicates that the equation is underidentified.
So, which coefficient am I identifying? x1=disnode20061991 or x2=disnode20061991dhistink (this is the interacted endogenous variable)?

Thanks a lot!

Here is the output:

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

First-stage regression of disnode20061991:

OLS estimation
--------------

Estimates efficient for homoskedasticity only
Statistics robust to heteroskedasticity

Number of obs =      603
F( 26,   464) =     2.21
Prob > F      =   0.0006
Total (centered) SS     =  2045.649523                Centered R2   =   0.2016
Total (uncentered) SS   =  2045.649523                Uncentered R2 =   0.2016
Residual SS             =  1633.166249                Root MSE      =    1.876

------------------------------------------------------------------------------
|               Robust
disnod~61991 |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
dhistlink |  -.0549742   .3248397    -0.17   0.866    -.6933134     .583365
lnpob1991 |   .0061794    .141505     0.04   0.965    -.2718907    .2842495
lnkm2 |   .1863085    .166866     1.12   0.265    -.1415981    .5142151
disCBD |  -.0709631   .0430135    -1.65   0.100    -.1554885    .0135622
discoast |  -.0602264   .0400691    -1.50   0.134    -.1389658    .0185131
alti |  -.0023203   .0027915    -0.83   0.406    -.0078058    .0031652
tri |  -.0115232   .0067075    -1.72   0.086    -.0247041    .0016577
lat1 |   5.500978   3.274879     1.68   0.094    -.9344523    11.93641
long1 |  -.9525434    2.43592    -0.39   0.696    -5.739344    3.834257
taxa_at~1991 |   6.955092   4.800384     1.45   0.148    -2.478093    16.38828
taxa_oc~1991 |    .008856   3.143292     0.00   0.998    -6.167996    6.185708
porc_ocup1~n |   -3.03856   1.642994    -1.85   0.065    -6.267191    .1900711
porc_pob1~25 |  -1.580318   3.761586    -0.42   0.675    -8.972172    5.811537
porc_pob19~i |   8.381571   3.778023     2.22   0.027     .9574171    15.80572
porc_pob19~r |  -2.879711   4.192779    -0.69   0.493     -11.1189    5.359476
lnpob1981 |  -.0628442   .0730382    -0.86   0.390    -.2063707    .0806824
lnpob1970 |  -.1758226   .1700468    -1.03   0.302    -.5099798    .1583347
lnpob1960 |   .5060852   .5099257     0.99   0.321    -.4959645    1.508135
lnpob1950 |  -.3825519   .4967032    -0.77   0.442    -1.358618    .5935145
lnpob1940 |  -.3062138   .7478307    -0.41   0.682    -1.775768    1.163341
lnpob1930 |   .6099881   1.073278     0.57   0.570    -1.499099    2.719075
lnpob1920 |  -1.898675    1.43143    -1.33   0.185    -4.711564    .9142143
lnpob1910 |   1.829188   1.056597     1.73   0.084    -.2471203    3.905495
lnpob1900 |  -.1280441   .0932029    -1.37   0.170    -.3111962    .0551081
dis1760 |  -.1942985    .045257    -4.29   0.000    -.2832326   -.1053645
dis1760dhi~k |  -.0141311   .0116053    -1.22   0.224    -.0369365    .0086743
------------------------------------------------------------------------------
Included instruments: dhistlink lnpob1991 lnkm2 disCBD discoast alti tri lat1
long1 taxa_atur1991 taxa_ocup1991 porc_ocup1991man
porc_pob1991m25 porc_pob1991uni porc_pob1991estr lnpob1981
lnpob1970 lnpob1960 lnpob1950 lnpob1940 lnpob1930
------------------------------------------------------------------------------
F test of excluded instruments:
F(  2,   464) =    11.50
Prob > F      =   0.0000
Angrist-Pischke multivariate F test of excluded instruments:
F(  1,   464) =    20.90
Prob > F      =   0.0000

OLS estimation
--------------

Estimates efficient for homoskedasticity only
Statistics robust to heteroskedasticity

Number of obs =      603
F( 26,   464) =     2.67
Prob > F      =   0.0000
Total (centered) SS     =  28055.52566                Centered R2   =   0.4866
Total (uncentered) SS   =  28055.52566                Uncentered R2 =   0.4866
Residual SS             =  14404.85354                Root MSE      =    5.572

------------------------------------------------------------------------------
|               Robust
disnode200~k |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
dhistlink |   2.515352   1.115445     2.26   0.025     .3234024    4.707301
lnpob1991 |   .3581472   .3807795     0.94   0.347    -.3901187    1.106413
lnkm2 |  -.8305778   .4571589    -1.82   0.070    -1.728936    .0677805
disCBD |    .035202   .1068078     0.33   0.742    -.1746849    .2450889
discoast |  -.0824591   .0797964    -1.03   0.302    -.2392662    .0743481
alti |   .0139589   .0089892     1.55   0.121    -.0037056    .0316234
tri |  -.0481706   .0227555    -2.12   0.035    -.0928872   -.0034541
lat1 |  -1.303162   8.268787    -0.16   0.875    -17.55207    14.94575
long1 |   4.330386   6.440689     0.67   0.502    -8.326146    16.98692
taxa_at~1991 |  -13.02405   17.44058    -0.75   0.456    -47.29635    21.24825
taxa_oc~1991 |   -.380474    8.68993    -0.04   0.965    -17.45697    16.69602
porc_ocup1~n |   3.577323   3.999994     0.89   0.372    -4.283023    11.43767
porc_pob1~25 |  -18.19801   11.58473    -1.57   0.117    -40.96303    4.567024
porc_pob19~i |   -2.35895   9.349228    -0.25   0.801    -20.73102    16.01312
porc_pob19~r |  -2.417754   7.014291    -0.34   0.730    -16.20147    11.36596
lnpob1981 |  -.5197725   .4901694    -1.06   0.290    -1.482999    .4434545
lnpob1970 |  -.4056388   1.066181    -0.38   0.704     -2.50078    1.689502
lnpob1960 |   .1810121   1.474015     0.12   0.902     -2.71556    3.077584
lnpob1950 |   .8724695   .9530778     0.92   0.360    -1.000414    2.745353
lnpob1940 |   .0072886   1.337592     0.01   0.996    -2.621199    2.635776
lnpob1930 |   .1341517    1.96242     0.07   0.946     -3.72218    3.990484
lnpob1920 |  -2.063717   3.313446    -0.62   0.534    -8.574937    4.447502
lnpob1910 |       2.01   2.898491     0.69   0.488    -3.685795    7.705795
lnpob1900 |  -.1108913    .319602    -0.35   0.729     -.738938    .5171553
dis1760 |   .2462499   .1164858     2.11   0.035      .017345    .4751549
dis1760dhi~k |  -.4080694    .086959    -4.69   0.000    -.5789517   -.2371871
------------------------------------------------------------------------------
Included instruments: dhistlink lnpob1991 lnkm2 disCBD discoast alti tri lat1
long1 taxa_atur1991 taxa_ocup1991 porc_ocup1991man
porc_pob1991m25 porc_pob1991uni porc_pob1991estr lnpob1981
lnpob1970 lnpob1960 lnpob1950 lnpob1940 lnpob1930
------------------------------------------------------------------------------
F test of excluded instruments:
F(  2,   464) =    11.53
Prob > F      =   0.0000
Angrist-Pischke multivariate F test of excluded instruments:
F(  1,   464) =    22.72
Prob > F      =   0.0000

Summary results for first-stage regressions
-------------------------------------------

(Underid)            (Weak id)
Variable     | F(  2,   464)  P-val | AP Chi-sq(  1) P-val | AP F(  1,   464)
disnode20061 |      11.50    0.0000 |       27.16   0.0000 |       20.90
disnode20061 |      11.53    0.0000 |       29.53   0.0000 |       22.72

NB: first-stage test statistics heteroskedasticity-robust

Stock-Yogo weak ID test critical values for single endogenous regressor:
10% maximal IV size             16.38
15% maximal IV size              8.96
20% maximal IV size              6.66
25% maximal IV size              5.53
Source: Stock-Yogo (2005).  Reproduced by permission.
NB: Critical values are for Cragg-Donald F statistic and i.i.d. errors.

Underidentification test
Ho: matrix of reduced form coefficients has rank=K1-1 (underidentified)
Ha: matrix has rank=K1 (identified)
Kleibergen-Paap rk LM statistic          Chi-sq(1)=0.00     P-val=0.9997

Weak identification test
Ho: equation is weakly identified
Cragg-Donald Wald F statistic                                      27.11
Kleibergen-Paap Wald rk F statistic                                 0.00

Stock-Yogo weak ID test critical values for K1=2 and L1=2:
10% maximal IV size              7.03
15% maximal IV size              4.58
20% maximal IV size              3.95
25% maximal IV size              3.63
Source: Stock-Yogo (2005).  Reproduced by permission.
NB: Critical values are for Cragg-Donald F statistic and i.i.d. errors.

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(2,464)=       4.17     P-val=0.0161
Anderson-Rubin Wald test           Chi-sq(2)=     10.83     P-val=0.0044
Stock-Wright LM S statistic        Chi-sq(2)=     10.18     P-val=0.0062

NB: Underidentification, weak identification and weak-identification-robust
test statistics heteroskedasticity-robust

Number of observations               N  =        603
Number of regressors                 K  =         26
Number of endogenous regressors      K1 =          2
Number of instruments                L  =         26
Number of excluded instruments       L1 =          2
Number of partialled-out regressors/IVs =        113
NB: K & L do not included partialled-out variables

IV (2SLS) estimation
--------------------

Estimates efficient for homoskedasticity only
Statistics robust to heteroskedasticity

Number of obs =      603
F( 26,   464) =    17.35
Prob > F      =   0.0000
Total (centered) SS     =  32.85467898                Centered R2   =   0.4789
Total (uncentered) SS   =  32.85467898                Uncentered R2 =   0.4789
Residual SS             =  17.12178597                Root MSE      =    .1685

------------------------------------------------------------------------------
|               Robust
lnp~20111991 |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
disnod~61991 |  -.0422962   .0157094    -2.69   0.007    -.0730861   -.0115064
disnode200~k |   .0033454    .002269     1.47   0.140    -.0011017    .0077925
dhistlink |  -.0193715   .0301388    -0.64   0.520    -.0784425    .0396996
lnpob1991 |  -.1716033   .0175352    -9.79   0.000    -.2059716   -.1372351
lnkm2 |   .0772166   .0201062     3.84   0.000     .0378092    .1166241
disCBD |  -.0014151   .0038103    -0.37   0.710    -.0088832     .006053
discoast |  -.0020445   .0030389    -0.67   0.501    -.0080007    .0039116
alti |  -.0003639   .0002803    -1.30   0.194    -.0009132    .0001854
tri |   .0002327   .0007257     0.32   0.748    -.0011896     .001655
lat1 |   .2161914     .27737     0.78   0.436    -.3274437    .7598266
long1 |  -.3242189   .1943732    -1.67   0.095    -.7051834    .0567457
taxa_at~1991 |  -.0633292   .4341575    -0.15   0.884    -.9142623    .7876039
taxa_oc~1991 |   .5256404   .2733951     1.92   0.055    -.0102043    1.061485
porc_ocup1~n |  -.2804171   .1410424    -1.99   0.047    -.5568552   -.0039791
porc_pob1~25 |  -2.038739   .4678653    -4.36   0.000    -2.955738   -1.121739
porc_pob19~i |    1.98907   .4010011     4.96   0.000     1.203123    2.775018
porc_pob19~r |   1.207574   .3368401     3.59   0.000     .5473792    1.867768
lnpob1981 |  -.0206563   .0138923    -1.49   0.137    -.0478848    .0065722
lnpob1970 |  -.0664541    .031215    -2.13   0.033    -.1276344   -.0052739
lnpob1960 |    .035141   .0807666     0.44   0.663    -.1231586    .1934405
lnpob1950 |   .0388572   .0753196     0.52   0.606    -.1087665    .1864808
lnpob1940 |  -.0780994   .0883634    -0.88   0.377    -.2512886    .0950897
lnpob1930 |   .0474178   .1058593     0.45   0.654    -.1600626    .2548983
lnpob1920 |   .2845001   .1418916     2.01   0.045     .0063977    .5626024
lnpob1910 |  -.2330463   .1296206    -1.80   0.072    -.4870979    .0210054
lnpob1900 |  -.0073257   .0135746    -0.54   0.589    -.0339315      .01928
------------------------------------------------------------------------------
Underidentification test (Kleibergen-Paap rk LM statistic):              0.000
Chi-sq(1) P-val =    0.9997
------------------------------------------------------------------------------
Weak identification test (Cragg-Donald Wald F statistic):               27.106
(Kleibergen-Paap rk Wald F statistic):          0.000
Stock-Yogo weak ID test critical values: 10% maximal IV size              7.03
15% maximal IV size              4.58
20% maximal IV size              3.95
25% maximal IV size              3.63
Source: Stock-Yogo (2005).  Reproduced by permission.
NB: Critical values are for Cragg-Donald F statistic and i.i.d. errors.
------------------------------------------------------------------------------
Hansen J statistic (overidentification test of all instruments):         0.000
(equation exactly identified)
------------------------------------------------------------------------------
Included instruments: dhistlink lnpob1991 lnkm2 disCBD discoast alti tri lat1
long1 taxa_atur1991 taxa_ocup1991 porc_ocup1991man
porc_pob1991m25 porc_pob1991uni porc_pob1991estr lnpob1981
lnpob1970 lnpob1960 lnpob1950 lnpob1940 lnpob1930
lnpob1920 lnpob1910 lnpob1900
Partialled-out:       _Iam129_2 _Iam129_3 _Iam129_4 _Iam129_5 _Iam129_6

Miquel

----- Missatge original -----
De: "Schaffer, Mark E" <M.E.Schaffer@hw.ac.uk>
Data: Divendres, Febrer 1, 2013 9:03 pm
Assumpte: st: RE: IVREG2 with two endogenous variables: CD/KP F-stat vs.	APF-stat

> Miguel,
>
> > -----Original Message-----
> > From: owner-statalist@hsphsun2.harvard.edu [owner-
> > statalist@hsphsun2.harvard.edu] On Behalf Of Miguel Àngel García
> López> Sent: 01 February 2013 09:22
> > To: statalist@hsphsun2.harvard.edu
> > Subject: st: IVREG2 with two endogenous variables: CD/KP F-stat
> vs. AP F-
> > stat
> >
> > Hi all,
> >
> > I am using ivreg2 for running my model with two endogenous
> variables:>
> > ivreg2 y1 (x1 x2 = z1 z2) x3, robust
> >
> > where x2 and z2 are interactions of x1 and z1, respectively. In
> other words,
> > x2=dummy*x1 is an interacted endogenous variable and z2=dummy*z1
> is an
> > interacted instrument.
> >
> > When I look at the first-stage statistics I find that the KP F-
> stat = 0.00 while
> > the individual AP F-stats are around 20.
> > And I am puzzle about which F-stat I should consider.
> >
> > Following previous discussions such as
> > http://www.stata.com/statalist/archive/2011-04/msg00853.html, I
> think I
> > should only use AP F-stats.
> > Am I right?
> >
> > Another question is why my CD F-stat is 0. Maybe because my
> instruments> are highly correlated?
>
> Can you show us the output?
>
> It sounds like your equation is underidentified: you can identify
> either the coeff on x1, or the coeff on x2, but not both coeffs
> simultaneously (hence the zero under- and weak-identification
> statistics).
> But it's hard to tell without seeing more.
>
> --Mark
>
> >
> > Thanks,
> >
> > Miquel
> >
> > *
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> > *   http://www.stata.com/support/faqs/resources/statalist-faq/
> > *   http://www.ats.ucla.edu/stat/stata/
>
>
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```