Instrument interpreation

[Maximiser John]

Question my second stage output is:
Summary results for first-stage regressions
-------------------------------------------

(Underid) (Weak id)
Variable | F( 2, 123) P-val | SW Chi-sq( 1) P-val | SW F( 1, 123)
pdiv_aa | 54.85 0.0000 | 47.09 0.0000 | 39.95
pdiv_aa_sqr | 60.29 0.0000 | 51.35 0.0000 | 43.56


-------------------+----------------------------------------------------------------
pdiv_aa | 827.9654 309.5326 2.67 0.007 221.2928 1434.638
pdiv_aa_sqr | -605.2247 213.5579 -2.83 0.005 -1023.79 -186.659
abslat | -29.77723 34.70237 -0.86 0.391 -97.79264 38.23817
ruggavg | -26.4531 20.99064 -1.26 0.208 -67.594 14.6878
elevavg | -2.059891 5.695568 -0.36 0.718 -13.223 9.103217
suitavg | -12.9747 6.915493 -1.88 0.061 -26.52882 .5794151
suitrng | -.4241705 6.7037 -0.06 0.950 -13.56318 12.71484
distcr | -14.45389 4.185995 -3.45 0.001 -22.65829 -6.249489
ln_Land_area_sq_km | -.1572494 .1191065 -1.32 0.187 -.3906938 .0761951
kgatr | -1.624356 .6316154 -2.57 0.010 -2.862299 -.3864122
asia | -.8476551 .4984571 -1.70 0.089 -1.824613 .1293029
namerica | .1946483 .8980334 0.22 0.828 -1.565465 1.954761
samerica | -.6844802 .9154519 -0.75 0.455 -2.478733 1.109773
europe | 1.030554 .7091502 1.45 0.146 -.3593553 2.420462
oceania | .5488568 1.657152 0.33 0.740 -2.699101 3.796815
efrac | -.2920346 .8056488 -0.36 0.717 -1.871077 1.287008
des_pol15 | -1.151414 .7883847 -1.46 0.144 -2.69662 .3937912
evercol_gbr | .8239021 .3722575 2.21 0.027 .0942909 1.553513
evercol_fra | -.1336626 .3332296 -0.40 0.688 -.7867806 .5194554
evercol_oth | -.3046437 .3578258 -0.85 0.395 -1.005969 .396682
mean1996_2023_temp | -.1467547 .0540767 -2.71 0.007 -.2527431 -.0407663
_cons | -274.0316 111.8777 -2.45 0.014 -493.308 -54.7553
------------------------------------------------------------------------------------
Underidentification test (Kleibergen-Paap rk LM statistic): 12.313
Chi-sq(1) P-val = 0.0004
------------------------------------------------------------------------------
Weak identification test (Cragg-Donald Wald F statistic): 19.188
(Kleibergen-Paap rk Wald F statistic): 7.746
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
From that I read that my instruments are not weak.
However in the first stage the coeffiecients of the two instruments are not significant does that matter in that case?

[George Ford]

From what I tell, this looks good. If you are going to test first stage, you need to test both variables jointly, but they individually look significant, so that should work out. rk stat is basically testing the same sort of thing but better.

[Maximiser John]

Dear Mr. Ford
Thank you very much for your answer, that was actually the second stage output so in the first stage individually as far as I can see they are not significant right? But in the second stage: here also the input line: ivreg2 composite_index_estimate (pdiv_aa pdiv_aa_sqr = mdist_rescaled pdiv_aa_hat_sqr) ${geovars} ${contall} ${ethfrac} ${ethpolr} ${history} ${climate} if smpl_flag1 == 1, robust first
Also, which F-statisitc to report here since (Kleibergen-Paap rk Wald F statistic are not valid for multiple instruments right?

So in that case should I report: F test of excluded instruments => Sanderson-Windmeijer multivariate F test of excluded instruments?


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


First-stage regression of pdiv_aa:

Statistics robust to heteroskedasticity
Number of obs = 145
------------------------------------------------------------------------------------
| Robust
pdiv_aa | Coefficient std. err. t P>|t| [95% conf. interval]
-------------------+----------------------------------------------------------------
mdist_rescaled | -.5285177 .3297421 -1.60 0.112 -1.181275 .1242397
pdiv_aa_hat_sqr | -4.770294 3.368589 -1.42 0.159 -11.43875 1.898166
abslat | 7.844749 4.786543 1.64 0.104 -1.630691 17.32019
ruggavg | 3.269151 2.093623 1.56 0.121 -.8753835 7.413686
elevavg | -.6541321 .4291573 -1.52 0.130 -1.503692 .1954277
suitavg | .5065486 .317801 1.59 0.114 -.1225701 1.135667
suitrng | -1.095397 .6898206 -1.59 0.115 -2.460966 .2701719
distcr | .1075163 .0750237 1.43 0.154 -.0410007 .2560332
landlock | .0157661 .0104469 1.51 0.134 -.0049145 .0364467
ln_Land_area_sq_km | .0144875 .0091004 1.59 0.114 -.0035277 .0325026
kgatr | .0879244 .0551093 1.60 0.113 -.02117 .1970189
mean1996_2023_temp | .003263 .001977 1.65 0.101 -.0006506 .0071766
asia | -.0680673 .0403631 -1.69 0.094 -.1479702 .0118356
namerica | .3670821 .2321189 1.58 0.116 -.0924203 .8265846
samerica | .618415 .3857674 1.60 0.112 -.1452502 1.38208
europe | -.1551637 .0947012 -1.64 0.104 -.3426342 .0323068
oceania | .2471924 .1611867 1.53 0.128 -.0718927 .5662776
efrac | .0884235 .0550809 1.61 0.111 -.0206147 .1974618
des_pol15 | -.1569791 .1005432 -1.56 0.121 -.3560145 .0420563
evercol_gbr | .0493934 .0311904 1.58 0.116 -.0123512 .1111379
evercol_fra | .0117573 .008232 1.43 0.156 -.0045388 .0280534
evercol_oth | .004101 .0039618 1.04 0.303 -.0037417 .0119437
_cons | 3.23856 1.780917 1.82 0.071 -.2869435 6.764063
------------------------------------------------------------------------------------
F test of excluded instruments:
F( 2, 122) = 51.50
Prob > F = 0.0000
Sanderson-Windmeijer multivariate F test of excluded instruments:
F( 1, 122) = 38.46
Prob > F = 0.0000


First-stage regression of pdiv_aa_sqr:

Statistics robust to heteroskedasticity
Number of obs = 145
------------------------------------------------------------------------------------
| Robust
pdiv_aa_sqr | Coefficient std. err. t P>|t| [95% conf. interval]
-------------------+----------------------------------------------------------------
mdist_rescaled | -.6518324 .4567438 -1.43 0.156 -1.556002 .2523376
pdiv_aa_hat_sqr | -5.730691 4.665399 -1.23 0.222 -14.96631 3.504932
abslat | 9.591849 6.635447 1.45 0.151 -3.543681 22.72738
ruggavg | 4.003559 2.898581 1.38 0.170 -1.734471 9.741589
elevavg | -.8018863 .5932866 -1.35 0.179 -1.976356 .3725839
suitavg | .6272194 .4403662 1.42 0.157 -.2445295 1.498968
suitrng | -1.345124 .9555741 -1.41 0.162 -3.236778 .5465307
distcr | .1304386 .1040592 1.25 0.212 -.0755569 .3364341
landlock | .0195231 .0145433 1.34 0.182 -.0092668 .048313
ln_Land_area_sq_km | .0178233 .0126122 1.41 0.160 -.0071439 .0427905
kgatr | .1074548 .0765271 1.40 0.163 -.0440382 .2589479
mean1996_2023_temp | .0039772 .0027501 1.45 0.151 -.0014669 .0094213
asia | -.0834641 .0558523 -1.49 0.138 -.1940293 .0271011
namerica | .454714 .3216926 1.41 0.160 -.1821086 1.091536
samerica | .7646056 .5347209 1.43 0.155 -.2939279 1.823139
europe | -.1903817 .1310366 -1.45 0.149 -.4497817 .0690183
oceania | .3068885 .2235477 1.37 0.172 -.1356466 .7494236
efrac | .1081901 .0763136 1.42 0.159 -.0428802 .2592605
des_pol15 | -.192093 .1391535 -1.38 0.170 -.4675612 .0833751
evercol_gbr | .0604573 .0431914 1.40 0.164 -.0250443 .1459589
evercol_fra | .0143638 .0114866 1.25 0.214 -.008375 .0371025
evercol_oth | .0052654 .0055721 0.94 0.347 -.0057651 .0162958
_cons | 3.548744 2.465886 1.44 0.153 -1.332723 8.430211
------------------------------------------------------------------------------------
F test of excluded instruments:
F( 2, 122) = 56.66
Prob > F = 0.0000
Sanderson-Windmeijer multivariate F test of excluded instruments:
F( 1, 122) = 41.74
Prob > F = 0.0000



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

(Underid) (Weak id)
Variable | F( 2, 122) P-val | SW Chi-sq( 1) P-val | SW F( 1, 122)
pdiv_aa | 51.50 0.0000 | 45.71 0.0000 | 38.46
pdiv_aa_sqr | 56.66 0.0000 | 49.61 0.0000 | 41.74

NB: first-stage test statistics heteroskedasticity-robust

Stock-Yogo weak ID F 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.
NB: Critical values are for i.i.d. errors only.

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)=13.24 P-val=0.0003

Weak identification test
Ho: equation is weakly identified
Cragg-Donald Wald F statistic 18.53
Kleibergen-Paap Wald rk F statistic 7.77

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(2,122)= 12.89 P-val=0.0000
Anderson-Rubin Wald test Chi-sq(2)= 30.63 P-val=0.0000
Stock-Wright LM S statistic Chi-sq(2)= 25.53 P-val=0.0000

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

Number of observations N = 145
Number of regressors K = 23
Number of endogenous regressors K1 = 2
Number of instruments L = 23
Number of excluded instruments L1 = 2

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

Estimates efficient for homoskedasticity only
Statistics robust to heteroskedasticity

Number of obs = 145
F( 22, 122) = 14.72
Prob > F = 0.0000
Total (centered) SS = 768.6246403 Centered R2 = 0.6344
Total (uncentered) SS = 798.2120898 Uncentered R2 = 0.6480
Residual SS = 280.9735171 Root MSE = 1.392

------------------------------------------------------------------------------------
| Robust
composite_index_~e | Coefficient std. err. z P>|z| [95% conf. interval]
-------------------+----------------------------------------------------------------
pdiv_aa | 833.0504 315.0121 2.64 0.008 215.6381 1450.463
pdiv_aa_sqr | -609.0082 217.2859 -2.80 0.005 -1034.881 -183.1357
abslat | -30.33134 34.78606 -0.87 0.383 -98.51076 37.84808
ruggavg | -26.93956 21.04093 -1.28 0.200 -68.17901 14.2999
elevavg | -1.728501 5.879383 -0.29 0.769 -13.25188 9.794877
suitavg | -12.71014 7.063893 -1.80 0.072 -26.55512 1.134833
suitrng | -.3616519 6.718226 -0.05 0.957 -13.52913 12.80583
distcr | -13.91236 5.874087 -2.37 0.018 -25.42535 -2.399357
landlock | -.0912905 .4950396 -0.18 0.854 -1.06155 .8789693
ln_Land_area_sq_km | -.1687202 .1397111 -1.21 0.227 -.4425488 .1051085
kgatr | -1.658272 .6462521 -2.57 0.010 -2.924903 -.3916412
mean1996_2023_temp | -.1457207 .0559764 -2.60 0.009 -.2554325 -.0360089
asia | -.8630755 .5051336 -1.71 0.088 -1.853119 .1269682
namerica | .1789509 .9257622 0.19 0.847 -1.63551 1.993412
samerica | -.6836664 .9244942 -0.74 0.460 -2.495642 1.128309
europe | 1.042462 .7071084 1.47 0.140 -.3434446 2.428369
oceania | .5491465 1.667622 0.33 0.742 -2.719332 3.817625
efrac | -.3013772 .8083067 -0.37 0.709 -1.885629 1.282875
des_pol15 | -1.133742 .7829309 -1.45 0.148 -2.668258 .4007742
evercol_gbr | .8195283 .3725962 2.20 0.028 .0892532 1.549803
evercol_fra | -.1317844 .3340091 -0.39 0.693 -.7864303 .5228614
evercol_oth | -.3120617 .3579539 -0.87 0.383 -1.013638 .389515
_cons | -275.5991 113.9126 -2.42 0.016 -498.8637 -52.33454
------------------------------------------------------------------------------------
Underidentification test (Kleibergen-Paap rk LM statistic): 13.243
Chi-sq(1) P-val = 0.0003
------------------------------------------------------------------------------
Weak identification test (Cragg-Donald Wald F statistic): 18.528
(Kleibergen-Paap rk Wald F statistic): 7.768
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)

[George Ford]

rk is valid

F test rejected on exclusions in first stage.

[Nick Cox]

Maximiser John Please note our longstanding requests that people use real names

https://www.statalist.org/forums/help#realnames

https://www.statalist.org/forums/help#adviceextras #3

[Carlo Lazzaro]

Maximiser John: please also use -CODE- delimiters (# toggle) to share what you typed and what Stata gave you back. Thanks.