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  • Instrument interpreation

    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?

  • #2
    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.

    Comment


    • #3
      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)

      Comment


      • #4
        rk is valid

        F test rejected on exclusions in first stage.

        Comment


        • #5
          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

          Comment


          • #6
            Maximiser John: please also use -CODE- delimiters (# toggle) to share what you typed and what Stata gave you back. Thanks.
            Kind regards,
            Carlo
            (Stata 19.0)

            Comment

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