Difference-in-Hansen test in two-step system gmm

[Constantin Domizlaff]

Dear all, I am running a two-step system GMM with the following output:

xtabond2 EMTOTAL EMTOTAL_L NOMCOMM NOMCOMM_IND COMPCOMM COMPCOMM_IND AUDCOMM AUDCOMM_IND ATT SUSCOMM BSIZE BGD INC INDEP DUAL ROA LEV FSIZE MULT SKILLS i.YEAR, gmm(EMTOTAL L.NOMCOMM L.NOMCOMM_IND L.COMPCOMM L.COMPCOMM_IND L.AUDCOMM L.AUDCOMM_IND L.AT
> T L.SUSCOMM L.BSIZE L.BGD L.INC L.INDEP L.DUAL L.ROA L.LEV L.FSIZE L.MULT L.SKILLS, collapse) iv(i.YEAR i.INDUSTRY) robust small orthogonal
Favoring space over speed. To switch, type or click on mata: mata set matafavor speed, perm.
2010b.YEAR dropped due to collinearity
2023.YEAR dropped due to collinearity
Warning: Two-step estimated covariance matrix of moments is singular.
  Using a generalized inverse to calculate robust weighting matrix for Hansen test.
  Difference-in-Sargan/Hansen statistics may be negative.

Dynamic panel-data estimation, one-step system GMM
------------------------------------------------------------------------------
Group variable: ID                              Number of obs      =      2197
Time variable : YEAR                            Number of groups   =       374
Number of instruments = 283                     Obs per group: min =         0
F(31, 373)    = 166700.43                                      avg =      5.87
Prob > F      =     0.000                                      max =        12
------------------------------------------------------------------------------
             |               Robust
     EMTOTAL | Coefficient  std. err.      t    P>|t|     [95% conf. interval]
-------------+----------------------------------------------------------------
   EMTOTAL_L |   .9880734   .0058455   169.03   0.000     .9765791    .9995677
     NOMCOMM |   .4258985   .3686094     1.16   0.249    -.2989145    1.150712
 NOMCOMM_IND |   -.005083   .0025218    -2.02   0.045    -.0100417   -.0001244
    COMPCOMM |  -.0037904   .0976262    -0.04   0.969    -.1957571    .1881763
COMPCOMM_IND |   .0032799   .0028082     1.17   0.244     -.002242    .0088017
     AUDCOMM |  -1.030725   .4061541    -2.54   0.012    -1.829363   -.2320859
 AUDCOMM_IND |  -.0030533   .0030183    -1.01   0.312    -.0089883    .0028817
         ATT |  -.0036664   .0015732    -2.33   0.020    -.0067598    -.000573
     SUSCOMM |  -.0325461   .0285238    -1.14   0.255    -.0886337    .0235415
       BSIZE |  -.0308647   .0591609    -0.52   0.602    -.1471954     .085466
         BGD |  -.0007986   .0014797    -0.54   0.590    -.0037082    .0021111
         INC |   .0024993   .0331529     0.08   0.940    -.0626908    .0676893
       INDEP |  -.0011563    .001843    -0.63   0.531    -.0047803    .0024676
        DUAL |   .0157086   .0339764     0.46   0.644    -.0511007    .0825179
         ROA |   .0017929   .0169667     0.11   0.916    -.0315695    .0351552
         LEV |   -.339208   .0819776    -4.14   0.000    -.5004042   -.1780118
       FSIZE |   .0676598   .0186926     3.62   0.000     .0309038    .1044159
        MULT |  -.1739042   .0419937    -4.14   0.000    -.2564782   -.0913302
      SKILLS |    .000721   .0008049     0.90   0.371    -.0008617    .0023038
             |
        YEAR |
       2011  |   .1030778   .0485648     2.12   0.034     .0075828    .1985729
       2012  |  -.0416549   .0354486    -1.18   0.241     -.111359    .0280492
       2013  |  -.0795695   .0374038    -2.13   0.034    -.1531183   -.0060207
       2014  |  -.0625643   .0369099    -1.70   0.091     -.135142    .0100133
       2015  |  -.0238024    .031641    -0.75   0.452    -.0860195    .0384146
       2016  |   -.041851   .0328001    -1.28   0.203    -.1063473    .0226453
       2017  |  -.0605293   .0325734    -1.86   0.064    -.1245797    .0035212
       2018  |  -.0355236   .0295336    -1.20   0.230    -.0935968    .0225497
       2019  |  -.0074437   .0302566    -0.25   0.806    -.0669385    .0520512
       2020  |  -.0192119   .0322941    -0.59   0.552    -.0827132    .0442895
       2021  |  -.1036215   .0219098    -4.73   0.000    -.1467038   -.0605392
       2022  |  -.0343733    .020788    -1.65   0.099    -.0752497    .0065031
             |
       _cons |   .4144471   .5623001     0.74   0.462    -.6912285    1.520123
------------------------------------------------------------------------------
Instruments for orthogonal deviations equation
  Standard
    FOD.(2010b.YEAR 2011.YEAR 2012.YEAR 2013.YEAR 2014.YEAR 2015.YEAR
    2016.YEAR 2017.YEAR 2018.YEAR 2019.YEAR 2020.YEAR 2021.YEAR 2022.YEAR
    2023.YEAR 211b.INDUSTRY 212.INDUSTRY 213.INDUSTRY 221.INDUSTRY
    236.INDUSTRY 237.INDUSTRY 238.INDUSTRY 311.INDUSTRY 312.INDUSTRY
    314.INDUSTRY 315.INDUSTRY 316.INDUSTRY 321.INDUSTRY 322.INDUSTRY
    324.INDUSTRY 325.INDUSTRY 326.INDUSTRY 327.INDUSTRY 331.INDUSTRY
    332.INDUSTRY 333.INDUSTRY 334.INDUSTRY 335.INDUSTRY 336.INDUSTRY
    339.INDUSTRY 423.INDUSTRY 424.INDUSTRY 441.INDUSTRY 444.INDUSTRY
    445.INDUSTRY 449.INDUSTRY 455.INDUSTRY 456.INDUSTRY 458.INDUSTRY
    459.INDUSTRY 481.INDUSTRY 482.INDUSTRY 483.INDUSTRY 484.INDUSTRY
    486.INDUSTRY 488.INDUSTRY 492.INDUSTRY 513.INDUSTRY 516.INDUSTRY
    517.INDUSTRY 518.INDUSTRY 519.INDUSTRY 531.INDUSTRY 532.INDUSTRY
    541.INDUSTRY 561.INDUSTRY 562.INDUSTRY 621.INDUSTRY 622.INDUSTRY
    721.INDUSTRY 722.INDUSTRY 812.INDUSTRY)
  GMM-type (missing=0, separate instruments for each period unless collapsed)
    L(1/13).(EMTOTAL L.NOMCOMM L.NOMCOMM_IND L.COMPCOMM L.COMPCOMM_IND
    L.AUDCOMM L.AUDCOMM_IND L.ATT L.SUSCOMM L.BSIZE L.BGD L.INC L.INDEP L.DUAL
    L.ROA L.LEV L.FSIZE L.MULT L.SKILLS) collapsed
Instruments for levels equation
  Standard
    2010b.YEAR 2011.YEAR 2012.YEAR 2013.YEAR 2014.YEAR 2015.YEAR 2016.YEAR
    2017.YEAR 2018.YEAR 2019.YEAR 2020.YEAR 2021.YEAR 2022.YEAR 2023.YEAR
    211b.INDUSTRY 212.INDUSTRY 213.INDUSTRY 221.INDUSTRY 236.INDUSTRY
    237.INDUSTRY 238.INDUSTRY 311.INDUSTRY 312.INDUSTRY 314.INDUSTRY
    315.INDUSTRY 316.INDUSTRY 321.INDUSTRY 322.INDUSTRY 324.INDUSTRY
    325.INDUSTRY 326.INDUSTRY 327.INDUSTRY 331.INDUSTRY 332.INDUSTRY
    333.INDUSTRY 334.INDUSTRY 335.INDUSTRY 336.INDUSTRY 339.INDUSTRY
    423.INDUSTRY 424.INDUSTRY 441.INDUSTRY 444.INDUSTRY 445.INDUSTRY
    449.INDUSTRY 455.INDUSTRY 456.INDUSTRY 458.INDUSTRY 459.INDUSTRY
    481.INDUSTRY 482.INDUSTRY 483.INDUSTRY 484.INDUSTRY 486.INDUSTRY
    488.INDUSTRY 492.INDUSTRY 513.INDUSTRY 516.INDUSTRY 517.INDUSTRY
    518.INDUSTRY 519.INDUSTRY 531.INDUSTRY 532.INDUSTRY 541.INDUSTRY
    561.INDUSTRY 562.INDUSTRY 621.INDUSTRY 622.INDUSTRY 721.INDUSTRY
    722.INDUSTRY 812.INDUSTRY
    _cons
  GMM-type (missing=0, separate instruments for each period unless collapsed)
    D.(EMTOTAL L.NOMCOMM L.NOMCOMM_IND L.COMPCOMM L.COMPCOMM_IND L.AUDCOMM
    L.AUDCOMM_IND L.ATT L.SUSCOMM L.BSIZE L.BGD L.INC L.INDEP L.DUAL L.ROA
    L.LEV L.FSIZE L.MULT L.SKILLS) collapsed
------------------------------------------------------------------------------
Arellano-Bond test for AR(1) in first differences: z =  -4.50  Pr > z =  0.000
Arellano-Bond test for AR(2) in first differences: z =   0.31  Pr > z =  0.753
------------------------------------------------------------------------------
Sargan test of overid. restrictions: chi2(251)  =1757.34  Prob > chi2 =  0.000
  (Not robust, but not weakened by many instruments.)
Hansen test of overid. restrictions: chi2(251)  = 271.57  Prob > chi2 =  0.178
  (Robust, but weakened by many instruments.)

Difference-in-Hansen tests of exogeneity of instrument subsets:
  GMM instruments for levels
    Hansen test excluding group:     chi2(232)  = 230.40  Prob > chi2 =  0.517
    Difference (null H = exogenous): chi2(19)   =  41.17  Prob > chi2 =  0.002
  gmm(EMTOTAL L.NOMCOMM L.NOMCOMM_IND L.COMPCOMM L.COMPCOMM_IND L.AUDCOMM L.AUDCOMM_IND L.ATT L.SUSCOMM L.BSIZE L.BGD L.INC L.INDEP L.DUAL L.ROA L.LEV L.FSIZE L.MULT L.SKILLS, collapse lag(1 .))
    Hansen test excluding group:     chi2(37)   =  28.93  Prob > chi2 =  0.826
    Difference (null H = exogenous): chi2(214)  = 242.65  Prob > chi2 =  0.087
  iv(2010b.YEAR 2011.YEAR 2012.YEAR 2013.YEAR 2014.YEAR 2015.YEAR 2016.YEAR 2017.YEAR 2018.YEAR 2019.YEAR 2020.YEAR 2021.YEAR 2022.YEAR 2023.YEAR 211b.INDUSTRY 212.INDUSTRY 213.INDUSTRY 221.INDUSTRY 236.INDUSTRY 237.INDUSTRY 238.INDUSTRY 311.INDUSTRY 3
> 12.INDUSTRY 314.INDUSTRY 315.INDUSTRY 316.INDUSTRY 321.INDUSTRY 322.INDUSTRY 324.INDUSTRY 325.INDUSTRY 326.INDUSTRY 327.INDUSTRY 331.INDUSTRY 332.INDUSTRY 333.INDUSTRY 334.INDUSTRY 335.INDUSTRY 336.INDUSTRY 339.INDUSTRY 423.INDUSTRY 424.INDUSTRY 441.
> INDUSTRY 444.INDUSTRY 445.INDUSTRY 449.INDUSTRY 455.INDUSTRY 456.INDUSTRY 458.INDUSTRY 459.INDUSTRY 481.INDUSTRY 482.INDUSTRY 483.INDUSTRY 484.INDUSTRY 486.INDUSTRY 488.INDUSTRY 492.INDUSTRY 513.INDUSTRY 516.INDUSTRY 517.INDUSTRY 518.INDUSTRY 519.IND
> USTRY 531.INDUSTRY 532.INDUSTRY 541.INDUSTRY 561.INDUSTRY 562.INDUSTRY 621.INDUSTRY 622.INDUSTRY 721.INDUSTRY 722.INDUSTRY 812.INDUSTRY)
    Hansen test excluding group:     chi2(183)  = 218.74  Prob > chi2 =  0.036
    Difference (null H = exogenous): chi2(68)   =  52.84  Prob > chi2 =  0.912

From what I know, the AR2 and Hansen statistic look good (Hansen also within the range of 0.1 < p < 0.25 as indicated in Roodman(2009)). However, I am not familiar with the difference-in-hansen test and its meaning and I have not found material from which I can understand it well. Can anyone maybe enlighten me and tell me under what conditions I should report the difference-in-hansen results? Because I have seen most of the studies in my research field not reporting them at all.

Thanks a lot in advance!

[Sebastian Kripfganz]

Difference-in-Hansen tests can be helpful to assess the validity of a particular subset of the instruments.The following presentation slides might be helpful, where difference-in-Hansen tests are covered as well:

• Kripfganz, S. (2019). Generalized method of moments estimation of linear dynamic panel data models. Proceedings of the 2019 London Stata Conference.

[Constantin Domizlaff]

Dear Prof. Kripfglanz, thank you very much for your response.

If you do not mind, I have another question: Am I correct in the assumption that it is often not justifiable to include instruments in the -iv()- brackets because they are then assumed to be uncorrelated with unobserved group-specific effects? This is why I only included year and industry dummies in the -iv()- bracket but I am not sure whether it is possible to include more variables there.

[Sebastian Kripfganz]

That is generally correct.

You can include variables in the iv() option if they are correlated with the unobserved group-specific effects, but only if you add the suboption eq(diff).