Xtabond2 - How to choose the instruments and how to interpret the Sargan/Hansen results

[Roman Sieler]

Hello,

I am currently working on a regression with the lagged dependent variable as an explanatory variable. Therefore, I am using the Arellano-Bond estimator for the first time. After using the stata command xtabond with no further specification, I realized that I had to do it more exact and tried to use xtabond2.

I read the paper by Roodman and many posts in this forum, but I still can not figure out how I have to choose the instruments. My current understanding is that I have to use gmm style instruments for variables that are exogenous and iv style instruments for variables that might be endogenous. Is that the right way or am I completely off?

My second question refers to the Sargan or Hansen test results that stata gives as an output once I run the regression. Is it right that the p-values in the difference-line refer to whether or not the set of instruments or the one instrument is exogenous? And - coming back to my first question - if it does, does the rejection of the H0 imply that the variable on hand is exogenous and should therefore used in gmm style?

What furthermore seems confusing is the same result for the instruments that are already specified as IV - what does the p-value imply in this case?



At the end of the message is one of my outputs, just as an example. It would be great if someone could describe what the different results imply.

Thank you very much for your help, I appreciate it.

Best,

Roman

. xtabond2 varcof lag_1 mortalitybirth urb waterprep waterwash ownsland ownsanimal varcofedu liferatiofm conflict1, ivstyle(lag_1) ivstyl
> e(waterprep) ivstyle(waterwash) ivstyle(ownsland) ivstyle(ownsanimal) gmmstyle(conflict1) gmmstyle(urb) gmmstyle(mortalitybirth) gmmsty
> le(varcofedu) gmmstyle(liferatiofm)
Favoring space over speed. To switch, type or click on mata: mata set matafavor speed, perm.
Warning: Number of instruments may be large relative to number of observations.

Dynamic panel-data estimation, one-step system GMM
------------------------------------------------------------------------------
Group variable: cocode                          Number of obs      =       167
Time variable : yeargroup                       Number of groups   =         6
Number of instruments = 167                     Obs per group: min =        24
Wald chi2(10) =   2140.75                                      avg =     27.83
Prob > chi2   =     0.000                                      max =        33
--------------------------------------------------------------------------------
        varcof |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
---------------+----------------------------------------------------------------
         lag_1 |   .8762793   .0437163    20.04   0.000     .7905968    .9619617
mortalitybirth |   9.46e-06   6.47e-06     1.46   0.143    -3.21e-06    .0000221
           urb |   -.000039   .0000302    -1.29   0.196    -.0000982    .0000201
     waterprep |  -.0018762   .0008111    -2.31   0.021    -.0034659   -.0002865
     waterwash |  -.0136607   .0057337    -2.38   0.017    -.0248986   -.0024229
      ownsland |   .0033537   .0019305     1.74   0.082    -.0004301    .0071374
    ownsanimal |  -.0089749   .0033845    -2.65   0.008    -.0156084   -.0023415
     varcofedu |  -.0009865   .0004918    -2.01   0.045    -.0019504   -.0000226
   liferatiofm |   .0007335   .0027273     0.27   0.788    -.0046119     .006079
     conflict1 |   .0006105   .0003898     1.57   0.117    -.0001534    .0013744
         _cons |   .0217442   .0067659     3.21   0.001     .0084833     .035005
--------------------------------------------------------------------------------
Instruments for first differences equation
  Standard
    D.ownsanimal
    D.ownsland
    D.waterwash
    D.waterprep
    D.lag_1
  GMM-type (missing=0, separate instruments for each period unless collapsed)
    L(1/43).liferatiofm
    L(1/43).varcofedu
    L(1/43).mortalitybirth
    L(1/43).urb
    L(1/43).conflict1
Instruments for levels equation
  Standard
    ownsanimal
    ownsland
    waterwash
    waterprep
    lag_1
    _cons
  GMM-type (missing=0, separate instruments for each period unless collapsed)
    D.liferatiofm
    D.varcofedu
    D.mortalitybirth
    D.urb
    D.conflict1
------------------------------------------------------------------------------
Arellano-Bond test for AR(1) in first differences: z =  -5.59  Pr > z =  0.000
Arellano-Bond test for AR(2) in first differences: z =   0.43  Pr > z =  0.666
------------------------------------------------------------------------------
Sargan test of overid. restrictions: chi2(156)  = 140.79  Prob > chi2 =  0.803
  (Not robust, but not weakened by many instruments.)

Difference-in-Sargan tests of exogeneity of instrument subsets:
  GMM instruments for levels
    Sargan test excluding group:     chi2(154)  = 140.79  Prob > chi2 =  0.769
    Difference (null H = exogenous): chi2(2)    =   0.00  Prob > chi2 =  1.000
  gmm(urb, lag(1 .))
    Sargan test excluding group:     chi2(133)  = 140.79  Prob > chi2 =  0.305
    Difference (null H = exogenous): chi2(23)   =   0.00  Prob > chi2 =  1.000
  gmm(mortalitybirth, lag(1 .))
    Sargan test excluding group:     chi2(16)   = 140.79  Prob > chi2 =  0.000
    Difference (null H = exogenous): chi2(140)  =  -0.00  Prob > chi2 =  1.000
  iv(waterprep)
    Sargan test excluding group:     chi2(155)  = 140.79  Prob > chi2 =  0.787
    Difference (null H = exogenous): chi2(1)    =   0.00  Prob > chi2 =  1.000
  iv(ownsland)
    Sargan test excluding group:     chi2(155)  = 140.79  Prob > chi2 =  0.787
    Difference (null H = exogenous): chi2(1)    =   0.00  Prob > chi2 =  1.000
  iv(ownsanimal)
    Sargan test excluding group:     chi2(155)  = 140.79  Prob > chi2 =  0.787
    Difference (null H = exogenous): chi2(1)    =   0.00  Prob > chi2 =  1.000