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  • #1

    xtabond2 System GMM

    Hi, is my command for xtabond2 correct?

    N=966, n=69, T=14 years
    Independent variable: WOB
    2 dependent variables: ROA, TQ
    Control variables: BS, FS, FA

    Code:
    xtset COMPANY YEAR, yearly
    Code:
     xtsum WOB ROA TQ BS FS FA

Variable         |      Mean   Std. Dev.       Min        Max |    Observations
-----------------+--------------------------------------------+----------------
WOB      overall |  .1495199   .1073334          0         .6 |     N =     966
         between |             .0772878          0   .3298424 |     n =      69
         within  |             .0750168  -.0692114   .4505403 |     T =      14
                 |                                            |
ROA      overall |  .0673593   .1032169  -1.104439   .6541691 |     N =     966
         between |                .0603  -.0711783   .2470477 |     n =      69
         within  |             .0840633  -1.048663   .6061372 |     T =      14
                 |                                            |
TQ       overall |  3.073908   2.173385   .5880593   26.99235 |     N =     966
         between |             1.494371   1.214629   8.949094 |     n =      69
         within  |             1.587621  -3.830402   21.11716 |     T =      14
                 |                                            |
BS       overall |  9.257764   2.182079          3         18 |     N =     966
         between |             1.880398   4.714286   15.14286 |     n =      69
         within  |             1.128364   4.114907   14.40062 |     T =      14
                 |                                            |
FS       overall |  8.414718   1.936693   3.070422   13.58957 |     N =     966
         between |             1.862711   5.032185   13.16478 |     n =      69
         within  |             .5725632   6.335153   10.44355 |     T =      14
                 |                                            |
FA       overall |  3.138765   .5719432   .6931472    4.85203 |     N =     966
         between |             .5307901   1.992805   4.799363 |     n =      69
         within  |             .2217574   1.839107    3.85401 |     T =      14
    Code:
    xtabond2 ROA L.ROA WOB BS FS FA YEAR*, gmm(L.ROA, collapse) iv(WOB BS FS FA YEAR*, equation(level)) nodiffsargan twostep robust orthogonal small
Favoring space over speed. To switch, type or click on mata: mata set matafavor speed, perm.
Warning: Two-step estimated covariance matrix of moments is singular.
  Using a generalized inverse to calculate optimal weighting matrix for two-step estimation.

Dynamic panel-data estimation, two-step system GMM
------------------------------------------------------------------------------
Group variable: COMPANY                         Number of obs      =       897
Time variable : YEAR                            Number of groups   =        69
Number of instruments = 19                      Obs per group: min =        13
F(6, 68)      =      7.88                                      avg =     13.00
Prob > F      =     0.000                                      max =        13
------------------------------------------------------------------------------
             |              Corrected
         ROA |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
         ROA |
         L1. |   .3128335   .0703953     4.44   0.000      .172362    .4533051
             |
         WOB |   .0455575    .043481     1.05   0.298    -.0412074    .1323224
          BS |  -.0079905   .0025715    -3.11   0.003    -.0131219   -.0028591
          FS |   .0090684   .0032495     2.79   0.007     .0025842    .0155526
          FA |   .0054749   .0072533     0.75   0.453    -.0089989    .0199487
        YEAR |  -.0015865   .0011235    -1.41   0.162    -.0038284    .0006554
       _cons |   3.211222   2.233996     1.44   0.155    -1.246648    7.669092
------------------------------------------------------------------------------
Instruments for orthogonal deviations equation
  GMM-type (missing=0, separate instruments for each period unless collapsed)
    L(1/13).L.ROA collapsed
Instruments for levels equation
  Standard
    WOB BS FS FA YEAR
    _cons
  GMM-type (missing=0, separate instruments for each period unless collapsed)
    D.L.ROA collapsed
------------------------------------------------------------------------------
Arellano-Bond test for AR(1) in first differences: z =  -2.72  Pr > z =  0.006
Arellano-Bond test for AR(2) in first differences: z =   1.24  Pr > z =  0.215
------------------------------------------------------------------------------
Sargan test of overid. restrictions: chi2(12)   =  33.19  Prob > chi2 =  0.001
  (Not robust, but not weakened by many instruments.)
Hansen test of overid. restrictions: chi2(12)   =  15.79  Prob > chi2 =  0.201
  (Robust, but weakened by many instruments.)
    Last edited by Nur Batrisya; 06 Feb 2022, 09:15.
    Tags: None
  • #2
    Your specification assumes that WOB BS FS FA are all uncorrelated with the unobserved group-specific effects. This is essentially a random-effects assumption, which might be hard to justify.

    You probably want to specify time dummies for each period instead of a linear time trend. Consider replacing YEAR* by i.YEAR.

    More on the GMM estimation of linear dynamic panel models:
    https://www.kripfganz.de/stata/

    Comment

    • #3
      Sebastian: Thank you for your comment. I tried the command from Slide 38 of Kripfganz (2019):

      Code:
      . xtdpdgmm L(0/1).ROA WOB BS FS FA, model(diff) collapse gmm(ROA, lag(2 4)) gmm(WOB BS FS FA, lag(1 3)) gmm(ROA, lag(1 1) diff mo
> del(level)) gmm(WOB BS FS FA, lag(0 0) diff model (level)) two vce(r)

Generalized method of moments estimation

Fitting full model:
Step 1         f(b) =  .00572726
Step 2         f(b) =  .26037833

Group variable: COMPANY                      Number of obs         =       897
Time variable: YEAR                          Number of groups      =        69

Moment conditions:     linear =      21      Obs per group:    min =        13
                    nonlinear =       0                        avg =        13
                        total =      21                        max =        13

                               (Std. Err. adjusted for 69 clusters in COMPANY)
------------------------------------------------------------------------------
             |              WC-Robust
         ROA |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
         ROA |
         L1. |   .2823596   .0942331     3.00   0.003     .0976661    .4670531
             |
         WOB |   .1035373   .0666367     1.55   0.120    -.0270683    .2341429
          BS |  -.0025939   .0034941    -0.74   0.458    -.0094422    .0042543
          FS |  -.0319235   .0198189    -1.61   0.107    -.0707679    .0069209
          FA |   .0408506   .0216966     1.88   0.060     -.001674    .0833751
       _cons |   .2001539   .1076643     1.86   0.063    -.0108643    .4111721
------------------------------------------------------------------------------
Instruments corresponding to the linear moment conditions:
 1, model(diff):
   L2.ROA L3.ROA L4.ROA
 2, model(diff):
   L1.WOB L2.WOB L3.WOB L1.BS L2.BS L3.BS L1.FS L2.FS L3.FS L1.FA L2.FA L3.FA
 3, model(level):
   L1.D.ROA
 4, model(level):
   D.WOB D.BS D.FS D.FA
 5, model(level):
   _cons
      Kindly advise if this is correct and applicable for my model.

      Thank you

      Comment

      • #4
        Your specification is correct for a system GMM estimator with predetermined variables WOB BS FS FA, assuming that there is no remaining serial correlation in the error term. You can check the latter by running the estat serial postestimation command. The AR(2) test should not reject the null hypothesis. Furthermore, you can check the model specification with the Hansen test using the estat overid postestimation command.

        If you want to use forward-orthogonal deviations instead of the first-difference transformation, amend the code as follows:
        Code:
        xtdpdgmm L(0/1).ROA WOB BS FS FA, model(fod) collapse gmm(ROA, lag(1 3)) gmm(WOB BS FS FA, lag(0 2)) gmm(ROA, lag(1 1) diff model(level)) gmm(WOB BS FS FA, lag(0 0) diff model (level)) two vce(r)
        (Note the different lag orders when switching from the first-difference to the forward-orthogonal transformation.)
        Last edited by Sebastian Kripfganz; 08 Feb 2022, 02:04.
        https://www.kripfganz.de/stata/

        Comment

        • #5
          Thank you Professor. Just to clarify, does this model solve for Simultaneity (between WOB and ROA) and Dynamic endogeneity (WOB and L.ROA)?

          Comment

          • #6
            Simultaneity between WOB and ROA would imply that WOB is endogenous, not predetermined. In that case, you need to modify the command as follows:
            Code:
            xtdpdgmm L(0/1).ROA WOB BS FS FA, model(diff) collapse gmm(ROA WOB, lag(2 4)) gmm(BS FS FA, lag(1 3)) gmm(ROA WOB, lag(1 1) diff model(level)) gmm(BS FS FA, lag(0 0) diff model (level)) two vce(r)
xtdpdgmm L(0/1).ROA WOB BS FS FA, model(fod) collapse gmm(ROA WOB, lag(1 3)) gmm(BS FS FA, lag(0 2)) gmm(ROA WOB, lag(1 1) diff model(level)) gmm(BS FS FA, lag(0 0) diff model (level)) two vce(r)
            https://www.kripfganz.de/stata/

            Comment

            • #7
              Thank you Professor, this was very helpful.
              I decided to use forward-orthogonal, following the benefits you've mentioned in another post: https://www.statalist.org/forums/for...tions-xtabond2

              My DV1: ROA results look good
              However for DV2: TQ (below), it shows using lagged TQ as IV are invalid. Is there a way to solve for this?

              Code:
              xtdpdgmm L(0/1).TQ WOB BS FS FA, model(fod) collapse gmm(TQ WOB, lag(1 3)) gmm(BS FS FA, lag(0 2)) gmm(TQ WOB, lag(1 1) diff mo
> del(level)) gmm(BS FS FA, lag(0 0) diff model (level)) two vce(r)

Generalized method of moments estimation

Fitting full model:
Step 1         f(b) =  4.0841813
Step 2         f(b) =  .62943154

Group variable: COMPANY                      Number of obs         =       897
Time variable: YEAR                          Number of groups      =        69

Moment conditions:     linear =      21      Obs per group:    min =        13
                    nonlinear =       0                        avg =        13
                        total =      21                        max =        13

                               (Std. Err. adjusted for 69 clusters in COMPANY)
------------------------------------------------------------------------------
             |              WC-Robust
          TQ |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
          TQ |
         L1. |   .7120205    .080307     8.87   0.000     .5546216    .8694194
             |
         WOB |   4.678788   1.456153     3.21   0.001      1.82478    7.532795
          BS |   .0418036   .0830809     0.50   0.615    -.1210318    .2046391
          FS |  -.1767585   .2386008    -0.74   0.459    -.6444075    .2908905
          FA |   .3158152   .2618978     1.21   0.228     -.197495    .8291254
       _cons |     .24514   1.225138     0.20   0.841    -2.156087    2.646367
------------------------------------------------------------------------------
Instruments corresponding to the linear moment conditions:
 1, model(fodev):
   L1.TQ L2.TQ L3.TQ L1.WOB L2.WOB L3.WOB
 2, model(fodev):
   BS L1.BS L2.BS FS L1.FS L2.FS FA L1.FA L2.FA
 3, model(level):
   L1.D.TQ L1.D.WOB
 4, model(level):
   D.BS D.FS D.FA
 5, model(level):
   _cons
              Code:
               estat overid

Sargan-Hansen test of the overidentifying restrictions
H0: overidentifying restrictions are valid

2-step moment functions, 2-step weighting matrix       chi2(15)    =   43.4308
                                                       Prob > chi2 =    0.0001

2-step moment functions, 3-step weighting matrix       chi2(15)    =   49.2412
                                                       Prob > chi2 =    0.0000

.
              Code:
              estat serial, ar(1/2)

Arellano-Bond test for autocorrelation of the first-differenced residuals
H0: no autocorrelation of order 1:     z =   -2.6061   Prob > |z|  =    0.0092
H0: no autocorrelation of order 2:     z =   -1.3702   Prob > |z|  =    0.1706

              Comment

              • #8
                It could possibly be that the assumptions for the level instruments are not satisfied. In this case, an estimator with the FOD transformation only might work:
                Code:
                xtdpdgmm L(0/1).TQ WOB BS FS FA, model(fod) collapse gmm(TQ WOB, lag(1 3)) gmm(BS FS FA, lag(0 2)) two vce(r)
                If this estimator still does not pass the tests, it could be that one or more of the variables BS FS FA are endogenous, and should be treated in the same way as WOB.

                The difference-in-Hansen test might help to shed some light on possible sources of misspecification. Based on the initial system GMM estimator, add the option overid and then the option difference to estat overid:
                Code:
                xtdpdgmm L(0/1).TQ WOB BS FS FA, model(fod) collapse gmm(TQ WOB, lag(1 3)) gmm(BS FS FA, lag(0 2)) gmm(TQ WOB, lag(1 1) diff model(level)) gmm(BS FS FA, lag(0 0) diff model (level)) two vce(r) overid
estat overid, difference
                https://www.kripfganz.de/stata/

                Comment

                • #9
                  Sebastian:

                  1. I tried
                  Code:
                  xtdpdgmm L(0/1).TQ WOB BS FS FA, model(fod) collapse gmm(TQ WOB, lag(1 3)) gmm(BS FS FA, lag(0 2)) two vce(r)
                  and there's still an overidentification issue

                  2. Tried treating one or more of the control variables the same way as WOB in my commands, but there's still an overidentification issue

                  3. Below is the results of the difference-in-Hansen test. Hopefully there's a solution to the issue. If there's no solution, could I conclude that the model for DV2 is overidentified and future research can look into finding a suitable IV to improve the robustness of results?
                  Code:
                   xtdpdgmm L(0/1).TQ WOB BS FS FA, model(fod) collapse gmm(TQ WOB, lag(1 3)) gmm(BS FS FA, lag(0 2)) gmm(TQ WOB, lag(1 1) diff mo
> del(level)) gmm(BS FS FA, lag(0 0) diff model (level)) two vce(r) overid

Generalized method of moments estimation

Fitting full model:
Step 1         f(b) =  4.0841813
Step 2         f(b) =  .62943154

Fitting reduced model 1:
Step 1         f(b) =  .56372736

Fitting reduced model 2:
Step 1         f(b) =  .29679668

Fitting reduced model 3:
Step 1         f(b) =  .55095006

Fitting reduced model 4:
Step 1         f(b) =  .57254652

Fitting no-fodev model:
Step 1         f(b) =  1.282e-08

Fitting no-level model:
Step 1         f(b) =  .38858043

Group variable: COMPANY                      Number of obs         =       897
Time variable: YEAR                          Number of groups      =        69

Moment conditions:     linear =      21      Obs per group:    min =        13
                    nonlinear =       0                        avg =        13
                        total =      21                        max =        13

                               (Std. Err. adjusted for 69 clusters in COMPANY)
------------------------------------------------------------------------------
             |              WC-Robust
          TQ |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
          TQ |
         L1. |   .7120205    .080307     8.87   0.000     .5546216    .8694194
             |
         WOB |   4.678788   1.456153     3.21   0.001      1.82478    7.532795
          BS |   .0418036   .0830809     0.50   0.615    -.1210318    .2046391
          FS |  -.1767585   .2386008    -0.74   0.459    -.6444075    .2908905
          FA |   .3158152   .2618978     1.21   0.228     -.197495    .8291254
       _cons |     .24514   1.225138     0.20   0.841    -2.156087    2.646367
------------------------------------------------------------------------------
Instruments corresponding to the linear moment conditions:
 1, model(fodev):
   L1.TQ L2.TQ L3.TQ L1.WOB L2.WOB L3.WOB
 2, model(fodev):
   BS L1.BS L2.BS FS L1.FS L2.FS FA L1.FA L2.FA
 3, model(level):
   L1.D.TQ L1.D.WOB
 4, model(level):
   D.BS D.FS D.FA
 5, model(level):
   _cons

                  Comment

                  • #10
                    I would need to see the results from the estat overid command with option difference.

                    Can you show me the output from the following two command lines?
                    Code:
                    xtdpdgmm L(0/1).TQ WOB BS FS FA, model(fod) collapse gmm(TQ, lag(1 3)) gmm(WOB BS FS FA, lag(1 3)) gmm(BS, lag(0 0)) gmm(FS, lag(0 0)) gmm(FA, lag(0 0)) two vce(r) overid
estat overid, difference
                    https://www.kripfganz.de/stata/

                    Comment

                    • #11
                      Hi Professor, kindly refer below:

                      Code:
                       xtdpdgmm L(0/1).TQ WOB BS FS FA, model(fod) collapse gmm(TQ, lag(1 3)) gmm(WOB BS FS FA, lag(1 3)) gmm(BS, lag(0 0)) gmm(FS, la
> g(0 0)) gmm(FA, lag(0 0)) two vce(r) overid

Generalized method of moments estimation

Fitting full model:
Step 1         f(b) =  1.2580081
Step 2         f(b) =  .54409505

Fitting reduced model 1:
Step 1         f(b) =  .48987107

Fitting reduced model 2:
Step 1         f(b) =   .0161543

Fitting reduced model 3:
Step 1         f(b) =  .43838225

Fitting reduced model 4:
Step 1         f(b) =  .54022658

Fitting reduced model 5:
Step 1         f(b) =  .53588481

Group variable: COMPANY                      Number of obs         =       897
Time variable: YEAR                          Number of groups      =        69

Moment conditions:     linear =      19      Obs per group:    min =        13
                    nonlinear =       0                        avg =        13
                        total =      19                        max =        13

                               (Std. Err. adjusted for 69 clusters in COMPANY)
------------------------------------------------------------------------------
             |              WC-Robust
          TQ |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
          TQ |
         L1. |     .22981   .1281562     1.79   0.073    -.0213716    .4809916
             |
         WOB |   .7539035   1.960281     0.38   0.701    -3.088177    4.595984
          BS |  -.0558791   .1026397    -0.54   0.586    -.2570492     .145291
          FS |   .3651178   .3000931     1.22   0.224    -.2230539    .9532895
          FA |   1.247386   .8503834     1.47   0.142    -.4193349    2.914107
       _cons |  -4.626744   2.212793    -2.09   0.037    -8.963739   -.2897493
------------------------------------------------------------------------------
Instruments corresponding to the linear moment conditions:
 1, model(fodev):
   L1.TQ L2.TQ L3.TQ
 2, model(fodev):
   L1.WOB L2.WOB L3.WOB L1.BS L2.BS L3.BS L1.FS L2.FS L3.FS L1.FA L2.FA L3.FA
 3, model(fodev):
   BS
 4, model(fodev):
   FS
 5, model(fodev):
   FA
 6, model(level):
   _cons

. estat overid, difference

Sargan-Hansen (difference) test of the overidentifying restrictions
H0: (additional) overidentifying restrictions are valid

2-step weighting matrix from full model

                  | Excluding                   | Difference                  
Moment conditions |       chi2     df         p |        chi2     df         p
------------------+-----------------------------+-----------------------------
  1, model(fodev) |    33.8011     10    0.0002 |      3.7415      3    0.2908
  2, model(fodev) |     1.1146      1    0.2911 |     36.4279     12    0.0003
  3, model(fodev) |    30.2484     12    0.0026 |      7.2942      1    0.0069
  4, model(fodev) |    37.2756     12    0.0002 |      0.2669      1    0.6054
  5, model(fodev) |    36.9761     12    0.0002 |      0.5665      1    0.4517
     model(fodev) |          .     -5         . |           .      .         .

                      Comment

                      • #12
                        Unfortunately, those results do not provide a trivial answer, because there is no reliable maintained model in rows 3 to 5 when suspicious instruments are excluded. The maintained model in row 2 is not reliable (despite a sufficiently high p-value for the "Excluding" test) because it implausibly assumes that contemporaneous instruments are valid while testing for the validity of the corresponding lagged instruments.

                        It might be necessary to allow for a richer dynamic model specification, e.g. by including lags of the independent variables. Initially, to find a reliable maintained model, we should also assume that all variables are endogenous:
                        Code:
                        xtdpdgmm L(0/1).TQ L(0/1).(WOB BS FS FA), model(fod) collapse gmm(TQ, lag(1 3)) gmm(WOB BS FS FA, lag(1 3)) two vce(r) overid
estat overid, difference
                        https://www.kripfganz.de/stata/

                        Comment

                        • #13
                          Hi Professor, thank you so much for your help.
                          These are the results:

                          Code:
                           xtdpdgmm L(0/1).TQ L(0/1).(WOB BS FS FA), model(fod) collapse gmm(TQ, lag(1 3)) gmm(WOB BS FS FA, lag(1 3)) two vce(r) overid

Generalized method of moments estimation

Fitting full model:
Step 1         f(b) =  .63630138
Step 2         f(b) =   .1339579

Fitting reduced model 1:
Step 1         f(b) =  .08835568

Group variable: COMPANY                      Number of obs         =       897
Time variable: YEAR                          Number of groups      =        69

Moment conditions:     linear =      16      Obs per group:    min =        13
                    nonlinear =       0                        avg =        13
                        total =      16                        max =        13

                               (Std. Err. adjusted for 69 clusters in COMPANY)
------------------------------------------------------------------------------
             |              WC-Robust
          TQ |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
          TQ |
         L1. |  -.1061156    .194801    -0.54   0.586    -.4879185    .2756873
             |
         WOB |
         --. |   8.791777   13.02015     0.68   0.500    -16.72725     34.3108
         L1. |  -8.024938   11.67822    -0.69   0.492    -30.91383    14.86395
             |
          BS |
         --. |  -.5245513   .4368392    -1.20   0.230     -1.38074    .3316377
         L1. |   .1259777   .2305606     0.55   0.585    -.3259128    .5778682
             |
          FS |
         --. |   1.436786   2.669923     0.54   0.590    -3.796166    6.669739
         L1. |  -.8439601    2.28386    -0.37   0.712    -5.320243    3.632323
             |
          FA |
         --. |   33.97388   74.91139     0.45   0.650    -112.8497    180.7975
         L1. |  -30.52342     68.392    -0.45   0.655    -164.5693    103.5224
             |
       _cons |  -10.98727   18.81945    -0.58   0.559    -47.87272    25.89818
------------------------------------------------------------------------------
Instruments corresponding to the linear moment conditions:
 1, model(fodev):
   L1.TQ L2.TQ L3.TQ
 2, model(fodev):
   L1.WOB L2.WOB L3.WOB L1.BS L2.BS L3.BS L1.FS L2.FS L3.FS L1.FA L2.FA L3.FA
 3, model(level):
   _cons

. estat overid, difference

Sargan-Hansen (difference) test of the overidentifying restrictions
H0: (additional) overidentifying restrictions are valid

2-step weighting matrix from full model

                  | Excluding                   | Difference                  
Moment conditions |       chi2     df         p |        chi2     df         p
------------------+-----------------------------+-----------------------------
  1, model(fodev) |     6.0965      3    0.1070 |      3.1466      3    0.3696
  2, model(fodev) |          .     -6         . |           .      .         .
     model(fodev) |          .     -9         . |           .      .         .

.

                          Comment

                          • #14
                            Hi Professor, is there any solution to the above results? Or do I proceed to use the original command
                            Code:
                            xtdpdgmm L(0/1).TQ WOB BS FS FA, model(fod) collapse gmm(TQ WOB, lag(1 3)) gmm(BS FS FA, lag(0 2)) gmm(TQ WOB, lag(1 1) diff model(level)) gmm(BS FS FA, lag(0 0) diff model (level)) two vce(r) overid
estat overid, difference
                            and conclude that the model for DV2 is overidentified, where future research should find a suitable IV to address this limitation?

                            Comment

                            • #15
                              It looks like the model from post #13 might satisfy the overidentification test. However, none of the coefficients is statistically significant, possibly due to a high degree of collinearity. The one thing we did not try yet is assuming that all variables are endogenous, without adding lagged regressors:
                              Code:
                              xtdpdgmm L(0/1).TQ WOB BS FS FA, model(fod) collapse gmm(TQ, lag(1 3)) gmm(WOB BS FS FA, lag(1 3)) two vce(r)
estat overid
estat serial
                              Last edited by Sebastian Kripfganz; 10 Feb 2022, 10:00.
                              https://www.kripfganz.de/stata/

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