[ismaila yusuf]

Hello, I am trying to fit a gmm model with the code below;

xtabond2 trisk l.trisk bind fenex femex feric crcomind femric fexric cbmeet l.rsanc inrel totd flev,  gmm (trisk fbric, lag(1  1) collapse eq(diff)) gmm(trisk fbric, lag(0 0) collapse eq(level)) iv(bind fenex femex feric crcomind femric fexri c cbmeet inrel l.rsanc totd flev, equation(level)) two robust orthogonal small nodiffsargan

I had the following result

avoring speed over space. To switch, type or click on mata: mata set matafavor space, perm.
Warning: Number of instruments may be large relative to number of observations.
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: bankid                          Number of obs      =       131
Time variable : year                            Number of groups   =        15
Number of instruments = 17                      Obs per group: min =         7
F(13, 14)     =     18.94                                      avg =      8.73
Prob > F      =     0.000                                      max =         9
------------------------------------------------------------------------------
             |              Corrected
       trisk |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
       trisk |
         L1. |  -.8749704   .2366954    -3.70   0.002    -1.382632   -.3673092
             |
        bind |    .460755   .3258479     1.41   0.179    -.2381191    1.159629
       fenex |   1.574508   .4650913     3.39   0.004     .5769862     2.57203
       femex |  -2.648738   .6300641    -4.20   0.001    -4.000091   -1.297385
       feric |  -.5341961    .297384    -1.80   0.094    -1.172021    .1036292
    crcomind |  -.5480378   .1801754    -3.04   0.009    -.9344756   -.1616001
      femric |   .8974255   .2398005     3.74   0.002     .3831045    1.411746
      fexric |   -.667802   .3699242    -1.81   0.093     -1.46121    .1256065
      cbmeet |   .0411593   .0421682     0.98   0.346    -.0492824     .131601
             |
       rsanc |
         L1. |   .4546769    1.04491     0.44   0.670    -1.786433    2.695787
             |
       inrel |   .0082195   .5229716     0.02   0.988    -1.113443    1.129882
        totd |    .807954   .1304721     6.19   0.000     .5281191    1.087789
        flev |   .4677679   .1245706     3.76   0.002     .2005905    .7349452
       _cons |  -.2411651   .1706182    -1.41   0.179    -.6071047    .1247745
------------------------------------------------------------------------------
Instruments for orthogonal deviations equation
  GMM-type (missing=0, separate instruments for each period unless collapsed)
    L.(trisk fbric) collapsed
Instruments for levels equation
  Standard
    bind fenex femex feric crcomind femric fexric cbmeet inrel L.rsanc totd
    flev
    _cons
  GMM-type (missing=0, separate instruments for each period unless collapsed)
    D.(trisk fbric) collapsed
------------------------------------------------------------------------------
Arellano-Bond test for AR(1) in first differences: z =  -1.69  Pr > z =  0.090
Arellano-Bond test for AR(2) in first differences: z =   0.01  Pr > z =  0.989
------------------------------------------------------------------------------
Sargan test of overid. restrictions: chi2(3)    =  16.41  Prob > chi2 =  0.001
  (Not robust, but not weakened by many instruments.)
Hansen test of overid. restrictions: chi2(3)    =   0.81  Prob > chi2 =  0.846
  (Robust, but weakened by many instruments.)

After incorporating year dummies (using only the year of crisis as the whole year dummies produced results with a lot of omission) with the below code

xtabond2 trisk l.trisk bind fenex femex feric crcomind femric fexric cbmeet l.rsanc inrel totd flev year2009,  gmm (trisk fbric, lag(1  1) collapse eq(diff)) gmm(trisk fbric, lag(0 0) collapse eq(level)) iv(bind fenex femex feric crcomind femric fexric cbmeet inrel l.rsanc totd flev year2009, equation(level)) two robust orthogonal small nodiffsargan

And got the following results.

Favoring speed over space. To switch, type or click on mata: mata set matafavor space, perm.
Warning: Number of instruments may be large relative to number of observations.
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: bankid                          Number of obs      =       131
Time variable : year                            Number of groups   =        15
Number of instruments = 17                      Obs per group: min =         7
F(14, 14)     =     17.44                                      avg =      8.73
Prob > F      =     0.000                                      max =         9
------------------------------------------------------------------------------
             |              Corrected
       trisk |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
       trisk |
         L1. |  -.8749704   .2377135    -3.68   0.002    -1.384815   -.3651257
             |
        bind |    .460755   .3272494     1.41   0.181     -.241125    1.162635
       fenex |   1.574508   .4670917     3.37   0.005     .5726958     2.57632
       femex |  -2.648738    .632774    -4.19   0.001    -4.005903   -1.291573
       feric |  -.5341961   .2986631    -1.79   0.095    -1.174765    .1063726
    crcomind |  -.5480378   .1809503    -3.03   0.009    -.9361377    -.159938
      femric |   .8974255   .2408319     3.73   0.002     .3808924    1.413959
      fexric |   -.667802   .3715153    -1.80   0.094    -1.464623     .129019
      cbmeet |   .0411593   .0423495     0.97   0.348    -.0496714      .13199
             |
       rsanc |
         L1. |   .4546769   1.049405     0.43   0.671    -1.796072    2.705426
             |
       inrel |   .0082195    .525221     0.02   0.988    -1.118267    1.134707
        totd |    .807954   .1310333     6.17   0.000     .5269155    1.088992
        flev |   .4677679   .1251064     3.74   0.002     .1994414    .7360944
    year2009 |          0  (omitted)
       _cons |  -.2411651    .171352    -1.41   0.181    -.6086787    .1263485
------------------------------------------------------------------------------
Instruments for orthogonal deviations equation
  GMM-type (missing=0, separate instruments for each period unless collapsed)
    L.(trisk fbric) collapsed
Instruments for levels equation
  Standard
    bind fenex femex feric crcomind femric fexric cbmeet inrel L.rsanc totd
    flev year2009
    _cons
  GMM-type (missing=0, separate instruments for each period unless collapsed)
    D.(trisk fbric) collapsed
------------------------------------------------------------------------------
Arellano-Bond test for AR(1) in first differences: z =  -1.69  Pr > z =  0.090
Arellano-Bond test for AR(2) in first differences: z =   0.01  Pr > z =  0.989
------------------------------------------------------------------------------
Sargan test of overid. restrictions: chi2(2)    =  16.41  Prob > chi2 =  0.000
  (Not robust, but not weakened by many instruments.)
Hansen test of overid. restrictions: chi2(2)    =   0.81  Prob > chi2 =  0.666
  (Robust, but weakened by many instruments.)


.

My concern however, is the number of instruments as literature suggests that number of instruments should be lower than number of groups. Can I use any of the above results? If not can you suggest what to do please.

[Sebastian Kripfganz]

A few remarks:

1. These estimators are designed for a large number of groups. 15 is definitely too small to expect reliable results. With that few observations, you need to resort to a much less sophisticated estimation strategy (maybe just a static fixed-effects estimation).
2. The coefficient of your lagged dependent variable is significantly negative. This hardly makes sense in any context and indicates that the applied method is not working properly for your data set.
3. xtabond2 suffers from several bugs that can invalidate your coefficient estimates or overidentification tests if you use forward-orthogonal deviations or have omitted coefficients in the estimation output. See my 2019 London Stata Conference presentation slides for details.

• Kripfganz, S. (2019). Generalized method of moments estimation of linear dynamic panel data models. Proceedings of the 2019 London Stata Conference.
• XTDPDGMM: new Stata command for GMM estimation of linear (dynamic) panel data models

[ismaila yusuf]

Dear Sebastian,
Thanks for your prompt response as well as your valuable suggestions. I really appreciate. As a follow-up, I have the following questions.
1. What is the minimum number of groups suitable for the estimation of GMM?
2. Considering the ability of GMM to address issues relating to endogeneity, what are the alternative estimation methods that can be used that will equally address endogeneity?
3. If a static fixed effects estimation is adopted as suggested how can endogeneity be addressed?

Thanks

[Sebastian Kripfganz]

1. There is no fixed threshold and I do not want to state a number that is then quoted by others out of context. The more groups, the merrier.
2. You could just use a simple 2SLS estimator. You could possibly still use the GMM estimator with few overidentifying restrictions but probably should restrict yourself to the one-step estimator then to avoid estimating the weighting matrix.
3. You could do a fixed-effects IV estimation, see xtivreg.

[ismaila yusuf]

Thanks once again for your response. One more question, please. How do I use the GMM estimator with few overidentifying restrictions? Some examples with Stata codes will be appreciated.

[Sebastian Kripfganz]

Your initial code would already be such an example. You were estimating 14 parameters with 17 instruments. This yields just 3 overidentifying restrictions. Just remove the twostep option. My remarks 2 and 3 in post #2 above still apply.

[ismaila yusuf]

After removing two as advised I have this code

 xtabond2 trisk l.trisk bind fenex femex feric crcomind femric fexric cbmeet l.rsanc inrel totd flev,  gmm (trisk fbric, lag(1  1) collapse eq(diff)) gmm(trisk fbric, lag(0 0) collapse eq(level)) iv(bind fenex femex feric crcomind femric fexri cbmeet inrel l.rsanc totd flev, equation(level)) robust orthogonal small nodiffsargan

with the below result

Favoring speed over space. To switch, type or click on mata: mata set matafavor space, per
> m.
Warning: Number of instruments may be large relative to number of observations.
Warning: Two-step estimated covariance matrix of moments is singular.
  Using a generalized inverse to calculate robust weighting matrix for Hansen test.

Dynamic panel-data estimation, one-step system GMM
------------------------------------------------------------------------------
Group variable: bankid                          Number of obs      =       131
Time variable : year                            Number of groups   =        15
Number of instruments = 17                      Obs per group: min =         7
F(13, 14)     =    148.09                                      avg =      8.73
Prob > F      =     0.000                                      max =         9
------------------------------------------------------------------------------
             |               Robust
       trisk |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
       trisk |
         L1. |   -.677591   .2109977    -3.21   0.006    -1.130136   -.2250458
             |
        bind |   .3086724   .2687741     1.15   0.270    -.2677907    .8851355
       fenex |   .2909774   .2071313     1.40   0.182    -.1532751    .7352298
       femex |   .4839643   .2103207     2.30   0.037     .0328713    .9350572
       feric |  -.2123313   .1866258    -1.14   0.274    -.6126039    .1879413
    crcomind |  -.0826788   .1277812    -0.65   0.528    -.3567422    .1913847
      femric |  -.2140739   .2293999    -0.93   0.367    -.7060878      .27794
      fexric |  -.1755199   .3046504    -0.58   0.574      -.82893    .4778902
      cbmeet |  -.0228536   .0514009    -0.44   0.663    -.1330975    .0873904
             |
       rsanc |
         L1. |   .1616112   .0558429     2.89   0.012     .0418401    .2813823
             |
       inrel |   .6103739    .499814     1.22   0.242    -.4616206    1.682368
        totd |   .6444273   .1382672     4.66   0.000     .3478736     .940981
        flev |   .5292525   .1035761     5.11   0.000     .3071038    .7514011
       _cons |  -.0469939   .1797152    -0.26   0.798    -.4324447    .3384568
------------------------------------------------------------------------------
Instruments for orthogonal deviations equation
  GMM-type (missing=0, separate instruments for each period unless collapsed)
    L.(trisk fbric) collapsed
Instruments for levels equation
  Standard
    bind fenex femex feric crcomind femric fexric cbmeet inrel L.rsanc totd
    flev
    _cons
  GMM-type (missing=0, separate instruments for each period unless collapsed)
    D.(trisk fbric) collapsed
------------------------------------------------------------------------------
Arellano-Bond test for AR(1) in first differences: z =  -1.56  Pr > z =  0.120
Arellano-Bond test for AR(2) in first differences: z =  -2.49  Pr > z =  0.013
------------------------------------------------------------------------------
Sargan test of overid. restrictions: chi2(3)    =  16.41  Prob > chi2 =  0.001
  (Not robust, but not weakened by many instruments.)
Hansen test of overid. restrictions: chi2(3)    =   0.81  Prob > chi2 =  0.846
  (Robust, but weakened by many instruments.)

Then with dummy as

. xtabond2 trisk l.trisk bind fenex femex feric crcomind femric fexric cbmeet l.rsanc inrel totd flev year2009,  gmm (trisk fbric, lag(1  1) collapse eq(diff)) gmm(trisk fbric, lag(0 0) collapse eq(level)) iv(bind fenex femex feric crcomind femric fexric cbmeet inrel l.rsanc totd flev year2009, equation(level)) robust orthogonal small nodiffsargan

with the following result

avoring speed over space. To switch, type or click on mata: mata set matafavor space, per
> m.
Warning: Number of instruments may be large relative to number of observations.
Warning: Two-step estimated covariance matrix of moments is singular.
  Using a generalized inverse to calculate robust weighting matrix for Hansen test.

Dynamic panel-data estimation, one-step system GMM
------------------------------------------------------------------------------
Group variable: bankid                          Number of obs      =       131
Time variable : year                            Number of groups   =        15
Number of instruments = 17                      Obs per group: min =         7
F(14, 14)     =    136.33                                      avg =      8.73
Prob > F      =     0.000                                      max =         9
------------------------------------------------------------------------------
             |               Robust
       trisk |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
       trisk |
         L1. |   -.677591   .2119053    -3.20   0.006    -1.132083   -.2230994
             |
        bind |   .3086724   .2699301     1.14   0.272    -.2702701    .8876149
       fenex |   .2909774   .2080222     1.40   0.184    -.1551859    .7371406
       femex |   .4839643   .2112253     2.29   0.038     .0309311    .9369974
       feric |  -.2123313   .1874285    -1.13   0.276    -.6143256    .1896629
    crcomind |  -.0826788   .1283308    -0.64   0.530     -.357921    .1925634
      femric |  -.2140739   .2303866    -0.93   0.369     -.708204    .2800562
      fexric |  -.1755199   .3059607    -0.57   0.575    -.8317403    .4807006
      cbmeet |  -.0228536   .0516219    -0.44   0.665    -.1335716    .0878645
             |
       rsanc |
         L1. |   .1616112   .0560831     2.88   0.012     .0413249    .2818975
             |
       inrel |   .6103739   .5019638     1.22   0.244    -.4662313    1.686979
        totd |   .6444273   .1388619     4.64   0.000     .3465981    .9422565
        flev |   .5292525   .1040216     5.09   0.000     .3061483    .7523566
    year2009 |          0  (omitted)
       _cons |  -.0469939   .1804882    -0.26   0.798    -.4341025    .3401147
------------------------------------------------------------------------------
Instruments for orthogonal deviations equation
  GMM-type (missing=0, separate instruments for each period unless collapsed)
    L.(trisk fbric) collapsed
Instruments for levels equation
  Standard
    bind fenex femex feric crcomind femric fexric cbmeet inrel L.rsanc totd
    flev year2009
    _cons
  GMM-type (missing=0, separate instruments for each period unless collapsed)
    D.(trisk fbric) collapsed
------------------------------------------------------------------------------
Arellano-Bond test for AR(1) in first differences: z =  -1.56  Pr > z =  0.120
Arellano-Bond test for AR(2) in first differences: z =  -2.49  Pr > z =  0.013
------------------------------------------------------------------------------
Sargan test of overid. restrictions: chi2(2)    =  16.41  Prob > chi2 =  0.000
  (Not robust, but not weakened by many instruments.)
Hansen test of overid. restrictions: chi2(2)    =   0.81  Prob > chi2 =  0.666
  (Robust, but weakened by many instruments.)

In both models, the AR(2) is significant, the lagged dependent variable has a negative coefficient while most of my main variables of interest are not significant. Should I then conclude that GMM cannot be used with my dataset?

[Sebastian Kripfganz]

It is hard to say why the coefficient of the lagged dependent variable is negative. It might be a consequence of the bug in xtabond2 that produces incorrect estimates when forward-orthogonal deviations are combined with standard instruments. I suggest to use my xtdpdgmm command instead to avoid this bug.

[ismaila yusuf]

Can you kindly assist to recommend how best to code my codes above using xtdpdgmm?

 
 xtabond2 trisk l.trisk bind fenex femex feric crcomind femric fexric cbmeet l.rsanc inrel totd flev,  gmm (trisk fbric, lag(1  1) collapse eq(diff)) gmm(trisk fbric, lag(0 0) collapse eq(level)) iv(bind fenex femex feric crcomind femric fexri cbmeet inrel l.rsanc totd flev, equation(level)) robust orthogonal small nodiffsargan

and

 
 xtabond2 trisk l.trisk bind fenex femex feric crcomind femric fexric cbmeet l.rsanc inrel totd flev year2009,  gmm (trisk fbric, lag(1  1) collapse eq(diff)) gmm(trisk fbric, lag(0 0) collapse eq(level)) iv(bind fenex femex feric crcomind femric fexric cbmeet inrel l.rsanc totd flev year2009, equation(level)) robust orthogonal small nodiffsargan

[Sebastian Kripfganz]

The first code can be translated as follows:

xtdpdgmm trisk l.trisk bind fenex femex feric crcomind femric fexric cbmeet l.rsanc inrel totd flev, gmm(trisk fbric, lag(0 0) collapse model(fodev)) gmm(trisk fbric, lag(0 0) collapse difference model(level)) iv(bind fenex femex feric crcomind femric fexri cbmeet inrel l.rsanc totd flev, model(level)) vce(robust) small

and similarly for the second code. Note that you are implicitly assuming that all the variables specified in the iv() option are exogenous, both with respect to the idiosyncratic error term and with respect to the unobserved unit-specific effects. That is a strong assumption.

[ismaila yusuf]

Thanks for helping out. I have tried the above code with the two-step option

xtdpdgmm trisk l.trisk bind fenex femex feric crcomind femric fexric cbmeet l.r
> sanc inrel totd flev, gmm(trisk fbric, lag(0 0) collapse model(fodev)) gmm(tris
> k fbric, lag(0 0) collapse difference model(level)) iv(bind fenex femex feric c
> rcomind femric fexri cbmeet inrel l.rsanc totd flev, model(level)) twostep vce(
> robust) small overid

Below is the result I obtained

Generalized method of moments estimation

Fitting full model:
Step 1         f(b) =  .01674888
Step 2         f(b) =   .0543286

Fitting reduced model 1:
Step 1         f(b) =  2.377e-20

Fitting reduced model 2:
Step 1         f(b) =  2.480e-19

Group variable: bankid                       Number of obs         =       131
Time variable: year                          Number of groups      =        15

Moment conditions:     linear =      17      Obs per group:    min =         7
                    nonlinear =       0                        avg =  8.733333
                        total =      17                        max =         9

                                (Std. Err. adjusted for 15 clusters in bankid)
------------------------------------------------------------------------------
             |              WC-Robust
       trisk |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
       trisk |
         L1. |  -.8750195   .2364837    -3.70   0.002    -1.382227   -.3678123
             |
        bind |   .4608648    .326181     1.41   0.180    -.2387238    1.160453
       fenex |   1.574367   .4644094     3.39   0.004     .5783082    2.570426
       femex |  -2.648058   .6272473    -4.22   0.001    -3.993369   -1.302746
       feric |  -.5341719   .2971813    -1.80   0.094    -1.171562    .1032186
    crcomind |  -.5480325   .1801222    -3.04   0.009    -.9343561   -.1617089
      femric |   .8972322   .2388865     3.76   0.002     .3848717    1.409593
      fexric |  -.6677633   .3696147    -1.81   0.092    -1.460508    .1249815
      cbmeet |   .0411668   .0421423     0.98   0.345    -.0492195    .1315531
             |
       rsanc |
         L1. |   .4544884    1.04386     0.44   0.670    -1.784368    2.693345
             |
       inrel |   .0082513   .5227057     0.02   0.988    -1.112841    1.129344
        totd |   .8078538   .1304895     6.19   0.000     .5279817    1.087726
        flev |   .4677845   .1245474     3.76   0.002     .2006568    .7349122
       _cons |  -.2411344   .1708703    -1.41   0.180    -.6076147     .125346
------------------------------------------------------------------------------
Instruments corresponding to the linear moment conditions:
 1, model(fodev):
   trisk fbric
 2, model(level):
   D.trisk D.fbric
 3, model(level):
   bind fenex femex feric crcomind femric fexric cbmeet inrel L.rsanc totd
   flev
 4, model(level):
   _cons

. estat overid

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

2-step moment functions, 2-step weighting matrix       chi2(3)     =    0.8149
                                                       Prob > chi2 =    0.8459

2-step moment functions, 3-step weighting matrix       chi2(3)     =   15.0000
                                                       Prob > chi2 =    0.0018

. 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) |     0.0000      2    1.0000 |      0.8149      1    0.3667
  2, model(level) |     0.0000      2    1.0000 |      0.8149      1    0.3667
  3, model(level) |          .     -9         . |           .      .         .
     model(level) |          .    -11         . |           .      .         .

I however, do not know whether this result is reliable considering you comment "The coefficient of your lagged dependent variable is significantly negative. This hardly makes sense in any context and indicates that the applied method is not working properly for your data set." And the moments condition exceeding number of groups.

[Mike Johnson]

1. There is no fixed threshold and I do not want to state a number that is then quoted by others out of context. The more groups, the merrier.
2. You could just use a simple 2SLS estimator. You could possibly still use the GMM estimator with few overidentifying restrictions but probably should restrict yourself to the one-step estimator then to avoid estimating the weighting matrix.
3. You could do a fixed-effects IV estimation, see xtivreg.

Dear Dr. Kripfganz,
if you could have please a look at my post I would be very thankful.
https://www.statalist.org/forums/for...eg-or-xtabond2