Xtabond2 for system GMM. Please help me for coding

[Celine Tran]

Dear all,

I am working with xtabond2 command in Stata to solve the endogenity problem of my estimation. I read the construction of doing xtabond2 from David Roodman. However, I am still confused that my coding is right or wrong. Could you please help?

Specifically, I want to write a code with xtabond2 command for system GMM as follows:

" lag2 and lag3 of the levels of firm performance variable, corporate governance variables (female, nonexe, dual, lnsize) and control variables (fsize lev) are employed as GMM-type instrumental variables for the first-differenced equation. Meanwhile, first lagged differences of firm performance, corporate governance, and control variables are used as GMM-type instruments for the levels equation.

Thank you very ,much in advance.

Regards,
Celine

[Roman Goossens]

Hi Celine,

I am no expert in xtabond2 but have used it a couple of times for my regressions but happy to try to help.

Could you please specify what is the equation that you are estimating (in your questions you only mention the instruments for the first difference and levels equations)? What are the exogenous regressors (if there are any)?

By the way, the discussion in the following link might be useful for you - although it focuses on the issue of using time dummies in xtabond2:

https://www.statalist.org/forums/for...m-time-dummies

Best,
Roman

[Eric de Souza]

This may help you start:
Stata comes with an built-in command called xtabond for dynamic panel data modelling. The command that we shall use has been developed by David Roodman of the Center for Global Development. It is called xtabond2 which can be downloaded from withing Stata with the command ssc install xtabond2.
1. Before using xtabond2 do not forget to xtset your data:
xtset panelid timeseriesid
where panelid is the variable identifying the “individual” and timeseriesid is the variable identifying the date.
2. xtabond2 first requires the name of the dependent variable followed by the list of explanatory variables. For instance (the data comes from:abdata.dta (-webuse abdata.dta-)
xtabond2 n L.n L2.n w L.w L(0/2).(k ys) yr*
n is the dependent variable (firm’s employment in log)
the other variables are the explanatory variables (the constant term is assumed)
L.n is n lagged once; L2.n is n lagged twice; w is firm’s wage level in log; L.w is w lagged once;
L(0/2) is short for lagged zero times, once and twice; the variables concerned follow in parentheses after a full-stop. Consequently, L(0/2).(k ys) stands for k, L.k, L2.k, y, L.y and L2.y.
yr* stands for all the variables in the dataset begining with yr.
After the names of the dependent variable and the explanatory variable follows a comma. After the comma follow the options.
3. It is almost always useful to put robust and small.
xtabond2 n L.n L2.n w L.w L(0/2).(k ys) yr*, robust small
4. The default is the one-step GMM estimator. If one wants a two-step GMM estimator, add twostep.
5. The default is the the Blundell-Bond system estimator which adds moment conditions on the levels. If one wants only the difference estimator, add noleveleq.
6. Now comes the list of instruments, both IV style instruments (the same variable for all the observations) and GMM style instruments (different variables for different observations). Note that there must be at least as many instruments as there are explanatory variables. Exogenous variables are their own instruments and must be listed here, either under ivstyle (strictly exogenous) or under gmmstyle (predetermined or endogenous).
6a. gmmstyle
For example, gmmstyle(L.(n w k)) states that all lagged values of L.n, L.w and L.k are to be treated as GMM instruments. To be clear, this means for n that L2.n, L3.n, and so on are the GMM instruments. Similarly, for w and for k.
For example, gmmstyle(L2.n L.(w k)) states that all lagged values of L2.n, L.w and L.k are to be treated as GMM instruments. Thus, for n, L3.n, L4.n, and so on are the GMM instruments, and for w and k, from the second lag on.
6b. ivstyle
For example, ivstyle(L(0/2).ys yr*) states that ys, L.ys, L2.ys and all the yr variables are to be considered as exogenous instruments.

Putting everything together we get:
xtabond2 n L(1/2).n L(0/1).w L(0/2).(k ys) yr*, gmmstyle(L2.n L.(w k)) ivstyle(L(0/2).ys yr*) robust small

7. We can, and mostly should, impose limits on the lags used as instruments in order to reduce the number of instruments.
xtabond2 n L(1/2).n L(0/1).w L(0/2).(k ys) yr*,
gmmstyle(L2.n L.(w k), laglimits(1 3)) ivstyle(L(0/2).ys yr*)
robust small.
The above command says to take as GMM instruments, L2.n, L.w and L.k lagged once, twice and three times.
Note that gmmstyle(L2.n) is equivalent to gmmstyle(n, laglimits(3 .), the dot indicating to go backwards till the start of the sample

[Sebastian Kripfganz]

More on GMM estimation of dynamic panel models (with a focus on another command as an alternative to xtabond2):
XTDPDGMM: new Stata command for efficient GMM estimation of linear (dynamic) panel models with nonlinear moment conditions

[Celine Tran]

Dear Eric, Sebastian and Roman,

First of all, thank you very much for your reply. You provide me a deep-understanding of using xtabond2. I try to write the code, but honestly, I am not self-confident. Back to my question, I need to code for this:

lag2 and lag3 of the levels of firm performance variable (lnTobin), corporate governance variables (female, nonexe, dual, lnsize) and control variables (fsize lev) are employed as GMM-type instrumental variables for the first-differenced equation. Meanwhile, first lagged differences of firm performance, corporate governance, and control variables are used as GMM-type instruments for the levels equation. Firm age (lnage) anf year dummies are exogenously determined


My code is: xtabond2 lnTobin L.lnTobin female nonexe dual lnsize fsize lev lnage i.year i.firmid, gmm(L.lnTobin,lag(1 2)) gmm(female nonexe dual lnsize fsize lev,lag(1 1)) iv(lnage i.year ) small two

I use i.year and i.firmid to control firm-fixed effect and year-fixed effect. So, from your point of view, my code is reasonable or not?

Also, I have 1355 observations and the number of instruments are 247. Is it too many instruments?

Moreover, choosing lag2 and lag3 as I am doing depends on each research, right? I mean that I can choose any levels of lag as long as system GMM gives me the good results? I am sorry if this question is stupid, but the more I read, the more confused I feel

In addition, do all of my explanatory variables have to be listed under gmm() or iv(). Because apart from variables in my code, I want to add two variables: after (dummy variable takes value of 1 if after crisis) and after*female (interaction variable) to my original equation in order to examine the effect of crisis for robustness check.

I look forward to hearing from you.

Regards.
Celine.

[Roman Goossens]

Hi Celine,

I will let the experts help on your more specific questions.

If not already done so, on your questions on the number of instruments, my advice is to carefully read Roodman's "A note on the theme of too many instruments" (see link below). In particular, in xtabond2 regression output make sure that you note the Hansen test of joint significance of instrument p-value. He mentions techniques to reduce instrument count like using "collapse" sub-option.

https://www.cgdev.org/publication/no...king-paper-125

Best,
Roman

[Sebastian Kripfganz]

1. Since Roman mentioned the Hansen test, note that there is a bug in xtabond2 that results in incorrect degrees of freedom for the overidentification test if time dummies (and possibly other dummies as well) are specified with the factor variable notation. Some dummies will be "omitted" from the regression due to the dynamic nature of the model but xtabond2 still lists them in the regression output. Moreover, it counts those variables as if there coefficients were estimated. As a consequence, the number of overidentifying restrictions is computed incorrectly. This in turn implies that the p-values from the overidentification tests are incorrect. To deal with this problem, you need to generate your time dummies as new variables first and then specify the correct number of them separately as regressors such that none of them is shown as "omitted". (The same applies to any other variable shown as "ommited".) Alternatively, you could use the xtdpdgmm command that I referenced earlier which has the option teffects that automatically adds the right number of time dummies and corresponding instruments.
2. You have specified firm dummies as regressors. If you want to do that, you also need to specify them as standard instruments (similar to time dummies). That said, your data appears to contain observations at the firm level. You then do not explicitly specify these firm-fixed effects at all. The idea of the GMM estimator is to treat those as unobserved effects and find instrumental variables that are uncorrelated with them.
3. I highly recommend to always specify the instruments for the first-differenced model and the level model separately with the suboption equation(diff) or equation(level). The default specification is easily misunderstood with unintended consequences. In particular the iv() option without an explicit specification of the equation is most likely not doing what you think it does.
4. I second Roman's recommendation to use the collapse suboption to reduce the number of instruments. Your large number of instruments indicates that the number of time periods in your data set is possibly relatively large. You want to keep in mind that these methods are designed for "small T, large N" data sets.
5. With a complete set of time dummies, you cannot add a post-crisis dummy because it would be perfectly collinear with the time dummies. However, you can add the interaction effect. You can as well add the interaction effect as an instrument similar to your variable female.
6. With the twostep estimator, you certainly should use robust standard errors (with the Windmeijer correction).
7. Besides the Hansen test, you also want to check the Arellano-Bond AR(2) test. The chosen lags of the dependent variable are only valid instruments if there is no second-order serial correlation in the first-differenced error term.

[Celine Tran]

Dear Roman and Sebastian,

Thank you very much for your reply. I think it will be better if I show you the result of my regression using xtabond2. However, I do not how to post it here. Now, I only know how to post the code. Could you please teach me?

Regards,
Celine

[Sebastian Kripfganz]

You can post the results in the same way as you post code by copying the results from Stata and posting them here with CODE delimiters:
Statalist FAQ 12.3

[Celine Tran]

Dear Sebastian,

Thank you very much for your support. I post my results with alternative suboptions. lnTobin is firm performance, PerFD is female, AfterFD is the interaction between female and after crisis. After takes value 1 if year is greater than 2009.

**** Fist, with collapse and no robust

xtabond2 lnTobin L.lnTobin PerFD After AfterFD PerInD Dual bsize lnage Firmsize blev i.ind i.year if year1!=0, gmm(lnTobin PerFD AfterFD PerInD Dual bsize Firmsize blev,lag(2 3) collapse) iv(After lnage i.year ) small two

 xtabond2 lnTobin L.lnTobin PerFD After AfterFD PerInD Dual bsize lnage Firmsize blev i.ind i.year if year1!=0, gmm(lnTobin PerFD AfterFD PerInD Dual bsize Firms
> ize blev,lag(2 3) collapse) iv(After lnage i.year ) small two
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.
  Difference-in-Sargan/Hansen statistics may be negative.

Dynamic panel-data estimation, two-step system GMM
------------------------------------------------------------------------------
Group variable: firmid                          Number of obs      =       394
Time variable : year                            Number of groups   =        56
Number of instruments = 43                      Obs per group: min =         2
F(34, 55)     =     24.87                                      avg =      7.04
Prob > F      =     0.000                                      max =         9
------------------------------------------------------------------------------
     lnTobin |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
     lnTobin |
         L1. |   .3523711   .1262988     2.79   0.007     .0992626    .6054796
             |
       PerFD |  -1.335537   .7433627    -1.80   0.078    -2.825269    .1541949
       After |   .2200987   .1249274     1.76   0.084    -.0302614    .4704588
     AfterFD |  -1.604136   .8986387    -1.79   0.080    -3.405048    .1967763
      PerInD |    .135925   .5363142     0.25   0.801    -.9388727    1.210723
        Dual |   .0342689   .2775003     0.12   0.902    -.5218542    .5903919
       bsize |   .2977324   .3432733     0.87   0.390    -.3902027    .9856675
       lnage |  -.0100809   .1031349    -0.10   0.922    -.2167679    .1966061
    Firmsize |  -.1116272   .1324036    -0.84   0.403      -.37697    .1537155
        blev |  -.0135714   .3042264    -0.04   0.965    -.6232548    .5961119
             |
         ind |
          1  |          0  (empty)
          2  |   1.660029   1.632061     1.02   0.314    -1.610694    4.930753
          3  |   1.129424   1.440401     0.78   0.436    -1.757205    4.016053
          5  |   .4687588   1.508648     0.31   0.757     -2.55464    3.492157
          6  |  -2.018105   4.693255    -0.43   0.669     -11.4236    7.387388
          7  |   2.196901   1.224097     1.79   0.078    -.2562451    4.650046
             |
        year |
       2000  |          0  (empty)
       2001  |    .598396   1.557236     0.38   0.702    -2.522374    3.719166
       2002  |   .5599786    1.44977     0.39   0.701    -2.345426    3.465383
       2003  |   .7640272   1.398761     0.55   0.587    -2.039153    3.567207
       2004  |   .8489094   1.400778     0.61   0.547    -1.958312    3.656131
       2005  |   .8253656   1.484976     0.56   0.581    -2.150592    3.801323
       2006  |   .7962406   1.458897     0.55   0.587    -2.127455    3.719936
       2007  |   .8973492   1.502829     0.60   0.553    -2.114387    3.909086
       2008  |   .4647732   1.481119     0.31   0.755    -2.503455    3.433001
       2009  |   .6074323    1.46098     0.42   0.679    -2.320437    3.535301
       2010  |   .7878192    1.49764     0.53   0.601    -2.213518    3.789157
       2011  |   .7057252   1.530876     0.46   0.647    -2.362219    3.773669
       2012  |   .7614529   1.539492     0.49   0.623    -2.323757    3.846663
       2013  |   .7369199   1.525574     0.48   0.631    -2.320399    3.794239
       2014  |   .5892848   1.486905     0.40   0.693    -2.390539    3.569109
       2015  |   .5317266   1.481738     0.36   0.721    -2.437743    3.501196
       2016  |   .4323573   1.473709     0.29   0.770    -2.521022    3.385737
       2017  |   .4389145    1.42488     0.31   0.759    -2.416609    3.294438
             |
       _cons |          0  (omitted)
------------------------------------------------------------------------------
Warning: Uncorrected two-step standard errors are unreliable.

Instruments for first differences equation
  Standard
    D.(After lnage 2000b.year 2001.year 2002.year 2003.year 2004.year
    2005.year 2006.year 2007.year 2008.year 2009.year 2010.year 2011.year
    2012.year 2013.year 2014.year 2015.year 2016.year 2017.year)
  GMM-type (missing=0, separate instruments for each period unless collapsed)
    L(2/3).(lnTobin PerFD AfterFD PerInD Dual bsize Firmsize blev) collapsed
Instruments for levels equation
  Standard
    After lnage 2000b.year 2001.year 2002.year 2003.year 2004.year 2005.year
    2006.year 2007.year 2008.year 2009.year 2010.year 2011.year 2012.year
    2013.year 2014.year 2015.year 2016.year 2017.year
    _cons
  GMM-type (missing=0, separate instruments for each period unless collapsed)
    DL.(lnTobin PerFD AfterFD PerInD Dual bsize Firmsize blev) collapsed
------------------------------------------------------------------------------
Arellano-Bond test for AR(1) in first differences: z =  -3.88  Pr > z =  0.000
Arellano-Bond test for AR(2) in first differences: z =  -1.25  Pr > z =  0.212
------------------------------------------------------------------------------
Sargan test of overid. restrictions: chi2(8)    =  12.96  Prob > chi2 =  0.113
  (Not robust, but not weakened by many instruments.)
Hansen test of overid. restrictions: chi2(8)    =   8.76  Prob > chi2 =  0.363
  (Robust, but weakened by many instruments.)

Difference-in-Hansen tests of exogeneity of instrument subsets:
  GMM instruments for levels
    Hansen test excluding group:     chi2(0)    =   3.09  Prob > chi2 =      . --> why missing is here? 
    Difference (null H = exogenous): chi2(8)    =   5.67  Prob > chi2 =  0.685

*** Second, with collapse and robust

xtabond2 lnTobin L.lnTobin PerFD After AfterFD PerInD Dual bsize lnage Firmsize blev i.ind i.year if year1!=0, gmm(lnTobin PerFD AfterFD PerInD Dual bsize Firmsize blev,lag(2 3) collapse) iv(After lnage i.year ) small two ro

. xtabond2 lnTobin L.lnTobin PerFD After AfterFD PerInD Dual bsize lnage Firmsize
>  blev i.ind i.year if year1!=0, gmm(lnTobin PerFD AfterFD PerInD Dual bsize Fir
> msize blev,lag(2 3) collapse) iv(After lnage i.year ) ro small two
Favoring space over speed. To switch, type or click on mata: mata set matafavor s
> peed, perm.
Warning: Two-step estimated covariance matrix of moments is singular.
  Using a generalized inverse to calculate optimal weighting matrix for two-step
> estimation.
  Difference-in-Sargan/Hansen statistics may be negative.

Dynamic panel-data estimation, two-step system GMM
------------------------------------------------------------------------------
Group variable: firmid                          Number of obs      =       394
Time variable : year                            Number of groups   =        56
Number of instruments = 43                      Obs per group: min =         2
F(34, 55)     =      8.58                                      avg =      7.04
Prob > F      =     0.000                                      max =         9
------------------------------------------------------------------------------
             |              Corrected
     lnTobin |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
     lnTobin |
         L1. |   .3523711   .2737338     1.29   0.203    -.1962038     .900946
             |
       PerFD |  -1.335537   1.405996    -0.95   0.346    -4.153216    1.482142
       After |   .2200987   .2543287     0.87   0.391    -.2895874    .7297847
     AfterFD |  -1.604136   1.855624    -0.86   0.391     -5.32289    2.114618
      PerInD |    .135925   .7967396     0.17   0.865    -1.460777    1.732627
        Dual |   .0342689     .48426     0.07   0.944    -.9362098    1.004747
       bsize |   .2977324   .5603885     0.53   0.597    -.8253113    1.420776
       lnage |  -.0100809   .1637304    -0.06   0.951    -.3382039    .3180421
    Firmsize |  -.1116272   .2365352    -0.47   0.639    -.5856544    .3623999
        blev |  -.0135714   .5798735    -0.02   0.981    -1.175664    1.148521
             |
         ind |
          1  |          0  (empty)
          2  |   1.660029   3.001084     0.55   0.582    -4.354278    7.674337
          3  |   1.129424   2.092185     0.54   0.591    -3.063409    5.322257
          5  |   .4687588   2.291292     0.20   0.839    -4.123093    5.060611
          6  |  -2.018105   6.388229    -0.32   0.753     -14.8204    10.78419
          7  |   2.196901   2.378022     0.92   0.360    -2.568763    6.962564
             |
        year |
       2000  |          0  (empty)
       2001  |    .598396   2.870038     0.21   0.836    -5.153288     6.35008
       2002  |   .5599786   2.640404     0.21   0.833    -4.731509    5.851466
       2003  |   .7640272   2.550259     0.30   0.766    -4.346807    5.874861
       2004  |   .8489094    2.56314     0.33   0.742    -4.287738    5.985557
       2005  |   .8253656   2.704881     0.31   0.761    -4.595336    6.246067
       2006  |   .7962406   2.613533     0.30   0.762    -4.441397    6.033878
       2007  |   .8973492   2.716127     0.33   0.742    -4.545891     6.34059
       2008  |   .4647732   2.663777     0.17   0.862    -4.873555    5.803101
       2009  |   .6074323   2.588356     0.23   0.815    -4.579749    5.794614
       2010  |   .7878192   2.676292     0.29   0.770    -4.575589    6.151227
       2011  |   .7057252   2.723513     0.26   0.797    -4.752316    6.163767
       2012  |   .7614529   2.746721     0.28   0.783    -4.743098    6.266004
       2013  |   .7369199   2.719152     0.27   0.787    -4.712383    6.186223
       2014  |   .5892848   2.651494     0.22   0.825    -4.724427    5.902997
       2015  |   .5317266   2.623048     0.20   0.840     -4.72498    5.788433
       2016  |   .4323573   2.622975     0.16   0.870    -4.824202    5.688917
       2017  |   .4389145   2.381903     0.18   0.854    -4.334525    5.212354
             |
       _cons |          0  (omitted)
------------------------------------------------------------------------------
Instruments for first differences equation
  Standard
    D.(After lnage 2000b.year 2001.year 2002.year 2003.year 2004.year
    2005.year 2006.year 2007.year 2008.year 2009.year 2010.year 2011.year
    2012.year 2013.year 2014.year 2015.year 2016.year 2017.year)
  GMM-type (missing=0, separate instruments for each period unless collapsed)
    L(2/3).(lnTobin PerFD AfterFD PerInD Dual bsize Firmsize blev) collapsed
Instruments for levels equation
  Standard
    After lnage 2000b.year 2001.year 2002.year 2003.year 2004.year 2005.year
    2006.year 2007.year 2008.year 2009.year 2010.year 2011.year 2012.year
    2013.year 2014.year 2015.year 2016.year 2017.year
    _cons
  GMM-type (missing=0, separate instruments for each period unless collapsed)
    DL.(lnTobin PerFD AfterFD PerInD Dual bsize Firmsize blev) collapsed
------------------------------------------------------------------------------
Arellano-Bond test for AR(1) in first differences: z =  -2.38  Pr > z =  0.017
Arellano-Bond test for AR(2) in first differences: z =  -1.22  Pr > z =  0.223
------------------------------------------------------------------------------
Sargan test of overid. restrictions: chi2(8)    =  12.96  Prob > chi2 =  0.113
  (Not robust, but not weakened by many instruments.)
Hansen test of overid. restrictions: chi2(8)    =   8.76  Prob > chi2 =  0.363
  (Robust, but weakened by many instruments.)

Difference-in-Hansen tests of exogeneity of instrument subsets:
  GMM instruments for levels
    Hansen test excluding group:     chi2(0)    =   3.09  Prob > chi2 =      . --> why missing is here? 
    Difference (null H = exogenous): chi2(8)    =   5.67  Prob > chi2 =  0.685

***** Third, no collapse and no robust

. xtabond2 lnTobin L.lnTobin PerFD After AfterFD PerInD Dual bsize lnage Firmsize
>  blev i.ind i.year if year1!=0, gmm(lnTobin PerFD AfterFD PerInD Dual bsize Fir
> msize blev,lag(2 3)) iv(After lnage i.year )small two
Favoring space over speed. To switch, type or click on mata: mata set matafavor s
> peed, 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.
  Difference-in-Sargan/Hansen statistics may be negative.

Dynamic panel-data estimation, two-step system GMM
------------------------------------------------------------------------------
Group variable: firmid                          Number of obs      =       394
Time variable : year                            Number of groups   =        56
Number of instruments = 312                     Obs per group: min =         2
F(34, 55)     =    339.92                                      avg =      7.04
Prob > F      =     0.000                                      max =         9
------------------------------------------------------------------------------
     lnTobin |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
     lnTobin |
         L1. |   .4805961   .1164257     4.13   0.000     .2472738    .7139184
             |
       PerFD |  -1.222444   .6661775    -1.84   0.072    -2.557494    .1126054
       After |  -.1627964   .0633084    -2.57   0.013    -.2896693   -.0359234
     AfterFD |   1.225304   .4666851     2.63   0.011     .2900464    2.160562
      PerInD |   -.457154   .5229581    -0.87   0.386    -1.505185    .5908775
        Dual |  -.0101742   .2949687    -0.03   0.973    -.6013047    .5809563
       bsize |   .1682281   .2121327     0.79   0.431    -.2568954    .5933515
       lnage |  -.0821159   .0638534    -1.29   0.204     -.210081    .0458491
    Firmsize |   .0280868   .0778619     0.36   0.720    -.1279519    .1841255
        blev |  -.4371834   .7731266    -0.57   0.574    -1.986564    1.112197
             |
         ind |
          1  |          0  (empty)
          2  |   .2839798   .4913256     0.58   0.566    -.7006587    1.268618
          3  |   .9052594   .8157604     1.11   0.272     -.729561     2.54008
          5  |    .636241    .520303     1.22   0.227    -.4064695    1.678951
          6  |   2.023066   1.879392     1.08   0.286    -1.743319    5.789451
          7  |   -.248122   .4014496    -0.62   0.539    -1.052645     .556401
             |
        year |
       2000  |          0  (empty)
       2001  |  -.4299022   1.179521    -0.36   0.717    -2.793715     1.93391
       2002  |  -.6989236   1.223122    -0.57   0.570    -3.150115    1.752268
       2003  |  -.5474336   1.222013    -0.45   0.656    -2.996403    1.901536
       2004  |  -.4911667   1.207034    -0.41   0.686    -2.910116    1.927783
       2005  |  -.6310194   1.212388    -0.52   0.605    -3.060699     1.79866
       2006  |   -.515228   1.191069    -0.43   0.667    -2.902183    1.871727
       2007  |  -.4534177   1.204957    -0.38   0.708    -2.868205     1.96137
       2008  |  -.8319659   1.205972    -0.69   0.493    -3.248788    1.584857
       2009  |  -.5871443   1.205153    -0.49   0.628    -3.002325    1.828036
       2010  |  -.5057532    1.19638    -0.42   0.674    -2.903352    1.891845
       2011  |  -.6096166   1.204785    -0.51   0.615     -3.02406    1.804827
       2012  |  -.5043277    1.19809    -0.42   0.675    -2.905354    1.896699
       2013  |   -.480569    1.19136    -0.40   0.688    -2.868109    1.906971
       2014  |  -.5283059   1.193195    -0.44   0.660    -2.919523    1.862911
       2015  |  -.5092208   1.187362    -0.43   0.670    -2.888747    1.870305
       2016  |  -.5385176   1.193336    -0.45   0.654    -2.930016    1.852981
       2017  |  -.3987228   1.191879    -0.33   0.739    -2.787301    1.989855
             |
       _cons |          0  (omitted)
------------------------------------------------------------------------------
Warning: Uncorrected two-step standard errors are unreliable.

Instruments for first differences equation
  Standard
    D.(After lnage 2000b.year 2001.year 2002.year 2003.year 2004.year
    2005.year 2006.year 2007.year 2008.year 2009.year 2010.year 2011.year
    2012.year 2013.year 2014.year 2015.year 2016.year 2017.year)
  GMM-type (missing=0, separate instruments for each period unless collapsed)
    L(2/3).(lnTobin PerFD AfterFD PerInD Dual bsize Firmsize blev)
Instruments for levels equation
  Standard
    After lnage 2000b.year 2001.year 2002.year 2003.year 2004.year 2005.year
    2006.year 2007.year 2008.year 2009.year 2010.year 2011.year 2012.year
    2013.year 2014.year 2015.year 2016.year 2017.year
    _cons
  GMM-type (missing=0, separate instruments for each period unless collapsed)
    DL.(lnTobin PerFD AfterFD PerInD Dual bsize Firmsize blev)
------------------------------------------------------------------------------
Arellano-Bond test for AR(1) in first differences: z =  -3.10  Pr > z =  0.002
Arellano-Bond test for AR(2) in first differences: z =  -0.72  Pr > z =  0.469
------------------------------------------------------------------------------
Sargan test of overid. restrictions: chi2(277)  = 299.23  Prob > chi2 =  0.171
  (Not robust, but not weakened by many instruments.)
Hansen test of overid. restrictions: chi2(277)  =  18.53  Prob > chi2 =  1.000
  (Robust, but weakened by many instruments.)

Difference-in-Hansen tests of exogeneity of instrument subsets:
  GMM instruments for levels
    Hansen test excluding group:     chi2(183)  =  19.62  Prob > chi2 =  1.000
    Difference (null H = exogenous): chi2(94)   =  -1.09  Prob > chi2 =  1.000
  iv(After lnage 2000b.year 2001.year 2002.year 2003.year 2004.year 2005.year 200
> 6.year 2007.year 2008.year 2009.year 2010.year 2011.year 2012.year 2013.year 20
> 14.year 2015.year 2016.year 2017.year)
    Hansen test excluding group:     chi2(259)  =  21.13  Prob > chi2 =  1.000
    Difference (null H = exogenous): chi2(18)   =  -2.60  Prob > chi2 =  1.000

*** Fourth, no collapse and robust

. xtabond2 lnTobin L.lnTobin PerFD After AfterFD PerInD Dual bsize lnage Firmsize
>  blev i.ind i.year if year1!=0, gmm(lnTobin PerFD AfterFD PerInD Dual bsize Fir
> msize blev,lag(2 3)) iv(After lnage i.year )small two ro
Favoring space over speed. To switch, type or click on mata: mata set matafavor s
> peed, 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.
  Difference-in-Sargan/Hansen statistics may be negative.

Dynamic panel-data estimation, two-step system GMM
------------------------------------------------------------------------------
Group variable: firmid                          Number of obs      =       394
Time variable : year                            Number of groups   =        56
Number of instruments = 312                     Obs per group: min =         2
F(34, 55)     =      6.17                                      avg =      7.04
Prob > F      =     0.000                                      max =         9
------------------------------------------------------------------------------
             |              Corrected
     lnTobin |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
     lnTobin |
         L1. |   .4805961   .1783996     2.69   0.009     .1230753     .838117
             |
       PerFD |  -1.222444   .9406888    -1.30   0.199    -3.107627    .6627385
       After |  -.1627964   .0735426    -2.21   0.031     -.310179   -.0154137
     AfterFD |   1.225304   .5153084     2.38   0.021      .192603    2.258005
      PerInD |   -.457154   .8177292    -0.56   0.578     -2.09592    1.181612
        Dual |  -.0101742   .3781457    -0.03   0.979    -.7679952    .7476467
       bsize |   .1682281   .3834558     0.44   0.663    -.6002345    .9366907
       lnage |  -.0821159    .100776    -0.81   0.419    -.2840756    .1198437
    Firmsize |   .0280868   .1502255     0.19   0.852    -.2729717    .3291453
        blev |  -.4371834    1.26591    -0.35   0.731    -2.974123    2.099756
             |
         ind |
          1  |          0  (empty)
          2  |   .2839798   .5457866     0.52   0.605     -.809801    1.377761
          3  |   .9052594    .944352     0.96   0.342    -.9872643    2.797783
          5  |    .636241   .2713932     2.34   0.023     .0923569    1.180125
          6  |   2.023066    2.34787     0.86   0.393    -2.682171    6.728303
          7  |   -.248122   .7343882    -0.34   0.737    -1.719869    1.223625
             |
        year |
       2000  |          0  (empty)
       2001  |  -.4299022   1.994269    -0.22   0.830    -4.426506    3.566702
       2002  |  -.6989236    2.05256    -0.34   0.735    -4.812346    3.414499
       2003  |  -.5474336   2.038021    -0.27   0.789     -4.63172    3.536852
       2004  |  -.4911667   2.015566    -0.24   0.808    -4.530452    3.548119
       2005  |  -.6310194   2.005022    -0.31   0.754    -4.649174    3.387135
       2006  |   -.515228   1.956104    -0.26   0.793    -4.435349    3.404893
       2007  |  -.4534177   1.978784    -0.23   0.820     -4.41899    3.512155
       2008  |  -.8319659   1.989813    -0.42   0.677    -4.819641    3.155709
       2009  |  -.5871443   1.986463    -0.30   0.769    -4.568106    3.393817
       2010  |  -.5057532    1.99128    -0.25   0.800    -4.496367     3.48486
       2011  |  -.6096166   1.998539    -0.31   0.761    -4.614778    3.395545
       2012  |  -.5043277   1.989052    -0.25   0.801    -4.490478    3.481822
       2013  |   -.480569   1.976756    -0.24   0.809    -4.442076    3.480938
       2014  |  -.5283059   1.992078    -0.27   0.792     -4.52052    3.463908
       2015  |  -.5092208   1.959989    -0.26   0.796    -4.437128    3.418686
       2016  |  -.5385176   1.955282    -0.28   0.784     -4.45699    3.379955
       2017  |  -.3987228   1.951972    -0.20   0.839    -4.310563    3.513117
             |
       _cons |          0  (omitted)
------------------------------------------------------------------------------
Instruments for first differences equation
  Standard
    D.(After lnage 2000b.year 2001.year 2002.year 2003.year 2004.year
    2005.year 2006.year 2007.year 2008.year 2009.year 2010.year 2011.year
    2012.year 2013.year 2014.year 2015.year 2016.year 2017.year)
  GMM-type (missing=0, separate instruments for each period unless collapsed)
    L(2/3).(lnTobin PerFD AfterFD PerInD Dual bsize Firmsize blev)
Instruments for levels equation
  Standard
    After lnage 2000b.year 2001.year 2002.year 2003.year 2004.year 2005.year
    2006.year 2007.year 2008.year 2009.year 2010.year 2011.year 2012.year
    2013.year 2014.year 2015.year 2016.year 2017.year
    _cons
  GMM-type (missing=0, separate instruments for each period unless collapsed)
    DL.(lnTobin PerFD AfterFD PerInD Dual bsize Firmsize blev)
------------------------------------------------------------------------------
Arellano-Bond test for AR(1) in first differences: z =  -2.67  Pr > z =  0.007
Arellano-Bond test for AR(2) in first differences: z =  -0.68  Pr > z =  0.499
------------------------------------------------------------------------------
Sargan test of overid. restrictions: chi2(277)  = 299.23  Prob > chi2 =  0.171
  (Not robust, but not weakened by many instruments.)
Hansen test of overid. restrictions: chi2(277)  =  18.53  Prob > chi2 =  1.000
  (Robust, but weakened by many instruments.)

Difference-in-Hansen tests of exogeneity of instrument subsets:
  GMM instruments for levels
    Hansen test excluding group:     chi2(183)  =  19.62  Prob > chi2 =  1.000
    Difference (null H = exogenous): chi2(94)   =  -1.09  Prob > chi2 =  1.000
  iv(After lnage 2000b.year 2001.year 2002.year 2003.year 2004.year 2005.year 200
> 6.year 2007.year 2008.year 2009.year 2010.year 2011.year 2012.year 2013.year 20
> 14.year 2015.year 2016.year 2017.year)
    Hansen test excluding group:     chi2(259)  =  21.13  Prob > chi2 =  1.000
    Difference (null H = exogenous): chi2(18)   =  -2.60  Prob > chi2 =  1.000

Which one is better? Or all of them are wrong?

Please give me some advice.

Thank you very much.


Regards,
Celine

[Sebastian Kripfganz]

Please see again my comment #7 above, in particular points 1, 3, and 6. (Point 1 applies both to "omitted" and "empty" coefficients.)

You should use the collapse option because your number of instruments otherwise becomes too large. You should always use robust standard errors.

[Celine Tran]

Dear Sebastian,

Thank you for your reply. Based on your suggestion,

you need to generate your time dummies as new variables first and then specify the correct number of them separately as regressors such that none of them is shown as "omitted". (The same applies to any other variable shown as "ommited".

, I correct my command and get the result as follows:

xtabond2 lnTobin L.lnTobin PerFD After AfterFD PerInD Dual bsize lnage Firmsize blev i.ind y* if year1!=0, gmm(lnTobin PerFD AfterFD PerInD Dual bsize Firmsize blev,lag(2 3) equation(diff) collapse) gmm(lnTobin PerFD AfterFD PerInD Dual bsize Firmsize blev,lag(1 1) equation(level) collapse) iv(After lnage y*) small two ro

Dynamic panel-data estimation, two-step system GMM
------------------------------------------------------------------------------
Group variable: firmid                          Number of obs      =       394
Time variable : year                            Number of groups   =        56
Number of instruments = 45                      Obs per group: min =         2
F(37, 55)     =      8.76                                      avg =      7.04
Prob > F      =     0.000                                      max =         9
------------------------------------------------------------------------------
             |              Corrected
     lnTobin |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
     lnTobin |
         L1. |   .4404488   .3807097     1.16   0.252    -.3225105    1.203408
             |
       PerFD |  -.8225264   1.230141    -0.67   0.507    -3.287784    1.642731
       After |   .1176677   .1190995     0.99   0.327    -.1210131    .3563485
     AfterFD |  -.9201294   1.632729    -0.56   0.575    -4.192191    2.351932
      PerInD |  -.0460676   1.726423    -0.03   0.979    -3.505896    3.413761
        Dual |   .0641464   .8186248     0.08   0.938    -1.576414    1.704707
       bsize |    .150266   .5300142     0.28   0.778    -.9119061    1.212438
       lnage |   .0095337   .1948223     0.05   0.961    -.3808989    .3999662
    Firmsize |  -.0507002   .3396815    -0.15   0.882    -.7314372    .6300367
        blev |   -.220553   .9226703    -0.24   0.812    -2.069626     1.62852
             |
         ind |
          1  |          0  (empty)
          2  |   2.302091   3.416848     0.67   0.503    -4.545425    9.149607
          3  |   2.421364   3.322556     0.73   0.469    -4.237187    9.079915
          5  |   2.137224   3.386171     0.63   0.531    -4.648815    8.923262
          6  |  -2.375508   6.733962    -0.35   0.726    -15.87067    11.11965
          7  |   .7392281   1.464321     0.50   0.616    -2.195336    3.673792
             |
        year |  -.0005673   .0022124    -0.26   0.799    -.0050011    .0038665
       year1 |  -.4763549   .5060122    -0.94   0.351    -1.490426    .5377162
       year2 |   .4678886    .520104     0.90   0.372    -.5744232      1.5102
       y2000 |          0  (omitted)
       y2001 |   .4996831   2.856119     0.17   0.862    -5.224108    6.223474
       y2002 |   .1572196   2.482985     0.06   0.950    -4.818794    5.133233
       y2003 |   .1615077   2.127877     0.08   0.940    -4.102853    4.425868
       y2004 |   .1740824    2.02272     0.09   0.932     -3.87954    4.227704
       y2005 |   .1318876   1.908488     0.07   0.945    -3.692807    3.956582
       y2006 |   .2134917   1.626055     0.13   0.896    -3.045194    3.472178
       y2007 |   .2938357   1.594246     0.18   0.854    -2.901105    3.488777
       y2008 |   -.139344   1.522774    -0.09   0.927    -3.191052    2.912364
       y2009 |   .0060844    1.23767     0.00   0.996    -2.474262    2.486431
       y2010 |   .1670342   1.190685     0.14   0.889    -2.219153    2.553221
       y2011 |   .0636042   1.171887     0.05   0.957    -2.284911    2.412119
       y2012 |   .1842879   1.043534     0.18   0.860       -1.907    2.275576
       y2013 |   .2021841   .9765195     0.21   0.837    -1.754805    2.159173
       y2014 |   .0727739   .8281574     0.09   0.930    -1.586891    1.732438
       y2015 |   .1036465   .6197596     0.17   0.868     -1.13838    1.345672
       y2016 |   .0880124   .4546119     0.19   0.847    -.8230502     .999075
       y2017 |          0  (omitted)
       _cons |          0  (omitted)
------------------------------------------------------------------------------
Instruments for first differences equation
  Standard
    D.(After lnage year year1 year2 y2000 y2001 y2002 y2003 y2004 y2005 y2006
    y2007 y2008 y2009 y2010 y2011 y2012 y2013 y2014 y2015 y2016 y2017)
  GMM-type (missing=0, separate instruments for each period unless collapsed)
    L(2/3).(lnTobin PerFD AfterFD PerInD Dual bsize Firmsize blev) collapsed
Instruments for levels equation
  Standard
    After lnage year year1 year2 y2000 y2001 y2002 y2003 y2004 y2005 y2006
    y2007 y2008 y2009 y2010 y2011 y2012 y2013 y2014 y2015 y2016 y2017
    _cons
  GMM-type (missing=0, separate instruments for each period unless collapsed)
    DL.(lnTobin PerFD AfterFD PerInD Dual bsize Firmsize blev) collapsed
------------------------------------------------------------------------------
Arellano-Bond test for AR(1) in first differences: z =  -1.75  Pr > z =  0.080
Arellano-Bond test for AR(2) in first differences: z =  -1.06  Pr > z =  0.288
------------------------------------------------------------------------------
Sargan test of overid. restrictions: chi2(7)    =  10.40  Prob > chi2 =  0.167
  (Not robust, but not weakened by many instruments.)
Hansen test of overid. restrictions: chi2(7)    =   8.76  Prob > chi2 =  0.270
  (Robust, but weakened by many instruments.)

However, Diff-in-Hansen tests of exogeneity disappear. Could you please explain why?

Moreover, in the case of that p-value of Hansen test excluding group is missing, does it mean? Could you please give me the explanation?

Difference-in-Hansen tests of exogeneity of instrument subsets:
  GMM instruments for levels
    Hansen test excluding group:     chi2(0)    =   3.09  Prob > chi2 =      .
    Difference (null H = exogenous): chi2(8)    =   5.67  Prob > chi2 =  0.685

Thank you very much.

Regards,
Anh.

[Sebastian Kripfganz]

The problem with your time dummies is still not solved. Using y* with the placeholder is dangerous because it includes all variables that start with y, not just the time dummies. Try y2000-y2017 instead. With the industry dummies, you have the same problem. None of the coefficients in the regression output should be listed as "(omitted)" or "(empty)". If you deal with these problems, the concern about the Hansen test might be addressed automatically because it is related to this problem.

[Celine Tran]

Dear Sebastian,

I try to do as your suggestion, but results does not change. Please have a look.

xtabond2 lnTobin L.lnTobin PerFD After AfterFD PerInD Dual bsize lnage Firmsize blev ind1-ind7 y2000-y2017 if year1!=0, gmm(lnTobin PerFD AfterFD PerInD Dual bsize Firmsize blev,lag(2 3) collapse) iv(After lnage y2000-y2017) small two ro

Dynamic panel-data estimation, two-step system GMM
------------------------------------------------------------------------------
Group variable: firmid                          Number of obs      =       394
Time variable : year                            Number of groups   =        56
Number of instruments = 43                      Obs per group: min =         2
F(35, 55)     =      8.31                                      avg =      7.04
Prob > F      =     0.000                                      max =         9
------------------------------------------------------------------------------
             |              Corrected
     lnTobin |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
     lnTobin |
         L1. |   .3523711   .2741159     1.29   0.204    -.1969694    .9017116
             |
       PerFD |  -1.335537   1.407958    -0.95   0.347    -4.157149    1.486074
       After |   .2200987   .2546836     0.86   0.391    -.2902987    .7304961
     AfterFD |  -1.604136   1.858214    -0.86   0.392     -5.32808    2.119809
      PerInD |    .135925   .7978516     0.17   0.865    -1.463005    1.734855
        Dual |   .0342689   .4849358     0.07   0.944    -.9375642    1.006102
       bsize |   .2977324   .5611707     0.53   0.598    -.8268787    1.422344
       lnage |  -.0100809   .1639589    -0.06   0.951    -.3386618       .3185
    Firmsize |  -.1116272   .2368653    -0.47   0.639     -.586316    .3630615
        blev |  -.0135714   .5806828    -0.02   0.981    -1.177286    1.150143
        ind1 |   2.018105   6.397145     0.32   0.754    -10.80206    14.83827
        ind2 |   3.678134   7.933658     0.46   0.645    -12.22127    19.57754
        ind3 |   3.147529   6.955576     0.45   0.653    -10.79176    17.08681
        ind4 |          0  (omitted)
        ind5 |   2.486864   6.943041     0.36   0.722     -11.4273    16.40103
        ind6 |          0  (omitted)
        ind7 |   4.215005   7.198206     0.59   0.561    -10.21052    18.64053
       y2000 |          0  (omitted)
       y2001 |  -1.419709   6.259732    -0.23   0.821    -13.96449    11.12507
       y2002 |  -1.458126   6.214618    -0.23   0.815     -13.9125    10.99625
       y2003 |  -1.254078   6.249519    -0.20   0.842    -13.77839    11.27024
       y2004 |  -1.169195   6.253608    -0.19   0.852     -13.7017    11.36331
       y2005 |  -1.192739   6.309744    -0.19   0.851    -13.83775    11.45227
       y2006 |  -1.221864   6.341947    -0.19   0.848    -13.93141    11.48768
       y2007 |  -1.120756   6.299741    -0.18   0.859    -13.74572    11.50421
       y2008 |  -1.553331   6.290769    -0.25   0.806    -14.16032    11.05365
       y2009 |  -1.410672   6.328202    -0.22   0.824    -14.09267    11.27133
       y2010 |  -1.230285   6.313336    -0.19   0.846    -13.88249    11.42192
       y2011 |  -1.312379   6.322832    -0.21   0.836    -13.98362    11.35886
       y2012 |  -1.256652   6.328579    -0.20   0.843    -13.93941     11.4261
       y2013 |  -1.281185    6.31299    -0.20   0.840     -13.9327    11.37033
       y2014 |   -1.42882    6.30573    -0.23   0.822    -14.06579    11.20815
       y2015 |  -1.486378   6.312048    -0.24   0.815    -14.13601    11.16325
       y2016 |  -1.585747   6.296255    -0.25   0.802    -14.20372    11.03223
       y2017 |   -1.57919   6.509219    -0.24   0.809    -14.62396    11.46558
       _cons |          0  (omitted)
------------------------------------------------------------------------------
Instruments for first differences equation
  Standard
    D.(After lnage y2000 y2001 y2002 y2003 y2004 y2005 y2006 y2007 y2008 y2009
    y2010 y2011 y2012 y2013 y2014 y2015 y2016 y2017)
  GMM-type (missing=0, separate instruments for each period unless collapsed)
    L(2/3).(lnTobin PerFD AfterFD PerInD Dual bsize Firmsize blev) collapsed
Instruments for levels equation
  Standard
    After lnage y2000 y2001 y2002 y2003 y2004 y2005 y2006 y2007 y2008 y2009
    y2010 y2011 y2012 y2013 y2014 y2015 y2016 y2017
    _cons
  GMM-type (missing=0, separate instruments for each period unless collapsed)
    DL.(lnTobin PerFD AfterFD PerInD Dual bsize Firmsize blev) collapsed
------------------------------------------------------------------------------
Arellano-Bond test for AR(1) in first differences: z =  -2.38  Pr > z =  0.017
Arellano-Bond test for AR(2) in first differences: z =  -1.22  Pr > z =  0.223
------------------------------------------------------------------------------
Sargan test of overid. restrictions: chi2(7)    =  12.96  Prob > chi2 =  0.073
  (Not robust, but not weakened by many instruments.)
Hansen test of overid. restrictions: chi2(7)    =   8.76  Prob > chi2 =  0.271
  (Robust, but weakened by many instruments.)


.

Do you have any suggestion for me?

Regards,
Celine

[Sebastian Kripfganz]

Why do you specify the if year1!=0 condition?

You need to specify the industry dummies in the list of instruments as well.

There is still perfect collinearity among the dummy variables. Please provide the Stata output of the following command after the estimation:

sum year if e(sample)