xtabond2

[Simon Briggs]

Dear Statalist members,

I have been trying to implement xtabond2 in my undergraduate thesis. I have decided that the first-difference of a democracy variable (polity) may not be a good instrument, since it will change slowly over time (i.e. many differences will be 0). Thus I would like to check I have told Stata to just used the lagged levels for this variable, rather than the differences as well.

In my model, predetermined variables are: gdp0, inflation, govsize. Endogenous variables are: mgdp, polity, aid, aidpol.

Also, is the warning Stata is providing something to be concerned over?

xtabond2 growth aid aidpol gdp0 polity inflation govsize mgdp i.year, gmm(gdp0 inflation govsize, lag (1 .)collapse) gmm(aid mgdp, lag(2 .)collapse) gmm(aidpol polity, lag(2 .) eq(level)) iv
> (i.year, eq(level)) robust
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 robust weighting matrix for Hansen test.
  Difference-in-Sargan/Hansen statistics may be negative.

Dynamic panel-data estimation, one-step system GMM
------------------------------------------------------------------------------
Group variable: countrynum                      Number of obs      =       348
Time variable : year                            Number of groups   =        58
Number of instruments = 46                      Obs per group: min =         6
Wald chi2(13) =    258.70                                      avg =      6.00
Prob > chi2   =     0.000                                      max =         6
------------------------------------------------------------------------------
             |               Robust
      growth |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
         aid |  -.0574378   .1154779    -0.50   0.619    -.2837704    .1688947
      aidpol |    .043429   .0184724     2.35   0.019     .0072237    .0796343
        gdp0 |   1.976001   .8199689     2.41   0.016     .3688917    3.583111
      polity |  -.1539181   .2680458    -0.57   0.566    -.6792782     .371442
   inflation |   -.007488   .0097597    -0.77   0.443    -.0266166    .0116406
     govsize |  -.0630577   .1085896    -0.58   0.561    -.2758895    .1497741
        mgdp |   .1684272   .0204182     8.25   0.000     .1284083    .2084461
             |
        year |
          1  |          0  (empty)
          2  |  -.5705357   .6530268    -0.87   0.382    -1.850445    .7093733
          3  |  -.9162101   .5882048    -1.56   0.119     -2.06907    .2366501
          4  |   .3565344   .5364327     0.66   0.506    -.6948544    1.407923
          5  |  -2.538261   .8779921    -2.89   0.004    -4.259094   -.8174283
          6  |  -3.248694   1.059512    -3.07   0.002      -5.3253   -1.172088
             |
       _cons |  -15.53429   5.980947    -2.60   0.009    -27.25674   -3.811853
------------------------------------------------------------------------------
Instruments for first differences equation
  GMM-type (missing=0, separate instruments for each period unless collapsed)
    L(2/5).(aid mgdp) collapsed
    L(1/5).(gdp0 inflation govsize) collapsed
Instruments for levels equation
  Standard
    1b.year 2.year 3.year 4.year 5.year 6.year
    _cons
  GMM-type (missing=0, separate instruments for each period unless collapsed)
    DL(2/4).(aidpol polity)
    DL.(aid mgdp) collapsed
    D.(gdp0 inflation govsize) collapsed
------------------------------------------------------------------------------
Arellano-Bond test for AR(1) in first differences: z =  -2.91  Pr > z =  0.004
Arellano-Bond test for AR(2) in first differences: z =   0.61  Pr > z =  0.539
------------------------------------------------------------------------------
Sargan test of overid. restrictions: chi2(32)   = 102.89  Prob > chi2 =  0.000
  (Not robust, but not weakened by many instruments.)
Hansen test of overid. restrictions: chi2(32)   =  41.97  Prob > chi2 =  0.112
  (Robust, but weakened by many instruments.)

Difference-in-Hansen tests of exogeneity of instrument subsets:
  GMM instruments for levels
    Hansen test excluding group:     chi2(15)   =  20.88  Prob > chi2 =  0.141
    Difference (null H = exogenous): chi2(17)   =  21.09  Prob > chi2 =  0.222
  gmm(gdp0 inflation govsize, collapse lag(1 .))
    Hansen test excluding group:     chi2(14)   =  22.00  Prob > chi2 =  0.079
    Difference (null H = exogenous): chi2(18)   =  19.97  Prob > chi2 =  0.334
  gmm(aid mgdp, collapse lag(2 .))
    Hansen test excluding group:     chi2(22)   =  38.83  Prob > chi2 =  0.015
    Difference (null H = exogenous): chi2(10)   =   3.14  Prob > chi2 =  0.978
  gmm(aidpol polity, eq(level) lag(2 .))
    Hansen test excluding group:     chi2(20)   =  30.11  Prob > chi2 =  0.068
    Difference (null H = exogenous): chi2(12)   =  11.86  Prob > chi2 =  0.457
  iv(1b.year 2.year 3.year 4.year 5.year 6.year, eq(level))
    Hansen test excluding group:     chi2(27)   =  38.58  Prob > chi2 =  0.069
    Difference (null H = exogenous): chi2(5)    =   3.39  Prob > chi2 =  0.639

Many thanks in advance,

Simon

[Sebastian Kripfganz]

A few remarks:

1. Your number of instruments is (too) large relative to the number of groups / observations. This is the likely source of the warning message. (After all, it is still just a warning and not an error message but it hints toward some potential problems with your model.) I recommend to further restrict the maximum number of lags used as instruments and to rethink whether you really need to assume that 4 of your variables are endogenous. (The more endogenous variables you have, the more difficult it becomes to obtain reliable estimates because you are relying on the strength of your instruments that might quickly turn weak the further you lag them in time.)
2. As you can see below your regression table, polity enters the set of instruments only in first-differenced form for the level equation. xtabond2 has a passthru suboption for gmm(). Alternatively, you can directly use the iv() option. In any case, keep in mind that using levels requires the assumption that policy is uncorrelated with the error term including the unit-specific effects.
3. There is a severe bug in xtabond2 that causes the degrees of freedom for the Sargan / Hansen tests to be calculated incorrectly when you specify time dummies with the factor notation. Consequently, the p-values will be incorrect. As a workaround, create separate dummy variables for each time period first and then specify only those that do not get omitted. (Whenever xtabond2 reports coefficients to be "omitted" or "empty", this bug kicks in.) Alternatively, you can use my xtseqreg command instead that has a teffects option for the correct inclusion of time effects.
4. I am worried a bit about your coefficient of gdp0. Assuming that the dependent variable is GDP growth and this is the log of lagged GDP, this coefficient should typically fall in the region between -1 and 0. Did you maybe forget to take the log of this variable?

[Simon Briggs]

Hi Sebastian,

Thank you for your useful comments. In regards to (2) and (3), have I successfully solved this?

 xtabond2 growth aid aidpol gdp0 polity inflation govsize mgdp time2 time3 time4 time5 time6, gmm(gdp0 inflation govsize, lag (1 .)collapse) gmm(aid mgdp, lag(2 .)collapse) gmm(aidpol polity,
> eq(level) p lag(2 .)) iv(time2 time3 time4 time5 time6, eq(level)) robust
Favoring space over speed. To switch, type or click on mata: mata set matafavor speed, perm.

Dynamic panel-data estimation, one-step system GMM
------------------------------------------------------------------------------
Group variable: countrynum                      Number of obs      =       348
Time variable : year                            Number of groups   =        58
Number of instruments = 54                      Obs per group: min =         6
Wald chi2(12) =    302.65                                      avg =      6.00
Prob > chi2   =     0.000                                      max =         6
------------------------------------------------------------------------------
             |               Robust
      growth |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
         aid |  -.0731343   .1269097    -0.58   0.564    -.3218728    .1756042
      aidpol |    .032537   .0150912     2.16   0.031     .0029587    .0621153
        gdp0 |   1.664245   1.043606     1.59   0.111    -.3811862    3.709676
      polity |  -.2180305   .1440524    -1.51   0.130    -.5003681    .0643071
   inflation |  -.0071849   .0098774    -0.73   0.467    -.0265443    .0121745
     govsize |  -.0532686   .0953484    -0.56   0.576    -.2401481    .1336108
        mgdp |   .1647532   .0149169    11.04   0.000     .1355166    .1939899
       time2 |  -.2851089   .6310224    -0.45   0.651     -1.52189    .9516724
       time3 |  -.5975558   .6009205    -0.99   0.320    -1.775338    .5802268
       time4 |   .8827259   .5615615     1.57   0.116    -.2179144    1.983366
       time5 |  -1.847135   .8141298    -2.27   0.023      -3.4428   -.2514702
       time6 |   -2.53298   .9308799    -2.72   0.007    -4.357472   -.7084893
       _cons |  -13.33185   7.925602    -1.68   0.093    -28.86574    2.202045
------------------------------------------------------------------------------
Instruments for first differences equation
  GMM-type (missing=0, separate instruments for each period unless collapsed)
    L(2/5).(aid mgdp) collapsed
    L(1/5).(gdp0 inflation govsize) collapsed
Instruments for levels equation
  Standard
    time2 time3 time4 time5 time6
    _cons
  GMM-type (missing=0, separate instruments for each period unless collapsed)
    L(2/5).(aidpol polity)
    DL.(aid mgdp) collapsed
    D.(gdp0 inflation govsize) collapsed
------------------------------------------------------------------------------
Arellano-Bond test for AR(1) in first differences: z =  -3.21  Pr > z =  0.001
Arellano-Bond test for AR(2) in first differences: z =   0.75  Pr > z =  0.451
------------------------------------------------------------------------------
Sargan test of overid. restrictions: chi2(41)   = 120.38  Prob > chi2 =  0.000
  (Not robust, but not weakened by many instruments.)
Hansen test of overid. restrictions: chi2(41)   =  44.20  Prob > chi2 =  0.338
  (Robust, but weakened by many instruments.)

Difference-in-Hansen tests of exogeneity of instrument subsets:
  GMM instruments for levels
    Hansen test excluding group:     chi2(16)   =  20.09  Prob > chi2 =  0.216
    Difference (null H = exogenous): chi2(25)   =  24.10  Prob > chi2 =  0.513
  gmm(gdp0 inflation govsize, collapse lag(1 .))
    Hansen test excluding group:     chi2(23)   =  25.70  Prob > chi2 =  0.315
    Difference (null H = exogenous): chi2(18)   =  18.50  Prob > chi2 =  0.423
  gmm(aid mgdp, collapse lag(2 .))
    Hansen test excluding group:     chi2(31)   =  41.85  Prob > chi2 =  0.092
    Difference (null H = exogenous): chi2(10)   =   2.35  Prob > chi2 =  0.993
  gmm(aidpol polity, passthru eq(level) lag(2 .))
    Hansen test excluding group:     chi2(21)   =  29.71  Prob > chi2 =  0.098
    Difference (null H = exogenous): chi2(20)   =  14.49  Prob > chi2 =  0.805
  iv(time2 time3 time4 time5 time6, eq(level))
    Hansen test excluding group:     chi2(36)   =  41.79  Prob > chi2 =  0.234
    Difference (null H = exogenous): chi2(5)    =   2.41  Prob > chi2 =  0.790

As for the assumption, is this required if I were to use differences as well?

4) Thank you for highlighting this. I have checked some empirical papers and those doing GMM sometimes get magnitudes greater than 1. However the sign is worrying - do you know of any other potential causes? gdp0 is the natural logarithm of GDP per capita at the beginning of each period (for example, if period 1 is 2000-04, then gdp0 in period 1 ln(GDPpc in 2000)

Many thanks,

Simon

[Sebastian Kripfganz]

2) This looks all right. If you were using differences as instruments for the level equation (as you are doing for some variables), these differences need to be uncorrelated with the error term (and thus the unobserved country-specific effects). This is essentially an assumption on the initial observations; see Blundell and Bond (1998).
3) Yes.
4) Is the dependent variable the growth rate of GDP per capita or just GDP? Instead of directly using the growth rate, you might want to use the log-approximation of the growth rate, log(GDP_t) - log(GDP_t-1).

[Simon Briggs]

Hi Sebastian,

Thanks again. The dependent variable is the growth rate of GDP per capita, obtained from the World Bank. Do you think a move from growth rate to log-approximation could make such a large difference?

Many thanks,

Simon

[Sebastian Kripfganz]

Depending on your sample of countries and years, there might be some extreme growth rates even in the range of plus/minus 40%. In that case, yes, it can make a big difference. There would be not much of a difference, if all growth rates were in a vicinity of zero.

[Simon Briggs]

Hi Sebastian,

Thank you for all your comments and guidance.

Simon

[Simon Briggs]

Hi all,

Sorry to re-bump this thread; if you are doing difference-GMM is it still required to specify the eq(level) with the time dummies: e.g. iv(time2 time3 time4 time5 time6, eq(level))

Many thanks,

Simon

[Sebastian Kripfganz]

You should specify the equation for the time dummies, yes. The natural way is to specify them for the level equation. If you are using a difference GMM estimator with the noleveleq option, you can specify them instead for the first-difference equation.

[Simon Briggs]

Hi Sebastian,

Are you then saying it should be iv(time2 time3...,eq(diff)) if specifying noleveleq?

Thanks,

Simon

[Sebastian Kripfganz]

Yes. (If you specify noleveleq, then you can actually ignore the eq(diff) suboption but it does not harm anyway.)

[Simon Briggs]

Hi Sebastian,

Thank you again!

Simon

[Merve Serifoglu]

Dear All,

I have just registered this forum. I am running two step GMM for my phd thesis. I have 31 countries in my sample. However,Number of groups looks less than 31 after analysis. I will be glad if you can help me.

Thank you.