XTABOND2 number of instruments

[Gao Yili]

I am struggling with GMM and XTABOND2. Authors of academic papers don't mention how many instruments they get after the computation of the model. As I understand the number of instruments cannot be greater than the number of groups. I read the materials from Roodman (2009) and Sebastian Kripfganz warning about the number of instruments. I am still not clear and have a lot of doubts about my output. My data have N=38 and T=30. 1 dependent and 7 independent variables. I am using 4 exogenous as instruments. I am coding the following:

xtabond2 gdp L.gdp fdi gfcf iq hc fd ele inf, gmm(L.gdp fdi gfcf inf, laglimits(2 2) eq(level) collapse) gmm(L.gdp fdi gfcf inf, laglimits(0 0)eq(diff) collapse) iv( ele hc iq fd, eq(level)) twostep robust nodiffsargan


Dynamic panel-data estimation, two-step system GMM
------------------------------------------------------------------------------
Group variable: egcode Number of obs = 1102
Time variable : year Number of groups = 38
Number of instruments = 13 Obs per group: min = 29
Wald chi2(8) = 2416.01 avg = 29.00
Prob > chi2 = 0.000 max = 29
------------------------------------------------------------------------------
| Corrected
gdppc | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
gdppc |
L1. | -.9990342 .0438995 -22.76 0.000 -1.085076 -.9129927

fdi | .2112965 .2501171 0.84 0.398 -.2789239 .701517
gfcf | .0605189 .2211572 0.27 0.784 -.3729413 .4939791
iq | 3.318989 1.314757 2.52 0.012 .7421124 5.895865
hc | 2.26246 .7812645 2.90 0.004 .7312095 3.79371
fd | 2.798065 1.395826 2.00 0.045 .0622961 5.533834
ele | -1.650007 .4392249 -3.76 0.000 -2.510872 -.7891425
inf | -.000655 .000234 -2.80 0.005 -.0011135 -.0001964
_cons | 22.31125 8.096417 2.76 0.006 6.442562 38.17993
------------------------------------------------------------------------------
Instruments for first differences equation
GMM-type (missing=0, separate instruments for each period unless collapsed)
.(L.gdppc fdi gfcf inflation) collapsed
Instruments for levels equation
Standard
lnele lnhc lniq lnfd
_cons
GMM-type (missing=0, separate instruments for each period unless collapsed)
DL2.(L.gdppc fdi gfcf inflation) collapsed
------------------------------------------------------------------------------
Arellano-Bond test for AR(1) in first differences: z = 3.42 Pr > z = 0.001
Arellano-Bond test for AR(2) in first differences: z = -4.18 Pr > z = 0.000
------------------------------------------------------------------------------
Sargan test of overid. restrictions: chi2(4) = 19.21 Prob > chi2 = 0.001
(Not robust, but not weakened by many instruments.)
Hansen test of overid. restrictions: chi2(4) = 6.69 Prob > chi2 = 0.153
(Robust, but weakened by many instruments.)



I am estimating the model and focus a lot on the number of instruments, is it the right approach?



Best regards,

Gao Yili

[Sebastian Kripfganz]

Given your relatively small cross-sectional dimension, I believe that it is indeed a good idea to focus a lot on keeping the number of instruments small.

In your particular case, notice that gmm(L.gdp, lagrange(0 0) eq(diff)) does not yield a valid instrument. This creates the first lag of gdp (the zeroth lag of L.gdp) as an instrument for the first-differenced model, but only the second lag of gdp (and lags further away) is a valid instrument. You should thus choose gmm(L.gdp, lagrange(1 1) eq(diff)).

The other way round, gmm(L.gdp, laglimits(2 2) eq(level)) is potentially going to far back in time. gmm(L.gdp, laglimits(0 0) eq(level)) would be valid as well for the level model (provided that there is no serial correlation in the idiosyncratic errors).

The coefficient of your lagged dependent variable, -.9990342, is worrying. This should normally fall into the interval from 0 to plus 1. Maybe the problem gets resolved, when you modify your instruments according to my suggestion.

[Gao Yili]

Hi Sebastian,

Thanks for your reply and suggestion! I really appreciate it.

I made the changes according to your suggestion and I got the following output:

xtabond2 gdppc L.gdppc fdi gfcf iq hc fd ele inf, gmm(L.gdppc fdi gfcf inf, laglimits(2 2)eq(level)collapse) gmm(L.gdppc fdi gfcf inf, laglimits(1 1)eq(diff) collapse) iv(ele hc iq fd, eq(level)) twostep robust nodiffsargan


Dynamic panel-data estimation, two-step system GMM
------------------------------------------------------------------------------
Group variable: egcode Number of obs = 1102
Time variable : year Number of groups = 38
Number of instruments = 13 Obs per group: min = 29
Wald chi2(8) = 148.48 avg = 29.00
Prob > chi2 = 0.000 max = 29
------------------------------------------------------------------------------
| Corrected
gdppc | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
gdppc |
L1. | .2025764 .1675159 1.21 0.227 -.1257487 5309016
|
fdi | .0436943 .1142995 0.38 0.702 -.1803287 2677172
gfcf | .0795385 .1309798 0.61 0.544 -.1771772 .3362543
iq | .65937 .9067753 0.73 0.467 -1.117877 2.436617
hc | 1.02063 . 3800626 2.69 0.007 .2757213 1.765539
fd | .9084523 .7697381 1.18 0.238 -.6002066 2.417111
ele | -.56887 .2474581 -2.30 0.022 -1.053879 -.0838609
inf | -.0023428 .000323 -7.25 0.000 -.0029759 -.0017096
_cons | 6.655052 4.72962 1.41 0.159 -2.614833 15.92494
------------------------------------------------------------------------------
Instruments for first differences equation
GMM-type (missing=0, separate instruments for each period unless collapsed)
L.(L.gdppc fdi gfcf inflation) collapsed
Instruments for levels equation
Standard
lnele lnhc lniq lnfd
_cons
GMM-type (missing=0, separate instruments for each period unless collapsed)
DL2.(L.gdppc fdi gfcf inflation) collapsed
------------------------------------------------------------------------------
Arellano-Bond test for AR(1) in first differences: z = -3.08 Pr > z = 0.002
Arellano-Bond test for AR(2) in first differences: z = -0.23 Pr > z = 0.816
------------------------------------------------------------------------------
Sargan test of overid. restrictions: chi2(4) = 26.85 Prob > chi2 = 0.000
(Not robust, but not weakened by many instruments.)
Hansen test of overid. restrictions: chi2(4) = 13.21 Prob > chi2 = 0.010
(Robust, but weakened by many instruments.)


xtabond2 gdppc L.gdppc fdi gfcf iq hc fd ele inf, gmm(L.gdppc fdi gfcf inf, laglimits(0 0)eq(level)collapse) gmm(L.gdppc fdi gfcf inf, laglimits(1 1)eq(diff) collapse) iv(ele hc iq fd, eq(level)) twostep robust nodiffsargan


Dynamic panel-data estimation, two-step system GMM
------------------------------------------------------------------------------
Group variable: egcode Number of obs = 1102
Time variable : year Number of groups = 38
Number of instruments = 13 Obs per group: min = 29
Wald chi2(8) = 52.60 avg = 29.00
Prob > chi2 = 0.000 max = 29
------------------------------------------------------------------------------
| Corrected
gdppc | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
gdppc |
L1. | .1953844 . 1214648 1.61 0.108 -.0426822 . 433451
|
fdi | . 0349125 .0870876 0.40 0.689 -.1357761 .2056011
gfcf | .5608869 .1920085 2.92 0.003 .1845571 .9372166
iq | -2.090898 1.966146 -1.06 0.288 -5.944474 1.762678
hc | .4086098 .8994869 0.45 0.650 -1.354352 2.171572
fd | -.5632829 1.273709 -0.44 0.658 -3.059706 1.933141
ele | -.1713473 .282975 -0.61 0.545 -.7259682 .3832736
inf | -.0024796 .000533 -4.65 0.000 -.0035243 -.001435
_cons | -10.65992 7.720079 -1.38 0.167 -25.791 4.471153
------------------------------------------------------------------------------
Instruments for first differences equation
GMM-type (missing=0, separate instruments for each period unless collapsed)
L.(L.gdppc fdi gfcf inflation) collapsed
Instruments for levels equation
Standard
lnele lnhc lniq lnfd
_cons
GMM-type (missing=0, separate instruments for each period unless collapsed)
D.(L.gdppc fdi gfcf inflation) collapsed
------------------------------------------------------------------------------
Arellano-Bond test for AR(1) in first differences: z = -3.73 Pr > z = 0.000
Arellano-Bond test for AR(2) in first differences: z = -0.85 Pr > z = 0.398
------------------------------------------------------------------------------
Sargan test of overid. restrictions: chi2(4) = 21.32 Prob > chi2 = 0.000
(Not robust, but not weakened by many instruments.)
Hansen test of overid. restrictions: chi2(4) = 5.73 Prob > chi2 = 0.220
(Robust, but weakened by many instruments.)

[Sebastian Kripfganz]

Your second specification looks very reasonable and both the AR(2) and the Hansen test support the specification.

[Gao Yili]

Thanks!

One more question, I am considering adding time dummies, but without going too far with the number of instruments or variables, I have T=30.

I tried different ways but the output was not good at all.

Any suggestion?

[Sebastian Kripfganz]

Your T is relatively large in comparison to N. It is not surprising that adding a separate time dummy for each period yields troublesome results. You could try to add dummies for, say, 5-year periods instead, or a few dummies for crisis years etc. Alternatively, you could add some variables that capture global economic developments (varying over time but constant across countries).

[Gao Yili]

Very helpful! Thanks!

[Gao Yili]

Hi Sebastian.

After including some time dummies in the specification I only get better results using iv compound option: iv( eq(diff) ) and iv(eq(level)), is it a right approach?


ivstyle( eq(level))

 xtabond2 gdp L.gdp gfcf fdi iq hc fd ele inf  y1990 y1991 y2001 y2007 y2009, gmm(L.gdp gfcf fdi inf, laglimits(0 0) eq(level) collapse) gmm(L.gdp gfcf fdi inf, eq(diff) laglimits(1 1)collapse)  iv( hc iq fd ele y1990 y1991 y2001 y2007 y2009, eq(level)) twostep robust nodiffsargan orthogonal

Dynamic panel-data estimation, two-step system GMM
------------------------------------------------------------------------------
Group variable: egcode                          Number of obs      =      1085
Time variable : year                            Number of groups   =        38
Number of instruments = 18                      Obs per group: min =        23
Wald chi2(13) =    452.65                                      avg =     28.55
Prob > chi2   =     0.000                                      max =        29
------------------------------------------------------------------------------
             |              Corrected
         gdp |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
         gdp |
         L1. |   .0755628   .0719789     1.05   0.294    -.0655133    .2166388
             |
        gfcf |   .0734045   .0152234     4.82   0.000     .0435673    .1032417
         fdi |   .0001025   .0001032     0.99   0.320    -.0000997    .0003047
          iq |   .0282243   .0156157     1.81   0.071    -.0023819    .0588305
          hc |  -.1564944   .0893842    -1.75   0.080    -.3316842    .0186954
          fd |   .0150725   .0096058     1.57   0.117    -.0037544    .0338994
         ele |   .1405175   .0343007     4.10   0.000     .0732894    .2077457
         inf |  -.0013352   .0002696    -4.95   0.000    -.0018635   -.0008069
       y1990 |  -.0413191   .6618428    -0.06   0.950    -1.338507    1.255869
       y1991 |   .2146626   .5157637     0.42   0.677    -.7962157    1.225541
       y2001 |  -1.855946   .3512207    -5.28   0.000    -2.544326   -1.167566
       y2007 |   1.515472   .2610916     5.80   0.000     1.003742    2.027202
       y2009 |  -2.730804   .5811994    -4.70   0.000    -3.869934   -1.591674
       _cons |   2.057906    .304801     6.75   0.000     1.460507    2.655305
------------------------------------------------------------------------------
Instruments for orthogonal deviations equation
  GMM-type (missing=0, separate instruments for each period unless collapsed)
    L.(L.gdp gfcf fdi inf) collapsed
Instruments for levels equation
  Standard
    hc iq fd ele y1990 y1991 y2001 y2007 y2009
    _cons
  GMM-type (missing=0, separate instruments for each period unless collapsed)
    D.(L.gdp gfcf fdi inf) collapsed
------------------------------------------------------------------------------
Arellano-Bond test for AR(1) in first differences: z =  -3.98  Pr > z =  0.000
Arellano-Bond test for AR(2) in first differences: z =   0.40  Pr > z =  0.690
------------------------------------------------------------------------------
Sargan test of overid. restrictions: chi2(4)    =   0.66  Prob > chi2 =  0.956
  (Not robust, but not weakened by many instruments.)
Hansen test of overid. restrictions: chi2(4)    =   0.84  Prob > chi2 =  0.933
  (Robust, but weakened by many instruments.)

Compound ivstyle

xtabond2 gdp L.gdp gfcf fdi iq hc fd ele inf  y1990 y1991 y2001 y2007 y2009, gmm(L.gdp gfcf fdi inf, laglimits(0 0) eq(level) collapse) gmm(L.gdp gfcf fdi inf, eq(diff) laglimits(1 1)collapse)  iv( hc iq fd ele y1990 y1991 y2001 y2007 y2009, eq(level))  iv( hc iq fd ele y1990 y1991 y2001 y2007 y2009, eq(diff))twostep robust nodiffsargan orthogonal

Dynamic panel-data estimation, two-step system GMM
------------------------------------------------------------------------------
Group variable: egcode                          Number of obs      =      1085
Time variable : year                            Number of groups   =        38
Number of instruments = 25                      Obs per group: min =        23
Wald chi2(13) =    329.28                                      avg =     28.55
Prob > chi2   =     0.000                                      max =        29
------------------------------------------------------------------------------
             |              Corrected
         gdp |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
         gdp |
         L1. |   .1778847   .1344312     1.32   0.186    -.0855955     .441365
             |
        gfcf |   .0640454   .0212203     3.02   0.003     .0224543    .1056365
         fdi |   .0001699   .0001774     0.96   0.338    -.0001778    .0005177
          iq |    .030694     .01824     1.68   0.092    -.0050557    .0664437
          hc |  -.1938678   .0902754    -2.15   0.032    -.3708043   -.0169314
          fd |    .004453   .0160067     0.28   0.781    -.0269195    .0358256
         ele |   .1404895   .0381513     3.68   0.000     .0657143    .2152647
         inf |  -.0012767    .000335    -3.81   0.000    -.0019333     -.00062
       y1990 |   .5238467   .9235504     0.57   0.571    -1.286279    2.333972
       y1991 |  -.0357782   .7253139    -0.05   0.961    -1.457367    1.385811
       y2001 |    -1.9954   .5407573    -3.69   0.000    -3.055265   -.9355348
       y2007 |   1.312422   .3421616     3.84   0.000     .6417976    1.983046
       y2009 |   -3.05845   .7919194    -3.86   0.000    -4.610584   -1.506317
       _cons |   1.976166   .3531009     5.60   0.000     1.284101    2.668231
------------------------------------------------------------------------------
Instruments for orthogonal deviations equation
  Standard
    FOD.(hc iq fd ele y1990 y1991 y2001 y2007 y2009)
  GMM-type (missing=0, separate instruments for each period unless collapsed)
    L.(L.gdp gfcf fdi inf) collapsed
Instruments for levels equation
  Standard
    hc iq fd ele y1990 y1991 y2001 y2007 y2009
    _cons
  GMM-type (missing=0, separate instruments for each period unless collapsed)
    D.(L.gdp gfcf fdi inf) collapsed
------------------------------------------------------------------------------
Arellano-Bond test for AR(1) in first differences: z =  -3.25  Pr > z =  0.001
Arellano-Bond test for AR(2) in first differences: z =   0.65  Pr > z =  0.517
------------------------------------------------------------------------------
Sargan test of overid. restrictions: chi2(11)   =  75.33  Prob > chi2 =  0.000
  (Not robust, but not weakened by many instruments.)
Hansen test of overid. restrictions: chi2(11)   =  17.45  Prob > chi2 =  0.095
  (Robust, but weakened by many instruments.)

[Sebastian Kripfganz]

Why do you believe the compound specification gives "better" results?

To me, your first results look perfectly fine. There is no good justification for adding the time dummies as instruments for the first-differenced model as well.

[Gao Yili]

Hi Sebastian, Thanks for your reply!

The P-value of Hansen test over 0.25. is not a sign of trouble?

Hansen test of overid. restrictions: chi2(4) = 0.84 Prob > chi2 = 0.933

[Sebastian Kripfganz]

Large p-values of the Hansen test would be a sign of trouble if there is a reason to suspect a too-many-instruments problem (which is actually a problem of too many overidentifying restrictions). Here, you just have 4 overidentifying restrictions (the degrees of freedom of the Hansen test). Personally, I would not worry about the large p-value in your example.

[Gao Yili]

it is clear now, Many thanks!

[Bruno De Menna]

Along the same lines as Gao Yili, I'd like to have some support on the following xtabond2 code, knowing that :

• equityassets L.pretaxprofitonassets expensesrevenues offbalance are endogenous
• totalassets GDP concentration_3 domcredit are predetermined
• shortrate is exogenous

  xi: xtabond2 NPLsgrossloans L.NPLsgrossloans shortrate equityassets L.pretaxprofitonassets expensesrevenues offbalance totalassets GDP concentration_3 domcredit i.year country_n, gmm(L.NPLsgrossloans equityassets L.pretaxprofitonassets expensesrevenues offbalance, laglimits(0 0) eq(level) collapse) gmm(L.NPLsgrossloans equityassets L.pretaxprofitonassets expensesrevenues offbalance, laglimits(1 1) eq(diff) collapse) iv(shortrate i.year country_n, eq(level)) twostep cluster(entity_n) nodiffsargan

I get the following results :

i.year            _Iyear_2009-2017    (naturally coded; _Iyear_2009 omitted)
Favoring speed over space. To switch, type or click on mata: mata set matafavor space, perm.
_Iyear_2011 dropped due to collinearity
_Iyear_2016 dropped due to collinearity
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: entity_n                        Number of obs      =     12652
Time variable : year                            Number of groups   =      2788
Number of instruments = 19                      Obs per group: min =         1
Wald chi2(17) =   1866.13                                      avg =      4.54
Prob > chi2   =     0.000                                      max =         8
                                       (Std. Err. adjusted for clustering on entity_n)
--------------------------------------------------------------------------------------
                     |              Corrected
      NPLsgrossloans |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
---------------------+----------------------------------------------------------------
      NPLsgrossloans |
                 L1. |    .911101   .2967232     3.07   0.002     .3295342    1.492668
                     |
           shortrate |    .162101   1.212265     0.13   0.894    -2.213896    2.538098
        equityassets |   .0304096   .2353199     0.13   0.897     -.430809    .4916281
                     |
pretaxprofitonassets |
                 L1. |  -.6053552   .5478198    -1.11   0.269    -1.679062    .4683519
                     |
    expensesrevenues |  -.0003392   .0021364    -0.16   0.874    -.0045264    .0038481
          offbalance |    .157122   .1179013     1.33   0.183    -.0739602    .3882043
         totalassets |    .000068    .000475     0.14   0.886    -.0008631    .0009991
                 GDP |  -1.198131    1.95335    -0.61   0.540    -5.026627    2.630364
     concentration_3 |   54.25937   48.43717     1.12   0.263    -40.67575    149.1945
           domcredit |  -.1925165   .2209086    -0.87   0.383    -.6254893    .2404563
         _Iyear_2010 |  -.1184613   1.880578    -0.06   0.950    -3.804327    3.567404
         _Iyear_2012 |  -2.562553   4.496527    -0.57   0.569    -11.37558    6.250477
         _Iyear_2013 |  -1.232831   5.699771    -0.22   0.829    -12.40418    9.938514
         _Iyear_2014 |   -.059447   1.889238    -0.03   0.975    -3.762285    3.643391
         _Iyear_2015 |   .3941095   1.017727     0.39   0.699    -1.600598    2.388817
         _Iyear_2017 |  -.8067855   1.430191    -0.56   0.573    -3.609908    1.996337
           country_n |  -.6561961   1.332347    -0.49   0.622    -3.267548    1.955156
               _cons |   1.387771   15.62793     0.09   0.929     -29.2424    32.01794
--------------------------------------------------------------------------------------
Instruments for first differences equation
  GMM-type (missing=0, separate instruments for each period unless collapsed)
    L.(L.NPLsgrossloans equityassets L.pretaxprofitonassets expensesrevenues
    offbalance) collapsed
Instruments for levels equation
  Standard
    shortrate _Iyear_2010 _Iyear_2011 _Iyear_2012 _Iyear_2013 _Iyear_2014
    _Iyear_2015 _Iyear_2016 _Iyear_2017 country_n
    _cons
  GMM-type (missing=0, separate instruments for each period unless collapsed)
    D.(L.NPLsgrossloans equityassets L.pretaxprofitonassets expensesrevenues
    offbalance) collapsed
------------------------------------------------------------------------------
Arellano-Bond test for AR(1) in first differences: z =  -1.92  Pr > z =  0.055
Arellano-Bond test for AR(2) in first differences: z =   0.41  Pr > z =  0.683
------------------------------------------------------------------------------
Sargan test of overid. restrictions: chi2(1)    =   2.70  Prob > chi2 =  0.101
  (Not robust, but not weakened by many instruments.)
Hansen test of overid. restrictions: chi2(1)    =   0.56  Prob > chi2 =  0.454
  (Robust, but weakened by many instruments.)

I'm particularly worried about the fact all regressors are not signifiant, excep the autoregressive one.

Thank your very much.

[Sebastian Kripfganz]

I'm particularly worried about the fact all regressors are not signifiant, excep the autoregressive one.

That is a typical issue in dynamic panel models when the coefficient of the lagged dependent variable is close to 1. It is generally difficult to find strong predictors of a variable that is highly persistent, after controlling for the unit-specific effects (which is done implicitly by construction of the GMM estimator).

I am afraid there is not really a recommendation I can make to improve the situation.

[Bruno De Menna]

Once final question Sebastian :

According to you, what would be the rule of thumb to choose between 'eq(level)' and 'eq(diff)' options once trying to set suitable instruments in a GMM specification (in particular regarding endogenous and predetermined variables) ?

Thank you.