I m trying to run a difference gmm model with both these commands but I have different results in terms of instrument counts.
I want to run a model like
pc_npl=l.pc_npl+l.gdp+avg_roa;
where pc_npl and avg_roa are considered as endogenous and l.gdp as strictly exogenous.
The first (silly) question concern with how to instrument l.pc_npl in the gmm option: as gmm( l.pc_npl) or gmm( pc_npl) ??
Secondly, I consider gdp as exogenous.
Reading the slide of Kripfganz I have read that an exogenous variable is also called with gmm specifying the correct lag to consider it as exogenous.
In xtabond2, I specifify it with with the iv() option, where I cannot specifiy the lag limit.
As far as I understand, in the first two comamnd I am instrumenting the exogenous l.gdp with its own values (lag (0)) and up to two lags, while with xtabond the variable is instrumented only by itself and not with deeper lags, am I correct?
However, here are some of the results of the very basic model.
Code:
xtdpdgmm L(0/1).pc_npl l.gdp avg_roa, model(diff) gmm(l.pc_npl, lag( 2 4)) ///
gmm(avg_roa, lag(2 4)) gmm(l.gdp, lag (0 2)) nocons vce(r)
estat ser, ar(1/3)
estat overid
Generalized method of moments estimation
Fitting full model:
Step 1 f(b) = 19.958954
Group variable: bank_id Number of obs = 1362
Time variable: year Number of groups = 125
Moment conditions: linear = 90 Obs per group: min = 5
nonlinear = 0 avg = 10.896
total = 90 max = 12
(Std. Err. adjusted for 125 clusters in bank_id)
------------------------------------------------------------------------------
| Robust
pc_npl | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
pc_npl |
L1. | .8485664 .031261 27.14 0.000 .7872958 .9098369
|
gdp |
L1. | -.1846946 .0442948 -4.17 0.000 -.2715108 -.0978784
|
avg_roa | -1.427724 .2082991 -6.85 0.000 -1.835983 -1.019465
------------------------------------------------------------------------------
Instruments corresponding to the linear moment conditions:
1, model(diff):
2009:L2.L.pc_npl 2010:L2.L.pc_npl 2011:L2.L.pc_npl 2012:L2.L.pc_npl
2013:L2.L.pc_npl 2014:L2.L.pc_npl 2015:L2.L.pc_npl 2016:L2.L.pc_npl
2017:L2.L.pc_npl 2018:L2.L.pc_npl 2010:L3.L.pc_npl 2011:L3.L.pc_npl
2012:L3.L.pc_npl 2013:L3.L.pc_npl 2014:L3.L.pc_npl 2015:L3.L.pc_npl
2016:L3.L.pc_npl 2017:L3.L.pc_npl 2018:L3.L.pc_npl 2011:L4.L.pc_npl
2012:L4.L.pc_npl 2013:L4.L.pc_npl 2014:L4.L.pc_npl 2015:L4.L.pc_npl
2016:L4.L.pc_npl 2017:L4.L.pc_npl 2018:L4.L.pc_npl
2, model(diff):
2008:L2.avg_roa 2009:L2.avg_roa 2010:L2.avg_roa 2011:L2.avg_roa
2012:L2.avg_roa 2013:L2.avg_roa 2014:L2.avg_roa 2015:L2.avg_roa
2016:L2.avg_roa 2017:L2.avg_roa 2018:L2.avg_roa 2009:L3.avg_roa
2010:L3.avg_roa 2011:L3.avg_roa 2012:L3.avg_roa 2013:L3.avg_roa
2014:L3.avg_roa 2015:L3.avg_roa 2016:L3.avg_roa 2017:L3.avg_roa
2018:L3.avg_roa 2010:L4.avg_roa 2011:L4.avg_roa 2012:L4.avg_roa
2013:L4.avg_roa 2014:L4.avg_roa 2015:L4.avg_roa 2016:L4.avg_roa
2017:L4.avg_roa 2018:L4.avg_roa
3, model(diff):
2008:L.gdp 2009:L.gdp 2010:L.gdp 2011:L.gdp 2012:L.gdp 2013:L.gdp
2014:L.gdp 2015:L.gdp 2016:L.gdp 2017:L.gdp 2018:L.gdp 2008:L1.L.gdp
2009:L1.L.gdp 2010:L1.L.gdp 2011:L1.L.gdp 2012:L1.L.gdp 2013:L1.L.gdp
2014:L1.L.gdp 2015:L1.L.gdp 2016:L1.L.gdp 2017:L1.L.gdp 2018:L1.L.gdp
2009:L2.L.gdp 2010:L2.L.gdp 2011:L2.L.gdp 2012:L2.L.gdp 2013:L2.L.gdp
2014:L2.L.gdp 2015:L2.L.gdp 2016:L2.L.gdp 2017:L2.L.gdp 2018:L2.L.gdp
2019:L2.L.gdp
. estat ser, ar(1/3)
Arellano-Bond test for autocorrelation of the first-differenced residuals
H0: no autocorrelation of order 1: z = -3.5568 Prob > |z| = 0.0004
H0: no autocorrelation of order 2: z = -0.8404 Prob > |z| = 0.4007
H0: no autocorrelation of order 3: z = 1.0810 Prob > |z| = 0.2797
. estat overid
Sargan-Hansen test of the overidentifying restrictions
H0: overidentifying restrictions are valid
1-step moment functions, 1-step weighting matrix chi2(87) = 356.0197
note: * Prob > chi2 = 0.0000
1-step moment functions, 2-step weighting matrix chi2(87) = 109.0580
note: * Prob > chi2 = 0.0550
* asymptotically invalid if the one-step weighting matrix is not optimal
xtdpdgmm L(0/1).pc_npl l.gdp avg_roa, model(diff) gmm(pc_npl, lag( 2 4)) ///
gmm(avg_roa, lag(2 4)) gmm(l.gdp, lag (0 2)) nocons vce(r)
estat ser, ar(1/3)
estat overid
Generalized method of moments estimation
Fitting full model:
Step 1 f(b) = 25.160125
Group variable: bank_id Number of obs = 1362
Time variable: year Number of groups = 125
Moment conditions: linear = 93 Obs per group: min = 5
nonlinear = 0 avg = 10.896
total = 93 max = 12
(Std. Err. adjusted for 125 clusters in bank_id)
------------------------------------------------------------------------------
| Robust
pc_npl | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
pc_npl |
L1. | .8158465 .0369234 22.10 0.000 .7434779 .8882151
|
gdp |
L1. | -.1962848 .0417855 -4.70 0.000 -.2781829 -.1143867
|
avg_roa | -1.279425 .2019118 -6.34 0.000 -1.675165 -.8836851
------------------------------------------------------------------------------
Instruments corresponding to the linear moment conditions:
1, model(diff):
2008:L2.pc_npl 2009:L2.pc_npl 2010:L2.pc_npl 2011:L2.pc_npl 2012:L2.pc_npl
2013:L2.pc_npl 2014:L2.pc_npl 2015:L2.pc_npl 2016:L2.pc_npl 2017:L2.pc_npl
2018:L2.pc_npl 2009:L3.pc_npl 2010:L3.pc_npl 2011:L3.pc_npl 2012:L3.pc_npl
2013:L3.pc_npl 2014:L3.pc_npl 2015:L3.pc_npl 2016:L3.pc_npl 2017:L3.pc_npl
2018:L3.pc_npl 2010:L4.pc_npl 2011:L4.pc_npl 2012:L4.pc_npl 2013:L4.pc_npl
2014:L4.pc_npl 2015:L4.pc_npl 2016:L4.pc_npl 2017:L4.pc_npl 2018:L4.pc_npl
2, model(diff):
2008:L2.avg_roa 2009:L2.avg_roa 2010:L2.avg_roa 2011:L2.avg_roa
2012:L2.avg_roa 2013:L2.avg_roa 2014:L2.avg_roa 2015:L2.avg_roa
2016:L2.avg_roa 2017:L2.avg_roa 2018:L2.avg_roa 2009:L3.avg_roa
2010:L3.avg_roa 2011:L3.avg_roa 2012:L3.avg_roa 2013:L3.avg_roa
2014:L3.avg_roa 2015:L3.avg_roa 2016:L3.avg_roa 2017:L3.avg_roa
2018:L3.avg_roa 2010:L4.avg_roa 2011:L4.avg_roa 2012:L4.avg_roa
2013:L4.avg_roa 2014:L4.avg_roa 2015:L4.avg_roa 2016:L4.avg_roa
2017:L4.avg_roa 2018:L4.avg_roa
3, model(diff):
2008:L.gdp 2009:L.gdp 2010:L.gdp 2011:L.gdp 2012:L.gdp 2013:L.gdp
2014:L.gdp 2015:L.gdp 2016:L.gdp 2017:L.gdp 2018:L.gdp 2008:L1.L.gdp
2009:L1.L.gdp 2010:L1.L.gdp 2011:L1.L.gdp 2012:L1.L.gdp 2013:L1.L.gdp
2014:L1.L.gdp 2015:L1.L.gdp 2016:L1.L.gdp 2017:L1.L.gdp 2018:L1.L.gdp
2009:L2.L.gdp 2010:L2.L.gdp 2011:L2.L.gdp 2012:L2.L.gdp 2013:L2.L.gdp
2014:L2.L.gdp 2015:L2.L.gdp 2016:L2.L.gdp 2017:L2.L.gdp 2018:L2.L.gdp
2019:L2.L.gdp
. estat ser, ar(1/3)
Arellano-Bond test for autocorrelation of the first-differenced residuals
H0: no autocorrelation of order 1: z = -3.4427 Prob > |z| = 0.0006
H0: no autocorrelation of order 2: z = -0.8221 Prob > |z| = 0.4110
H0: no autocorrelation of order 3: z = 0.9634 Prob > |z| = 0.3354
. estat overid
Sargan-Hansen test of the overidentifying restrictions
H0: overidentifying restrictions are valid
1-step moment functions, 1-step weighting matrix chi2(90) = 482.2268
note: * Prob > chi2 = 0.0000
1-step moment functions, 2-step weighting matrix chi2(90) = 109.3207
note: * Prob > chi2 = 0.0812
* asymptotically invalid if the one-step weighting matrix is not optimal
xtabond2 pc_npl l.pc_npl l.gdp avg_roa, noleveleq iv(l.gdp) gmm(l.pc_npl, lag(2 4)) gmm(avg_roa, lag(2 4)) ///
nocons cluster(bank_id) ar(3) small
xtabond2 pc_npl l.pc_npl l.gdp avg_roa, noleveleq iv(l.gdp) gmm(l.pc_npl, lag(2 4)) gmm(avg_roa, lag(2 4)) ///
> nocons cluster(bank_id) ar(3) small
Favoring speed over space. To switch, type or click on mata: mata set matafavor space, 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 difference GMM
------------------------------------------------------------------------------
Group variable: bank_id Number of obs = 1232
Time variable : year Number of groups = 125
Number of instruments = 59 Obs per group: min = 4
F(3, 125) = 120.46 avg = 9.86
Prob > F = 0.000 max = 11
(Std. Err. adjusted for clustering on bank_id)
------------------------------------------------------------------------------
| Robust
pc_npl | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
pc_npl |
L1. | .8271255 .0443198 18.66 0.000 .7394111 .9148399
|
gdp |
L1. | -.1652723 .0434872 -3.80 0.000 -.2513389 -.0792057
|
avg_roa | -1.554786 .2433993 -6.39 0.000 -2.036504 -1.073069
------------------------------------------------------------------------------
Instruments for first differences equation
Standard
D.L.gdp
GMM-type (missing=0, separate instruments for each period unless collapsed)
L(2/4).avg_roa
L(2/4).L.pc_npl
------------------------------------------------------------------------------
Arellano-Bond test for AR(1) in first differences: z = -3.74 Pr > z = 0.000
Arellano-Bond test for AR(2) in first differences: z = -0.87 Pr > z = 0.384
Arellano-Bond test for AR(3) in first differences: z = 1.08 Pr > z = 0.281
------------------------------------------------------------------------------
Sargan test of overid. restrictions: chi2(56) = 276.04 Prob > chi2 = 0.000
(Not robust, but not weakened by many instruments.)
Hansen test of overid. restrictions: chi2(56) = 82.41 Prob > chi2 = 0.012
(Robust, but weakened by many instruments.)
Difference-in-Hansen tests of exogeneity of instrument subsets:
gmm(L.pc_npl, lag(2 4))
Hansen test excluding group: chi2(28) = 51.61 Prob > chi2 = 0.004
Difference (null H = exogenous): chi2(28) = 30.80 Prob > chi2 = 0.326
gmm(avg_roa, lag(2 4))
Hansen test excluding group: chi2(26) = 41.14 Prob > chi2 = 0.030
Difference (null H = exogenous): chi2(30) = 41.28 Prob > chi2 = 0.082
iv(L.gdp)
Hansen test excluding group: chi2(55) = 79.60 Prob > chi2 = 0.017
Difference (null H = exogenous): chi2(1) = 2.82 Prob > chi2 = 0.093
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