GMM xtabond2

[Rijad Kovac]

Dear

I am trying to do GMM xtabond2 and I have few questions. My specification is measuring inequality logINEQit= a + logINEQit-1 + logM2+ logGDP growth + logInflation+ logEMPin Agric + loggdp_pc + GovEXPEN+ institutions + e. It analyses impact of institutions and financial depth on inequality, it is unbalanced panel with years 2000, 2010-2016

My command is
xtabond2 Log_WGINI l.Log_WGINI Log_Bro_Mon_GDP Log_GDP_Growth Log_INFL_DEF Log_AGR_EMP Log_EXP_GDP Log_os y57 y56 y55 y54 y53 y52 , gmm ( Log_WGINI Log_Bro_Mon_GDP Log_GDP_Growth Log_INFL_DEF Log_AGR_EMP Log_EXP_GDP Log_os , lag(2 3)collapse) ivstyle(Log_RINTR y57 y56 y55 y54 y53 y52 , equation(level) ) twostep robust small orthog

My variables are macro and there might be some collinearity
Questions:
1. Is this command correctly specified? I want GMM in levels, trying not to go to deep with lags
2. My specification is very sensitive to changes in variables (I tried without time dummies and it was more stable...but it seems that time dummies are must)
3. it is sensitive to option "collapse" (I keep less instruments than groups, but when I put collapse my significance and magnitude of the coefficients changes) do I haave to use it in an unbalanced panel
4.is there some rule or good practice about size of the correlation among variables in the specification
5. Can someone tell something on short vs long term coefficients magnitude in GMM
5. I would like to validate the results using maximum likelihood but and I have seen the command xtdpdqml but I do not know how to "translate" my xtabond conditions, also post estimation is not clear to me.

Thank you, best
rijad


My command is
xtabond2 Log_WGINI l.Log_WGINI Log_Bro_Mon_GDP Log_GDP_Growth Log_INFL_DEF Log_AGR_EMP Log_EXP_GDP Log_os y57 y56 y55 y54 y53 y52 , gmm ( Log_WGINI Log_Bro_Mon_GDP Log_GDP_Growth Log_INFL_DEF Log_AGR_EMP Log_EXP_GDP Log_os , lag(2 3)collapse) ivstyle(Log_RINTR y57 y56 y55 y54 y53 y52 , equation(level) ) twostep robust small orthog
OUTPUT is:


. xtabond2 Log_WGINI l.Log_WGINI Log_Bro_Mon_GDP Log_GDP_Growth Log_INFL_DEF Log_AGR_EMP Log_EXP_GDP Log_os y57 y56 y55 y54 y53 y52 , gmm ( Log_WGI
> NI Log_Bro_Mon_GDP Log_GDP_Growth Log_INFL_DEF Log_AGR_EMP Log_EXP_GDP Log_os , lag(2 3)collapse) ivstyle(Log_RINTR y57 y56 y55 y54 y53 y52 , e
> quation(level) ) twostep robust small orthog
Favoring space over speed. To switch, type or click on mata: mata set matafavor speed, perm.
y54 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.
Difference-in-Sargan/Hansen statistics may be negative.

Dynamic panel-data estimation, two-step system GMM
------------------------------------------------------------------------------
Group variable: Country Number of obs = 260
Time variable : year Number of groups = 80
Number of instruments = 28 Obs per group: min = 0
F(12, 79) = 5.62 avg = 3.25
Prob > F = 0.000 max = 6
---------------------------------------------------------------------------------
| Corrected
Log_WGINI | Coef. Std. Err. t P>|t| [95% Conf. Interval]
----------------+----------------------------------------------------------------
Log_WGINI |
L1. | .3934571 .1321549 2.98 0.004 .1304094 .6565047
|
Log_Bro_Mon_GDP | .2073853 .0797135 2.60 0.011 .0487196 .366051
Log_GDP_Growth | .0158236 .0332168 0.48 0.635 -.0502928 .0819399
Log_INFL_DEF | -.0106071 .0149894 -0.71 0.481 -.0404426 .0192285
Log_AGR_EMP | .0576048 .0348487 1.65 0.102 -.0117599 .1269695
Log_EXP_GDP | -.0359691 .0777016 -0.46 0.645 -.1906302 .118692
Log_os | -.8000739 .3165686 -2.53 0.013 -1.430188 -.16996
y57 | .0604502 .0249565 2.42 0.018 .0107755 .1101249
y56 | .0319879 .018417 1.74 0.086 -.0046703 .0686461
y55 | .0388815 .0214744 1.81 0.074 -.0038622 .0816253
y53 | .0166005 .0128533 1.29 0.200 -.0089834 .0421844
y52 | .0252226 .0143333 1.76 0.082 -.0033071 .0537524
_cons | 2.193212 1.012806 2.17 0.033 .1772707 4.209152
---------------------------------------------------------------------------------
Instruments for orthogonal deviations equation
GMM-type (missing=0, separate instruments for each period unless collapsed)
L(2/3).(Log_WGINI Log_Bro_Mon_GDP Log_GDP_Growth Log_INFL_DEF Log_AGR_EMP
Log_EXP_GDP Log_os) collapsed
Instruments for levels equation
Standard
Log_RINTR y57 y56 y55 y54 y53 y52
_cons
GMM-type (missing=0, separate instruments for each period unless collapsed)
DL.(Log_WGINI Log_Bro_Mon_GDP Log_GDP_Growth Log_INFL_DEF Log_AGR_EMP
Log_EXP_GDP Log_os) collapsed
------------------------------------------------------------------------------
Arellano-Bond test for AR(1) in first differences: z = -2.25 Pr > z = 0.024
Arellano-Bond test for AR(2) in first differences: z = -0.31 Pr > z = 0.758
------------------------------------------------------------------------------
Sargan test of overid. restrictions: chi2(15) = 14.41 Prob > chi2 = 0.495
(Not robust, but not weakened by many instruments.)
Hansen test of overid. restrictions: chi2(15) = 10.77 Prob > chi2 = 0.768
(Robust, but weakened by many instruments.)

Difference-in-Hansen tests of exogeneity of instrument subsets:
GMM instruments for levels
Hansen test excluding group: chi2(8) = 7.85 Prob > chi2 = 0.448
Difference (null H = exogenous): chi2(7) = 2.92 Prob > chi2 = 0.892
iv(Log_RINTR y57 y56 y55 y54 y53 y52, eq(level))
Hansen test excluding group: chi2(9) = 8.65 Prob > chi2 = 0.470
Difference (null H = exogenous): chi2(6) = 2.12 Prob > chi2 = 0.908

[Sebastian Kripfganz]

Questions:
1. Is this command correctly specified? I want GMM in levels, trying not to go to deep with lags
2. My specification is very sensitive to changes in variables (I tried without time dummies and it was more stable...but it seems that time dummies are must)
3. it is sensitive to option "collapse" (I keep less instruments than groups, but when I put collapse my significance and magnitude of the coefficients changes) do I haave to use it in an unbalanced panel
4. is there some rule or good practice about size of the correlation among variables in the specification
5. Can someone tell something on short vs long term coefficients magnitude in GMM
6. I would like to validate the results using maximum likelihood but and I have seen the command xtdpdqml but I do not know how to "translate" my xtabond conditions, also post estimation is not clear to me.

1. Your command combines moment conditions for the forward-orthogonal transformed model with moment conditions for the model in levels. This is a system-GMM estimator. If that is what you want, then your specification appears to be fine.
2. Unfortunately, such a sensitivity to the specification is quite common, in particular with small sample sizes. In macroeconomic applications, the inclusion of time dummies is indeed usually recommended to capture global shocks that affect all countries equally.
3. In case of doubt, the collapse option should be used, in particular when your sample is largely unbalanced.
5. Not sure what you have in mind. You can compute the long-run coefficients with the nlcom command, e.g. nlcom _b[Log_os] / (1 - _b[L.Log_WGINI])
6. You could specify the xtdpdqml command as follows:

xtdpdqml Log_WGINI Log_Bro_Mon_GDP Log_GDP_Growth Log_INFL_DEF Log_AGR_EMP Log_EXP_GDP Log_os y57 y56 y55 y54 y53, projection(Log_Bro_Mon_GDP Log_GDP_Growth Log_INFL_DEF Log_AGR_EMP Log_EXP_GDP Log_os y57 y56 y55 y54 y53, leads(0))

Note that the lagged dependent variable is added automatically and should not be specified manually. The projection() option specifies the variables used to explain the initial observations of the dependent variables. I have used the suboption leads(0) here to avoid an overparameterization (similar to the lag restriction in GMM). More information:
XTDPDQML: new Stata command for quasi-maximum likelihood estimation of linear dynamic panel models

[Rijad Kovac]

dear Sir
thank you, I applied the command and I get quite different results, where lagged variable of wealth is with smaller coefficient, and new variable appeared to be significant. it is interesting comparison.I do not know much about xtdpdqml I will try to learn.
best regards
rijad

. xtdpdqml Log_WGINI Log_Bro_Mon_GDP Log_GDP_Growth Log_INFL_DEF Log_AGR_EMP Log_EXP_GDP Log_os y57 y56 y55 y54 y53, projection(Log_Bro_Mon_GDP Log_
> GDP_Growth Log_INFL_DEF Log_AGR_EMP Log_EXP_GDP Log_os y57 y56 y55 y54 y53, leads(0))
note: 32 groups are dropped due to gaps or insufficient number of observations

Quasi-maximum likelihood estimation
Iteration 0: f(p) = 365.71162
Iteration 1: f(p) = 373.36118
Iteration 2: f(p) = 374.31185
Iteration 3: f(p) = 374.31903
Iteration 4: f(p) = 374.31904

Group variable: Country Number of obs = 238
Time variable: year Number of groups = 59

Fixed effects Obs per group: min = 2
avg = 4.033898
(Estimation in first differences) max = 6
---------------------------------------------------------------------------------
Log_WGINI | Coef. Std. Err. z P>|z| [95% Conf. Interval]
----------------+----------------------------------------------------------------
Log_WGINI |
L1. | .1515227 .0523622 2.89 0.004 .0488947 .2541507
|
Log_Bro_Mon_GDP | -.0023457 .032254 -0.07 0.942 -.0655624 .060871
Log_GDP_Growth | .0050074 .0047447 1.06 0.291 -.0042922 .0143069
Log_INFL_DEF | .0049546 .0041001 1.21 0.227 -.0030816 .0129907
Log_AGR_EMP | .016715 .0462376 0.36 0.718 -.0739089 .107339
Log_EXP_GDP | .0982492 .0469503 2.09 0.036 .0062282 .1902701
Log_os | .2192783 .1425535 1.54 0.124 -.0601215 .4986781

y57 | .0867251 .0134498 6.45 0.000 .060364 .1130863
y56 | -.002869 .0103216 -0.28 0.781 -.0230989 .0173609
y55 | .0038386 .0088254 0.43 0.664 -.0134589 .0211361
y54 | -.0074828 .0080887 -0.93 0.355 -.0233363 .0083707
y53 | -.0066833 .0071666 -0.93 0.351 -.0207295 .007363
_cons | -1.491089 .6359936 -2.34 0.019 -2.737613 -.2445641
---------------------------------------------------------------------------------