Equation Specification xtabond2

[Fillipe Soares]

Dear all,

I'm using xtabond2 program to run a System-GMM regression but due to my lack of experience in estimating such a kind of model I'm not sure if I'm doing this correctly.

To summarize, my dependent variable is I (co2 emissions) and my regressors are Lagged I, P (population), Arpc (per capita GDP), T (technology), Jovens (% of the young population), Urb (% of the urbanized population). I'm also controlling for time fixed effects and to do that I have manually created time dummies for each period of 11 years (year1-year11). Moreover, I'm considering P, Arpc and T as endogenous on the other hand Jovens and Urb as exogenous.

Then I've wrtitten:

xtabond2  L(0/1).I P Arpc T Jovens Urb year3-year11, gmm( (L.I P Arpc T ), laglimits(1 2) collapse equation(diff)) gmm( (L.I P Arpc T), laglimits (1 2) collapse eq(level)) ivstyle(year3-year11 Jovens Urb, eq(level)) robust

Output:

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: Ufs                             Number of obs      =       243
Time variable : Year                        Number of groups   =        27
Number of instruments = 27                      Obs per group: min =         9
Wald chi2(15) =  12631.21                                      avg =      9.00
Prob > chi2   =     0.000                                      max =         9

Robust
I       Coef.   Std. Err.      z    P>z     [95% Conf. Interval]

I
L1.    .6907989   .1206875     5.72   0.000     .4542556    .9273421
            
P    .3544818   .1373551     2.58   0.010     .0852707    .6236929
Arpc    .0193619   .1761628     0.11   0.912    -.3259108    .3646347
T    .2768321   .1494431     1.85   0.064     -.016071    .5697353
Jovens    .5500081   .6569872     0.84   0.402    -.7376632    1.837679
Urb    .1433756   .3570893     0.40   0.688    -.5565066    .8432577
year3    .1007848   .0325687     3.09   0.002     .0369514    .1646182
year4    .0568161   .0276051     2.06   0.040      .002711    .1109211
year5    .0044997   .0342335     0.13   0.895    -.0625967    .0715962
year6           0  (omitted)
year7   -.0018433   .0437424    -0.04   0.966    -.0875769    .0838903
year8    .0895687    .047629     1.88   0.060    -.0037824    .1829197
year9    .0757619   .0492587     1.54   0.124    -.0207834    .1723072
year10    .0882288   .0575049     1.53   0.125    -.0244787    .2009363
year11   -.0233054   .0688169    -0.34   0.735     -.158184    .1115732
_cons   -2.485526    3.38637    -0.73   0.463    -9.122689    4.151637

Instruments for first differences equation
GMM-type (missing=0, separate instruments for each period unless collapsed)
L(1/2).(L.I P Arpc T) collapsed
Instruments for levels equation
Standard
year3 year4 year5 year6 year7 year8 year9 year10 year11 Jovens Urb
_cons
GMM-type (missing=0, separate instruments for each period unless collapsed)
DL(1/2).(L.I P Arpc T) collapsed

Arellano-Bond test for AR(1) in first differences: z =  -2.02  Pr > z =  0.043
Arellano-Bond test for AR(2) in first differences: z =  -0.05  Pr > z =  0.958

Sargan test of overid. restrictions: chi2(11)   =  21.87  Prob > chi2 =  0.025
(Not robust, but not weakened by many instruments.)
Hansen test of overid. restrictions: chi2(11)   =   9.95  Prob > chi2 =  0.535
(Robust, but weakened by many instruments.)

Difference-in-Hansen tests of exogeneity of instrument subsets:
GMM instruments for levels
Hansen test excluding group:     chi2(3)    =   4.92  Prob > chi2 =  0.177
Difference (null H = exogenous): chi2(8)    =   5.03  Prob > chi2 =  0.754
gmm(L.I P Arpc T, collapse eq(diff) lag(1 2))
Hansen test excluding group:     chi2(3)    =   6.95  Prob > chi2 =  0.074
Difference (null H = exogenous): chi2(8)    =   3.00  Prob > chi2 =  0.934
gmm(L.I P Arpc T, collapse eq(level) lag(1 2))
Hansen test excluding group:     chi2(3)    =   4.92  Prob > chi2 =  0.177
Difference (null H = exogenous): chi2(8)    =   5.03  Prob > chi2 =  0.754
iv(year3 year4 year5 year6 year7 year8 year9 year10 year11 Jovens Urb, eq(level))
Hansen test excluding group:     chi2(1)    =   0.50  Prob > chi2 =  0.482
Difference (null H = exogenous): chi2(10)   =   9.46  Prob > chi2 =  0.489

Question:
1) Is my equation correctly specified in terms of what I want to estimate?
2) In the two-step estimate case, is Windmeijer (2005) finite sample corrected standard errors automatically considered?

Thanks in advance

[Sebastian Kripfganz]

1) One of your time dummies was omitted due to the dynamic nature of the model. You should only specify them as year4-year11 to avoid incorrect degrees of freedom for the overidentification tests.
2) The Windmeijer correction is automatically applied when you combine the twostep and the robust options.

[Fillipe Soares]

Thank you very much again, Dr. Kripfganz

Besides the incorrect time dummies specification, is there any other issue in my equation? Especially about the way I have done to define my endogenous and exogenous variables.

[Sebastian Kripfganz]

You have specified your instruments currently as if variables P Arpc T are predetermined. If they are supposed to be endogenous, you would need to specify the following instead:

xtabond2  L(0/1).I P Arpc T Jovens Urb year4-year11, gmm(L.I, laglimits(1 2) collapse equation(diff)) gmm(P Arpc T, laglimits(2 3) collapse equation(diff)) gmm(L.I, laglimits(0 1) collapse eq(level)) gmm(P Arpc T, laglimits(1 2) collapse eq(level)) ivstyle(year4-year11 Jovens Urb, eq(level)) robust

Further note that it is unusual to specify more than one lag in the gmm option for the level equation (although this is not necessarily incorrect).

[Fillipe Soares]

Dr. Kripfganz, I’m deeply grateful.

I really appreciate what you have done!

[Fillipe Soares]

Dr. Kripfganz,

I want to check my results considering my variable Jovens as predetermined.

Is my code below appropriated?

xtabond2  L(0/1).I P Arpc T Jovens ano4-ano11, gmm(L.I, laglimits(1 2) collapse equation(diff)) gmm(Jovens, laglimits(1 2) collapse equation(diff)) gmm(P Arpc T, laglimits(1 2) collapse equation(diff)) gmm(Jovens, laglimits(1 2) collapse equation(level)) gmm(L.I, laglimits(0 1) collapse eq(level)) gmm(P Arpc T, laglimits(1 2) collapse eq(level)) ivstyle(ano4-ano11, eq(level)) twostep small robust