I am a first-time user of STATA. I am trying to use system GMM to estimate a social welfare function. I don't know how to deal with the problem of number of instruments that is larger than the number of groups. I will be glad if I can be guided on how to address the problem. The STATA commands I used and the results are as follows:
import excel "C:\Users\ACER\Documents\phd prop\FLORENCE\PhD Proceed\swf
> model_phd.xlsx", sheet("SWF_E_G100_una_STATA") cellrange(A1:P67) firstro
> w case(lower)
(16 vars, 66 obs)
. describe
Contains data
Observations: 66
Variables: 16
--------------------------------------------------------------------------
Variable Storage Display Value
name type format label Variable label
--------------------------------------------------------------------------
region str13 %13s Region
year int %10.0g Year
socialwelfare double %10.0g Social Welfare
meanincome double %10.0g Mean Income
ginicomplement double %10.0g Gini Complement
y_1 byte %10.0g Y_1
y_2 byte %10.0g Y_2
y_3 byte %10.0g Y_3
y_4 byte %10.0g Y_4
y_5 byte %10.0g Y_5
y_6 byte %10.0g Y_6
y_7 byte %10.0g Y_7
y_8 byte %10.0g Y_8
y_9 byte %10.0g Y_9
y_10 byte %10.0g Y_10
y_11 byte %10.0g Y_11
--------------------------------------------------------------------------
Sorted by:
Note: Dataset has changed since last saved.
.
.
. . xtset Regnam year
Panel variable: Regnam (strongly balanced)
Time variable: year, 2010 to 2020
Delta: 1 unit
eststo: xtabond2 socialwelfareg L.socialwelfareg meanincomeg ginicomplem
> entg y*, twostep robust nomata iv(meanincomeg ginicomplementg) gmm(L.soc
> ialwelfareg, collapse)
y_1 dropped because of collinearity.
y_2 dropped because of collinearity.
y_11 dropped because of collinearity.
Building GMM instruments..
Estimating.
Warning: Two-step estimated covariance matrix of moment conditions is sing
> ular.
Number of instruments may be large relative to number of groups.
Using a generalized inverse to calculate optimal weighting matrix for two-
> step estimation.
Computing Windmeijer finite-sample correction.......
Performing specification tests.
Dynamic panel-data estimation, two-step system GMM
--------------------------------------------------------------------------
> ----
Group variable: Regnam Number of obs =
> 60
Time variable : year Number of groups =
> 6
Number of instruments = 13 Obs per group: min =
> 10
Wald chi2(11) = 777649.73 avg = 1
> 0.00
Prob > chi2 = 0.000 max =
> 10
--------------------------------------------------------------------------
> ----
| Corrected
socialwelf~g | Coefficient std. err. z P>|z| [95% conf. inter
> val]
-------------+------------------------------------------------------------
> ----
socialwelf~g |
L1. | .9976556 .0336563 29.64 0.000 .9316904 1.06
> 3621
|
meanincomeg | .0055871 .0285993 0.20 0.845 -.0504664 .061
> 6407
ginicomple~g | -.014318 .0999197 -0.14 0.886 -.2101571 .181
> 5211
year | -1.67e-22 1.49e-11 -0.00 1.000 -2.92e-11 2.92
> e-11
y_3 | .053454 .0865675 0.62 0.537 -.1162152 .223
> 1231
y_4 | 0 (omitted)
y_5 | 0 (omitted)
y_6 | .1317248 .0409457 3.22 0.001 .0514727 .21
> 1977
y_7 | 0 (omitted)
y_8 | 0 (omitted)
y_9 | 0 (omitted)
y_10 | 0 (omitted)
_cons | 0 (omitted)
--------------------------------------------------------------------------
> ----
Instruments for first differences equation
Standard
D.(meanincomeg ginicomplementg)
GMM-type (missing=0, separate instruments for each period unless collaps
> ed)
L(1/.).L.socialwelfareg collapsed
Instruments for levels equation
Standard
_cons
meanincomeg ginicomplementg
GMM-type (missing=0, separate instruments for each period unless collaps
> ed)
D.L.socialwelfareg collapsed
--------------------------------------------------------------------------
> ----
Arellano-Bond test for AR(1) in first differences: z = -1.82 Pr > z = 0
> .069
Arellano-Bond test for AR(2) in first differences: z = 0.84 Pr > z = 0
> .402
--------------------------------------------------------------------------
> ----
Sargan test of overid. restrictions: chi2(0) = 0.00 Prob > chi2 =
> .
(Not robust, but not weakened by many instruments.)
Hansen test of overid. restrictions: chi2(0) = 0.00 Prob > chi2 =
> .
(Robust, but weakened by many instruments.)
(est1 stored)
Thank you.
Florence Ijagbone
import excel "C:\Users\ACER\Documents\phd prop\FLORENCE\PhD Proceed\swf
> model_phd.xlsx", sheet("SWF_E_G100_una_STATA") cellrange(A1:P67) firstro
> w case(lower)
(16 vars, 66 obs)
. describe
Contains data
Observations: 66
Variables: 16
--------------------------------------------------------------------------
Variable Storage Display Value
name type format label Variable label
--------------------------------------------------------------------------
region str13 %13s Region
year int %10.0g Year
socialwelfare double %10.0g Social Welfare
meanincome double %10.0g Mean Income
ginicomplement double %10.0g Gini Complement
y_1 byte %10.0g Y_1
y_2 byte %10.0g Y_2
y_3 byte %10.0g Y_3
y_4 byte %10.0g Y_4
y_5 byte %10.0g Y_5
y_6 byte %10.0g Y_6
y_7 byte %10.0g Y_7
y_8 byte %10.0g Y_8
y_9 byte %10.0g Y_9
y_10 byte %10.0g Y_10
y_11 byte %10.0g Y_11
--------------------------------------------------------------------------
Sorted by:
Note: Dataset has changed since last saved.
.
.
. . xtset Regnam year
Panel variable: Regnam (strongly balanced)
Time variable: year, 2010 to 2020
Delta: 1 unit
eststo: xtabond2 socialwelfareg L.socialwelfareg meanincomeg ginicomplem
> entg y*, twostep robust nomata iv(meanincomeg ginicomplementg) gmm(L.soc
> ialwelfareg, collapse)
y_1 dropped because of collinearity.
y_2 dropped because of collinearity.
y_11 dropped because of collinearity.
Building GMM instruments..
Estimating.
Warning: Two-step estimated covariance matrix of moment conditions is sing
> ular.
Number of instruments may be large relative to number of groups.
Using a generalized inverse to calculate optimal weighting matrix for two-
> step estimation.
Computing Windmeijer finite-sample correction.......
Performing specification tests.
Dynamic panel-data estimation, two-step system GMM
--------------------------------------------------------------------------
> ----
Group variable: Regnam Number of obs =
> 60
Time variable : year Number of groups =
> 6
Number of instruments = 13 Obs per group: min =
> 10
Wald chi2(11) = 777649.73 avg = 1
> 0.00
Prob > chi2 = 0.000 max =
> 10
--------------------------------------------------------------------------
> ----
| Corrected
socialwelf~g | Coefficient std. err. z P>|z| [95% conf. inter
> val]
-------------+------------------------------------------------------------
> ----
socialwelf~g |
L1. | .9976556 .0336563 29.64 0.000 .9316904 1.06
> 3621
|
meanincomeg | .0055871 .0285993 0.20 0.845 -.0504664 .061
> 6407
ginicomple~g | -.014318 .0999197 -0.14 0.886 -.2101571 .181
> 5211
year | -1.67e-22 1.49e-11 -0.00 1.000 -2.92e-11 2.92
> e-11
y_3 | .053454 .0865675 0.62 0.537 -.1162152 .223
> 1231
y_4 | 0 (omitted)
y_5 | 0 (omitted)
y_6 | .1317248 .0409457 3.22 0.001 .0514727 .21
> 1977
y_7 | 0 (omitted)
y_8 | 0 (omitted)
y_9 | 0 (omitted)
y_10 | 0 (omitted)
_cons | 0 (omitted)
--------------------------------------------------------------------------
> ----
Instruments for first differences equation
Standard
D.(meanincomeg ginicomplementg)
GMM-type (missing=0, separate instruments for each period unless collaps
> ed)
L(1/.).L.socialwelfareg collapsed
Instruments for levels equation
Standard
_cons
meanincomeg ginicomplementg
GMM-type (missing=0, separate instruments for each period unless collaps
> ed)
D.L.socialwelfareg collapsed
--------------------------------------------------------------------------
> ----
Arellano-Bond test for AR(1) in first differences: z = -1.82 Pr > z = 0
> .069
Arellano-Bond test for AR(2) in first differences: z = 0.84 Pr > z = 0
> .402
--------------------------------------------------------------------------
> ----
Sargan test of overid. restrictions: chi2(0) = 0.00 Prob > chi2 =
> .
(Not robust, but not weakened by many instruments.)
Hansen test of overid. restrictions: chi2(0) = 0.00 Prob > chi2 =
> .
(Robust, but weakened by many instruments.)
(est1 stored)
Thank you.
Florence Ijagbone
