I have to perform a difference GMM regression on my panel data. It's not important that it works, but if it does not I need robust motivation for why not.
My panel data is divided in two bigger groups, say A and B. Group A is the one I'm interested in, but I can also use group B in order to have more observations.
I'll report the analysis for group A here.
Group A has the following structure:
Time range: 2000 - 2017
Countries: 46
Total Observation: 855
I have run the following command:
xtabond2 y L(1/2).y L(1/5).x1 L(1/5).x2 x3 x4 x5 i.year x6 x7 , gmm(y, laglimits(3 17)) level(95) robust nolevel
See below for the output. My question is about the interpretation of the test results.
Best,
Al
Results without collapse:
Warning: Number of instruments may be large relative to number of observations.
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: rec_num Number of obs = 421
Time variable : year Number of groups = 38
Number of instruments = 114 Obs per group: min = 1
Wald chi2(0) = . avg = 11.08
Prob > chi2 = . max = 12
----------------------------------------------------------------------------------------
| Robust
y | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-----------------------+----------------------------------------------------------------
y |
L1. | 1.036468 .1018369 10.18 0.000 .8368714 1.236065
L2. | -.0963504 .0962006 -1.00 0.317 -.2849002 .0921994
|
x1 |
L1. | .089542 .0441289 2.03 0.042 .003051 .176033
L2. | .0393409 .0382197 1.03 0.303 -.0355683 .1142501
L3. | .0478129 .0426604 1.12 0.262 -.0358 .1314258
L4. | .0198056 .039333 0.50 0.615 -.0572856 .0968968
L5. | .0234038 .0162282 1.44 0.149 -.0084029 .0552104
|
x2 |
L1. | .2041297 .4241463 0.48 0.630 -.6271818 1.035441
L2. | -1.406561 .9287444 -1.51 0.130 -3.226867 .4137444
L3. | 1.443707 1.04289 1.38 0.166 -.6003206 3.487735
L4. | -.8051038 1.117525 -0.72 0.471 -2.995412 1.385205
L5. | .1804152 .6355273 0.28 0.777 -1.065195 1.426026
|
x3 | -.0055827 .0121747 -0.46 0.647 -.0294446 .0182793
x4 | -.8350265 .5592689 -1.49 0.135 -1.931173 .2611204
x5 | -.0019361 .0019381 -1.00 0.318 -.0057347 .0018624
|
year |
2005 | .2457214 .9466613 0.26 0.795 -1.609701 2.101143
2006 | .1571051 .7962133 0.20 0.844 -1.403444 1.717655
2007 | .2607094 .7426875 0.35 0.726 -1.194931 1.71635
2008 | .0978737 .6215058 0.16 0.875 -1.120255 1.316003
2009 | .0229705 .5160136 0.04 0.964 -.9883975 1.034338
2010 | -.0131881 .4455538 -0.03 0.976 -.8864576 .8600813
2011 | -.0884742 .3828411 -0.23 0.817 -.838829 .6618805
2012 | -.1563695 .3273156 -0.48 0.633 -.7978962 .4851573
2013 | -.1322291 .2503104 -0.53 0.597 -.6228286 .3583703
2014 | -.0865552 .1865422 -0.46 0.643 -.4521712 .2790608
2015 | -.0423805 .1207112 -0.35 0.726 -.2789701 .1942091
2016 | -.019548 .0672854 -0.29 0.771 -.151425 .1123291
|
x6 | -544.3496 737.4712 -0.74 0.460 -1989.767 901.0674
x7 | 543.7989 737.9421 0.74 0.461 -902.541 1990.139
----------------------------------------------------------------------------------------
Instruments for first differences equation
GMM-type (missing=0, separate instruments for each period unless collapsed)
L(3/17).hiv_inf
------------------------------------------------------------------------------
Arellano-Bond test for AR(1) in first differences: z = -1.49 Pr > z = 0.137
Arellano-Bond test for AR(2) in first differences: z = 1.34 Pr > z = 0.180
------------------------------------------------------------------------------
Sargan test of overid. restrictions: chi2(85) = 142.00 Prob > chi2 = 0.000
(Not robust, but not weakened by many instruments.)
Hansen test of overid. restrictions: chi2(85) = 7.86 Prob > chi2 = 1.000
(Robust, but weakened by many instruments.)
Result with collapse:
Dynamic panel-data estimation, one-step difference GMM
------------------------------------------------------------------------------
Group variable: rec_num Number of obs = 422
Time variable : year Number of groups = 38
Number of instruments = 15 Obs per group: min = 1
Wald chi2(0) = . avg = 11.11
Prob > chi2 = . max = 12
----------------------------------------------------------------------------------------
| Robust
y | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-----------------------+----------------------------------------------------------------
y |
L1. | -1.547281 17.0422 -0.09 0.928 -34.94939 31.85483
L2. | 1.268705 14.11864 0.09 0.928 -26.40332 28.94073
|
x1 |
L1. | .5364254 5.925459 0.09 0.928 -11.07726 12.15011
L2. | 1.118569 8.584004 0.13 0.896 -15.70577 17.94291
L3. | -.9398232 12.59783 -0.07 0.941 -25.63112 23.75147
L4. | 1.369626 8.409769 0.16 0.871 -15.11322 17.85247
L5. | -.3716305 2.506262 -0.15 0.882 -5.283814 4.540553
|
x2 |
L1. | 13.32372 169.2516 0.08 0.937 -318.4034 345.0508
L2. | -1.634898 59.74055 -0.03 0.978 -118.7242 115.4544
L3. | -20.85329 226.6722 -0.09 0.927 -465.1226 423.416
L4. | 22.77116 243.3968 0.09 0.925 -454.2778 499.8201
L5. | -7.901386 52.83028 -0.15 0.881 -111.4468 95.64406
|
x3 | .2881728 3.929217 0.07 0.942 -7.412952 7.989297
x4 | -13.31332 99.59179 -0.13 0.894 -208.5096 181.883
x5 | .0391301 .1761786 0.22 0.824 -.3061737 .3844339
----------------------------------------------------------------------------------------
Instruments for first differences equation
GMM-type (missing=0, separate instruments for each period unless collapsed)
L(3/17).hiv_inf collapsed
------------------------------------------------------------------------------
Arellano-Bond test for AR(1) in first differences: z = 0.11 Pr > z = 0.910
Arellano-Bond test for AR(2) in first differences: z = 0.13 Pr > z = 0.899
------------------------------------------------------------------------------
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.)
My panel data is divided in two bigger groups, say A and B. Group A is the one I'm interested in, but I can also use group B in order to have more observations.
I'll report the analysis for group A here.
Group A has the following structure:
Time range: 2000 - 2017
Countries: 46
Total Observation: 855
I have run the following command:
xtabond2 y L(1/2).y L(1/5).x1 L(1/5).x2 x3 x4 x5 i.year x6 x7 , gmm(y, laglimits(3 17)) level(95) robust nolevel
See below for the output. My question is about the interpretation of the test results.
- First: Number of instruments = 114, where does this number come from? I have counted 17-3 = 14 instruments using gmm(y, laglimits(3 17)).
- Second: My interpretation of the Sargan and Hansen test to be so extremely different is that I have too many instruments. Is this correct? What would be a correct amount of instruments for this panel data frame?
- Third: Following my guess in "Second" I have collapsed the instruments, with the result of not having enough of them for all the independent variables. Reducing the variables (using only L(1/2).y L(1/5).x1 L(1/5).x2 x3 x4 x5), I get Sargan and Hansen test both 0. I interpret this result as not enough instruments for the GMM to work (see also that the confidence intervals are huge!). Is this correct?
Best,
Al
Results without collapse:
Warning: Number of instruments may be large relative to number of observations.
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: rec_num Number of obs = 421
Time variable : year Number of groups = 38
Number of instruments = 114 Obs per group: min = 1
Wald chi2(0) = . avg = 11.08
Prob > chi2 = . max = 12
----------------------------------------------------------------------------------------
| Robust
y | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-----------------------+----------------------------------------------------------------
y |
L1. | 1.036468 .1018369 10.18 0.000 .8368714 1.236065
L2. | -.0963504 .0962006 -1.00 0.317 -.2849002 .0921994
|
x1 |
L1. | .089542 .0441289 2.03 0.042 .003051 .176033
L2. | .0393409 .0382197 1.03 0.303 -.0355683 .1142501
L3. | .0478129 .0426604 1.12 0.262 -.0358 .1314258
L4. | .0198056 .039333 0.50 0.615 -.0572856 .0968968
L5. | .0234038 .0162282 1.44 0.149 -.0084029 .0552104
|
x2 |
L1. | .2041297 .4241463 0.48 0.630 -.6271818 1.035441
L2. | -1.406561 .9287444 -1.51 0.130 -3.226867 .4137444
L3. | 1.443707 1.04289 1.38 0.166 -.6003206 3.487735
L4. | -.8051038 1.117525 -0.72 0.471 -2.995412 1.385205
L5. | .1804152 .6355273 0.28 0.777 -1.065195 1.426026
|
x3 | -.0055827 .0121747 -0.46 0.647 -.0294446 .0182793
x4 | -.8350265 .5592689 -1.49 0.135 -1.931173 .2611204
x5 | -.0019361 .0019381 -1.00 0.318 -.0057347 .0018624
|
year |
2005 | .2457214 .9466613 0.26 0.795 -1.609701 2.101143
2006 | .1571051 .7962133 0.20 0.844 -1.403444 1.717655
2007 | .2607094 .7426875 0.35 0.726 -1.194931 1.71635
2008 | .0978737 .6215058 0.16 0.875 -1.120255 1.316003
2009 | .0229705 .5160136 0.04 0.964 -.9883975 1.034338
2010 | -.0131881 .4455538 -0.03 0.976 -.8864576 .8600813
2011 | -.0884742 .3828411 -0.23 0.817 -.838829 .6618805
2012 | -.1563695 .3273156 -0.48 0.633 -.7978962 .4851573
2013 | -.1322291 .2503104 -0.53 0.597 -.6228286 .3583703
2014 | -.0865552 .1865422 -0.46 0.643 -.4521712 .2790608
2015 | -.0423805 .1207112 -0.35 0.726 -.2789701 .1942091
2016 | -.019548 .0672854 -0.29 0.771 -.151425 .1123291
|
x6 | -544.3496 737.4712 -0.74 0.460 -1989.767 901.0674
x7 | 543.7989 737.9421 0.74 0.461 -902.541 1990.139
----------------------------------------------------------------------------------------
Instruments for first differences equation
GMM-type (missing=0, separate instruments for each period unless collapsed)
L(3/17).hiv_inf
------------------------------------------------------------------------------
Arellano-Bond test for AR(1) in first differences: z = -1.49 Pr > z = 0.137
Arellano-Bond test for AR(2) in first differences: z = 1.34 Pr > z = 0.180
------------------------------------------------------------------------------
Sargan test of overid. restrictions: chi2(85) = 142.00 Prob > chi2 = 0.000
(Not robust, but not weakened by many instruments.)
Hansen test of overid. restrictions: chi2(85) = 7.86 Prob > chi2 = 1.000
(Robust, but weakened by many instruments.)
Result with collapse:
Dynamic panel-data estimation, one-step difference GMM
------------------------------------------------------------------------------
Group variable: rec_num Number of obs = 422
Time variable : year Number of groups = 38
Number of instruments = 15 Obs per group: min = 1
Wald chi2(0) = . avg = 11.11
Prob > chi2 = . max = 12
----------------------------------------------------------------------------------------
| Robust
y | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-----------------------+----------------------------------------------------------------
y |
L1. | -1.547281 17.0422 -0.09 0.928 -34.94939 31.85483
L2. | 1.268705 14.11864 0.09 0.928 -26.40332 28.94073
|
x1 |
L1. | .5364254 5.925459 0.09 0.928 -11.07726 12.15011
L2. | 1.118569 8.584004 0.13 0.896 -15.70577 17.94291
L3. | -.9398232 12.59783 -0.07 0.941 -25.63112 23.75147
L4. | 1.369626 8.409769 0.16 0.871 -15.11322 17.85247
L5. | -.3716305 2.506262 -0.15 0.882 -5.283814 4.540553
|
x2 |
L1. | 13.32372 169.2516 0.08 0.937 -318.4034 345.0508
L2. | -1.634898 59.74055 -0.03 0.978 -118.7242 115.4544
L3. | -20.85329 226.6722 -0.09 0.927 -465.1226 423.416
L4. | 22.77116 243.3968 0.09 0.925 -454.2778 499.8201
L5. | -7.901386 52.83028 -0.15 0.881 -111.4468 95.64406
|
x3 | .2881728 3.929217 0.07 0.942 -7.412952 7.989297
x4 | -13.31332 99.59179 -0.13 0.894 -208.5096 181.883
x5 | .0391301 .1761786 0.22 0.824 -.3061737 .3844339
----------------------------------------------------------------------------------------
Instruments for first differences equation
GMM-type (missing=0, separate instruments for each period unless collapsed)
L(3/17).hiv_inf collapsed
------------------------------------------------------------------------------
Arellano-Bond test for AR(1) in first differences: z = 0.11 Pr > z = 0.910
Arellano-Bond test for AR(2) in first differences: z = 0.13 Pr > z = 0.899
------------------------------------------------------------------------------
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.)
