Dear Statalist members,
I have a problem with some output from xtabond2 (two step sys-gmm)
When i run my estimations without dummy variables, more than half are omitted. In addition my Sargan and Hansen statistics increase too much (in my opinion).
Back ground on my research: I am running a dynamic panel model with the aim at assessing the cyclicality of labour compensation growth across Canadian provinces for the period of 1997-2013. Hence, my N=10 and my T=15, which i know is not entirely favourable for this estimation method but my thesis supervisor insists i run this model. Theoretically, non of my variables are endogenous apart from the dependant variable (labour compensation growth), thus this is the only internal instrument i intend to use. Further, i have ran simple OLS, FE and RE estimations, with the hausman test indicating my data fits the RE specification better.
Please find my out put below (inc year dummies):
xtabond2 L(0/1).gr_comp_r fisc_def_gdp_r elections gr_gap_r gdp_pc_r union_rate fiscal_rule
> s yr_1999-yr_2013, artests (3) gmmstyle(L.gr_comp_r, equation(diff) lag(1 2) collapse) ivst
> yle(gr_gap_r elections fiscal_rules fisc_def_gdp_r gdp_pc_r union_rate, equation(diff)) ivs
> tyle(yr_1999-yr_2013, equation(level)) robust two
Favoring space over speed. To switch, type or click on mata: mata set matafavor speed, perm.
yr_2002 dropped due to collinearity
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 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: province Number of obs = 150
Time variable : year Number of groups = 10
Number of instruments = 23 Obs per group: min = 15
Wald chi2(21) = 148342.93 avg = 15.00
Prob > chi2 = 0.000 max = 15
--------------------------------------------------------------------------------
| Corrected
gr_comp_r | Coef. Std. Err. z P>|z| [95% Conf. Interval]
---------------+----------------------------------------------------------------
gr_comp_r |
L1. | .0902523 .3070858 0.29 0.769 -.5116248 .6921295
|
fisc_def_gdp_r | -.0135247 .0040063 -3.38 0.001 -.021377 -.0056725
elections | 1.178697 .6221003 1.89 0.058 -.040597 2.397991
gr_gap_r | -.2798814 .0795031 -3.52 0.000 -.4357046 -.1240582
gdp_pc_r | -.000209 .0003148 -0.66 0.507 -.000826 .000408
union_rate | .1323513 .146787 0.90 0.367 -.1553459 .4200485
fiscal_rules | 0 (omitted)
yr_1999 | 0 (omitted)
yr_2000 | 2.160893 3.425384 0.63 0.528 -4.552736 8.874521
yr_2001 | 0 (omitted)
yr_2003 | 0 (omitted)
yr_2004 | 0 (omitted)
yr_2005 | -.7708339 .8262825 -0.93 0.351 -2.390318 .8486501
yr_2006 | 0 (omitted)
yr_2007 | 0 (omitted)
yr_2008 | 1.988903 2.298823 0.87 0.387 -2.516707 6.494512
yr_2009 | 0 (omitted)
yr_2010 | 0 (omitted)
yr_2011 | 0 (omitted)
yr_2012 | -.0870417 1.653714 -0.05 0.958 -3.328261 3.154178
yr_2013 | 0 (omitted)
_cons | 0 (omitted)
--------------------------------------------------------------------------------
Instruments for first differences equation
Standard
D.(gr_gap_r elections fiscal_rules fisc_def_gdp_r gdp_pc_r union_rate)
GMM-type (missing=0, separate instruments for each period unless collapsed)
L(1/2).L.gr_comp_r collapsed
Instruments for levels equation
Standard
yr_1999 yr_2000 yr_2001 yr_2002 yr_2003 yr_2004 yr_2005 yr_2006 yr_2007
yr_2008 yr_2009 yr_2010 yr_2011 yr_2012 yr_2013
_cons
------------------------------------------------------------------------------
Arellano-Bond test for AR(1) in first differences: z = -2.04 Pr > z = 0.041
Arellano-Bond test for AR(2) in first differences: z = 0.23 Pr > z = 0.817
Arellano-Bond test for AR(3) in first differences: z = -0.71 Pr > z = 0.475
------------------------------------------------------------------------------
Sargan test of overid. restrictions: chi2(1) = 0.03 Prob > chi2 = 0.860
(Not robust, but not weakened by many instruments.)
Hansen test of overid. restrictions: chi2(1) = 0.00 Prob > chi2 = 1.000
(Robust, but weakened by many instruments.)
without year dummies:
. xtabond2 L(0/1).gr_comp_r fisc_def_gdp_r elections gr_gap_r gdp_pc_r union_rate fiscal_rule
> s, artests (3) gmmstyle(L.gr_comp_r, equation(diff) lag(1 2) collapse) ivstyle(gr_gap_r ele
> ctions fiscal_rules fisc_def_gdp_r gdp_pc_r union_rate, equation(diff)) robust two
Favoring space over speed. To switch, type or click on mata: mata set matafavor speed, perm.
Dynamic panel-data estimation, two-step system GMM
------------------------------------------------------------------------------
Group variable: province Number of obs = 150
Time variable : year Number of groups = 10
Number of instruments = 9 Obs per group: min = 15
Wald chi2(7) = 1522.55 avg = 15.00
Prob > chi2 = 0.000 max = 15
--------------------------------------------------------------------------------
| Corrected
gr_comp_r | Coef. Std. Err. z P>|z| [95% Conf. Interval]
---------------+----------------------------------------------------------------
gr_comp_r |
L1. | .2848518 .1807544 1.58 0.115 -.0694203 .6391239
|
fisc_def_gdp_r | -.0166521 .0031338 -5.31 0.000 -.0227941 -.01051
elections | .8123819 .5155152 1.58 0.115 -.1980093 1.822773
gr_gap_r | -.292718 .0801691 -3.65 0.000 -.4498464 -.1355895
gdp_pc_r | 4.33e-06 .0001704 0.03 0.980 -.0003296 .0003383
union_rate | -.0652441 .2687818 -0.24 0.808 -.5920467 .4615585
fiscal_rules | -4.301556 3.783878 -1.14 0.256 -11.71782 3.114709
_cons | 9.507943 23.32165 0.41 0.684 -36.20165 55.21754
--------------------------------------------------------------------------------
Instruments for first differences equation
Standard
D.(gr_gap_r elections fiscal_rules fisc_def_gdp_r gdp_pc_r union_rate)
GMM-type (missing=0, separate instruments for each period unless collapsed)
L(1/2).L.gr_comp_r collapsed
Instruments for levels equation
Standard
_cons
------------------------------------------------------------------------------
Arellano-Bond test for AR(1) in first differences: z = -2.22 Pr > z = 0.026
Arellano-Bond test for AR(2) in first differences: z = 1.34 Pr > z = 0.179
Arellano-Bond test for AR(3) in first differences: z = -1.30 Pr > z = 0.194
------------------------------------------------------------------------------
Sargan test of overid. restrictions: chi2(1) = 0.64 Prob > chi2 = 0.422
(Not robust, but not weakened by many instruments.)
Hansen test of overid. restrictions: chi2(1) = 0.99 Prob > chi2 = 0.321
(Robust, but weakened by many instruments.)
From what i understand, my instruments are valid, since the Hansen/Sargan tests cannot be rejected. My SC (1), (2) and (3) also seem quite adequate. I welcome any advice from where i should proceed from here, mainly in relation to the year dummies but also if i have made any fatal errors in my syntax or interpretation.
ps. i have read some papers where they have reported significant Sargan tests, and others whether the Sargan tests is not significant. From what i have read it should not be <5% (as a rule of thumb) but these papers have me second guessing...clarification on this would also be great!!
I look forward to any relevant input,
with appreciation,
Jordan
I have a problem with some output from xtabond2 (two step sys-gmm)
When i run my estimations without dummy variables, more than half are omitted. In addition my Sargan and Hansen statistics increase too much (in my opinion).
Back ground on my research: I am running a dynamic panel model with the aim at assessing the cyclicality of labour compensation growth across Canadian provinces for the period of 1997-2013. Hence, my N=10 and my T=15, which i know is not entirely favourable for this estimation method but my thesis supervisor insists i run this model. Theoretically, non of my variables are endogenous apart from the dependant variable (labour compensation growth), thus this is the only internal instrument i intend to use. Further, i have ran simple OLS, FE and RE estimations, with the hausman test indicating my data fits the RE specification better.
Please find my out put below (inc year dummies):
xtabond2 L(0/1).gr_comp_r fisc_def_gdp_r elections gr_gap_r gdp_pc_r union_rate fiscal_rule
> s yr_1999-yr_2013, artests (3) gmmstyle(L.gr_comp_r, equation(diff) lag(1 2) collapse) ivst
> yle(gr_gap_r elections fiscal_rules fisc_def_gdp_r gdp_pc_r union_rate, equation(diff)) ivs
> tyle(yr_1999-yr_2013, equation(level)) robust two
Favoring space over speed. To switch, type or click on mata: mata set matafavor speed, perm.
yr_2002 dropped due to collinearity
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 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: province Number of obs = 150
Time variable : year Number of groups = 10
Number of instruments = 23 Obs per group: min = 15
Wald chi2(21) = 148342.93 avg = 15.00
Prob > chi2 = 0.000 max = 15
--------------------------------------------------------------------------------
| Corrected
gr_comp_r | Coef. Std. Err. z P>|z| [95% Conf. Interval]
---------------+----------------------------------------------------------------
gr_comp_r |
L1. | .0902523 .3070858 0.29 0.769 -.5116248 .6921295
|
fisc_def_gdp_r | -.0135247 .0040063 -3.38 0.001 -.021377 -.0056725
elections | 1.178697 .6221003 1.89 0.058 -.040597 2.397991
gr_gap_r | -.2798814 .0795031 -3.52 0.000 -.4357046 -.1240582
gdp_pc_r | -.000209 .0003148 -0.66 0.507 -.000826 .000408
union_rate | .1323513 .146787 0.90 0.367 -.1553459 .4200485
fiscal_rules | 0 (omitted)
yr_1999 | 0 (omitted)
yr_2000 | 2.160893 3.425384 0.63 0.528 -4.552736 8.874521
yr_2001 | 0 (omitted)
yr_2003 | 0 (omitted)
yr_2004 | 0 (omitted)
yr_2005 | -.7708339 .8262825 -0.93 0.351 -2.390318 .8486501
yr_2006 | 0 (omitted)
yr_2007 | 0 (omitted)
yr_2008 | 1.988903 2.298823 0.87 0.387 -2.516707 6.494512
yr_2009 | 0 (omitted)
yr_2010 | 0 (omitted)
yr_2011 | 0 (omitted)
yr_2012 | -.0870417 1.653714 -0.05 0.958 -3.328261 3.154178
yr_2013 | 0 (omitted)
_cons | 0 (omitted)
--------------------------------------------------------------------------------
Instruments for first differences equation
Standard
D.(gr_gap_r elections fiscal_rules fisc_def_gdp_r gdp_pc_r union_rate)
GMM-type (missing=0, separate instruments for each period unless collapsed)
L(1/2).L.gr_comp_r collapsed
Instruments for levels equation
Standard
yr_1999 yr_2000 yr_2001 yr_2002 yr_2003 yr_2004 yr_2005 yr_2006 yr_2007
yr_2008 yr_2009 yr_2010 yr_2011 yr_2012 yr_2013
_cons
------------------------------------------------------------------------------
Arellano-Bond test for AR(1) in first differences: z = -2.04 Pr > z = 0.041
Arellano-Bond test for AR(2) in first differences: z = 0.23 Pr > z = 0.817
Arellano-Bond test for AR(3) in first differences: z = -0.71 Pr > z = 0.475
------------------------------------------------------------------------------
Sargan test of overid. restrictions: chi2(1) = 0.03 Prob > chi2 = 0.860
(Not robust, but not weakened by many instruments.)
Hansen test of overid. restrictions: chi2(1) = 0.00 Prob > chi2 = 1.000
(Robust, but weakened by many instruments.)
without year dummies:
. xtabond2 L(0/1).gr_comp_r fisc_def_gdp_r elections gr_gap_r gdp_pc_r union_rate fiscal_rule
> s, artests (3) gmmstyle(L.gr_comp_r, equation(diff) lag(1 2) collapse) ivstyle(gr_gap_r ele
> ctions fiscal_rules fisc_def_gdp_r gdp_pc_r union_rate, equation(diff)) robust two
Favoring space over speed. To switch, type or click on mata: mata set matafavor speed, perm.
Dynamic panel-data estimation, two-step system GMM
------------------------------------------------------------------------------
Group variable: province Number of obs = 150
Time variable : year Number of groups = 10
Number of instruments = 9 Obs per group: min = 15
Wald chi2(7) = 1522.55 avg = 15.00
Prob > chi2 = 0.000 max = 15
--------------------------------------------------------------------------------
| Corrected
gr_comp_r | Coef. Std. Err. z P>|z| [95% Conf. Interval]
---------------+----------------------------------------------------------------
gr_comp_r |
L1. | .2848518 .1807544 1.58 0.115 -.0694203 .6391239
|
fisc_def_gdp_r | -.0166521 .0031338 -5.31 0.000 -.0227941 -.01051
elections | .8123819 .5155152 1.58 0.115 -.1980093 1.822773
gr_gap_r | -.292718 .0801691 -3.65 0.000 -.4498464 -.1355895
gdp_pc_r | 4.33e-06 .0001704 0.03 0.980 -.0003296 .0003383
union_rate | -.0652441 .2687818 -0.24 0.808 -.5920467 .4615585
fiscal_rules | -4.301556 3.783878 -1.14 0.256 -11.71782 3.114709
_cons | 9.507943 23.32165 0.41 0.684 -36.20165 55.21754
--------------------------------------------------------------------------------
Instruments for first differences equation
Standard
D.(gr_gap_r elections fiscal_rules fisc_def_gdp_r gdp_pc_r union_rate)
GMM-type (missing=0, separate instruments for each period unless collapsed)
L(1/2).L.gr_comp_r collapsed
Instruments for levels equation
Standard
_cons
------------------------------------------------------------------------------
Arellano-Bond test for AR(1) in first differences: z = -2.22 Pr > z = 0.026
Arellano-Bond test for AR(2) in first differences: z = 1.34 Pr > z = 0.179
Arellano-Bond test for AR(3) in first differences: z = -1.30 Pr > z = 0.194
------------------------------------------------------------------------------
Sargan test of overid. restrictions: chi2(1) = 0.64 Prob > chi2 = 0.422
(Not robust, but not weakened by many instruments.)
Hansen test of overid. restrictions: chi2(1) = 0.99 Prob > chi2 = 0.321
(Robust, but weakened by many instruments.)
From what i understand, my instruments are valid, since the Hansen/Sargan tests cannot be rejected. My SC (1), (2) and (3) also seem quite adequate. I welcome any advice from where i should proceed from here, mainly in relation to the year dummies but also if i have made any fatal errors in my syntax or interpretation.
ps. i have read some papers where they have reported significant Sargan tests, and others whether the Sargan tests is not significant. From what i have read it should not be <5% (as a rule of thumb) but these papers have me second guessing...clarification on this would also be great!!
I look forward to any relevant input,
with appreciation,
Jordan
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