Hello Everyone!
First of all, I'm a beginner in Stata and learned it about 2 months back. In my research, I am estimating 2 equations: labor demand equation and wage equation. I am trying to estimate these two equations using xtabond2 by Roodman. However, I am not getting the good or required results and i have been unable to find the fault. So, here i am, posting my results below and eagerly waiting for some insightful comments.
Labor demand equation:
xtabond2 log_L l.log_L log_Y log_W log_K log_tr_share log_rer log_LP Timetrend, gmm (log_W log_Y, lag(4 4)) iv(log_tr_share log_K log_LP log_rer) small
Favoring space over speed. To switch, type or click on mata: mata set matafavor speed, perm.
Warning: Number of instruments may be large relative to number of observations.
Dynamic panel-data estimation, one-step system GMM
------------------------------------------------------------------------------
Group variable: id Number of obs = 512
Time variable : Time Number of groups = 32
Number of instruments = 57 Obs per group: min = 16
F(8, 503) = 195177.35 avg = 16.00
Prob > F = 0.000 max = 16
------------------------------------------------------------------------------
log_L | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
log_L |
L1. | .9899778 .0211435 46.82 0.000 .9484374 1.031518
|
log_Y | .0120626 .0269896 0.45 0.655 -.0409636 .0650889
log_W | .0009886 .0011234 0.88 0.379 -.0012185 .0031957
log_K | .0013748 .0154829 0.09 0.929 -.0290443 .0317939
log_tr_share | .0073258 .0081577 0.90 0.370 -.0087017 .0233532
log_rer | .001907 .0007947 2.40 0.017 .0003456 .0034683
log_LP | -.0142728 .0238305 -0.60 0.549 -.0610923 .0325467
Timetrend | -.0004422 .0002001 -2.21 0.028 -.0008354 -.0000489
_cons | -.0740626 .1434995 -0.52 0.606 -.3559948 .2078695
------------------------------------------------------------------------------
Instruments for first differences equation
Standard
D.(log_tr_share log_K log_LP log_rer)
GMM-type (missing=0, separate instruments for each period unless collapsed)
L4.(log_W log_Y)
Instruments for levels equation
Standard
log_tr_share log_K log_LP log_rer
_cons
GMM-type (missing=0, separate instruments for each period unless collapsed)
DL3.(log_W log_Y)
------------------------------------------------------------------------------
Arellano-Bond test for AR(1) in first differences: z = -9.76 Pr > z = 0.000
Arellano-Bond test for AR(2) in first differences: z = 2.91 Pr > z = 0.004
------------------------------------------------------------------------------
Sargan test of overid. restrictions: chi2(48) = 45.95 Prob > chi2 = 0.557
(Not robust, but not weakened by many instruments.)
Difference-in-Sargan tests of exogeneity of instrument subsets:
GMM instruments for levels
Sargan test excluding group: chi2(22) = 13.55 Prob > chi2 = 0.917
Difference (null H = exogenous): chi2(26) = 32.40 Prob > chi2 = 0.180
iv(log_tr_share log_K log_LP log_rer)
Sargan test excluding group: chi2(44) = 43.01 Prob > chi2 = 0.514
Difference (null H = exogenous): chi2(4) = 2.94 Prob > chi2 = 0.569
Questions: (i) How can i limit my instruments to be less than number of groups? (I have heard that number of instruments must be less than number of groups.) I have tried to use "collapse" for limiting number of instruments but it results in making all variables insignificant and does not report probability value for the Sargan test.
(ii) How can i take care of the autocorrelation in AR(2)?
Wage equation:
xtabond2 log_W l.log_W log_Y log_L log_K log_tr_share log_rer log_LP Timetrend, gmm (log_L log_Y, lag(4 4)) iv( log_K log_tr_share log_rer log_LP) small
Favoring space over speed. To switch, type or click on mata: mata set matafavor speed, perm.
Warning: Number of instruments may be large relative to number of observations.
Dynamic panel-data estimation, one-step system GMM
------------------------------------------------------------------------------
Group variable: id Number of obs = 512
Time variable : Time Number of groups = 32
Number of instruments = 57 Obs per group: min =16
F(8, 503) = 168.65 avg = 16.00
Prob > F = 0.000 max = 16
------------------------------------------------------------------------------
log_W | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
log_W |
L1. | .794888 .0767214 10.36 0.000 .6441541 .9456219
|
log_Y | .4202281 .9795193 0.43 0.668 -1.504225 2.344681
log_L | -.4565687 .7599877 -0.60 0.548 -1.94971 1.036573
log_K | .0339147 .5368819 0.06 0.950 -1.020893 1.088722
log_tr_share | -.5827278 .3510951 -1.66 0.098 -1.272521 .1070658
log_rer | -.0799704 .0485431 -1.65 0.100 -.1753427 .0154018
log_LP | -.2794251 .8735632 -0.32 0.749 -1.995707 1.436857
Timetrend | -.0208901 .0072011 -2.90 0.004 -.0350381 -.0067421
_cons | -2.80464 5.196058 -0.54 0.590 -13.01329 7.40401
------------------------------------------------------------------------------
Instruments for first differences equation
Standard
D.(log_K log_tr_share log_rer log_LP)
GMM-type (missing=0, separate instruments for each period unless collapsed)
L4.(log_L log_Y)
Instruments for levels equation
Standard
log_K log_tr_share log_rer log_LP
_cons
GMM-type (missing=0, separate instruments for each period unless collapsed)
DL3.(log_L log_Y)
------------------------------------------------------------------------------
Arellano-Bond test for AR(1) in first differences: z = -5.20 Pr > z = 0.000
Arellano-Bond test for AR(2) in first differences: z = 0.20 Pr > z = 0.838
------------------------------------------------------------------------------
Sargan test of overid. restrictions: chi2(48) = 56.33 Prob > chi2 = 0.192
(Not robust, but not weakened by many instruments.)
Difference-in-Sargan tests of exogeneity of instrument subsets:
GMM instruments for levels
Sargan test excluding group: chi2(22) = 22.02 Prob > chi2 = 0.459
Difference (null H = exogenous): chi2(26) = 34.31 Prob > chi2 = 0.128
iv(log_K log_tr_share log_rer log_LP)
Sargan test excluding group: chi2(44) = 50.27 Prob > chi2 = 0.239
Difference (null H = exogenous): chi2(4) = 6.06 Prob > chi2 = 0.195
Concern: Sargan test says that my instruments are valid. The results of AR(1) and AR(2) are also as per expectations i.e. we can reject H0 in AR(1) but autocorrelation is not allowed in AR(2). Am i right in all my interpretations. If yes, what is possibly wrong with my results since only 2 of the variables are significant in the model.
>>In case of wage equation, the use of collapse option has made results very much better but the probability of Sargan test is not reported,once again. Here are the results with collapse option:
xtabond2 log_W l.log_W log_Y log_L log_K log_tr_share log_rer log_LP Timetrend, gmm (log_L log_Y, lag(2 2)collapse) iv( log_K log_tr_share log_rer log_LP) small
Favoring space over speed. To switch, type or click on mata: mata set matafavor speed, perm.
Dynamic panel-data estimation, one-step system GMM
------------------------------------------------------------------------------
Group variable: id Number of obs =512
Time variable : Time Number of groups = 32
Number of instruments = 9 Obs per group: min =16
F(8, 503) = 114.51 avg = 16.00
Prob > F = 0.000 max = 16
------------------------------------------------------------------------------
log_W | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
log_W |
L1. | -.7140952 .4484259 -1.59 0.112 -1.595114 .1669233
|
log_Y | -6.613687 2.557495 -2.59 0.010 -11.63838 -1.588999
log_L | 9.25286 3.017932 3.07 0.002 3.323555 15.18216
log_K | -3.578592 1.363675 -2.62 0.009 -6.257793 -.8993916
log_tr_share | -5.582639 1.255654 -4.45 0.000 -8.049612 -3.115666
log_rer | -1.018132 .2575967 -3.95 0.000 -1.52423 -.512034
log_LP | 11.755 3.391226 3.47 0.001 5.092286 18.41771
Timetrend | -.0126204 .0223941 -0.56 0.573 -.0566178 .031377
_cons | 60.35817 19.65259 3.07 0.002 21.74689 98.96944
------------------------------------------------------------------------------
Instruments for first differences equation
Standard
D.(log_K log_tr_share log_rer log_LP)
GMM-type (missing=0, separate instruments for each period unless collapsed)
L2.(log_L log_Y) collapsed
Instruments for levels equation
Standard
log_K log_tr_share log_rer log_LP
_cons
GMM-type (missing=0, separate instruments for each period unless collapsed)
DL.(log_L log_Y) collapsed
------------------------------------------------------------------------------
Arellano-Bond test for AR(1) in first differences: z = 1.65 Pr > z = 0.099
Arellano-Bond test for AR(2) in first differences: z = 0.34 Pr > z = 0.734
------------------------------------------------------------------------------
Sargan test of overid. restrictions: chi2(0) = 0.00 Prob > chi2 = .
(Not robust, but not weakened by many instruments.)
I am very much cluless about all of above concerns so i will appreciate some insighful comments. Thanks in anticipation.
P.S. Sorry for the long post.
First of all, I'm a beginner in Stata and learned it about 2 months back. In my research, I am estimating 2 equations: labor demand equation and wage equation. I am trying to estimate these two equations using xtabond2 by Roodman. However, I am not getting the good or required results and i have been unable to find the fault. So, here i am, posting my results below and eagerly waiting for some insightful comments.
Labor demand equation:
xtabond2 log_L l.log_L log_Y log_W log_K log_tr_share log_rer log_LP Timetrend, gmm (log_W log_Y, lag(4 4)) iv(log_tr_share log_K log_LP log_rer) small
Favoring space over speed. To switch, type or click on mata: mata set matafavor speed, perm.
Warning: Number of instruments may be large relative to number of observations.
Dynamic panel-data estimation, one-step system GMM
------------------------------------------------------------------------------
Group variable: id Number of obs = 512
Time variable : Time Number of groups = 32
Number of instruments = 57 Obs per group: min = 16
F(8, 503) = 195177.35 avg = 16.00
Prob > F = 0.000 max = 16
------------------------------------------------------------------------------
log_L | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
log_L |
L1. | .9899778 .0211435 46.82 0.000 .9484374 1.031518
|
log_Y | .0120626 .0269896 0.45 0.655 -.0409636 .0650889
log_W | .0009886 .0011234 0.88 0.379 -.0012185 .0031957
log_K | .0013748 .0154829 0.09 0.929 -.0290443 .0317939
log_tr_share | .0073258 .0081577 0.90 0.370 -.0087017 .0233532
log_rer | .001907 .0007947 2.40 0.017 .0003456 .0034683
log_LP | -.0142728 .0238305 -0.60 0.549 -.0610923 .0325467
Timetrend | -.0004422 .0002001 -2.21 0.028 -.0008354 -.0000489
_cons | -.0740626 .1434995 -0.52 0.606 -.3559948 .2078695
------------------------------------------------------------------------------
Instruments for first differences equation
Standard
D.(log_tr_share log_K log_LP log_rer)
GMM-type (missing=0, separate instruments for each period unless collapsed)
L4.(log_W log_Y)
Instruments for levels equation
Standard
log_tr_share log_K log_LP log_rer
_cons
GMM-type (missing=0, separate instruments for each period unless collapsed)
DL3.(log_W log_Y)
------------------------------------------------------------------------------
Arellano-Bond test for AR(1) in first differences: z = -9.76 Pr > z = 0.000
Arellano-Bond test for AR(2) in first differences: z = 2.91 Pr > z = 0.004
------------------------------------------------------------------------------
Sargan test of overid. restrictions: chi2(48) = 45.95 Prob > chi2 = 0.557
(Not robust, but not weakened by many instruments.)
Difference-in-Sargan tests of exogeneity of instrument subsets:
GMM instruments for levels
Sargan test excluding group: chi2(22) = 13.55 Prob > chi2 = 0.917
Difference (null H = exogenous): chi2(26) = 32.40 Prob > chi2 = 0.180
iv(log_tr_share log_K log_LP log_rer)
Sargan test excluding group: chi2(44) = 43.01 Prob > chi2 = 0.514
Difference (null H = exogenous): chi2(4) = 2.94 Prob > chi2 = 0.569
Questions: (i) How can i limit my instruments to be less than number of groups? (I have heard that number of instruments must be less than number of groups.) I have tried to use "collapse" for limiting number of instruments but it results in making all variables insignificant and does not report probability value for the Sargan test.
(ii) How can i take care of the autocorrelation in AR(2)?
Wage equation:
xtabond2 log_W l.log_W log_Y log_L log_K log_tr_share log_rer log_LP Timetrend, gmm (log_L log_Y, lag(4 4)) iv( log_K log_tr_share log_rer log_LP) small
Favoring space over speed. To switch, type or click on mata: mata set matafavor speed, perm.
Warning: Number of instruments may be large relative to number of observations.
Dynamic panel-data estimation, one-step system GMM
------------------------------------------------------------------------------
Group variable: id Number of obs = 512
Time variable : Time Number of groups = 32
Number of instruments = 57 Obs per group: min =16
F(8, 503) = 168.65 avg = 16.00
Prob > F = 0.000 max = 16
------------------------------------------------------------------------------
log_W | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
log_W |
L1. | .794888 .0767214 10.36 0.000 .6441541 .9456219
|
log_Y | .4202281 .9795193 0.43 0.668 -1.504225 2.344681
log_L | -.4565687 .7599877 -0.60 0.548 -1.94971 1.036573
log_K | .0339147 .5368819 0.06 0.950 -1.020893 1.088722
log_tr_share | -.5827278 .3510951 -1.66 0.098 -1.272521 .1070658
log_rer | -.0799704 .0485431 -1.65 0.100 -.1753427 .0154018
log_LP | -.2794251 .8735632 -0.32 0.749 -1.995707 1.436857
Timetrend | -.0208901 .0072011 -2.90 0.004 -.0350381 -.0067421
_cons | -2.80464 5.196058 -0.54 0.590 -13.01329 7.40401
------------------------------------------------------------------------------
Instruments for first differences equation
Standard
D.(log_K log_tr_share log_rer log_LP)
GMM-type (missing=0, separate instruments for each period unless collapsed)
L4.(log_L log_Y)
Instruments for levels equation
Standard
log_K log_tr_share log_rer log_LP
_cons
GMM-type (missing=0, separate instruments for each period unless collapsed)
DL3.(log_L log_Y)
------------------------------------------------------------------------------
Arellano-Bond test for AR(1) in first differences: z = -5.20 Pr > z = 0.000
Arellano-Bond test for AR(2) in first differences: z = 0.20 Pr > z = 0.838
------------------------------------------------------------------------------
Sargan test of overid. restrictions: chi2(48) = 56.33 Prob > chi2 = 0.192
(Not robust, but not weakened by many instruments.)
Difference-in-Sargan tests of exogeneity of instrument subsets:
GMM instruments for levels
Sargan test excluding group: chi2(22) = 22.02 Prob > chi2 = 0.459
Difference (null H = exogenous): chi2(26) = 34.31 Prob > chi2 = 0.128
iv(log_K log_tr_share log_rer log_LP)
Sargan test excluding group: chi2(44) = 50.27 Prob > chi2 = 0.239
Difference (null H = exogenous): chi2(4) = 6.06 Prob > chi2 = 0.195
Concern: Sargan test says that my instruments are valid. The results of AR(1) and AR(2) are also as per expectations i.e. we can reject H0 in AR(1) but autocorrelation is not allowed in AR(2). Am i right in all my interpretations. If yes, what is possibly wrong with my results since only 2 of the variables are significant in the model.
>>In case of wage equation, the use of collapse option has made results very much better but the probability of Sargan test is not reported,once again. Here are the results with collapse option:
xtabond2 log_W l.log_W log_Y log_L log_K log_tr_share log_rer log_LP Timetrend, gmm (log_L log_Y, lag(2 2)collapse) iv( log_K log_tr_share log_rer log_LP) small
Favoring space over speed. To switch, type or click on mata: mata set matafavor speed, perm.
Dynamic panel-data estimation, one-step system GMM
------------------------------------------------------------------------------
Group variable: id Number of obs =512
Time variable : Time Number of groups = 32
Number of instruments = 9 Obs per group: min =16
F(8, 503) = 114.51 avg = 16.00
Prob > F = 0.000 max = 16
------------------------------------------------------------------------------
log_W | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
log_W |
L1. | -.7140952 .4484259 -1.59 0.112 -1.595114 .1669233
|
log_Y | -6.613687 2.557495 -2.59 0.010 -11.63838 -1.588999
log_L | 9.25286 3.017932 3.07 0.002 3.323555 15.18216
log_K | -3.578592 1.363675 -2.62 0.009 -6.257793 -.8993916
log_tr_share | -5.582639 1.255654 -4.45 0.000 -8.049612 -3.115666
log_rer | -1.018132 .2575967 -3.95 0.000 -1.52423 -.512034
log_LP | 11.755 3.391226 3.47 0.001 5.092286 18.41771
Timetrend | -.0126204 .0223941 -0.56 0.573 -.0566178 .031377
_cons | 60.35817 19.65259 3.07 0.002 21.74689 98.96944
------------------------------------------------------------------------------
Instruments for first differences equation
Standard
D.(log_K log_tr_share log_rer log_LP)
GMM-type (missing=0, separate instruments for each period unless collapsed)
L2.(log_L log_Y) collapsed
Instruments for levels equation
Standard
log_K log_tr_share log_rer log_LP
_cons
GMM-type (missing=0, separate instruments for each period unless collapsed)
DL.(log_L log_Y) collapsed
------------------------------------------------------------------------------
Arellano-Bond test for AR(1) in first differences: z = 1.65 Pr > z = 0.099
Arellano-Bond test for AR(2) in first differences: z = 0.34 Pr > z = 0.734
------------------------------------------------------------------------------
Sargan test of overid. restrictions: chi2(0) = 0.00 Prob > chi2 = .
(Not robust, but not weakened by many instruments.)
I am very much cluless about all of above concerns so i will appreciate some insighful comments. Thanks in anticipation.
P.S. Sorry for the long post.
