I'm estimating a TFP growth convergence regression type model in a panel with 20 NUTS-2 regions (reg) and N=17, from 1995 to 2012.
I've estimated the model with POLS (clustering by reg), FE (clustering by NUTS-1 geo1 area, i.e. North-west, North East, Centre and South), and RE.
My questions are:
1) I get similar results between POLS and RE. I've read previous posts on this issue, and I guess this is because my dependent variable is in difference. Or is it also due to limited between variability in the data. I've included an xtsum below, however some of the variable show high between variability. Please I'm not clear on this point.
2) The tests below also show that I should go for FE. Is this correct?
Thanks a lot.
These are my POLS FE and RE estimation codes and results:
#
Code:
xi: xtreg gtfp_100 lagltfp_rel_lev95 lagdettotoccrfl lagnetai lagpsii lagnetae lagpsie ///
lagrspri_stock_va lagtotroadskms tau1995-tau2012 i.geo1 ///
if cod_reg<21 , vce(cluster reg)
i.geo1 _Igeo1_1-4 (_Igeo1_1 for geo1==Centro omitted)
note: tau1995 omitted because of collinearity
note: tau2012 omitted because of collinearity
Random-effects GLS regression Number of obs = 340
Group variable: cod_reg Number of groups = 20
R-sq: within = 0.6088 Obs per group: min = 17
between = 0.2743 avg = 17.0
overall = 0.6005 max = 17
Wald chi2(19) = .
corr(u_i, X) = 0 (assumed) Prob > chi2 = .
(Std. Err. adjusted for 20 clusters in reg)
-----------------------------------------------------------------------------------
| Robust
gtfp_100 | Coef. Std. Err. z P>|z| [95% Conf. Interval]
------------------+----------------------------------------------------------------
lagltfp_rel_lev95 | -.04525 .0178226 -2.54 0.011 -.0801817 -.0103184
lagdettotoccrfl | -.0940007 .0516523 -1.82 0.069 -.1952374 .007236
lagnetai | -.0144664 .0082807 -1.75 0.081 -.0306964 .0017635
lagpsii | .011355 .0316344 0.36 0.720 -.0506473 .0733574
lagnetae | .0014869 .006694 0.22 0.824 -.0116331 .0146069
lagpsie | -.0566569 .0332526 -1.70 0.088 -.1218307 .0085169
lagrspri_stock_va | .0000626 .0006108 0.10 0.918 -.0011346 .0012598
lagtotroadskms | .0053038 .0036947 1.44 0.151 -.0019376 .0125452
tau1995 | 0 (omitted)
tau1996 | .0251443 .003433 7.32 0.000 .0184157 .0318728
tau1997 | .0282562 .0043658 6.47 0.000 .0196994 .036813
tau1998 | .0249205 .0036223 6.88 0.000 .017821 .03202
tau1999 | .0308059 .0043438 7.09 0.000 .0222922 .0393196
tau2000 | .0397295 .0053952 7.36 0.000 .029155 .0503039
tau2001 | .0232508 .005381 4.32 0.000 .0127043 .0337972
tau2002 | .0056954 .0059057 0.96 0.335 -.0058796 .0172705
tau2003 | .0090072 .0066685 1.35 0.177 -.0040628 .0220772
tau2004 | .0257581 .004193 6.14 0.000 .01754 .0339763
tau2005 | .0195458 .0042295 4.62 0.000 .0112561 .0278355
tau2006 | .0227237 .0039394 5.77 0.000 .0150026 .0304447
tau2007 | .0216878 .0037919 5.72 0.000 .0142557 .0291198
tau2008 | .0013876 .0042288 0.33 0.743 -.0069007 .009676
tau2009 | -.025776 .0030627 -8.42 0.000 -.0317788 -.0197732
tau2010 | .0301896 .0056313 5.36 0.000 .0191525 .0412267
tau2011 | .0166942 .0038948 4.29 0.000 .0090605 .0243279
tau2012 | 0 (omitted)
_Igeo1_2 | -.0012142 .0019681 -0.62 0.537 -.0050716 .0026431
_Igeo1_3 | -.0031313 .0028951 -1.08 0.279 -.0088056 .002543
_Igeo1_4 | -.0062082 .0037191 -1.67 0.095 -.0134974 .0010811
_cons | .0355761 .0402259 0.88 0.376 -.0432652 .1144173
------------------+----------------------------------------------------------------
sigma_u | 0
sigma_e | .01185219
rho | 0 (fraction of variance due to u_i)
-----------------------------------------------------------------------------------
xtreg gtfp_100 lagltfp_rel_lev95 lagdettotoccrfl lagnetai lagpsii lagnetae lagpsie ///
lagrspri_stock_va lagtotroadskms ///
tau1995-tau2012 ///
if cod_reg<21 , vce(cluster geo1) fe
note: tau1995 omitted because of collinearity
note: tau2012 omitted because of collinearity
Fixed-effects (within) regression Number of obs = 340
Group variable: cod_reg Number of groups = 20
R-sq: within = 0.6611 Obs per group: min = 17
between = 0.0470 avg = 17.0
overall = 0.1783 max = 17
F(3,3) = .
corr(u_i, Xb) = -0.8272 Prob > F = .
(Std. Err. adjusted for 4 clusters in geo1)
-----------------------------------------------------------------------------------
| Robust
gtfp_100 | Coef. Std. Err. t P>|t| [95% Conf. Interval]
------------------+----------------------------------------------------------------
lagltfp_rel_lev95 | -.3010526 .0451169 -6.67 0.007 -.4446346 -.1574707
lagdettotoccrfl | -.0210583 .1237399 -0.17 0.876 -.414854 .3727375
lagnetai | .0117222 .0296807 0.39 0.719 -.0827351 .1061794
lagpsii | .048451 .0132737 3.65 0.035 .0062082 .0906938
lagnetae | .0238814 .0094674 2.52 0.086 -.0062481 .0540109
lagpsie | -.0255698 .0479345 -0.53 0.631 -.1781187 .126979
lagrspri_stock_va | .003575 .000634 5.64 0.011 .0015572 .0055928
lagtotroadskms | .0138893 .0075632 1.84 0.164 -.0101802 .0379588
tau1995 | 0 (omitted)
tau1996 | .0602008 .008763 6.87 0.006 .0323128 .0880887
tau1997 | .0673868 .0051916 12.98 0.001 .0508649 .0839088
tau1998 | .0629318 .0064116 9.82 0.002 .0425271 .0833365
tau1999 | .0665205 .0052882 12.58 0.001 .049691 .0833499
tau2000 | .0746015 .0103181 7.23 0.005 .0417646 .1074384
tau2001 | .0585666 .0081672 7.17 0.006 .0325748 .0845584
tau2002 | .0425568 .0071275 5.97 0.009 .019874 .0652397
tau2003 | .0389972 .0106292 3.67 0.035 .0051705 .072824
tau2004 | .0509879 .0076617 6.65 0.007 .0266048 .0753709
tau2005 | .0442269 .007049 6.27 0.008 .0217939 .06666
tau2006 | .0460886 .0057566 8.01 0.004 .0277686 .0644086
tau2007 | .0434926 .0064391 6.75 0.007 .0230006 .0639846
tau2008 | .021933 .0079666 2.75 0.071 -.0034205 .0472864
tau2009 | -.0124006 .0024856 -4.99 0.015 -.0203108 -.0044903
tau2010 | .0305118 .0096626 3.16 0.051 -.0002389 .0612624
tau2011 | .0185516 .007333 2.53 0.085 -.0047853 .0418885
tau2012 | 0 (omitted)
_cons | -.1294257 .0594517 -2.18 0.118 -.3186275 .0597761
------------------+----------------------------------------------------------------
sigma_u | .02448668
sigma_e | .01185219
rho | .81018832 (fraction of variance due to u_i)
-----------------------------------------------------------------------------------
xi: xtreg gtfp_100 lagltfp_rel_lev95 lagdettotoccrfl lagnetai lagpsii lagnetae lagpsie ///
lagrspri_stock_va lagtotroadskms ///
tau1995-tau2012 i.geo1 ///
if cod_reg<21, robust re
i.geo1 _Igeo1_1-4 (_Igeo1_1 for geo1==Centro omitted)
note: tau1995 omitted because of collinearity
note: tau2012 omitted because of collinearity
Random-effects GLS regression Number of obs = 340
Group variable: cod_reg Number of groups = 20
R-sq: within = 0.6088 Obs per group: min = 17
between = 0.2743 avg = 17.0
overall = 0.6005 max = 17
Wald chi2(19) = .
corr(u_i, X) = 0 (assumed) Prob > chi2 = .
(Std. Err. adjusted for 20 clusters in cod_reg)
-----------------------------------------------------------------------------------
| Robust
gtfp_100 | Coef. Std. Err. z P>|z| [95% Conf. Interval]
------------------+----------------------------------------------------------------
lagltfp_rel_lev95 | -.04525 .0178226 -2.54 0.011 -.0801817 -.0103184
lagdettotoccrfl | -.0940007 .0516523 -1.82 0.069 -.1952374 .007236
lagnetai | -.0144664 .0082807 -1.75 0.081 -.0306964 .0017635
lagpsii | .011355 .0316344 0.36 0.720 -.0506473 .0733574
lagnetae | .0014869 .006694 0.22 0.824 -.0116331 .0146069
lagpsie | -.0566569 .0332526 -1.70 0.088 -.1218307 .0085169
lagrspri_stock_va | .0000626 .0006108 0.10 0.918 -.0011346 .0012598
lagtotroadskms | .0053038 .0036947 1.44 0.151 -.0019376 .0125452
tau1995 | 0 (omitted)
tau1996 | .0251443 .003433 7.32 0.000 .0184157 .0318728
tau1997 | .0282562 .0043658 6.47 0.000 .0196994 .036813
tau1998 | .0249205 .0036223 6.88 0.000 .017821 .03202
tau1999 | .0308059 .0043438 7.09 0.000 .0222922 .0393196
tau2000 | .0397295 .0053952 7.36 0.000 .029155 .0503039
tau2001 | .0232508 .005381 4.32 0.000 .0127043 .0337972
tau2002 | .0056954 .0059057 0.96 0.335 -.0058796 .0172705
tau2003 | .0090072 .0066685 1.35 0.177 -.0040628 .0220772
tau2004 | .0257581 .004193 6.14 0.000 .01754 .0339763
tau2005 | .0195458 .0042295 4.62 0.000 .0112561 .0278355
tau2006 | .0227237 .0039394 5.77 0.000 .0150026 .0304447
tau2007 | .0216878 .0037919 5.72 0.000 .0142557 .0291198
tau2008 | .0013876 .0042288 0.33 0.743 -.0069007 .009676
tau2009 | -.025776 .0030627 -8.42 0.000 -.0317788 -.0197732
tau2010 | .0301896 .0056313 5.36 0.000 .0191525 .0412267
tau2011 | .0166942 .0038948 4.29 0.000 .0090605 .0243279
tau2012 | 0 (omitted)
_Igeo1_2 | -.0012142 .0019681 -0.62 0.537 -.0050716 .0026431
_Igeo1_3 | -.0031313 .0028951 -1.08 0.279 -.0088056 .002543
_Igeo1_4 | -.0062082 .0037191 -1.67 0.095 -.0134974 .0010811
_cons | .0355761 .0402259 0.88 0.376 -.0432652 .1144173
------------------+----------------------------------------------------------------
sigma_u | 0
sigma_e | .01185219
rho | 0 (fraction of variance due to u_i)
-----------------------------------------------------------------------------------#
Code:
1)
F test that all u_i=0: F(19, 296) = 3.35 Prob > F = 0.0000
2)
xttest0
Breusch and Pagan Lagrangian multiplier test for random effects
gtfp_100[cod_reg,t] = Xb + u[cod_reg] + e[cod_reg,t]
Estimated results:
| Var sd = sqrt(Var)
---------+-----------------------------
gtfp_100 | .0003688 .0192045
e | .0001405 .0118522
u | 0 0
Test: Var(u) = 0
chibar2(01) = 0.00
Prob > chibar2 = 1.0000
3)
hausman FE RE , sigmamore
Note: the rank of the differenced variance matrix (8) does not equal the number of coefficients being tested (24); be sure this is what you expect, or there may be
problems computing the test. Examine the output of your estimators for anything unexpected and possibly consider scaling your variables so that the
coefficients are on a similar scale.
---- Coefficients ----
| (b) (B) (b-B) sqrt(diag(V_b-V_B))
| FE RE Difference S.E.
-------------+----------------------------------------------------------------
lagltfp_r~95 | -.3010526 -.04525 -.2558026 .0405769
lagdettoto~l | -.0210583 -.0940007 .0729425 .0689508
lagnetai | .0117222 -.0144664 .0261886 .0158818
lagpsii | .048451 .011355 .037096 .0283857
lagnetae | .0238814 .0014869 .0223945 .0222148
lagpsie | -.0255698 -.0566569 .031087 .0484602
lagrspri_s~a | .003575 .0000626 .0035124 .0023246
lagtotroad~s | .0138893 .0053038 .0085855 .0118428
tau1996 | .0602008 .0251443 .0350565 .0069425
tau1997 | .0673868 .0282562 .0391306 .0061284
tau1998 | .0629318 .0249205 .0380113 .0060186
tau1999 | .0665205 .0308059 .0357146 .0058911
tau2000 | .0746015 .0397295 .034872 .0060373
tau2001 | .0585666 .0232508 .0353158 .0066595
tau2002 | .0425568 .0056954 .0368614 .0059096
tau2003 | .0389972 .0090072 .0299901 .0051444
tau2004 | .0509879 .0257581 .0252297 .0043123
tau2005 | .0442269 .0195458 .0246811 .0044523
tau2006 | .0460886 .0227237 .0233649 .0039436
tau2007 | .0434926 .0216878 .0218048 .0037612
tau2008 | .021933 .0013876 .0205453 .0035564
tau2009 | -.0124006 -.025776 .0133755 .0025573
tau2010 | .0305118 .0301896 .0003222 .000566
tau2011 | .0185516 .0166942 .0018574 .0005124
------------------------------------------------------------------------------
b = consistent under Ho and Ha; obtained from xtreg
B = inconsistent under Ha, efficient under Ho; obtained from xtreg
Test: Ho: difference in coefficients not systematic
chi2(8) = (b-B)'[(V_b-V_B)^(-1)](b-B)
= 46.11
Prob>chi2 = 0.0000
(V_b-V_B is not positive definite)#
Code:
xtsum gtfp_100 lagltfp_rel_lev95 lagdettotoccrfl lagnetai lagpsii lagnetae lagpsie ///
lagrspri_stock_va lagtotroadskms if cod_reg<21
Variable | Mean Std. Dev. Min Max | Observations
-----------------+--------------------------------------------+----------------
gtfp_100 overall | -.0090632 .0192045 -.0827193 .0452053 | N = 340
between | .002689 -.01442 -.0049467 | n = 20
within | .0190242 -.0802943 .0410888 | T = 17
| |
laglt~95 overall | -.0750882 .0964169 -.3628312 .1190492 | N = 340
between | .0834291 -.2464719 .080493 | n = 20
within | .0516171 -.2183106 .0482665 | T = 17
| |
lagdet~l overall | .0978757 .0232197 .0589524 .1836198 | N = 340
between | .0211351 .0666674 .149588 | n = 20
within | .0106559 .0645574 .1319075 | T = 17
| |
lagnetai overall | .4892074 .1627707 .233325 1.23396 | N = 340
between | .1571984 .2725485 .928585 | n = 20
within | .0543073 .2613606 .7945828 | T = 17
| |
lagpsii overall | 1.089251 .032663 1.00995 1.179449 | N = 340
between | .0264269 1.045245 1.145038 | n = 20
within | .0200364 1.018452 1.167375 | T = 17
| |
lagnetae overall | .4741275 .1603552 .2287767 .9504244 | N = 340
between | .1582435 .2668897 .790624 | n = 20
within | .0430657 .3174492 .6424334 | T = 17
| |
lagpsie overall | 1.101113 .0261305 1.034469 1.17758 | N = 340
between | .0217327 1.068396 1.148636 | n = 20
within | .0152572 1.060608 1.155469 | T = 17
| |
lagrspr~ overall | 2.16662 2.037671 .0784046 10.12346 | N = 340
between | 2.04059 .1297701 8.967184 | n = 20
within | .4296822 .9524957 3.921881 | T = 17
| |
lagtot~s overall | .599534 .1451635 .2292234 .992353 | N = 340
between | .1359085 .2333248 .8243992 | n = 20
within | .0589331 .4515679 .9143746 | T = 17
0 Response to POLS, FE and RE
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