Hello all,
I working with a panel design. I have data on the 50 U.S. states over 16 years. In the past, I used fixed-effects model (with xtreg, fe), but I've recently discovered the xthybrid command. I am interested in using it because I have some variables that vary little (if at all) within states. My problem is that I understand how to estimate time with xtreg, but I'm more confused when it comes to using xthybrid.
I used two strategies:
1) xi: xthybrid y x i.year
2) xthybrid y x year yearsq
In the 2nd approach I use year squared because my dependent variable has a slightly quadratic trend over time.
I will post the output below. I initially ran the models with both within and between effects for all the variables, and I only asked them for the variables that show significantly different effects according to the Wald test.
I have two questions:
1) do you have any thoughts on which specification is preferable and why?
2) do you know why the between effect of the year variables (in either specification) are omitted?
I working with a panel design. I have data on the 50 U.S. states over 16 years. In the past, I used fixed-effects model (with xtreg, fe), but I've recently discovered the xthybrid command. I am interested in using it because I have some variables that vary little (if at all) within states. My problem is that I understand how to estimate time with xtreg, but I'm more confused when it comes to using xthybrid.
I used two strategies:
1) xi: xthybrid y x i.year
2) xthybrid y x year yearsq
In the 2nd approach I use year squared because my dependent variable has a slightly quadratic trend over time.
I will post the output below. I initially ran the models with both within and between effects for all the variables, and I only asked them for the variables that show significantly different effects according to the Wald test.
I have two questions:
1) do you have any thoughts on which specification is preferable and why?
2) do you know why the between effect of the year variables (in either specification) are omitted?
Code:
. * specification 1: xi: xthybrid y x i.year
.
. xi: xthybrid y x x1 x2 x3 x4 x5 x6 i.year, clusterid(id) vce(robust) full test
i.year _Iyear_2000-2015 (naturally coded; _Iyear_2000 omitted)
-----------------------------------------------------------------------------------------------------
Model model
-----------------------------------------------------------------------------------------------------
Mixed-effects GLM Number of obs = 800
Family: Gaussian
Link: identity
Group variable: id Number of groups = 50
Obs per group:
min = 16
avg = 16.0
max = 16
Integration method: mvaghermite Integration pts. = 7
Wald chi2(29) = 3271.42
Log pseudolikelihood = -1197.7914 Prob > chi2 = 0.0000
(Std. Err. adjusted for 50 clusters in id)
--------------------------------------------------------------------------------
| Robust
y | Coef. Std. Err. z P>|z| [95% Conf. Interval]
---------------+----------------------------------------------------------------
W__x | 27.48495 6.561976 4.19 0.000 14.62371 40.34619
W__x1 | -.128807 .0519909 -2.48 0.013 -.2307074 -.0269067
W__x2 | -.7764989 1.333392 -0.58 0.560 -3.389898 1.836901
W__x3 | .0551888 .0633226 0.87 0.383 -.0689212 .1792988
W__x4 | -8.633653 6.936338 -1.24 0.213 -22.22863 4.96132
W__x5 | 2.592232 4.944466 0.52 0.600 -7.098743 12.28321
W__x6 | 23.33109 6.995832 3.33 0.001 9.619507 37.04266
W___Iyear_2001 | .3138501 .2144448 1.46 0.143 -.1064541 .7341543
W___Iyear_2002 | .6563101 .2037253 3.22 0.001 .2570158 1.055604
W___Iyear_2003 | .6809543 .2860453 2.38 0.017 .1203159 1.241593
W___Iyear_2004 | 1.015131 .2775332 3.66 0.000 .4711755 1.559086
W___Iyear_2005 | 1.098209 .357019 3.08 0.002 .3984651 1.797954
W___Iyear_2006 | 1.331302 .4187316 3.18 0.001 .5106026 2.152
W___Iyear_2007 | 1.599586 .4363303 3.67 0.000 .7443946 2.454778
W___Iyear_2008 | 2.165149 .5064014 4.28 0.000 1.172621 3.157678
W___Iyear_2009 | 2.321855 .6678414 3.48 0.001 1.01291 3.6308
W___Iyear_2010 | 3.426708 .7355992 4.66 0.000 1.98496 4.868456
W___Iyear_2011 | 3.795471 .8447231 4.49 0.000 2.139844 5.451097
W___Iyear_2012 | 4.391039 .9418207 4.66 0.000 2.545104 6.236973
W___Iyear_2013 | 4.904557 .8365469 5.86 0.000 3.264955 6.544158
W___Iyear_2014 | 5.837984 .8030856 7.27 0.000 4.263965 7.412003
W___Iyear_2015 | 6.919046 .9309145 7.43 0.000 5.094487 8.743605
B__x | -20.60284 10.90525 -1.89 0.059 -41.97673 .7710576
B__x1 | -.0982664 .1719508 -0.57 0.568 -.4352838 .238751
B__x2 | 20.4087 2.8359 7.20 0.000 14.85044 25.96696
B__x3 | .3592356 .3220065 1.12 0.265 -.2718855 .9903567
B__x4 | -6.470888 10.29149 -0.63 0.530 -26.64184 13.70006
B__x5 | 42.22544 8.847803 4.77 0.000 24.88407 59.56682
B__x6 | -4.399137 3.009327 -1.46 0.144 -10.29731 1.499035
B___Iyear_2001 | 0 (omitted)
B___Iyear_2002 | 0 (omitted)
B___Iyear_2003 | 0 (omitted)
B___Iyear_2004 | 0 (omitted)
B___Iyear_2005 | 0 (omitted)
B___Iyear_2006 | 0 (omitted)
B___Iyear_2007 | 0 (omitted)
B___Iyear_2008 | 0 (omitted)
B___Iyear_2009 | 0 (omitted)
B___Iyear_2010 | 0 (omitted)
B___Iyear_2011 | 0 (omitted)
B___Iyear_2012 | 0 (omitted)
B___Iyear_2013 | 0 (omitted)
B___Iyear_2014 | 0 (omitted)
B___Iyear_2015 | 0 (omitted)
_cons | -18.69707 15.28658 -1.22 0.221 -48.65821 11.26407
---------------+----------------------------------------------------------------
id |
var(_cons)| 3.116874 .669193 2.046285 4.747579
---------------+----------------------------------------------------------------
var(e.y)| .9095621 .1635097 .6394608 1.293751
--------------------------------------------------------------------------------
Tests of the random effects assumption:
_b[B__x] = _b[W__x]; p-value: 0.0008
_b[B__x1] = _b[W__x1]; p-value: 0.8419
_b[B__x2] = _b[W__x2]; p-value: 0.0000
_b[B__x3] = _b[W__x3]; p-value: 0.3530
_b[B__x4] = _b[W__x4]; p-value: 0.8616
_b[B__x5] = _b[W__x5]; p-value: 0.0000
_b[B__x6] = _b[W__x6]; p-value: 0.0002
_b[B___Iyear_2001] = _b[W___Iyear_2001]; p-value: 0.1433
_b[B___Iyear_2002] = _b[W___Iyear_2002]; p-value: 0.0013
_b[B___Iyear_2003] = _b[W___Iyear_2003]; p-value: 0.0173
_b[B___Iyear_2004] = _b[W___Iyear_2004]; p-value: 0.0003
_b[B___Iyear_2005] = _b[W___Iyear_2005]; p-value: 0.0021
_b[B___Iyear_2006] = _b[W___Iyear_2006]; p-value: 0.0015
_b[B___Iyear_2007] = _b[W___Iyear_2007]; p-value: 0.0002
_b[B___Iyear_2008] = _b[W___Iyear_2008]; p-value: 0.0000
_b[B___Iyear_2009] = _b[W___Iyear_2009]; p-value: 0.0005
_b[B___Iyear_2010] = _b[W___Iyear_2010]; p-value: 0.0000
_b[B___Iyear_2011] = _b[W___Iyear_2011]; p-value: 0.0000
_b[B___Iyear_2012] = _b[W___Iyear_2012]; p-value: 0.0000
_b[B___Iyear_2013] = _b[W___Iyear_2013]; p-value: 0.0000
_b[B___Iyear_2014] = _b[W___Iyear_2014]; p-value: 0.0000
_b[B___Iyear_2015] = _b[W___Iyear_2015]; p-value: 0.0000
.
. xi: xthybrid y x x1 x2 x3 x4 x5 x6 i.year, clusterid(id) vce(robust) use (x x2 x5 x6 _Iyear_2002 _I
> year_2003 _Iyear_2004 _Iyear_2005 _Iyear_2006 _Iyear_2007 _Iyear_2008 _Iyear_2009 _Iyear_2010 _Iyea
> r_2011 _Iyear_2012 _Iyear_2013 _Iyear_2014 _Iyear_2015) full test
i.year _Iyear_2000-2015 (naturally coded; _Iyear_2000 omitted)
-----------------------------------------------------------------------------------------------------
Model model
-----------------------------------------------------------------------------------------------------
Mixed-effects GLM Number of obs = 800
Family: Gaussian
Link: identity
Group variable: id Number of groups = 50
Obs per group:
min = 16
avg = 16.0
max = 16
Integration method: mvaghermite Integration pts. = 7
Wald chi2(26) = 2217.47
Log pseudolikelihood = -1198.5026 Prob > chi2 = 0.0000
(Std. Err. adjusted for 50 clusters in id)
--------------------------------------------------------------------------------
| Robust
y | Coef. Std. Err. z P>|z| [95% Conf. Interval]
---------------+----------------------------------------------------------------
R__x1 | -.1261339 .0532073 -2.37 0.018 -.2304183 -.0218495
R__x3 | .0633807 .0628135 1.01 0.313 -.0597316 .186493
R__x4 | -9.130167 5.568717 -1.64 0.101 -20.04465 1.784317
R___Iyear_2001 | .3156233 .2130639 1.48 0.139 -.1019742 .7332208
W__x | 27.78369 6.505358 4.27 0.000 15.03342 40.53395
W__x2 | -.7374598 1.334721 -0.55 0.581 -3.353466 1.878546
W__x5 | 2.735612 4.953238 0.55 0.581 -6.972556 12.44378
W__x6 | 23.4502 7.004207 3.35 0.001 9.722207 37.17819
W___Iyear_2002 | .6509489 .2019093 3.22 0.001 .255214 1.046684
W___Iyear_2003 | .6750173 .279622 2.41 0.016 .1269682 1.223066
W___Iyear_2004 | 1.011967 .2698932 3.75 0.000 .4829864 1.540948
W___Iyear_2005 | 1.097031 .3487383 3.15 0.002 .4135163 1.780545
W___Iyear_2006 | 1.331346 .4137273 3.22 0.001 .520455 2.142236
W___Iyear_2007 | 1.601597 .426051 3.76 0.000 .7665522 2.436642
W___Iyear_2008 | 2.158867 .4983493 4.33 0.000 1.18212 3.135614
W___Iyear_2009 | 2.286841 .6604286 3.46 0.001 .9924242 3.581257
W___Iyear_2010 | 3.38746 .7353506 4.61 0.000 1.946199 4.828721
W___Iyear_2011 | 3.758626 .8416914 4.47 0.000 2.108941 5.408311
W___Iyear_2012 | 4.361262 .9331158 4.67 0.000 2.532389 6.190135
W___Iyear_2013 | 4.886226 .8309126 5.88 0.000 3.257667 6.514785
W___Iyear_2014 | 5.836347 .7932212 7.36 0.000 4.281662 7.391032
W___Iyear_2015 | 6.932657 .9024717 7.68 0.000 5.163845 8.701469
B__x | -20.73066 9.848327 -2.10 0.035 -40.03303 -1.428293
B__x2 | 20.33603 2.720781 7.47 0.000 15.0034 25.66866
B__x5 | 38.16482 9.565075 3.99 0.000 19.41762 56.91203
B__x6 | -5.235565 2.992847 -1.75 0.080 -11.10144 .6303082
B___Iyear_2002 | 0 (omitted)
B___Iyear_2003 | 0 (omitted)
B___Iyear_2004 | 0 (omitted)
B___Iyear_2005 | 0 (omitted)
B___Iyear_2006 | 0 (omitted)
B___Iyear_2007 | 0 (omitted)
B___Iyear_2008 | 0 (omitted)
B___Iyear_2009 | 0 (omitted)
B___Iyear_2010 | 0 (omitted)
B___Iyear_2011 | 0 (omitted)
B___Iyear_2012 | 0 (omitted)
B___Iyear_2013 | 0 (omitted)
B___Iyear_2014 | 0 (omitted)
B___Iyear_2015 | 0 (omitted)
_cons | -11.19267 13.47014 -0.83 0.406 -37.59365 15.20831
---------------+----------------------------------------------------------------
id |
var(_cons)| 3.204795 .6627161 2.136885 4.806393
---------------+----------------------------------------------------------------
var(e.y)| .9096307 .163521 .6395105 1.293846
--------------------------------------------------------------------------------
Tests of the random effects assumption:
_b[B__x] = _b[W__x]; p-value: 0.0005
_b[B__x2] = _b[W__x2]; p-value: 0.0000
_b[B__x5] = _b[W__x5]; p-value: 0.0006
_b[B__x6] = _b[W__x6]; p-value: 0.0002
_b[B___Iyear_2002] = _b[W___Iyear_2002]; p-value: 0.0013
_b[B___Iyear_2003] = _b[W___Iyear_2003]; p-value: 0.0158
_b[B___Iyear_2004] = _b[W___Iyear_2004]; p-value: 0.0002
_b[B___Iyear_2005] = _b[W___Iyear_2005]; p-value: 0.0017
_b[B___Iyear_2006] = _b[W___Iyear_2006]; p-value: 0.0013
_b[B___Iyear_2007] = _b[W___Iyear_2007]; p-value: 0.0002
_b[B___Iyear_2008] = _b[W___Iyear_2008]; p-value: 0.0000
_b[B___Iyear_2009] = _b[W___Iyear_2009]; p-value: 0.0005
_b[B___Iyear_2010] = _b[W___Iyear_2010]; p-value: 0.0000
_b[B___Iyear_2011] = _b[W___Iyear_2011]; p-value: 0.0000
_b[B___Iyear_2012] = _b[W___Iyear_2012]; p-value: 0.0000
_b[B___Iyear_2013] = _b[W___Iyear_2013]; p-value: 0.0000
_b[B___Iyear_2014] = _b[W___Iyear_2014]; p-value: 0.0000
_b[B___Iyear_2015] = _b[W___Iyear_2015]; p-value: 0.0000
.
. * specification 2: xthybrid y x year yearsq
.
. gen yearsq = year*year
.
. xthybrid y x x1 x2 x3 x4 x5 x6 year yearsq, clusterid(id) vce(robust) full test
-----------------------------------------------------------------------------------------------------
Model model
-----------------------------------------------------------------------------------------------------
Mixed-effects GLM Number of obs = 800
Family: Gaussian
Link: identity
Group variable: id Number of groups = 50
Obs per group:
min = 16
avg = 16.0
max = 16
Integration method: mvaghermite Integration pts. = 7
Wald chi2(16) = 1095.19
Log pseudolikelihood = -1208.2773 Prob > chi2 = 0.0000
(Std. Err. adjusted for 50 clusters in id)
------------------------------------------------------------------------------
| Robust
y | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
W__x | 24.25765 5.35374 4.53 0.000 13.76451 34.75079
W__x1 | -.1344042 .0438872 -3.06 0.002 -.2204215 -.0483869
W__x2 | -1.516852 1.212306 -1.25 0.211 -3.892928 .8592233
W__x3 | .0599774 .0287017 2.09 0.037 .0037231 .1162317
W__x4 | -5.197346 6.734602 -0.77 0.440 -18.39692 8.002232
W__x5 | -1.778408 4.424572 -0.40 0.688 -10.45041 6.893594
W__x6 | 24.38065 6.896454 3.54 0.000 10.86384 37.89745
W__year | -103.3558 13.86083 -7.46 0.000 -130.5225 -76.18905
W__yearsq | .0258488 .0034574 7.48 0.000 .0190725 .0326251
B__x | -20.60284 10.90525 -1.89 0.059 -41.97673 .7710575
B__x1 | -.0982663 .1719508 -0.57 0.568 -.4352837 .2387511
B__x2 | 20.4087 2.8359 7.20 0.000 14.85044 25.96696
B__x3 | .3592355 .3220065 1.12 0.265 -.2718855 .9903566
B__x4 | -6.470888 10.29149 -0.63 0.530 -26.64184 13.70006
B__x5 | 42.22545 8.847803 4.77 0.000 24.88407 59.56682
B__x6 | -4.399137 3.009327 -1.46 0.144 -10.29731 1.499035
B__year | 0 (omitted)
B__yearsq | 0 (omitted)
_cons | -18.69707 15.28658 -1.22 0.221 -48.65821 11.26407
-------------+----------------------------------------------------------------
id |
var(_cons)| 3.11528 .6690461 2.044988 4.745735
-------------+----------------------------------------------------------------
var(e.y)| .9353547 .1686279 .656931 1.331781
------------------------------------------------------------------------------
Tests of the random effects assumption:
_b[B__x] = _b[W__x]; p-value: 0.0009
_b[B__x1] = _b[W__x1]; p-value: 0.8165
_b[B__x2] = _b[W__x2]; p-value: 0.0000
_b[B__x3] = _b[W__x3]; p-value: 0.3517
_b[B__x4] = _b[W__x4]; p-value: 0.9165
_b[B__x5] = _b[W__x5]; p-value: 0.0000
_b[B__x6] = _b[W__x6]; p-value: 0.0001
_b[B__year] = _b[W__year]; p-value: 0.0000
_b[B__yearsq] = _b[W__yearsq]; p-value: 0.0000
.
. xthybrid y x x1 x2 x3 x4 x5 x6 year yearsq, clusterid(id) vce(robust) use(x x2 x5 x6 year yearsq) f
> ull test
-----------------------------------------------------------------------------------------------------
Model model
-----------------------------------------------------------------------------------------------------
Mixed-effects GLM Number of obs = 800
Family: Gaussian
Link: identity
Group variable: id Number of groups = 50
Obs per group:
min = 16
avg = 16.0
max = 16
Integration method: mvaghermite Integration pts. = 7
Wald chi2(13) = 941.16
Log pseudolikelihood = -1209.133 Prob > chi2 = 0.0000
(Std. Err. adjusted for 50 clusters in id)
------------------------------------------------------------------------------
| Robust
y | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
R__x1 | -.1317118 .0450499 -2.92 0.003 -.2200079 -.0434157
R__x3 | .0615175 .0289401 2.13 0.034 .004796 .118239
R__x4 | -6.474502 5.563331 -1.16 0.245 -17.37843 4.429427
W__x | 24.01769 5.350782 4.49 0.000 13.53035 34.50503
W__x2 | -1.521848 1.205595 -1.26 0.207 -3.884771 .8410747
W__x5 | -1.805144 4.34951 -0.42 0.678 -10.33003 6.719739
W__x6 | 24.44828 6.874908 3.56 0.000 10.97371 37.92285
W__year | -103.1623 13.8708 -7.44 0.000 -130.3486 -75.97603
W__yearsq | .0258013 .0034601 7.46 0.000 .0190198 .0325829
B__x | -18.55783 9.749117 -1.90 0.057 -37.66575 .5500894
B__x2 | 20.9162 2.746813 7.61 0.000 15.53255 26.29985
B__x5 | 37.08718 9.914084 3.74 0.000 17.65593 56.51843
B__x6 | -5.42266 3.01079 -1.80 0.072 -11.3237 .4783787
B__year | 0 (omitted)
B__yearsq | 0 (omitted)
_cons | -12.30471 13.61443 -0.90 0.366 -38.98849 14.37908
-------------+----------------------------------------------------------------
id |
var(_cons)| 3.220027 .6751044 2.135002 4.85647
-------------+----------------------------------------------------------------
var(e.y)| .9354643 .1686319 .6570296 1.331893
------------------------------------------------------------------------------
Tests of the random effects assumption:
_b[B__x] = _b[W__x]; p-value: 0.0009
_b[B__x2] = _b[W__x2]; p-value: 0.0000
_b[B__x5] = _b[W__x5]; p-value: 0.0004
_b[B__x6] = _b[W__x6]; p-value: 0.0001
_b[B__year] = _b[W__year]; p-value: 0.0000
_b[B__yearsq] = _b[W__yearsq]; p-value: 0.0000
Comment