Do Han Kim wrote:
> I'm trying to run weighted least square with time dummy variables.
[...]
> My question is that, when I change the reference group, the regression
> coefficients also change.
> Could you please explain why?
> From my understanding, changing reference group should not influence on
> regression coefficients.
Not quite sure how or where you picked up this misunderstanding:
. webuse grunfeld, clear
. tab time, gen(t)
time | Freq. Percent Cum.
------------+-----------------------------------
1 | 10 5.00 5.00
2 | 10 5.00 10.00
3 | 10 5.00 15.00
4 | 10 5.00 20.00
5 | 10 5.00 25.00
6 | 10 5.00 30.00
7 | 10 5.00 35.00
8 | 10 5.00 40.00
9 | 10 5.00 45.00
10 | 10 5.00 50.00
11 | 10 5.00 55.00
12 | 10 5.00 60.00
13 | 10 5.00 65.00
14 | 10 5.00 70.00
15 | 10 5.00 75.00
16 | 10 5.00 80.00
17 | 10 5.00 85.00
18 | 10 5.00 90.00
19 | 10 5.00 95.00
20 | 10 5.00 100.00
------------+-----------------------------------
Total | 200 100.00
Notice that there are equal numbers of observations in each time dummy in
this data.
. g weight=(1/invnorm(uniform()))^2
. reg invest t2-t20 [pw=weight]
(sum of wgt is 1.0540e+04)
Linear regression Number of obs = 200
F( 19, 180) = 437.53
Prob > F = 0.0000
R-squared = 0.6361
Root MSE = 82.401
----------------------------------------------------------------------------
| Robust
invest | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-----------+----------------------------------------------------------------
t2 | 160.1355 97.52668 1.64 0.102 -32.30721 352.5781
t3 | -50.43065 53.12961 -0.95 0.344 -155.2676 54.40634
t4 | -91.05831 52.99991 -1.72 0.088 -195.6394 13.52275
t5 | 23.48066 101.7299 0.23 0.818 -177.2559 224.2173
t6 | -91.37126 53.00416 -1.72 0.086 -195.9607 13.21819
t7 | 30.59899 102.2527 0.30 0.765 -171.1692 232.3672
t8 | -65.49078 56.19894 -1.17 0.245 -176.3843 45.4027
t9 | -61.20838 54.64624 -1.12 0.264 -169.038 46.62126
t10 | 131.403 69.50193 1.89 0.060 -5.740389 268.5463
t11 | -92.06036 58.5703 -1.57 0.118 -207.6331 23.51236
t12 | 151.1909 134.5932 1.12 0.263 -114.3926 416.7745
t13 | 365.5336 96.6863 3.78 0.000 174.7492 556.318
t14 | -10.58412 63.97232 -0.17 0.869 -136.8163 115.648
t15 | -67.78393 58.72797 -1.15 0.250 -183.6678 48.09991
t16 | -69.49276 55.74378 -1.25 0.214 -179.4881 40.50258
t17 | 19.29812 53.70033 0.36 0.720 -86.66503 125.2613
t18 | 26.87425 53.01444 0.51 0.613 -77.73547 131.484
t19 | 216.3049 209.707 1.03 0.304 -197.4954 630.1052
t20 | 104.5794 108.5028 0.96 0.336 -109.5217 318.6805
_cons | 118.8594 52.99888 2.24 0.026 14.28041 223.4384
----------------------------------------------------------------------------
. reg invest t1-t19 [pw=weight]
(sum of wgt is 1.0540e+04)
Linear regression Number of obs = 200
F( 19, 180) = 437.53
Prob > F = 0.0000
R-squared = 0.6361
Root MSE = 82.401
----------------------------------------------------------------------------
| Robust
invest | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-----------+----------------------------------------------------------------
t1 | -104.5794 108.5028 -0.96 0.336 -318.6805 109.5217
t2 | 55.55602 125.1661 0.44 0.658 -191.4256 302.5376
t3 | -155.0101 94.75154 -1.64 0.104 -341.9767 31.95657
t4 | -195.6377 94.67887 -2.07 0.040 -382.461 -8.814478
t5 | -81.09877 128.4682 -0.63 0.529 -334.5961 172.3986
t6 | -195.9507 94.68125 -2.07 0.040 -382.7787 -9.122731
t7 | -73.98044 128.8825 -0.57 0.567 -328.2955 180.3346
t8 | -170.0702 96.50605 -1.76 0.080 -360.4989 20.35851
t9 | -165.7878 95.61019 -1.73 0.085 -354.4488 22.87317
t10 | 26.82353 104.8123 0.26 0.798 -179.9953 233.6424
t11 | -196.6398 97.90596 -2.01 0.046 -389.8309 -3.448725
t12 | 46.61149 155.7897 0.30 0.765 -260.7976 354.0206
t13 | 260.9541 124.5124 2.10 0.037 15.26244 506.6459
t14 | -115.1636 101.2302 -1.14 0.257 -314.9141 84.58702
t15 | -172.3634 98.00037 -1.76 0.080 -365.7407 21.01399
t16 | -174.0722 96.24171 -1.81 0.072 -363.9793 15.83491
t17 | -85.28131 95.07273 -0.90 0.371 -272.8817 102.3191
t18 | -77.70518 94.687 -0.82 0.413 -264.5445 109.1341
t19 | 111.7254 223.902 0.50 0.618 -330.0849 553.5358
_cons | 223.4389 94.67829 2.36 0.019 36.61674 410.261
----------------------------------------------------------------------------
OK, now I know this is WOLS and not WLS, but you get the drift: changing
values of parameter estimates along with changing which time dummies you
have in your model is perfectly normal, regardless. Notice that the model
diagnostics are exactly the same.
Whenever I've run a model with dummies, I've _never_ had to worry about
which one of them would make the most sense to drop, largely because:
(1) I know which one will be omitted beforehand;
and
(2) my problem is normally keeping them all _in_ my model! You should thank
your lucky stars...
Anyway, if you want to perform WLS regressions, you may find Phil Ender's
-wls0- routine, downloadable from SSC, of use:
. wls0 invest t2-t20, wvar(weight) type(abse)
WLS regression - type: proportional to abs(e)
(sum of wgt is 1.3769e+00)
Source | SS df MS Number of obs = 200
-------------+------------------------------ F( 19, 180) = 0.69
Model | 638334.902 19 33596.5738 Prob > F = 0.8233
Residual | 8730858.56 180 48504.7698 R-squared = 0.0681
-------------+------------------------------ Adj R-squared = -0.0302
Total | 9369193.46 199 47081.3742 Root MSE = 220.24
----------------------------------------------------------------------------
invest | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-----------+----------------------------------------------------------------
t2 | 28.91055 98.52813 0.29 0.770 -165.5082 223.3293
t3 | 50.02784 98.53465 0.51 0.612 -144.4038 244.4595
t4 | 5.039467 98.47842 0.05 0.959 -189.2812 199.3601
t5 | 7.772377 98.39881 0.08 0.937 -186.3912 201.9359
t6 | 40.05533 98.55082 0.41 0.685 -154.4082 234.5188
t7 | 66.91102 98.50374 0.68 0.498 -127.4596 261.2816
t8 | 49.90693 98.47082 0.51 0.613 -144.3987 244.2126
t9 | 45.60642 98.4746 0.46 0.644 -148.7067 239.9195
t10 | 48.16045 98.39934 0.49 0.625 -146.0042 242.3251
t11 | 51.50525 98.55601 0.52 0.602 -142.9685 245.979
t12 | 88.94119 98.54166 0.90 0.368 -105.5042 283.3866
t13 | 73.73731 98.47266 0.75 0.455 -120.572 268.0466
t14 | 81.49318 98.57705 0.83 0.410 -113.0221 276.0084
t15 | 68.16292 98.41564 0.69 0.489 -126.0338 262.3597
t16 | 76.87898 97.9299 0.79 0.433 -116.3593 270.1173
t17 | 127.194 98.57688 1.29 0.199 -67.32097 321.7089
t18 | 152.1969 98.51953 1.54 0.124 -42.20491 346.5987
t19 | 207.6927 99.13833 2.09 0.038 12.06987 403.3155
t20 | 201.0773 98.48557 2.04 0.043 6.742499 395.412
_cons | 72.65918 69.65713 1.04 0.298 -64.79042 210.1088
----------------------------------------------------------------------------
The above output is garbage (note the negative adjusted R^2): yours
shouldn't be! Alternatively, there's also -xtreg, be wls-. Whether either
solution fits your data is a question only you can answer.
CLIVE NICHOLAS |t: 0(044)7903 397793
Politics |e: [email protected]
Newcastle University |http://www.ncl.ac.uk/geps
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