I am doing an OLS regression with quite a large number of variables. This is one of the specifications I am working with:
To test for multicollinearity using -collin-, I exclude (besides the dependent variable) dquarter* and dprimarysiccode*, ie, the fixed effects. Otherwise, I get the following message:
.
Question 1. Is this correct?
All the variables have a reasonable value of VIF. However, the conditioning index seems too high. As far as I know, this could suggest that there is a collinearity problem associated to the constant term.
Question 2. Is this correct?
To exclude the constant term from the analysis, I run -collin- with the option -corr-:
Thus, if the constant term is dropped, the collinearity problem seems not to be present.
I have also used -colldiag- to analyze the conditioning matrix. However, since -fit- has be to run before -colldiag-, but -fit- cannot be used without constant term, I cannot check the conditioning matrix without the constant term.
Question 3. Does anyone know a way to do this?
[NOTE: I do not include the results from running -colldiag- because I would exceed the maximum numer of characters]
The results from running -colldiag- show that just two conditioning indexes are above 30 (their values are 79.0018 and 35.8414). The variances associated to them that are above 0.5 correspond to some dquarter* variables (ie, time fixed effects variables and their values are just slightly above the threshold) and to the constant term.
Indeed, the variance of the constant is almost 1 (0.9610).
Question 4. Would this provide additional evidence that if I keep the constant term a potential multicollineartiy problem is present?
The variables xx, xm and mm are mutually exclusive dummies that, if equal to 1, account for 87.5% of the observations. Something similar occurs as regards the variables dco and dan.
Question 5. Taking into account this, and given the results from -collin- and -colldiag- would it be advisable to estimate the model without the constant term?
Thanks in advance for any help.
Code:
regress y xm xx mm $st $fes $fas $fis dquarter* dprimarysiccode*, cluster(firm)
Linear regression Number of obs = 1549
F( 55, 106) = 12.72
Prob > F = 0.0000
R-squared = 0.4078
Root MSE = .23525
(Std. Err. adjusted for 107 clusters in firm)
------------------------------------------------------------------------------
| Robust
y | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
xm | .0350857 .0530344 0.66 0.510 -.0700602 .1402316
xx | -.1241785 .0472125 -2.63 0.010 -.2177819 -.0305751
mm | -.1093333 .0456007 -2.40 0.018 -.1997411 -.0189255
zs | -.0113633 .0092922 -1.22 0.224 -.029786 .0070593
dur | -.0655198 .039015 -1.68 0.096 -.1428707 .0118311
dco | .2530042 .0943562 2.68 0.009 .0659339 .4400745
dan | .2723561 .1063543 2.56 0.012 .0614983 .4832139
dut | .0419444 .0713666 0.59 0.558 -.0995468 .1834355
dup | -.0193242 .0347322 -0.56 0.579 -.0881841 .0495357
dca | -.0648063 .0478411 -1.35 0.178 -.159656 .0300433
dse | -.0399489 .0429487 -0.93 0.354 -.1250987 .045201
dsy | -.0358723 .0587616 -0.61 0.543 -.152373 .0806284
yl | -.0963299 .0432366 -2.23 0.028 -.1820506 -.0106091
pur | -.0504213 .0283916 -1.78 0.079 -.1067104 .0058677
mat | .0011013 .0010494 1.05 0.296 -.0009792 .0031819
amt | .0001559 .0000992 1.57 0.119 -.0000408 .0003525
ycv | .0734919 .0517773 1.42 0.159 -.0291617 .1761454
pro | .4624523 .4935774 0.94 0.351 -.516113 1.441018
mb | -.0337071 .0159716 -2.11 0.037 -.0653723 -.002042
ta | .0165495 .0940275 0.18 0.861 -.1698691 .2029682
lev | .531612 .0906072 5.87 0.000 .3519745 .7112496
li | -.0336324 .0163566 -2.06 0.042 -.0660609 -.0012039
si | -.0641883 .0194685 -3.30 0.001 -.1027865 -.02559
unr | .2487435 .0704326 3.53 0.001 .109104 .3883831
spe | .1181584 .0627558 1.88 0.062 -.006261 .2425779
dquarter1 | -.138636 .0757786 -1.83 0.070 -.2888745 .0116025
dquarter2 | -.1464862 .0738429 -1.98 0.050 -.2928868 -.0000855
dquarter3 | -.1559278 .0753829 -2.07 0.041 -.3053817 -.0064739
dquarter4 | -.1208113 .0738601 -1.64 0.105 -.2672462 .0256235
dquarter5 | -.1211856 .0741939 -1.63 0.105 -.2682822 .0259109
dquarter6 | -.1000479 .0762635 -1.31 0.192 -.2512476 .0511519
dquarter7 | -.0960139 .0767273 -1.25 0.214 -.2481333 .0561055
dquarter8 | -.0625375 .0779553 -0.80 0.424 -.2170914 .0920164
dquarter9 | -.0596899 .0758053 -0.79 0.433 -.2099812 .0906015
dquarter10 | -.0391873 .0774287 -0.51 0.614 -.1926973 .1143227
dquarter11 | -.0083287 .0788968 -0.11 0.916 -.1647492 .1480918
dquarter12 | .0267371 .08208 0.33 0.745 -.1359945 .1894687
dquarter13 | .0008081 .0787844 0.01 0.992 -.1553896 .1570058
dquarter14 | -.0341349 .0728937 -0.47 0.641 -.1786537 .1103839
dquarter15 | -.0422517 .0719317 -0.59 0.558 -.1848633 .1003598
dquarter16 | -.0721815 .0675334 -1.07 0.288 -.206073 .06171
dquarter17 | -.0450987 .0717747 -0.63 0.531 -.1873989 .0972015
dquarter18 | -.0837943 .0745701 -1.12 0.264 -.2316368 .0640482
dquarter19 | -.0872572 .0734328 -1.19 0.237 -.2328449 .0583306
dquarter20 | -.117614 .0707423 -1.66 0.099 -.2578675 .0226395
dquarter21 | -.0987901 .0715946 -1.38 0.171 -.2407335 .0431532
dquarter22 | -.0597826 .0693939 -0.86 0.391 -.1973626 .0777975
dquarter23 | -.0227661 .0628482 -0.36 0.718 -.1473688 .1018366
dquarter24 | (dropped)
dquarter25 | -.027545 .0914456 -0.30 0.764 -.2088448 .1537547
dprimarysi~1 | -.0624944 .105257 -0.59 0.554 -.2711766 .1461879
dprimarysi~2 | -.0201591 .0481707 -0.42 0.676 -.1156622 .0753441
dprimarysi~3 | .0293575 .0502924 0.58 0.561 -.0703521 .1290672
dprimarysi~4 | -.117912 .0627035 -1.88 0.063 -.2422278 .0064037
dprimarysi~5 | -.0167383 .0669127 -0.25 0.803 -.1493992 .1159226
dprimarysi~6 | (dropped)
dprimarysi~7 | .0414913 .0712774 0.58 0.562 -.0998231 .1828057
_cons | .3202686 .1846133 1.73 0.086 -.0457453 .6862825
------------------------------------------------------------------------------
Code:
corr(): matrix has zero or negative values on diagonal
Question 1. Is this correct?
Code:
collin xm xx mm $st $fes $fas $fis
(obs=1549)
Collinearity Diagnostics
SQRT R-
Variable VIF VIF Tolerance Squared
----------------------------------------------------
xm 3.29 1.81 0.3037 0.6963
xx 3.03 1.74 0.3305 0.6695
mm 3.19 1.79 0.3134 0.6866
zs 3.06 1.75 0.3263 0.6737
dur 1.37 1.17 0.7305 0.2695
dco 5.59 2.36 0.1788 0.8212
dan 7.46 2.73 0.1341 0.8659
dut 2.22 1.49 0.4498 0.5502
dup 1.13 1.06 0.8887 0.1113
dca 1.21 1.10 0.8296 0.1704
dse 2.05 1.43 0.4875 0.5125
dsy 1.38 1.18 0.7233 0.2767
yl 1.36 1.17 0.7340 0.2660
pur 1.16 1.08 0.8612 0.1388
mat 1.46 1.21 0.6852 0.3148
amt 2.70 1.64 0.3708 0.6292
ycv 1.10 1.05 0.9095 0.0905
pro 2.09 1.44 0.4795 0.5205
mb 1.76 1.33 0.5666 0.4334
ta 1.41 1.19 0.7107 0.2893
lev 1.82 1.35 0.5492 0.4508
li 1.78 1.33 0.5612 0.4388
si 3.37 1.83 0.2971 0.7029
unr 6.12 2.47 0.1633 0.8367
spe 4.05 2.01 0.2468 0.7532
----------------------------------------------------
Mean VIF 2.61
Cond
Eigenval Index
---------------------------------
1 12.6253 1.0000
2 2.3336 2.3260
3 1.7757 2.6664
4 1.3940 3.0094
5 1.1074 3.3765
6 0.8993 3.7469
7 0.8329 3.8935
8 0.7367 4.1397
9 0.6745 4.3263
10 0.6550 4.3902
11 0.5188 4.9333
12 0.4313 5.4105
13 0.4056 5.5790
14 0.3061 6.4224
15 0.2463 7.1600
16 0.1891 8.1705
17 0.1810 8.3517
18 0.1605 8.8704
19 0.1307 9.8284
20 0.1118 10.6248
21 0.0935 11.6230
22 0.0750 12.9734
23 0.0478 16.2546
24 0.0392 17.9361
25 0.0230 23.4378
26 0.0058 46.5849
---------------------------------
Condition Number 46.5849
Eigenvalues & Cond Index computed from scaled raw sscp (w/ intercept)
Det(correlation matrix) 0.0000
Question 2. Is this correct?
To exclude the constant term from the analysis, I run -collin- with the option -corr-:
Code:
collin xm xx mm $st $fes $fas $fis, corr
(obs=1549)
Collinearity Diagnostics
SQRT R-
Variable VIF VIF Tolerance Squared
----------------------------------------------------
xm 3.29 1.81 0.3037 0.6963
xx 3.03 1.74 0.3305 0.6695
mm 3.19 1.79 0.3134 0.6866
zs 3.06 1.75 0.3263 0.6737
dur 1.37 1.17 0.7305 0.2695
dco 5.59 2.36 0.1788 0.8212
dan 7.46 2.73 0.1341 0.8659
dut 2.22 1.49 0.4498 0.5502
dup 1.13 1.06 0.8887 0.1113
dca 1.21 1.10 0.8296 0.1704
dse 2.05 1.43 0.4875 0.5125
dsy 1.38 1.18 0.7233 0.2767
yl 1.36 1.17 0.7340 0.2660
pur 1.16 1.08 0.8612 0.1388
mat 1.46 1.21 0.6852 0.3148
amt 2.70 1.64 0.3708 0.6292
ycv 1.10 1.05 0.9095 0.0905
pro 2.09 1.44 0.4795 0.5205
mb 1.76 1.33 0.5666 0.4334
ta 1.41 1.19 0.7107 0.2893
lev 1.82 1.35 0.5492 0.4508
li 1.78 1.33 0.5612 0.4388
si 3.37 1.83 0.2971 0.7029
unr 6.12 2.47 0.1633 0.8367
spe 4.05 2.01 0.2468 0.7532
----------------------------------------------------
Mean VIF 2.61
Cond
Eigenval Index
---------------------------------
1 4.2709 1.0000
2 3.3002 1.1376
3 2.1975 1.3941
4 1.5268 1.6725
5 1.4322 1.7269
6 1.3057 1.8086
7 1.1789 1.9034
8 1.1252 1.9482
9 1.0541 2.0129
10 0.8856 2.1961
11 0.8616 2.2264
12 0.8253 2.2748
13 0.7241 2.4286
14 0.6657 2.5329
15 0.6308 2.6020
16 0.5993 2.6694
17 0.5105 2.8925
18 0.4487 3.0853
19 0.4239 3.1743
20 0.3123 3.6980
21 0.2173 4.4334
22 0.1886 4.7592
23 0.1394 5.5350
24 0.0941 6.7352
25 0.0815 7.2412
---------------------------------
Condition Number 7.2412
Eigenvalues & Cond Index computed from deviation sscp (no intercept)
Det(correlation matrix) 0.0000
I have also used -colldiag- to analyze the conditioning matrix. However, since -fit- has be to run before -colldiag-, but -fit- cannot be used without constant term, I cannot check the conditioning matrix without the constant term.
Question 3. Does anyone know a way to do this?
[NOTE: I do not include the results from running -colldiag- because I would exceed the maximum numer of characters]
The results from running -colldiag- show that just two conditioning indexes are above 30 (their values are 79.0018 and 35.8414). The variances associated to them that are above 0.5 correspond to some dquarter* variables (ie, time fixed effects variables and their values are just slightly above the threshold) and to the constant term.
Indeed, the variance of the constant is almost 1 (0.9610).
Question 4. Would this provide additional evidence that if I keep the constant term a potential multicollineartiy problem is present?
The variables xx, xm and mm are mutually exclusive dummies that, if equal to 1, account for 87.5% of the observations. Something similar occurs as regards the variables dco and dan.
Question 5. Taking into account this, and given the results from -collin- and -colldiag- would it be advisable to estimate the model without the constant term?
Thanks in advance for any help.
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