1

Guten Tag from Germany community :)

I'm working with panel data and fixed effects (= FE) for both, time and firm. I wanted to check my model for multicollinearity by using the variance inflation factor (= VIF), but R is giving me a warning message instead of the output.

How do I interpret this warning message and is there a solution to this?

I thought about calculating the VIF by myself:

VIF = 1 / (1 - R-squared)
VIF = 1 / (1 - 0.26632)
VIF = 1.36299

Is that solving the problem?

How do I get the VIF for every variable like I used to, when there are no FE?

Thanks in advance! :)

CODE 1:

### Creating a baseline formular ###
FORMULAR.PLM.BASELINE <- StockPrice ~ EPS + BookValuePS + AssetsTotal.LOG + LeverageRatio + AvgAnnualDividendyield + Dummy.ESG + Dummy.Sektor

### Creating FE-model ###
MOD.FE <- plm(FORMULAR.PLM.BASELINE, data = PD.Datensatz_so, model = "within", effect = "twoways")
summary(MOD.FE)

OUTCOME 1:

Twoways effects Within Model

Call:
plm(formula = FORMULAR.PLM.BASELINE, data = PD.Datensatz_so, 
    effect = "twoways", model = "within")

Balanced Panel: n = 17, T = 7, N = 119

Residuals:
     Min.   1st Qu.    Median   3rd Qu.      Max. 
-30.90756  -7.42737  -0.66878   6.97856  37.45463 

Coefficients:
                         Estimate Std. Error t-value Pr(>|t|)
EPS                       0.33624    0.26725  1.2581   0.2117
BookValuePS               0.46793    0.32815  1.4260   0.1574
AssetsTotal.LOG          14.21471   12.38404  1.1478   0.2542
LeverageRatio            38.60903   40.14368  0.9618   0.3388
AvgAnnualDividendyield -402.35998  249.04744 -1.6156   0.1098
Dummy.ESGbefriedigend    -3.17031   14.06732 -0.2254   0.8222
Dummy.ESGgut            -21.72112   16.71391 -1.2996   0.1971
Dummy.ESGexzellent      -21.21610   17.62499 -1.2038   0.2319

Total Sum of Squares:    25242
Residual Sum of Squares: 18519

R-Squared: 0.26632

Adj. R-Squared: 0.016197
F-statistic: 3.99284 on 8 and 88 DF, p-value: 0.00044688

CODE 2:

### Checking for multicollinearity ###
vif(MOD.FE)
1/vif(MOD.FE)

OUTCOME 2:

# Error in R[subs, subs] : subscript out of bounds
# In addition: Warning message:
#  In vif.default(MOD.FE) : No intercept: vifs may not be sensible.

DATA:

structure(list(Company = c("AIR PRODUCTS & CHEMICALS INC", "AIR PRODUCTS & CHEMICALS INC", 
"AIR PRODUCTS & CHEMICALS INC", "AIR PRODUCTS & CHEMICALS INC", 
"AIR PRODUCTS & CHEMICALS INC", "AIR PRODUCTS & CHEMICALS INC", 
"AIR PRODUCTS & CHEMICALS INC", "HESS CORP", "HESS CORP", "HESS CORP", 
"HESS CORP", "HESS CORP", "HESS CORP", "HESS CORP", "APACHE CORP", 
"APACHE CORP", "APACHE CORP", "APACHE CORP", "APACHE CORP", "APACHE CORP", 
"APACHE CORP", "AVERY DENNISON CORP", "AVERY DENNISON CORP", 
"AVERY DENNISON CORP", "AVERY DENNISON CORP", "AVERY DENNISON CORP", 
"AVERY DENNISON CORP", "AVERY DENNISON CORP", "BALL CORP", "BALL CORP", 
"BALL CORP", "BALL CORP", "BALL CORP", "BALL CORP", "BALL CORP", 
"CHEVRON CORP", "CHEVRON CORP", "CHEVRON CORP", "CHEVRON CORP", 
"CHEVRON CORP", "CHEVRON CORP", "CHEVRON CORP", "ECOLAB INC", 
"ECOLAB INC", "ECOLAB INC", "ECOLAB INC", "ECOLAB INC", "ECOLAB INC", 
"ECOLAB INC", "EXXON MOBIL CORP", "EXXON MOBIL CORP", "EXXON MOBIL CORP", 
"EXXON MOBIL CORP", "EXXON MOBIL CORP", "EXXON MOBIL CORP", "EXXON MOBIL CORP", 
"FMC CORP", "FMC CORP", "FMC CORP", "FMC CORP", "FMC CORP", "FMC CORP", 
"FMC CORP", "HALLIBURTON CO", "HALLIBURTON CO", "HALLIBURTON CO", 
"HALLIBURTON CO", "HALLIBURTON CO", "HALLIBURTON CO", "HALLIBURTON CO", 
"HELMERICH & PAYNE", "HELMERICH & PAYNE", "HELMERICH & PAYNE", 
"HELMERICH & PAYNE", "HELMERICH & PAYNE", "HELMERICH & PAYNE", 
"HELMERICH & PAYNE", "HOLLYFRONTIER CORP", "HOLLYFRONTIER CORP", 
"HOLLYFRONTIER CORP", "HOLLYFRONTIER CORP", "HOLLYFRONTIER CORP", 
"HOLLYFRONTIER CORP", "HOLLYFRONTIER CORP", "INTL FLAVORS & FRAGRANCES", 
"INTL FLAVORS & FRAGRANCES", "INTL FLAVORS & FRAGRANCES", "INTL FLAVORS & FRAGRANCES", 
"INTL FLAVORS & FRAGRANCES", "INTL FLAVORS & FRAGRANCES", "INTL FLAVORS & FRAGRANCES", 
"INTL PAPER CO", "INTL PAPER CO", "INTL PAPER CO", "INTL PAPER CO", 
"INTL PAPER CO", "INTL PAPER CO", "INTL PAPER CO", "MARATHON OIL CORP", 
"MARATHON OIL CORP", "MARATHON OIL CORP", "MARATHON OIL CORP", 
"MARATHON OIL CORP", "MARATHON OIL CORP", "MARATHON OIL CORP", 
"NEWMONT CORP", "NEWMONT CORP", "NEWMONT CORP", "NEWMONT CORP", 
"NEWMONT CORP", "NEWMONT CORP", "NEWMONT CORP", "NUCOR CORP", 
"NUCOR CORP", "NUCOR CORP", "NUCOR CORP", "NUCOR CORP", "NUCOR CORP", 
"NUCOR CORP"), Year = structure(c(1L, 2L, 3L, 4L, 5L, 6L, 7L, 
1L, 2L, 3L, 4L, 5L, 6L, 7L, 1L, 2L, 3L, 4L, 5L, 6L, 7L, 1L, 2L, 
3L, 4L, 5L, 6L, 7L, 1L, 2L, 3L, 4L, 5L, 6L, 7L, 1L, 2L, 3L, 4L, 
5L, 6L, 7L, 1L, 2L, 3L, 4L, 5L, 6L, 7L, 1L, 2L, 3L, 4L, 5L, 6L, 
7L, 1L, 2L, 3L, 4L, 5L, 6L, 7L, 1L, 2L, 3L, 4L, 5L, 6L, 7L, 1L, 
2L, 3L, 4L, 5L, 6L, 7L, 1L, 2L, 3L, 4L, 5L, 6L, 7L, 1L, 2L, 3L, 
4L, 5L, 6L, 7L, 1L, 2L, 3L, 4L, 5L, 6L, 7L, 1L, 2L, 3L, 4L, 5L, 
6L, 7L, 1L, 2L, 3L, 4L, 5L, 6L, 7L, 1L, 2L, 3L, 4L, 5L, 6L, 7L
), .Label = c("2011", "2012", "2013", "2014", "2015", "2016", 
"2017"), class = "factor"), ggroup = c(1510, 1510, 1510, 1510, 
1510, 1510, 1510, 1010, 1010, 1010, 1010, 1010, 1010, 1010, 1010, 
1010, 1010, 1010, 1010, 1010, 1010, 1510, 1510, 1510, 1510, 1510, 
1510, 1510, 1510, 1510, 1510, 1510, 1510, 1510, 1510, 1010, 1010, 
1010, 1010, 1010, 1010, 1010, 1510, 1510, 1510, 1510, 1510, 1510, 
1510, 1010, 1010, 1010, 1010, 1010, 1010, 1010, 1510, 1510, 1510, 
1510, 1510, 1510, 1510, 1010, 1010, 1010, 1010, 1010, 1010, 1010, 
1010, 1010, 1010, 1010, 1010, 1010, 1010, 1010, 1010, 1010, 1010, 
1010, 1010, 1010, 1510, 1510, 1510, 1510, 1510, 1510, 1510, 1510, 
1510, 1510, 1510, 1510, 1510, 1510, 1010, 1010, 1010, 1010, 1010, 
1010, 1010, 1510, 1510, 1510, 1510, 1510, 1510, 1510, 1510, 1510, 
1510, 1510, 1510, 1510, 1510), gvkey = structure(c(1L, 1L, 1L, 
1L, 1L, 1L, 1L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 3L, 3L, 3L, 3L, 3L, 
3L, 3L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 
6L, 6L, 6L, 6L, 6L, 6L, 6L, 7L, 7L, 7L, 7L, 7L, 7L, 7L, 8L, 8L, 
8L, 8L, 8L, 8L, 8L, 9L, 9L, 9L, 9L, 9L, 9L, 9L, 10L, 10L, 10L, 
10L, 10L, 10L, 10L, 11L, 11L, 11L, 11L, 11L, 11L, 11L, 12L, 12L, 
12L, 12L, 12L, 12L, 12L, 13L, 13L, 13L, 13L, 13L, 13L, 13L, 14L, 
14L, 14L, 14L, 14L, 14L, 14L, 15L, 15L, 15L, 15L, 15L, 15L, 15L, 
16L, 16L, 16L, 16L, 16L, 16L, 16L, 17L, 17L, 17L, 17L, 17L, 17L, 
17L), .Label = c("1209", "1380", "1678", "1913", "1988", "2991", 
"4213", "4503", "4510", "5439", "5581", "5667", "6078", "6104", 
"7017", "7881", "8030"), class = "factor"), StockPrice = c(85.19, 
84.02, 111.78, 144.23, 130.11, 143.82, 164.08, 56.8, 52.96, 83, 
73.82, 48.48, 62.29, 47.47, 90.58, 78.5, 85.94, 62.67, 44.47, 
63.47, 42.22, 28.68, 34.92, 50.19, 51.88, 62.66, 70.22, 114.86, 
17.86, 22.38, 25.83, 34.09, 36.37, 37.54, 37.85, 106.4, 108.14, 
124.91, 112.18, 89.96, 117.7, 125.19, 57.81, 71.9, 104.27, 104.52, 
114.38, 117.22, 134.18, 84.76, 86.55, 101.2, 92.45, 77.95, 90.26, 
83.64, 43.02, 58.52, 75.46, 57.03, 39.13, 56.56, 94.66, 34.51, 
34.69, 50.75, 39.33, 34.04, 54.09, 48.87, 58.36, 56.01, 84.08, 
67.42, 53.55, 77.4, 64.64, 23.4, 46.55, 49.69, 37.48, 39.89, 
32.76, 51.22, 52.42, 66.54, 85.98, 101.36, 119.64, 117.83, 152.61, 
29.6, 39.84, 49.03, 53.58, 37.7, 53.06, 57.94, 29.27, 30.66, 
35.3, 28.29, 12.59, 17.31, 16.93, 60.01, 46.44, 23.03, 18.9, 
17.99, 34.07, 37.52, 39.57, 43.16, 53.38, 49.05, 40.3, 59.52, 
63.58), EPS = c(5.75, 5.53, 4.74, 4.66, 5.95, 2.92, 13.76, 5.01, 
5.93, 15.53, 8.11, -10.68, -19.37, -12.93, 11.94, 5.14, 5.65, 
-14.07, -61.16, -3.71, 3.42, 1.78, 1.65, 2.49, 2.69, 3.01, 3.63, 
3.2, 1.34, 1.3, 1.39, 1.7, 1.02, 0.83, 1.07, 13.54, 13.42, 11.18, 
10.21, 2.46, -0.27, 4.88, 1.95, 2.41, 3.23, 4.01, 3.38, 4.2, 
5.21, 8.43, 9.7, 7.37, 7.6, 3.85, 1.88, 4.63, 2.58, 3.02, 2.17, 
2.31, 3.66, 1.56, 3.99, 3.09, 2.85, 2.37, 4.13, -0.79, -6.69, 
-0.53, 4.07, 5.44, 6.93, 3.57, 3.92, -0.53, -1.18, 6.46, 8.41, 
3.67, 1.43, 3.92, -1.48, 4.57, 3.32, 3.13, 4.35, 5.12, 5.21, 
5.09, 3.74, 3.1, 1.82, 3.15, 1.3, 2.25, 2.2, 5.19, 4.15, 2.24, 
2.49, 4.48, -3.26, -2.53, -6.73, 0.74, 3.65, -4.94, 1.02, 0.43, 
-1.18, -0.18, 2.45, 1.59, 1.53, 2.23, 1.12, 2.49, 4.12), BookValuePS = c(27.21, 
30.67, 33.58, 34.63, 33.73, 32.72, 46.27, 54.46, 61.75, 75.99, 
77.68, 67.77, 45.92, 35.08, 75.5, 80.54, 84.55, 67.54, 6.79, 
16.46, 19.46, 15.53, 12.13, 17.21, 11.53, 10.61, 10.48, 11.88, 
3.69, 3.6, 4.11, 3.73, 4.56, 10.85, 11.25, 61.1, 70, 77.78, 82.3, 
81.76, 77.72, 78.67, 23.92, 20.78, 24.49, 24.38, 23.31, 23.59, 
26.31, 31.7, 35.84, 39.36, 40.76, 40.72, 40.12, 44.1, 8.74, 10.75, 
11.24, 11.48, 13.95, 14.62, 19.97, 14.38, 17.02, 15.12, 19.18, 
18.13, 10.93, 9.57, 30.66, 35.9, 41.81, 45.37, 45.45, 42.23, 
38.38, 32.84, 29.49, 29.94, 28, 27.84, 6.58, 30.49, 13.73, 15.4, 
17.99, 18.76, 19.77, 20.42, 21.3, 15.32, 14.45, 18.3, 11.89, 
9.32, 10.65, 15.79, 24.16, 25.9, 27.44, 30.91, 27.4, 20.71, 13.77, 
26.11, 27.77, 20.35, 20.63, 22.18, 20.18, 19.9, 23.58, 24.02, 
23.96, 24.3, 23.14, 24.66, 27.31), ESGscore = c(84.2750015258789, 
81.9225006103516, 77.4024963378906, 80.1125030517578, 78.6449966430664, 
76.3775024414062, 79.2699966430664, 69.4899978637695, 65.8300018310547, 
64.4300003051758, 74.3000030517578, 75.7600021362305, 71.4599990844727, 
74.6900024414062, 55.8300018310547, 56.0900001525879, 57.5, 60.75, 
60.8800010681152, 67.379997253418, 71.9899978637695, 82.9000015258789, 
77.3899993896484, 76.9300003051758, 78.7399978637695, 76.2283325195312, 
74.2125015258789, 68.3600006103516, 64.4100036621094, 65.6600036621094, 
63.75, 67.7300033569336, 67.5699996948242, 74.4300003051758, 
68.5699996948242, 86.5100021362305, 84.3099975585938, 82.6600036621094, 
82.3399963378906, 88.4100036621094, 90.0800018310547, 92.25, 
74.6999969482422, 72.3600006103516, 68.3899993896484, 67.9300003051758, 
65.629997253418, 74.9000015258789, 74.8600006103516, 81.6999969482422, 
79.370002746582, 79.0899963378906, 75.25, 81.9499969482422, 81.0199966430664, 
88.3399963378906, 59.8199996948242, 55.6500015258789, 52.2999992370605, 
51.8499984741211, 56.9199981689453, 66.620002746582, 65.3300018310547, 
85.9800033569336, 83.9499969482422, 85.1100006103516, 67.4300003051758, 
76.4400024414062, 69.9199981689453, 78.4599990844727, 19.0599994659424, 
17.5200004577637, 18.1200008392334, 23.5025005340576, 35.5349998474121, 
36.7350006103516, 41.1725006103516, 27.8700008392334, 33.7700004577637, 
37.6699981689453, 47.7599983215332, 50.2400016784668, 55.25, 
58.3800010681152, 70.7600021362305, 71.9800033569336, 75.1500015258789, 
75.1399993896484, 79.4100036621094, 70.1500015258789, 76.5299987792969, 
71.3399963378906, 80.1900024414062, 72.9899978637695, 66.9400024414062, 
73.8000030517578, 76.2399978637695, 72.0500030517578, 80.4700012207031, 
80.5100021362305, 79.6800003051758, 76.4300003051758, 78.6399993896484, 
77.2300033569336, 76.5899963378906, 81.6399993896484, 77.8600006103516, 
79.5100021362305, 85.9800033569336, 81.120002746582, 78.75, 80.7099990844727, 
59.8600006103516, 52.3400001525879, 54.9300003051758, 54.8899993896484, 
64.120002746582, 62.4900016784668, 61.7200012207031), LeverageRatio = c(0.594435561205841, 
0.617679355403529, 0.605486789891209, 0.585704565106127, 0.584301032659383, 
0.607893538666041, 0.453831624609765, 0.526880621422731, 0.514513938445248, 
0.421808485755719, 0.424412877806003, 0.433075010966516, 0.492225987910974, 
0.521893388715819, 0.466561641467023, 0.50435484136523, 0.458182585135552, 
0.536441950243066, 0.863814881647384, 0.722989475553977, 0.661709698020254, 
0.666478988304306, 0.690341393278699, 0.676354504930841, 0.755401139345263, 
0.766383635343921, 0.789486848203547, 0.796336317416944, 0.832646959442815, 
0.85152722608109, 0.846556170952766, 0.863545109551454, 0.872015950820485, 
0.787608977926173, 0.77045838429728, 0.420539064513973, 0.414014816595273, 
0.412369508931914, 0.417244930946599, 0.426101922939614, 0.440337129630342, 
0.416388895455584, 0.689339285962852, 0.654171637758199, 0.625987329478904, 
0.624183852632949, 0.629331005652438, 0.623511997043816, 0.618357519590785, 
0.53362009593659, 0.503099207597478, 0.498272819542802, 0.50099429745374, 
0.492778196806015, 0.493436548254086, 0.461735462056663, 0.668598911289985, 
0.661560602236253, 0.709695906149125, 0.713416346784009, 0.705069637526097, 
0.681119995202526, 0.70869946604795, 0.442581408117582, 0.424844947099599, 
0.535263319987681, 0.495440446650124, 0.581452005847003, 0.651518518518518, 
0.668247956946382, 0.346499145342847, 0.329672942621959, 0.290686407542856, 
0.272377520553529, 0.315234369479579, 0.33241919028586, 0.353323181006733, 
0.495472522128971, 0.413984333584541, 0.403422922342673, 0.401603334682229, 
0.373721043240805, 0.503861576091451, 0.497685035920943, 0.627590017963253, 
0.615704103314394, 0.560867296803568, 0.565457600575885, 0.572662204137801, 
0.595157943268954, 0.633783603720298, 0.754751231800837, 0.803937424190589, 
0.74292692210099, 0.821677590294241, 0.873017948801779, 0.869815564552407, 
0.807627643571365, 0.453253004367091, 0.482156007477483, 0.456934306569343, 
0.416289467107273, 0.425799263408746, 0.435871872386956, 0.468108304561148, 
0.530610759263303, 0.535480607082631, 0.590494265869811, 0.58765451918446, 
0.549281232626479, 0.490228709999525, 0.484073335602782, 0.486979724850567, 
0.460038216337232, 0.497097505794197, 0.502272882334361, 0.479531926496852, 
0.482388666486795, 0.448336979534749), AvgAnnualDividendyield = c(0.0266, 
0.0314, 0.0298, 0.0253, 0.0241, 0.025, 0.0245, 0.006, 0.009, 
0.01, 0.012, 0.016, 0.021, 0.025, 0.007, 0.01, 0.011, 0.011, 
0.018, 0.019, 0.019, 0.029, 0.028, 0.03, 0.023, 0.02, 0.023, 
0.019, 0.008, 0.01, 0.011, 0.009, 0.008, 0.007, 0.009, 0.031, 
0.033, 0.033, 0.035, 0.045, 0.043, 0.039, 0.013, 0.016, 0.008, 
0.011, 0.012, 0.013, 0.012, 0.023, 0.025, 0.027, 0.028, 0.035, 
0.037, 0.041, 0.011, 0.008, 0.01, 0.01, 0.015, 0.017, 0.01, 0.008, 
0.011, 0.011, 0.011, 0.018, 0.017, 0.015, 0.0043, 0.0055, 0.0131, 
0.0254, 0.0443, 0.0447, 0.0481, 0.054, 0.09, 0.068, 0.071, 0.03, 
0.045, 0.042, 0.019, 0.027, 0.014, 0.017, 0.017, 0.019, 0.019, 
0.037, 0.035, 0.029, 0.032, 0.036, 0.044, 0.036, 0.028, 0.023, 
0.021, 0.023, 0.03, 0.014, 0.014, 0.021, 0.027, 0.037, 0.01, 
0.005, 0.004, 0.007, 0.036, 0.036, 0.031, 0.029, 0.034, 0.031, 
0.026), AssetsTotal.LOG = c(9.56736426869569, 9.73753926605387, 
9.78976436754936, 9.78577886714304, 9.76641272417325, 9.80119459273923, 
9.82375142221191, 10.5747980384869, 10.6791589746007, 10.6632180372392, 
10.5604374447842, 10.4398347135322, 10.261895993101, 10.0481072421461, 
10.8599792861544, 11.0143083465337, 11.0290176185546, 10.9322494593032, 
9.84384369960861, 10.0221146762943, 9.99524597777567, 8.51171827041292, 
8.53803445653107, 8.43611330054631, 8.38027325164503, 8.3269282159168, 
8.38854128098197, 8.5442050446523, 8.89351782318383, 8.92360453139329, 
8.96441423278807, 8.93208043810331, 9.18778796750567, 9.69109846411978, 
9.75086071107721, 12.2523549056307, 12.3587164763448, 12.4441166319283, 
12.4913493273481, 12.4916387308594, 12.4687368650067, 12.4443254746449, 
9.81141616514545, 9.77407912202464, 9.88514535828826, 9.87646055234287, 
9.83315624388896, 9.81630520922804, 9.90160580268615, 12.7100307417182, 
12.7182823110683, 12.7565265916732, 12.7642388118431, 12.7271198504863, 
12.7077989961906, 12.7619414221787, 8.22777628167074, 8.38341031627978, 
8.56316036427592, 8.58307456052975, 8.7524075805257, 8.72246597631381, 
9.12764329007411, 10.072259391783, 10.2186631892968, 10.2827113494391, 
10.3809631966206, 10.5171043941393, 10.2035921449865, 10.1300253369184, 
8.51797111141425, 8.65191374487273, 8.74270627691564, 8.81312030587554, 
8.87514902365156, 8.8293755227843, 8.77028192359486, 9.24131769131151, 
9.2427104683695, 9.21599826167033, 9.13028362611817, 9.03459301705783, 
9.15225152771786, 9.27726550821295, 7.99482826345879, 8.0862872208779, 
8.11124725483796, 8.15898023498527, 8.22186975840737, 8.29828662307883, 
8.43357802939057, 10.2033328521137, 10.3782610379096, 10.3586313188748, 
10.2640947550025, 10.3283303610705, 10.4146631150664, 10.4312587850283, 
10.3536391782667, 10.4718082001492, 10.4806625568437, 10.4915797263212, 
10.3831630085098, 10.3447701535097, 9.99934303817965, 10.2209953818852, 
10.2972174044259, 10.1171462646391, 10.123265446374, 10.1338847325616, 
9.95375281868368, 9.93124862332152, 9.58674389405408, 9.55761537614691, 
9.62926668371527, 9.65604661844032, 9.56454021436101, 9.63059672022673, 
9.67037306957062), Dummy.ESG = structure(c(4L, 4L, 4L, 4L, 4L, 
4L, 4L, 3L, 3L, 3L, 3L, 4L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 
4L, 4L, 4L, 4L, 4L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 4L, 4L, 
4L, 4L, 4L, 4L, 4L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 4L, 4L, 4L, 4L, 
4L, 4L, 4L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 4L, 4L, 4L, 3L, 4L, 3L, 
4L, 1L, 1L, 1L, 1L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 3L, 3L, 3L, 3L, 
3L, 4L, 4L, 4L, 3L, 4L, 3L, 4L, 3L, 3L, 3L, 4L, 3L, 4L, 4L, 4L, 
4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 3L, 3L, 3L, 3L, 3L, 
3L, 3L), .Label = c("schlecht", "befriedigend", "gut", "exzellent"
), class = "factor"), Dummy.Sektor = structure(c(2L, 2L, 2L, 
2L, 2L, 2L, 2L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 
1L, 1L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 
1L, 1L, 1L, 1L, 1L, 1L, 1L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 1L, 1L, 
1L, 1L, 1L, 1L, 1L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 1L, 1L, 1L, 1L, 
1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 
1L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 1L, 
1L, 1L, 1L, 1L, 1L, 1L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 
2L, 2L, 2L, 2L), .Label = c("Energie", "Material"), class = "factor")), row.names = c("1209-2011", 
"1209-2012", "1209-2013", "1209-2014", "1209-2015", "1209-2016", 
"1209-2017", "1380-2011", "1380-2012", "1380-2013", "1380-2014", 
"1380-2015", "1380-2016", "1380-2017", "1678-2011", "1678-2012", 
"1678-2013", "1678-2014", "1678-2015", "1678-2016", "1678-2017", 
"1913-2011", "1913-2012", "1913-2013", "1913-2014", "1913-2015", 
"1913-2016", "1913-2017", "1988-2011", "1988-2012", "1988-2013", 
"1988-2014", "1988-2015", "1988-2016", "1988-2017", "2991-2011", 
"2991-2012", "2991-2013", "2991-2014", "2991-2015", "2991-2016", 
"2991-2017", "4213-2011", "4213-2012", "4213-2013", "4213-2014", 
"4213-2015", "4213-2016", "4213-2017", "4503-2011", "4503-2012", 
"4503-2013", "4503-2014", "4503-2015", "4503-2016", "4503-2017", 
"4510-2011", "4510-2012", "4510-2013", "4510-2014", "4510-2015", 
"4510-2016", "4510-2017", "5439-2011", "5439-2012", "5439-2013", 
"5439-2014", "5439-2015", "5439-2016", "5439-2017", "5581-2011", 
"5581-2012", "5581-2013", "5581-2014", "5581-2015", "5581-2016", 
"5581-2017", "5667-2011", "5667-2012", "5667-2013", "5667-2014", 
"5667-2015", "5667-2016", "5667-2017", "6078-2011", "6078-2012", 
"6078-2013", "6078-2014", "6078-2015", "6078-2016", "6078-2017", 
"6104-2011", "6104-2012", "6104-2013", "6104-2014", "6104-2015", 
"6104-2016", "6104-2017", "7017-2011", "7017-2012", "7017-2013", 
"7017-2014", "7017-2015", "7017-2016", "7017-2017", "7881-2011", 
"7881-2012", "7881-2013", "7881-2014", "7881-2015", "7881-2016", 
"7881-2017", "8030-2011", "8030-2012", "8030-2013", "8030-2014", 
"8030-2015", "8030-2016", "8030-2017"), class = c("pdata.frame", 
"data.frame"), index = structure(list(gvkey = structure(c(1L, 
1L, 1L, 1L, 1L, 1L, 1L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 3L, 3L, 3L, 
3L, 3L, 3L, 3L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 5L, 5L, 5L, 5L, 5L, 
5L, 5L, 6L, 6L, 6L, 6L, 6L, 6L, 6L, 7L, 7L, 7L, 7L, 7L, 7L, 7L, 
8L, 8L, 8L, 8L, 8L, 8L, 8L, 9L, 9L, 9L, 9L, 9L, 9L, 9L, 10L, 
10L, 10L, 10L, 10L, 10L, 10L, 11L, 11L, 11L, 11L, 11L, 11L, 11L, 
12L, 12L, 12L, 12L, 12L, 12L, 12L, 13L, 13L, 13L, 13L, 13L, 13L, 
13L, 14L, 14L, 14L, 14L, 14L, 14L, 14L, 15L, 15L, 15L, 15L, 15L, 
15L, 15L, 16L, 16L, 16L, 16L, 16L, 16L, 16L, 17L, 17L, 17L, 17L, 
17L, 17L, 17L), .Label = c("1209", "1380", "1678", "1913", "1988", 
"2991", "4213", "4503", "4510", "5439", "5581", "5667", "6078", 
"6104", "7017", "7881", "8030"), class = "factor"), Year = structure(c(1L, 
2L, 3L, 4L, 5L, 6L, 7L, 1L, 2L, 3L, 4L, 5L, 6L, 7L, 1L, 2L, 3L, 
4L, 5L, 6L, 7L, 1L, 2L, 3L, 4L, 5L, 6L, 7L, 1L, 2L, 3L, 4L, 5L, 
6L, 7L, 1L, 2L, 3L, 4L, 5L, 6L, 7L, 1L, 2L, 3L, 4L, 5L, 6L, 7L, 
1L, 2L, 3L, 4L, 5L, 6L, 7L, 1L, 2L, 3L, 4L, 5L, 6L, 7L, 1L, 2L, 
3L, 4L, 5L, 6L, 7L, 1L, 2L, 3L, 4L, 5L, 6L, 7L, 1L, 2L, 3L, 4L, 
5L, 6L, 7L, 1L, 2L, 3L, 4L, 5L, 6L, 7L, 1L, 2L, 3L, 4L, 5L, 6L, 
7L, 1L, 2L, 3L, 4L, 5L, 6L, 7L, 1L, 2L, 3L, 4L, 5L, 6L, 7L, 1L, 
2L, 3L, 4L, 5L, 6L, 7L), .Label = c("2011", "2012", "2013", "2014", 
"2015", "2016", "2017"), class = "factor")), row.names = c(NA, 
119L), class = c("pindex", "data.frame")))
wrangjangler
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  • I am going to look at this a bit closer. Usually, when you get an error with `VIF` it's due to multicollinearity. Influential factors and multicollinearity go hand-in-hand, but they aren't the same thing. – Kat Jan 22 '22 at 20:40
  • The problem seems to be solved [here](https://stackoverflow.com/questions/20281055/test-for-multicollinearity-in-panel-data-r). – riccardo-df Jan 22 '22 at 20:57
  • From the Hausman test, it looks like collinearity is occurring between the unique errors and the regressors, inferring that a random model may be better suited for your data. Since there is heteroskedasticity and a bit of serial correlation (although that could be mitigated by the size of the data set), it may be worth it to consider the function `vcovHC`, whether you go with FE or RE. The large variation between R^2 and adjusted R^2 may be telling you something, as well. Mach's gut! – Kat Jan 23 '22 at 03:22
  • Hi @Kat, first of all: thank you! I did the Hausmann test to check wether to use the RE or FE and p-value is way smaller than 0,05 so I went with the FE. At the moment I'm going with the `vcovDC` for multidimensional clustering. There must be a way to check for multicollinearity between the independent variables. I just didn't find it yet, do you? :) – wrangjangler Jan 23 '22 at 12:13

1 Answers1

1

I spent time looking for evidence to back up my thoughts that multicollinearity wasn't something to validate because your model is clustering. If anything, checking within the clusters might be something to look at. Checking the variables independent of the groups? Not so much. However, I found nothing I would consider "evidence."

This is what I would do (what I did):

First, I created the MOD.FE (precisely as you demonstrated). Next, I made MOD.RE.

# random effects
MOD.RE <- plm(FORMULAR.PLM.BASELINE, 
              data = PD.Datensatz_so, 
              model = "random")
summary(MOD.RE)

Then I ran Hausman's Test.

#------------ testing the suitability of the test method --------------
# this tests whether you should use random or fixed effects
# it tests whether ui is correlated with the regressors
# the H0: not correlated
phtest(MOD.FE, MOD.RE)
# 
#   Hausman Test
# 
# data:  FORMULAR.PLM.BASELINE
# chisq = 12.983, df = 8, p-value = 0.1125
# alternative hypothesis: one model is inconsistent
#  
# if p < .05 FE is needed, it is not, so RE is needed
# this infers that the ui (unique errors) correlated with regressors **

This led me to believe that using the RE model was better. However, I investigated further with both options. I used a few different packages, so I appended the package name to any function I used (other than plm functions).

Serial correlation of the residuals

pbgtest(MOD.FE)
# 
#   Breusch-Godfrey/Wooldridge test for serial correlation in panel models
# 
# data:  FORMULAR.PLM.BASELINE
# chisq = 18.501, df = 7, p-value = 0.009903
# alternative hypothesis: serial correlation in idiosyncratic errors
#  
# problem with serial correlation, but may not matter (small sample size)

pbgtest(MOD.RE)
# 
#   Breusch-Godfrey/Wooldridge test for serial correlation in panel models
# 
# data:  FORMULAR.PLM.BASELINE
# chisq = 26.98, df = 7, p-value = 0.0003361
# alternative hypothesis: serial correlation in idiosyncratic errors
#  
# problem with serial correlation, but may not matter (small sample size)

Stationary time series

# test for stochastic trends
# H0: series is non-stationary
tseries::adf.test(PD.Datensatz_so$StockPrice, k = 2)
# 
#   Augmented Dickey-Fuller Test
# 
# data:  PD.Datensatz_so$StockPrice
# Dickey-Fuller = -3.4907, Lag order = 2, p-value = 0.04612
# alternative hypothesis: stationary
#  
# this is good; no differencing needed

Equal variance

# test for homoskedasticity
lmtest::bptest(FORMULAR.PLM.BASELINE,
               data = PD.Datensatz_so,
               studentize = F)
# 
#   Breusch-Pagan test
# 
# data:  FORMULAR.PLM.BASELINE
# BP = 25.903, df = 9, p-value = 0.002119
#  
# there is a problem of heteroskedasticity**

Controls for issues with serial correlation and variance

#------- controlling for serial corr/heteroskedasticity FE -------

t(sapply(c("HC0", "HC1", "HC2", "HC3", "HC4"), 
         function(x) sqrt(diag(vcovHC(MOD.FE, type = x)))))
# all of the variables saw larger error terms with the increase in HC value
   # except for Dummy.ESG == excellent

lmtest::coeftest(MOD.FE, vcovHC(MOD.FE, type = "HC0"))
# 
# t test of coefficients:
# 
#                          Estimate Std. Error t value Pr(>|t|)  
# EPS                       0.33624    0.28454  1.1817  0.24051  
# BookValuePS               0.46793    0.32077  1.4588  0.14818  
# AssetsTotal.LOG          14.21471   13.98026  1.0168  0.31205  
# LeverageRatio            38.60903   48.75079  0.7920  0.43051  
# AvgAnnualDividendyield -402.35998  374.68585 -1.0739  0.28582  
# Dummy.ESGbefriedigend    -3.17031   11.29811 -0.2806  0.77967  
# Dummy.ESGgut            -21.72112    9.52367 -2.2808  0.02498 *
# Dummy.ESGexzellent      -21.21610   11.14826 -1.9031  0.06030 .
# ---
# Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Saw further improvement with method= "white1"

lmtest::coeftest(MOD.FE, vcovHC(MOD.FE, method = "white1", type = "HC0"))
# 
# t test of coefficients:
# 
#                          Estimate Std. Error t value Pr(>|t|)  
# EPS                       0.33624    0.29827  1.1273  0.26269  
# BookValuePS               0.46793    0.25116  1.8630  0.06579 .
# AssetsTotal.LOG          14.21471    9.44197  1.5055  0.13578  
# LeverageRatio            38.60903   34.45018  1.1207  0.26546  
# AvgAnnualDividendyield -402.35998  239.65196 -1.6789  0.09671 .
# Dummy.ESGbefriedigend    -3.17031    8.71336 -0.3638  0.71685  
# Dummy.ESGgut            -21.72112   10.45950 -2.0767  0.04075 *
# Dummy.ESGexzellent      -21.21610   11.68868 -1.8151  0.07292 .
# ---
# Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
# It looks like `satisfactory` isn't doing a whole lot for the model.
# Das ist mir Wurst -> Das is ihn Wurst (befriedigend auf die Ergebnisvariable)

Now for the RE model

#------- controlling for serial corr/heteroskedasticity RE -------
t(sapply(c("HC0", "HC1", "HC2", "HC3", "HC4"), 
         function(x) sqrt(diag(vcovHC(MOD.RE, type = x)))))
# all had more error as the HC when higher, except BookValuePS (up, then down)
# same resulting use of vcovHC as the FE model, not surprising    

lmtest::coeftest(MOD.RE, vcovHC(MOD.RE, type = "HC0"))
# 
# t test of coefficients:
# 
#                           Estimate  Std. Error t value Pr(>|t|)  
# (Intercept)             -56.340871   40.407060 -1.3943  0.16605  
# EPS                       0.177625    0.111367  1.5949  0.11362  
# BookValuePS               0.604870    0.248151  2.4375  0.01641 *
# AssetsTotal.LOG           8.616948    5.009664  1.7201  0.08826 .
# LeverageRatio            28.749759   46.126681  0.6233  0.53440  
# AvgAnnualDividendyield -219.316248  275.288817 -0.7967  0.42737  
# Dummy.ESGbefriedigend    -0.072336    8.476523 -0.0085  0.99321  
# Dummy.ESGgut             -5.251316    6.127045 -0.8571  0.39329  
# Dummy.ESGexzellent       -7.244158   12.488032 -0.5801  0.56305  
# Dummy.SektorMaterial     22.719709   16.087360  1.4123  0.16072  
# ---
# Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Saw further improvement with method= "white1"

lmtest::coeftest(MOD.RE, vcovHC(MOD.RE, method = "white1", type = "HC0"))
# 
# t test of coefficients:
# 
#                           Estimate  Std. Error t value Pr(>|t|)   
# (Intercept)             -56.340871   43.309326 -1.3009 0.196038   
# EPS                       0.177625    0.199284  0.8913 0.374723   
# BookValuePS               0.604870    0.199899  3.0259 0.003093 **
# AssetsTotal.LOG           8.616948    4.898411  1.7591 0.081361 . 
# LeverageRatio            28.749759   38.256011  0.7515 0.453966   
# AvgAnnualDividendyield -219.316248  211.106676 -1.0389 0.301156   
# Dummy.ESGbefriedigend    -0.072336   11.143110 -0.0065 0.994832   
# Dummy.ESGgut             -5.251316   11.087409 -0.4736 0.636712   
# Dummy.ESGexzellent       -7.244158   12.887762 -0.5621 0.575205   
# Dummy.SektorMaterial     22.719709   13.114915  1.7324 0.086039 . 
# ---
# Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Kat
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  • Hi @Kat, first of all thank you very much for your time and solution! Das ist große Klasse :) So let's se if I got it right: **1. Serial correlation of the residuals** There is no problem with serial correlation of the residuals due to the fact, that the data size is small. I ran the code with my/the whole data set and the p-value = 2.578e-11 with 17 variables and 287 observations. Is that still considered small? **2. Stationary ime series** p-value = 0,01 with the warning, that it could be smaller than the printed one **3. Homosskedasticity** p-value = 4.69e-11 --> Hetero – wrangjangler Jan 24 '22 at 11:05
  • Sadly I didn't quite get, what you are doing/trying to show/proof with the **Controls for issues with serial correlation and variance** and the following **white1 method**, sorry(!), could you please explain what's the idea behind this? **satisfactory isn't doing a whole lot for the model** --> this is the reason I picked it as reference for the dummy variables. :) – wrangjangler Jan 24 '22 at 11:09
  • 1
    The large or small contingency for contemporaneous correlation in the error terms has to do with the time—a few years versus something like 20 years. However, I am not fond of these types of sometimes in, sometimes out model validation methods. However, with homoskedasticity and the *potential* presence of autocorrelated standard errors, the `vcovHC` function is a method to mitigate these threats to the validity. This function is in the `plm` package, but they are just borrowing it from the `sandwich` package. There are several scholarly references in help. Let me know if that doesn't help. – Kat Jan 24 '22 at 16:11