Removing correlation from my panel regression model.

Giles German

Join Date: Dec 2017
Posts: 84

Removing correlation from my panel regression model.

05 May 2018, 07:49

My model essentially predicts stock market returns across quarterly and annual investment periods against the items seen in a company annual report collected over the years. The results from one sector of my results is as follows: -

xtreg return QuickRatio TotalAssetsPerShare CashEndofYear EBITDA, fe

Fixed-effects (within) regression Number of obs = 5,969
Group variable: n_ticker Number of groups = 224

R-sq: Obs per group:
within = 0.0239 min = 1
between = 0.7945 avg = 26.6
overall = 0.0774 max = 64

F(4,5741) = 35.11
corr(u_i, Xb) = 0.4445 Prob > F = 0.0000

-------------------------------------------------------------------------------------
return | Coef. Std. Err. t P>|t| [95% Conf. Interval]
--------------------+----------------------------------------------------------------
QuickRatio | 192.9672 16.28389 11.85 0.000 161.0447 224.8898
TotalAssetsPerShare | .1166588 1.108847 0.11 0.916 -2.0571 2.290417
CashEndofYear | -2.37e-10 5.14e-09 -0.05 0.963 -1.03e-08 9.84e-09
EBITDA | -5.84e-10 1.05e-08 -0.06 0.955 -2.11e-08 1.99e-08
_cons | 1.126133 268.8208 0.00 0.997 -525.8641 528.1163
--------------------+----------------------------------------------------------------
sigma_u | 3364.255
sigma_e | 15284.022
rho | .04621196 (fraction of variance due to u_i)
-------------------------------------------------------------------------------------
F test that all u_i=0: F(223, 5741) = 1.34 Prob > F = 0.0006

As you can see this model suffers from correlation.

So to resolve this I can do one of the following...

Move to a random effects model...

xtreg return QuickRatio TotalAssetsPerShare CashEndofYear EBITDA, re

Random-effects GLS regression Number of obs = 5,969
Group variable: n_ticker Number of groups = 224

R-sq: Obs per group:
within = 0.0239 min = 1
between = 0.7983 avg = 26.6
overall = 0.0775 max = 64

Wald chi2(4) = 500.89
corr(u_i, X) = 0 (assumed) Prob > chi2 = 0.0000

-------------------------------------------------------------------------------------
return | Coef. Std. Err. z P>|z| [95% Conf. Interval]
--------------------+----------------------------------------------------------------
QuickRatio | 312.4005 13.9602 22.38 0.000 285.039 339.7619
TotalAssetsPerShare | -.0204513 .3766925 -0.05 0.957 -.758755 .7178524
CashEndofYear | 1.87e-11 2.75e-09 0.01 0.995 -5.37e-09 5.41e-09
EBITDA | 1.88e-10 7.54e-09 0.02 0.980 -1.46e-08 1.50e-08
_cons | -219.04 204.2272 -1.07 0.283 -619.3179 181.2379
--------------------+----------------------------------------------------------------
sigma_u | 0
sigma_e | 15284.022
rho | 0 (fraction of variance due to u_i)
-------------------------------------------------------------------------------------

or apply the XTGLS generalized least squares regression

How should I proceed?

An example of my data is as follows: -

Code:

* Example generated by -dataex-. To install: ssc install dataex
clear
input double(TotalDebttoEquity TotalLiabilities TotalRevenue WeightAvgSharesOutBasic WeightAvgSharesOutDiluted) str3(currency countrycode) str13 region str3 country str10 fye str1 sector str6 web float date str6 ticker double close float return
 .211503   4.252e+08   2.892e+08 128160000 135290000 "EUR" "FIN" "Europe"       "FIN" "2016-12-31" "1" "google" 614 "0FFY"                  .          .
 .221637   4.359e+08   3.388e+08 128680000 1.359e+08 "EUR" "FIN" "Europe"       "FIN" "2016-12-31" "1" "google" 617 "0FFY"                  .          .
 .429978   6.786e+08   3.463e+08 128970000 135770000 "EUR" "FIN" "Europe"       "FIN" "2016-12-31" "1" "google" 620 "0FFY"                  .          .
 .388767   6.900e+08   4.825e+08 129570000 135486000 "EUR" "FIN" "Europe"       "FIN" "2016-12-31" "1" "google" 623 "0FFY"                  .          .
 .163034   4.597e+08   3.843e+08 1.300e+08 136610000 "EUR" "FIN" "Europe"       "FIN" "2016-12-31" "1" "google" 626 "0FFY"                  .          .
 .417138   7.578e+08   4.138e+08 130550000 137070000 "EUR" "FIN" "Europe"       "FIN" "2016-12-31" "1" "google" 629 "0FFY"                  .          .
 .402861   8.056e+08   3.680e+08 1.310e+08 137290000 "EUR" "FIN" "Europe"       "FIN" "2016-12-31" "1" "google" 632 "0FFY"                  .          .
 .254089   5.828e+08   4.464e+08 131944000 137682000 "EUR" "FIN" "Europe"       "FIN" "2016-12-31" "1" "google" 635 "0FFY"                  .          .
       .           .  4.2802e+10  10503500         . "JPY" "JPN" "Asia Pacific" "JPN" "2017-03-31" "1" "quandl" 617 "1301"  1632.237548828125          0
       .           .  4.4961e+10         .         . "JPY" "JPN" "Asia Pacific" "JPN" "2017-03-31" "1" "quandl" 620 "1301"  1632.237548828125  -3.260867
       .           .  5.2222e+10         .         . "JPY" "JPN" "Asia Pacific" "JPN" "2017-03-31" "1" "quandl" 623 "1301"  1579.012451171875  13.949024
2.804256  6.7971e+10   4.190e+10         .         . "JPY" "JPN" "Asia Pacific" "JPN" "2017-03-31" "1" "quandl" 626 "1301"  1799.269287109375 -4.0404043
2.756379  6.7874e+10  4.3191e+10  10503400         . "JPY" "JPN" "Asia Pacific" "JPN" "2017-03-31" "1" "quandl" 629 "1301"  1726.571533203125  -8.947366
 2.79183  6.7166e+10   4.235e+10         .         . "JPY" "JPN" "Asia Pacific" "JPN" "2017-03-31" "1" "quandl" 632 "1301"    1572.0888671875  12.138725
2.793245  7.4302e+10  5.2252e+10         .         . "JPY" "JPN" "Asia Pacific" "JPN" "2017-03-31" "1" "quandl" 635 "1301"   1762.92041015625  11.158547
 2.29815  6.4807e+10  4.0253e+10         .         . "JPY" "JPN" "Asia Pacific" "JPN" "2017-03-31" "1" "quandl" 638 "1301"      1959.63671875  20.853075
2.373263  6.9169e+10  4.4858e+10  10503300         . "JPY" "JPN" "Asia Pacific" "JPN" "2017-03-31" "1" "quandl" 641 "1301"         2368.28125   11.37255
2.328558  6.8962e+10  4.9243e+10         .         . "JPY" "JPN" "Asia Pacific" "JPN" "2017-03-31" "1" "quandl" 644 "1301"     2637.615234375   -6.33803
2.600085  7.9622e+10  6.3055e+10         .         . "JPY" "JPN" "Asia Pacific" "JPN" "2017-03-31" "1" "quandl" 647 "1301"    2470.4423828125   .3831432
2.160753  6.4617e+10  4.5231e+10         .         . "JPY" "JPN" "Asia Pacific" "JPN" "2017-03-31" "1" "quandl" 650 "1301"   2479.90771484375          .
       .           .  2.0285e+11 508440000 542162000 "JPY" "JPN" "Asia Pacific" "JPN" "2017-03-31" "1" "quandl" 617 "1333"                  .          .
       .           . 1.99489e+11         .         . "JPY" "JPN" "Asia Pacific" "JPN" "2017-03-31" "1" "quandl" 620 "1333"                  .          .
       .           . 2.28943e+11         .         . "JPY" "JPN" "Asia Pacific" "JPN" "2017-03-31" "1" "quandl" 623 "1333"                  .          .
4.754813  4.0686e+11 1.84839e+11         .         . "JPY" "JPN" "Asia Pacific" "JPN" "2017-03-31" "1" "quandl" 626 "1333"                  .          .
4.425029 4.27607e+11 1.95009e+11 509621000 542133000 "JPY" "JPN" "Asia Pacific" "JPN" "2017-03-31" "1" "quandl" 629 "1333"                  .          .
4.734306 4.24418e+11 1.94387e+11         .         . "JPY" "JPN" "Asia Pacific" "JPN" "2017-03-31" "1" "quandl" 632 "1333"                  .          .
4.625941 4.46004e+11 2.32924e+11         .         . "JPY" "JPN" "Asia Pacific" "JPN" "2017-03-31" "1" "quandl" 635 "1333"                  .          .
3.995184 3.93363e+11 1.87469e+11         .         . "JPY" "JPN" "Asia Pacific" "JPN" "2017-03-31" "1" "quandl" 638 "1333"                  .          .
3.889017 4.07061e+11 2.02903e+11 494325000 526606000 "JPY" "JPN" "Asia Pacific" "JPN" "2017-03-31" "1" "quandl" 641 "1333"                  .          .
3.672455 3.98688e+11  2.0847e+11         .         . "JPY" "JPN" "Asia Pacific" "JPN" "2017-03-31" "1" "quandl" 644 "1333"                  .          .
3.937651 4.43243e+11 2.47149e+11         .         . "JPY" "JPN" "Asia Pacific" "JPN" "2017-03-31" "1" "quandl" 647 "1333"                  .          .
3.766789 3.98126e+11 1.93186e+11         .         . "JPY" "JPN" "Asia Pacific" "JPN" "2017-03-31" "1" "quandl" 650 "1333"                  .          .
       .           .  1.1751e+10  45009000         . "JPY" "JPN" "Asia Pacific" "JPN" "2017-05-31" "1" "quandl" 619 "1377" 1036.9000244140625 -3.2593796
       .           .   9.661e+09         .         . "JPY" "JPN" "Asia Pacific" "JPN" "2017-05-31" "1" "quandl" 622 "1377"     1003.103515625  4.1551223
       .           .  1.0298e+10         .         . "JPY" "JPN" "Asia Pacific" "JPN" "2017-05-31" "1" "quandl" 625 "1377"   1044.78369140625  -5.235488
 .025559  1.2091e+10  1.5278e+10         .         . "JPY" "JPN" "Asia Pacific" "JPN" "2017-05-31" "1" "quandl" 628 "1377"  990.0841674804688  -3.682721
 .025633  1.0699e+10  1.1158e+10  45008000         . "JPY" "JPN" "Asia Pacific" "JPN" "2017-05-31" "1" "quandl" 631 "1377"  953.6221313476563   5.772533
  .02124  1.0784e+10  1.0479e+10         .         . "JPY" "JPN" "Asia Pacific" "JPN" "2017-05-31" "1" "quandl" 634 "1377" 1008.6702880859375  14.686627
  .02709  1.2548e+10  1.2054e+10         .         . "JPY" "JPN" "Asia Pacific" "JPN" "2017-05-31" "1" "quandl" 637 "1377" 1156.8099365234375   8.795698
 .027469  1.2208e+10  1.6583e+10         .         . "JPY" "JPN" "Asia Pacific" "JPN" "2017-05-31" "1" "quandl" 640 "1377" 1258.5594482421875  -1.364669
 .044512  1.3747e+10  1.2263e+10  45007000         . "JPY" "JPN" "Asia Pacific" "JPN" "2017-05-31" "1" "quandl" 643 "1377"   1241.38427734375   3.450344
 .042956  1.4504e+10  1.2015e+10         .         . "JPY" "JPN" "Asia Pacific" "JPN" "2017-05-31" "1" "quandl" 646 "1377"   1284.21630859375 -.14970106
 .043916  1.5032e+10  1.3591e+10         .         . "JPY" "JPN" "Asia Pacific" "JPN" "2017-05-31" "1" "quandl" 649 "1377" 1282.2938232421875   3.142438
 .044003  1.5144e+10  1.6053e+10         .         . "JPY" "JPN" "Asia Pacific" "JPN" "2017-05-31" "1" "quandl" 652 "1377"  1322.589111328125          .
       .           .  1.0223e+10  33022000         . "JPY" "JPN" "Asia Pacific" "JPN" "2017-03-31" "1" "quandl" 617 "1379" 1461.9373779296875   2.526304
       .           .  1.1355e+10         .         . "JPY" "JPN" "Asia Pacific" "JPN" "2017-03-31" "1" "quandl" 620 "1379"  1498.870361328125  -6.451612
       .           .  1.6229e+10         .         . "JPY" "JPN" "Asia Pacific" "JPN" "2017-03-31" "1" "quandl" 623 "1379" 1402.1690673828125   6.720954
 .188781  1.9798e+10   1.369e+10         .         . "JPY" "JPN" "Asia Pacific" "JPN" "2017-03-31" "1" "quandl" 626 "1379"     1496.408203125  -8.605853
 .277535  2.2861e+10  1.0066e+10  33021000         . "JPY" "JPN" "Asia Pacific" "JPN" "2017-03-31" "1" "quandl" 629 "1379" 1367.6295166015625  4.3291807
 .285915  2.2445e+10   9.891e+09         .         . "JPY" "JPN" "Asia Pacific" "JPN" "2017-03-31" "1" "quandl" 632 "1379"  1426.836669921875   2.542373
 .251042  2.1134e+10  1.5789e+10         .         . "JPY" "JPN" "Asia Pacific" "JPN" "2017-03-31" "1" "quandl" 635 "1379" 1463.1121826171875   6.021317
 .260177   2.119e+10  1.2656e+10         .         . "JPY" "JPN" "Asia Pacific" "JPN" "2017-03-31" "1" "quandl" 638 "1379" 1551.2108154296875  -1.314285
 .339351   2.457e+10  1.0326e+10  31783000         . "JPY" "JPN" "Asia Pacific" "JPN" "2017-03-31" "1" "quandl" 641 "1379"  1530.823486328125  3.5900385
 .444865  3.1585e+10  1.2098e+10         .         . "JPY" "JPN" "Asia Pacific" "JPN" "2017-03-31" "1" "quandl" 644 "1379" 1585.7806396484375  11.017423
 .363587  3.0882e+10   1.949e+10         .         . "JPY" "JPN" "Asia Pacific" "JPN" "2017-03-31" "1" "quandl" 647 "1379" 1760.4927978515625  11.341138
 .327634  2.8392e+10  1.5111e+10         .         . "JPY" "JPN" "Asia Pacific" "JPN" "2017-03-31" "1" "quandl" 650 "1379" 1960.1527099609375          .
       .           .  5024569000  26966000         . "JPY" "JPN" "Asia Pacific" "JPN" "2016-08-31" "2" "google" 622 "1407"                  .          .
       .           .  5527268000         .         . "JPY" "JPN" "Asia Pacific" "JPN" "2016-08-31" "2" "google" 625 "1407"                  .          .
       .           .  6127102000         .         . "JPY" "JPN" "Asia Pacific" "JPN" "2016-08-31" "2" "google" 628 "1407"                  .          .
2.408544 14803851000  9084813000         .         . "JPY" "JPN" "Asia Pacific" "JPN" "2016-08-31" "2" "google" 631 "1407"                  .          .
 2.20876 17660325000 10353611000  27064000  27306000 "JPY" "JPN" "Asia Pacific" "JPN" "2016-08-31" "2" "google" 634 "1407"                  .          .
2.431635 23108080000 12661638000         .         . "JPY" "JPN" "Asia Pacific" "JPN" "2016-08-31" "2" "google" 637 "1407"                  .          .
2.140511 20952757000 11827837000         .         . "JPY" "JPN" "Asia Pacific" "JPN" "2016-08-31" "2" "google" 640 "1407"                  .          .
1.690398 24250675000 17902470000         .         . "JPY" "JPN" "Asia Pacific" "JPN" "2016-08-31" "2" "google" 643 "1407"                  .          .
2.299629 26596512000 11671770000  27209000         . "JPY" "JPN" "Asia Pacific" "JPN" "2016-08-31" "2" "google" 646 "1407"                  .          .
1.985486 28233740000 15931759000         .         . "JPY" "JPN" "Asia Pacific" "JPN" "2016-08-31" "2" "google" 649 "1407"                  .          .
1.654242 33072507000           .         .         . "JPY" "JPN" "Asia Pacific" "JPN" "2016-08-31" "2" "google" 655 "1407"                  .          .
       .           .  4.8036e+10  82357000         . "JPY" "JPN" "Asia Pacific" "JPN" "2017-03-31" "7" "quandl" 617 "1417"    530.88525390625 -1.2070903
       .           .  5.2997e+10         .         . "JPY" "JPN" "Asia Pacific" "JPN" "2017-03-31" "7" "quandl" 620 "1417"  524.4769897460938  -5.996755
       .           .  5.2352e+10         .         . "JPY" "JPN" "Asia Pacific" "JPN" "2017-03-31" "7" "quandl" 623 "1417"      493.025390625   5.761125
 .002241  5.3306e+10  8.2653e+10         .         . "JPY" "JPN" "Asia Pacific" "JPN" "2017-03-31" "7" "quandl" 626 "1417"    521.42919921875  -5.804313
 .001058  4.9911e+10  5.2263e+10  82406000         . "JPY" "JPN" "Asia Pacific" "JPN" "2017-03-31" "7" "quandl" 629 "1417"   491.163818359375   12.77026
 .000915  4.9201e+10  6.4239e+10         .         . "JPY" "JPN" "Asia Pacific" "JPN" "2017-03-31" "7" "quandl" 632 "1417"       553.88671875   24.28572
 .009868  5.1625e+10  6.2107e+10         .         . "JPY" "JPN" "Asia Pacific" "JPN" "2017-03-31" "7" "quandl" 635 "1417"   688.402099609375   25.12224
 .007806  6.9115e+10  9.2409e+10         .         . "JPY" "JPN" "Asia Pacific" "JPN" "2017-03-31" "7" "quandl" 638 "1417"  861.3441162109375  -8.152733
 .003703  5.1567e+10   5.678e+10  82406401         . "JPY" "JPN" "Asia Pacific" "JPN" "2017-03-31" "7" "quandl" 641 "1417"  791.1210327148438  -4.815114
 .001783   5.286e+10  6.2966e+10         .         . "JPY" "JPN" "Asia Pacific" "JPN" "2017-03-31" "7" "quandl" 644 "1417"  753.0276489257813   11.70848
 .001445  5.3296e+10  6.6072e+10         .         . "JPY" "JPN" "Asia Pacific" "JPN" "2017-03-31" "7" "quandl" 647 "1417"  841.1957397460938 -2.2130654
 .001119  6.5163e+10  9.1902e+10         .         . "JPY" "JPN" "Asia Pacific" "JPN" "2017-03-31" "7" "quandl" 650 "1417"  822.5795288085938          .
       .           .  2.5392e+10  83274000         . "JPY" "JPN" "Asia Pacific" "JPN" "2017-03-31" "8" "quandl" 617 "1515"   3256.10107421875 -10.528297
       .           .  2.5097e+10         .         . "JPY" "JPN" "Asia Pacific" "JPN" "2017-03-31" "8" "quandl" 620 "1515"       2913.2890625  -5.279501
       .           .  2.5516e+10         .         . "JPY" "JPN" "Asia Pacific" "JPN" "2017-03-31" "8" "quandl" 623 "1515"   2759.48193359375  31.312923
 .361393  6.3056e+10   2.550e+10         .         . "JPY" "JPN" "Asia Pacific" "JPN" "2017-03-31" "8" "quandl" 626 "1515"  3623.556396484375 -19.395466
 .301705  6.2903e+10  2.4928e+10  83266000         . "JPY" "JPN" "Asia Pacific" "JPN" "2017-03-31" "8" "quandl" 629 "1515"  2920.750732421875    1.69711
 .288148   6.148e+10  2.4375e+10         .         . "JPY" "JPN" "Asia Pacific" "JPN" "2017-03-31" "8" "quandl" 632 "1515"  2970.319091796875   18.01242
 .268035  6.1158e+10  2.7235e+10         .         . "JPY" "JPN" "Asia Pacific" "JPN" "2017-03-31" "8" "quandl" 635 "1515"  3505.345458984375  27.767963
 .325446  6.9265e+10  2.6302e+10         .         . "JPY" "JPN" "Asia Pacific" "JPN" "2017-03-31" "8" "quandl" 638 "1515"   4478.70849609375  -20.74689
 .298461  6.4578e+10  2.5948e+10  83259000         . "JPY" "JPN" "Asia Pacific" "JPN" "2017-03-31" "8" "quandl" 641 "1515"  3549.515869140625   44.32795
 .311652  6.9447e+10  2.7607e+10         .         . "JPY" "JPN" "Asia Pacific" "JPN" "2017-03-31" "8" "quandl" 644 "1515"     5122.943359375  -5.291977
 .368275  8.1591e+10  2.9339e+10         .         . "JPY" "JPN" "Asia Pacific" "JPN" "2017-03-31" "8" "quandl" 647 "1515"   4851.83837890625  -21.14192
 .390141  7.9733e+10  3.1423e+10         .         . "JPY" "JPN" "Asia Pacific" "JPN" "2017-03-31" "8" "quandl" 650 "1515"  3826.066650390625          .
       .           .  2.3203e+10  13865000         . "JPY" "JPN" "Asia Pacific" "JPN" "2017-03-31" "8" "quandl" 617 "1518"   1409.67919921875 -17.469873
       .           .  2.4814e+10         .         . "JPY" "JPN" "Asia Pacific" "JPN" "2017-03-31" "8" "quandl" 620 "1518" 1163.4100341796875   2.919705
       .           .  2.7467e+10         .         . "JPY" "JPN" "Asia Pacific" "JPN" "2017-03-31" "8" "quandl" 623 "1518"  1197.378173828125   26.98315
 .394109  1.9325e+10  2.2579e+10         .         . "JPY" "JPN" "Asia Pacific" "JPN" "2017-03-31" "8" "quandl" 626 "1518"  1520.468505859375 -26.285715
 .360768  2.0249e+10  2.2111e+10  13864900         . "JPY" "JPN" "Asia Pacific" "JPN" "2017-03-31" "8" "quandl" 629 "1518"  1120.802490234375  -14.72868
 .467954  2.2136e+10  2.3898e+10         .         . "JPY" "JPN" "Asia Pacific" "JPN" "2017-03-31" "8" "quandl" 632 "1518"  955.7230834960938   30.90909
 .454723  2.1818e+10   1.804e+10         .         . "JPY" "JPN" "Asia Pacific" "JPN" "2017-03-31" "8" "quandl" 635 "1518"   1251.12841796875  26.137693
 .380345  2.5151e+10   1.996e+10         .         . "JPY" "JPN" "Asia Pacific" "JPN" "2017-03-31" "8" "quandl" 638 "1518"      1578.14453125          .
       .           .  5.2462e+10  57152000         . "JPY" "JPN" "Asia Pacific" "JPN" "2017-03-31" "9" "quandl" 617 "1662"  3485.923583984375  -23.89642
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Phil Bromiley

Join Date: Apr 2014

Posts: 4348
#2

07 May 2018, 12:07

You'll increase your chances of a useful answer by following the FAQ on asking questions - provide Stata code in code delimiters, readable Stata output (fixed spacing fonts help), and sample data using dataex.

That the fixed effects correlate with the x's is not a problem. Indeed, the reason for fixed effects is the possibility that the panel effects correlate with the x's. If the panel effects do not correlate with the x's, then the random effects model is appropriate. With such large parameter differences between fe and re, a Hausman is probably going to reject that the random gives the same parameters as fe, and so favor fe.

Whether you should move to xtgls is a different issue. That depends a lot on number of observations within panels, and what you believe about the error covariance structure.
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Removing correlation from my panel regression model.

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