I would like to ask the community to share their thoughts on using levels instead of changes relating to variables while invoking fixed effects. Thus is it correct to run regression
1. (Debtt- Debtt-1) /Total assets as a dependent variable with firm fixed effects and year dummies
OR
2. Debt/Total assets as a dependent variable with firm fixed effects and year dummies
Let me give a sample dataset and the results
Code:
* Example generated by -dataex-. For more info, type help dataex
clear
input long code int year float(debt totass nsales cashban)
11 2011 1206 2191.1 2544.6 112
11 2012 1586.8 2784.9 3014 91.4
11 2013 1648.4 3057.6 3121.9 63.9
11 2014 1767.2 3425 3278.5 92
11 2015 1665.4 3498.9 3565.2 184
11 2016 1634.2 3532.9 3573.3 93.9
11 2017 1522.9 3900.3 3907.1 122
11 2018 1345.3 4068 4258.2 105.6
11 2019 1244.6 4383.7 4793.7 113
289 2011 897 1658.2 2084.9 87.9
289 2012 970.3 1746.5 2552.1 78.5
289 2013 781.3 1522 1767.9 47.9
289 2014 655.5 1349.4 1613.9 41.1
363 2011 5522.6 11598.8 2268.4 1251.2
363 2012 5084 10745.7 2518.6 1160.4
363 2013 6046.2 11366 1672.5 412.7
363 2014 5591.8 11196.6 1065.4 583.8
363 2015 5108.9 9910.3 1088.5 629
363 2016 5289.9 10009.8 1169.9 239.3
363 2017 5551.8 9490.9 995.3 262.8
363 2018 4247.8 9618.1 3711 202.9
363 2019 6453.3 9361.4 1254.6 172.9
414 2016 219.4 483 1089.3 98.1
414 2017 2.5 389.4 1423.1 60.1
414 2018 1.8 322.7 886.4 60.6
415 2018 . 1981.9 619.6 73.7
415 2019 . 1874.7 604.9 358.9
771 2013 352.6 758 572.5 39.7
771 2014 515.2 990.1 788 52.2
771 2015 567.1 1228.3 1077.3 110.8
771 2016 984.8 1799.1 1324.9 106.3
771 2017 1176.8 2155.4 1439.3 105.1
771 2018 1175.2 2373.5 1403.8 101.7
771 2019 1218.1 2622.1 1762.4 194.1
783 2011 341.8 1723.5 1283.4 208.4
783 2012 380.1 1816.7 1553.5 200.9
783 2013 436.7 2208.3 1782.4 133.6
783 2014 283.9 2182.6 2070.7 126.2
783 2015 189.5 2183.8 2025.3 108.8
783 2016 72.6 2179 2089.5 93.1
783 2017 55.2 2148.1 2007.5 138.3
783 2018 31.3 2149.7 2083.1 317.9
783 2019 2 2042.7 2433.6 184
1120 2011 211.5 12945.2 11594.1 1530.6
1120 2012 480 14937.2 14159.4 1501.1
1120 2013 1609.6 18524.6 17505.2 2807.8
1120 2014 1206.2 22357.9 20788.3 2199.2
1120 2015 986.2 25511.6 21819.1 1897.6
1120 2016 1837.8 27984 20970.3 1241.3
1120 2017 1402.1 32081 22398 2477.9
1120 2018 1234.3 35691.3 24426.1 2650
1120 2019 1282.7 40503.9 30719.8 2163.2
2248 2017 413.9 2791.9 2486.1 15.8
2248 2018 470.2 3008.9 2720.9 20.3
2717 2011 10862.9 27241.1 13842.9 3385.1
2717 2012 14223.7 26358.5 18895.6 3988.4
2717 2013 16455.5 31555.2 19001.2 3741.9
2717 2014 14241.2 27709.6 22572.6 3499.6
2717 2015 15050.4 31702.5 24580.6 4452.9
2717 2016 12312.8 39717.1 28932.3 3419.1
2717 2017 11369.2 43337.1 30106.6 2926.1
2717 2018 34008.7 153908 46070 5862.7
2717 2019 28086.1 146343 61632.7 1828.5
2842 2011 164.6 659.7 1116.1 64.9
2842 2012 335 871.9 1454.5 92.4
2842 2013 391.1 1079.5 1749.7 93.5
2842 2014 443.1 1172.1 1666.1 83.3
2842 2015 430.2 1178 1637.2 100
2842 2016 172.7 901.6 625.8 131.2
2842 2017 7.5 617.9 813.4 71.1
2842 2018 79.5 693.2 825.4 17.5
2842 2019 147.1 864.7 890.7 104.5
3335 2011 558.7 1399.2 1459 26.5
3335 2012 387.5 1962.2 2481.1 78.4
3335 2013 355 2284 2677.8 90.8
3335 2014 54.6 2388.1 2907 155.9
3335 2015 68 2382.3 2542.6 150.7
3335 2016 97.5 2505.9 2689.4 112
3335 2017 153.2 2772.8 3098.2 126.5
3335 2018 360.7 3321.9 3268.2 90.4
3335 2019 814.2 3918.8 3377.2 117.3
3990 2011 2674.8 5235.1 5010.6 52.7
3990 2015 4479 10051.1 10942.7 35.8
3990 2016 4834.1 11028.9 11348.9 48.3
3990 2017 4831.4 11910.4 11951.7 41.8
3990 2018 5498.9 13901.6 12436.3 42.7
3990 2019 5099 14559.1 15609.4 55.6
3998 2011 5285.3 13991 14523.6 128.7
3998 2012 6279.5 16611.5 16722.8 105.6
3998 2013 8505.1 21759.9 20937.7 124.2
3998 2014 10467.7 26701.3 26324.7 148.6
3998 2015 12022.5 29385.6 29079.4 337.1
3998 2016 12917.6 29668.1 30067.2 289.9
3998 2017 15644.5 35009.8 31612.9 285
3998 2018 20831.7 43914.5 38053.5 321
3998 2019 24012.3 58579.4 41676.3 5839.8
4024 2018 3793.4 9195.7 8260.4 230.9
4024 2019 4342.2 9639 7508.9 175.4
4030 2016 94.3 525.5 1101.6 40
4030 2017 145 834 1531.7 66.4
4030 2018 39.3 1030.9 1734.4 159.7
4030 2019 81.5 1072.7 2060.1 89.4
4253 2011 133738 161118 33452.6 5950.6
4253 2012 138563 174367 31612 1343.9
4253 2013 139615 183003 36719.5 1491
4253 2014 148554 202496 39342.6 1479.6
4253 2015 143481 212612 40407 1177.2
4253 2016 147260 206305 33339.2 1342.1
4253 2017 148265 187277 17543.6 946.1
4253 2018 157117 169377 14650.1 842.4
4253 2019 174717 136854 8475.1 728.1
4671 2016 9609.1 26413 16036.4 144.9
4671 2017 8012.2 24671.6 16264.5 149.4
4671 2018 5935.1 23826.2 17381.7 245
4671 2019 3374.4 23116.3 20411.2 190.1
4709 2012 22836.5 34277.7 27394 230.3
4709 2013 22398.1 34175.5 33370.4 335.7
4709 2014 18622.7 33484.3 38657.1 250.1
4709 2015 25801.4 47409.1 37859.7 170.1
4709 2016 35026.6 69299.2 36712.3 819.4
4709 2017 28494.1 64290.2 46216 1326.4
4709 2018 27978.1 62933.2 45653.4 1665.5
4709 2019 24357.5 61972.9 52437.2 257.2
5003 2011 324.8 2974.9 3945.8 289.3
5003 2012 1008.1 3460.2 4823.4 117.1
5003 2013 1083.7 3606.5 3951.8 268
5003 2014 1557 3799.9 4194.3 199.5
5003 2015 1984.7 4703.8 4840.3 472.5
5003 2016 2127.8 3678.1 5092.3 421.8
5003 2017 2565.1 4151.5 4922.5 562.1
5003 2018 1824.3 3037.2 4833.9 220.3
5003 2019 1778 3909.9 5450.5 214.7
5284 2011 3.1 170.2 17.6 6.4
5284 2012 1.7 173.2 25.3 9.3
5284 2013 2.1 173.7 38.4 9.5
5284 2014 .5 182.2 47.5 12.6
5284 2015 . 193.9 59.4 9.6
5284 2016 .5 204.3 80.9 8.5
5284 2017 . 225.2 84.7 7.5
5284 2018 . 240.6 87.4 7.4
5284 2019 3.5 263.6 80.8 11.2
5574 2011 211.6 607.9 551.6 12.7
5574 2012 234.5 619.7 616.5 20
5574 2013 310.8 791.8 784.8 21.9
5574 2014 391.7 981.3 1040.6 24.1
5574 2015 729.5 1480.9 1270.9 66.9
5574 2016 672.5 2003.6 1731 284.5
5574 2017 800.8 2409.2 1809.6 222.3
5574 2018 916.2 2680.4 1963.9 174.4
5574 2019 968.8 2994.9 2515.6 139.9
5747 2011 333750 641331 263300 28502.5
5747 2012 692325 1100000 391570 69707.3
5747 2013 693318 1100000 463023 72388.5
5747 2014 719799 1200000 548869 38739.4
5747 2015 835706 1300000 644144 37189
5747 2016 191694 417704 339139 15395
5747 2017 208457 477452 365142 17150.9
5747 2018 176367 566000 358946 18842.5
5747 2019 116317 431150 402893 17092.8
5757 2011 245027 352616 20864.1 9643.2
5757 2012 386003 513941 39424 36669.3
5757 2013 417955 547011 66616.1 18724
5757 2014 441502 622419 153261 9413.3
5757 2015 448396 640669 186828 8916.4
5757 2016 528778 831851 251477 8938.3
5757 2017 524844 790838 225611 6659.3
5757 2018 530426 752180 203099 9223.1
5757 2019 469799 745419 238978 10201.6
5838 2017 14.8 85.5 4.9 .7
5838 2018 11 90.5 11 .3
5838 2019 31.7 106.7 5.2 .1
6584 2014 . 1205.5 1406.3 252.1
6584 2015 . 1297.2 1392.8 322.8
6584 2016 8.6 1339.4 1449.6 297.8
6584 2017 22.4 1316.2 1465.5 249.6
6584 2018 21.8 1314.1 1520.4 266.6
6584 2019 30.1 1390.1 1856.4 259.9
6585 2016 23.2 62.5 56.5 5.3
6585 2017 25.7 102.5 67 5.1
6585 2018 5 62.4 65.8 6.1
6585 2019 5.9 87.6 72.8 6
6819 2011 651.6 1542.5 1165.9 148.8
6819 2013 1843.7 3978.3 2200.5 38
6819 2014 1685.4 4063 2385.1 27.6
6819 2015 1150.3 4171.8 2219.5 43.6
6819 2016 1013.5 4520.2 2922.3 264.5
6819 2017 540.5 5830.4 3291.8 80.1
6819 2018 667.7 7337.6 3872.1 614.4
6819 2019 350.3 8126.5 4150.4 234.1
6923 2013 96.8 2672.8 3644.3 53.6
6923 2014 185.8 3149.8 3710.7 222.9
6923 2015 4.9 3183.9 3884.1 204.6
6923 2016 2 3738.2 4081 151.7
6923 2017 356.4 4190.4 4425.2 236.1
6923 2018 813.2 4674.4 4660.1 209.5
6923 2019 649.9 4717.3 5147.1 334.5
7068 2011 1243.5 5513.5 18085.8 867.9
7068 2012 21094.2 29597.2 44615.7 19120.2
7068 2013 3318.7 10096.2 39777.8 2045.5
7068 2014 2409.7 8915.7 50282.5 725.6
7068 2015 2180.9 9413.9 39137.8 1054
7068 2016 1883.6 9043.7 22110 966.9
7068 2017 2864.6 20362.5 39256.9 622.8
7068 2018 3040.4 22147 47885.5 1619.9
7068 2019 2387.7 24476 56133.4 4129.2
7077 2011 105.7 1017.4 3142.6 25.3
7077 2012 14.9 847.4 2807.7 49.6
7077 2013 80.3 954.6 2747.5 26.4
7077 2014 90.7 1008.8 2748.5 28.5
7077 2015 238.4 1210 2318.2 41.5
7077 2016 403.3 1271.6 3552.8 34.7
7077 2017 453.9 2450.4 3558.5 34.5
7077 2018 636.1 2610.3 3329.3 43.7
7633 2013 702.4 7079.9 40132.2 735.6
7633 2014 1236.7 7965.5 17340.6 886.8
7633 2015 1821.7 10231.9 31982 1742.9
7633 2016 2367 10310.3 39315 812.2
7633 2017 5926.9 11085 49355.1 774.3
7633 2018 3995.1 8068 52971.2 538.7
7633 2019 5762.8 9847.4 42622.9 812.3
8183 2011 . 2814.7 7145.9 447.6
8183 2012 . 2876.1 6996.3 410
8183 2013 . 3340.8 7821.5 109.7
8183 2014 150 3852.8 7583.5 63.4
8183 2015 258.6 4344.8 7520.6 96.5
8183 2016 956.5 5174.6 7759 66.6
8183 2017 176.2 4259 7978.6 43.6
8183 2018 . 4500.5 8417.7 308.1
8183 2019 . 4845.3 8640 48.7
8312 2011 2043 11582.5 17543 1504.8
8312 2012 2483.1 11745.8 14469 988.5
8312 2013 2745 10794.9 14357.2 926.4
8312 2014 2388.5 10539.6 9605 632.2
8312 2015 1734.5 10455.5 10598.8 903.1
8312 2016 1427.3 11599.5 12494.5 967.2
8312 2017 901.6 12402.2 14261.6 1385.8
8312 2018 298 12635.4 16461.4 1369.9
8312 2019 611.1 14981.8 17542.5 2194.3
8523 2014 15.7 651.8 1399.4 23.8
8523 2015 13.6 532.5 1643.4 16.4
8523 2016 .3 584 953.9 25.3
8523 2017 7.6 628.7 986.3 4.4
8523 2018 13.4 752.9 1097.8 18.8
8523 2019 7.9 1101.5 2019.1 37.1
8628 2017 126.7 506.4 288.2 130.4
8628 2018 151.7 994.9 371.2 18.9
8628 2019 110.3 971.2 483.5 27
8893 2011 1906.4 5301.2 4980.9 147.7
8893 2012 1996.4 6505.3 6759.1 125.8
8893 2013 1248.4 7189 9306.1 529.8
8893 2014 1304.9 9494.7 12074 683.1
8893 2015 723.8 11480.5 14732.5 1411.6
8893 2016 929.4 14995.5 17335.9 582.3
8893 2017 68.1 18646.2 19827.2 713
8893 2018 41.2 24753.9 21248 969.8
8893 2019 542.5 29736.7 20547.6 1030.5
9395 2011 436.4 3785.6 12075.9 336.2
9395 2012 1708.5 5481.3 18549.4 546.5
9395 2013 2452 6863.9 28296 719.5
9395 2014 4005.9 8752.2 40847.8 1170.1
9395 2015 3355 9207.7 25245 1146
9395 2016 2554.3 6745.3 19143.4 1204.3
9395 2017 3367.7 10558.5 15403.9 1233.9
9395 2018 3974 10083.6 7128.1 1054.1
9395 2019 2632 8689.3 11717.8 401.8
9505 2016 106.7 701.3 862.2 88.4
9505 2017 58.7 960.8 1105.6 161
9505 2018 261.4 1330.6 1581.4 152.8
9505 2019 242.9 1485.3 916.8 157.1
9793 2011 1051.3 4935.8 1309.6 106
9793 2012 1109.9 5309.8 2727.7 133.7
9793 2013 890 5479.2 2517.9 141
9793 2014 1314.3 5808.6 2380.5 153.3
9793 2015 1378.4 6491.8 3547.9 201.6
9793 2016 1037.7 6734.6 4456.3 250.3
9793 2017 1499.4 7658.8 4831.7 101.3
9793 2018 2701.3 9512.3 6131.6 297.5
9793 2019 3105.6 10152.3 5284 234.3
10714 2011 148.2 457.1 204.8 14.6
10714 2012 165.5 448 186.9 15.1
10714 2013 120.9 379.4 214.3 12.7
10714 2014 75.4 339.8 261.2 15.3
10714 2015 66.2 340.2 263.2 19.9
10714 2016 92.8 332.3 266.7 23.9
10714 2017 94.5 531.2 256.6 23.5
10714 2018 78.4 668.8 462.5 26
10714 2019 73.6 629.5 647.3 61.7
10735 2018 246 435.9 986 2.2
10735 2019 293 615.4 1164.6 3.4
10867 2018 27.5 292.9 6.8 1.3
10867 2019 27.5 246.1 . .5
10884 2015 13059.2 53349.1 36822.7 12423.5
10884 2016 6575 55523.7 48859.3 10230.9
10884 2017 6594.6 66935.5 56496.2 7985.6
10884 2018 9975.6 80082.1 63553.5 6597.8
10884 2019 9440.7 86161.3 105061 6981.9
10903 2011 1200.8 2754.6 2351.6 14.7
10903 2012 1235.1 3022.7 2876.9 112.6
10903 2013 1460.1 3709 3644 155.2
10903 2014 1506.5 4377.5 4454.6 240
end
*SETTING PANEL
xtset code year
*GENERATING VARIABLES
gen deb_ta=debt/totass
gen del_deb_ta=d.debt/totass
gen nsal_ta=nsales/totass
gen cash_ta=cashban/totass
*RUNNING REGRESSION WITH deb_ta as Dep var
xtreg deb_ta nsal_ta cash_ta i.year, fe vce(robust)
Fixed-effects (within) regression Number of obs = 287
Group variable: code Number of groups = 44
R-squared: Obs per group:
Within = 0.1126 min = 1
Between = 0.0080 avg = 6.5
Overall = 0.0049 max = 9
F(10,43) = 1.62
corr(u_i, Xb) = -0.1167 Prob > F = 0.1342
(Std. err. adjusted for 44 clusters in code)
------------------------------------------------------------------------------
| Robust
deb_ta | Coefficient std. err. t P>|t| [95% conf. interval]
-------------+----------------------------------------------------------------
nsal_ta | -.0079448 .0258297 -0.31 0.760 -.0600354 .0441458
cash_ta | .4298472 .2545228 1.69 0.098 -.0834469 .9431413
|
year |
2012 | .0326785 .0187599 1.74 0.089 -.0051544 .0705114
2013 | .0134876 .0261732 0.52 0.609 -.0392957 .066271
2014 | -.003149 .0319634 -0.10 0.922 -.0676093 .0613113
2015 | -.0206513 .032175 -0.64 0.524 -.0855383 .0442358
2016 | -.0172078 .0358528 -0.48 0.634 -.0895118 .0550962
2017 | -.0488981 .0409587 -1.19 0.239 -.1314992 .0337031
2018 | -.0535187 .0435004 -1.23 0.225 -.1412456 .0342081
2019 | -.0506827 .0443039 -1.14 0.259 -.1400301 .0386647
|
_cons | .3030418 .0539048 5.62 0.000 .1943324 .4117512
-------------+----------------------------------------------------------------
sigma_u | .19621982
sigma_e | .10471008
rho | .77835062 (fraction of variance due to u_i)
------------------------------------------------------------------------------
xtreg del_deb_ta nsal_ta cash_ta i.year, fe vce(robust)
Fixed-effects (within) regression Number of obs = 239
Group variable: code Number of groups = 43
R-squared: Obs per group:
Within = 0.1039 min = 1
Between = 0.0271 avg = 5.6
Overall = 0.0490 max = 8
F(9,42) = 5.24
corr(u_i, Xb) = -0.5162 Prob > F = 0.0001
(Std. err. adjusted for 43 clusters in code)
------------------------------------------------------------------------------
| Robust
del_deb_ta | Coefficient std. err. t P>|t| [95% conf. interval]
-------------+----------------------------------------------------------------
nsal_ta | -.0813427 .047161 -1.72 0.092 -.1765174 .013832
cash_ta | .327098 .2078102 1.57 0.123 -.0922799 .7464759
|
year |
2013 | -.1362373 .084005 -1.62 0.112 -.3057662 .0332916
2014 | -.0803605 .0236895 -3.39 0.002 -.1281678 -.0325532
2015 | -.0893466 .0299759 -2.98 0.005 -.1498403 -.0288529
2016 | -.1536604 .0773283 -1.99 0.053 -.3097153 .0023945
2017 | -.1061033 .0367209 -2.89 0.006 -.1802092 -.0319975
2018 | -.1031997 .0368414 -2.80 0.008 -.1775486 -.0288508
2019 | -.0932153 .0397741 -2.34 0.024 -.1734826 -.0129479
|
_cons | .1700746 .0688796 2.47 0.018 .0310699 .3090793
-------------+----------------------------------------------------------------
sigma_u | .0868477
sigma_e | .18768043
rho | .17636537 (fraction of variance due to u_i)
------------------------------------------------------------------------------Kindly note that when I use Levels, even the model fit is poor (Low F-Stats), but when I use change in debt over assets, we have a better Model fit and the variable of interest (nsal_t) seems to significant preditor.
Other than from the perspective of interpretation, I would like ask,
IF WE HAVE FIXED EFFECTS (BOTH ENTITY AND YEAR), SHOULD WE USE LEVEL OR CHANGE IN LEVEL AS THE DEP VARIABLE?
REFERENCES
"First, including fixed effects can exacerbate measurement problems (Griliches and Mairesse, 1995). Second, if the dependent variable is a first differenced variable, such as investment or the change in corporate cash balances, and if the fixed effect is related to the level of the dependent variable, then the fixed effect has already been differenced out of the regression, and using a fixedeffects specification reduces efficiency. In practice, for example, fixed effects rarely tend to make important qualitative differences on the coefficients in investment regressions (Erickson and Whited, 2012), because investment is (roughly) the first difference of the capital stock. However, fixed effects do make important differences in the estimated coefficients in leverage 77 regressions (Lemmon, Roberts, and Zender, 2008), because leverage is a level and not a change" - Endogeneity in Empirical Corporate Finance (Michael R. Roberts and Toni M. Whited)
"Note that in our experimental design, a fixed-effects specification is not appropriate. By construction, all of the sample firms exhibit a large shift in leverage. Labeling such a shift as a “fixed effect” would mask much of the information about leverage dynamics that we seek to uncover"- Debt Financing and Financial Flexibility Evidence from Proactive Leverage Increases (David J. Denis and Stephen B. McKeon)
"Note that in our experimental design, a fixed-effects specification is not appropriate. By construction, all of the sample firms exhibit a large shift in leverage. Labeling such a shift as a “fixed effect” would mask much of the information about leverage dynamics that we seek to uncover"- Debt Financing and Financial Flexibility Evidence from Proactive Leverage Increases (David J. Denis and Stephen B. McKeon)
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