serial autocorrelation in panel data

[Huda Amin]

Hi STATA community

I have a panel data for period 2012-2020, with #obs 1988 and #groups 223, I run the xtreg, fe and the results as shown below, after that I run xtserial and I have serial autocorrelation issue! How can I deal with this problem please?

xtreg WROAI FEMproportion ln_FS1 LEV_PERCENT BS BIND CEO_DUA firmage i.year i.INDUSTRY*, fe

note: 2020.year omitted because of collinearity
note: 1.INDUSTRY1 omitted because of collinearity
note: 1.INDUSTRY2 omitted because of collinearity
note: 1.INDUSTRY3 omitted because of collinearity
note: 1.INDUSTRY4 omitted because of collinearity
note: 1.INDUSTRY5 omitted because of collinearity
note: 1.INDUSTRY6 omitted because of collinearity
note: 1.INDUSTRY7 omitted because of collinearity
note: 1.INDUSTRY8 omitted because of collinearity
note: 1.INDUSTRY9 omitted because of collinearity
note: 1.INDUSTRY10 omitted because of collinearity

Number of obs = 1,988
Group variable: id Number of groups = 223

R-sq: Obs per group:
within = 0.1469 min = 6
between = 0.0006 avg = 8.9
overall = 0.0001 max = 9

F(14,1751) = 21.54
corr(u_i, Xb) = -0.9574 Prob > F = 0.0000




WROAI Coef. Std. Err. t P>t [95% Conf. Interval]

FEMproportion 2.219943 2.045081 1.09 0.278 -1.791114 6.231
ln_FS1 .9539394 .5602033 1.70 0.089 -.1447984 2.052677
LEV_PERCENT -.1649817 .0163612 -10.08 0.000 -.1970713 -.1328922
BS .3332249 .1401214 2.38 0.018 .0584019 .6080478
BIND -.8364824 2.397737 -0.35 0.727 -5.539211 3.866246
CEO_DUA -10.46369 4.086443 -2.56 0.011 -18.47852 -2.448872
firmage -.7101108 .0989218 -7.18 0.000 -.9041281 -.5160936

year
2013 -.0385384 .5529471 -0.07 0.944 -1.123044 1.045968
2014 1.556931 .5258847 2.96 0.003 .5255028 2.588359
2015 1.800889 .508461 3.54 0.000 .8036348 2.798144
2016 1.858767 .5045516 3.68 0.000 .8691804 2.848354
2017 3.16199 .5125383 6.17 0.000 2.156739 4.167242
2018 3.066505 .5300157 5.79 0.000 2.026975 4.106035
2019 2.695152 .5482957 4.92 0.000 1.619768 3.770535
2020 0 (omitted)

1.INDUSTRY1 0 (omitted)
1.INDUSTRY2 0 (omitted)
1.INDUSTRY3 0 (omitted)
1.INDUSTRY4 0 (omitted)
1.INDUSTRY5 0 (omitted)
1.INDUSTRY6 0 (omitted)
1.INDUSTRY7 0 (omitted)
1.INDUSTRY8 0 (omitted)
1.INDUSTRY9 0 (omitted)
1.INDUSTRY10 0 (omitted)
_cons 25.41833 7.117782 3.57 0.000 11.45809 39.37858

sigma_u 25.773241
sigma_e 6.0717567
rho .94741855 (fraction of variance due to u_i)

F test that all u_i=0: F(222, 1751) = 11.62 Prob > F = 0.0000


xtserial WROAI FEMproportion ln_FS1 LEV_PERCENT BS BIND CEO_DUA firmage

Wooldridge test for autocorrelation in panel data
H0: no first order autocorrelation
F( 1, 222) = 12.314
Prob > F = 0.0005


How can I deal with this problem? I tried robust and lagging 1, 2 and the same results. How many lagging can I generate to fix this issue?

[Carlo Lazzaro]

Huda:
1) if -i.industry- id a time-invariant variable and you go -fe-, no wonder that -i.industry- has been omitted due to perfect collinearity with the fixed effect;
2) just invoke standard-robust standard errors (via -robust- or -vce(cluster panelid)- options) to deal with both heteroskedasticity and/or autocorrelation. No need to repeat -xtserial- after that.

[Huda Amin]

Hi Carlo,

Thanks for your reply. I have run it with robust/cluster and the same result. How can I make sure there is no auto correlation after doing that.

My supervisor commented why the ind.variable has a significant correlation with all other variables? (no multicollinearity and VIF below 2). Can I use lagging to solve this issue and how ?



| WROAI WTQI FEMpro~n ln_FS1 LEV_PE~T BS BIND
-------------+---------------------------------------------------------------
WROAI | 1.0000
WTQI | 0.4647* 1.0000
FEMproport~n | 0.0370 0.0442* 1.0000
ln_FS1 | -0.1518* -0.3822* 0.3252* 1.0000
LEV_PERCENT | -0.1806* -0.1425* 0.0812* 0.2941* 1.0000
BS | -0.0127 -0.0778* 0.2050* 0.6362* 0.1780* 1.0000
BIND | -0.0896* -0.1216* 0.2651* 0.3787* 0.1921* 0.1858* 1.0000
CEO_DUA | -0.0222 0.0177 -0.0224 0.0144 0.0048 0.0316 0.0473*
firmage | 0.0044 -0.1093* 0.1196* 0.1680* 0.0038 0.1105* 0.0578*

| CEO_DUA firmage
-------------+------------------
CEO_DUA | 1.0000
firmage | -0.0444* 1.0000

[Carlo Lazzaro]

Huda:
1) with such a large sample, a significant correlation is expected;
2) after going cluster-robust standard error, there's no gain in reopeating -xtserial-, as the results will be the same (as the non-default standarda error has no bearing on residuals distribution);
3) that said, I'd more concerned with the low within R-sq. In this respect, an investigation of the functional form of the regressand is recommended.