after having found heteroscedasticity and autocorrelation in my panel data, I account for it with -xtreg ..., fe/re vce (cluster Company_ID)-. Because of this, I am unable to execute the conventional -hausman- command.
My regression is as follows: ROA = c.Var1_c##i.Industry Var2 Var3 Var4 Var5 i.Year, with Var1 being compensation to the CEO, Var2-5 control variables and Industry being a dummy variable (1 to 10 for different industries). I winsorized at (5 95). Var1_c is the mean-centered version of Var1, which itself is the squareroot of compensation to the CEO. This was done to account for multicollinearity arising from the interaction term.
I have come across two ways to determine whether to use RE or FE: 1) the -xtoverid- command and 2) Variable Addition Test (VAT) as discussed by J. Wooldridge.
1) -xtoverid-
Code:
. gen Interaction = Var1_c*Industry . xi: xtreg ROA c.Var1_c i.Industry Interaction Var2 Var3 Var4 Var5 i.Year, re vce(cluster Company_ID) . xtoverid Test of overidentifying restrictions: fixed vs random effects Cross-section time-series model: xtreg re robust cluster(Company_ID) Sargan-Hansen statistic 26.143 Chi-sq(11) P-value = 0.0062
2) Variable Addition Test
Code:
. egen Var1bar = mean(Var1_c), by(Company_ID) . xtreg ROA c.Var1_c Var1bar i.Industry c.Var1_c#i.Industry Var2 Var3 Var4 Var5 i.Year, re vce(cluster Company_ID) Random-effects GLS regression Number of obs = 466 Group variable: Company_ID Number of groups = 99 R-sq: Obs per group: within = 0.2107 min = 1 between = 0.3837 avg = 4.7 overall = 0.4470 max = 6 Wald chi2(29) = 312.45 corr(u_i, X) = 0 (assumed) Prob > chi2 = 0.0000 (Std. Err. adjusted for 99 clusters in Company_ID) ----------------------------------------------------------------------------------------- | Robust ROA_new | Coef. Std. Err. z P>|z| [95% Conf. Interval] ------------------------+---------------------------------------------------------------- Var1_c | .0004388 .0002735 1.60 0.109 -.0000973 .0009749 Var1bar | .0001705 .000198 0.86 0.389 -.0002176 .0005585 | ... | Year | 2015 | .0009689 .0020876 0.46 0.643 -.0031227 .0050605 2016 | .0001361 .0021731 0.06 0.950 -.004123 .0043952 2017 | .0041183 .0030348 1.36 0.175 -.0018297 .0100663 2018 | -.0000602 .0035568 -0.02 0.986 -.0070314 .006911 2019 | -.0037212 .0041598 -0.89 0.371 -.0118744 .0044319 | _cons | .1900278 .0648387 2.93 0.003 .0629462 .3171093 ------------------------+---------------------------------------------------------------- sigma_u | .03361633 sigma_e | .01488897 rho | .83600278 (fraction of variance due to u_i) -----------------------------------------------------------------------------------------
What method should I use? Did I execute both commands/methods correctly?
Thank you,
Pietro
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