Pooled, fixed effect or random effect

[Erasmo Silva]

I have these regressions. I would like to know what is the better options.

The test xtoverid show that I can chose the randon effects, but I dont understand very much.

reg vm capgir lnat roe, vce (cluster cod)

Linear regression Number of obs = 749 F( 3, 184) = 42.83 Prob > F = 0.0000 R-squared = 0.4751 Root MSE = 3.9e+06 (Std. Err. adjusted for 185 clusters in cod) ------------------------------------------------------------------------------ | Robust vm | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- capgir | 1.685738 .3949142 4.27 0.000 .9065955 2.46488 lnat | 1996273 248645.1 8.03 0.000 1505711 2486835 roe | 15454.81 4703.384 3.29 0.001 6175.314 24734.31 _cons | -2.58e+07 3436346 -7.51 0.000 -3.26e+07 -1.90e+07 ------------------------------------------------------------------------------

xtreg capgir lnat roe, fe vce (cluster cod)

Fixed-effects (within) regression Number of obs = 749 Group variable: cod Number of groups = 185 R-sq: within = 0.0948 Obs per group: min = 1 between = 0.5134 avg = 4.0 overall = 0.4505 max = 5 F(3,184) = 13.15 corr(u_i, Xb) = 0.0115 Prob > F = 0.0000 (Std. Err. adjusted for 185 clusters in cod) ------------------------------------------------------------------------------ | Robust vm | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- capgir | .8108888 .4202563 1.93 0.055 -.018252 1.640029 lnat | 2214233 587288.4 3.77 0.000 1055548 3372919 roe | 2707.187 2423.25 1.12 0.265 -2073.742 7488.115 _cons | -2.87e+07 8491240 -3.38 0.001 -4.54e+07 -1.19e+07 -------------+---------------------------------------------------------------- sigma_u | 3939428.2 sigma_e | 1879713.3 rho | .8145473 (fraction of variance due to u_i) ------------------------------------------------------------------------------

xtreg capgir lnat roe, re vce (cluster cod)

Random-effects GLS regression Number of obs = 749 Group variable: cod Number of groups = 185 R-sq: within = 0.0927 Obs per group: min = 1 between = 0.5321 avg = 4.0 overall = 0.4617 max = 5 Wald chi2(3) = 124.72 corr(u_i, X) = 0 (assumed) Prob > chi2 = 0.0000 (Std. Err. adjusted for 185 clusters in cod) ------------------------------------------------------------------------------ | Robust vm | Coef. Std. Err. z P>|z| [95% Conf. Interval] -------------+---------------------------------------------------------------- capgir | 1.106154 .3818139 2.90 0.004 .357812 1.854495 lnat | 2143280 245806.2 8.72 0.000 1661509 2625051 roe | 4136.752 2380.596 1.74 0.082 -529.1303 8802.635 _cons | -2.75e+07 3377511 -8.13 0.000 -3.41e+07 -2.08e+07 -------------+---------------------------------------------------------------- sigma_u | 3579910.2 sigma_e | 1879713.3 rho | .7838825 (fraction of variance due to u_i) ------------------------------------------------------------------------------

xtoverid

Test of overidentifying restrictions: fixed vs random effects Cross-section time-series model: xtreg re robust cluster(cod) Sargan-Hansen statistic 7.262 Chi-sq(3) P-value = 0.0640

[John Riveros]

According to Rosales et al (2010) there's actually a path to establish which model is suitable for you (assuming you have a short panel with N bigger than T).

1) What are you trying to estimate? with what objective? if you're trying to stablish long-run dynamic relations you should give a try to the be estimation (it technically estimates a deviation of the variables from the mean in the long run, however it's not used that much in economics since the mean process ignores intra-effects heterogenity in the individuals simplifying the panel data base to a cross sectional one).

So let's suppose you want to take in consideration the inter-temporal effect on the variables. 2) Estimate xtreg regression with random effects and proceed to the xttest0 which it's the Breush Pagan test to check heterogenity. The null hypothesis H0: of the breush pagan test assumes that there are no evidence of constant effects in the error. and H1: Assumes that there are constant effects in the error, in this case you should proceed to estimate random / fixed effects regression. but if you accept the H0, then your model is better suit with a pooled OLS. (since there is no evidence of constant effects in the error).

Example: if xttest0 right after the xtreg ,re estimation gives you a pvalue of 0.004 you should reject the null hypothesis and proceed the Hausmann test. this one will help you to choose between random and fixed effects.

3) Hausman test: command is hausman . and the H0: no evidence of endogenity (proceed with random effects) and H1: Evidence of endogenity (proceed with fixed effects. p value of hausman test equivalent of 0.100 tells you that H0 may be true, so randoom effects it's the way.

To use Hausman test you need to store your regressions first, so estimate first the xtreg , fe and then type " estimates store fe " then estimate the random model, xtreg , re and after the regression type "estimates store re" and then type the test "hausman fe re" and this give you the result.

Rosales et al (2010, PP-378) Intermediate Econometrics Theory and Apllications. Taken from https://mpra.ub.uni-muenchen.de/3718...aper_37183.pdf book is in spanish by the way.

[Carlo Lazzaro]

Erasmo:
as an aside to John's helpful comments, the user-written command -xtoverid- checks whether the no-correlation assumption of both the group specific and idiosyncratic errors with the verctor of regressors (which is a theorethical requirement for -re- specififcation) holds, as in your case. If -xtoverid- rejects the null, you should switch to -fe-.
As you are already aware of, -hausman- does not allow non-default standard errors: that's why -xtoverid- comes in handy.

[Erasmo Silva]

Another detail, please. I need to exclude variables that not are significant in my final model? Or not?
For exemple: variable roe in Random-effects model show z=0.082. In this case can I exclude and process the model again?

[Carlo Lazzaro]

Erasmo:
you should maintain in the model all the predictors that give a fair and true view of the data generating process, regardless their statistical significance.

[Erasmo Silva]

Thank you!