A question about high values of corr(u_i, Xb)

[Bruno Hoepers]

Hi all. I have estimated several fixed effects models using Brazilian state-level panel data I want to use for a paper. In all models' specifications corr(u_i, Xb) presents high values (i.e., .90 and higher).

Question: Do such high values for corr(u_i, Xb) deserve any concern and clarification? Are they worrying in any way that justify the use of other panel data models?

Below follows an example of the FE's output with high corr(u_i, Xb).

Thanks.

xtreg perc_incumb_party_votos i.pres_pt i.pres_bolsonaro i_unempl_rate i.pres_pt#c.i_unempl_rate i.pres_bolsonaro#c.i_unempl_rate perc_fam_benef_wf c.i_unempl_rate#c.perc_fam_benef_wf i.pres_pt#c.i_unempl_rate#c.perc_fam_benef_wf i.pres_bolsonaro#c.i_unempl_rate#c.perc_fam_benef_wf i_perc_dom_with_tv ln_i_mean_yrs_schooling i_perc_pop_preta ln_i_hdi ln_pop_total i.year, fe vce(robust)

Fixed-effects (within) regression Number of obs = 162
Group variable: ibge_uf_code Number of groups = 27

R-squared: Obs per group:
Within = 0.8901 min = 6
Between = 0.0104 avg = 6.0
Overall = 0.1108 max = 6

F(17,26) = 859.69
corr(u_i, Xb) = -0.9210 Prob > F = 0.0000

[Joro Kolev]

No, I do not think that high correlation between the unobserved "fixed effect" and the regressors is worrisome. This is what the fixed effects model is supposed to deal with.

[Carlo Lazzaro]

Bruno:
in addition, Within Rsq = 0.8901 is a very encouraging result (provided that your model is correctly specified).

[Bruno Hoepers]

Thank you Joro and Carlo for the comments. Best.