Inconsistency between correlation analysis and regression results

[suyi mcmaster]

Hi Statalist,

I have the panel data (state-year) and run a correlations analysis between my y and x (pwcorr y x), which shows that they are negatively correlated （significant at 1% level). However, when I run the univariate fixed effect regression (xtreg y x or xtreg y x, fe), the coefficient is significantly positive. I find it confusing because I expect them to have at least the same direction.
Besides, I get the significantly negative coefficient when I run the pooled regression (reg y x, r). Does that mean I should choose the pooled regression instead of the xtreg? Many thanks!

Best regards,
Suyi Liu

[Jackson Monroe]

There are unobserved confounders at the group level that the correlation does not account for or correct. You probably should not choose the pooled regression because it will lead to omitted variables bias.

[Carlo Lazzaro]

Suyi:
as an aside to Jackson's helpful reply, you should first check whether your dataset shows evidence of a panel-wise effect.
In addition, sharing what you typed and what Stata gave you back (as per FAQ) will increase your chances of getting more helpful replies. Thanks.

[suyi mcmaster]

I really appreciate your help! Is there any correlation command in Stata that can show the unobserved confounders at the group level? or some specific code for conducting correlation analysis for panel data?

[Carlo Lazzaro]

Suyi:
what's the aim of running correlation before regressions (no matter if cross-sectional or panel datasets)?
In addition, running a set of univariate regressions does not help either, since you hopefully have more than one predictor and the goal of regression is to investigate the contributoon of each predictor to variation of the regressand when adjusted for the other ones.

[suyi mcmaster]

Hi Carlo,

Thanks for your guidance!
Since I am writing a empirical paper, the correlation analysis is a must-have in the descriptive statistics, and then I should run the regression. Usually the regression results are like showing specific correlation (that's why I expect them to at least have the same sign). Here I attach the screenshot what Stata gives me, many thanks!

[Carlo Lazzaro]

Suyi:
the issue here seems to rest on a misspecification of -xtreg,re-.
It is really difficult to believe that the right-hand side of your regression equation contains one predictor only, not to say that this specification can give a fair and true view of the data generating process you're investigating.
If your regression were correcly specified, you should retrieve that one unit increase in education (whatever it maìy mean) increases crime (episodes? rates? something else measured on a continuous scale?): hence, jails should be overcrowded of PhD holders! .
As Jackson wisely warned you about, there are other predictors that you did not make explicit in the right-hand side of your regression and that you should definitely plug in.
As an aside, I 've never heard that correlation is a must-have statistic if you move to regression thereafter.

[Clyde Schechter]

Carlo Lazzaro

As an aside, I 've never heard that correlation is a must-have statistic if you move to regression thereafter.

In the United States, although in my opinion it is completely ridiculous, a correlation table is a standard requirement in doctoral dissertations in the field of psychology. Many psychology journals also insist on it. It makes no sense, but that's the way it is.

[Carlo Lazzaro]

Thanks Clyde, very interesting.
I've often wonder why even high standing scientific journals require the abovementioned correlation table and/or a set of univariate regressions!