Same coefficients from Fixed Effect, Random Effect and OLS estimation

[Aslihan Tutuncu]

I have a panel data on nonperforming loans from 1990q1 till 2014q4 with 30 banks, 100 units of observation per bank. I would like to estimate the impact of real gdp growth, unemployment, exchange rate, house price index, and equity market index on nonperforming loans (dependent variable in my regression) with fixed effect, random effect and OLS estimation. By using the commands of regress, xtreg ..,fe, xtreg... re, i get almost identical coefficients for fixed effect,random effect and OLS estimation for each independent variable, and even the t statistics are the same across the models with the exception of constant's t statistics (t stat for constant is -85 in random effect, -112 for fixed effect), and the corr(u_i, Xb) = 0.0000 in the fixed effect model, which I did not expect. When I apply the Hausman test, I get (V_b-V_B is not positive definite). I have also problems with R squares. In fixed effect, I do not have any numerical value for R square between groups, and R squares for within and between are 0 in random effect model. Unfortunately I cannot establish another model other than these three. I would really appreciate if you could give some hints where the problem might be.

[Clyde Schechter]

Well, I think you should post the exact commands you used and the exact complete results you got from Stata. Do that by setting up a code block in the Forum post (see #12 in FAQ if you don't know how to do this), and copy directly from Stata's Results window or your log file and paste into the code block. Please don't retype anything.

That said, while your results seem a bit unusual, they may or may not be an actual problem. The -fe- and -re- regression coefficients are usually rather similar to each other. And if there is very little intra-panel correlation in the data those will also be similar to those obtained with OLS. It is somewhat surprising to see corr(u_i, Xb) = 0 in the fixed effects model: are you sure that wasn't the -re- model: this result is expected (in fact, assumed) in random effects models. But it can happen in fixed effects as well; it's just uncommon. The R squares within and between being both 0 is distinctly unusual. Anyway, if we can see the information requested above, we may be able to get some specific sense of what is going on.

[Aslihan Tutuncu]

regress npllog realgdpgrowth unemployment spread eurusd housepricechange djuschange

xtreg npllog realgdpgrowth unemployment spread eurusd housepricechange djuschange, fe

xtreg npllog realgdpgrowth unemployment spread eurusd housepricechange djuschange, re

Dear Prof. Schechter,

Thank you very much for your reply. I post my code above hopefully in a correct way. Just to be sure, I also post my log pdf file with the results. Unfortunately, both fe and re show corr(u_i, Xb) = 0, and i know that re should show 0 correlation. Actually, I am afraid that my data might not be suitable for these models. I have Nonperforming loans from 30 US Banks from 1990q1 till 2014q4, and I have only macro data such as gdp growth and unemployment, and no explanatory variables which are bank specific such as leverage of the each bank etc. So all explanatory variables repeat itself from 1990 till 2014 in my model. I would really appreciate any suggestion to get over this problem.

[Carlo Lazzaro]

Aslihan:
your codes look fine.
The problem lies within your dataset, as you guessed:

So all explanatory variables repeat itself from 1990 till 2014 in my model

[Aslihan Tutuncu]

Dear Carlo,

Thank you very much for your reply. Could you maybe advise a solution for the data structure? I need to establish a model based on these nonperforming loans and macro variables. For example, my explanatory variables are the same for each 1990q1 with a different nonperforming loan ratio which is bank specific. I created the model with average NPL of these 30 banks, and i need to compare this aggregate model with panel data model. To make it more clear how my data looks like, i created a small table below.

Bank	Time	Nonperforming Loans (Y)	Real GDP Growth (X1)	UNEMPLOYMENT(X2)
Bank1	1990q1	2,5%	4,5%	5,3%
Bank1	1990q2	3%	1,6%	5,7%
...	...	...	...	...
Bank3	1990q1	2%	4,5%	5,3%
...	...	...	...	...
Bank30	1990q1	1,5%	4,5%	5,3%
Bank30	1990q2	0,9%	1,6%	5,7%

Kind regards,

Aslihan Tutuncu