Panel data with fixed effects

[Jan Geurst]

Hi,

I'm running a regression with panel data and I want to use several fixed effects; firm specific, country specific, industry specific. Only when I run my model including firm specific fixed effects the r-squared increases sharply but my independent variables remain insignificant. When I include only country and industry specific effects the independent variables become significant but only the r-squared tends to be lower.

Can someone explain to me why the r-squared is high when I use firm specific effect. And would it be logical to only look at my model including country and industry fixed effects?

reghdfe bda announcement_eligible l_lnassets l_roa, absorb(indus incorp) vce(cluster c)
(converged in 9 iterations)

HDFE Linear regression                            Number of obs   =      3,944
Absorbing 2 HDFE groups                           F(   3,    492) =       5.04
Statistics robust to heteroskedasticity           Prob > F        =     0.0019
                                                  R-squared       =     0.4422
                                                  Adj R-squared   =     0.4317
                                                  Within R-sq.    =     0.2642
Number of clusters (c)       =        493         Root MSE        =     0.3304

                                             (Std. Err. adjusted for 493 clusters in c)
---------------------------------------------------------------------------------------
                      |               Robust
                  bda |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
----------------------+----------------------------------------------------------------
announcement_eligible |   .0797131   .0234105     3.41   0.001     .0337163      .12571
           l_lnassets |  -.0348046   .0159292    -2.18   0.029    -.0661023   -.0035069
                l_roa |  -3.438988   1.468924    -2.34   0.020    -6.325126   -.5528497
---------------------------------------------------------------------------------------

Absorbed degrees of freedom:
------------------------------------------------------------------------+
          Absorbed FE |  Num. Coefs.  =   Categories  -   Redundant     |
----------------------+-------------------------------------------------|
                indus |           56              56              0     |
               incorp |           15              16              1     |
------------------------------------------------------------------------+

reghdfe bda announcement_eligible l_lnassets l_roa, absorb(c indus incorp) vce(cluster c)
(converged in 3 iterations)

HDFE Linear regression                            Number of obs   =      3,944
Absorbing 3 HDFE groups                           F(   3,    492) =       0.93
Statistics robust to heteroskedasticity           Prob > F        =     0.4281
                                                  R-squared       =     0.8968
                                                  Adj R-squared   =     0.8796
                                                  Within R-sq.    =     0.0389
Number of clusters (c)       =        493         Root MSE        =     0.1521

                                             (Std. Err. adjusted for 493 clusters in c)
---------------------------------------------------------------------------------------
                      |               Robust
                  bda |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
----------------------+----------------------------------------------------------------
announcement_eligible |    .004275   .0071644     0.60   0.551    -.0098017    .0183516
           l_lnassets |  -.0143254   .0292794    -0.49   0.625    -.0718535    .0432027
                l_roa |  -.8736434   .5363002    -1.63   0.104    -1.927365    .1800779
---------------------------------------------------------------------------------------

Absorbed degrees of freedom:
------------------------------------------------------------------------+
          Absorbed FE |  Num. Coefs.  =   Categories  -   Redundant     |
----------------------+-------------------------------------------------|
                    c |            0             493            493 *   |
                indus |           55              56              1     |
               incorp |           15              16              1     |
------------------------------------------------------------------------+
* = fixed effect nested within cluster; treated as redundant for DoF computation

.

[Amin Sofla]

The discussion is being continued. See the link for the original question: https://www.statalist.org/forums/for...-effects-model

Can someone explain to me why the r-squared is high when I use firm-specific effect.

In your case, I speculate that the problem arises because most likely your fixed effects are strongly correlated with each other (near multicollinearity). To understand the effect of near multicollinearity on the adjusted R-squared please see below (see here for the source):

* Clear the old data from memory
clear
* Set the number of observations to generate to 1000
set obs 1000
set seed 1234
* Generate a positive explanatory variable.
gen x = abs(rnormal())
* Imagine we are interested in the coefficient on x.
* Next, we create correlated control variables
gen z1 = x^2 + rnormal()*10
gen z2 = x^1.75 + rnormal()*10
gen y  = 0.001*x + 0.03*z1 + 0.02*z2 + 0.01*rnormal()
// Now, we run a regression without controls
reg y x
* adjusted R-squared often is quite low.
* Next, we add controls
reg y x z1 z2
* Please see the sharp increase in the adjusted R-squared.

In addition, in your results, the adj R-squared is high; however that of ‘within’ is low in the second output. It is likely that Stata drops the correlated fixed effect. To check this, try

xtreg y x i.ind_id i.cnt_id, fe vce(robust)

Where, ind_id = industry id and cnt_id = country id
In addition, you should investigate the ‘Absorbed degrees of freedom’ in your results. You did not share a sample of your data so I have created the following demonstration data-set (Note: It is often quite challenging to mimic the real panel data. Therefore, I stick to a very naïve example.)

clear all
set obs 500
set seed 1234
gen firm_id = _n
gen ind_id2 = runiformint(1,10)+ (firm_id/100)
gen ind_id3 =round(ind_id2,1)
egen ind_id = group(ind_id3)
drop ind_id2 ind_id3
gen cnt_id2 = runiformint(1,10) + (firm_id/100)
gen cnt_id3 =round(cnt_id2,1)
egen cnt_id = group(cnt_id3)
drop cnt_id2 cnt_id3
gen y= (firm_id^3+ rnormal())/1000
gen x =  y*0.05 + rnormal()*1000
gen z1= firm_id^0.2+ rnormal()
expand 20
bysort firm_id: gen year=_n+1998
sort firm_id year
by firm_id year: replace x = x + runiformint(-x+0.02,x)
by firm_id year: replace y = y + runiformint(-y+0.02,y)
by firm_id year: replace z1 = z1 + runiformint(-z1+0.05,z1)
drop if y==.
drop if x==.
xtset firm_id year
order year firm_id y x ind_id cnt_id
label variable firm_id "Firm id"
label variable ind_id "Industry id"
label variable cnt_id "Country id"
label variable y "Dependent Variable"
label variable x "Independent Variable"
label variable z1 "A Control Variable"
label variable year "year"
label data "Demonstration Datasets for the Panel Data"
ssc install univar
save  “demodata.dta"

We check the descriptive statistics:

use “demodata.dta", clear
tab year
univar year y x firm_id ind_id cnt_id
pwcorr y x z1 firm_id ind_id cnt_id

Next, we run the regressions:

reghdfe y x z1 , absorb(ind_id cnt_id) vce(cluster firm_id)
reghdfe y x z1, absorb(firm_id ind_id cnt_id)
xtreg y x z1 i.ind_id i.cnt_id, fe vce(robust)

Check (1) the changes in the coefficient of x (2) the change in R-squared and Within R-squared, the absorbed degrees of freedom, and etc.

And would it be logical to only look at my model including country and industry fixed effects?

Theoretically speaking, I do not think so. The reason is that firm-specific fixed effect might be one of the main drivers of your dependent variable. Instead, you might want to drop the industry-specific fixed effect. Alternatively, you might want to skim over the prior research in your field and follow their design.