Constant difference, why?

[Joonho Hwang]

Dear Stata users,

I am a novice stata user, so this could be a silly question.

I am trying to estimate the one-way fixed effect estimator using Grunfeld data. It includes investment data for 10 firms from 1935 to 1954.

First, I tried to estimate the estimator without using 'xtreg' as follows

'

* Use Grunfeld data
import excel using "Grunfeld.xlsx", firstrow
xtset firm year

***** Balanced Case *****
*** One-Way ***
* Fixed Effect Regression *
egen inv_mean1 = mean(inv), by(firm)
gen inv_dot = inv - inv_mean1

egen value_mean1 = mean(value), by(firm)
gen value_dot = value - value_mean1

egen capital_mean1 = mean(capital), by(firm)
gen capital_dot = capital - capital_mean1

reg inv_dot value_dot capital_dot, vce(cl firm)

The result is

. reg inv_dot value_dot capital_dot, vce(cl firm)

Linear regression                               Number of obs     =   
>      200
                                                F(2, 9)           =   
>    28.31
                                                Prob > F          =   
>   0.0001
                                                R-squared         =   
>   0.7668
                                                Root MSE          =   
>   51.549

                                  (Std. err. adjusted for 10 clusters 
> in firm)
----------------------------------------------------------------------
> --------
             |               Robust
     inv_dot | Coefficient  std. err.      t    P>|t|     [95% conf. i
> nterval]
-------------+--------------------------------------------------------
> --------
   value_dot |   .1101238   .0151945     7.25   0.000     .0757515    
> .1444961
 capital_dot |   .3100653   .0527518     5.88   0.000     .1907325    
> .4293981
       _cons |  -7.49e-08   1.74e-06    -0.04   0.967    -4.00e-06    
> 3.85e-06
----------------------------------------------------------------------

When I regress using 'xtreg', the result of constant term is different.

. xtreg inv value capital, fe vce(cl firm)

Fixed-effects (within) regression               Number of obs     =   
>      200
Group variable: firm                            Number of groups  =   
>       10

R-squared:                                      Obs per group:
     Within  = 0.7668                                         min =   
>       20
     Between = 0.8194                                         avg =   
>     20.0
     Overall = 0.8060                                         max =   
>       20

                                                F(2, 9)           =   
>    28.31
corr(u_i, Xb) = -0.1517                         Prob > F          =   
>   0.0001

                                  (Std. err. adjusted for 10 clusters 
> in firm)
----------------------------------------------------------------------
> --------
             |               Robust
         inv | Coefficient  std. err.      t    P>|t|     [95% conf. i
> nterval]
-------------+--------------------------------------------------------
> --------
       value |   .1101238   .0151945     7.25   0.000     .0757515    
> .1444961
     capital |   .3100653   .0527518     5.88   0.000     .1907325    
> .4293981
       _cons |  -58.74394   27.60286    -2.13   0.062     -121.186    
> 3.698079
-------------+--------------------------------------------------------
> --------
     sigma_u |  85.732502
     sigma_e |  52.767966
         rho |  .72525011   (fraction of variance due to u_i)
----------------------------------------------------------------------

I don't understand why only the constant term is different from the previous one. Can someone please explain about this?

[Andrew Musau]

You cannot separate the constant from the fixed effects, and therefore, the estimates of the constant terms are meaningless in FE models. See https://www.stata.com/support/faqs/s...effects-model/

[FernandoRios]

I agreed with Andrew Musau.
In models with high order fixed effects, the constant is not identified. However, you could "recover" it, by adding the "grand mean" to all your variables.
See the example below

webuse grunfeld, clear
ren company firm
ren invest inv
ren mvalue value
ren kstock capital


egen inv_mean1 = mean(inv), by(firm)
gen inv_dot = inv - inv_mean1
egen value_mean1 = mean(value), by(firm)
gen value_dot = value - value_mean1
egen capital_mean1 = mean(capital), by(firm)
gen capital_dot = capital - capital_mean1


reg inv_dot value_dot capital_dot, vce(cl firm)
// Adding grand mean
sum inv, meanonly
replace inv_dot = inv_dot + r(mean)
sum value, meanonly

replace value_dot = value_dot + r(mean)
sum capital, meanonly
replace capital_dot = capital_dot + r(mean)

reg inv_dot value_dot capital_dot, vce(cl firm)


. reg inv_dot value_dot capital_dot, vce(cl firm)

Linear regression                               Number of obs     =        200
                                                F(1, 9)           =          .
                                                Prob > F          =          .
                                                R-squared         =     0.7668
                                                Root MSE          =     51.549

                                  (Std. err. adjusted for 10 clusters in firm)
------------------------------------------------------------------------------
             |               Robust
     inv_dot | Coefficient  std. err.      t    P>|t|     [95% conf. interval]
-------------+----------------------------------------------------------------
   value_dot |   .1101238   .0151945     7.25   0.000     .0757515    .1444961
 capital_dot |   .3100653   .0527518     5.88   0.000     .1907325    .4293982
       _cons |  -58.74393   27.60286    -2.13   0.062    -121.1859    3.698081
------------------------------------------------------------------------------

[Joonho Hwang]

Dear Musau and FernandoRios, I appreciate it!