Correlated variables in fixed-effects model

[Anusha Singh]

Hi,
I am working with a fixed-effects estimation on a panel data set for 15 countries.

Suppose the following is the 'central' model: xtreg depvar var1 var2, fe

I then introduce a control variable: xtreg depvar var1 var2 var3, fe

Inclusion of the control variable var3 makes one of my previous explanatory variables, say, var2 insignificant. Therefore I suspect that the possibility that var2 and var3 might be correlated such that the control variable draws the effect of the original explanatory variable. To test the correlation, I run: bysort Country: correl var2 var3

The country-wise correlation coefficients range from 0.7 to 0.85. I am wondering whether this is sufficient evidence to indeed explain why var2 becomes an insignficant predictor upon the inclusion of var3. If not ,advice to run any other tests as a check for correlation to explain loss of significance of var2 would be very helpful. Thank you.

[Carlo Lazzaro]

Anusha:
you may want to take a look at -estat vce, corr-, too.

[Anusha Singh]

Anusha:
you may want to take a look at -estat vce, corr-, too.

Hi Carlo, thanks for replying.

Are you asking me to use the -estat vce, corr- command after -regress var2 var3-? Because when I do that the matrix I get includes the correlation between only the constant term and var3 which does not tell me anything... How can I see the matrix of corrleation for both var2 and var3?

[Carlo Lazzaro]

Anusha:
it may well be that -var2- was omitted due to collinearity (however, if that were the case, Stata should have informed you with a note).
I do hope that the following two toy-example can be useful:
1) after -regress-:

. sysuse auto.dta
(1978 Automobile Data)

. regress price mpg i.foreign

      Source |       SS           df       MS      Number of obs   =        74
-------------+----------------------------------   F(2, 71)        =     14.07
       Model |   180261702         2  90130850.8   Prob > F        =    0.0000
    Residual |   454803695        71  6405685.84   R-squared       =    0.2838
-------------+----------------------------------   Adj R-squared   =    0.2637
       Total |   635065396        73  8699525.97   Root MSE        =    2530.9

------------------------------------------------------------------------------
       price |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
         mpg |  -294.1955   55.69172    -5.28   0.000    -405.2417   -183.1494
             |
     foreign |
    Foreign  |   1767.292    700.158     2.52   0.014     371.2169    3163.368
       _cons |   11905.42   1158.634    10.28   0.000     9595.164    14215.67
------------------------------------------------------------------------------

. estat vce, corr

Correlation matrix of coefficients of regress model

             |                  1.         
        e(V) |      mpg   foreign     _cons
-------------+------------------------------
         mpg |   1.0000                    
   1.foreign |  -0.3934    1.0000          
       _cons |  -0.9530    0.2231    1.0000

2) after -xtreg, fe-:

. use "http://www.stata-press.com/data/r14/nlswork.dta", clear
(National Longitudinal Survey.  Young Women 14-26 years of age in 1968)

. xtreg ln_wage age tenure , fe

Fixed-effects (within) regression               Number of obs     =     28,101
Group variable: idcode                          Number of groups  =      4,699

R-sq:                                           Obs per group:
     within  = 0.1296                                         min =          1
     between = 0.1916                                         avg =        6.0
     overall = 0.1456                                         max =         15

                                                F(2,23400)        =    1742.76
corr(u_i, Xb)  = 0.1302                         Prob > F          =     0.0000

------------------------------------------------------------------------------
     ln_wage |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
         age |   .0121949   .0004131    29.52   0.000     .0113852    .0130045
      tenure |   .0211313   .0008015    26.37   0.000     .0195604    .0227023
       _cons |   1.256467   .0109792   114.44   0.000     1.234947    1.277987
-------------+----------------------------------------------------------------
     sigma_u |  .39034493
     sigma_e |  .29808194
         rho |  .63165531   (fraction of variance due to u_i)
------------------------------------------------------------------------------
F test that all u_i=0: F(4698, 23400) = 8.02                 Prob > F = 0.0000

. estat vce, corr

Correlation matrix of coefficients of xtreg model

        e(V) |      age    tenure     _cons
-------------+------------------------------
         age |   1.0000                    
      tenure |  -0.5515    1.0000          
       _cons |  -0.9683    0.3753    1.0000