Collinearity Dropping Everything in Fixed Effects Regression

[Jose Williams]

Hi,

I am running individual-level fixed on panel data. The panel is perfectly balanced. My main outcome is a dummy variable. I have a gender dummy and year categorical variable and the interaction between the two.

The codes that I have tried:

. xtreg emp_in_lockdown male time male##i.time, fe
note: male omitted because of collinearity
note: time omitted because of collinearity
note: 1.male omitted because of collinearity
note: 4.time omitted because of collinearity
note: 1.male#4.time omitted because of collinearity

Fixed-effects (within) regression               Number of obs     =     50,439
Group variable: id                              Number of groups  =     50,439

R-sq:                                           Obs per group:
     within  =      .                                         min =          1
     between =      .                                         avg =        1.0
     overall =      .                                         max =          1

                                                F(0,0)            =       0.00
corr(u_i, Xb)  =      .                         Prob > F          =          .

------------------------------------------------------------------------------
emp_in_loc~n |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
        male |          0  (omitted)
        time |          0  (omitted)
      1.male |          0  (omitted)
      4.time |          0  (omitted)
             |
   male#time |
        1 4  |          0  (omitted)
             |
       _cons |   .2222288          .        .       .            .           .
-------------+----------------------------------------------------------------
     sigma_u |  .41574825
     sigma_e |          .
         rho |          .   (fraction of variance due to u_i)
------------------------------------------------------------------------------
F test that all u_i=0: F(50438, 0) = .                       Prob > F =      .

The output from reghdfe:

. reghdfe emp_in_lockdown male time male##i.time, absorb(id)
(dropped 50439 singleton observations)
insufficient observations

I think so the sample strength is not large enough to support any regression or time may be collinear with fixed effects. Example of data using dataex:

* Example generated by -dataex-. To install: ssc install dataex
clear
input float id byte(emp_in_lockdown male) float time
 1 . 1 1
 1 . 1 2
 1 . 1 3
 1 0 . 4
 2 . 0 1
 2 . 0 2
 2 . 0 3
 2 0 . 4
 3 . 0 1
 3 . 0 2
 3 . 0 3
 3 0 . 4
 4 . 0 1
 4 . 0 2
 4 . 0 3
 4 0 . 4
 5 . 0 1
 5 . 0 2
 5 . 0 3
 5 0 . 4
 6 . 1 1
 6 . 1 2
 6 . 1 3
 6 0 1 4
 7 . 0 1
 7 . 0 2
 7 . 0 3
 7 1 0 4
 8 . 0 1
 8 . 0 2
 8 . 0 3
 8 0 0 4
 9 . . 1
 9 . . 2
 9 . . 3
 9 0 . 4
10 . . 1
10 . . 2
10 . . 3
10 0 . 4
11 . 1 1
11 . 1 2
11 . 1 3
11 0 . 4
12 . 0 1
12 . 0 2
12 . 0 3
12 0 . 4
13 . 1 1
13 . 1 2
13 . 1 3
13 0 . 4
14 . 0 1
14 . 0 2
14 . 0 3
14 0 . 4
15 . 1 1
15 . 1 2
15 . 1 3
15 0 . 4
16 . 1 1
16 . 1 2
16 . 1 3
16 0 . 4
17 . 0 1
17 . 0 2
17 . 0 3
17 0 . 4
18 . 1 1
18 . 1 2
18 . 1 3
18 0 . 4
19 . 1 1
19 . 1 2
19 . 1 3
19 0 . 4
20 . 1 1
20 . 1 2
20 . 1 3
20 0 1 4
21 . 0 1
21 . 0 2
21 . 0 3
21 0 0 4
22 . 1 1
22 . 1 2
22 . 1 3
22 0 1 4
23 . 1 1
23 . 1 2
23 . 1 3
23 0 1 4
24 . 0 1
24 . 0 2
24 . 0 3
24 0 0 4
28 . 1 1
28 . 1 2
28 . 1 3
28 0 . 4
end

[Carlo Lazzaro]

Jose:
1) your regressand is a two-level categorical variable: so why going -xtreg- (linear probability model?);
2) your dataset is full of missing values, that save only one observation per panel: hence, any panel data regression (that needs at least two waves of data) fails.

[Jose Williams]

Jose:
1) your regressand is a two-level categorical variable: so why going -xtreg- (linear probability model?);
2) your dataset is full of missing values, that save only one observation per panel: hence, any panel data regression (that needs at least two waves of data) fails.

Dear Carlo Lazzaro ,

I tried using the simple reg. Again everything other than gender dummy gets omitted. I tried areg but did not work. I tried to use household fixed effects but I encountered the same problems.

. reg emp_in_lockdown male time male##i.time
note: time omitted because of collinearity
note: 1.male omitted because of collinearity
note: 4.time omitted because of collinearity
note: 1.male#4.time omitted because of collinearity

      Source |       SS           df       MS      Number of obs   =    50,439
-------------+----------------------------------   F(1, 50437)     =   9452.45
       Model |  1375.98189         1  1375.98189   Prob > F        =    0.0000
    Residual |  7342.05514    50,437  .145568831   R-squared       =    0.1578
-------------+----------------------------------   Adj R-squared   =    0.1578
       Total |  8718.03703    50,438  .172846604   Root MSE        =    .38153

------------------------------------------------------------------------------
emp_in_loc~n |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
        male |   .3311417    .003406    97.22   0.000     .3244659    .3378175
        time |          0  (omitted)
      1.male |          0  (omitted)
      4.time |          0  (omitted)
             |
   male#time |
        1 4  |          0  (omitted)
             |
       _cons |      .0451    .002491    18.10   0.000     .0402175    .0499824
------------------------------------------------------------------------------

[Carlo Lazzaro]

Jose:
missing values (that imply casewise deletion) strike back.
If you do not manage this issue, you cannot move forward.