I am using an individual fixed effect method in a panel data. I look whether the working hours changed differently between men and women following the 2008 financial crisis.
Here is a simple model in Stata and R
xtreg workhours c.age i.sex i.education i.sex##i.crisis, fe # Stata
plm(workhours ~ age + sex + education + sex*crisis, index=c("id", "year"), data=df) # R
In the model above sex and education are time fixed and hence constant over time. The crisis variable is a dummy variable (0= before 2008, 1= post 2008).
The interaction of interest sex*crisis tells me whether the gap in working hours has increased or decreased following the financial crisis. The findings show that the gap increases following the crisis, however, I am interested to see whether this increase is driven by a decrease in working hours for men or by an increase in working hours for women or whether it is driven by both cases. Thus, I would like to run the average marginal effects to see graphically the association between both variables. As there is no easy way to do it in R, I run it in Stata. After running margins crisis##sex, I get the following text: . (not estimable).
I tried to see whether it is possible to run it using a random effect model instead of FE. Both in R and Stata I can run the average marginal effects for the random effect models with no problem. This leaves me with the conclusion that the error I get for average marginal effects using FE is related to the FE itself. Maybe my question is stupid, but could someone explain to me if I am missing something here? Why the FE does not give me average marginal effects? I don't want to get into the discussion of why it is better to use RE over FE or vice versa. I am interested in understanding why this issue could occur if I use FE.
EDIT 20/10/2021:
Below you find the Stata output using the code suggested by Dimitri. Education and sex are dropped out in FE model because they are time-invariant. Then I include the average marginal effects using Random Effects and Dimitriy's code.
xtset id year
Panel variable: id (unbalanced)
Time variable: year, 2005 to 2015, but with gaps
Delta: 1 unit
. xtreg workhours c.age i.sex i.education i.sex##i.crisis, fe
note: 2.sex omitted because of collinearity.
note: 2.education omitted because of collinearity.
note: 3.education omitted because of collinearity.
Fixed-effects (within) regression Number of obs = 472,757
Group variable: id Number of groups = 196,088
R-squared: Obs per group:
Within = 0.0014 min = 1
Between = 0.0020 avg = 2.4
Overall = 0.0011 max = 8
F(3,276666) = 128.29
corr(u_i, Xb) = -0.2447 Prob > F = 0.0000
----------------------------------------------------------------------------------
workhours | Coefficient Std. err. t P>|t| [95% conf. interval]
-----------------+----------------------------------------------------------------
age | -.1713355 .0103908 -16.49 0.000 -.1917011 -.1509698
|
sex |
Female | 0 (omitted)
|
education |
Upper-secondary | 0 (omitted)
Tertiary | 0 (omitted)
|
1.crisis | -.1401835 .050655 -2.77 0.006 -.239466 -.040901
|
sex#crisis |
Female#1 | .2906291 .0690111 4.21 0.000 .1553693 .425889
|
_cons | 46.62693 .4306217 108.28 0.000 45.78292 47.47093
-----------------+----------------------------------------------------------------
sigma_u | 9.7706582
sigma_e | 5.5553808
rho | .75569746 (fraction of variance due to u_i)
----------------------------------------------------------------------------------
F test that all u_i=0: F(196087, 276666) = 5.87 Prob > F = 0.0000
.
end of do-file
. do "/var/folders/wb/2v3hpch94wd3_r_6q8ssng300000gp/T//SD86690.000000"
. margins sex, dydx(crisis)
Average marginal effects Number of obs = 472,757
Model VCE: Conventional
Expression: Linear prediction, predict()
dy/dx wrt: 1.crisis
------------------------------------------------------------------------------
| Delta-method
| dy/dx std. err. z P>|z| [95% conf. interval]
-------------+----------------------------------------------------------------
0.crisis | (base outcome)
-------------+----------------------------------------------------------------
1.crisis |
sex |
Male | . (not estimable)
Female | . (not estimable)
------------------------------------------------------------------------------
Note: dy/dx for factor levels is the discrete change from the base level.
Random effects models using Dimitriy's code:
xtset id year
Panel variable: id (unbalanced)
Time variable: year, 2005 to 2015, but with gaps
Delta: 1 unit
. xtreg workhours c.age i.sex i.education i.sex##i.crisis, re
Random-effects GLS regression Number of obs = 472,757
Group variable: id Number of groups = 196,088
R-squared: Obs per group:
Within = 0.0003 min = 1
Between = 0.0885 avg = 2.4
Overall = 0.0764 max = 8
Wald chi2(6) = 19144.98
corr(u_i, X) = 0 (assumed) Prob > chi2 = 0.0000
----------------------------------------------------------------------------------
workhours | Coefficient Std. err. z P>|z| [95% conf. interval]
-----------------+----------------------------------------------------------------
age | .0209332 .0017377 12.05 0.000 .0175275 .0243389
|
sex |
Female | -5.770971 .0491049 -117.52 0.000 -5.867215 -5.674727
|
education |
Upper-secondary | .0708841 .0486 1.46 0.145 -.0243701 .1661382
Tertiary | -.2056841 .0543011 -3.79 0.000 -.3121124 -.0992559
|
1.crisis | -.7906896 .0369781 -21.38 0.000 -.8631654 -.7182138
|
sex#crisis |
Female#1 | .5714118 .0544573 10.49 0.000 .4646775 .6781461
|
_cons | 41.22829 .0851835 483.99 0.000 41.06133 41.39525
-----------------+----------------------------------------------------------------
sigma_u | 8.0439189
sigma_e | 5.5553808
rho | .6770612 (fraction of variance due to u_i)
----------------------------------------------------------------------------------
. margins sex, dydx(crisis)
Average marginal effects Number of obs = 472,757
Model VCE: Conventional
Expression: Linear prediction, predict()
dy/dx wrt: 1.crisis
------------------------------------------------------------------------------
| Delta-method
| dy/dx std. err. z P>|z| [95% conf. interval]
-------------+----------------------------------------------------------------
0.crisis | (base outcome)
-------------+----------------------------------------------------------------
1.crisis |
sex |
Male | -.7906896 .0369781 -21.38 0.000 -.8631654 -.7182138
Female | -.2192778 .0402583 -5.45 0.000 -.2981825 -.1403731
------------------------------------------------------------------------------
Note: dy/dx for factor levels is the discrete change from the base level.
.
