Hi everyone,

I have some questions about the difference-in-differences (DID) model with fixed effects.

I am dealing with a monthly panel dataset – from 2005 to 2016 – for workers and I want to study the effect of a policy introduced on January 2015.

I run the following fixed effect model, where I decided also to put the fixed effects for years and months.

Post is a dummy equal to one if year>=2015 and treat is the dummy equal to one for workers who were eligible for the treatment. To make to question simple to understand, Y is the outcome variable and is equal to one if the worker finds a job and zero otherwise.

Code:
xtset id_worker year_m
xtreg Y i.treat##i.post i.year i.month, fe vce(robust)
The outcome is the following:
Code:
. xtreg Y i.treat##i.post i.year i.month, fe vce(robust)
note: 2016.year omitted because of collinearity

Fixed-effects (within) regression               Number of obs     = 14,449,651
Group variable: id_worker                       Number of groups  =    170,670

R-sq:                                           Obs per group:
     within  = 0.0244                                         min =          6
     between = 0.0015                                         avg =       84.7
     overall = 0.0191                                         max =        156

                                                F(25,170669)      =    1094.01
corr(u_i, Xb)  = -0.3293                        Prob > F          =     0.0000

                    (Std. Err. adjusted for 170,670 clusters in id_lavoratore)
------------------------------------------------------------------------------
             |               Robust
           Y |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
     1.treat |   .0109051   .0000801   136.08   0.000      .010748    .0110622
      1.post |   .0017448   .0004856     3.59   0.000     .0007931    .0026965
             |
  treat#post |
        1 1  |    .003317   .0001612    20.57   0.000      .003001     .003633
             |
        year |
       2005  |   .0022443   .0004834     4.64   0.000     .0012969    .0031917
       2006  |   .0020643   .0004861     4.25   0.000     .0011117     .003017
       2007  |    .001732   .0004855     3.57   0.000     .0007803    .0026836
       2008  |   .0020534   .0004858     4.23   0.000     .0011013    .0030055
       2009  |   .0016452   .0004855     3.39   0.001     .0006936    .0025967
       2010  |   .0013525   .0004855     2.79   0.005     .0004009    .0023042
       2011  |   .0013109   .0004856     2.70   0.007     .0003592    .0022625
       2012  |   .0013895   .0004855     2.86   0.004     .0004379    .0023411
       2013  |   .0014791   .0004856     3.05   0.002     .0005272    .0024309
       2014  |   .0010583   .0004855     2.18   0.029     .0001067    .0020098
       2015  |  -.0012254   .0000607   -20.20   0.000    -.0013444   -.0011065
       2016  |          0  (omitted)
             |
       month |
          2  |  -.0174946   .0001178  -148.47   0.000    -.0177256   -.0172637
          3  |  -.0174899   .0001178  -148.44   0.000    -.0177208   -.0172589
          4  |  -.0175043   .0001179  -148.43   0.000    -.0177355   -.0172732
          5  |  -.0175121    .000118  -148.40   0.000    -.0177434   -.0172808
          6  |  -.0175214   .0001181  -148.38   0.000    -.0177529     -.01729
          7  |  -.0179749   .0001211  -148.39   0.000    -.0182123   -.0177375
          8  |  -.0179795   .0001212  -148.38   0.000     -.018217    -.017742
          9  |  -.0180004   .0001213  -148.39   0.000    -.0182382   -.0177627
         10  |  -.0180103   .0001214  -148.38   0.000    -.0182482   -.0177724
         11  |  -.0180065   .0001214  -148.35   0.000    -.0182444   -.0177686
         12  |  -.0180912   .0001219  -148.46   0.000    -.0183301   -.0178524
             |
       _cons |   .0135575   .0004917    27.57   0.000     .0125937    .0145212
-------------+----------------------------------------------------------------
     sigma_u |  .00646775
     sigma_e |   .0373691
         rho |  .02908457   (fraction of variance due to u_i)
------------------------------------------------------------------------------

I have the following three questions:
1) It is correct to also insert months and years fixed effects? I performed the -testparm- test and it seems ok; but this cause some collinearity problem and it is quite different from the standard diff-in-diff strategy.

2) My outcome variable is a dummy equal to zero or one. Is it ok to perform a linear model? I read that for a diff-in-diff model it should be ok – I also use vce(robust) for the SE. Moreover, I also tried to use xtlogit but it takes too much time – more than 10 hours and it does not show any results.

3) How should I interpret the coefficients? I tried to use the -margins- command but I only get "(not estimable)". Instead, when I run the xtreg without the months and years fixed effect, the -margins- command works well. What should I do?

Thanks a lot!