identical marginal effects after xtpoisson with fixed-effects

[Celine Aerts]

I am trying to estimate the impact of a program introduced in the US in 2007 on the yearly number of clinical trials. Some diseases are eligible for the program (eligible=1) and others are not (eligible=0). Most diseases became eligible for the program in 2007 but a few diseases became eligible later on. As a result, I have a staggered introduction of the program and my variable after=1 differs across diseases.

Here is a sample of my dataset:

* Example generated by -dataex-. To install: ssc install dataex
clear
input float trials long diseases int year float(eligible after)
 0 1 2000 0 0
 0 1 2001 0 0
 1 1 2002 0 0
 0 1 2003 0 0
 0 1 2004 0 0
11 1 2005 0 0
 5 1 2006 0 0
 8 1 2007 0 1
 5 1 2008 0 1
 8 1 2009 0 1
10 1 2010 0 1
 7 1 2011 0 1
 8 1 2012 0 1
 7 1 2013 0 1
 9 1 2014 0 1
 5 1 2015 0 1
13 1 2016 0 1
12 1 2017 0 1
11 1 2018 0 1
 0 2 2000 1 0
 0 2 2001 1 0
 0 2 2002 1 0
 0 2 2003 1 0
 0 2 2004 1 0
 0 2 2005 1 0
 1 2 2006 1 0
 0 2 2007 1 1
 0 2 2008 1 1
 0 2 2009 1 1
 0 2 2010 1 1
 0 2 2011 1 1
 1 2 2012 1 1
 0 2 2013 1 1
 1 2 2014 1 1
 0 2 2015 1 1
 0 2 2016 1 1
 0 2 2017 1 1
 0 2 2018 1 1
 0 3 2000 1 0
 0 3 2001 1 0
 0 3 2002 1 0
 0 3 2003 1 0
 0 3 2004 1 0
 1 3 2005 1 0
 1 3 2006 1 0
 0 3 2007 1 0
 2 3 2008 1 0
 0 3 2009 1 0
 1 3 2010 1 0
 2 3 2011 1 0
 9 3 2012 1 0
 0 3 2013 1 0
 3 3 2014 1 0
 5 3 2015 1 1
 0 3 2016 1 1
 2 3 2017 1 1
 1 3 2018 1 1
 0 4 2000 1 0
 0 4 2001 1 0
 0 4 2002 1 0
 0 4 2003 1 0
 0 4 2004 1 0
 0 4 2005 1 0
 1 4 2006 1 0
 0 4 2007 1 1
 0 4 2008 1 1
 0 4 2009 1 1
 1 4 2010 1 1
 0 4 2011 1 1
 1 4 2012 1 1
 0 4 2013 1 1
 4 4 2014 1 1
 3 4 2015 1 1
 3 4 2016 1 1
 6 4 2017 1 1
 5 4 2018 1 1
 0 5 2000 1 0
 0 5 2001 1 0
 0 5 2002 1 0
 0 5 2003 1 0
 0 5 2004 1 0
 5 5 2005 1 0
 1 5 2006 1 0
 2 5 2007 1 1
 6 5 2008 1 1
 1 5 2009 1 1
 4 5 2010 1 1
 0 5 2011 1 1
 3 5 2012 1 1
 3 5 2013 1 1
 4 5 2014 1 1
 2 5 2015 1 1
 2 5 2016 1 1
 3 5 2017 1 1
 5 5 2018 1 1
 0 6 2000 1 0
 0 6 2001 1 0
 0 6 2002 1 0
 0 6 2003 1 0
 0 6 2004 1 0
end
label values diseases diseases
label def diseases 1 "Ischemic heart disease", modify
label def diseases 2 "buruli", modify
label def diseases 3 "chagas", modify
label def diseases 4 "chikungunya", modify
label def diseases 5 "cholera", modify
label def diseases 6 "congo fever", modify

In order to estimate the impact of the program, I am using a difference-in-differences approach. I have a panel data (trials for 40 diseases across 19 years), and I want to control for disease FE and year FE.

xtset diseases year

As my dependent variable is a count variable, I ran a poisson estimation:

xtpoisson trials i.after##i.eligible user_fee PRV_value_lag_1 i.year, fe vce(robust)
note: 1 group (19 obs) dropped because of all zero outcomes

Iteration 0:   log pseudolikelihood =  -3482.899  
Iteration 1:   log pseudolikelihood = -1438.5172  
Iteration 2:   log pseudolikelihood = -1326.6942  
Iteration 3:   log pseudolikelihood = -1323.9955  
Iteration 4:   log pseudolikelihood = -1323.9843  
Iteration 5:   log pseudolikelihood = -1323.9843  

Conditional fixed-effects Poisson regression    Number of obs     =        760
Group variable: diseases                        Number of groups  =         40

                                                Obs per group:
                                                              min =         19
                                                              avg =       19.0
                                                              max =         19

                                                Wald chi2(21)     =  541403.70
Log pseudolikelihood  = -1323.9843              Prob > chi2       =     0.0000

                                  (Std. Err. adjusted for clustering on diseases)
---------------------------------------------------------------------------------
                |               Robust
         trials |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
----------------+----------------------------------------------------------------
        1.after |   .7540807    .617699     1.22   0.222    -.4565871    1.964748
     1.eligible |          0  (omitted)
                |
 after#eligible |
           1 1  |  -.2196316   .1756016    -1.25   0.211    -.5638045    .1245412
                |
       user_fee |   1.03e-08   2.06e-08     0.50   0.618    -3.02e-08    5.07e-08
PRV_value_lag_1 |   5.30e-10   6.08e-10     0.87   0.383    -6.61e-10    1.72e-09
                |
           year |
          2001  |  -.2732933   .2078431    -1.31   0.189    -.6806583    .1340717
          2002  |   .4410561   .1786783     2.47   0.014     .0908531     .791259
          2003  |   .4480247   .1444247     3.10   0.002     .1649575    .7310919
          2004  |   .5901992   .1549172     3.81   0.000      .286567    .8938314
          2005  |   2.292754   .3627732     6.32   0.000     1.581732    3.003777
          2006  |   2.255858   .3615834     6.24   0.000     1.547167    2.964549
          2007  |     1.4224   .6965394     2.04   0.041     .0572083    2.787593
          2008  |   1.504672   .6946449     2.17   0.030     .1431928    2.866151
          2009  |   1.423661   .6912332     2.06   0.039     .0688686    2.778453
          2010  |   1.338251   .7091325     1.89   0.059    -.0516231    2.728125
          2011  |   1.362411   .7026438     1.94   0.053    -.0147454    2.739568
          2012  |   1.420266   .7100725     2.00   0.045     .0285491    2.811982
          2013  |    1.45651   .6847051     2.13   0.033      .114513    2.798508
          2014  |   1.551972   .6872168     2.26   0.024     .2050519    2.898892
          2015  |   1.657939   .6661534     2.49   0.013     .3523026    2.963576
          2016  |   1.656704   .6659423     2.49   0.013     .3514812    2.961927
          2017  |   1.644959   .6718924     2.45   0.014     .3280741    2.961844
          2018  |   1.532055   .6453066     2.37   0.018     .2672774    2.796833
---------------------------------------------------------------------------------

I see that my variable eligible drops because it is collinear with the disease FE while the variable after does not drop as it is not collinear with the year FE (the variable after varies across diseases)

I then want to estimate the marginal effect for the interaction between after and eligible:

. margins after#eligible, predict(nu0) 

Predictive margins                              Number of obs     =        760
Model VCE    : Robust

Expression   : Predicted number of events (assuming u_i=0), predict(nu0)

--------------------------------------------------------------------------------
               |            Delta-method
               |     Margin   Std. Err.      z    P>|z|     [95% Conf. Interval]
---------------+----------------------------------------------------------------
after#eligible |
          0 0  |   4.678461   2.342815     2.00   0.046     .0866278    9.270295
          0 1  |   4.678461   2.342815     2.00   0.046     .0866278    9.270295
          1 0  |   9.944802   4.023562     2.47   0.013     2.058765    17.83084
          1 1  |   7.983831   2.830039     2.82   0.005     2.437056    13.53061
--------------------------------------------------------------------------------

The marginal effects are identical for the eligible and non-eligible diseases in the before period. Is it because the variable eligible is collinear with the disease FE? Would that mean that I cannot run the marginal effects in this case? Or can I ignore the fact that they are equal and assume that the program effect is 7.98-9.94?

Thank you very much!

[Phil Bromiley]

"Is it because the variable eligible is collinear with the disease FE? " - yes, because i.eligible is not estimated, you get the same for 00 and 01. By the way, you can run it without i.eligable as a variable by using # instead of ## in the interactions. Since both period 1 are identical, then your difference seems correct. However, I'm not a d-i-d person, so I'm not sure if you should be doing something else in period 1.