Pre- post- pooled regression and interpreation of squared term

[Kenneth Colombe]

Hello,

I am interested in the change in my variable of interest between period 1 and period 2. It is the square of abs_crew_mean_diff. I understand how to read the table when there is no polynomial, but having trouble reading the output below. I will first put the model specifications. Then the output.

* Run joint regression with appropriate weights, clustering, and interactions 
reghdfe fouls_rate c.abs_crew_mean_diff##c.abs_crew_mean_diff##c.post_abs_crew_mean_diff ///
        $controls ///
        [aw=min] if inrange(year, 2004, 2010), absorb(player_year gameid) nocons vce(cluster player_year gameid)

(dropped 8 singleton observations)
(MWFE estimator converged in 14 iterations)

HDFE Linear regression                            Number of obs   =     30,094
Absorbing 2 HDFE groups                           F(  10,   1162) =      31.47
Statistics robust to heteroskedasticity           Prob > F        =     0.0000
                                                  R-squared       =     0.2501
                                                  Adj R-squared   =     0.1757
Number of clusters (player_year) =      1,163     Within R-sq.    =     0.0074
Number of clusters (gameid)  =      1,543         Root MSE        =     2.7740

                              (Std. err. adjusted for 1,163 clusters in player_year gameid)
-------------------------------------------------------------------------------------------
                          |               Robust
               fouls_rate | Coefficient  std. err.      t    P>|t|     [95% conf. interval]
--------------------------+----------------------------------------------------------------
       abs_crew_mean_diff |   .0386534   .0205213     1.88   0.060    -.0016096    .0789163
                          |
     c.abs_crew_mean_diff#|
     c.abs_crew_mean_diff |  -.0019905   .0009891    -2.01   0.044    -.0039311     -.00005
                          |
  post_abs_crew_mean_diff |  -.0896262   .0449813    -1.99   0.047    -.1778799   -.0013725
                          |
     c.abs_crew_mean_diff#|
c.post_abs_crew_mean_diff |   .0066749   .0037847     1.76   0.078    -.0007506    .0141005
                          |
     c.abs_crew_mean_diff#|
     c.abs_crew_mean_diff#|
c.post_abs_crew_mean_diff |  -.0001767   .0000963    -1.84   0.067    -.0003657    .0000122
                          |
                      age |   1.860165   5.376674     0.35   0.729     -8.68891    12.40924
                  starter |  -.5399211   .0622378    -8.68   0.000    -.6620322     -.41781
                     home |  -.3526476   .0246707   -14.29   0.000    -.4010516   -.3042436
                 out_cont |   .0412472   .1391525     0.30   0.767    -.2317711    .3142655
              coach_l_lab |   .0025744   .0064034     0.40   0.688    -.0099891    .0151379
-------------------------------------------------------------------------------------------

Absorbed degrees of freedom:
-----------------------------------------------------+
 Absorbed FE | Categories  - Redundant  = Num. Coefs |
-------------+---------------------------------------|
 player_year |      1163        1163           0    *|
      gameid |      1543        1543           0    *|
-----------------------------------------------------+
* = FE nested within cluster; treated as redundant for DoF computation

Best,
KC

[George Ford]

What is this:
post_abs_crew_mean_diff

[Kenneth Colombe]

Hi George,

Thank you for checking in. That term is our coefficient of interest post-treatment period.

Best,
KC

[Carlo Lazzaro]

Kenneth:
your interaction is too complicated and, in all likelihood, very hard to explain,
That said:
1) I would go with a more parsimonious model;
2) your within Rsq is really low. Your model specification should be double-checked;
3) if you're planning to run a DID, you may want to consider -xtdidregress-.

[George Ford]

Is post_abs_crew_mean_diff an interaction term of post with abs_crew_mean_diff ?

[Kenneth Colombe]

Hello Carlo and George,

Thank you very much for your comments. I will maybe investigate a simpler model and use xtdidregress.

As for the interaction term, that is exactly correct post_abs_crew_mean_diff is an interaction term of post with abs_crew_mean_diff. I want to see the change from pre treatment to post treatment in the standard abs_crew_mean_diff as well as the squared term.

Best,
KC

[George Ford]

to get the margins, it's better to use c.post#c.abs_crew_mean_diff.

clear all

sysuse auto, clear

expand 2 , generate(post)

g y = 1000 + 0.5*mpg -0.05*mpg^2 + 200*post + 0.5*mpg*post - 0.2*mpg^2 + rnormal()

reghdfe y c.mpg##c.mpg c.post#(c.mpg##c.mpg) , absorb(rep78)
margins, dydx(mpg) over(post)
margins, at(mpg = (1760(200)4840)) over(post)
marginsplot

[George Ford]

altered the model to include the post dummy.

clear all  
sysuse auto, clear  
expand 2 , generate(post)  
g y = 1000 + 0.5*mpg -0.05*mpg^2 + 200*post + 0.5*mpg*post - 0.2*mpg^2 + rnormal()  
reghdfe y c.mpg##c.mpg post c.post#(c.mpg##c.mpg) , absorb(rep78)
margins, dydx(mpg) over(post)
margins, at(mpg = (1760(200)4840)) over(post)
marginsplot