In Dif in Dif, what is a suitable group level?

[Mahtab Karimi]

Hi all,

I am studying the effect of a shock at the industry level on firms. Shock happens at diffrent times in different industries, so I use a staggered dif-in-dif. My main question is: what is a good treatment group in this setup? one industry or all industries hit by the shock at the same time?
so this is my main specification:

Yigt=a_g+a_t+beta*Dit+epsilon

Yigt: firm i, group g, time t
a_g: group FE
a_t: year FE
Dit: Treatment*Post
(I am not controlling for covariants at this point)


If I define my treatment groups as all industries hitting by the shock for the first time at the same time:

reg Y Dit i.shock i.fyear, vce(cluster cik)

Linear regression                               Number of obs     =      2,002
                                                F(12, 399)        =       2.31
                                                Prob > F          =     0.0073
                                                R-squared         =     0.0250
                                                Root MSE          =     .30748

                                  (Std. err. adjusted for 400 clusters in cik)
------------------------------------------------------------------------------
             |               Robust
Y           | Coefficient  std. err.      t    P>|t|     [95% conf. interval]
-------------+----------------------------------------------------------------
         Dit |   .0481019   .0171934     2.80   0.005      .014301    .0819029
             |

If I define the treatment groups as all industries hitting by the shock for the first time at the same time and adding an industry FE:

 reg Y Dit i.shock i.fyear i.sic, vce(cluster cik)

Linear regression                               Number of obs     =      2,002
                                                F(72, 399)        =          .
                                                Prob > F          =          .
                                                R-squared         =     0.6156
                                                Root MSE          =     .20145

                                  (Std. err. adjusted for 400 clusters in cik)
------------------------------------------------------------------------------
             |               Robust
Y           | Coefficient  std. err.      t    P>|t|     [95% conf. interval]
-------------+----------------------------------------------------------------
         Dit |   .0273507   .0132821     2.06   0.040      .001239    .0534624
             |

If I define the treatment groups just as industries; so two industries hitting by the shock at the same time will be two different treatment groups:

reg Y Dit i.fyear i.sic, vce(cluster cik)

Linear regression                               Number of obs     =      2,002
                                                F(71, 399)        =          .
                                                Prob > F          =          .
                                                R-squared         =     0.6066
                                                Root MSE          =     .20346

                                  (Std. err. adjusted for 400 clusters in cik)
------------------------------------------------------------------------------
             |               Robust
           Y | Coefficient  std. err.      t    P>|t|     [95% conf. interval]
-------------+----------------------------------------------------------------
         Dit |   .0132233   .0156425     0.85   0.398    -.0175288    .0439753

If I define my treatment groups as all industries hitting by the shock for the first time at the same time, but instead of a year FE include an industry*year FE, then:

reg Y Dit i.shock i.sic#i.fyear, vce(cluster cik)

Linear regression                               Number of obs     =      2,002
                                                F(136, 399)       =          .
                                                Prob > F          =          .
                                                R-squared         =     0.6510
                                                Root MSE          =     .24646

                                  (Std. err. adjusted for 400 clusters in cik)
------------------------------------------------------------------------------
             |               Robust
           Y | Coefficient  std. err.      t    P>|t|     [95% conf. interval]
-------------+----------------------------------------------------------------
         Dit |   .3175529    .177229     1.79   0.074    -.0308664    .6659722

And if I define a treatment group as one industry and control for both year and year*industry FE:

reg Y Dit  i.sic##i.fyear, vce(cluster cik)

Linear regression                               Number of obs     =      2,002
                                                F(134, 399)       =          .
                                                Prob > F          =          .
                                                R-squared         =     0.6438
                                                Root MSE          =     .24835

                                  (Std. err. adjusted for 400 clusters in cik)
------------------------------------------------------------------------------
             |               Robust
         Y  | Coefficient  std. err.      t    P>|t|     [95% conf. interval]
-------------+----------------------------------------------------------------
         Dit |   .3050812    .248455     1.23   0.220    -.1833634    .7935257

I am sure the last one has serious collinearity problems and I am just adding it here for reference. But I do not know what the best specification among others is.


Thank you,
Mahtab

[Mahtab Karimi]

This is the summary of all results above in one table:

	(1)	(2)	(3)	(4)	(5)
VARIABLES	Y	Y	Y	Y	Y
Dit	0.05***	0.03**	0.01	0.32*	0.31
	(0.02)	(0.01)	(0.02)	(0.18)	(0.25)
Constant	0.68***	0.63***	0.63***	0.68***	0.68
	(0.02)	(0.00)	(0.00)	(0.00)	(.)
Observations	2,002	2,002	2,002	2,002	2,002
R-squared	0.02	0.62	0.61	0.65	0.64
shock FE	Y	Y	N	Y	N
Year FE	Y	Y	Y	N	Y
Industry FE	N	Y	Y	N	Y
Year*Industry FE	N	N	N	Y	Y