For a Dif in Dif, reg or xtreg?

[Mahtab Karimi]

Hi all,

I am running the following staggered dif in dif where the variable of interest is Dit(Treatment*Post), group is my group variable showing treatment(it is a group of firms not a single firm) and fyear is the time variable:

reg Ya Dit log_at q_w roa_w sales_growth_w fyear_stock_performace leverage_w financial_constraint ret_sd instblckown_ratio_w rdassets_w rdassets_change_indicator capxassets_w assetintangibility_w fortune_500 containsrisk uniquecommitteecount log_wage i.fyear i.group,  vce(cluster cik)



Linear regression                               Number of obs     =      1,711
                                                F(29, 329)        =       9.30
                                                Prob > F          =     0.0000
                                                R-squared         =     0.2761
                                                Root MSE          =     .26475

                                               (Std. err. adjusted for 330 clusters in cik)
-------------------------------------------------------------------------------------------
                          |               Robust
                     Ya | Coefficient  std. err.      t    P>|t|     [95% conf. interval]
--------------------------+----------------------------------------------------------------
                      Dit |   .0433924   .0200312     2.17   0.031     .0039869    .0827979
                   log_at |  -.0033164   .0115973    -0.29   0.775    -.0261306    .0194977
                      q_w |  -.0190526   .0224108    -0.85   0.396    -.0631393     .025034
                    roa_w |  -.0384923   .2222948    -0.17   0.863    -.4757908    .3988061
           sales_growth_w |   .3146239   .0619365     5.08   0.000     .1927823    .4364655
   fyear_stock_performace |   .0235292   .0240789     0.98   0.329    -.0238389    .0708973
               leverage_w |    .000235   .0057096     0.04   0.967    -.0109969    .0114668
     financial_constraint |   .0213999   .0420888     0.51   0.611    -.0613973     .104197
                   ret_sd |   2.795826   1.329521     2.10   0.036     .1803918    5.411261
      instblckown_ratio_w |    .081117   .1175083     0.69   0.490    -.1500455    .3122794
               rdassets_w |   .2935391   .7718691     0.38   0.704    -1.224882    1.811961
rdassets_change_indicator |   .2371774   .0450438     5.27   0.000     .1485672    .3257876
             capxassets_w |  -1.136542   .6557137    -1.73   0.084    -2.426463    .1533783
     assetintangibility_w |  -.1576374   .1026244    -1.54   0.125    -.3595203    .0442455
              fortune_500 |  -.0609666   .0450022    -1.35   0.176     -.149495    .0275617
             containsrisk |   .0820526   .0758179     1.08   0.280    -.0670964    .2312016
     uniquecommitteecount |   .0083096   .0109137     0.76   0.447    -.0131599    .0297792
                 log_wage |   .0060976   .0378791     0.16   0.872    -.0684181    .0806134

....

Then, I thought why not to try xtreg?! And then I ran the following model. My quesiton is, which specificaiton is more reliable/reasonable/correct to report? xtreg with fe is very similar to the reg results mentioned above and it ends up removing my group indicators due to the collinearity between the group effects and the fixed effect. But I do not know why/how to rule out the RE model.

tsset cik fyear
xtreg Ya Dit log_at q_w roa_w sales_growth_w fyear_stock_performace leverage_w financial_constraint ret_sd instblckown_ratio_w rdassets_w rdassets_change_indicator capxassets_w assetintangibility_w fortune_500 containsrisk uniquecommitteecount log_wage i.fyear i.group,re vce(cluster cik)

Random-effects GLS regression                   Number of obs     =      1,711
Group variable: cik                             Number of groups  =        330

R-squared:                                      Obs per group:
     Within  = 0.0306                                         min =          1
     Between = 0.2408                                         avg =        5.2
     Overall = 0.2352                                         max =          6

                                                Wald chi2(29)     =     107.84
corr(u_i, X) = 0 (assumed)                      Prob > chi2       =     0.0000

                                               (Std. err. adjusted for 330 clusters in cik)
-------------------------------------------------------------------------------------------
                          |               Robust
                     Ya | Coefficient  std. err.      z    P>|z|     [95% conf. interval]
--------------------------+----------------------------------------------------------------
                      Dit |    .032265   .0129934     2.48   0.013     .0067984    .0577316
                   log_at |  -.0066793   .0084666    -0.79   0.430    -.0232736     .009915
                      q_w |   .0030271   .0095897     0.32   0.752    -.0157684    .0218226
                    roa_w |   .1366377   .0691293     1.98   0.048     .0011469    .2721286
           sales_growth_w |   .0533237   .0238901     2.23   0.026     .0064999    .1001475
   fyear_stock_performace |   .0028065    .008552     0.33   0.743    -.0139551     .019568
               leverage_w |  -.0010619   .0009059    -1.17   0.241    -.0028375    .0007136
     financial_constraint |   .0442714   .0192372     2.30   0.021     .0065672    .0819756
                   ret_sd |  -.3657277    .414918    -0.88   0.378    -1.178952    .4474966
      instblckown_ratio_w |   .0111513   .0606325     0.18   0.854    -.1076862    .1299888
               rdassets_w |   1.042973   .5368405     1.94   0.052    -.0092152    2.095161
rdassets_change_indicator |   .2472112   .0536758     4.61   0.000     .1420087    .3524138
             capxassets_w |  -.2267981   .2185544    -1.04   0.299    -.6551568    .2015607
     assetintangibility_w |  -.0415342   .0551871    -0.75   0.452    -.1496989    .0666306
              fortune_500 |  -.0346659   .0192657    -1.80   0.072    -.0724259    .0030942
             containsrisk |    .004988   .0195374     0.26   0.798    -.0333045    .0432806
     uniquecommitteecount |   .0081462   .0045533     1.79   0.074    -.0007781    .0170705
                 log_wage |   .0129669   .0281526     0.46   0.645    -.0422111     .068145
                          |
                    ...
                          |
                    _cons |   .3344413   .2971543     1.13   0.260    -.2479703     .916853
--------------------------+----------------------------------------------------------------
                  sigma_u |  .24998514
                  sigma_e |   .0814166
                      rho |  .90410091   (fraction of variance due to u_i)
-------------------------------------------------------------------------------------------

Many Thanks,
Mahtab

[Clyde Schechter]

The most efficient approach to this problem is to use -xtreg, fe-. Your -regress- version is completely equivalent to -xtreg, fe- and gives the same results you would have gotten with the latter. The -xtreg, fe- output is organized a bit more compactly than the way regress showed it, but substantively there would be no difference.

You have, however, used -xtreg, re-, which is simply not appropriate for this problem. Your goal is to estimate a treatment effect, and the treatment effect is manifested in the real world as an outcome change within a group over time. These within-group parameters are properly estimated by -xtreg, fe-. -xtreg, re- estimates something different: it estimates a weighted average of that treatment effect along with the between-group differences in the outcome variable. So the -xtreg, re- result is "contaminated" by between-group differences that have nothing to do with the treatment effect. This is one way of explaining what is usually said more tersely in technical terms: the -re- estimator is not consistent.

Yes, there are circumstances where an -re- estimator is appropriate. Foremost among those is when the treatment has been assigned by randomization or is otherwise demonstrably exogenous. Another is when the between-group differences are actually the same as the within-group differences--and there are some tests available for that. But, absent one of these exceptional conditions, you should use -xtreg, fe- (or your equivalent -regress ... i.group i.fyear-) for this kind of problem. (Also, if you were in a situation where the use of -xtreg, re- is appropriate, you would need to omit the i.group term from the fixed part of the model.)

[Mahtab Karimi]

Thank you so much.

[George Ford]

you could use reghdfe and absorb both id and time fixed effects. cleaner output.

[Mahtab Karimi]

thank you.