Difference in difference testing pre-treatment trend

[Leon Poon]

Dear Statalist community,

I'm using the difference-in-difference technique to investigate the impact of a law reform (effective as of October 2012) intended to lower entry barriers for setting up a new business.

The treatment group consists of Dutch firms, whereas the control group are Belgian firms. Both the pre-treatment and post-period are precisely 12 months. My data is repeated cross-sections as it consists of the daily number of new firms. I use the nbreg command because my data is heavily dispersed count data.

drop pick
gen PostreformXTreated =  Postreform*Treated
gen month_date = month(Date)
nbreg Nfirms Postreform Treated PostreformXTreated IndustryOutput i.month_date, irr

IndustryOutput is a production index that controls for economic conditions.

My current analysis appears to show that the law change has had a positive effect on the number of new firms and now I am doing robustness checks.


Now, similar to Branstetter et al. (2014), I wish to estimate the monthly values of the coefficient of interest (PostXTreated) in the pre-treatment period to show that there hasn't been an existing trend leading up to the introduction of the law change. Please find below the graph used in that paper as a visual representation, note that this graph includes both leads and lags.




My question: How do I code this in Stata?
Do I use monthly time dummies for each month in the pre-treatment period and interact those with the dummy Treated (which indicates the treated group)? If so, shouldn't I omit one month dummy which would serve as a reference and to avoid perfect collinearity?

Thank you for your time.

Leon

A sample of my data is attached here:

* Example generated by -dataex-. To install: ssc install dataex
clear
input int(Date Nfirms) double IndustryOutput byte(Treated Postreform pick)
18904  26  97.9 1 0 1
18911  18  97.9 1 0 1
18914  23  97.9 1 0 1
18915   6  97.9 1 0 1
18917  13  97.9 1 0 1
18921  26  97.9 1 0 1
18925  31  97.9 1 0 1
18932  70  98.1 1 0 1
18935  21  98.1 1 0 1
18938  27  98.1 1 0 1
18946  28  98.1 1 0 1
18949  34  98.1 1 0 1
18952  22  98.1 1 0 1
18954  32  98.1 1 0 1
18956  31  98.1 1 0 1
18973  18 100.2 1 0 1
18974  22 100.2 1 0 1
18976  24 100.2 1 0 1
18980  25 100.2 1 0 1
18981  24 100.2 1 0 1
18996  56  99.9 1 0 1
18997  59  99.9 1 0 1
19001  71  99.9 1 0 1
19010  68  99.9 1 0 1
19013   1  99.9 1 0 1
19015  63  99.9 1 0 1
19019  61  99.9 1 0 1
19022  71  99.9 1 0 1
19023  63  99.9 1 0 1
19024 132  97.7 1 0 1
19027   1  97.7 1 0 1
19028   1  97.7 1 0 1
19031  51  97.7 1 0 1
19035   1  97.7 1 0 1
19038  55  97.7 1 0 1
19043  50  97.7 1 0 1
19045  69  97.7 1 0 1
19046  53  97.7 1 0 1
19048   1  97.7 1 0 1
19051  58  97.7 1 0 1
19052  62  97.7 1 0 1
19061  46   102 1 0 1
19067  56   102 1 0 1
19076   0   102 1 0 1
19093  43  98.3 1 0 1
19102  53  98.3 1 0 1
19108  54  98.3 1 0 1
19110  71  98.3 1 0 1
19113   0  98.3 1 0 1
19117  36  98.1 1 0 1
19120  44  98.1 1 0 1
19121  42  98.1 1 0 1
19128  68  98.1 1 0 1
19129  72  98.1 1 0 1
19134  58  98.1 1 0 1
19135  60  98.1 1 0 1
19137  66  98.1 1 0 1
19139   4  98.1 1 0 1
19149  39  98.7 1 0 1
19157  45  98.7 1 0 1
19159  63  98.7 1 0 1
19164  32  98.7 1 0 1
19167   2  98.7 1 0 1
19168   1  98.7 1 0 1
19170  52  98.7 1 0 1
19179  56    97 1 0 1
19181   4    97 1 0 1
19185  44    97 1 0 1
19186  46    97 1 0 1
19193  45    97 1 0 1
19194  46    97 1 0 1
19197  22    97 1 0 1
19198  43    97 1 0 1
19199  22    97 1 0 1
19202   1    97 1 0 1
19205  44    97 1 0 1
19208  26  98.8 1 0 1
19214  38  98.8 1 0 1
19218  23  98.8 1 0 1
19219  55  98.8 1 0 1
19220  31  98.8 1 0 1
19222  30  98.8 1 0 1
19225  29  98.8 1 0 1
19229  32  98.8 1 0 1
19230   1  98.8 1 0 1
19232  36  98.8 1 0 1
19237  50  97.6 1 0 1
19240  29  97.6 1 0 1
19243  27  97.6 1 0 1
19244   2  97.6 1 0 1
19245   1  97.6 1 0 1
19249  28  97.6 1 0 1
19251  11  97.6 1 0 1
19253  28  97.6 1 0 1
19261  32  97.6 1 0 1
19270  62  96.4 1 1 1
19272   1  96.4 1 1 1
19276  52  96.4 1 1 1
19281  47  96.4 1 1 1
19283  55  96.4 1 1 1
19285  59  96.4 1 1 1
19289  36  96.4 1 1 1
19297  38  96.4 1 1 1
19299  54  98.4 1 1 1
19302  55  98.4 1 1 1
19305  56  98.4 1 1 1
19307   3  98.4 1 1 1
19314   5  98.4 1 1 1
19317  42  98.4 1 1 1
19320  43  98.4 1 1 1
19321   2  98.4 1 1 1
19325  48  98.4 1 1 1
19326  64  98.4 1 1 1
19328  14  99.4 1 1 1
19332  36  99.4 1 1 1
19340  34  99.4 1 1 1
19351  15  99.4 1 1 1
19356  15  99.4 1 1 1
19360 137  96.6 1 1 1
19362  96  96.6 1 1 1
19367  87  96.6 1 1 1
19371   1  96.6 1 1 1
19373  60  96.6 1 1 1
19379  65  96.6 1 1 1
19381  82  96.6 1 1 1
19382  80  96.6 1 1 1
19388  75  96.6 1 1 1
19389  79  96.6 1 1 1
19393  58  96.1 1 1 1
19401  64  96.1 1 1 1
19408  73  96.1 1 1 1
19409  60  96.1 1 1 1
19410  76  96.1 1 1 1
19411  79  96.1 1 1 1
19412   1  96.1 1 1 1
19418 131  96.9 1 1 1
19419   0  96.9 1 1 1
19420   1  96.9 1 1 1
19421  83  96.9 1 1 1
19422  66  96.9 1 1 1
19423  60  96.9 1 1 1
19424  66  96.9 1 1 1
19428  64  96.9 1 1 1
19430  62  96.9 1 1 1
19432  86  96.9 1 1 1
19438  81  96.9 1 1 1
19456  51    97 1 1 1
19459  74    97 1 1 1
19460 226    97 1 1 1
19466  71    97 1 1 1
19467  83    97 1 1 1
19470  64    97 1 1 1
19471  62    97 1 1 1
19472  60    97 1 1 1
19474 102    97 1 1 1
19478   1    97 1 1 1
19481  66  96.2 1 1 1
19484  50  96.2 1 1 1
19485  41  96.2 1 1 1
19486  56  96.2 1 1 1
19487   1  96.2 1 1 1
19495  70  96.2 1 1 1
19498   1  96.2 1 1 1
19506  77  96.2 1 1 1
19507  75  96.2 1 1 1
19510  32  97.4 1 1 1
19513  67  97.4 1 1 1
19515  73  97.4 1 1 1
19516  64  97.4 1 1 1
19517   3  97.4 1 1 1
19519  53  97.4 1 1 1
19522  71  97.4 1 1 1
19530  74  97.4 1 1 1
19533  77  97.4 1 1 1
19535 112  97.4 1 1 1
19544  62  96.6 1 1 1
19548  57  96.6 1 1 1
19555  50  96.6 1 1 1
19557  73  96.6 1 1 1
19558  60  96.6 1 1 1
19565  48  96.6 1 1 1
19566   3  96.6 1 1 1
19568  29  96.6 1 1 1
19569  34  96.6 1 1 1
19572  41  97.2 1 1 1
19576  35  97.2 1 1 1
19578  32  97.2 1 1 1
19584  38  97.2 1 1 1
19592  49  97.2 1 1 1
19598  43  97.2 1 1 1
19600  61  97.2 1 1 1
19602  13  97.5 1 1 1
19603  43  97.5 1 1 1
19611  41  97.5 1 1 1
19614  39  97.5 1 1 1
19616   1  97.5 1 1 1
19618  49  97.5 1 1 1
19620  53  97.5 1 1 1
19621  49  97.5 1 1 1
18903   2  96.7 0 0 1
18904   0  96.7 0 0 1
18905   2  96.7 0 0 1
18906   1  96.7 0 0 1
18908   0  96.7 0 0 1
18913   0  96.7 0 0 1
18914   1  96.7 0 0 1
18917   0  96.7 0 0 1
18928   1  96.7 0 0 1
18931   0  96.7 0 0 1
18935   0  96.7 0 0 1
18940   1  96.7 0 0 1
18941   1  96.7 0 0 1
18947   0  96.7 0 0 1
18948   0  96.7 0 0 1
18952   1  96.7 0 0 1
18956   2  96.7 0 0 1
18959   1  96.7 0 0 1
18966   0  96.8 0 0 1
18977   0  96.8 0 0 1
18982   0  96.8 0 0 1
18984   0  96.8 0 0 1
18991   0  96.8 0 0 1
18992   0  96.8 0 0 1
18993   1  97.6 0 0 1
18996  41  97.6 0 0 1
18997  47  97.6 0 0 1
19002  49  97.6 0 0 1
19006   0  97.6 0 0 1
19012  38  97.6 0 0 1
19017  42  97.6 0 0 1
19018  50  97.6 0 0 1
19023  35  97.6 0 0 1
19024  48  99.8 0 0 1
19025  41  99.8 0 0 1
19027   1  99.8 0 0 1
19032  18  99.8 0 0 1
19033  39  99.8 0 0 1
19036  31  99.8 0 0 1
19038  41  99.8 0 0 1
19039  39  99.8 0 0 1
19040  45  99.8 0 0 1
19047  24  99.8 0 0 1
19051  39  99.8 0 0 1
19054  30 102.4 0 0 1
19055   2 102.4 0 0 1
19058  31 102.4 0 0 1
19059  32 102.4 0 0 1
19060  25 102.4 0 0 1
19066  39 102.4 0 0 1
19067  29 102.4 0 0 1
19069   1 102.4 0 0 1
19072  30 102.4 0 0 1
19074  26 102.4 0 0 1
19078  12 102.4 0 0 1
19080  41 102.4 0 0 1
19086  29  95.7 0 0 1
19095  28  95.7 0 0 1
19100  18  95.7 0 0 1
19102  19  95.7 0 0 1
19103  16  95.7 0 0 1
19105   0  95.7 0 0 1
19106  15  95.7 0 0 1
19107  12  95.7 0 0 1
19108  18  95.7 0 0 1
19109  15  95.7 0 0 1
19117  12  97.9 0 0 1
19118   1  97.9 0 0 1
19121  23  97.9 0 0 1
19138  14  97.9 0 0 1
19139   0  97.9 0 0 1
19141   0  97.9 0 0 1
19150   8  98.2 0 0 1
19153   1  98.2 0 0 1
19155   8  98.2 0 0 1
19156   9  98.2 0 0 1
19157   6  98.2 0 0 1
19162  17  98.2 0 0 1
19163   8  98.2 0 0 1
19165   5  98.2 0 0 1
19172   9  98.2 0 0 1
19175   0  97.8 0 0 1
19179   6  97.8 0 0 1
19180   2  97.8 0 0 1
19181   0  97.8 0 0 1
19183   1  97.8 0 0 1
19192   4  97.8 0 0 1
19193   6  97.8 0 0 1
19201   3  97.8 0 0 1
19205   3  97.8 0 0 1
19207   3  99.7 0 0 1
19212   3  99.7 0 0 1
19227   1  99.7 0 0 1
19230   0  99.7 0 0 1
19232   1  99.7 0 0 1
19233   3  99.7 0 0 1
19235   2  99.7 0 0 1
19242   2  99.7 0 0 1
19245   0  99.7 0 0 1
19246   1  99.7 0 0 1
19247   3  99.7 0 0 1
19249   0  99.7 0 0 1
19253   4  99.7 0 0 1
19260   1  99.7 0 0 1
19261   2  99.7 0 0 1
19263   1  99.7 0 0 1
19264   0  99.7 0 0 1
19269   0  96.3 0 1 1
19270   1  96.3 0 1 1
19271   0  96.3 0 1 1
19277   1  96.3 0 1 1
19284   0  96.3 0 1 1
19289   1  96.3 0 1 1
19290   1  96.3 0 1 1
19292   2  96.3 0 1 1
19295   0  96.3 0 1 1
19297   2  96.3 0 1 1
19298   0  95.1 0 1 1
19303   0  95.1 0 1 1
19304   0  95.1 0 1 1
19309   0  95.1 0 1 1
19310   0  95.1 0 1 1
19316   0  95.1 0 1 1
19317   0  95.1 0 1 1
19321   0  95.1 0 1 1
19323   0  95.1 0 1 1
19332   0  96.3 0 1 1
19335   0  96.3 0 1 1
19338   1  96.3 0 1 1
19339   0  96.3 0 1 1
19345   0  96.3 0 1 1
19351   0  96.3 0 1 1
19357   0  96.3 0 1 1
19360  32  95.1 0 1 1
19361  50  95.1 0 1 1
19362  37  95.1 0 1 1
19366  35  95.1 0 1 1
19368  50  95.1 0 1 1
19370   2  95.1 0 1 1
19371   1  95.1 0 1 1
19374  48  95.1 0 1 1
19382  44  95.1 0 1 1
19393  36  93.9 0 1 1
19395  48  93.9 0 1 1
19400  20  93.9 0 1 1
19404  12  93.9 0 1 1
19407  32  93.9 0 1 1
19410  46  93.9 0 1 1
19411  32  93.9 0 1 1
19416  38  93.9 0 1 1
19419   1  96.5 0 1 1
19421  22  96.5 0 1 1
19425  35  96.5 0 1 1
19426   0  96.5 0 1 1
19433   1  96.5 0 1 1
19438  21  96.5 0 1 1
19441   0  96.5 0 1 1
19445  38  96.5 0 1 1
19452  26  97.4 0 1 1
19459  15  97.4 0 1 1
19467  20  97.4 0 1 1
19468   1  97.4 0 1 1
19472  14  97.4 0 1 1
19477  22  97.4 0 1 1
19482   0  99.3 0 1 1
19491  13  99.3 0 1 1
19492  10  99.3 0 1 1
19500  10  99.3 0 1 1
19501  15  99.3 0 1 1
19509   8  99.3 0 1 1
19513   3  98.3 0 1 1
19523   4  98.3 0 1 1
19529   1  98.3 0 1 1
19532   0  98.3 0 1 1
19534   8  98.3 0 1 1
19541   4  99.4 0 1 1
19545   0  99.4 0 1 1
19548   6  99.4 0 1 1
19549   2  99.4 0 1 1
19550   2  99.4 0 1 1
19551   7  99.4 0 1 1
19553   1  99.4 0 1 1
19555   5  99.4 0 1 1
19556   3  99.4 0 1 1
19558   1  99.4 0 1 1
19565   2  99.4 0 1 1
19566   0  99.4 0 1 1
19572   0  97.5 0 1 1
19575   4  97.5 0 1 1
19576   4  97.5 0 1 1
19580   0  97.5 0 1 1
19582   1  97.5 0 1 1
19586   0  97.5 0 1 1
19591   1  97.5 0 1 1
19593   1  97.5 0 1 1
19602   0  96.4 0 1 1
19606   1  96.4 0 1 1
19611   5  96.4 0 1 1
19613   3  96.4 0 1 1
19614   0  96.4 0 1 1
19618   0  96.4 0 1 1
end
format %td Date

[Liu Qiang]

Hi Leon, the graph you posted can not be seen. I guess the graph should be something like:

tw (line Nfirms Date if Treated==0,sort) ///
   (line Nfirms Date if Treated==1,sort),xline(19263)

But your dataset is quite strange as it is neither consecutive for a specific country nor parallel comparable within the treated variable. That wold make your graph very peculiar.

[Leon Poon]

Hi Liu Qiang, thank you for your quick response. To comment on your reply.

Hi Leon, the graph you posted can not be seen.

The graph, taken from Branstetter et al. (2014), is a just a representation of something I would like to recreate in my own thesis. In other words, I haven't created the monthly treatment coefficients yet, which is what I need to do first.

My question is how to create/code in Stata the monthly coefficients of interest (that measure the treatment effect) for each month in the pre-treatment period.

But your dataset is quite strange as it is neither consecutive for a specific country nor parallel comparable within the treated variable. That wold make your graph very peculiar.

Perhaps I was unclear in my original post, my apologies.

The variable Nfirms is the number of daily new firms.
Treated is a dummy variable taking on the value 1 for Dutch firms and 0 for Belgian firms.
Postreform is the dummy variable taking on the value 1 when the daily new firms are created in the post-reform period.

 sort Date

Now the data is sorted. Is this what you are looking for? This makes the data consecutive by date.

[Liu Qiang]

Hi Liu Qiang, thank you for your quick response. To comment on your reply.



The graph, taken from Branstetter et al. (2014), is a just a representation of something I would like to recreate in my own thesis. In other words, I haven't created the monthly treatment coefficients yet, which is what I need to do first.

My question is how to create/code in Stata the monthly coefficients of interest (that measure the treatment effect) for each month in the pre-treatment period.



Perhaps I was unclear in my original post, my apologies.

The variable Nfirms is the number of daily new firms.
Treated is a dummy variable taking on the value 1 for Dutch firms and 0 for Belgian firms.
Postreform is the dummy variable taking on the value 1 when the daily new firms are created in the post-reform period.

 sort Date

Now the data is sorted. Is this what you are looking for? This makes the data consecutive by date.

sorry for my misunderstanding. I now know what you want. Here's a reference.

nbreg Nfirms Postreform Treated PostreformXTreated IndustryOutput i.month_date
mat b=r(table)'
drop *
svmat b
keep b1 b5 b6
keep in 6/l
gen n=_n+1
tw (rcap b5 b6 n) ///
(scatter b1 n,msize(small)), xlabel(2(2)15) xline(13,lp(dash)) yline(0,lp(dash))

I can only advise on how to draw graphs. As for the possion model, I am not familiar with it. The results won't report the IRR statistics in the macros. And you also need to change the event month in the graph. I just randomly assigned 13 in my code.
About your thought on dummy, I think you are right. One dummy would be omitted. The coefficients in the graph are the fixed effect estimations.
Hope it helps.

[Leon Poon]

Thank you Liu Qiang!