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Background information:

The investigation is under event study framework. The topic is on how the conversion to academies affects students' KS4 performance. The dataset is at school-level. Conversion before 2009 would be in the treatment group while schools converted after 2009 would be in the control group. I have school-level students' performance from year 2002 to year 2009. From year 2006 to year 2009 every year there were conversion taking place.

Therefore, in my dataset, there are two groups: the control group contains schools didn't convert to academies up to the year 2009; the treatment group is those converted to academies before (including year 2009) , but the conversion took place in different years.

Variable explanation:

year is the year when the data is observed

schstdks4_cappedpts is the average KT4 performance of a school

earlyconverters =1 for those converted to academies up to 2009; =0 otherwise

Suppose year=c is the year when the conversion took place;

afterconversion =1 if the $year\geqslant c$

Problem:

I was hoping to get DID coefficient by

regress schstdks4_cappedpts i.year earlyconverters#afterconversion, r

What I found puzzling is:

Linear regression                               Number of obs     =        816
                                                F(9, 806)         =       7.81
                                                Prob > F          =     0.0000
                                                R-squared         =     0.0679
                                                Root MSE          =     .39251

-------------------------------------------------------------------------------------------------
                                |               Robust
            schstdks4_cappedpts |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
--------------------------------+----------------------------------------------------------------
                           year |
                          2003  |  -.2799424   .2312072    -1.21   0.226    -.7337818    .1738969
                          2004  |  -.2039077   .2140511    -0.95   0.341     -.624071    .2162556
                          2005  |   -.200673    .208598    -0.96   0.336    -.6101324    .2087864
                          2006  |  -.1890817    .206715    -0.91   0.361    -.5948449    .2166816
                          2007  |  -.1416356   .2069297    -0.68   0.494    -.5478203    .2645492
                          2008  |  -.0700349   .2070475    -0.34   0.735    -.4764509     .336381
                          2009  |   -.017034   .2091049    -0.08   0.935    -.4274884    .3934205
                                |
earlyconverters#afterconversion |
                           0 1  |          0  (empty)
                           1 0  |   .1236718   .0343675     3.60   0.000     .0562113    .1911322
                           1 1  |   .1886763   .0400589     4.71   0.000     .1100443    .2673084
                                |
                          _cons |  -.3158101   .2065066    -1.53   0.127    -.7211644    .0895441

I don't understand why would I have coefficient for (earlyconverter==1)*(afterconversion=0), shouldn't this combination in theory==0?

If the model set up is correct, (earlyconverters==1#afterconversion==0) is supposed to measure?

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    $\begingroup$ In principle, this seems statistical at root. In practice, it is hard to imagine anyone wading through this who wasn't fluent in both difference-in-difference analyses and Stata [NB not STATA]. In practice, you'd be better asking this on Statalist, where many questions are asked on this territory. $\endgroup$
    – Nick Cox
    Nov 20 '17 at 14:48
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This coefficient picks up any pre-existing differences between the treated group and the control that already exists prior to the treatment.

However, you don't really have a diff-in-diff specification here. You need to have

i.earlyconverters##i.afterconversion

so you include both the own effects and the DID interaction. NB the use of i. prefix in front of the categorical variables.

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  • $\begingroup$ I tried this command before...but I think this set-up would only work for cases such that the event happens at a particular point in time. For example, observations in the control group (as in earlyconverters==0) would also have a chance of having (afterconversion==1). But in this setting, this wouldn't happen because having earlyconverters==0 necessarily implies afterconversion==0... $\endgroup$
    – JoZ
    Nov 20 '17 at 18:40
  • $\begingroup$ @ChloeZhou You can have a time-varying treatment with this setup: you need a full set of time dummies plus the term I mentioned above (3 additional coefficients). The DID interaction is one for units and time periods subject to the policy and zero otherwise. See the first paragraph in Section 3 from [Wooldridge's 2007 NBER slides(nber.org/WNE/lect_10_diffindiffs.pdf) for more on this. $\endgroup$
    – dimitriy
    Nov 20 '17 at 18:53
  • $\begingroup$ I do have full set of time dummies in my regression, specified by i.year ... problem with my data is that if the observation has earlyconverters==0 , (afterconversion) would always ==0; similarly, observation with afterconversion==1 would always have earlyconverter==1; controlling for (earlyconverters) and (afterconversion) and then introduce the interactive dummies would have perfect colinearity problem.. $\endgroup$
    – JoZ
    Nov 21 '17 at 0:42
  • $\begingroup$ I think it would be better if I only use afterconversion*earlyconverter to estimate the DID.... I think to vilify this regression I only need to impose an additional assumption that treatment group before been treated is on average identical to the control group? $\endgroup$
    – JoZ
    Nov 21 '17 at 0:43
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    $\begingroup$ @ChloeZhou If I understand your data correctly, I am not sure if you can do DID with this data. $\endgroup$
    – dimitriy
    Nov 21 '17 at 0:49

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