Collinearity problem in Difference in Difference

[Carlos Noyola]

I am trying to evaluate a government program where poor schools were selected and given money to improve their infrastructure. I am using results of standardized tests as the outcome variable, and I have a dummy for whether the school received the treatment (aid from government) or not, and I want to compare 2013 results (before treatment) with 2015 results (after treatment)

First, I matched schools considered for aid with their 2013 results, eliminated those that did not match, and created a variable called dummy2013 with a value of one for all.

Second, I matched schools considered for aid with their 2015 results, eliminated those that did not match, and created a variable called dummy2015 with a value of one for all.

Note that most schools matched for both years, but some do not.

Finally, I used the append command to combine the databases and created a dummy called after_dummy, with a value of 1 when dummy2015 was equal to 1 and 0 when dummy2013 was equal to 1. I created the dummy for the interaction and then I run the regression, but stata dropped both the after_dummy variable and the interaction term due to collinearity, what I am doing wrong? How can I solve this?

Thanks a lot in advance.

[Clyde Schechter]

Even the best description in words of what you've done can never be an adequate basis for troubleshooting. Nobody can answer your question without seeing your exact code and the exact output you got from Stata. Please post back with those, using code delimiters (see Forum FAQ #12 if you are not familiar with code delimiters) to make it all readable.

[Carlos Noyola]

Clyde: thank you for your answer and sorry for not posting my output. Here is an example of my data set. My database is from the mexican government, so nombre_escuela is the name of the school, beneficiaria means treatment, and logro_mate_porcentalum_nivel4_15 is the outcome variable, whereas logro_mate_porcentalum_nivel4_13 is the result for the test in 2013:

* Example generated by -dataex-. To install: ssc install dataex
clear
input str10 school_code_compatible str99 nombre_escuela str26 turno str2 beneficiaria_14 float beneficiaria_dum double(logro_mate_porcentalum_nivel4_13 logro_mate_porcentalum_nivel4_15) float(dummy2013 dummy2015 after_dum DD)
"01DPR0044T" "MIGUEL ALEMAN"                                                  "MATUTINO"   "NO" 0    0 . 1 . 0 0
"01DPR0196Y" "CARLOS BARRON"                                                  "MATUTINO"   "SI" 1    0 . 1 . 0 0
"01DPR0507K" "DON MIGUEL HIDALGO Y COSTILLA"                                  "MATUTINO"   "SI" 1    0 . 1 . 0 0
"01DPR0627X" "BENITO JUAREZ"                                                  "MATUTINO"   "SI" 1    0 . 1 . 0 0
"01DST0014K" "SECUNDARIA TECNICA NUM. 14"                                     "MATUTINO"   "SI" 1 .028 . 1 . 0 0
"01DTV0062H" "ETV NUM. 62, JOSE MA. PINO SUAREZ"                              "MATUTINO"   "SI" 1    0 . 1 . 0 0
"01DTV0099V" "ETV NUM. 99; JESUS F. CONTRERAS"                                "MATUTINO"   "NO" 0    0 . 1 . 0 0
"01KPR0025O" "CURSO COMUNITARIO"                                              "MATUTINO"   "SI" 1    . . 1 . 0 0
"01KPR0033X" "CURSO COMUNITARIO"                                              "MATUTINO"   "NO" 0    0 . 1 . 0 0
"01KPR0035V" "CURSO COMUNITARIO"                                              "MATUTINO"   "NO" 0    . . 1 . 0 0
"01KPR0050N" "CURSO COMUNITARIO"                                              "MATUTINO"   "SI" 1    0 . 1 . 0 0
"01KPR0060U" "CURSO COMUNITARIO"                                              "MATUTINO"   "NO" 0    0 . 1 . 0 0
"01KPR0087A" "CURSO COMUNITARIO"                                              "MATUTINO"   "NO" 0    0 . 1 . 0 0
"01KPR0203A" "CURSO COMUNITARIO"                                              "MATUTINO"   "ND" .    0 . 1 . 0 .
"01KPR0221Q" "CURSO COMUNITARIO"                                              "MATUTINO"   "NO" 0    . . 1 . 0 0
"01KPR0237R" "CURSO COMUNITARIO"                                              "MATUTINO"   "NO" 0    . . 1 . 0 0
"01KPR0239P" "CURSO COMUNITARIO"                                              "MATUTINO"   "NO" 0    . . 1 . 0 0
"01KPR0243B" "CURSO COMUNITARIO"                                              "MATUTINO"   "SI" 1    0 . 1 . 0 0
"01KTV0007Y" "SECUNDARIA COMUNITARIA DE CONAFE"                               "MATUTINO"   "NO" 0    0 . 1 . 0 0
"01KTV0008X" "SECUNDARIA COMUNITARIA DE CONAFE"                               "MATUTINO"   "NO" 0    0 . 1 . 0 0
"01KTV0018D" "SECUNDARIA COMUNITARIA DE CONAFE"                               "MATUTINO"   "NO" 0    0 . 1 . 0 0
"02DES0005J" "MTRO JAVIER M ZU�IGA NUM. 4"                                    "MATUTINO"   "SI" 1    0 . 1 . 0 0
"02DES0018N" "SECUNDARIA 5 IGNACIO MANUEL ALTAMIRANO"                         "MATUTINO"   "SI" 1 .021 . 1 . 0 0
"02DES0018N" "SECUNDARIA 5 IGNACIO MANUEL ALTAMIRANO"                         "VESPERTINO" "SI" 1    0 . 1 . 0 0
"02DES0022Z" "ESCUELA SECUNDARIA GENERAL NUM. 11 ABELARDO L. RODRIGUEZ"       "MATUTINO"   "SI" 1  .01 . 1 . 0 0
"02DES0022Z" "ESCUELA SECUNDARIA GENERAL NUM. 11 ABELARDO L. RODRIGUEZ"       "VESPERTINO" "SI" 1 .034 . 1 . 0 0
"02DES0051V" "ESCUELA SECUNDARIA GENERAL NUMERO 24"                           "MATUTINO"   "SI" 1    0 . 1 . 0 0
"02DES0052U" "ESCUELA GENERAL NUMERO 25"                                      "MATUTINO"   "SI" 1 .154 . 1 . 0 0
"02DES0054S" "ESCUELA SECUNDARIA GENERAL NO. 27"                              "MATUTINO"   "SI" 1    0 . 1 . 0 0
"02DES0057P" "ESCUELA SECUNDARIA GENERAL  28"                                 "MATUTINO"   "SI" 1    0 . 1 . 0 0
"02DES0058O" "ESCUELA SECUNDARIA GENERAL  29"                                 "MATUTINO"   "SI" 1    0 . 1 . 0 0
"02DES0060C" "ESCUELA SECUNDARIA GENERAL31"                                   "MATUTINO"   "SI" 1    0 . 1 . 0 0
"02DPB0001T" "UNIDAD Y PROGRESO"                                              "MATUTINO"   "ND" .    0 . 1 . 0 .
"02DPB0060I" "LEYES DE REFORMA"                                               "VESPERTINO" "ND" . .095 . 1 . 0 .
"02DPB0061H" "LUIS DONALDO COLOSIO MURRIETA"                                  "MATUTINO"   "SI" 1 .074 . 1 . 0 0
"02DPB0065D" "VALENTIN GOMEZ FARIAS"                                          "MATUTINO"   "SI" 1    0 . 1 . 0 0
"02DPB0070P" "TZAUINDANDA"                                                    "MATUTINO"   "SI" 1    0 . 1 . 0 0
"02DPB0071O" "TIERRA Y LIBERTAD"                                              "MATUTINO"   "SI" 1 .045 . 1 . 0 0
"02DPB0076J" "BICENTENARIO"                                                   "MATUTINO"   "SI" 1    0 . 1 . 0 0
"02DPB0081V" "GERTRUDIS BOCANEGRA"                                            "VESPERTINO" "SI" 1 .143 . 1 . 0 0
"02DPB0082U" "LA PATRIA ES PRIMERO"                                           "MATUTINO"   "SI" 1 .071 . 1 . 0 0
"02DPB0084S" "NUEVA CREACION"                                                 "MATUTINO"   "SI" 1    0 . 1 . 0 0
"02DPB0085R" "ANGELA VERDUZCO GALVAN"                                         "MATUTINO"   "SI" 1    0 . 1 . 0 0
"02DPB0087P" "NUEVA CREACION"                                                 "MATUTINO"   "SI" 1    0 . 1 . 0 0
"02DPR0003S" "GABRIELA MISTRAL"                                               "VESPERTINO" "SI" 1 .175 . 1 . 0 0
"02DPR0110A" "RAFAEL MORALES GUTIERREZ"                                       "MATUTINO"   "ND" .  .05 . 1 . 0 .
"02DPR0111Z" "13 DE SEPTIEMBRE DE 1847"                                       "MATUTINO"   "SI" 1 .042 . 1 . 0 0
"02DPR0162G" "JOSE E AMADOR"                                                  "MATUTINO"   "SI" 1    0 . 1 . 0 0
"02DPR0182U" "PABLO NERUDA"                                                   "VESPERTINO" "SI" 1    0 . 1 . 0 0
"02DPR0190C" "TEHUANTEPEC"                                                    "MATUTINO"   "ND" .  .05 . 1 . 0 .
"02DPR0256V" "VALENTIN GOMEZ FARIAS"                                          "MATUTINO"   "SI" 1 .091 . 1 . 0 0
"02DPR0274K" "LA MISION"                                                      "MATUTINO"   "SI" 1 .037 . 1 . 0 0
"02DPR0292Z" "MIGUEL HIDALGO"                                                 "MATUTINO"   "SI" 1 .328 . 1 . 0 0
"02DPR0327Z" "FELIPE CARRILLO PUERTO"                                         "VESPERTINO" "SI" 1 .043 . 1 . 0 0
"02DPR0360G" "PROF. ENRIQUE CORONA"                                           "MATUTINO"   "ND" . .083 . 1 . 0 .
"02DPR0386O" "MTRO JUSTO SIERRA MENDEZ"                                       "MATUTINO"   "SI" 1    . . 1 . 0 0
"02DPR0428X" "VICENTE GUERRERO"                                               "VESPERTINO" "SI" 1 .133 . 1 . 0 0
"02DPR0434H" "GABRIELA MISTRAL"                                               "MATUTINO"   "SI" 1 .125 . 1 . 0 0
"02DPR0478E" "V AYUNTAMIENTO"                                                 "MATUTINO"   "SI" 1 .097 . 1 . 0 0
"02DPR0480T" "NI�OS HEROES DE CHAPULTEPEC"                                    "MATUTINO"   "SI" 1 .052 . 1 . 0 0
"02DPR0482R" "ING. ELIGIO ESQUIVEL MENDEZ"                                    "MATUTINO"   "SI" 1    0 . 1 . 0 0
"02DPR0492Y" "CRISTOBAL COLON"                                                "VESPERTINO" "SI" 1 .089 . 1 . 0 0
"02DPR0510X" "PADRE SALVATIERRA"                                              "MATUTINO"   "SI" 1 .222 . 1 . 0 0
"02DPR0515S" "CENTENARIO DE LA REVOLUCION MEXICANA"                           "MATUTINO"   "SI" 1 .039 . 1 . 0 0
"02DPR0653U" "EVA SAMANO"                                                     "MATUTINO"   "SI" 1 .036 . 1 . 0 0
"02DPR0676E" "MARCELINO MAGANA MEJIA"                                         "MATUTINO"   "SI" 1    . . 1 . 0 0
"02DPR0694U" "NI�O ARTILLERO"                                                 "MATUTINO"   "SI" 1 .224 . 1 . 0 0
"02DPR0730I" "AGAPITO GALINDO PLASCENCIA"                                     "VESPERTINO" "SI" 1   .2 . 1 . 0 0
"02DPR0744L" "JOSE SANTOS VALDEZ"                                             "MATUTINO"   "SI" 1 .132 . 1 . 0 0
"02DPR0798P" "RAMON  ALCARAZ GUTIERREZ"                                       "VESPERTINO" "SI" 1 .074 . 1 . 0 0
"02DPR0830H" "18 DE MARZO"                                                    "VESPERTINO" "ND" . .053 . 1 . 0 .
"02DPR0888H" "LAS MISIONES"                                                   "MATUTINO"   "SI" 1 .014 . 1 . 0 0
"02DPR0889G" "IGNACIO ALDAMA"                                                 "VESPERTINO" "NO" 0 .052 . 1 . 0 0
"02DPR0895R" "NUEVA CREACION"                                                 "VESPERTINO" "ND" .    0 . 1 . 0 .
"02DPR0904I" "NUEVA CREACION"                                                 "MATUTINO"   "SI" 1    0 . 1 . 0 0
"02DPR0907F" "NUEVA CREACION"                                                 "MATUTINO"   "SI" 1 .011 . 1 . 0 0
"02DPR0908E" "NUEVA CREACION"                                                 "VESPERTINO" "SI" 1 .073 . 1 . 0 0
"02DPR0914P" "NUEVA CREACION"                                                 "VESPERTINO" "SI" 1    0 . 1 . 0 0
"02DST0005B" "ESCUELA SECUNDARIA TECNICA 5"                                   "MATUTINO"   "SI" 1    0 . 1 . 0 0
"02DST0034X" "ESCUELA SECUNDARIA TECNICA NUM. 33"                             "MATUTINO"   "SI" 1 .023 . 1 . 0 0
"02DST0049Z" "SECUNDARIA TECNICA NUMERO 51"                                   "VESPERTINO" "SI" 1    0 . 1 . 0 0
"02DST0050O" "ESCUELA SECUNDARIA TECNICA NO. 52"                              "MATUTINO"   "ND" .    0 . 1 . 0 .
"02DTV0006O" "TELESECUNDARIA NUMERO 102"                                      "MATUTINO"   "SI" 1    0 . 1 . 0 0
"02DTV0007N" "TELESECUNDARIA 103"                                             "MATUTINO"   "SI" 1 .077 . 1 . 0 0
"02DTV0009L" "TELESECUNDARIA NO 105"                                          "MATUTINO"   "SI" 1 .333 . 1 . 0 0
"02DTV0011Z" "TELESECUNDARIA NO 107"                                          "MATUTINO"   "SI" 1    0 . 1 . 0 0
"02DTV0015W" "TELESECUNDARIA NO. 111"                                         "MATUTINO"   "SI" 1    0 . 1 . 0 0
"02DTV0017U" "TELESECUNDARIA NO. 113"                                         "MATUTINO"   "SI" 1    0 . 1 . 0 0
"02DTV0018T" "TELESECUNDARIA NO. 114"                                         "MATUTINO"   "SI" 1    0 . 1 . 0 0
"02DTV0020H" "TELESECUNDARIA NO. 116"                                         "MATUTINO"   "SI" 1    . . 1 . 0 0
"02EES0003K" "SECUNDARIA NUM. 112"                                            "MATUTINO"   "ND" .    0 . 1 . 0 .
"02EES0007G" "GUELATAO NUM. 14"                                               "MATUTINO"   "SI" 1    0 . 1 . 0 0
"02EES0010U" "EMILIANO ZAPATA NUM. 26"                                        "MATUTINO"   "SI" 1    0 . 1 . 0 0
"02EES0020A" "DR. FEDERICO MARTINEZ MANAUTOU NUM. 42"                         "MATUTINO"   "ND" .    0 . 1 . 0 .
"02EES0035C" "FRANCISCO SANTANA PERALTA NUM. 65"                              "MATUTINO"   "SI" 1 .041 . 1 . 0 0
"02EES0055Q" "ESCUELA SECUNDARIA GENERAL NO. 210"                             "MATUTINO"   "ND" .    0 . 1 . 0 .
"02EES0074E" "ESCUELA SECUNDARIA GENERAL 215 FORJADORES DE ROSARITO"          "MATUTINO"   "ND" .    0 . 1 . 0 .
"02EES0086J" "PROFA. JOSEFINA RENDON PARRA NUM. 82"                           "MATUTINO"   "ND" . .025 . 1 . 0 .
"02EES0096Q" "ESCUELA SECUNDARIA GENERAL NUM. 66 MARIA ROSALVA FELIX BELTRAN" "MATUTINO"   "SI" 1    0 . 1 . 0 0
"02EES0125V" "PROF. OTILIO MONTANO NUM. 83"                                   "MATUTINO"   "ND" . .014 . 1 . 0 .
end

And when I run the regression this is what I get:

regress logro_mate_porcentalum_nivel4_15 beneficiaria_dum after_dum DD
note: after_dum omitted because of collinearity
note: DD omitted because of collinearity

      Source |       SS           df       MS      Number of obs   =     7,451
-------------+----------------------------------   F(1, 7449)      =      2.30
       Model |  1011.73056         1  1011.73056   Prob > F        =    0.1291
    Residual |  3271530.39     7,449  439.190547   R-squared       =    0.0003
-------------+----------------------------------   Adj R-squared   =    0.0002
       Total |  3272542.12     7,450  439.267398   Root MSE        =    20.957

----------------------------------------------------------------------------------
logro_mate_~4_15 |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-----------------+----------------------------------------------------------------
beneficiaria_dum |    1.76085   1.160156     1.52   0.129    -.5133837    4.035084
       after_dum |          0  (omitted)
              DD |          0  (omitted)
           _cons |   6.631287   1.133218     5.85   0.000     4.409859    8.852714
----------------------------------------------------------------------------------

I hope you can help me, or let me know if there is something more that I have to post.

Thanks again in advance.

[Clyde Schechter]

Thank you. The data example you posted is not workable: the variable DD takes on only the value 0, other than being missing in 15 observations. Now, if that's also true in your whole data set, that explains why it would be omitted: if it doesn't vary it's colinear with the constant and it's gone. But if that's true, then you have done something very wrong in calculating DD. The same is true of variable after_dum.

But what I actually get in trying to run your code with this data example is a "no observations" error message. This is due to missing values. Bear in mind that any observation in the data set that has a missing value for any of the variables mentioned in the regression command will be omitted from the calculations. In this case, every single observation in your data set is missing one of these variables. It may be that in your real data, the pattern of missing data is such that all observations with all non-missing values for the regression variables have the same value of DD--which would lead to its being non-varying and colinaer with the constant, hence omitted. One preliminary step in investigating this is to note that the regression output shows a sample size of 7,451. How does that compare with the total number of observations in your data set? Are you losing enormous numbers of observations here? Try running this in the whole data set:

tab DD if !missing(logro_mate_porcentalum_nivel4_15, beneficiaria_dum, after_dum)

and you will see if DD actually varies among the observations that the regression can include.

I also notice that dummy_2015 has exclusively missing values in this example, whereas dummy_2013 is always 1. This leads me to think that when you created these two variables you coded them as 1 vs missing value. That is almost always a recipe for trouble in Stata. In all but rare circumstances, the useful way to code dichotomous variables is 1 vs 0, not 1 vs missing. And it may well be that those missing values are messing up your calculations of after_dum and DD. When creating a dichotomous variable in Stata, only use missing values for those observations where it is not possible to determine which of the two classes the observation belongs on. Do not use missing value to code one of the actual classes--that technique causes lots of trouble in Stata except in very special circumstances which do not apply here.

Another quick observation: the variable beneficiaria_14 takes on three values, "SI", "NO", and "ND". Is "ND" a typographical error for "NO" or is it truly a third category?

Finally, I recommend that you not do your own calculation of interaction variables. It is error-prone, and the results you get will be somewhat complicated to interpret. If I were doing this project, I would do it something like this:

gen byte pre_post = (dummy2015 == 1)
replace pre_post = . if missing(dummy2015, dummy2013)
regress logro_mate_porcentalum_nivel4_15 i.pre_post##i.beneficiaria_dum

The difference in differences estimator of treatment effect will be the coefficient of 1.pre_post#1.beneficiaria_dum. If you want statistics on the expected outcomes in each group, before and after treatment, you can get that with

margins pre_post#beneficiaria_dum

If you want to see the change in outcome separately in each group:

margins beneficiaria_dum, dydx(pre_post)

But before even trying my code, do check your data set over very carefully, as I am inclined to believe it contains a number of problems outlined above. If the data are not right, no code will get you useful results.

[Carlos Noyola]

Clyde:
Thank you for your detailed answer. Variables DD and after_dum do not only take on the value of 0, but only zeros appear in the observations I put. How can I tell command to show obeservations from both?
Here is the output for the code you gave me:

 tab DD if !missing(logro_mate_porcentalum_nivel4_15, beneficiaria_dum, after_dum)

         DD |      Freq.     Percent        Cum.
------------+-----------------------------------
          0 |        342        4.59        4.59
          1 |      7,109       95.41      100.00
------------+-----------------------------------
      Total |      7,451      100.00

I am losing almost 70% of the observations.

About dummy2013 and dummy2015: I created separately in order to create the after treatment dummy. First I matched schools considered for aid with their 2013 results and assigned a value of 1 to all of them, and in another do-file I matched schools to their 2015 results, and created dummy2015 with a value of 1 for all, so when I use append to combine databases, dummy2013 gets missing for all observations that have 1 in dummy2015, and viceversa (the school database that I used is the same, but some schools only matched to results in one year). That is why the regression that you suggest me is not working when I run it, because every observation either has a one for dummy2013 or dummy2015, but never missing in both. What can I do?

[Clyde Schechter]

Well, from your description, I now understand how you created dummy2013 and dummy2015. It's not what I would have done, but it's not lethal, and now I think it is not the cause of your problems.

First verify that benificiaria_dum takes on both 0 and 1 values in your actual data. Then do

gen byte pre_post = (dummy2015 == 1)
tab pre_post beneficiaria_dum

and verify that you have some observations for all four combinations of those two variables.


If you do, you can run

regress logro_mate_porcentalum_nivel4_15 i.pre_post##i.beneficiaria_dum

and no variables ought to be excluded for colinearity. Refer to the final three paragraphs of #4 for additional information about interpreting the results.

If you do get some variables omitted for colinearity, then it will be due to missing values. Run

tab pre_post beneficiaria_dum if e(sample)

to see what combination(s) are missing. As pre_post will have no missing values, and presumably beneficiaria_dum has few or none, the problem will be missing values of logro_mate_porecentalum_nivel4_15 patterning in such a way that you are left with a defective subsample of the data.

Even assuming everything runs without difficulty, pay attention to the number of observations reported in the regression output. If it is substantially smaller than the size of your data set, then you have a problem just from that: if large amounts of data are missing you need a good understanding of why they are missing so you can try to figure out whether the results are usable or not.

[Carlos Noyola]

I get this:

 tab pre_post beneficiaria_dum if e(sample)

           |   beneficiaria_dum
  pre_post |         0          1 |     Total
-----------+----------------------+----------
         1 |       342      7,109 |     7,451 
-----------+----------------------+----------
     Total |       342      7,109 |     7,451

which means that I have no observations for the year before the reform (either receiving or no receiving aid), right? And therefore the data is not usable, right?

[Clyde Schechter]

Correct. Now, the question is why this happened. If the original data you got contained observations from the year before, then either you somehow lost those observations somewhere in data management, or you miscoded them, or the observations in the original data didn't include the variable logro_mate_porcentalum_nivel4_15.

You need to go back and review the data management, starting with the original data you received and checking every step along the way to see what happened.

[Carlos Noyola]

I think I fixed the problem, I had logro_mate_porcentalum_nivel4_15 and logro_mate_porcentalum_nivel4_13, that is, results for 2013 and 2015, and I was running the regression for the results of 2015. The problem is that by definition, every observation has results either for 2013 or for 2015, but not for both, and since the idea is to compare (as if to say that the standardized test is the same in both years) I have to treat both outcome variables as the same variable, obviously without affecting the dummies for 2013 or 2015. Then, using your code I get:

regress logro_mate_porcentajealum_nivel4 i.pre_post##i.beneficiaria_dum

      Source |       SS           df       MS      Number of obs   =    21,792
-------------+----------------------------------   F(3, 21788)     =    740.92
       Model |  333810.044         3  111270.015   Prob > F        =    0.0000
    Residual |  3272063.94    21,788  150.177343   R-squared       =    0.0926
-------------+----------------------------------   Adj R-squared   =    0.0924
       Total |  3605873.99    21,791  165.475379   Root MSE        =    12.255

-------------------------------------------------------------------------------------------
logro_mate_porcentajeal~4 |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
--------------------------+----------------------------------------------------------------
               1.pre_post |   6.605387   .7424765     8.90   0.000     5.150079    8.060695
       1.beneficiaria_dum |   .0519173   .3517196     0.15   0.883    -.6374787    .7413133
                          |
pre_post#beneficiaria_dum |
                     1 1  |   1.708933    .764164     2.24   0.025     .2111157     3.20675
                          |
                    _cons |   .0258992   .3348975     0.08   0.938    -.6305243    .6823227
-------------------------------------------------------------------------------------------

Is this correct?
If it is, one last question: my outcome variable is the percentage of students of the school that have scores in the highest level of attainment of the test (according to the government classification), so this would say that treated schools have, on average, 1.7 per cent more percentage of students in the highest level of attainment? or 1.7 more percentage points more students in the highest level of attainment?

[Clyde Schechter]

Yes, these results look sensible to me. As I don't really understand the variables, etc., I'll refrain from giving an opinion as to whether or not they are "correct." There may be aspects of the problem that have been overlooked, etc., that I wouldn't know anything about. But this looks like a correct implementation of the model you have selected.

The result should be interpreted as the treated schools experienced an increase in percentage of students in the highest level of attainment of 1.7 percentage points more than the untreated schools did following the intervention. Differences in percentages are denominated in percentage points.