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      name:  <unnamed>
       log:  /Users/bernardofanfani/Desktop/teaching/research_topics_labor/lab_4/fourth_lab/example_late.log
  log type:  text
 opened on:   1 Nov 2024, 10:45:08

. 
. *********
. * ESTIMATING LATE WITH AN RCT
. 
. use "rapporti_lavoro_2001.dta", clear

. 
. su retrib03

    Variable |        Obs        Mean    Std. dev.       Min        Max
-------------+---------------------------------------------------------
    retrib03 |    610,951    37372.78     24332.5        479     399924

. 
. * define a treatment that gives a positive shock on income of approximately 10%, and which has a given variability across individuals (10
> % of the income standard deviation)
. ge treatment=rnormal(`r(mean)'/10, `r(sd)'/10)

. 
. * there is a lottery that gives access to the treatment with 50% probability
. ge lottery=runiform()<.5

. * however, only 50% of the lottery winners actually get the treatment (the compliers)
. ge compliers=runiform()<.5 & lottery==1

. 
. * thus, only compliers have non-zero treatment effect
. replace treatment = 0 if compliers!=1
(457,894 real changes made)

. 
. * let's add the treatment effect to the income variable
. replace retrib03=retrib03+treatment
(153,057 real changes made)

. 
. * expected LATE
. su treatment if compliers

    Variable |        Obs        Mean    Std. dev.       Min        Max
-------------+---------------------------------------------------------
   treatment |    153,057    3729.075    2438.309  -7245.364   14267.17

. * expected Intent to Treat
. su treatment if lottery

    Variable |        Obs        Mean    Std. dev.       Min        Max
-------------+---------------------------------------------------------
   treatment |    305,826    1866.293    2540.073  -7245.364   14267.17

. 
. * let's check if the ITT and LATE models estimate the correct parameter
. reg retrib03 lottery

      Source |       SS           df       MS      Number of obs   =   610,951
-------------+----------------------------------   F(1, 610949)    =    869.87
       Model |  5.1778e+11         1  5.1778e+11   Prob > F        =    0.0000
    Residual |  3.6366e+14   610,949   595244366   R-squared       =    0.0014
-------------+----------------------------------   Adj R-squared   =    0.0014
       Total |  3.6418e+14   610,950   596090899   Root MSE        =     24398

------------------------------------------------------------------------------
    retrib03 | Coefficient  Std. err.      t    P>|t|     [95% conf. interval]
-------------+----------------------------------------------------------------
     lottery |   1841.202   62.42733    29.49   0.000     1718.847    1963.558
       _cons |   37385.34    44.1681   846.43   0.000     37298.78    37471.91
------------------------------------------------------------------------------

. ivregress 2sls retrib03 (compliers=lottery)

Instrumental variables 2SLS regression            Number of obs   =    610,951
                                                  Wald chi2(1)    =     872.43
                                                  Prob > chi2     =     0.0000
                                                  R-squared       =     0.0044
                                                  Root MSE        =      24362

------------------------------------------------------------------------------
    retrib03 | Coefficient  Std. err.      z    P>|z|     [95% conf. interval]
-------------+----------------------------------------------------------------
   compliers |    3678.94   124.5539    29.54   0.000     3434.819    3923.061
       _cons |   37385.34   44.10319   847.68   0.000      37298.9    37471.78
------------------------------------------------------------------------------
Instrumented: compliers
 Instruments: lottery

. 
. log close
      name:  <unnamed>
       log:  /Users/bernardofanfani/Desktop/teaching/research_topics_labor/lab_4/fourth_lab/example_late.log
  log type:  text
 closed on:   1 Nov 2024, 10:45:10
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