Future covariate on the right hand side

[Valentina Rutigliano]

Dear Statalist,

I have a panel of individuals, some of whom are treated at a future date and some of whom are not. The treatment is a voluntary decision, rather than randomly assigned. Let's say treatment is equal to migration at some point in the future.
This is a minimum data example:

* Example generated by -dataex-. For more info, type help dataex
clear
input float(ID year treatment income) str8 marst float group_marst
1 2003 1 10000 "single"   3
1 2004 1 15000 "married"  2
1 2005 1 12000 "divorced" 1
1 2006 1 14000 "married"  2
1 2007 1 16000 "married"  2
1 2008 1 16000 "married"  2
2 2001 0  8000 "single"   3
2 2004 0  7000 "single"   3
2 2005 0  6000 "single"   3
3 2007 0  7500 "divorced" 1
4 2008 0   990 "single"   3
4 2009 0  8900 "married"  2
4 2010 0  5400 "married"  2
4 2011 0  6000 "married"  2
4 2013 0  5000 "divorced" 1
5 2005 1 25000 "single"   3
5 2007 1 18000 "married"  2
5 2009 1 17500 "married"  2
5 2010 1 16500 "married"  2
end

I want to compare the treated and control group along some covariates, for example I want to know whether many years before migration future migrants had a higher or lower income than non-migrants, controlling for other factors.
I do not want to study the effect of income on the decision to migrate; I am just interested in seeing whether the two groups are different along the income dimension.
I could estimate the following:

reg income treatment i.year i.group_marst

By doing so, I am putting on the right hand side a future outcome which happens after the dependent variable on the left hand side is realized. In general, this sounds questionable, but I think it might be alright in this case since I am not trying to estimate the effect of x on y.
I am not sure how else to put this problem and I would appreciate some suggestion or reference. I have been referred to Cox time dependent covariates but it doesn't sound very related.
Thank you!

[Carlo Lazzaro]

Valentina:
difference-in-difference regression may be the way to go (see

https://www.princeton.edu/~otorres/DID101.pdf).

. reg income i.treatment##c.year

      Source |       SS           df       MS      Number of obs   =        19
-------------+----------------------------------   F(3, 15)        =     14.22
       Model |   482333648         3   160777883   Prob > F        =    0.0001
    Residual |   169622026        15    11308135   R-squared       =    0.7398
-------------+----------------------------------   Adj R-squared   =    0.6878
       Total |   651955674        18  36219759.6   Root MSE        =    3362.8

----------------------------------------------------------------------------------
          income | Coefficient  Std. err.      t    P>|t|     [95% conf. interval]
-----------------+----------------------------------------------------------------
     1.treatment |   -1453624    1196410    -1.21   0.243     -4003712     1096463
            year |  -200.0396   317.4359    -0.63   0.538    -876.6382     476.559
                 |
treatment#c.year |
              1  |   729.3189    596.199     1.22   0.240    -541.4493    2000.087
                 |
           _cons |   407678.4   637271.2     0.64   0.532    -950633.1     1765990
----------------------------------------------------------------------------------

.

2) as far as the future income flows are concerned, they should be discounted via a real social discount rate (3% on annual basis) (http://global.oup.com/academic/produ...&lang=en&cc=it ; page 244).