Sharp RDD - Restrict by age cohort

[Cat Santos]

Dear Statalist Community,

I am trying to run a sharp regression discontinuity design (RDD), however I am unsure about how to operationalise my running variable.

I want to assess the impact of a territorial occupation in 1940 on individuals who were between 7 to 14 years old at that time, using survey data from 1990. I believe a sharp RDD is more appropriate than a fuzzy RDD for my study because there was no possibility to opt out of the treatment (the occupation), as it occurred throughout the entire country. The running variable I have chosen is the year in which respondents turned 15. My logic is that individuals who were 15 at the start of the occupation in 1940 were the last cohort not exposed to the treatment, whereas those who turned 15 in 1931, a year after the occupation began, had been exposed to the treatment for one year (when they were 14 years old in 1940).

However, I am unsure how to operationalize the criterion that individuals must be older than 7 years to be considered exposed to the treatment. Is that possible to do with an RDD?

rdplot dv1 yearat15 , c(1940) all 

Thank you very much.

Best wishes,
Cat

[Jared Greathouse]

Data example please.

[Cat Santos]

Apologies: here it goes.

gen yearat15 = birthyear + 15

id    dv1    birthyear    yearat15
606403    0    1956    1971
606404    1    1943    1958
606405    0    1950    1965
606406    0    1967    1982
606407    0    1938    1953
606408    0    1984    1999
606409    1    1932    1947
606410    0    1975    1990
606411    0    1950    1965
606412    0    1942    1957
606413    0    1977    1992
606414    0    1966    1981
606415    0    1966    1981
606416    0    1939    1954
606417    0    1938    1953
606418    0    1984    1999
606419    0    1956    1971
606421    0    1969    1984
606425    0    1967    1982
606426    0    1950    1965
606427    0    1947    1962
606428    0    1949    1964

I was now wondering if I should be using a regression kink design. The years of schooling before the occupation is constant until 1940 (14 years). After that date, each additional year of exposure to the educational system after the occupation will have a different effect on my outcome variable. The number of years individuals have spent in school after the occupation is a continuous function of the year of their birth, and will decrease year after year after 1940.

My goal is to determine the impact of attending school between 7 and 14 years old before the occupation versus after, as the exposure to the new school system will have an important impact on individual economic/political preferences (my outcomes).

However, I don't know how to operationalize that using Stata... or if thats the best way to go about it.

Thank you so much.

Best regards,
Cat

[Cat Santos]

I forgot to add the actual model:

rdrobust dv1 yearat15, c(1940) p(1) 

. rdrobust dv1 yearat15, c(1940) p(1)
Mass points detected in the running variable.

Sharp RD estimates using local polynomial regression.

   Cutoff c = 1940 | Left of c  Right of c            Number of obs =       2310
-------------------+----------------------            BW type       =      mserd
     Number of obs |        55        2255            Kernel        = Triangular
Eff. Number of obs |        34         154            VCE method    =         NN
    Order est. (p) |         1           1
    Order bias (q) |         2           2
       BW est. (h) |     5.771       5.771
       BW bias (b) |     8.242       8.242
         rho (h/b) |     0.700       0.700
        Unique obs |        14          58

Outcome: dv1. Running variable: yearat15.
--------------------------------------------------------------------------------
            Method |   Coef.    Std. Err.    z     P>|z|    [95% Conf. Interval]
-------------------+------------------------------------------------------------
      Conventional | -.37848      .1732   -2.1853  0.029   -.717944     -.039021
            Robust |     -          -     -2.0062  0.045   -.946315      -.01103
--------------------------------------------------------------------------------
Estimates adjusted for mass points in the running variable.

And my attempt at a regression kink design (I'm aware the results are not significant, but wanted to understand if the intuition makes sense)

 rdrobust dv1 yearat15, c(1940) p(1) deriv(1)

. rdrobust dv1 yearat15, c(1940) p(1) deriv(1)
Mass points detected in the running variable.

Sharp Kink RD estimates using local polynomial regression.

   Cutoff c = 1940 | Left of c  Right of c            Number of obs =       2310
-------------------+----------------------            BW type       =      mserd
     Number of obs |        55        2255            Kernel        = Triangular
Eff. Number of obs |        34         154            VCE method    =         NN
    Order est. (p) |         1           1
    Order bias (q) |         2           2
       BW est. (h) |     5.217       5.217
       BW bias (b) |     8.242       8.242
         rho (h/b) |     0.633       0.633
        Unique obs |        14          58

Outcome: dv1. Running variable: yearat15.
--------------------------------------------------------------------------------
            Method |   Coef.    Std. Err.    z     P>|z|    [95% Conf. Interval]
-------------------+------------------------------------------------------------
      Conventional |  -.1071     .07324   -1.4623  0.144   -.250644      .036448
            Robust |     -          -     -1.2497  0.211    -.52888      .117027
--------------------------------------------------------------------------------
Estimates adjusted for mass points in the running variable.

Thank you very much.