rdrobust and reg do not yield same results

[Lea Berg]

Hello Stata community,

I'm trying to implement an RDD design and am following Cattaneo et al. (2019). Following their paper,

reg y x T c.x#i.T
rdrobust y x, kernel(uniform) p(1)

should yield the same coefficient for T - this works with test data but not with my actual data. Below you find my output. Any idea what the problem might be? I'm using STATA version 16.

. reg y x T c.x#i.T

      Source |       SS           df       MS      Number of obs   =     3,214
-------------+----------------------------------   F(3, 3210)      =      1.84
       Model |  .440886445         3  .146962148   Prob > F        =    0.1382
    Residual |  256.816114     3,210   .08000502   R-squared       =    0.0017
-------------+----------------------------------   Adj R-squared   =    0.0008
       Total |  257.257001     3,213  .080067538   Root MSE        =    .28285

------------------------------------------------------------------------------
           y |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
           x |   .0002407   .0012055     0.20   0.842     -.002123    .0026044
           T |  -.0313921   .0218523    -1.44   0.151     -.074238    .0114538
             |
       T#c.x |
          1  |   .0003826   .0021991     0.17   0.862    -.0039291    .0046943
             |
       _cons |   .0990177   .0135144     7.33   0.000     .0725199    .1255154
------------------------------------------------------------------------------

.
.
. rdrobust y x, kernel(uniform) p(1) h(200) c(0) masspoints(adjust)

Sharp RD estimates using local polynomial regression.

      Cutoff c = 0 | Left of c  Right of c            Number of obs =       3214
-------------------+----------------------            BW type       =     Manual
     Number of obs |      1955        1259            Kernel        =    Uniform
Eff. Number of obs |      1955        1259            VCE method    =         NN
    Order est. (p) |         1           1
    Order bias (q) |         2           2
       BW est. (h) |   200.000     200.000
       BW bias (b) |   200.000     200.000
         rho (h/b) |     1.000       1.000

Outcome: y. Running variable: x.
--------------------------------------------------------------------------------
            Method |   Coef.    Std. Err.    z     P>|z|    [95% Conf. Interval]
-------------------+------------------------------------------------------------
      Conventional |  -.0438     .02038   -2.1488  0.032   -.083744     -.003849
            Robust |     -          -     -1.4766  0.140   -.108161      .015214
--------------------------------------------------------------------------------

sum y x T

    Variable |        Obs        Mean    Std. Dev.       Min        Max
-------------+---------------------------------------------------------
           y |      3,214    .0877411    .2829621          0          1
           x |      3,214   -3.172993     10.0653        -19         17
           T |      3,214     .372122    .4834459          0          1

Thank you in advance!

[Øyvind Snilsberg]

please use the -dataex- command to show a data example that reproduces the problem.

[Lea Berg]

Here is the data example:

id wave x T y yT
  111000 1 -16 0 1  0
 1299000 2  -3 0 0  0
 1300000 3  13 1 1 13
 1624000 3   9 1 0  9
 1818000 1 -17 0 0  0
 1993000 3  16 1 0 16
 2088000 1 -13 0 1  0
 2322000 3  13 1 0 13
 2767000 1 -18 0 0  0
 2931000 3  10 1 0 10
 3023000 1 -13 0 0  0
 3134000 3  13 1 0 13
 3450000 1 -15 0 0  0
 3491000 1 -14 0 0  0
 3902000 1 -18 0 0  0
 4189000 1 -15 0 0  0
 4273000 2   0 0 0  0
 4330000 1 -14 0 1  0
 4548000 1 -13 0 0  0
 4814000 3  15 1 0 15
 4835000 1  -9 0 0  0
 5559000 1 -13 0 1  0
 5678000 3  12 1 0 12
 5780000 2   1 1 0  1
 6008000 3   9 1 0  9
 6151000 2  -4 0 0  0
 6519000 1 -18 0 0  0
 6780000 1 -14 0 0  0
 7167000 2   4 1 0  4
 7256000 2  -2 0 0  0
 7586000 3   9 1 0  9
 7656000 1 -11 0 0  0
 7892000 1 -18 0 0  0
 8075000 1  -4 0 0  0
 8075000 2  -4 0 0  0
 8807000 1 -11 0 0  0
 8948000 2  -3 0 0  0
 9161000 1  -9 0 0  0
 9657000 1 -10 0 0  0
 9729000 2  -4 0 0  0
 9917000 3  15 1 0 15
 9980000 2  -3 0 0  0
10208000 2  -6 0 0  0
10564000 1 -16 0 0  0
10578000 1 -16 0 0  0
10665000 3  11 1 0 11
10789000 2   2 1 0  2
10809000 2   0 0 0  0
10957000 1 -16 0 1  0
11295000 3   6 1 0  6
11585000 1  -6 0 0  0
11714000 1 -14 0 0  0
12027000 1 -17 0 0  0
12101000 2   0 0 0  0
12266000 3   7 1 0  7
12490000 2   1 1 0  1
13345000 1  -7 0 0  0
13588000 2   6 1 0  6
13588000 3   6 1 0  6
13937000 2   1 1 0  1
14066000 1 -16 0 0  0
14660000 1 -13 0 0  0
14685000 1 -12 0 0  0
14722000 2  -3 0 0  0
14898000 1 -15 0 0  0
15310000 1 -15 0 0  0
15350000 1 -16 0 0  0
15595000 1 -11 0 0  0
15701000 1 -15 0 0  0
15975000 1 -10 0 0  0
16373000 1  -4 0 0  0
16373000 2  -4 0 0  0
16441000 1  -8 0 0  0
16512000 2   2 1 0  2
16671000 1 -15 0 0  0
16829000 2   1 1 0  1
17018000 1  -6 0 0  0
17154000 1 -16 0 0  0
17261000 3   9 1 0  9
17464000 1  -5 0 0  0
17663000 1 -17 0 0  0
18011000 1 -16 0 0  0
18129000 3  11 1 0 11
18494000 2  -3 0 0  0
18850000 1 -16 0 0  0
19562000 3  11 1 0 11
19656000 2  -1 0 1  0
19673000 1 -14 0 0  0
20041000 2   0 0 0  0
20226000 1 -11 0 0  0
20277000 1 -10 0 0  0
20839000 3  13 1 0 13
20970000 1 -17 0 0  0
21256000 3  14 1 0 14
21446000 2   6 1 0  6
21454000 1 -14 0 0  0
21637000 2  -5 0 0  0
21830000 1 -16 0 0  0
21888000 3   9 1 0  9
22234000 3  10 1 0 10

[Øyvind Snilsberg]

. rdrobust y x, kernel(uniform) p(1) h(200)

Sharp RD estimates using local polynomial regression.

      Cutoff c = 0 | Left of c  Right of c            Number of obs =        100
-------------------+----------------------            BW type       =     Manual
     Number of obs |        65          35            Kernel        =    Uniform
Eff. Number of obs |        65          35            VCE method    =         NN
    Order est. (p) |         1           1
    Order bias (q) |         2           2
       BW est. (h) |   200.000     200.000
       BW bias (b) |   200.000     200.000
         rho (h/b) |     1.000       1.000

Outcome: y. Running variable: x.
--------------------------------------------------------------------------------
            Method |   Coef.    Std. Err.    z     P>|z|    [95% Conf. Interval]
-------------------+------------------------------------------------------------
      Conventional | -.07176     .08091   -0.8869  0.375   -.230346      .086818
            Robust |     -          -     -0.4919  0.623   -.548734      .328566
--------------------------------------------------------------------------------

. reg y x T c.x#i.T, noheader
------------------------------------------------------------------------------
           y | Coefficient  Std. err.      t    P>|t|     [95% conf. interval]
-------------+----------------------------------------------------------------
           x |   -.004389   .0054818    -0.80   0.425    -.0152703    .0064923
           T |  -.0673279   .1181587    -0.57   0.570    -.3018711    .1672154
             |
       T#c.x |
          1  |   .0112835   .0115265     0.98   0.330    -.0115965    .0341635
             |
       _cons |   .0406492   .0656291     0.62   0.537    -.0896236     .170922
------------------------------------------------------------------------------

. count if T
  31

. replace T = 1 if x == 0
(4 real changes made)

. count if T
  35

. reg y x T c.x#i.T, noheader
------------------------------------------------------------------------------
           y | Coefficient  Std. err.      t    P>|t|     [95% conf. interval]
-------------+----------------------------------------------------------------
           x |  -.0033402   .0061796    -0.54   0.590    -.0156066    .0089262
           T |  -.0717637   .1091199    -0.66   0.512     -.288365    .1448377
             |
       T#c.x |
          1  |   .0093415   .0105589     0.88   0.379    -.0116178    .0303009
             |
       _cons |    .054897   .0762257     0.72   0.473      -.09641    .2062039
------------------------------------------------------------------------------

[Lea Berg]

Thank you! Now it works

[Margarita Petrusevich]

Hello,
I was wondering what the logic behind this solution is? Why is it appropriate to substitute T values based on x values?

[Øyvind Snilsberg]

the treatment status variable, T, should be equal to 1 for observations with running variable, x, greater than or equal to the cutoff, 0.

[Jeff Wooldridge]

Hello,
I was wondering what the logic behind this solution is? Why is it appropriate to substitute T values based on x values?

In addition, when you set the bandwidth large enough to include all observations then local linear regression becomes global linear regression.