13.12 Exercise

  1. Above (see Table 1) we used a series of falsification tests. Among other things we checked whether there is an effect of the treatment on pre-treatment covariates that should be unaffected. We did so for “Total money in race” and “Total votes in race”. Do the same for the other covariates namely “Democratic incumbent”, “Republican incumbent” and “Total group money”.
## [1] "Mass points detected in the running variable."
## Call: rdrobust
## 
## Number of Obs.                32670
## BW type                       mserd
## Kernel                   Triangular
## VCE method                       NN
## 
## Number of Obs.               16281       16389
## Eff. Number of Obs.           4016        3568
## Order est. (p)                   1           1
## Order bias  (q)                  2           2
## BW est. (h)                  7.864       7.864
## BW bias (b)                 14.648      14.648
## rho (h/b)                    0.537       0.537
## Unique Obs.                  11187       10946
## 
## =============================================================================
##         Method     Coef. Std. Err.         z     P>|z|      [ 95% C.I. ]       
## =============================================================================
##   Conventional     0.012     0.019     0.637     0.524    [-0.025 , 0.048]     
## Bias-Corrected     0.004     0.019     0.238     0.812    [-0.032 , 0.041]     
##         Robust     0.004     0.021     0.210     0.833    [-0.037 , 0.046]     
## =============================================================================

## [1] "Mass points detected in the running variable."
## Call: rdrobust
## 
## Number of Obs.                32670
## BW type                       mserd
## Kernel                   Triangular
## VCE method                       NN
## 
## Number of Obs.               16281       16389
## Eff. Number of Obs.           3544        3183
## Order est. (p)                   1           1
## Order bias  (q)                  2           2
## BW est. (h)                  6.952       6.952
## BW bias (b)                 16.320      16.320
## rho (h/b)                    0.426       0.426
## Unique Obs.                  11187       10946
## 
## =============================================================================
##         Method     Coef. Std. Err.         z     P>|z|      [ 95% C.I. ]       
## =============================================================================
##   Conventional    -0.019     0.019    -0.995     0.320    [-0.056 , 0.018]     
## Bias-Corrected    -0.010     0.019    -0.533     0.594    [-0.048 , 0.027]     
##         Robust    -0.010     0.021    -0.495     0.620    [-0.050 , 0.030]     
## =============================================================================

## [1] "Mass points detected in the running variable."
## Call: rdrobust
## 
## Number of Obs.                32670
## BW type                       mserd
## Kernel                   Triangular
## VCE method                       NN
## 
## Number of Obs.               16281       16389
## Eff. Number of Obs.           6347        5384
## Order est. (p)                   1           1
## Order bias  (q)                  2           2
## BW est. (h)                 12.193      12.193
## BW bias (b)                 18.917      18.917
## rho (h/b)                    0.645       0.645
## Unique Obs.                  11187       10946
## 
## =============================================================================
##         Method     Coef. Std. Err.         z     P>|z|      [ 95% C.I. ]       
## =============================================================================
##   Conventional  2712.823  5979.432     0.454     0.650 [-9006.649 , 14432.295] 
## Bias-Corrected  3734.085  5979.432     0.624     0.532 [-7985.386 , 15453.557] 
##         Robust  3734.085  7157.025     0.522     0.602[-10293.425 , 17761.596] 
## =============================================================================

  1. Reiterate why both the density test and the test using the predetermined covariates are helpful. What do they ideally show?
  2. Come up with three research ideas (ideally in your areay of research) that would lend themselves to apply a regression discontinuity. Think of any running variables/score that may determine whether individuals or other entities get treatments you are interested in.
  3. What is the “problem” of the local nature of RD effects (Skovron and Titiunik 2015, 9)?
  4. In what way is the functional form (of the regression functions) important in a RDD in line with/as opposed to a randomized experiment(Skovron and Titiunik 2015, 7–8)? (See also Gelman and Zelizer (2015))
  5. Which role does the bandwith around the score play both conceptually and in terms of estimation? (e.g. Skovron and Titiunik 2015, 14–15)

References

Gelman, Andrew, and Adam Zelizer. 2015. “Evidence on the Deleterious Impact of Sustained Use of Polynomial Regression on Causal Inference.” Research & Politics 2 (1): 2053168015569830.

Skovron, Christopher, and Rocıo Titiunik. 2015. “A Practical Guide to Regression Discontinuity Designs in Political Science.”