rdd_fit1 <-rdrobust(y = df$outcome, x = df$rv, c =0)summary(rdd_fit1)
Sharp RD estimates using local polynomial regression.
Number of Obs. 1266
BW type mserd
Kernel Triangular
VCE method NN
Number of Obs. 479 787
Eff. Number of Obs. 318 381
Order est. (p) 1 1
Order bias (q) 2 2
BW est. (h) 8.064 8.064
BW bias (b) 12.613 12.613
rho (h/b) 0.639 0.639
Unique Obs. 479 787
=====================================================================
Point Robust Inference
Estimate z P>|z| [ 95% C.I. ]
---------------------------------------------------------------------
RD Effect 0.725 0.528 0.598 [-2.692 , 4.677]
=====================================================================
rdd_bw1 <-rdrobust(y = df$outcome, x = df$rv, c =0, h =8.064)summary(rdd_bw1)
Sharp RD estimates using local polynomial regression.
Number of Obs. 1266
BW type Manual
Kernel Triangular
VCE method NN
Number of Obs. 479 787
Eff. Number of Obs. 318 381
Order est. (p) 1 1
Order bias (q) 2 2
BW est. (h) 8.064 8.064
BW bias (b) 8.064 8.064
rho (h/b) 1.000 1.000
Unique Obs. 479 787
=====================================================================
Point Robust Inference
Estimate z P>|z| [ 95% C.I. ]
---------------------------------------------------------------------
RD Effect 0.725 0.013 0.990 [-4.461 , 4.521]
=====================================================================
先ほどと同じ結果が得られている(Robust行はこの講義では無視する。Robust推定値についてはCalonico et al. (2015)を参照されたい3。)。頑健性を報告する際は最適バンド幅における処置効果に加え、最適バンド幅を半分にした場合、2倍にした場合の結果も報告するケースが多い。それではhを8.064の半分、2倍にしたモデルも推定してみよう。
rdd_bw2 <-rdrobust(y = df$outcome, x = df$rv, c =0, h =8.064/2)summary(rdd_bw2)
Sharp RD estimates using local polynomial regression.
Number of Obs. 1266
BW type Manual
Kernel Triangular
VCE method NN
Number of Obs. 479 787
Eff. Number of Obs. 188 185
Order est. (p) 1 1
Order bias (q) 2 2
BW est. (h) 4.032 4.032
BW bias (b) 4.032 4.032
rho (h/b) 1.000 1.000
Unique Obs. 479 787
=====================================================================
Point Robust Inference
Estimate z P>|z| [ 95% C.I. ]
---------------------------------------------------------------------
RD Effect 0.162 0.316 0.752 [-5.326 , 7.375]
=====================================================================
rdd_bw3 <-rdrobust(y = df$outcome, x = df$rv, c =0, h =8.064*2)summary(rdd_bw3)
Sharp RD estimates using local polynomial regression.
Number of Obs. 1266
BW type Manual
Kernel Triangular
VCE method NN
Number of Obs. 479 787
Eff. Number of Obs. 453 650
Order est. (p) 1 1
Order bias (q) 2 2
BW est. (h) 16.128 16.128
BW bias (b) 16.128 16.128
rho (h/b) 1.000 1.000
Unique Obs. 479 787
=====================================================================
Point Robust Inference
Estimate z P>|z| [ 95% C.I. ]
---------------------------------------------------------------------
RD Effect -0.006 0.580 0.562 [-2.309 , 4.250]
=====================================================================
rdd_kernel1 <-rdrobust(y = df$outcome, x = df$rv, c =0, kernel ="triangular")rdd_kernel2 <-rdrobust(y = df$outcome, x = df$rv, c =0, kernel ="uniform")rdd_kernel3 <-rdrobust(y = df$outcome, x = df$rv, c =0, kernel ="epanechnikov")summary(rdd_kernel1)
Sharp RD estimates using local polynomial regression.
Number of Obs. 1266
BW type mserd
Kernel Triangular
VCE method NN
Number of Obs. 479 787
Eff. Number of Obs. 318 381
Order est. (p) 1 1
Order bias (q) 2 2
BW est. (h) 8.064 8.064
BW bias (b) 12.613 12.613
rho (h/b) 0.639 0.639
Unique Obs. 479 787
=====================================================================
Point Robust Inference
Estimate z P>|z| [ 95% C.I. ]
---------------------------------------------------------------------
RD Effect 0.725 0.528 0.598 [-2.692 , 4.677]
=====================================================================
summary(rdd_kernel2)
Sharp RD estimates using local polynomial regression.
Number of Obs. 1266
BW type mserd
Kernel Uniform
VCE method NN
Number of Obs. 479 787
Eff. Number of Obs. 245 264
Order est. (p) 1 1
Order bias (q) 2 2
BW est. (h) 5.651 5.651
BW bias (b) 10.115 10.115
rho (h/b) 0.559 0.559
Unique Obs. 479 787
=====================================================================
Point Robust Inference
Estimate z P>|z| [ 95% C.I. ]
---------------------------------------------------------------------
RD Effect 0.611 0.516 0.606 [-2.878 , 4.933]
=====================================================================
summary(rdd_kernel3)
Sharp RD estimates using local polynomial regression.
Number of Obs. 1266
BW type mserd
Kernel Epanechnikov
VCE method NN
Number of Obs. 479 787
Eff. Number of Obs. 298 349
Order est. (p) 1 1
Order bias (q) 2 2
BW est. (h) 7.420 7.420
BW bias (b) 12.211 12.211
rho (h/b) 0.608 0.608
Unique Obs. 479 787
=====================================================================
Point Robust Inference
Estimate z P>|z| [ 95% C.I. ]
---------------------------------------------------------------------
RD Effect 0.722 0.560 0.575 [-2.633 , 4.740]
=====================================================================
rdd_p1 <-rdrobust(y = df$outcome, x = df$rv, c =0, p =1)rdd_p2 <-rdrobust(y = df$outcome, x = df$rv, c =0, p =2)rdd_p3 <-rdrobust(y = df$outcome, x = df$rv, c =0, p =3)rdd_p4 <-rdrobust(y = df$outcome, x = df$rv, c =0, p =4)summary(rdd_p1)
Sharp RD estimates using local polynomial regression.
Number of Obs. 1266
BW type mserd
Kernel Triangular
VCE method NN
Number of Obs. 479 787
Eff. Number of Obs. 318 381
Order est. (p) 1 1
Order bias (q) 2 2
BW est. (h) 8.064 8.064
BW bias (b) 12.613 12.613
rho (h/b) 0.639 0.639
Unique Obs. 479 787
=====================================================================
Point Robust Inference
Estimate z P>|z| [ 95% C.I. ]
---------------------------------------------------------------------
RD Effect 0.725 0.528 0.598 [-2.692 , 4.677]
=====================================================================
summary(rdd_p2)
Sharp RD estimates using local polynomial regression.
Number of Obs. 1266
BW type mserd
Kernel Triangular
VCE method NN
Number of Obs. 479 787
Eff. Number of Obs. 358 433
Order est. (p) 2 2
Order bias (q) 3 3
BW est. (h) 9.205 9.205
BW bias (b) 12.622 12.622
rho (h/b) 0.729 0.729
Unique Obs. 479 787
=====================================================================
Point Robust Inference
Estimate z P>|z| [ 95% C.I. ]
---------------------------------------------------------------------
RD Effect 0.260 -0.030 0.976 [-4.804 , 4.661]
=====================================================================
summary(rdd_p3)
Sharp RD estimates using local polynomial regression.
Number of Obs. 1266
BW type mserd
Kernel Triangular
VCE method NN
Number of Obs. 479 787
Eff. Number of Obs. 379 476
Order est. (p) 3 3
Order bias (q) 4 4
BW est. (h) 10.311 10.311
BW bias (b) 13.458 13.458
rho (h/b) 0.766 0.766
Unique Obs. 479 787
=====================================================================
Point Robust Inference
Estimate z P>|z| [ 95% C.I. ]
---------------------------------------------------------------------
RD Effect -0.389 -0.240 0.811 [-6.462 , 5.055]
=====================================================================
summary(rdd_p4)
Sharp RD estimates using local polynomial regression.
Number of Obs. 1266
BW type mserd
Kernel Triangular
VCE method NN
Number of Obs. 479 787
Eff. Number of Obs. 420 567
Order est. (p) 4 4
Order bias (q) 5 5
BW est. (h) 12.653 12.653
BW bias (b) 15.671 15.671
rho (h/b) 0.807 0.807
Unique Obs. 479 787
=====================================================================
Point Robust Inference
Estimate z P>|z| [ 95% C.I. ]
---------------------------------------------------------------------
RD Effect -0.472 -0.124 0.902 [-6.776 , 5.972]
=====================================================================
rdplot(y = df$outcome, x = df$rv, c =0, p =1,kernel ="triangular",x.label ="Vote Margin in Election t",y.label ="Vote Share in Election t+1",title ="")
assumption_fit1 <-rdrobust(y = df$total_cand, x = df$rv)assumption_fit2 <-rdrobust(y = df$en_cand, x = df$rv)assumption_fit3 <-rdrobust(y = df$total_votes, x = df$rv)
summary(assumption_fit1)
Sharp RD estimates using local polynomial regression.
Number of Obs. 1266
BW type mserd
Kernel Triangular
VCE method NN
Number of Obs. 479 787
Eff. Number of Obs. 243 261
Order est. (p) 1 1
Order bias (q) 2 2
BW est. (h) 5.547 5.547
BW bias (b) 8.621 8.621
rho (h/b) 0.643 0.643
Unique Obs. 479 787
=====================================================================
Point Robust Inference
Estimate z P>|z| [ 95% C.I. ]
---------------------------------------------------------------------
RD Effect -0.066 -0.415 0.678 [-0.593 , 0.385]
=====================================================================
summary(assumption_fit2)
Sharp RD estimates using local polynomial regression.
Number of Obs. 1266
BW type mserd
Kernel Triangular
VCE method NN
Number of Obs. 479 787
Eff. Number of Obs. 280 314
Order est. (p) 1 1
Order bias (q) 2 2
BW est. (h) 6.629 6.629
BW bias (b) 10.114 10.114
rho (h/b) 0.655 0.655
Unique Obs. 479 787
=====================================================================
Point Robust Inference
Estimate z P>|z| [ 95% C.I. ]
---------------------------------------------------------------------
RD Effect 0.032 0.149 0.881 [-0.242 , 0.282]
=====================================================================
summary(assumption_fit3)
Sharp RD estimates using local polynomial regression.
Number of Obs. 1266
BW type mserd
Kernel Triangular
VCE method NN
Number of Obs. 479 787
Eff. Number of Obs. 291 341
Order est. (p) 1 1
Order bias (q) 2 2
BW est. (h) 7.131 7.131
BW bias (b) 11.445 11.445
rho (h/b) 0.623 0.623
Unique Obs. 479 787
=====================================================================
Point Robust Inference
Estimate z P>|z| [ 95% C.I. ]
---------------------------------------------------------------------
RD Effect 1222.634 0.042 0.967[-16145.541 , 16846.362]
=====================================================================
Calonico, S., M. D. Cattaneo, and R. Titiunik. 2015b. “rdrobust: An R Package for Robust Nonparametric Inference in Regression-Discontinuity Designs,” R Journal, 7(1): 38-51.↩︎