The Discontinuity Design ·The local average treatment effect(局部平均处理效应)： LATE =E(y.-yo.lx=500) =E(y.x=500)-E(yo|x=500) lim E(yux)-lim E(yolx) x1500 x1500 Why the local average treatment effect can be used for causal inference? The unconfoundedness in LATE 6
• The local average treatment effect (局部平均处理效应): • Why the local average treatment effect can be used for causal inference? • The unconfoundedness in LATE. 6 The Discontinuity Design
The Discontinuity Design The potential outcome around the cutoff point: C 7
• The potential outcome around the cutoff point: 7 The Discontinuity Design
The Discontinuity Design The discontinuity design for causal inference: Randomized assignment around the cutoff point. Local randomized experiment. Internal validity and external validity. 8
• The discontinuity design for causal inference: • Randomized assignment around the cutoff point. • Local randomized experiment. • Internal validity and external validity. 8 The Discontinuity Design
Outline The Discontinuity Design for Causal Inference The Regression Discontinuity Design The Application for Regression Discontinuity Design 9
• The Discontinuity Design for Causal Inference • The Regression Discontinuity Design • The Application for Regression Discontinuity Design 9 Outline
The Regression Discontinuity Design Sharp Regression Discontinuity and Fuzzy Regression Discontinuity: The cutoff point for treatment. .Sharp Regression Discontinuity:Pr[D =1xo]=1,Pr[D,=1X,<xo]=0. Fuzzy Regression Discontinuity:Pr[D,=1X,>xo]=a,Pr[D,=1X,<xo]=b,0<b<a<1. What is the difference between SRD and FRD? 10
• Sharp Regression Discontinuity and Fuzzy Regression Discontinuity: • The cutoff point for treatment. • Sharp Regression Discontinuity: Pr[Di = 1 | Xi ≥ x0 ] = 1, Pr[Di = 1 | Xi < x0 ] = 0. • Fuzzy Regression Discontinuity: Pr[Di = 1 | Xi ≥ x0 ] = a, Pr[Di = 1 | Xi < x0 ] = b, 0<b<a<1. • What is the difference between SRD and FRD? 10 The Regression Discontinuity Design