The Regression Discontinuity Design Sharp Regression Discontinuity and Fuzzy Regression Discontinuity: 1若x,≥C D,= 若x,<C 11
• Sharp Regression Discontinuity and Fuzzy Regression Discontinuity: 11 The Regression Discontinuity Design
The Regression Discontinuity Design Sharp Regression Discontinuity and Fuzzy Regression Discontinuity: (D:（x)x≥x0 D,= Do:(x）x<xo 精确断点回归 a 模糊断点回归 12
• Sharp Regression Discontinuity and Fuzzy Regression Discontinuity: 12 The Regression Discontinuity Design
The Regression Discontinuity Design Causal Directed Acyclic Graph: X X T D D (a)精确断点 (b)模糊断点 13
• Causal Directed Acyclic Graph: 13 The Regression Discontinuity Design
The Condition for RDD ·The Discontinuity Assumption(断点假设)： lim E[D;X;=x],=lim E[D;X;=x] →x0 p≠p D=D(T,e),T:=1(X:≥xa） p(x)=E[D,X;=x]=Pr[D,=1X;=x] Sharp Regression Discontinuity: D,=T: p*=1,p=0 14
• The Discontinuity Assumption (断点假设): • Sharp Regression Discontinuity: 14 The Condition for RDD
The Condition for RDD ·The Continuity Assumption(连续性假设)： ·E[YalX,=x]、E[Y:lX,=x].is a function ofx. The function is continuous at x=xo limE[Yi Xi xo +e]=limE[Yi Xi=xo-8],j=0,1 The Continuity Assumption is for what? The continuity is not limited to a range around the cutoff point. 15
• The Continuity Assumption (连续性假设): • is a function of x. • The function is continuous at x = x0 . • The Continuity Assumption is for what? • The continuity is not limited to a range around the cutoff point. 15 The Condition for RDD