Financial Econometrics Chapter 11.Regression Discontinuity Design Jin Ling School of Finance,Zhongnan University of Economics and Law
Financial Econometrics Chapter 11. Regression Discontinuity Design Jin Ling School of Finance, Zhongnan University of Economics and Law 1
Outline The Discontinuity Design for Causal Inference The Regression Discontinuity Design The Application for Regression Discontinuity Design 2
• The Discontinuity Design for Causal Inference • The Regression Discontinuity Design • The Application for Regression Discontinuity Design 2 Outline
The Discontinuity Design ·The cutoff point: The assignment mechanism. Assignment variable for treatment. The assignment variable meet a specific condition-Treatment. ·Education and wage. 3
• The cutoff point: • The assignment mechanism. • Assignment variable for treatment. • The assignment variable meet a specific condition→Treatment. • Education and wage. 3 The Discontinuity Design
The Discontinuity Design ·A typical example: D:= 若x,≥500 0 若x:<500 ·D,is a function of x Ifx,is given,the D,is independent with the potential outcome. A set of covariates affect x.x,can be regarded as the general characteristic. Can we use PSM to mitigate the confounding bias from the assignment mechanism?
• A typical example: • Di is a function of xi . • If xi is given, the Di is independent with the potential outcome. • A set of covariates affect xi . xi can be regarded as the general characteristic. • Can we use PSM to mitigate the confounding bias from the assignment mechanism? 4 The Discontinuity Design
The Discontinuity Design The cutoff point for causal inference: ·x=498,499,500,501. The difference between treatment group(x,=500,501)and control group (x,=498,499) Randomized factor leads to the difference. Randomized assignment for the range ofx,:[500-8,500 +8] 5
• The cutoff point for causal inference: • xi = 498, 499, 500, 501. • The difference between treatment group (xi = 500, 501) and control group (xi = 498, 499). • Randomized factor leads to the difference. • Randomized assignment for the range of xi : [500 - ε, 500 + ε] 5 The Discontinuity Design
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]=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