The Instrumental Variable Instrumental variable for causal inference:The condition ·Independence Assumption(独立性假设)， {(Y;(d,);Yd,z),Doi,D)I Zi E[D:I Z =1]-E[D,Z=0] =E[D:|Z:=1]-E[Do:|Z:=0]=ELD:-Do E[Y:|Z=1]-E[Y,IZ=0]=EY:(D:,1)]一E[Y:(Do,0)] 11
• Instrumental variable for causal inference: The condition • Independence Assumption (独立性假设). 11 The Instrumental Variable
The Instrumental Variable Instrumental variable for causal inference:The condition ·Exclusivity Assumption(排除性假设)， Y,(d,0)=Y,(d,1),d=0,1 Y=Y,(0,1)=Y,(0,0) Y1a=Y:(1,1)=Y:(1,0) What will happen if instrumental variable violates Independence Assumption or Exclusivity Assumption. Take a review of mediation effect. 12
• Instrumental variable for causal inference: The condition • Exclusivity Assumption (排除性假设). • What will happen if instrumental variable violates Independence Assumption or Exclusivity Assumption. • Take a review of mediation effect. 12 The Instrumental Variable
The Instrumental Variable Instrumental variable for causal inference:The condition ·Monotonicity Assumption(单调性假设)， D:≥Do或者 Di≤D E[Y:1Z:=1]-EY:IZ=0] E[D,I Z;1]-E[D,Z=0] =E[Y-Yoi I D>Doi] E[Yui-Yoi I D:=1]=E[Yi;-Yor I Dor =1]Pr[Dor=1 D,=1] 干预组平均四架效应 总通梦与者平均因果效位 E[Yi-Yo:Du>Doi]Pr[D>Doi,Z;=1[D.=1] 依从岩平均因架效应 E[Y1-Yoi I D:=0]=E[Y:-Yoi I Di=0]Pr[Du=0I D,=0] 控制组平均因果效应 从不多与者平找但果效应 ECY1-Yoi I D1>Doi]Pr[D>Doi,Z=0 D=0] 依从者平均烟果效应 13
• Instrumental variable for causal inference: The condition • Monotonicity Assumption (单调性假设). 13 The Instrumental Variable
The Instrumental Variable Instrumental variable for causal inference: Introduce covariate variable X. (Yoi,Yu,Doi,D:)LLZ:X E[Y:IX,Z=1]-E[Y,|X,Z,=0] E[D:Xi,Z=1]-E[D;Xi,Z=0] =E[Y-Yoi X;,Di Doi]t(Xi) 14
• Instrumental variable for causal inference: • Introduce covariate variable X. 14 The Instrumental Variable
Outline The Instrumental Variable The Estimation for Instrumental Variable Regression The application for Instrumental Variable Regression 15
• The Instrumental Variable • The Estimation for Instrumental Variable Regression • The Application for Instrumental Variable Regression 15 Outline