The Propensity Score Matching The Propensity Score: The condition probability for treatment: P(Di=1X) Probit or logit model to estimate the condition probability. The advantage:Dimension reduction and range limitation. P(Xi)=P(Xj) Treatment probability The matching using propensity score:Propensity Score Matching
• The Propensity Score: • The condition probability for treatment: 𝑃(𝐷𝑖 = 1|𝑿) • Probit or logit model to estimate the condition probability. • The advantage: Dimension reduction and range limitation. 𝑃(𝑿𝑖) = 𝑃(𝑿𝑗) • Treatment probability. • The matching using propensity score: Propensity Score Matching. 11 The Propensity Score Matching
The Propensity Score Matching The causal inference when using Propensity Score Matching: (y,)1Dx→(oy)⊥DP(x) tie=E[Y:-Yoi]=E(E[Yi-Yo l p(X)] =EE[YI(X)]-E[Yo:(X:)] =E{E[Y:|(X),D=1]一E[Y|(X),D,=0]} =E{E[Y:}p(X;),D:=1]-E[Y:|(X:),D:=0]} =E[x] E[Y;(X)=p,D:1]-E[Y;I p(X;)=p,D;=0] t=E[x。|D,=1] 12
• The causal inference when using Propensity Score Matching: 12 The Propensity Score Matching