The Instrumental Variable If we can not control for all confounding factors: An instrumental variable is correlated with treatment but not correlated with confounding factors. Yi=a+rDi+Aiy+vi Relevance:The instrumental variable can represent the change for treatment. Cov(D,Z,)≠0 Exogeneity:The instrumental variable can eliminate the disturbance from confounding factors. Cov(7,Z,)=0 n=A:Y+v 6
• If we can not control for all confounding factors: • An instrumental variable is correlated with treatment but not correlated with confounding factors. • Relevance: The instrumental variable can represent the change for treatment. • Exogeneity: The instrumental variable can eliminate the disturbance from confounding factors. 6 The Instrumental Variable
The Instrumental Variable The methodology for instrumental variable: The correlation between instrumental variable and potential outcome: Cov(Yi,Z;)=Cov(a,Z,)+rCov(D,Z)+Cov(n:,2,) a is constant,so Cov(a,Z)=0. Exogeneity:Cov(n,Z)=0 ·Relevance:Cov(D,Z,)≠0 Cov(Y,Z)Cov(Y:,Z:)/Var(Z) Cov(D:,Zi) Cov(Di,Z;)/Var(Z:)
• The methodology for instrumental variable: • The correlation between instrumental variable and potential outcome: • α is constant, so . • Exogeneity: . • Relevance: . 7 The Instrumental Variable
The Instrumental Variable The methodology for instrumental variable: v二 Cov(Y,Z)Cov(Y:,Z:)/Var(Z) Cov(D:,Zi) Cov(D:,Z;)/Var(Zi) The denominator is coefficient obtained from regression of D on Z The numerator is coefficient obtained from regression of Y on Z. 之(z,-2Y-Y) iN= =』 (2-2)(D,-B.) The economic implication for instrumental variable?The coefficient is dependent on what?
• The methodology for instrumental variable: • The denominator is coefficient obtained from regression of D on Z. • The numerator is coefficient obtained from regression of Y on Z. • The economic implication for instrumental variable? The coefficient is dependent on what? 8 The Instrumental Variable
The Instrumental Variable How to choose instrumental variable: Institutional background:Real estate market. Financial Theory:Fund distance. Exogenous shock:Bank deregulation. 9
• How to choose instrumental variable: • Institutional background: Real estate market. • Financial Theory: Fund distance. • Exogenous shock: Bank deregulation. 9 The Instrumental Variable
The Instrumental Variable Instrumental variable for causal inference: Correlation in different situation. ·Z=0→Z=1 ·Do=0andD1=0 ·Do=0andD1=1 ·Do=1andD1=1 ·Do=1andD,=0 D:=Do:十(D:一Do)Z=xo十r1Z:十e 0=E[Doi],D-Doi,E;=Doi-E[Doi] 10
• Instrumental variable for causal inference: • Correlation in different situation. • Z = 0→Z = 1 • D0 = 0 and D1 = 0 • D0 = 0 and D1 = 1 • D0 = 1 and D1 = 1 • D0 = 1 and D1 = 0 10 The Instrumental Variable