中南财经政法大学：《金融计量学》课程教学课件（双语讲稿）Chapter 09 Instrumental Variable Regression

■ Financial Econometrics Chapter 9.Instrumental Variable Regression Jin Ling School of Finance,Zhongnan University of Economics and Law

Financial Econometrics Chapter 9. Instrumental Variable Regression Jin Ling School of Finance, Zhongnan University of Economics and Law 1

Outline The Instrumental Variable The Estimation for Instrumental Variable Regression The application for Instrumental Variable Regression 2

• The Instrumental Variable • The Estimation for Instrumental Variable Regression • The Application for Instrumental Variable Regression 2 Outline

The Instrumental Variable The control variable for causal inference: Control variables can help eliminate confounding bias. Can we control for all confounding factors? 。Omitted variables. D (a) (b) 3

• The control variable for causal inference: • Control variables can help eliminate confounding bias. • Can we control for all confounding factors? • Omitted variables. 3 The Instrumental Variable

The Instrumental Variable Can we control for all confounding factors? 。Omitted variables. What will happen if there is omitted variable in OLS model: Y=a+ps;+Ay+8 Cov(YS)=p+r8x V(S,)

• Can we control for all confounding factors? • Omitted variables. • What will happen if there is omitted variable in OLS model: 4 The Instrumental Variable

The Instrumental Variable The instrumental variable: (a)控制法 (b)工具变量法 5

• The instrumental variable: 5 The Instrumental Variable

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