■ Financial Econometrics Chapter 6.Control Variable and Fixed Effect Jin Ling School of Finance,Zhongnan University of Economics and Law 1
Financial Econometrics Chapter 6. Control Variable and Fixed Effect Jin Ling School of Finance, Zhongnan University of Economics and Law 1
Outline Causal Inference and OLS Regression 。Control Variable ·Fixed Effect 2
• Causal Inference and OLS Regression • Control Variable • Fixed Effect 2 Outline
Causal Inference and OLS Regression The methodology for causal inference: Potential outcomes with or without treatment under same condition. Assignment mechanism. Experiment design:Randomized experiment. Testable implication:Mediation Effect and Moderating Effect. 3
• The methodology for causal inference: • Potential outcomes with or without treatment under same condition. • Assignment mechanism. • Experiment design: Randomized experiment. • Testable implication: Mediation Effect and Moderating Effect. 3 Causal Inference and OLS Regression
Causal Inference and OLS Regression The OLS regression for causal inference: Yi=DYL+(1-Di)Yoi=Yoi+(Yu-Yoi)D =Yo+6:D:=o十8D:+o =+(h一)D,+[%+D(yh:一%：)] Ho=E[Yo],voi=Yoi-E[Yoi],=E[Y:],v=Yu-E[Yii] ·Equivalently, Yi a+TATE D:+e E[Y;I D:1]=a+TATE +E[e;I X E[Y,I D:=0]=a+ECeX:] 4
• The OLS regression for causal inference: • Equivalently, 4 Causal Inference and OLS Regression
Causal Inference and OLS Regression The OLS regression for causal inference: x=E[Y,ID=1]-E[Y,|D,=0] =tE+E[e:ID:=1]-E[e|D,=0] =xAE+E[h:|D:=1]-E[o:ID,=0] =TATE +E[Yo D,=1]-E[Yor I D;=0] +(1-p)(E[YH-Y{D:=1]-E[Y:-Yo|D,=0]} 全期望公式E[Y]=E[EYIX]] t=EY:-Y]+E[Yo I D,=1]-E[Yo|D,=0]+{1-Pr[D,=1} ATE 选择偏艺 ·{EYi-Y1D,=1]-EY:-Y|D,=0]》 两组因果效应差舞 5
• The OLS regression for causal inference: 5 Causal Inference and OLS Regression