第九章 多元回归分析模型设定和数据

——•y=β0+β1x1+β2x2+...+βkxk+u••••••••x•x••••xy•x1x1x2•••Ramsey’s(Ramsey’sregressionspecificationerrortest,RESET)RESET•RESETWhite•ŷx•y=β0+β1x1+…+βkxk+δ1ŷ2+δ1ŷ3+error•H0:δ1=0,δ2=0F~F2,n-k-3LM~22••Davidson-MacKinnon••••x3*=δ0+δ3x3+v3,“*”•x3x3*•β1β2?•E(x3*|x1,x2,x3)=E(x3*|x3)=δ0+δ3x3•ux1,x2x3*v3x1,x2x3•y=(β0+β3δ0)+β1x1+β2x2+β3δ3x3+(u+β3v3)x3••x3*=δ0+δ1x1+δ2x2+δ3x3+v3•y=(β0+β3δ0)+(β1+β3δ1)x1+(β2+β3δ2)x2+β3δ3x3+(u+β3v3)•β3δj•••y•yy•••yx•e0=y–y*•y=β0+β1x1+…+βkxk+u+e0•OLS•e0xj,u•E(e0)0β0••e1=x1–x1*•E(e1)=0,E(y|x1*,x1)=E(y|x1*)•y=β0+β1x1+(u–β1e1)•e1x1•Cov(x1,e1)=0•OLS•Cov(x1*,e1)=0•Cov(x1,e1)=E(x1e1)=E(x1*e1)+E(e12)=0+σe2•X1()()()⎟⎟⎠⎞⎜⎜⎝⎛+=⎟⎟⎠⎞⎜⎜⎝⎛+−=+−=−+=22*2*122*2122*2111111111,ˆplimexxexeexexVareuxCovσσσβσσσβσσσβββββ•Var(x1*)/Var(x1)•Var(x1*)/Var(x1)1,•?••••x•y••••••••Statapp306-3099.49.5