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Ct=α+β*yt + Ut (1)

{

yt=Ct+It (2)

 

Ct=α/(1-β) + β*It/(1-β) + Ut/(1-β)

α׳= α/(1-β) (3)

β׳=β/(1-β) (4) Ct=α׳+β׳*It+U׳t (5)

(5) α׳ β׳

(3) (4)

α= α׳/(1+ β׳) β= β׳/(1+ β׳)

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y=α+β*x+U x, z.

β

β= cov(y;z) / cov(x;z)

β=cov(y;z) / cov(x;z) = ov[(α+β*x+u);z] / cov(x;z) =

= ( cov(α;z) + cov(β-x;z) + cov(u;z) ) / cov(x;z) = β + ( cov(u;z) / cov(x;z) )

cov(u;z) =>0 cov (x;z), , x z , .

, x z .

, x z 1 , z .

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t=α+β*yt+Ut

{

yt=Ct+It

, Yt 2 Yt , .

.

Ct=α+β*It+Ut

b=cov(Ct,It) / cov(yt,It)

b=b׳/(1+b׳)= ( cov(Ct;It)/var(It) ) / ( cov(Ct;It)/var(It) ) = cov(Ct;It) / ( var(It)+cov(Ct;It) )

yt=Ct+It => cov(y;I)=cov[(C+I);I]=cov(Ct;It)+var(I) => b=b

.

.

y1=α+β1*x12*x23*y2+U1

{

y2=j+β4*x45*y1+U2

 

y1=α+β1*x12*x23*j+β34*x43β5*y1

y1=(α+β3*j)/(1-β35) + β1*x1/(1-β35) + β2*x2/(1-β35) + β34*x4/(1-β35)

y2=j+β4*x45*α+β51*x152*x253*y2

y2=(j+β5*α)/(1-β53) + β4*x4/(1-β53) + β51*x1/(1-β53) +β52*x2/(1-β53)

 

y1=α׳+β׳1*x1+β׳2*x2+β׳3*x4+U׳4

{ (2)

y2=j׳+β׳4*x4+β׳5*x1+β׳6*x2+U׳2

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