Question

1) Given the simple Keynesian model of income determination Ct=a0+a1Yt+u1 It=b0+b1Yt+b2Yt-1+u2 Yt= Ct + It + Gt i) Derive the reduced form coefficients of the behavioural equations. ii) Show that the reduced-form parameters measure the total effect, direct and indirect, of a change in the exogenous variable on the endogenous variables. Use as an example the reduced form of the above investment function. 2) Consider the following simultaneous equation model Y= b0+b1X1+b2X2+u1 X= c0+c1Y+u2 i) Show that under the usual assumptions ( regardiong each one of the random terms u1 and u2 ), X2 and u1 are not independent, that is E[X2u1] = (c1 * σ2u1)/ (1-c1b2) + cov(u1,u2) / (1-c1b2) ≠0 ii) What are the implications of this findings? iii) What is the appripriate procedure for estimating the coefficients of the model, given E(X2u1) ≠0 ?

          1) Given the simple Keynesian model of income determination
Ct=a0+a1Yt+u1  
It=b0+b1Yt+b2Yt-1+u2
Yt= Ct + It + Gt
i) Derive the reduced form coefficients of the behavioural equations. 
ii) Show that the reduced-form parameters measure the total effect, direct and indirect, of a change in the exogenous variable on the endogenous variables. Use as an example the reduced form of the above investment function.  

2) Consider the following simultaneous equation model  
Y= b0+b1X1+b2X2+u1
X= c0+c1Y+u2
i) Show that under the usual assumptions ( regardiong each one of the random terms u1 and u2 ), X2 and u1 are not independent, that is  E[X2u1] = (c1 * σ2u1)/ (1-c1b2) + cov(u1,u2) / (1-c1b2) ≠0  
ii) What are the implications of this findings?  
iii) What is the appripriate procedure for estimating the coefficients of the model, given E(X2u1) ≠0 ?

Added by Kimberly B.

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