Consider the following bivariate VAR(1) model: Yt Yt-1 - ( * ) = ( 22 )...

 

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Consider the following bivariate VAR(1) model: Yt Yt-1 - ( * ) = ( 22 ) ( * ) + ( ) Zt 0.4 0.1 0.2 0.5 Zt-1 e1t e2t where (e1t, e2t) is a vector of white noise with non-zero covariance. Answer the following questions. (i) Using lag polynomials, solve yt as a function of e1t, e2t. Discuss whether {y} is a stationary process. (ii) Compute the impulse response function of yt+h for h = 1, 2, 3 to a unit shock in e1t and e2t. (iii) Assume that (e1t, e2t) is related to fundamental shocks (Eyt, Ext) in the following manner: e1t 1 0.5 Eyt (3)-(67)(2) :) e2t 0 1 Ezt = 0. Compute where (Eyt, Ext) is a vector white noise with Var(yt) = Var(Ezt) = 1 and Cov(Eyt, Ezt) = the impulse response function of Yt+h for h = 1, 2, 3 to a unit shock in zt. 4 (iv) Assume now the structural relationship changes as follows: e1t e2t 1 :) - (as i ) ( 0.5 Compute the impulse response function of Yt+h for h Eyt Ezt = 1, 2, 3 to a unit shock in Ezt. Discuss how the ordering of the variables may affect the impulse response function under recursive identification framework. Consider the following bivariate VAR(1) model: Yt Yt-1 - ( * ) = ( 22 ) ( * ) + ( ) Zt 0.4 0.1 0.2 0.5 Zt-1 e1t e2t where (e1t, e2t) is a vector of white noise with non-zero covariance. Answer the following questions. (i) Using lag polynomials, solve yt as a function of e1t, e2t. Discuss whether {y} is a stationary process. (ii) Compute the impulse response function of yt+h for h = 1, 2, 3 to a unit shock in e1t and e2t. (iii) Assume that (e1t, e2t) is related to fundamental shocks (Eyt, Ext) in the following manner: e1t 1 0.5 Eyt (3)-(67)(2) :) e2t 0 1 Ezt = 0. Compute where (Eyt, Ext) is a vector white noise with Var(yt) = Var(Ezt) = 1 and Cov(Eyt, Ezt) = the impulse response function of Yt+h for h = 1, 2, 3 to a unit shock in zt. 4 (iv) Assume now the structural relationship changes as follows: e1t e2t 1 :) - (as i ) ( 0.5 Compute the impulse response function of Yt+h for h Eyt Ezt = 1, 2, 3 to a unit shock in Ezt. Discuss how the ordering of the variables may affect the impulse response function under recursive identification framework.