Consider the following simultaneous equations system y1t = 0 + 1 y2t + 2 y3t + 3X1t + 4X2t + u1t (6.94) y2t = 0

Consider the following simultaneous equations system y1t = α0 + α1 y2t + α2 y3t + α3X1t + α4X2t + u1t (6.94)

y2t = β0 + β1 y3t + β2X1t + β3X3t + u2t (6.95)

y3t = γ0 + γ1 y1t + γ2X2t + γ3X3t + u3t

(a) Derive the reduced form equations corresponding to (6.94)–(6.96).

(b) What do you understand by the term ‘identification’? Describe a rule for determining whether a system of equations is identified. Apply this rule to (6.94–6.96). Does this rule guarantee that estimates of the structural parameters can be obtained?

(c) Which would you consider the more serious misspecification: treating exogenous variables as endogenous, or treating endogenous variables as exogenous? Explain your answer.

(d) Describe a method of obtaining the structural form coefficients corresponding to an overidentified system.

(e) Using EViews, estimate a VAR model for the interest rate series used in the principal components example of chapter 3. Use a method for selecting the lag length in the VAR optimally. Determine whether certain maturities lead or lag others, by conducting Granger causality tests and plotting impulse responses and variance decompositions. Is there any evidence that new information is reflected more quickly in some maturities than others?

AppendixLO1