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Macro1_PS3_solutions

# Macro1_PS3_solutions - Macroeconomics 1 PSE Master...

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Unformatted text preview: Macroeconomics 1. PSE. Master APE.2010-2011. PS3 Prof. Xavier Ragot / T.A : Eric Monnet 1 Yield Curve Answer the following questions using your course and, if necessary, the article by John Campbell ( Some lessons form the yield curve , JEP, 1995). 1)What is the yield curve ? 2)why is it relevant for policy decisions ? 3)What is the main standard theory used to explain this curve ? and what are the main assumptions and limits of this theory ? 2 Monetary policy, regime changes and the term structures of interest rates Consider an economy 1 where money is neutral (keep in mind this assumption while interpretating the results). Speci cally, assume that π t = Δ m t and that r (real interest rate) is constant at zero. Suppose the money supply is given by Δ m t = k Δ m t- 1 + t , where is a white noise disturbance. 1- Assume that the rational expectation theory of the term structure of interest rates holds (see Romer's chp 10) ; speci cally the two-period interest rate is given by R t = ( i t + E t i t +1 ) / 2 . i t denotes the nominal interest rate from t to t + 1 ; thus by the Fisher identity, it equals 2 r t + E t ( p t +1- p t ) i) what is i t as a function of Δ m t and k ? (assume that Δ m t is known at time t) The one period interest rate given by i t = E t π t +1 since the real interest rate is assumed constant at zero. Since money is neutral we have π t +1 = Δ m t +1 and 1 See Mankiw and Miron (QJE, 1986) and Mankiw,Miron and Weil (AER, 1987) (and Romer's Advanced Macroeconomics chp 10).This exercise is based on Romer's problems, chp 10. 2 note that the following equation is in fact the log approximation of the Fisher identity 1 Macroeconomics 1. PSE. Master APE.2010-2011. PS3 Prof. Xavier Ragot / T.A : Eric Monnet thus : i t = E t Δ m t +1 . And given the de nition of the money growth that holds in all periods, we get i t = E t ( k Δ m t + t +1 ) = k Δ m t where we have used the fact that Δ m t is known as of time t and E t ( t +1 ) = 0 ( is a white noise). ii) what is E t ( i t +1 ) as a function of Δ m t and k ? The expectation, as of time t , of the nominal interest rate form period t + 1 to t + 2 is E t i t +1 = E t π t +2 = E t Δ m t +2 and once again, since the equation of money growth holds every period, we get Δ m t +2 = k 2 Δ m t + k t +1 + t +2 Substituting this equation into the previous one, we have : E t i t +1 = E t h k 2 Δ m t + k t +1 + t +2 i = k 2 Δ m t where we have used the fact that Δ m t is known at t and the 's are mean zero disturbances. iii) what is the relation between R t and i t ; that is, what is R t as a function of i t and k ? Give an interpretation of this function. Under the rational expectations theory of the term structure, the two-period in- terest rate is given by : R t = ( i t + E t i t +1 ) / 2 2 Macroeconomics 1. PSE. Master APE.2010-2011. PS3 Prof. Xavier Ragot / T.A : Eric Monnet then using the anwser to part (ii)we have : R t = ( i t + k 2 Δ m t ) / 2 and since we have shown that...
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Macro1_PS3_solutions - Macroeconomics 1 PSE Master...

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