This preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: Macroeconomics 1. PSE. Master APE.20102011. 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 twoperiod 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.20102011. 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 twoperiod in terest rate is given by : R t = ( i t + E t i t +1 ) / 2 2 Macroeconomics 1. PSE. Master APE.20102011. 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...
View
Full Document
 Fall '09
 MrRaggillpol
 Economics, Macroeconomics, Monetary Policy, Rational expectations, Prof. Xavier Ragot, Eric Monnet, Master APE.20102011

Click to edit the document details