ECO
Macro1_PS3

# Iv how would a change in k a ect the relation between

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Unformatted text preview: iv) How would a change in k a ect the relation between R t and i t ? Explain intuitively. 2- Suppose that the two-period rate includes a time varying term premium : R t = ( i t + E t i t +1 ) / 2 + θ t , where θ is a white noise disturbance that is independent of . Consider the OLS regression i t +1- i t = a + b ( R t- i t ) + e t +1 . 3 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 3 Make sure you understand why we choose this speci cation of the regression : The rst part of the problem gives predictions of the rational expectations theory of the term structure. Using these predictions, we can then test for the theory. The regression we consider comes directly from R t = ( i t + E t i t +1 ) / 2 where we give up E t 1 Macroeconomics 1. PSE. Master APE.2010-2011. PS3 Prof. Xavier Ragot / T.A : Eric Monnet i) Under the rational -expectations theory of the term structure (i.e with θ t = 0 , ∀ t ), what value would one expect for b ? Hint : rst just nd the theoretical value of b . Then, if you want, nd this value using the de nition of the OLS estimator (but the calculus are a little bit long) : recall that for a univariate OLS regression, the coe cient on the right hand side variable equals the covariance between the right hand side and left hand side variables divided by the variance of the right hand side variable.) ii) Now suppose that θ has a variance...
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