Fall 2009 Social Sciences 7418 University of Wisconsin-Madison. Problem Set 2 Answers (4) (6) di = D (10)

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1 Publc Affars 974 Menze D. Chnn Fall 2009 Socal Scences 7418 Unversy of Wsconsn-Madson Problem Se 2 Answers Due n lecure on Thursday, November 12. " Box n" your answers o he algebrac quesons. 1. Consder a CC-LM model, where CC s gven by: y = (, ) (4) = ϕ(, y, R, Z) (6) So ha: d ( 1 ) = ( + ) d + dr dz (8) R + Z and d ( + ) d + RdR + Z dz = (8 ) (1 ) And he LM curve s gven by: d = m( dr) D d D (10) 1.1 Show wha happens f he nvesmen projecs ha are funded by loans suddenly look more rsky han hey used o (e.g., loans for buyng houses or loans for buldng shoppng malls). When Z rses, rses, (accordng o equaon 7); hs means ha loan supply decreases, whch n urn means ha he CC curve shfs n. 1

2 LM R 0, m CC Z 0, R 0, m 0 CC Z 1, R 0, m Show wha happens f he Fed ncreases he amoun of reserves n he economy by underakng open marke operaons. Assume ha he Fed does no pay neres on reserves. LM R 0, m 0 LM R 1, m CC Z 1, R 1, m 0 CC Z 1, R 0, m

3 The ncrease n reserves ncreases he money sock, n he usual fashon, hus shfng ou he LM curve. However, ncreased reserves also resuls n ncreased cred supply (decreased lendng rae). Ths means he CC curve shfs ou as well. Economc acvy rses o 2, he neres rae falls o R Wll an ncrease n governmen spendng have a posve or negave mpac on ncome? Explan, usng a graph. The CC curve essenally augmens he IS curve wh addonal shf varables; so hngs ha shfed he IS curve, lke an ncrease n auonomous spendng o A 1 from A 0 wll shf ou he CC curve. Oupu unambguously ncreases. LM R 0, m CC A 1, Z 1, R 0, m 0 CC A 0, Z 1, R 0, m Daa exercse: Taylor rule. Consder he Taylor rule: FF = π + 0.5( y y ) + 0.5( π π ) + r FF s he arge Fed Funds rae, y s log GDP, Where oupu gap), π s he nflaon rae, and y s he measure of poenal GDP (so y y s he π s he arge nflaon rae, and r s he naural rae of neres. 2.1 Download daa for real GDP and core CPI from he S. Lous Fed s FREDII webse, for he 1967Q1-2009Q3 perod. Esmae he oupu gap by run a regresson of log GDP on a consan, me rend (and possbly me rend squared), and akng he resdual as he oupu gap. Seng he arge nflaon rae a 0.02 (2%) and he naural rae of neres as (2.5%), calculae he arge Fed Funds rae for 2009Q3. 3

4 Dependen Varable: LGDP05 Mehod: Leas Squares Dae: 11/13/09 Tme: 19:08 Sample: 1967Q1 2009Q3 Included observaons: 171 Coeffcen Sd. Error -Sasc Prob. C TIME E R-squared Mean dependen var Adjused R-squared S.D. dependen var S.E. of regresson Akake nfo creron Sum squared resd Schwarz creron Log lkelhood Hannan-Qunn crer F-sasc Durbn-Wason sa Prob(F-sasc) The oupu gap looks lke hs: Core nflaon (y/y) oupu gap (dev'n from me rend) Wh he 2009Q3 oupu gap equal o , and y/y CPI core nflaon s Le s use he Taylor rule. 4

5 FF = π + 0.5( y y ) + 0.5( π π ) + r = ( 0.084) + 0.5( ) So he arge neres rae accordng o he Taylor rule should be negave 0.5 percen. 2.2 Download an alernave oupu gap from hp:// Redo your calculaons for problem 2.1. How have your answers changed as a consequence of hs alernave oupu gap? oupu gap (dev'n from me rend) Oupu gap (HP devaon) The oupu gap defned as a devaon from an HP-rend s n 2009Q = ( 0.024) + 0.5( ) So he arge neres rae should be 2.6 percen. 3. Suppose we have an economy gven by he followng equaons (IS-LM-BP=0) under floang exchange raes. (1) = α[ A + EXP IMP + ( n+ v) q b] <IS curve> (1 ) = A + EXP IMP + ( n + v) q 1 c( 1 ) + m b b <IS curve> (2) = μ h 1 h (3) ( ) M P k + h m = 1 EXP IMP + KA + n + v q + κ [( ) ( ) ] + κ <LM curve> <BP=0 curve> 5

6 And assume we wsh o ncrease oupu, and m/κ s small. 3.1 Show wha happens when governmen spendng s ncreased. LM M, P, μ BP=0 E XP,, BP=0 EXP, q, A ', EXP, q A ', EXP, Show wha happens f he money supply s ncreased. LM M ', P, μ 0 BP=0 E XP, q, 2 BP=0 E XP,, 1 A, EXP, A, EXP, q Show wha happens f he money supply s ncreased, boh a home and abroad? Wll he currency deprecae or apprecae (.e., can you accomplsh expendure swchng)? 6

7 LM M ', P, μ BP=0 E XP, q, 2 BP=0 EXP,, BP=0 E XP,, 3 A, EXP, A, EXP, q" 3 2 The decrease n foregn neres raes nduces a drop n he BP=0 schedule. The neres rae now exceeds ha necessary for exernal balance, so he home currency apprecaes. As a consequence, he IS curve shfs n. 3.4 Suppose mpor demand s gven by: IM = IMP + m nq( 1+ τ ) Where τ s he arff rae. Suppose he governmen rases he arff rae from zero o τ > 0 0. Wha happens o oupu? The effec s he same as n he answer o queson Suppose he foregn counry responds o 3.4 by reducng E XP. Wha happens o he home counry? In macroeconomc erms, realaon nullfes he curve shfs n he answer o queson 3.4. Pa974ps2a_f09,