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
LM R 0, m 0 0 1 CC Z 0, R 0, m 0 CC Z 1, R 0, m 0 1 0 1.2 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 0 1 2 CC Z 1, R 1, m 0 CC Z 1, R 0, m 0 1 2 2
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 2. 1.3 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 0 3 1 CC A 1, Z 1, R 0, m 0 CC A 0, Z 1, R 0, m 0 1 3 2. 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 0.025 (2.5%), calculae he arge Fed Funds rae for 2009Q3. 3
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 8.271451 0.003774 2191.976 0.0000 TIME 0.007566 3.84E-05 197.0944 0.0000 R-squared 0.995668 Mean dependen var 8.914603 Adjused R-squared 0.995643 S.D. dependen var 0.375412 S.E. of regresson 0.024781 Akake nfo creron -4.545865 Sum squared resd 0.103781 Schwarz creron -4.509120 Log lkelhood 390.6714 Hannan-Qunn crer. -4.530955 F-sasc 38846.19 Durbn-Wason sa 0.117402 Prob(F-sasc) 0.000000 The oupu gap looks lke hs:.15.10 Core nflaon (y/y).05.00 -.05 -.10 oupu gap (dev'n from me rend) 70 75 80 85 90 95 00 05 Wh he 2009Q3 oupu gap equal o -0.084, and y/y CPI core nflaon s 0.015.. Le s use he Taylor rule. 4
FF = π + 0.5( y y ) + 0.5( π π ) + r 0.0045 = 0.015 + 0.5( 0.084) + 0.5(0.015 0.02) + 0.025 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://www.ssc.wsc.edu/~mchnn/oupugap.xls. Redo your calculaons for problem 2.1. How have your answers changed as a consequence of hs alernave oupu gap?.06.04.02.00 -.02 -.04 -.06 -.08 -.10 oupu gap (dev'n from me rend) Oupu gap (HP devaon) 70 75 80 85 90 95 00 05 The oupu gap defned as a devaon from an HP-rend s -0.024 n 2009Q3. 0.0255 = 0.015 + 0.5( 0.024) + 0.5(0.015 0.02) + 0.025 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
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 0 1 2 BP=0 E XP,, BP=0 EXP, q, A ', EXP, q A ', EXP, 0 2 1 3.2 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 0 1 2 3.3 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
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 3.1. 3.5 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, 13.11.2009 7