1 Inermediae Macroeconomics: Mid-erm exam May 30 h, 2016 Makoo Saio Try he following hree roblems, and submi your answer in handwrien A4 aers. You are execed o dro your aers ino he mailbox assigned for our course a he educaional affairs secion ( 教務課 ) on he firs floor of he main building ( 本館 ) by 3:00 m on June 10 h, 2016. Any of your commen on my lecure including is conens and syle, he exbook, he handous, he emirical exercises, and his mid-erm would be areciaed.
2 1. GDP deflaors and erms of rade Figure PS1-1 deics he quarerly ime series of he GDP deflaor for he eriod from he firs quarer of 1994 o he firs quarer of 2016. Inerre his series along equaion (PS1-1) using he acual SNA daases. GDP No min al GDP P = Real GDP No min al GDP Real GDP+Trading Gain/Loss = Real GDI Real GDP GDI Trading Gain/Loss = P 1+ Real GDP (PS1-1) For his urose, you may wan o exloi he relaionshi beween he rading gain/loss and he erms of rade. The SNA daases are available from he nominal series, he real series, and he deflaor series a my websie. If you are ineresed in using grahs for your argumen, you can ase heir hardcoies on your answer shees by glues. Reviewing Chaer 2 may be quie helful in solving he above roblem.
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4 2. Inroducing wo-eriod nominal rigidiy In he ninh secion of Chaer 7, I resen he following inflaion version of AS-AD model. + 1 ( y y ) π = π + θ (7-31) ( π ) y = y + κ m (7-19) Togeher wih equaion (7-19), equaion (7-31) may rewrien as 1 κθ π = π+ 1 + m 1+ κθ 1+ κθ. (7-32) 1 Noe ha 0< < 1 1+ κθ. (Q1) Solve equaion (7-32) for he curren inflaion rae π by exloiing a mahemaical echnique resened in he second secion of Chaer 1. You can assume ha < π < π < π < for all. τ = 0 m+ τ π ++ 1 lim τ + 1 τ+ 1 κθ π = + τ τ ( 1+ κθ ) ( 1+ κθ ). (7-33) π = κθ m τ τ ( + ) 1 τ 0 1 + = + κθ (7-34)
5 (Q2) Suose ha κ = θ = 1. How much do π and y increase by moneary exansion in he following hree cases? Case 1: Case 2: +3 on. Case 3: m = m+ m, and m + τ = m from ime +1 on. m = m+ m, m = + 1 m + m, m + 2 = m+ m, and m + τ = m from ime m + τ = m+ m from ime on forever. (Q3) Inerre your resuls on Q2 inuiively by word.
6 3. AS-AD analysis on he Jaanese economy Le us make a simle emirical exercise o exlore how he AS-AD model works in a real world using Jaanese macroeconomic daa. We emloy he following sandard AS-AD model under he adaive execaions hyohesis: ( y y ) π = π + θ + ξ, (PS3-1) 1 ( π ) y = y + κ m, (PS3-2) where ξ in equaion (PS3-1) reresens a suly shock. Iniially, he π = m. economy is assumed o says a y = y and (Q1) Suose ha wih a suly shock ξ fixed, moneary exansion shifs u he downward sloing AD curve. As learned in class, moneary exansion iniially hels raise real ouu beyond he oenial ouu wih a mild acceleraion of inflaion raes, bu such olicy imacs gradually hase ou, and real ouu evenually reurns o he oenial ouu. You are asked o draw he rocess in which real ouu increases, bu finally comes back o he oenial ouu on he sace of he ouu ga ( y π Y Y y ) as a Y horizonal axis and a change in inflaion raes ( 1 ) as a verical axis. Consider he case of moneary conracion on he same sace. π (Q2) Now, a eculiar form of a emorary suly shock is inroduced ino his sysem. Wih moneary olicy m fixed, ξ akes ξ in ime, m π in ime +1, and zero from ime +2 on. ξ may be osiive or negaive. Draw he rocess immediaely afer he realizaion of such emorary suly shocks on he same sace as above.
7 Through Q1 and Q2, you may see ha he movemen induced by eiher moneary exansion or conracion emerges as an uward-sloing relaion on π π he sace of ( y y ) and ( 1 ), and ha driven by emorary suly shocks as a downward-sloing relaion on he same sace. Now, i is your urn o examine which aern is consisen wih Jaanese macroeconomic daa. Choose as an ouu measure he real GNI which conrols for rading gain/loss and ne income ransfer from foreign counries, and as a rice measure he GNI deflaor. Le us esimae he oenial ouu by a heroic aroximaion. Suose ha real ouu Y grow a a consan rae ϕ or Y Y ( ϕ ) 0 1 = +. Then, he Y Y Y ouu ga is comued by lny lny y y y ( y0 ϕ ) = +. Using he seasonally adjused daa of real GNI for he eriod from he firs quarer of 1994 o he firs quarer of 2013, he series of logarihmic ouu can be aroximaed by a linear equaion y0 + ϕ as in Figure PS3-1, and
8 aroximaion errors may be regarded as ouu gas ( y y ). A change in inflaion raes π π 1 is defined as a firs difference of he annual inflaion from one year earlier, or ( ) ( ), where 4 4 8 = ln P. Figure PS3-2 los he ime series of boh ouu gas and changes in inflaion raes. In addiion, changes in inflaion raes are loed agains ouu gas for he hree suberiods in he scaer diagrams of Figures PS3-3, PS3-4, and PS3-5.
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10 (Q3) Inerre he above hree scaer diagrams by exloiing imlicaions available from Q1 and Q2. (Q4) Do you have any alernaive idea, oher han wha is imlied by your answer o Q1 and Q2 for inerreing hese scaer diagrams?