Problem Se 4 ECN 101 Inermediae Macroeconomics SOLUTIONS Numerical Quesions 1. Assume ha he demand for real money balance (M/P) is M/P = 0.6-100i, where is naional income and i is he nominal ineres rae. The real ineres rae r is fixed a 3 percen by he invesmen and saving funcions. The expeced inflaion rae equals he rae of nominal money growh. a. If is 1,000, M is 100, and he growh rae of nominal money is 1 percen, wha mus i and P be? i = 4%, P = ½ b. If is 1,000, M is 100, and he growh rae of nominal money is 2 percen, wha mus i and P be? i = 5%, P = 1 2. Assume ha he long-run aggregae supply curve is verical a = 3,000 while he shor-run aggregae supply curve is horizonal a P = 1.0. The aggregae demand curve is = 3(M/P) and M = 1,000. a. If he economy is iniially in long-run equilibrium, wha are he values of P and? P = 1.0; = 3,000 b. Now suppose a supply shock moves he shor-run aggregae supply curve o P = 1.5. Wha are he new shor-run P and? P = 1.5; = 2,000 c. If he aggregae demand curve and long-run aggregae supply curves are unchanged, wha are he long-run equilibrium P and afer he supply shock? P = 1.0; = 3,000 d. Suppose ha afer he supply shock he Fed waned o hold oupu a is long-run level. Wha level of M would be required? If his level of M were mainained, wha would be long-run equilibrium P and? M = 1,500; P = 1.5; = 3,000 1
Problem Se 4 ECN 101 Inermediae Macroeconomics 3. Suppose you are an economis working for he Federal Reserve when droughs in he souheas and floods in he Midwes subsanially reduce food producion in he Unied Saes. Use he aggregae demand/aggregae supply model o graphically illusrae your policy recommendaion o accommodae his adverse supply shock assuming ha your op prioriy is mainaining full employmen in he economy. Be sure o label: i. he axes; ii. he curves; iii. he iniial equilibrium values; iv. he direcion he curves shif; and v. he erminal equilibrium values. Sae in words wha happens o prices and oupu as a combined resul of he supply shock and he recommended Fed accommodaion. P LRAS P2 P 1 B A SRAS 2 SRAS1 AD 2 AD1 1 2
Problem Se 4 ECN 101 Inermediae Macroeconomics Compuer Quesions This Par is Due June 7 This secion is a lile more involved han usual, hence he expanded due dae. Hopefully, you will also find i more ineresing. The EXCEL file for his par of he homework is labeled ps4.xls and conains he following daa (furher deails are available in he EXCEL file) exraced from he S. Louis Fed websie: DPIC96: Real Disposable Income GDPC96: Real Gross Domesic Produc GDPPOT2: Real Poenial Gross Domesic Produc PCECC96: Real Personal Consumpion Expendiures PCECTPI: PCE deflaor TB3: 3-monh T-Bill Rae Recession: 1 if recession, 0 oherwise. a) The firs goal will be o consruc an esimae of he Phillips Curve. Recall, he Phillips curve can be expressed as: e π = π + γ ( ) For his purpose, you will need o consruc he yearly rae of inflaion using he PCE deflaor. One way o do his is by using he usual logarihmic approximaion: π = ln( PCE Deflaor) ln( PCE Deflaor) 4 and noicing ha he daa is in quarerly frequency. As an approximaion o π e you can use π -1. Nex you will need o consruc, i.e., he difference beween acual and poenial oupu, also called he oupu gap. This can be easily calculaed, in percenage, by consrucing he following logarihmic difference: GAP = 100 (ln( rgdp) ln( rgdp)) ou are now in a posiion o calculae he coefficien γ by doing a scaer plo of ( π π 1) on GAP and fiing a rend line in EXCEL wih he opion se inercep o = 0 seleced. For his par you should repor he scaer plo wih he regression line and he regression oupu. b) The second iem in he agenda will consis in fiing a Taylor rule o he daa and finding he sensiiviy of ineres raes o variaions in he oupu gap. From he previous par, you have already calculaed all he variables ha you will need. To be sure, here is one way o wrie down he Taylor rule (he acual coefficiens 3
Problem Se 4 ECN 101 Inermediae Macroeconomics proposed by Taylor are somewha differen bu I use slighly differen daa. Also noice ha I am lagging inflaion and he oupu gap o indicae ha he cenral bank observed hese variables wih a one quarer delay): i = 4 + ( π 1 2) + β ( 1 1) As you can see, I have assumed ha if inflaion goes up by 1% above he inflaion arge (2%), nominal ineres raes will be raised by 1%. If inflaion and oupu are a heir argeed levels, hen nominal ineres raes will be se a 4%. To esimae he coefficien β you will need o consruc an adjused, nominal ineres rae series by aking he curren hree-monh T-Bill rae and subracing 2 and he lagged rae of inflaion (i.e. moving o he lef hand side of he previous expression he erms 4 + ( π 1 2). Noice ha was already calculaed as he variable GAP in he previous quesion so all you need o do is make sure ha you use is lag, raher han he curren value. Similar o par a), you will need o do a scaer plo of he adjused ineres rae series jus described on o he lag of he variable GAP. Be sure o add a rend line wih he se inercep opion seleced. This will give you an esimae of β. Repor he scaer plo wih rend line and he regression oupu. c) Using he previous par, check o see how well your esimaed Taylor rule does hisorically. For ha purpose you will need o creae a series of prediced ineres raes as follows: iˆ = 4 + ( π 1 2) + βgap 1 ˆ where he has denoe esimaes. Do a line plo of he acual series for he hree-monh T-Bill, he series prediced by he expression jus described, and he series recession imes 20 (so ha you can see more clearly where he recession periods are). Repor he line plo and commen on how well you predic ineres raes wih his simple Taylor rule, and he relaion beween your predicions and he acual ineres rae over he business cycle. Be sure o label your X-axis so ha he daes show. d) This one is an easy one. Use he daa on personal consumpion expendiures and personal income o calculae he consumpion rae over ime (a crude approximaion o he marginal propensiy o consume). Call his φˆ. Do a simple plo over ime (make sure ha you pu he daes on he x-axis) and calculae he average over he sample. e) Suppose ha he IS curve is given by: = a + ˆ φ ( T ) + G 2i and he Taylor rule is given by your esimaes in par c) by 4
Problem Se 4 ECN 101 Inermediae Macroeconomics i = 4 + ( π 2) + ˆ( β ) Solve for he aggregae demand curve as a funcion of I and calculae he following mulipliers (noice ha you do no acually need he specific values of a or o answer his quesion since hey do no ener in he mulipliers): a) The governmen expendiures muliplier b) The ax muliplier c) The slope of he aggregae demand curve Soluions: Noice, he average MPC for he daa provided is φ = 0.9. The esimae of β = 0.12. Hence, subsiuing he Taylor rule ino he IS curve, we ge: Combining erms in or more specifically [ + ( 2) + 0.12( )] = a + 0.9( T ) + G 2 4 π ( 1 0.9 + 0.24) = ( a 4 + 0.12 ) 0.9T + G 2π ( a 4 + 0.12 ) = 2.65T + 2.94G 5.88π 0.34 from where: The governmen expendiures mulilplier is 2.94 The ax muliplier is -2.65 The slope is -5.88. 5