11/6/2013. Chapter 14: Dynamic ADAS. Introduction. Introduction. Keeping track of time. The model s elements


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1 Inroducion Chaper 14: Dynamic DS dynamic model of aggregae and aggregae supply gives us more insigh ino how he economy works in he shor run. I is a simplified version of a DSGE model, used in cuingedge macroeconomic research. DSGE = Dynamic, Sochasic, General Equilibrium) 0 1 Inroducion dynamic model of aggregae and aggregae supply is buil from familiar conceps, such as: he IS curve, which negaively relaes he real ineres rae and for goods & services he Phillips curve, which relaes inflaion o he gap beween oupu and is naural level, expeced inflaion, and supply shocks adapive expecaions, a simple model of inflaion expecaions How he dynamic DS model is differen from he sandard model Insead of fixing he money supply, he cenral bank follows a moneary policy rule ha adjuss ineres raes when oupu or inflaion change. verical axis of he DDDS diagram measures he inflaion rae, no he price level. Subsequen ime periods are linked ogeher: Changes in inflaion in one period aler expecaions of fuure inflaion, which changes aggregae supply in fuure periods, which furher alers inflaion and inflaion expecaions. 3 Keeping rack of ime model s elemens subscrip denoes he ime period, e.g. = real GDP in period 1 = real GDP in period 1 +1 = real GDP in period + 1 We can hink of ime periods as years. E.g., if = 008, hen = 008 = real GDP in = 007 = real GDP in = 009 = real GDP in 009 model has five equaions and five endogenous variables: oupu, inflaion, he real ineres rae, he ineres rae, and expeced inflaion. equaions may use differen noaion, bu hey are concepually similar o hings you ve already learned. firs equaion is for oupu 4 5 1
2 Oupu: Demand for Goods and Services r ) Oupu: Demand for Goods and Services r ) oupu naural level of real ineres 0, 0 oupu rae Negaive relaion beween oupu and ineres rae, same inuiion as IS curve. measures he ineresrae sensiiviy of naural rae of ineres in absence of shocks, when r shock, random and zero on average 6 7 ex ane i.e. expeced) real ineres rae 1 E 1 Real Ineres Rae: Fisher Equaion r i E 1 ineres rae expeced inflaion rae increase in price level from period o +1, no known in period expecaion, formed in period, of inflaion from o +1 curren inflaion Inflaion: Phillips Curve E 1 ) previously expeced inflaion 0 indicaes how much inflaion responds when oupu flucuaes around is naural level supply shock, random and zero on average 8 9 Expeced Inflaion: dapive Expecaions E 1 Nominal Ineres Rae: MonearyPolicy Rule i ) ) For simpliciy, we assume people expec prices o coninue rising a he curren inflaion rae. ineres rae, se each period by he cenral bank naural rae of ineres cenral bank s inflaion arge 0,
3 Nominal Ineres Rae: MonearyPolicy Rule i ) ) measures how much he cenral bank adjuss he ineres rae when inflaion deviaes from is arge measures how much he cenral bank adjuss he ineres rae when oupu deviaes from is naural rae 1 CSE STUD Taylor Rule Economis John Taylor proposed a moneary policy rule very similar o ours: i ff = ) 0.5GDP gap) where i ff = federal funds rae arge GDP gap = 100 x = percen by which real GDP is below is naural rae Taylor Rule maches Fed policy fairly well. 13 Percen n CSE STUD Taylor Rule acual Federal Funds rae Taylor s rule model s variables and parameers Endogenous variables: r i E 1 Oupu Inflaion Real ineres rae Nominal ineres rae Expeced inflaion model s variables and parameers model s variables and parameers Exogenous variables: Naural level of oupu Cenral bank s arge inflaion rae Demand shock Supply shock Predeermined variable: Previous period s inflaion 1 Parameers: Responsiveness of o he real ineres rae Naural rae of ineres Responsiveness of inflaion o oupu in he Phillips Curve Responsiveness of i o inflaion in he monearypolicy rule Responsiveness of i o oupu in he monearypolicy rule
4 model s longrun equilibrium normal sae around which he economy flucuaes. Two condiions required for longrun equilibrium: re are no shocks: 0 Inflaion is consan: 1 model s longrun equilibrium Plugging he preceding condiions ino he model s five equaions and using algebra yields hese longrun values: r 1 E i Dynamic ggregae Supply Curve DS curve shows a relaion beween oupu and inflaion ha comes from he Phillips Curve and dapive Expecaions: 1 DS) 1 ) Dynamic ggregae Supply Curve 1 ) DS slopes upward: high levels of oupu DS are associaed wih high inflaion. DS shifs in response o changes in he naural level of oupu, previous inflaion, and supply shocks. 0 1 Dynamic ggregae Demand Curve To derive he DD curve, we will combine four equaions and hen eliminae all he endogenous variables oher han oupu and inflaion. Sar wih he for goods and services: r ) i E ) 1 using he Fisher eq n Dynamic ggregae Demand Curve resul from previous slide i E ) 1 using he expecaions eq n i ) using moneary policy rule [ ) ) ] [ ) )] 3 4
5 Dynamic ggregae Demand Curve resul from previous slide [ ) )] combine like erms, solve for ) B, where 1 0, B DD) Dynamic ggregae Demand Curve ) B DD slopes downward: When inflaion rises, he cenral bank raises he real ineres rae, reducing he for goods & services. DD shifs in response o changes in he naural level of oupu, DD he inflaion arge, and shocks. 4 5 shorrun equilibrium Longrun growh DD DS In each period, he inersecion of DD and DS deermines he shorrun eq m values of inflaion and oupu. In he eq m shown here a, oupu is below is naural level. +1 Period DS : shifs iniial because eq m a economy can DS produce more DS +1 g&s Period + 1 : B New Longrun eq m a B, = DD shifs income growh grows because bu increases inflaion he higher income remains naural sable. rae raises of oupu. DD DD +1 for g&s shock o aggregae supply Parameer values for simulaions + 1 B C D + 1 DD DS DS +1 DS + DS 1 Period : + 1: 1 : : Supply s iniial inflaion eq m shock falls, a is inflaion ν over > 0) ν shifs = 0) bu expecaions DS DS upward; does fall, no reurn DS inflaion moves o is rises, iniial posiion downward, cenral bank due o higher oupu responds inflaion rises. by expecaions. This raising process real coninues ineres rae, unil oupu reurns falls. o is naural rae. LR eq m a Thus, we can inerpre as he percenage deviaion of Cenral bank s inflaion oupu from is naural level. arge 1percenagepoin following is percen. graphs are increase called impulse in he real response ineres rae funcions. reduces y oupu by 1 percen of response naural show he rae of ineres of is he is naural level. percen. endogenous variables o When oupu is 1 percen he impulse, i.e. he shock. above is naural level, inflaion rises by 0.5 percenage poin. se values are from he Taylor Rule, which approximaes he acual behavior of he Federal Reserve
6 dynamic response o a supply shock dynamic response o a supply shock oneperiod supply shock affecs oupu for many periods. Because inflaion expecaions adjus slowly, l acual inflaion remains high for many periods. dynamic response o a supply shock dynamic response o a supply shock r real ineres rae akes many periods o reurn o is naural rae. i behavior of he ineres rae depends on ha of he inflaion and real ineres raes. shock o aggregae DS +5 DS +4 DS +3 F G DS E D DS + 1 C B DS 1, 1 DD,+1,,+4 DD 1, Periods : + 1: + 1 5: 6 : Higher DS and iniial o Posiive + higher: is 4 eq m inflaion : in due DS Higher raised o gradually higher inflaion shock expecaions inflaion shifs ε previous > 0) down shifs in as for preceding inflaion period D + o 1, he raises and period, righ; shifing bu inflaion oupu ao inflaion DS rise. up. Inflaion shock expecaions, ends rises and fall, more, DD economy shifs reurns oupu DS up. falls. o is gradually Inflaion iniial posiion. rises, Eq m recovers oupu a falls. G. unil reaching LR eq m a. 34 dynamic response o a shock shock raises oupu for five periods. When he shock ends, oupu falls below is naural level, and recovers gradually. 6
7 dynamic response o a shock shock causes inflaion o rise. When he shock ends, inflaion gradually falls oward is iniial level. dynamic response o a shock shock raises he real ineres rae. fer he shock ends, he real ineres r rae falls and approaches is iniial level. dynamic response o a shock shif in moneary policy i behavior of he ineres rae depends on ha of he inflaion and real ineres raes. 1 = % final = 1% B C Z DS 1, DS +1 DD, +1, DS final DD 1 Period Subsequen 1: : + 1 : arge periods: Cenral fall inflaion bank rae reduced This lowers process = arge %, iniial inflaion coninues o eq m = 1%, a unil expecaions oupu raises reurns real for o ineres is + naural 1,, rae, shifing rae shifs and DD DS downward. inflaion lefward. Oupu reaches rises, and is new inflaion arge. falls. fall. 1, final 39 dynamic response o a reducion in arge inflaion dynamic response o a reducion in arge inflaion Reducing he arge inflaion rae causes oupu o fall below is naural level for a while. Oupu recovers gradually. Because expecaions adjus slowly, i akes many periods for inflaion o reach he new arge. 7
8 dynamic response o a reducion in arge inflaion r To reduce inflaion, he cenral bank raises he real ineres rae o reduce aggregae. real ineres rae gradually reurns o is naural rae. dynamic response o a reducion in arge inflaion i iniial increase in he real ineres rae raises he ineres rae. s he inflaion and real ineres raes fall, he rae falls. Oupu variabiliy vs. inflaion variabiliy supply shock reduces oupu bad) and raises inflaion also bad). cenral bank faces a radeoff beween hese bads i can reduce he effec on oupu, bu only by oleraing i an increase in he effec on inflaion. 44 Oupu variabiliy vs. inflaion variabiliy 1 CSE 1: θ is large, θ is small supply shock In his case, a shifs DS up. small change in DS inflaion has a large effec on DS 1 oupu, so DD is relaively fla. 1 DD 1, shock has a large effec on oupu, bu a small effec on inflaion. 45 Oupu variabiliy vs. inflaion variabiliy 1 CSE : θ is small, θ is large 1 DS DD 1, DS 1 In his case, a large change in inflaion has only a small effec on oupu, so DD is relaively seep. Now, he shock has only a small effec on oupu, bu a big effec on inflaion. 46 Taylor Principle Taylor Principle named afer John Taylor): proposiion ha a cenral bank should respond o an increase in inflaion wih an even greaer increase in he ineres rae so ha he real ineres rae rises). I.e., cenral bank should se θ > 0. Oherwise, DD will slope upward, economy may be unsable, and inflaion may spiral ou of conrol. 47 8
9 Taylor Principle 1 ) 1 1 ) ) DD) i MP rule) Taylor Principle 1 ) 1 1 ) ) DD) i MP rule) If θ > 0: When inflaion rises, he cenral bank increases he ineres rae even more, which increases he real ineres rae and reduces he for goods & services. DD has a negaive slope. 48 If θ < 0: When inflaion rises, he cenral bank increases he ineres rae by a smaller amoun. real ineres rae falls, which increases he for goods & services. DD has a posiive slope. 49 Taylor Principle If DD is upwardsloping and seeper han DS, hen he economy is unsable: oupu will no reurn o is naural level, and inflaion will spiral upward for posiive shocks) or downward for negaive ones). Esimaes of θ from published research: θ = 0.14 from , before Paul Volcker became Fed chairman. Inflaion was high during his ime, especially during he 1970s. θ = 0.7 during he Volcker and Greenspan years. Inflaion was much lower during hese years. 50 Chaper Summary DDDS model combines five relaionships: an IScurvelike equaion of he goods marke, he Fisher equaion, a Phillips curve equaion, an equaion for expeced inflaion, and a moneary policy rule. longrun equilibrium of he model is classical. Oupu and he real ineres rae are a heir naural levels, independen of moneary policy. cenral bank s inflaion arge deermines inflaion, expeced inflaion, and he ineres rae. Chaper Summary DDDS model can be used o deermine he immediae impac of any shock on he economy, and can be used o race ou he effecs of he shock over ime. parameers of he moneary policy rule influence he slope of he DS curve, so hey deermine wheher a supply shock has a greaer effec on oupu or inflaion. Thus, he cenral bank faces a radeoff beween oupu variabiliy and inflaion variabiliy. Chaper Summary DDDS model assumes ha he Taylor Principle holds, i.e. ha he cenral bank responds o an increase in inflaion by raising he real ineres rae. Oherwise, he economy may become unsable and inflaion may spiral ou of conrol. 9
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