A Dynamic Model of Economic Fluctuations

Transcription

1 CHAPTER 15 A Dynamic Model of Economic Flucuaions Modified for ECON 2204 by Bob Murphy 2016 Worh Publishers, all righs reserved

2 IN THIS CHAPTER, OU WILL LEARN: how o incorporae dynamics ino he AD-AS model we previously sudied how o use he dynamic AD-AS model o illusrae longrun economic growh how o use he dynamic AD-AS model o race ou he effecs over ime of various shocks and policy changes on oupu, inflaion, and oher endogenous variables 1

3 Inroducion The dynamic model of aggregae demand 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 cuing-edge macroeconomic research. (DSGE = Dynamic, Sochasic, General Equilibrium) Dynamic Model of Economic Flucuaions 2

4 Inroducion The dynamic model of aggregae demand and aggregae supply is buil from familiar conceps, such as: he IS curve, which negaively relaes he real ineres rae and demand 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 Dynamic Model of Economic Flucuaions 3

5 How he dynamic AD-AS 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. The verical axis of he DAD-DAS 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. Dynamic Model of Economic Flucuaions 4

6 Keeping rack of ime The 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 = 2010, hen = 2010 = real GDP in = 2009 = real GDP in = 2011 = real GDP in 2011 Dynamic Model of Economic Flucuaions 5

7 The model s elemens The model has five equaions and five endogenous variables: oupu, inflaion, he real ineres rae, he nominal ineres rae, and expeced inflaion. The equaions may use differen noaion, bu hey are concepually similar o hings you ve already learned. The firs equaion is for oupu Dynamic Model of Economic Flucuaions 6

8 Oupu: The Demand for Goods and Services = ( r ) + α ρ ε oupu naural level of oupu real ineres rae α > 0, ρ > 0 Negaive relaion beween oupu and ineres rae, same inuiion as IS curve. Dynamic Model of Economic Flucuaions 7

9 Oupu: The Demand for Goods and Services = ( r ) + α ρ ε measures he ineres-rae sensiiviy of demand Naural rae of ineres. In absence of demand shocks, = when r = ρ demand shock, random and zero on average Dynamic Model of Economic Flucuaions 8

10 The Real Ineres Rae: The Fisher Equaion ex ane (i.e. expeced) real ineres rae r = i E π + 1 nominal ineres rae expeced inflaion rae π + = 1 E π + = 1 increase in price level from period o +1, no known in period expecaion, formed in period, of inflaion from o +1 Dynamic Model of Economic Flucuaions 9

11 Inflaion: The Phillips Curve π π φ ν = E + ( ) + 1 curren inflaion previously expeced inflaion φ > 0 indicaes how much inflaion responds when oupu flucuaes around is naural level supply shock, random and zero on average Dynamic Model of Economic Flucuaions 10

12 Expeced Inflaion: Adapive Expecaions E π π = + 1 For simpliciy, we assume people expec prices o coninue rising a he curren inflaion rae. Dynamic Model of Economic Flucuaions 11

13 The Nominal Ineres Rae: The Moneary-Policy Rule = π + ρ + θ π π * + θ π i ( ) ( ) nominal ineres rae, se each period by he cenral bank naural rae of ineres cenral bank s inflaion arge θπ > 0, θ > 0 Dynamic Model of Economic Flucuaions 12

14 The Nominal Ineres Rae: The Moneary-Policy Rule = π + ρ + θ π π * + θ π 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 Dynamic Model of Economic Flucuaions 13

15 CASE STUD The Taylor rule Economis John Taylor proposed a moneary policy rule very similar o ours: i ff where = π (π 2) 0.5(GDP gap) i ff = nominal federal funds rae arge GDP gap = 100 x = percen by which real GDP is below is naural rae The Taylor rule maches Fed policy fairly well. Dynamic Model of Economic Flucuaions 14

16 percen CASE STUD The Taylor rule acual federal funds rae Taylor s rule

17 The model s variables and parameers Endogenous variables: = π = r = i = E π + = 1 Oupu Inflaion Real ineres rae Nominal ineres rae Expeced inflaion Dynamic Model of Economic Flucuaions 16

18 The model s variables and parameers Exogenous variables: = π * = Naural level of oupu Cenral bank s arge inflaion rae ε = ν = Demand shock Supply shock Predeermined variable: π = 1 Previous period s inflaion Dynamic Model of Economic Flucuaions 17

19 The model s variables and parameers Parameers: α = ρ = φ = θ = π θ = Responsiveness of demand 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 moneary-policy rule Responsiveness of i o oupu in he moneary-policy rule Dynamic Model of Economic Flucuaions 18

20 The model s long-run equilibrium The normal sae around which he economy flucuaes. Two condiions required for long-run equilibrium: There are no shocks: Inflaion is consan: ε π = ν = 1 = π 0 Dynamic Model of Economic Flucuaions 19

21 The model s long-run equilibrium Plugging he preceding condiions ino he model s five equaions and using algebra yields hese long-run values: r π = = = ρ π * = π * + 1 E π i = ρ + π * Dynamic Model of Economic Flucuaions 20

22 The Dynamic Aggregae Supply Curve The DAS curve shows a relaion beween oupu and inflaion ha comes from he Phillips Curve and Adapive Expecaions: π π φ ν (DAS) = + ( ) + 1 Dynamic Model of Economic Flucuaions 21

23 The Dynamic Aggregae Supply Curve π π = π 1 + φ( ) + ν DAS DAS slopes upward: high levels of oupu are associaed wih high inflaion. DAS shifs in response o changes in he naural level of oupu, previous inflaion, and supply shocks. Dynamic Model of Economic Flucuaions 22

24 The Dynamic Aggregae Demand Curve To derive he DAD curve, we will combine four equaions and hen eliminae all he endogenous variables oher han oupu and inflaion. Sar wih he demand for goods and services: = α( r ρ) + ε = α( i E π ρ) + ε + 1 using he Fisher eq n Dynamic Model of Economic Flucuaions 23

25 The Dynamic Aggregae Demand Curve resul from previous slide = α( i E π ρ) + ε + 1 = α( i π ρ) + ε using he expecaions eq n using moneary policy rule απ ρ θ π π θ π ρ ε * = [ + + π ( ) + ( ) ] + αθ π π θ ε * = [ π ( ) + ( )] + Dynamic Model of Economic Flucuaions 24

26 The Dynamic Aggregae Demand Curve resul from previous slide = [ ( * ) + ( )] + π αθ π π θ ε combine like erms, solve for = * + A( π π ) B ε, (DAD) where αθ 1 A = π > 0, B = > 0 1+ αθ 1+ αθ Dynamic Model of Economic Flucuaions 25

27 The Dynamic Aggregae Demand Curve π = A( * ) + B π π ε DAD slopes downward: When inflaion rises, he cenral bank raises he real ineres rae, reducing he demand for goods & services. DAD DAD shifs in response o changes in he naural level of oupu, he inflaion arge, and demand shocks. Dynamic Model of Economic Flucuaions 26

28 The shor-run equilibrium π π A DAS In each period, he inersecion of DAD and DAS deermines he shor-run eq m values of inflaion and oupu. DAD In he eq m shown here a A, oupu is below is naural level. Dynamic Model of Economic Flucuaions 27

29 π = π + 1 Long-run growh Period : iniial eq m a A π π A B +1 DAS DAS +1 Period + 1: Long-run growh increases he naural rae of oupu. DAD +1 DAD +1 Dynamic Model of Economic Flucuaions 28

30 Long-run growh π +1 DAS shifs because economy can produce more g&s. π = π + 1 π A B DAS DAS +1 DAD shifs because higher income raises demand for g&s. DAD +1 DAD +1 Dynamic Model of Economic Flucuaions New eq m a B; income grows bu inflaion remains sable. 29

31 A shock o aggregae supply π π + 2 π 1 π B C D A DAD DAS DAS +1 DAS +2 DAS -1 Period 1: iniial eq m a A Period : Supply shock (ν > 0) shifs DAS upward; inflaion rises, cenral bank responds by raising real ineres rae, oupu falls. Dynamic Model of Economic Flucuaions 30

32 A shock o aggregae supply π π + 2 π 1 π B C D A DAD DAS DAS +1 DAS +2 DAS -1 Dynamic Model of Economic Flucuaions Period + 1 : Supply shock is over (ν = 0) bu DAS does no reurn o is iniial posiion due o higher inflaion expecaions. Period + 2: As inflaion falls, inflaion expecaions fall, DAS moves downward, oupu rises. 31

33 A shock o aggregae supply π DAS DAS +1 π π + 2 π 1 B C D A DAD DAS +2 DAS -1 This process coninues unil oupu reurns o is naural rae. LR eq m a A. Dynamic Model of Economic Flucuaions 32

34 Parameer values for simulaions π * = = Thus, we can inerpre as he percenage deviaion of oupu from is naural level. α ρ = = Cenral bank s inflaion arge is 2 percen. φ θ π θ = = = A 1-percenage-poin increase in he real ineres rae reduces oupu demand by 1 percen of is naural level. Dynamic Model of Economic Flucuaions 33

35 Parameer values for simulaions π * α ρ φ θ π θ = = = = = = = The naural rae of ineres is 2 percen. When oupu is 1 percen above is naural level, inflaion rises by 0.25 percenage poin. These values are from he Taylor rule, which approximaes he acual behavior of he Federal Reserve. The following graphs are called impulse response funcions. They show he response of he endogenous variables o he impulse (he shock). Dynamic Model of Economic Flucuaions 34

36 The dynamic response o a supply shock ν A oneperiod supply shock affecs oupu for many periods.

37 The dynamic response o a supply shock ν π Because inflaion expecaions adjus slowly, acual inflaion remains high for many periods.

38 The dynamic response o a supply shock ν r The real ineres rae akes many periods o reurn o is naural rae.

39 The dynamic response o a supply shock ν i The behavior of he nominal ineres rae depends on ha of he inflaion and real ineres raes.

40 A shock o aggregae demand π DAS +5 DAS +4 Period 1: iniial eq m a A π π 1 G A 1 F E D C DAD -1, +5 DAS +3 DAS +2 π + 5 Period : + 5 B DAS + 1 DAS -1, DAD,+1,,+4 Posiive demand shock (ε > 0) shifs DAD o he righ; oupu and inflaion rise. Dynamic Model of Economic Flucuaions 39

41 A shock o aggregae demand π + 5 π π G F E D C B DAS +5 DAS +4 DAS +3 DAS +2 DAS + 1 DAS -1, Period + 1 : Higher inflaion in raised inflaion expecaions for + 1, shifing DAS up. Inflaion rises more, oupu falls. π 1 A DAD,+1,, DAD -1, +5 Dynamic Model of Economic Flucuaions 40

42 A shock o aggregae demand π + 5 π π 1 π G A F E D C B DAS +5 DAS +4 DAS +3 DAS +2 DAS + 1 DAS -1, DAD,+1,,+4 Periods + 2 o + 4 : Higher inflaion in previous period raises inflaion expecaions, shifs DAS up. Inflaion rises, oupu falls. + 5 DAD -1, +5 1 Dynamic Model of Economic Flucuaions 41

43 A shock o aggregae demand π + 5 π π 1 π G A F E D C B DAS +5 DAS +4 DAS +3 DAS +2 DAS + 1 DAS -1, DAD,+1,,+4 Period + 5: DAS is higher due o higher inflaion in preceding period, bu demand shock ends and DAD reurns o is iniial posiion. Eq m a G. + 5 DAD -1, +5 1 Dynamic Model of Economic Flucuaions 42

44 A shock o aggregae demand π + 5 π π 1 π G + 5 F E D C B A DAD -1, +5 1 DAS +5 DAS +4 DAS +3 DAS +2 DAS + 1 DAS -1, DAD,+1,,+4 Periods + 6 and higher: DAS gradually shifs down as inflaion and inflaion expecaions fall, economy gradually recovers unil reaching LR eq m a A. Dynamic Model of Economic Flucuaions 43

45 The dynamic response o a demand shock ε The demand shock raises oupu for five periods. When he shock ends, oupu falls below is naural level and recovers gradually.

46 The dynamic response o a demand shock ε π The demand shock causes inflaion o rise. When he shock ends, inflaion gradually falls oward is iniial level.

47 ε The dynamic response o a demand shock r The demand shock raises he real ineres rae. Afer he shock ends, he real ineres rae falls and approaches is iniial level.

48 The dynamic response o a demand shock ε i The behavior of he nominal ineres rae depends on ha of he inflaion and real ineres raes.

49 A shif in moneary policy π 1 = 2% π π final = 1% π B C A Z 1, final DAS -1, DAS +1 DAD, + 1, DAS final DAD 1 Dynamic Model of Economic Flucuaions Period 1: arge inflaion rae π* = 2%, iniial eq m a A Period : Cenral bank lowers arge o π* = 1%, raises real ineres rae, shifs DAD lefward. Oupu and inflaion fall. 48

50 A shif in moneary policy π 1 = 2% π π final = 1% π B C A Z 1, final DAS -1, DAS +1 DAD, + 1, DAS final DAD 1 Dynamic Model of Economic Flucuaions Period + 1 : The fall in π reduced inflaion expecaions for + 1, shifing DAS downward. Oupu rises, inflaion falls. 49

51 A shif in moneary policy π 1 = 2% π π final = 1% π B C A Z 1, final DAS -1, DAS +1 DAD, + 1, DAS final DAD 1 Dynamic Model of Economic Flucuaions Subsequen periods: This process coninues unil oupu reurns o is naural rae and inflaion reaches is new arge. 50

52 The dynamic response o a reducion in arge inflaion * π Reducing he arge inflaion rae causes oupu o fall below is naural level for a while. Oupu recovers gradually.

53 The dynamic response o a reducion in arge inflaion * π π Because expecaions adjus slowly, i akes many periods for inflaion o reach he new arge.

54 * π The dynamic response o a reducion in arge inflaion r To reduce inflaion, he cenral bank raises he real ineres rae o reduce aggregae demand. The real ineres rae gradually reurns o is naural rae.

55 * π The dynamic response o a reducion in arge inflaion i The iniial increase in he real ineres rae raises he nominal ineres rae. As he inflaion and real ineres raes fall, he nominal rae falls.

56 APPLICATION: Oupu variabiliy vs. inflaion variabiliy A supply shock reduces oupu (bad) and raises inflaion (also bad). The cenral bank faces a radeoff beween hese bads i can reduce he effec on oupu, bu only by oleraing an increase in he effec on inflaion. Dynamic Model of Economic Flucuaions 55

57 APPLICATION: Oupu variabiliy vs. inflaion variabiliy π π 1 π CASE 1: θ π is large, θ is small A supply shock shifs DAS up. 1 DAS DAS 1 DAD 1, Dynamic Model of Economic Flucuaions In his case, a small change in inflaion has a large effec on oupu, so DAD is relaively fla. The shock has a large effec on oupu bu a small effec on inflaion. 56

58 APPLICATION: Oupu variabiliy vs. inflaion variabiliy π π 1 π CASE 2: θ π is small, θ is large 1 DAS DAD 1, DAS 1 Dynamic Model of Economic Flucuaions In his case, a large change in inflaion has only a small effec on oupu, so DAD is relaively seep. Now, he shock has only a small effec on oupu, bu a big effec on inflaion. 57

59 APPLICATION: The Taylor principle The Taylor principle (named afer John Taylor): The proposiion ha a cenral bank should respond o an increase in inflaion wih an even greaer increase in he nominal ineres rae (so ha he real ineres rae rises). I.e., cenral bank should se θ π > 0. Oherwise, DAD will slope upward, economy may be unsable, and inflaion may spiral ou of conrol. Dynamic Model of Economic Flucuaions 58

60 APPLICATION: The Taylor principle αθπ * 1 = ( π π ) + ε 1+ αθ 1+ αθ If θ π > 0: When inflaion rises, he cenral bank increases he nominal ineres rae even more, which increases he real ineres rae and reduces he demand for goods & services. DAD has a negaive slope. * = + + π ( ) + ( ) Dynamic Model of Economic Flucuaions (DAD) i π ρ θ π π θ (MP rule) 59

61 APPLICATION: The Taylor principle αθπ * 1 = ( π π ) + ε 1+ αθ 1+ αθ (DAD) i π ρ θ π π θ (MP rule) * = + + π ( ) + ( ) If θ π < 0: When inflaion rises, he cenral bank increases he nominal ineres rae by a smaller amoun. The real ineres rae falls, which increases he demand for goods & services. DAD has a posiive slope. Dynamic Model of Economic Flucuaions 60

62 APPLICATION: The Taylor principle If DAD is upward-sloping and seeper han DAS, hen he economy is unsable: oupu will no reurn o is naural level, and inflaion will spiral upward (for posiive demand shocks) or downward (for negaive ones). Esimaes of θ π from published research: θ π = 0.14 from , before Paul Volcker became Fed chairman. Inflaion was high during his ime, especially during he 1970s. θ π = 0.72 during he Volcker and Greenspan years. Inflaion was much lower during hese years. Dynamic Model of Economic Flucuaions 61

63 CHAPTER SUMMAR The DAD-DAS model combines five relaionships: an IS-curve-like equaion of he goods marke, he Fisher equaion, a Phillips curve equaion, an equaion for expeced inflaion, and a moneary policy rule. The long-run equilibrium of he model is classical. Oupu and he real ineres rae are a heir naural levels, independen of moneary policy. The cenral bank s inflaion arge deermines inflaion, expeced inflaion, and he nominal ineres rae. 62

64 CHAPTER SUMMAR The DAD-DAS 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. The parameers of he moneary policy rule influence he slope of he DAS 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. 63

65 CHAPTER SUMMAR The DAD-DAS 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. 64