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Prof. Dr. Thomas Steger Advanced Macroeconomics II | Lecture| SS 2013 1 Basic Macroeconomic Models 1. Textbook (static) macromodel Dynamic AS-AD model Basic dynamic macromodel with expectations Schools of macroeconomic thought g Institut für Theoretische Volkswirtschaftslehre Makroökonomik Basic Macroeconomic Models Institut für Theoretische Volkswirtschaftslehre Makroökonomik P li i i (1) Preliminaries Macroeconomics: two defining characteristics studies the economic interactions in society as a whole aims at understanding empirical regularities in the behavior of aggregate economic variables such as production, investment, unemployment, price level… Macroeconomics: three purposes explain the level of the aggregate variables as well as their movement over time in the short run and the long run make well well-founded founded forecasts possible provide foundations for rational macroeconomic policy 2 Basic Macroeconomic Models Institut für Theoretische Volkswirtschaftslehre Makroökonomik P li i i (2) Preliminaries The short run… concentrates on the behavior of the macroeconomic variables within a time horizon of a few years. focuses on mechanisms that determine how fully an economy uses its productive capacity and are typically demand dominated. shifts in aggregate demand tend to be accommodated by changes in the produced quantities rather than in the prices of goods. The Th long l run… deals with a time horizon long enough such that changes in the capital stock, population, and technology have a dominating influence on the level of production. uses analytical frameworks which are supply dominated. Variations in the employment rate for labor and capital due to demand fluctuations are ignored. The medium run run… medium run models (business cycle models) attempt to understand the pattern of economic fluctuations. focuses on the dynamic interaction between demand and supply factors factors. equally important is the formation of expectations, and the adjustment of wages and prices. 3 Basic Macroeconomic Models Institut für Theoretische Volkswirtschaftslehre Makroökonomik T tb k ((static) Textbook t ti ) macromodel: d l aggregate t labor l b market k t The problem of the typical firm reads W=Peg(NS) {PF ( K , N ) − WN } max N The firm can observe (hence knows) the going price of its own output good (P) and the wage rate (W). W=PFN(K,N) The demand schedule may be expressed as: W/P=FN(K,N). The problem of the typical household is max U (C ,,1 − N S ) s.t. P eC = WN S C ,N S The household cannot observe the prices of all consumption goods and hence bases its decision on the expected price level (Pe). ) Optimal NS results from W/Pe=U1-N/UC=:g(NS). The labor supply curve may be expressed as W=Peg(NS) with g’(NS)>0, i.e. we assume that the substitution effect dominates the income effect. 4 Basic Macroeconomic Models Institut für Theoretische Volkswirtschaftslehre Makroökonomik T tb k ((static) Textbook t ti ) macromodel: d l aggregate t goods d supply l (1) The adaptive expectations hypothesis (AEH) P = Pt + (1 − λ ) e t +1 −P ) (P t 2,00 1,00 expectational error in t ΔPt = P − Pt = λ ( Pt − Pt e e t +1 e e ) 4,00 3,00 e t 5,00 0≤λ ≤1 0,00 1 3 5 7 9 11 13 15 17 19 21 23 25 27 29t Under the AEH the expected price level (Pe) is adjusted to correct for past expectational errors. errors The problem with the AEH is that it may lead to permanent incorrect expectations. In the face of informational and cognitive constraints, the AEH may represent a valid approximation. The perfect foresight hypothesis (PFH) Pt e = Pt The PFH simply states that households expect the price level that actually holds. The PFH is the deterministic counterpart to the rational expectations hypothesis (REH). 5 Basic Macroeconomic Models Institut für Theoretische Volkswirtschaftslehre Makroökonomik T tb k ((static) Textbook t ti ) macromodel: d l aggregate t goods d supply l (2) nominal wage! The AS-curve under AEH Suppose P0e=P0. HH make no expectational i l error, supply l the h ““correct”” * amount of labor (N ) and output is at its potential level Y* (point E0). Assume now that P increases to P1>P0, while hile P0e=P P0 initially initiall impl implying ing that the labor supply curve is unchanged. However, the demand for labor shifts up so that labor market equilibrium is at point A. A Associated output is Y1>Y*. Employment and output increase. The reason is that the real wage decreased such that firms demand more labor. HH must accept this lower real wage (they have underestimated P and overestimated W/P). curve under PFH The AS AS-curve Expected and actual P always coincide and, hence, labor supply is always based on correct estimations of W/P. Employment is always N* and output equals Y*. The AS curve is vertical. 6 Basic Macroeconomic Models Institut für Theoretische Volkswirtschaftslehre Makroökonomik T tb k ((static) Textbook t ti ) macromodel: d l aggregate t goods d supply l (3) nominal wage! AS-curve under downward nominal wage rigidity The rigid nominal wage equals W0. P0 is the price level such that full employment holds (point E0). The PFH is assumed to hold, i.e. Pte=Pt. For P1>P0 , the nominal wage rises such that the real wage and employment remain constant (point B). For P2<P0 , the demand for labor is W=P2FN but the effective labor supply is horizontal at the segment W0C (point A). Since it is assumed that the wage is not allowed to fall, employment equals N2 (<N*), while unemployment equals N2SN2. 7 Basic Macroeconomic Models Institut für Theoretische Volkswirtschaftslehre Makroökonomik T tb k ((static) Textbook t ti ) macromodel: d l aggregate t goods d d demand d (1) The demand side of the economy can be described by means of the IS-LM model IS : = C (Y − T ) + I ( R ) + G output=income t t i Y 0 < CY < 1, I R ≤ 0 goods demand LM : M / P = L(Y , R ) , money supply LY > 0, LR ≤ 0 money demand d d There are two endogenous g variables: Y ((aggregate gg g demand)) and R ((interest rate). ) These two equations define Y and R. Usually, U ll th the (i (inverse)) AD curve iin (Y (Y,P)-plane P) l iis negatively ti l sloped. l d Provided that LR=-∞ (liquidity trap) and / or IR=0 (investments are insensitive w.r.t. R), the AD curve is vertical in (Y,P) (Y P)-plane plane (→ goods market equilibrium may not exist) exist). 8 Basic Macroeconomic Models Institut für Theoretische Volkswirtschaftslehre Makroökonomik T tb k ((static) Textbook t ti ) macromodel: d l aggregate t goods d d demand d (2) Assume the following specific (linear) functional forms Y = C + cY + I − bR, IS : LM : M / P = kY − hR, 0 < c < 1, b ≥ 0 k > 0, h ≥ 0 The (inverse) AD-curve then reads bM P= [(1 − c)h + bk ]Y − h(C + I ) Usually, ll this h is a h hyperbola b l in ((Y,P)-plane ) l ((we ffocus only l on the h positive b branch). h) For h=0 one gets P=M/(kY). This AD curve is basically the same as P=(VM)/Y (resulting from PY=VM). Two T special i l cases: AD curve iindependent d d off P, P i.e. i AD iis vertical i l iin (Y (Y,P)-plane. P) l For b=0, one gets Y=(C+I)/(1-c). For h=∞,, one gets g (→ ( q quo ent rule)) ∂Y bM =− ∂P [(1 − c)h + bk ]P2 ∂Y = 0 for h = ∞ ∂P Y= bM + h(C + I ) P [(1 − c)h + bk ]P 9 Basic Macroeconomic Models Institut für Theoretische Volkswirtschaftslehre Makroökonomik D Dynamic i AS AS-AD AD model: d l AD AD-curve The goods market (IS-Curve) C = C0 + b(1 − τ )Y real interest rate (Fisher-equation) I = I 0 − h(i − π e ) Y =C + I +G For technical reasons we assume that the demand for real money balances is non-linear. The money market (LM-Curve) ln M d = kY − qi (⇔ M d = e kY − qi ) ln M s = ln M − ln P (⇔ M s = M ) P ln M s = ln M d The AD-Curve Y= C0 + I 0 + G + qh ⋅ ln ( MP ) + h ⋅ π e 1 − b(1 − τ ) + h⋅k q = a0 + a1 ⋅ (ln M − ln P ) + a2 ⋅ π e a0 := C0 + I 0 + G 1 − b(1 − τ ) + hq⋅k a1 := h/q 1 − b(1 − τ ) + hq⋅k a2 := h 1 − b(1 − τ ) + hq⋅k 10 Basic Macroeconomic Models Institut für Theoretische Volkswirtschaftslehre Makroökonomik D Dynamic i AS AS-AD AD model: d l AS AS-curve and d iinflationary fl ti expectations t ti The AS-Curve π = α (Y − Yn ) + π e , α > 0 This AS-Curve results from a modified Phillips-Curve, π=πe-a(u-un), together with Okun‘s law of the form u-un=-b(Y-Yn), where a,b>0. Inflationary expectations π e = β (π − π e ), ) β >0 Definition x(t):=dx(t)/dt If the actual inflation rate exceeds the expected inflation rate, π-πe>0, inflationary expectations are revised upwards, upwards i.e. i e πe>0. >0 Written in time discrete form this expectations hypothesis can be expressed as π te+1 − π te = β (π t − π te ) π te+1 = π te + β (π t − π te ) 11 Basic Macroeconomic Models Institut für Theoretische Volkswirtschaftslehre Makroökonomik D Dynamic i AS AS-AD AD model d l (3) Reduced form π e = βα (Y − Yn ) (*) Y = a1Mˆ − α (a1 − a2 β )(Y − Yn ) − a1π e ((**)) Equation (*) shows that a positive output gap, Y-Yn>0, induces an increase in expected inflation πe. Reason: According to the AS-Curve Y-Yn>0 requires π-πe>0. The latter induces a revision of inflationary expectations. Equation (**) shows that Output p increases,, Y>0,, if M>0: an increase of nominal moneyy supply pp y increases AD. Output decreases, Y<0, if Y-Yn>0 and a1-a2β>0. Reason: Y-Yn>0 unfolds two opposing effects: (i) π increases, which reduces M/P and hence AD falls, (ii) πe increases, which reduces the real interest rate and hence AD goes up. Steady State (Y, πe): time invariant solutions π e = βα (Y − Yn ) = 0 Y = a1Mˆ − α (a1 − a2 β )(Y − Yn ) − a1π e = 0 Y = Yn π e = π = Mˆ 12 Basic Macroeconomic Models Institut für Theoretische Volkswirtschaftslehre Makroökonomik D Dynamic i AS AS-AD AD model d l (3 (3a)) Determination of the reduced form: elimination of π π e = β ( π −π e) π e = βα (Y − Yn ) (***) α (Y −Yn ) Y = a0 + a1 ⋅ (ln M − ln P ) + a2 ⋅ π e e ˆ Y = a1 ⋅ ( M − π ) + a2 ⋅ π d ln M dt d ln P dt Y = a1[ Mˆ − (α (Y − Yn ) + π e )] + a2 βα (Y − Yn ) = a1Mˆ − α (a1 − a2 β )(Y − Yn ) − a1π e π (****) π e Equ. (***) and (****) represent two linear differential equations in Y and πe. Boundary conditions are given by the steady state solutions. On M and π. Recall: d ln x(t ) = dt 1 x(t ) dx(t ) x (t ) = =: xˆ (t ) dt x(t ) outer derivative inner derivative 13 Basic Macroeconomic Models Institut für Theoretische Volkswirtschaftslehre Makroökonomik D Dynamic i AS AS-AD AD model d l (4) Dynamic responses (1): expansionary monetary policy (permanent increase of M) 14 Basic Macroeconomic Models Institut für Theoretische Volkswirtschaftslehre Makroökonomik D Dynamic i AS AS-AD AD model d l (5) Dynamic responses (2): expansionary fiscal policy (temporary increase of G) 15 Basic Macroeconomic Models Institut für Theoretische Volkswirtschaftslehre Makroökonomik D Dynamic i AS AS-AD AD model d l (5) Dynamic responses (3): negative supply shock (permanent) 16 Basic Macroeconomic Models Institut für Theoretische Volkswirtschaftslehre Makroökonomik B i d Basic dynamic i macromodel d l with ith expectations: t ti model d l setup t (1) Firms produces a homogenous output good under perfect competition using Yt = Lαt , 0 < α < 1 Firms are assumed to maximize profits given by Π t = PY t t − Wt Lt The first-order condition (FOC) for optimal labor input implies α Lαt −1 = Wt Lt = α Pt 1 1−α Wt Pt 1 α −1 The indirect production function, Y=F(W/P), is hence given by Yt = α α 1−α Wt P t α α −1 17 Basic Macroeconomic Models Institut für Theoretische Volkswirtschaftslehre Makroökonomik B i d Basic dynamic i macromodel d l with ith expectations: t ti model d l setup t (2) Labor unions have a target real wage, which is normalized to one, i.e. Wt/Pt=1. Moreover, l b unions labor i h have th the power tto sett Wt/Pt=1. 1 Hence, H llabor b unions i sett Wt, negotiated ti t d att th the beginning of each period t, such that Wt = Pt e There is "substantial unemployment" at Wt/Pt=1. Accordingly, if the real wage falls below one, the additional labor demand by firms can be satisfied. satisfied This assumption is compatible with collective bargaining models of unemployment. The AS AS-curve curve can hence be expressed as Yt = α α 1−α α 1−α Pt Pe t yt = y ∗ + a ( pt − pte ) α α = ln α 1−α Lower case letters denote (natural) logarithms, i.e. xt:=lnXt. = 1−α 18 Basic Macroeconomic Models Institut für Theoretische Volkswirtschaftslehre Makroökonomik B i d Basic dynamic i macromodel d l with ith expectations: t ti model d l setup t (3) The AD-schedule is described by the quantity equation of money, MtVt=YtPt, expressed in logarithms mt + vt = yt + pt =0 nominal transaction volume per period, YtPt, must equal the nominal money supply times the velocity of money per period, MtVt. assuming that Vt=1 for all t, we have vt=0. Price expectations p are formed accordingg to an adaptive p expectations p scheme pte = pte−1 + β ( pt −1 − pte−1 ), 0 ≤ β ≤ 1 Alternatively, we consider the rational expectation hypothesis such that pte = E ( pt Ωt −1 ) E(.) denotes the expectations operator. Ωtt-11 the information set at the end of p period t-1. Monetary policy controls nominal money supply according to Mt=M*exp(εt) or mt = m∗ + ε t εt represents an i.i.d. error term with E(εt)=0, V(εt)=const. and Cov(εt, εt+i)=0 for all t and i. 19 Basic Macroeconomic Models Institut für Theoretische Volkswirtschaftslehre Makroökonomik B i d Basic dynamic i macromodel d l with ith expectations: t ti d dynamic i system t and d steady t d state t t The complete dynamic system AS : yt = y ∗ + a ( pt − pte ), 0 < a < 1 AD : mt = yt + pt MP : mt = m∗ + ε t Expectations : pte+1 = pte + β ( pt − pte ), 0 ≤ β ≤ 1 Steady state The steady state is defined by yt=yt-1, pt=pt-1, pte=pt-1e for all t. t Letting x denote the (pseudo) steady state value of variable xt (assuming εt=0 for all t), one can express the steady state as follows y = y ∗ , p = m∗ − y ∗ , p e = p 20 Basic Macroeconomic Models Institut für Theoretische Volkswirtschaftslehre Makroökonomik B i d Basic dynamic i macromodel d l with ith expectations: t ti reduced-form d df d dynamic i system t Combining the AS curve, the AD curve, and the monetary policy schedule one gets m∗ + ε t = y ∗ + a ( pt − pte ) + pt The equilibrium price level (AD=AS), given pte. Solving for pt gives pt = 1 a e m∗ + ε t − y ∗ ) + pt ( 1+ a 1+ a (*) Next, substitute pte by the RHS of the adaptive expectations scheme to yield pt = 1 a pte−1 + β ( pt −1 − pte−1 ) m∗ + ε t − y ∗ ) + ( 1+ a 1+ a The reduced-form dynamic y system y then comprises p pte = pte−1 + β ( pt −1 − pte−1 ) pt = (**) 1 a pte−1 + β ( pt −1 − pte−1 ) m∗ + ε t − y ∗ ) + ( 1+ a 1+ a (***) 21 Basic Macroeconomic Models Institut für Theoretische Volkswirtschaftslehre Makroökonomik B i d Basic dynamic i macromodel d l with ith expectations: t ti monetary t policy li (1) Adaptive expectations Assuming that the economy is i a steady in t d state t t iinitially, iti ll we have the following initial conditions p₀=p₀e=p. The complete time paths {pt} and {pte} for t∈{0,…, ∞} can then be traced out by recursively solving (**) and (***). The time path {yt} can be calculated by evaluating the AS-curve. AS The associated excel file illustrates the dynamic consequences of an expansionary policy in the sense of a permanent increase in m*. 22 Basic Macroeconomic Models Institut für Theoretische Volkswirtschaftslehre Makroökonomik B i d Basic dynamic i macromodel d l with ith expectations: t ti monetary t policy li (2) Rational expectations (RE) R ti Rational l expectations t ti are ttaken k tto representt model d l consistent i t t expectations. t ti To determine the expected price level under REH, we simply determine the equilibrium price level, implied by the underlying model, and then form the expected value, denoted E(p ( t). ) Taking expectations on both sides of (*), noting that E(εt)=0 and that pte=E(pt) is a fixed number, one gets E ( pt ) = 1 a ∗ ∗ − y + E ( pt ) m ( ) 1+ a 1+ a 1 a ∗ ∗ − = − ( p ) m y 1 E ( ) t 1 + a 1+ a E ( pt ) = m∗ − y ∗ 23 Basic Macroeconomic Models Institut für Theoretische Volkswirtschaftslehre Makroökonomik B i d Basic dynamic i macromodel d l with ith expectations: t ti monetary t policy li (3) Rational expectations Assume that the economy is in a steady state initially, initially i.e. i e y=y*, p=m*-y*, pe=p. Monetary authorities increase the moneyy supply pp y from m* to m**>m* at the end of period t. Agents can anticipate this policy action. Initially, E(pt)=m*-y*=pt. Right after the monetary expansion, the expected price l l jjumps up such h that h level E(pt+1)= m**-y*=pt+1. As a result, an expected expansionary policy does not exert any real effects under the REH, but increases only the price level. The adjustment to the new steady state is immediate. 24 Basic Macroeconomic Models Institut für Theoretische Volkswirtschaftslehre Makroökonomik S h l iin M Schools Macroeconomics: i Cl Classical i lM Macroeconomics i Demand side: Quantity theory of money implies a demand function like L=kPY. Money demand is not interest sensitive. The velocity of circulation (V=1/k) is constant. The (inverse) AD curve reads: P P=M/(kY). M/(kY). Supply side: Strong belief in markets and the efficacy of the price mechanism. Wages and prices are flexible, flexible there is perfect foresight. foresight The labor market clears (at every instant of time), such that N=N*, the AS curve is vertical at Y=Y*. Fiscal and monetary policy cannot affect output and employment. Policy implications LR=0 implies that the LM-curve is vertical. Expansionary fiscal policy crowds out, via an increase in R, private investment (no shift in AD). Expansionary monetary policy shifts AD, but does not exert any real effects (only P rises). 25 Basic Macroeconomic Models Institut für Theoretische Volkswirtschaftslehre Makroökonomik S h l iin M Schools Macroeconomics: i K Keynesianism i i One prominent Keynes interpretation is based on the liquidity trap. Suppose that R is so low that the economy is on the horizontal part of the LM-curve. Suppose also that the level of spending is too low to support full f ll employment l and d that h prices i and d wages are flexible. The interest rate is RMIN and output is Y0<Y*. AS is vertical at Y=Y*, but demand falls short of Y*, and no price/wage change can restore equilibrium (goods market). Monetary policy would be ineffective in increasing AD. Fiscall policy, l on the h other h h hand, d is effective ff in increasing AD. Pigou pointed out that this result (no equilibrium in ggoods market)) disappears pp once wealth effects are taken into account. The position of the IS curve then depends on M/P, the AD curve will slope downward and full employment will be restored provided that P and W are flexible. 26 Basic Macroeconomic Models Institut für Theoretische Volkswirtschaftslehre Makroökonomik S h l iin M Schools Macroeconomics: i N Neoclassical l i l SSynthesis th i A synthesis of short run Keynesian elements and long run classical elements. elements There are different versions of the Neoclassical Synthesis. The 1st version maintains that nominal wages are rigid downwards. The AS curve has an upward sloping branch. To get some adjustment over time, one can add a Phillips curve, i.e. W=α(NS-N)/NS with α<0. There h may b be temporary unemployment, l b but ffullll employment l willll be restored over time. The 2nd version allows nominal wages to be fully flexible, but uses the AEH to make P a slowlyy movingg variable. The model comprises the AS curve, the AD curve and the AEH (see figure on the left). For instance, an increase in bond financed public spending G shifts the AD curve outwards outwards. Output rises temporarily above Y* and the price level increase from P0 to P1. The increased P implies a contraction in M/P such that AD falls. Since P has increased, the short run AS curve shifts up as soon as Pe rises. This process lasts until Y=Y*. 27 Basic Macroeconomic Models Institut für Theoretische Volkswirtschaftslehre Makroökonomik S h l iin M Schools Macroeconomics: i M Monetarism t i Monetarism: basic “assumptions and tenets” The interest sensitivity of investment is very high (IR≤0 large in absolute value) so that the IS curve is flat. The interest sensitivity of money demand is very low (LR≈0), i.e. money demand looks like, say, L=kPY. Expectations p follow the AEH. Monetarism: policy implications Fiscal policy is largely ineffective in increasing AD AD. An increase in G leads to a strong crowding out of private investment. Monetary policy may exert real effects: M=kPY implies that dM>0 leads to d(PY)=(1/k)dM>0. The relative importance of real effects effects, dY, dY and nominal effects effects, dP, dP depends on the assumptions made about the labor market and the formation of expectations. Under AEH there are temporary effects on real output and employment. Policy makers may be tempted to use monetary expansion to combat unemployment. unemployment Policymakers are, are however, however not very good at timing monetary policy and there are long and variable lags. As a result, monetary policy is likely to accentuate business cycle fluctuations. Hence, Friedman suggested gg that the central bank should follow a constant growth g rate rule for some monetaryy aggregate. gg g 28 Basic Macroeconomic Models Institut für Theoretische Volkswirtschaftslehre Makroökonomik S h l iin M Schools Macroeconomics: i N New Cl Classical i l and dN New K Keynesian i EEconomics i New Classical Economics: basic “assumptions and tenets” Prices and wages are flexible. flexible Expectations are formed rational. Macroeconomic theory should be based on microeconomic principles. New Classical Economics: main implications The decentralized allocation of resources is efficient and full employment prevails. Observed fluctuations are not caused by nominal rigidities. Instead rational agents respond to (possibly changing) economic incentives. Policy ineffectiveness proposition (PIP) applies: Either policy makers cannot (strong version of the PIP) or should not (weak version of the PIP) use countercyclical policy to smooth business cycle fluctuations. New Keynesian Economics: basic “assumptions assumptions and tenets” tenets Markets may not be as perfect as classical economics suggests. Early New Keynesians accepted the REH but stressed nominal wage rigidities (e.g., “multi-period wage contracts”). The most recent wave of New Keynesian y economics is more micro-based. The predominance of imperfect competition, coordination failures and credit constraints are stressed. New Keynesian Economics: main implications The decentralized allocation of resources may be inefficient and full employment may not prevail prevail. The PIP is invalidated: The government can and should stabilize the economy, even under REH. 29 Basic Macroeconomic Models Institut für Theoretische Volkswirtschaftslehre Makroökonomik N t ti and Notation d abbreviations bb i ti Notation 0<c<1 p rate consumption 0<λ<1 constant parameter b≥0 sensitivity of I w.r.t. R β>0 sensitivity of I w.r.t. π C consumption h≥0 sensitivity of L w.r.t. R I investment K physical capital k>0 sensitivity of L w.r.t. Y L money demand M money N labor NS labor supply P price level Pe expected price level τ t rate tax t R interest rate U utility V velocity of circulation W nominal wage W :=dW/dt rate of change of W per period dt Y output α>0 constant parameter Abbreviations AD aggregate demand AEH adaptive expectations hypothesis AS aggregate supply IS goods market equilibrium condition LM money market equilibrium condition PFH perfect foresight hypothesis PIP policy ineffectiveness proposition REF rational expectations hypothesis 30