Lecture 8: Aggregate demand and supply dynamics, closed economy case.

Lecture 8: Aggregate demand and supply dynamics, closed economy case. Ragnar Nymoen Department of Economics, University of Oslo October 20, 2008 1

Ch 17, 19 and 20 in IAM Since our primary concern is to develop and apply the methodology of dynamic analysis we focus on the main properties of the models. This is not a course in business cycle analysis, so the book s focus on how well the AD-AS model fit the business cycle is not emphasized here. The focus is instead on the representation of the transmission mechanism of monetary policy: How changes in the monetary policy instruments affects the real economy. The transmission mechanisms resides both on the demand side and on the supply side of the economy. Ch 20: The main point here is a (simplified) discussion of the book s discussion of optimal choice of weights in the Taylor rule. 2

Aggregate demand theory: Private consumption and investment In the following we will use a simple representation (as in IAM): C t = C(Y t T t,r t ), C Y > 0,C r < 0, (1) where C = Private consumption in real terms (the price level of the base year). Y = GDP in real terms, T = The tax level, in real terms. r = The real interest rate: r t = i t πt+1 e (2) i = Nominal interest rate π e = The expected rate of inflation 3

In IDM we had a consumption function with fewer explanatory variables, essentially only Y t T t. We could have added r t, for example, but left it out for simplicity. On the other hand, IDM had lagged C t of course! The specification here (and in IAM) thus assumes that adjustment of C t to changes in Y t T t for example is all done within the period of analysis. The important extension compared to IDM is the real interest rate r t which has a negative derivative to capture intertemporal substitution. Note also the definition of the real exchange rate: it is in terms of inflation expectations. 4

I t = I(Y t,r t ), I Y > 0, I r < 0. (3) Investment is growing when output is increased because there are strong incentives to increase capacity in such a growth situation (with increased capacity, the expected dividends to shareholders become higher). A higher real interest rate reduces the present value of expected dividend increases, and reduces the incentive to invest. Increased r t also makes other types of investment more attractive compared to investment in physical capital (bond, bank deposits). 5

TheaggregatedemandfunctionandtheIScurve We define the aggregate private demand function D t as with derivatives: D t C(Y t T t,r t )+I(Y t,r t )=D(Y t,t t,r t ) 0 <D Y D t Y t C Y + I Y < 1 D r D t r t C r + I r < 0 D T D t T t C Y < 0 If we let G t denote public sector expenditure (in real terms) the equilibrium condition on the product market becomes (4) Y t = D(Y t,t t,r t )+G t (5) which defines Y t the IS-curve: the downward sloping curve between GDP and interest rate, known from the Keynesian macro model of earlier courses. 6

(Graph from IAM with negative relationship between interest rate and aggregate demand) 7

Balanced government budget We know from before that (in this model) a balanced change in the budget has an expansionary effect on GDP. For simplicity, we will impose this in the form of: T = G so that the IS curve we will use in the following is meaning that Y t = D(Y t,g t,r t )+G t (6) from the demand side. Y t G t C Y +1> 0 (7) 8

Steady state and linearization Our model of aggregate demand is now: and Y t = D(Y t,g t,r t )+G t (8) r t = i t π e t+1. Which, despite all the simplifications, is a dynamic model of the demand side, because of the expectations variable (remember expectations as a source of dynamics ). In the case where all the arguments in the demand function are at their long-run (steady state) values, the long-run aggregate demand function becomes: Ȳ = D(Ȳ,Ḡ, r)+ḡ the IAM textbook shows how (8) can be log-linearized around the steady state to give y t ȳ = α 1 (g t ḡ) α 2 (r t r)+v t, α 1 > 0, α 2 > 0 (9) where y t =ln(y t ), etc., and we introduce v t as random demand-shock variable. 9

The model of aggregate demand and supply (IAM 19.1 and 19.2) y t = α 0 + α 1 g t α 2 r t + v t,α 1 > 0,α 2 > 0 (10) r t = i t πt+1 e (11) i t = r + πt+1 e + h(π t π )+b(y t ȳ),h>0,b>0 (12) m t π t p t 1 = m 0 m 1 i t + m 2 y t,m i > 0, i =1, 2 (13) π t = πt e + γ(y t ȳ)+s t (14) (10) is linearized IS curve, supplemented with a variable v t that represents arbitrary demand disturbances ( shocks ), possibly due to shifts in private sector confidence. Compared to IAM ch 19 we collect ȳ, α 1 ḡ and α 2 r in a constant term. (11) is the definition of the real interest rate. πt+1 e is the expected rate of inflation, one period ahead. (12) is the Taylor rule of Ch 17 in IAM. 10

The Taylor rule equation i t = r + π e t+1 + h(π t π )+b(y t ȳ),h>0,b>0 represents how a central bank that has the nominal interest rate as its policy instrument, putssomeweightoninflation stabilization, π denotes the inflation target, and some on GDP stabilization. The coefficient h and b reflect policy priorities and preferences. Note that the central bank puts separate weight on inflation expectations, so if πt+1 e goes up, the interest rate is increased (even before) actual inflation is affected. In this sense, the Taylor-rule captures forward lookingness of interest rate setting. 11

Equation (13) of the model represents equilibrium in the money market (13). We prefer to represent this explicitly since it is otherwise easy to forget the role of money (once the Taylor rule has been included). Note that m t p t m t π t p t 1 has been used. (14) is the Phillips curve model and represents the supply side. From the first part of the lectures we remember that this representation of wage-and price settings strongly restricts how the nominal dynamics (wage and price evolution through time) can be stabilized. Instead of unemployment, product and labour market pressure is represented by the output gap (y t ȳ), ȳ represents output at full employment, Remember that y t,g t,m t and p t are in logs. (10)-(14) represents a dynamic system of equations. 12

We next follow the 3-step approach to the analysis of dynamic models: 1. Define the short-run model 2. Define the long-run model (i.e., for a long-run steady state, assuming that it exists) 3. The question about dynamic stability of the long-run solution 13

The short-run model In the short run, in period t, the following variables are exogenous: g t, v t, s t and p t 1. If we do not specify a model for πt+1 e,inflation expectations are also exogenous However, that would leave the model incomplete since it is realistic that expectations are endogenous also in the short-run. Hence we follow the book and specify π e t+j = π t+j 1, forj =0, 1 (15) as the 6th equation of the short-run model. The 6 endogenous variables are y t, i t, r t,π t, π e t and m t. We solve the short-run model by using (10), (11), (12) and (15) to obtain the semi-reduced form equation: π t = π 1 α (y t z t ), (16) with α = α 2h 1+α 2 b and z t = α 0 + v t + α 1 g t α 2 r + α 2 bȳ. 1+α 2 b 14

Equation (16), and: π t = π t 1 + γ(y t ȳ)+s t (17) are 2 equations, referred to as the short-run aggregate demand (SRAD) function, and the short-run aggregate supply (SRAS) function. They define the equilibrium solutions for y t and π t as functions of the exogenous and predetermined variables:g t, v t, s t and π t 1. The solutions for y t,andπ t can be substituted back into the Taylor rule to give the solution for i t, and to in the money market equilibrium condition to give m t. In each period, the money market is equilibrated with the aid of central bank market operations, which can change the stock of money instantaneously. 15

The long-run model The long-run model is defined for the following definition of a steady-state situation π t = π t 1 = π (18) which implies that expectations are correct in steady state: π e t = π t The Phillips curve has to hold also in this situation, hence the steady-state value of y t has to be equal to ȳ, y =ȳ (19) which we express by saying that the long-run aggregate supply function (LRAS) is vertical, see figure 19.3 in AIR. The corresponding long-run aggregate demand (LRAD) function is π = π 1 (y z) (20) α 16

where z is given by z = α 0 + α 1 ḡ α 2 r + α 2 bȳ 1+α 2 b where ḡ is the constant value of g t and the two shock variables s t and v t are set to zero. (19) and (20) define the long-run model. There are two endogenous variables namely π and y. We see immediately that the long-run solution is y =ȳ (21) π = π (22) if the inflation target is to be attained. In that case a third variable is determined in the long-run, for example the equilibrium interest rate r. Remember that is a property of this model that the steady-state GDP level is given from the supply-side. Specifically, think of ȳ as ȳ = γ 0 /γ where γ 0 is the constant term in the PCM, which is implicit in the formulation in equation (14). 17

The dynamic analysis SRAD in (16) holds in each period, hence π t 1 = π 1 α (y t 1 z t 1 ), Substitution in the SRAS function gives π t = π 1 α (y t 1 z t 1 )+γ(y t ȳ)+s t Finally, substitution on the left hand side by the SRAD in (16) gives π 1 α (y t z t )=π 1 α (y t 1 z t 1 )+γ(y t ȳ)+s t (23) which we can write as an ADL equation for y t : y t = 1 1+γα y t 1 + 1 1+γα (z t z t 1 )+ which is similar to (19) in AIR ch 19. α 1+γα γȳ α 1+γα s t (24) 18

Since both γ and α are positive (as long as h>0) we know from the first part of the lectures that the dynamic model for y t is dynamically stable. Specifically, since 0 < 1/(1 + γα) < 1, the autoregressive parameter of (24) satisfies the stability requirement that we know from before (i.e., the IDM part of the lectures) We also know that since π t dependsonlagsofy t 1,andy t depends on π t,we cannot have stability in y t without also stability of inflation. 19

Dynamic responses to demand shocks. Assume that we are in a steady-state situation initially, in period t 1, with s t 1 = v t 1 =0. Then v t =1butv t+1 = v t+2... arezero. Hencewehavea temporary demand shock. Using (24): y t = 1 z t > 0 v t 1+γα v t y t+1 = 1 y t 1 z t = 1 v t 1+γα v t 1+γα v t 1+γα ( 1 1+γα 1) z t < 0 v t y t+2 = 1 y t+1 v t 1+γα v t The first multiplier is positive, but less than one, since interest rates are increased in the period of the shock. The second multiplier is negative, since the PCM has shifted up in the same period as SRAD shifts back to its original position. All the subsequent multipliers, or impulse responses as they are called in IAM, are also negative, but they are diminishing in magnitude. 20

Inthecaseofapermanent demand shock, all the multipliers are positive and declining. But the long-run multiplier is zero, as can be seen directly from the long-run model. For multiplier number j + 1: δ j = 1 1+γα δ j 1. Note that you can lift the expressions for the multipliers from IDM, Table 2.1. Inflation responds more smoothly to a temporary demand shock. This due to two features of the model. 1. Demand shocks only affect inflation indirectly, through y t. 2. Movements in y t are smoothed by inflation expectations, which weights heavily in inflation dynamics. See for example figure 19.6 and 19.8 in IAM. Take care to study the examples of supply shocks as well. 21

The AD-AS model with adaptive expectations (Ch 19.3) Which properties of the model are dictated by the choice of static inflation expectations in the basic version of the closed economy AD-AS model? In order to investigate, consider adaptive expectation instead. In the short-run model, replace (15) by or, equivalently: πt e πt 1 e =(1 φ)(π t 1 πt 1 e ), 0 φ 1, (25) π e t = φπ e t 1 +(1 φ)π t 1. (26) Note first the SRAD is unaffected since in the Taylor rule has been specified in such at way that πt+1 e cancels out when we substitute to derive the SRAD function. 22

With adaptive expectations the SRAS function replaces (17). π t = φπ e t 1 +(1 φ)π t 1 + γ(y t ȳ)+s t (27) Short-run model. Since the SRAD function is unchanged, and SRAS is given by (27) we conclude that the short-run model is unaffected by changing the model of expectations. The impact multipliers are therefore unaffected. Long-run model It is also the same as with static expectations. This generic, to models with expectations: the long-run model is always unaffected by changes in the specification of how expectations are formed. The dynamic analysis This is affected, since π e t 1 enters into the model, not only π t 1. Intuitively however, dynamic stability is not endangered. 23

The model with a downward sloping long-run Phillips curve ThePCMaboveisaspecialcaseof π t = γ e π e t + γ(y t ȳ)+s t, 0 <γ e 1. With a non-homogeneous PCM, the case of γ e < 1, the AD-AS framework has the same short-run and dynamic properties as above. The long-run model becomes π = π 1 (ȳ z) α π = γ e π + γ(y ȳ), 0 <γ e < 1 since the LRAS function is no longer vertical but upward sloping. A main criticism of model with a downward sloping long-run Phillips curve is that it implies that there is a long-run trade off between inflation and output (or unemployment), which is now regarded as naive policy optimism. However, this conclusion is avoided in the IAM specification of the AD-AS model, since the Taylor rule for monetary policy ties down y =ȳ in any case. 24

Stabilization policy in the closed economy model (Ch 20 in IDM) In the model of Ch 19, with all its simplifications, nevertheless captures the gist of the standard model for policy analysis in a closed economy. Since the model economy is dynamically stable, and full employment GDP is independent of both monetary and fiscal policy, the remaining rationale for doing macroeconomic policy is to reduce the welfare losses which are due to the temporary disturbances in demand and supply, and their propagation. Welfare losses are assumed to be linked to variations in demand and in inflation. IAM, ch 20.1, formalizes this by assuming that the government seeks to minimize the sum of standard deviations in output and inflation, see equation (1) on page 599. 25

In this course we need to bypass the calculation of standard deviations. However, a discussion along the same lines can utilize the dynamic multipliers, which of course depends on the shocks, but also on the parameters of the Taylor-rule. Graphical analysis of the AD-AS model can also be used. Themainquestiontoanswerishowtheparametersb and h in the Taylor rule can be chosen to avoid unwanted variability. Policy response to demand shocks We derived the multipliers for a demand shock above. Denote them by δo,v, y δ y 1,v,etc.Thefirst multiplier: δo,v y = 1 z t,with z t 1 = (28) 1+γα v t v t 1+α 2 b If the government has a strong preference for output stabilization, then it chooses b to be sufficiently high so that the demand shock triggered by the increase in v t is very small. 26

Or, it can neutralize the response of y t to any given increase in z t by choosing ahighh. Thisfollowssinceα is increasing in h. α = α 2h 1+α 2 b If the government instead has a preference for inflation stabilization, we can use (17) and (28) to obtain δo,v π = γδo,v y and δ1,v π = δπ o,v + γδo,v. y Hence, a policy which stabilizes output also reduces the variability of inflation. There is no trade-off when the source of variability is demand shocks, see Table 20.2 and the associated text. 27

Policy response to supply shocks Using (17) and (28) again. we obtain: δo,s y = α 1+γα δ y 1,s = 1 1+γα δy o,s and δ π o,s =1+γδ y o,s Using the expression for α = α 2 h/(1 + α 2 b), we see that the absolute value of δ o,s can be reduced by choosing h as low as possible, while maintaining dynamic stability. b>0 also helps reducing. δ y o,s However, if the preference is for inflation stability, it is preferred that δ y o,s is as negative as possible, and this suggest h>0 and b<0. Hence, in the face of supply shocks, there is a trade off between inflation stabilization and output stabilization. 28

In theory a balanced choice of b and h values are chosen by minimize the welfare loss function. The Taylor principle In most constellations we have h>0 as a good choice of weight on the inflationterminthetaylor-rule. In the model specification with static inflation expectations this implies that the nominal interest rate increases with more than one percentage point if π t increases by one percentage point. Therefore the real interest rate increases in the period of the inflation shock. 29

Rulesvsdiscretion. In the AD-AS model in Ch 19 and 20, there is a Taylor-rule for monetary policy. A version with full discretion would be with i t exogenous (no Taylor rule). The interest rate can then be set on a period to period basis, or with respect to different goals (or targets) from period to period. In modern macro economic policy rules have become popular. Taylor rule and fiscal policy rules (Norway for example). There are good reasons for this: reduce influence of pressure groups, a stable framework for policy; transparency, tie oneself to the mast (Ulysses and the sirens), and time consistent policy (which we will review in the next lecture). 30