Macroeconomics II. Dynamic AD-AS model

Transcription

1 Macroeconomics II Dynamic AD-AS model Vahagn Jerbashian Ch. 14 from Mankiw (2010) Spring 2018

2 Where we are heading to We will incorporate dynamics into the standard AD-AS model This will offer another way to analyze economic fluctuations and the effects of monetary and fiscal policy, e.g., we will use the dynamic AD-AS model to trace out the over-time effects of various exogenous shocks and policy changes on endogenous variables (e.g., Y and π) We will show that dynamic AD-AS model can accommodate long-run economic growth

3 Dynamic AD-AS model vs. AD-AS model In contrast to the standard AD-AS model, dynamic AD-AS model explicitly incorporates the response of monetary policy to economic conditions (i.e., endogenizes monetary policy) It takes into account that CBs set monetary policy according to economic conditions, including Y and π assumes that CBs set/target the interest rate and allow the money supply to adjust to whatever level is necessary to achieve that target Previously, we have assumed that CBs set money supply to simplify the matter

4 Dynamic AD-AS model vs. AD-AS model In contrast to the standard AD-AS model, dynamic AD-AS model uses inflation rate (but not the price level) links subsequent time periods Changes in inflation in a period affect future expected inflation, which changes AS in future periods, which further changes inflation and expected inflation

5 Dynamic AD-AS model in a few words Dynamic AD-AS model is a very simplified Dynamic, Stochastic, General Equilibrium (DSGE) model These models are used in cutting-edge macroeconomic research in academia and policy institutions such as central banks built from familiar concepts: IS curve, Phillips curve, and adaptive expectations It consists of 5 equations and has 5 endogenous variables: Y, π, r, i, and π e = E π

6 Notation to incorporate time-dimension We will use subscripts, "t", to denote time period Y t = Real GDP in period t Y t+k = Real GDP in period t + k where k Z e.g., if t = 2012 then Y t = Y 2012 = Real GDP in 2012

7 Output: Demand for Goods and Services (IS curve) In this model demand for goods and services is given by Y t = Ȳ t α(r t ρ) + ɛ t Y t is the current output, r t is the real interest, ɛ t is a random demand shock (E t 1 ɛ t = 0) Ȳ t is the "natural" level of output For time being we can assume that Ȳ t Ȳ. Notice however that Ȳ t Y t ρ, α > 0 are parameters r t = ρ when Y t = Ȳ t and ɛ t = 0: ρ is the level of "natural" real interest rate α shows how sensitive demand is to changes in r t

8 Output: Demand for Goods and Services (IS curve) In output equation Y t and r t are negatively related This is basically our IS curve Y t = Ȳ t α(r t ρ) + ɛ t When r t increases firms reduce investments (and consumer s increase savings but reduce demand for goods and services) which reduces Y t

9 The real interest rate: The Fisher equation The Fisher equation is r t = i t E t π t+1 i t is the nominal interest rate Both r t and i t are determined at time t (i.e., their values are known at time t) These are ex ante returns: Returns that people anticipate to earn at time t + 1 on savings made at time t π t+1 is inflation in [t, t + 1] period and its value is not known at time t E t π t+1 is the expected inflation given the information available to forecast inflation at time t

10 Inflation: The Phillips Curve The Phillips Curve (with output) is π t = E t 1 π t + φ ( Y t Ȳ t ) + υt This is basically SRAS curve where E t 1 π t is the previously expected level of inflation π t depends on E t 1 π t because some firms set prices in advance When they expect high π, they anticipate that their costs will be rising quickly and that their competitors will be increasing prices and they increase prices

11 Inflation: The Phillips Curve In π t = E t 1 π t + φ ( Y t Ȳ t ) + υt φ > 0 shows how much π t responds when Y t fluctuates around its natural level Ȳ t When economy is booming, Y t > Ȳ t, firms face higher demand and higher marginal costs and they increase prices υ t is exogenous supply shock (E t υ t+1 = 0; e.g., oil price shock)

12 Expected inflation: Adaptive expectations For simplicity, we assume people have adaptive expectations They expect prices to continue rising at the current inflation rate E t π t+1 = π t This is a significant simplification! It could make sense if people are not sophisticated in forming their expectations e.g., with such expectations people do not take into account (understand) that current policy changes affect future outcomes such as π t+1 An alternative could be Rational Expectations

13 The nominal interest rate: The monetary-policy rule We assume that the CB sets a target for i t based on the deviation of Y t from natural level Ȳ t and π t from targeted level π t using this rule i t = π t + ρ + θ π (π t π t ) + θ Y ( Yt Ȳ t ) θ π, θ Y > 0 are parameters θ π measures how much the CB adjusts i t when π t deviates from its target π t θ Y measures how much the CB adjusts i t when Y t deviates from its natural level Ȳ t This equation is called Taylor Rule

14 The nominal interest rate: The monetary-policy rule The CB controls i t through open market operations and influences real economy through r t i t = π t + ρ + θ π (π t π t ) + θ Y ( Yt Ȳ t ) e.g., in case when π t > π t the CB sells government bonds (i.e., reduces money supply) so that i t r t I (r t ) Y t π t e.g., in case when Y t < Ȳ t the CB buys government bonds (i.e., increases money supply) so that i t r t I (r t ) Y t

15 Taylor Rule The hard part of the CBs job is to choose the target for i t and how much to respond to changes in π and Y We have hypothesized a rule. In reality, however, CBs governing boards do not (need to exactly) follow this formula Economist John Taylor proposed a monetary policy rule very similar to ours i t = π t (π t 2.0) (Y t Ȳ t )

16 Taylor Rule The Taylor Rule matches Fed policy fairly well This figure shows the actual i t and the target rate as determined by Taylor Rule

17 All Equations Together AD-AS model (in full scale) is IS : Y t = Ȳ t α(r t ρ) + ɛ t FE : r t = i t E t π t+1 AS (PC ) : π t = E t 1 π t + φ (Y t Ȳ t ) + υ t EX (AE ) : E t π t+1 = π t MP (TR) : i t = π t + ρ + θ π (π t πt ) + θ Y (Y t Ȳ t )

18 Endogenous variables Endogenous variables of dynamic AD-AS model are Y t = Output π t = Inflation r t = Real interest rate i t = Nominal interest rate E t π t+1 = Expected inflation

19 Exogenous variables Exogenous and predetermined variables of dynamic AD-AS model are Ȳ t = Natural level of output πt = CB s target inflation rate ɛ t = Demand shock υ t = Supply shock Predetermined: π t 1 = Previous period s inflation

20 Parameters Parameters of dynamic AD-AS model are α = Responsiveness of demand (Y ) to r ρ = Natural rate of interest φ = Responsiveness of π to Y in the Phillips Curve θ π = Responsiveness of i to π in the monetary-policy rule θ Y = Responsiveness of i to Y in the monetary-policy rule

21 The model s long-run equilibrium Long-run equilibrium: The normal state around which the economy fluctuates Two conditions required for long-run equilibrium: There are no shocks ɛ t = υ t = 0 and inflation is constant π t 1 = π t

22 The model s long-run equilibrium Combining these conditions with model s 5 equations gives the long-run values of endogenous variables Y t = Ȳ t r t = ρ π t = π t E t π t+1 = π t i t = ρ + π t

23 The dynamic AS curve The dynamic AS (DAS) curve combines the Phillips Curve and Adaptive Expectations and shows a relation between Y and π On a graph: π t = π t 1 + φ (Y t Ȳ t ) + υ t

24 The dynamic AS curve DAS slopes upward since high levels of output are associated with high inflation DAS shifts in response to changes in Ȳ t, π t 1, and υ t

25 The dynamic AD curve The dynamic AD (DAD) curve combines output equation (IS curve), Fisher s equation, Adaptive Expectations, and monetary-policy (Taylor) rule and shows a relation between Y and π From Y t = Ȳ t α(r t ρ) + ɛ t r t = i t E t π t+1 E t π t+1 = π t it follows that Y t = Ȳ t α(i t π t ρ) + ɛ t

26 The dynamic AD curve Combining Y t = Ȳ t α(i t π t ρ) + ɛ t with monetary-policy (Taylor) rule i t = π t + ρ + θ π (π t πt ) + θ Y (Y t Ȳ t ) gives the dynamic AD curve Y t = Ȳ t A (π t πt ) + Bɛ t, A = αθ π 1, B = 1 + αθ Y 1 + αθ Y

27 The dynamic AD curve DAD slopes downward When inflation rises, the central bank raises r, reducing the demand for goods and services It shifts in response to changes in the Ȳ t, π t, and demand shocks ɛ t On a graph:

28 Short-run equilibrium in the model Short-run equilibrium in dynamic AD-AS model is the combination of output and inflation that solve the DAD and DAS equations On a graph: DAD : Y t = Ȳ t A (π t π t ) + Bɛ t DAS : π t = π t 1 + φ (Y t Ȳ t ) + υ t

29 Short-run equilibrium in the model From DAD and DAS equations DAD : Y t = Ȳ t A (π t π t ) + Bɛ t DAS : π t = π t 1 + φ (Y t Ȳ t ) + υ t we have the values of Y t and π t At time t + 1, π t will become the lagged value of inflation that influences the position of the DAS curve and connecting time periods generates dynamic patterns that we will now examine

30 Long-run growth Ȳ t changes over-time because of population growth, accumulation of capital, and tech-progress Since Ȳ t affects DAD and DAS curves in the same way, both curves shift to the right by the amount that Ȳ t has increased

31 Long-run growth Higher Ȳ t implies that firms can produce more and DAS shifts to the right consumers are richer therefore can consume more and DAD shifts to the right This is why there is no pressure on inflation

32 Supply shock Consider a shock to DAS curve e.g., υ t increases to 1 at time t and returns to 0 afterwards this can happen because of oil price shock, unions setting higher wages, etc Higher υ t at time t shifts DAS t upward and does not affect DAD t lower Y t and higher π t At time t + 1, υ returns to 0 but expectation of π is high DAS shifts a little downward a little higher Y and lower π At time t + 2, expectation of π falls DAS shifts a little downward a little higher Y and lower π... On a graph...

33 Supply shock

34 Parameter values for simulations Ȳ t = 100: Y t Ȳ t we can interpret as percentage deviation π t = 2: CB s inflation target is 2 percent α = 1: 1-percentage point increase in r reduces Y by 1 percent of its natural level Ȳ ρ = 2: natural rate of interest is 2 percent φ = 0.25: When Y is 1 percent above Ȳ, π increases by 0.25 percentage points θ π = 0.5; θ Y = 0.5: From the Taylor Rule which approximates the behavior of the Fed

35 Dynamic response to a supply shock The following graphs are called impulse response functions They show the dynamic "response" of the endogenous variables to the shock/"impulse"

36 Dynamic response to a supply shock A one-period supply shock affects Y for many periods

37 Dynamic response to a supply shock Since inflation expectations change slowly, inflation remains high for many periods

38 Dynamic response to a supply shock It takes many periods r to return to its natural rate

39 Dynamic response to a supply shock i mimics r and π

40 Demand shock Consider a (persistent) shock to DAD curve e.g., ɛ t increases to 1 at time t and returns to 0 at time t + 5 this can happen because of increases government expenditures, stock market bubble that increases wealth, etc Higher ɛ t at time t shifts DAD t upward and does not affect DAD t higher Y t and higher π t In period [t + 1, t + 4], expectation of π is high DAS shifts a upward a lower Y and higher π At time t + 5, ɛ returns to 0 but π and its expected value are high DAD shifts back but Y is lower and π is higher After t + 5, DAS gradually shifts down as π and expected π fall, economy transitions to back long-run levels On a graph...

41 Demand shock

42 Dynamic response to a demand shock The (persistent) demand shock raises Y above Ȳ for 5 periods. After 5 periods Y falls below Ȳ and gradually recovers

43 Dynamic response to a demand shock The (persistent) demand shock raises π. After 5 periods π starts falling

44 Dynamic response to a demand shock The (persistent) demand shock raises r for 5 periods. After 5 periods r starts declining

45 Dynamic response to a demand shock i mimics r and π

46 Change in monetary policy Suppose that the CB decides to reduce its target for the inflation rate e.g., at time t, πt level falls from 2% to 1% and remains at that lower Lower π t at time t shifts DAD t downward and does not affect DAS t lower Y t and lower π t At time t + 1, expected π declines DAS shifts downward higher Y and lower π... On a graph...

47 Change in monetary policy

48 Dynamic response to a change in MP Reducing π t causes Y to decline and and gradually recover

49 Dynamic response to a change in MP Since expectations adjust gradually, it takes several periods for π to reach the new target

50 Dynamic response to a change in MP To reduce inflation, the CB reduces money supply (i.e., sells govt. bonds) raises r

51 Dynamic response to a change in MP The initial increase in r raises i. Later, as the π and r fall i falls

52 Where do the parameters of MP come from? Thus far we have assumed that in monetary policy rule θ Y and θ π are exogenously given constants i t = π t + ρ + θ π (π t π t ) + θ Y (Y t Ȳ t ) These parameters determine the sensitivity of CB s targeted i to deviations of π and Y CB chooses the sensitivity A question then is what should θ Y and θ π be?

53 Affecting the slope of the DAD curve The DAD curve is Y t = Ȳ t A (π t πt ) + Bɛ t, A = αθ π 1, B = 1 + αθ Y 1 + αθ Y Therefore, CB can select θ Y and θ π to influence the slope of the DAD

54 The trade-off between variability Consider a supply shock Supply shock reduces Y (bad) and increases π (bad) The CB faces a trade-off between these "bads" it can reduce the effect on Y or π, but not both and by tolerating an increase of another

55 The trade-off between variability Case 1: θ π is large and θ Y is small Case 2: θ π is small and θ Y is large In Case 1 changes in π have big effects on Y DAD is flatter Supply shocks have a large effect on Y, but small effect on π In Case 2 changes in π have small effects on Y DAD is steeper Supply shocks have a small effect on Y, but large effect on π

56 The Taylor Principle The Taylor Principle (named after economist John Taylor) is a proposition that CBs should respond to an increase in π with an even greater increase in i (so that r rises) i.e., CBs should set θ π > 0 Otherwise, DAD will slope upward In such a case economy may be unstable and inflation may get out of control

57 The Taylor Principle In case when θ π > 0 Y t = Ȳ t A (π t πt ) + Bɛ t, A = αθ π 1, B =, 1 + αθ Y 1 + αθ Y i t = π t + ρ + θ π (π t πt ) + θ Y (Y t Ȳ t ) If π t rises, CB increases i t even more r t rises and reduces demand for goods and services π t declines The DAD curve in this case is downward sloping

58 The Taylor Principle In case when θ π < 0 Y t = Ȳ t A (π t πt ) + Bɛ t, A = αθ π 1, B =, 1 + αθ Y 1 + αθ Y i t = π t + ρ + θ π (π t πt ) + θ Y (Y t Ȳ t ) If π t rises, CB increases i t less r t declines and increases demand for goods and services π t increases The DAD curve in this case is upward sloping

59 The Taylor Principle If DAD is upward-sloping and steeper than DAS, then the economy is not stable Y will not return to its natural level, and π will spiral upward (for positive demand shocks) or downward (for negative ones)

60 DAS-DAD curves: First order difference equation Our DAS and DAD give a first order difference equation in π t π t Aφ π t 1 = πt + φbɛ t + υ t 1 + Aφ This equation describes the dynamics of π t and Y t

61 Solution of the first order difference equation The solution of a difference equation x t + ax t 1 = y t is equal to the sum of the solution of the homogenous part x t + ax t 1 = 0 and a particular solution of x t + ax t 1 = y t

62 Solution of the first order difference equation The solution of the homogenous part is x h t = x 0 ( a) t whereas a particular solution of general difference equation is x p t = t ( a) t i y i i=1 Therefore, x t = x 0 ( a) t + t i=1 ( a) t i y i

63 Solution of the first order difference equation Let at t = 0 our economy be at a steady-state where π = π 0. Therefore, π t = π 0 = ( ) 1 t Aφ t i=1 t ( ) 1 t i π i=0 1 + Aφ ( ) 1 t i ( πi + φbɛ ) i + υ i 1 + Aφ 1 + Aφ t i + i=1 Y t = Ȳ t A (π t π t ) + Bɛ t ( 1 ) t i φbɛ i + υ i 1 + Aφ 1 + Aφ