For this question, consider the DAD-DAS framework of the macroeconomy. The following equations hold throughout the parts of the question.

IS Curve: Aggregate Supply: TaylorRule: Fisher Equation:

Yt = Y ? + (2 ? rt) + mt + ?t ?t = ?te + (Yt ? Y ? ) + ?t

it =(?t+2)+??(?t???)+?Y(Yt?Y ?) i = r + ?e

t t t+1

Variable/Parameter

Description

Yt

Output at time t

Y ?

Natural level of output

rt

Real interest rate at time t

mt

Shock to the money supply

?t

Demand shock

?t

Rate of inflation at time t

?te

Expected inflation for time t

?t

Supply shock

it

Nominal interest rate

??

Inflation target (constant over time)

?Y

Monetary policy parameter, positive

??

Monetary policy parameter, positive

The variables are described in the table above. The three shock terms, mt, ?t, and ?t, are stochastic and uncorrelated, with expected value of zero. Consider mt to be an arbitrary deviation from the intended monetary policy.

(a) (3 A4 sheets, both sides)

Suppose initially that?te = ?t?1, so that expectations are adaptive.

Solve for the equilibrium output and inflation at time t.

Find the long run equilibrium output and inflation, and the long run real interest rate.

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(b) (2 A4, front and back)

Suppose initially that the Taylor rule is targeted for an inflation goal of 4%, so that?? = 4. Suppose that at time t ? 1, the economy is at the long run equilibrium.

At time t, the central bank decides instead to target an inflation rate of 2%, so that ?? = 2.

Complete the following table to indicate whether each of the variables increases, decreases, or stays the same relative to their values before the policy change.

Illustrate your answer with a graph of the DAD-DAS model. Your graph should include the old equilibrium (period t ? 1), the short run (period t), and the long run (well after period t).

(c) (2 A4 sheets, both sides)

Suppose instead that consumers have rational expectations. Consider again the change in policy from the previous part of the question, lowering the inflation target from 4% to 2%. In particular, assume that the central bank announced the policy change.

Complete the following table to indicate whether each of the variables increases, decreases, or stays the same relative to their values before the policy change.

Illustrate your answer with a similar graph to the previous part of the question.

(d) (1 A4 sheet, one side)

Which of the two types of expectations (adaptive or rational) yields higher output?

Name one policy that the government can follow to help make expec- tations fit your answer (that is to say, name a policy that can help make expectations adaptive or rational, whichever was your answer). Briefly explain why.For this question, consider the DAD-DAS framework of the macroeconomy. The following equations hold throughout the parts of the question.

IS Curve: Aggregate Supply: TaylorRule: Fisher Equation:

Yt = Y ? + (2 ? rt) + mt + ?t ?t = ?te + (Yt ? Y ? ) + ?t

it =(?t+2)+??(?t???)+?Y(Yt?Y ?) i = r + ?e

t t t+1

Variable/Parameter

Description

Yt

Output at time t

Y ?

Natural level of output

rt

Real interest rate at time t

mt

Shock to the money supply

?t

Demand shock

?t

Rate of inflation at time t

?te

Expected inflation for time t

?t

Supply shock

it

Nominal interest rate

??

Inflation target (constant over time)

?Y

Monetary policy parameter, positive

??

Monetary policy parameter, positive

The variables are described in the table above. The three shock terms, mt, ?t, and ?t, are stochastic and uncorrelated, with expected value of zero. Consider mt to be an arbitrary deviation from the intended monetary policy.

(a) (3 A4 sheets, both sides)

Suppose initially that?te = ?t?1, so that expectations are adaptive.

Solve for the equilibrium output and inflation at time t.

Find the long run equilibrium output and inflation, and the long run real interest rate.

25

Page 3

20

(b) (2 A4, front and back)

Suppose initially that the Taylor rule is targeted for an inflation goal of 4%, so that?? = 4. Suppose that at time t ? 1, the economy is at the long run equilibrium.

At time t, the central bank decides instead to target an inflation rate of 2%, so that ?? = 2.

Complete the following table to indicate whether each of the variables increases, decreases, or stays the same relative to their values before the policy change.

Illustrate your answer with a graph of the DAD-DAS model. Your graph should include the old equilibrium (period t ? 1), the short run (period t), and the long run (well after period t).

(c) (2 A4 sheets, both sides)

Suppose instead that consumers have rational expectations. Consider again the change in policy from the previous part of the question, lowering the inflation target from 4% to 2%. In particular, assume that the central bank announced the policy change.

Complete the following table to indicate whether each of the variables increases, decreases, or stays the same relative to their values before the policy change.

Illustrate your answer with a similar graph to the previous part of the question.

(d) (1 A4 sheet, one side)

Which of the two types of expectations (adaptive or rational) yields higher output?

Name one policy that the government can follow to help make expec- tations fit your answer (that is to say, name a policy that can help make expectations adaptive or rational, whichever was your answer). Briefly explain why.

Dynamic IS-MP-AS: For this exercise you will need to download the spreadsheet IS MP AS_Q2.xIsx. (a) Simulate a supply shock by changing the "bar o" cell from zero to one. De- scribe the effect of the supply shock. (b) Simulate a demand shock by changing the "bar o" cell from one to zero and the "bar a" cell from zero to one. Based on the path of output, inflation, and the interest rates is it possible to distinguish a supply shock (your answer from part (a) ) from a demand shock? Explain. (c) Finally, consider a central bank with a dual mandate i.e. MP : Rt - F = m(5-1 - 7) +3Y-1. Assume that + = 0.2. Modify the spreadsheet to reflect this assumption. What is the effect of this change on the prediction for the effect of a demand shock (a = 1)? Explain and include a picture of the dynamics. (Note: I do not want the whole spreadsheet, just the picture of the path of output, inflation, and the interest rate.)InflationOutput GeInterest Rates time Shocks bar a har o 0 Parameters bar b 0. 5 bar m 1. 5 IAGNESOONOUAUN- har r 2 bar pi 2 2.5 bar v 0.5 18 19 1.5 20 Inflation 21 - Output Gap 22 Interest Rates 23 24 22 1 25 26 27 28 29 0.5 30 31 32 30 33 34 32 35 33 of 1 2 3 4 5 6 / 8 9 101412131415161/1819202122232425262/2829303132333435363/38394041 36 34 37 35 38 36 39 37 40 38 41 39 42 10