question text.

Style requirements [1 point]: This assignment requires the submission of a spreadsheet or a simple

script. Please keep THREE decimal places in your answers and include your spreadsheet or script

as an appendix. You can use Excel, Google Sheets, Matlab, Python etc. in your calculations. Please

take care in presenting your work and answers clearly.

Question 1 — Labor Market Model [8 points]

A model of the labor market. In this question, your task is to understand how the labor market

responds to an economic downturn using the model we developed in Lecture 8. Suppose the matching

function is given by

M(u, v) = A

uv

(u

η + v

η

)

1/η ,

where A governs the efficiency of the matching process, u is the unemployment rate and v is the

vacancy rate. Here, η is a parameter that governs the elasticity of the matching function. Assume

each period in the model corresponds to a month. Parameter values are provided in Table 1.

Separate rate: s 0.02 Matching efficiency: A 1.0

Matching elasticity: η 0.5 Vacancy posting cost: c 0.5

Match value: J 4

Table 1: Parameter values for labor market model

(1) Using the parameter values in Table 1, calculate the steady-state values of labor market tightness

θ, unemployment rate u and vacancy rate v. (2 points)

(2) Suppose the economy is initially in steady state (t = 0). At t = 1, a recession causes the value

of filled jobs J to decrease to J = 2 for 15 months. Starting from the steady state, use the

other parameter values in Table 1 and a spreadsheet/script to calculate and plot the time paths

of market tightness, unemployment rate and vacancy rate for 15 months (t = 0, 1, …, 15) after

the economy was hit by the recession. Describe how market tightness, unemployment rate and

vacancy rate respond to the decrease in J. Has the economy settled to a new equilibrium by

the end of 15 months? Explain your findings. (2 points)

Intermediate macro: Assignment #1 2

(3) Some economists believe that the matching process becomes less efficient in recessions, as indicated by the shifting out of the Beveridge curve. Suppose the economy is initially in steady

state. At t = 1, a recession causes the matching efficiency parameter A to decrease to A = 0.5

for 15 months. Starting from the steady state, use the other parameter values in Table 1 and

a spreadsheet/script to calculate and plot the time paths of market tightness, unemployment

rate and vacancy rate for 15 months (t = 0, 1, …, 15) after the economy was hit by the recession.

Describe how market tightness, unemployment rate and vacancy rate respond to the decrease

in A. Has the economy settled to a new equilibrium by the end of 15 months? Explain your

findings. (2 points)

(4) Recessions are associated with mass layoffs, as indicated by a countercyclical job separation

rate. Suppose the economy is initially in steady state. At t = 1, a recession causes separation

rate s to increase to s = 0.04 for 15 months. Starting from the steady state, use the other

parameter values in Table 1 and a spreadsheet/script to calculate and plot the time paths of

market tightness, unemployment rate and vacancy rate for 15 months (t = 0, 1, …, 15) after

the economy was hit by the recession. Describe how market tightness, unemployment rate and

vacancy rate respond to the increase in s. Has the economy settled to a new equilibrium by the

end of 15 months? Explain your findings. (2 points)

Question 2 — DAS-DAD Model [16 points]

Dynamic AS-AD model. The recession caused by the COVID-19 pandemic has reduced demand for

Australian goods. Your task is to understand how this adverse aggregate demand shock affects the

Australian economy and the use of monetary policy in stabilizing the economy. You will use the

Dynamic Aggregate Supply-Aggregate Demand model (developed in Lectures 10, 11 and 12) in your

analysis.

For simplicity, suppose the natural level of output is constant. Each period in the model corresponds

to a year. Interest rate and inflation are expressed in percentage points. The parameter values of the

model are provided in Table 2.

Y 50 φ 0.60

π

∗ 2 θπ 1

ρ 2 θY 0.30

α 1

Table 2: DAS-DAD model – Benchmark Parameter Values

(1) Using the parameter values in Table 2, calculate the long-run equilibrium values of inflation,

output, and the nominal and real interest rates. (1 point)

(2) Suppose the economy was initially in its long-run equilibrium. At year t = 1 the economy was

hit by a persistent adverse aggregate demand shock (captured by ε < 0) that lasts for four years

and then reverts to zero. In particular, the adverse aggregate demand shock takes the value

Intermediate macro: Assignment #1 3

εt = −2 for four years (t = 1, 2, 3, 4) before reverting back to zero at t = 5. Starting from the

long-run equilibrium at t = 0, use the parameter values in Table 2 to calculate the magnitudes

of the impact effects at t = 1 on inflation, output, nominal and real interest rates. Also explain

how you can recover the values of inflation, output, nominal and real interest rates from t = 2

onward. (3 points)

(3) Now use a spreadsheet/script to calculate and plot the time paths of inflation, output, nominal

and real interest rates for 50 years after the initial shock (t = 0, 1, … , 50). Describe inflation,

output, nominal and real interest rate dynamics associated with this adverse aggregate demand

shock. Explain how monetary policy responds to the inflation and output gaps. (3 points)

(4) Suppose the RBA decides to respond more aggressively to output gap by setting θπ = 0.3 and

θY = 1. Keeping all other parameters as in Table 2, recompute the time paths of output,

inflation, nominal and real interest rates for 50 years after the initial shock (t = 0, 1, … , 50).

Explain how the policy change affects the time paths of inflation, output, nominal and real

interest rate. Is there a policy tradeoff between inflation and output? Explain. (3 points)

For the remainder of this question consider the implications of a modified version of the dynamic

AS-AD model, where people’s inflation expectations may be subject to random shocks.

(5) Suppose that people’s expectations of inflation are subject to random shocks. That is, instead of

being merely adaptive, expected inflation in period t, as of period t−1, is Et−1(πt) = πt−1+ηt−1,

where ηt−1 is a random shock. This shock is normally zero, but it deviates from zero when some

event beyond past inflation causes expected inflation to change. Similarly, Et(πt+1) = πt + ηt

.

Derive both the DAD and the DAS equations in this slightly more general model. (3 points)

(6) Following part (5), suppose that the economy experiences an inflation scare. That is, at year

t = 1, people come to believe that inflation in year t = 1 is going to be higher, so η1 = 1 for this

year only. Starting in the long-run equilibrium, use the parameter values in Table 2 and the new

DAD and DAS equations to calculate and plot the time paths of inflation, output, nominal and

real interest rates for 50 years after the inflation expectation shock hits the economy (assuming

no other shocks). In what sense are inflation scares self-fulfilling? Explain. (3 points)

Intermediate macro: Assignment #1 4

Deadline and format

This assignment contributes 12.5% toward your final grade. The assignment is due by 2pm on Monday

September 12th. Your assignment should not exceed 1500 words in length. You should use relevant

diagrams and/or algebra to reinforce your argument where appropriate. Citations, labels in diagrams,

symbols in equations and numbers in tables will not count towards the word limit.

The assignment can be done in groups subject to the following rules: All members of the group will

be given the same mark. No more than three students may make up a group. Students may choose

to work and hand in an assignment on their own. No two groups may hand in the same assignment.

All assignments will be electronically screened for plagiarism.

Assignments must be submitted in electronic format by 2pm on the due date. No extension

will be considered. You can apply for special consideration if you cannot complete the assignment

because of illness or other circumstances. In case that your application is successful, the weight of

this assignment will be shifted to the final exam in the overall assessment. Moreover:

• You must keep a copy of your assignment.

• Plagiarism or other forms of academic dishonesty will result in disciplinary proceedings being

brought against you.

• 10% of the available marks will be deducted for each full hour of delay after the due date for

up to 10 hours.

Fine print

Plagiarism and collusion

Plagiarism is the presentation by a student of an assignment identified as his or her own work even

though it has been copied in whole or in part from another student’s work, or from any other source

(e.g., published books, web-based materials or periodicals), without due acknowledgment in the text.

Plagiarism is heavily penalized. Penalties for plagiarism can include a mark of zero for the piece of

assessment or a failing grade for the subject.

Collusion is the presentation by a student of an assignment as his or her own work when it is, in fact,

the result (in whole or in part) of unauthorized collaboration with another person or persons. Both

the student presenting the assignment and the student(s) willingly supplying unauthorized material

are considered participants in the act of academic misconduct.

Special consideration

Students who have been significantly affected by illness or other serious circumstances during the

semester may be eligible to apply for Special Consideration at STOP1.

Intermediate macro: Assignment #1 5

The following website contains detailed information relating to who can apply for Special Consideration and the process for making an application:

https://students.unimelb.edu.au/admin/special

You should not approach the lecturers or the tutors about special consideration.

Referencing

All sources used for a written piece of assessment must be referenced. This is to acknowledge that

your material is not based entirely on your own ideas, but is based, in part, on the ideas, information,

and evidence of others.

It is important that all material you present for assessment is referenced correctly. Material that

has not been referenced correctly may be considered to be plagiarised, and as such may be penalised

(as discussed above). We will also look for evidence that material included in the bibliography has

been used in the assignment. Including references that have not been used may also result in your

assignment being penalised

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