labor Market Model

The assignment is marked out of 25 points. The weight for each part is indicated following the
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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