Final Assessment
ECON 6002
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You have 2 hours (plus 15 minutes upload time). This is an open-book assessment.
But you must not collaborate and you must write answers in your own words.
Parameter values and assumptions in questions will depend on the last three digits of your Student
ID. Write final numerical answers to two decimals and put a box around each final answer.
1. Consider the Romer model and note the equilibrium output (per capita) growth is
max
{
(1− φ)2
φ
BL¯− (1− φ)ρ, 0
}
(a) Explain within the context of this model why is it necessary that ρ < (1−φ)φ BL¯. (3
points)
(b) Why does Kremer’s example about separation of populations after the last ice age sup-
port the importance of population growth for economic growth. (2 points)
(c) Why do Canada and the United States have similar growth despite very different pop-
ulations? (2 points)
(d) Why are patents necessary in the Romer model to deliver endogenous growth? (2
points)
(e) Explain in words why the decentralized equilibrium in the Romer model is socially
suboptimal. (3 points)
2. Consider the canonical New Keynesian DSGE model:
y˜t = Et[y˜t+1]− 1
θ
rt
pit = βEt[pit+1] + κy˜t + u
pi
t
rt = φpiEt[pit+1] + φyEt[y˜t+1]
where upit = ρpiu
pi
t−1 + epit is a cost-push shock and epit ∼ iidN(0, σ2pi). The solution for the
model takes the form y˜t = apiu
pi
t , pit = bpiu
pi
t and rt = cpiu
pi
t .
Table 1: Parameters for Q2
Last digit of SID θ β κ φpi φy ρ
′
pi u
pi
1
0 1 1 0.1 0.2 0 0.3 5
1 1 1 0.2 0.5 0 0.3 -2
2 1 1 0.1 0.2 0 0.3 5
3 1 1 0.2 0.5 0 0.3 -2
4 1 1 0.1 0.2 0 0.3 5
5 1 1 0.2 0.5 0 0.9 -2
6 1 1 0.3 0.5 0 0.9 4
7 1 1 0.5 0.2 0 0.9 -10
8 1 1 0.3 0.5 0 0.9 4
9 1 1 0.5 0.2 0 0.9 -10
(a) Write out your SID and circle the last digit. Then write out parameter values based on
the last digit of your SID and the corresponding numbers in Table 1. (1 point)
(b) Suppose that there is no serial correlation so that ρpi = 0. Use the method of undeter-
mined coefficients to solve for api, bpi and cpi algebraically and numerically. Then solve
numerically for how a positive cost-push shock at time t = 1 equal to upi1 would affect
the output gap, inflation, and the real interest rate. Explain your answer. (4 points)
Page 1 of 3
(c) Assume instead that the cost-push shock exhibits persistence so that ρpi = ρ
′
pi. Use
the method of undetermined coefficients to solve for api, bpi and cpi algebraically and
numerically. Then solve numerically for how a positive cost-push shock at time t = 1
equal to upi1 would affect the output gap, inflation, and the real interest rate. Explain why
the results are different than in the case with no persistence in the shock. (4 points)
(d) The IS curve and the New Keynesian Phillips curve are derived from a microfounded
model with optimizing agents. Describe in words the “microfoundations” of each of these
two curves. (4 points)
3. This question considers the possible costs of business cycles and inflation using the following
parameter values:
Table 2: Parameters for Q3
Second-last digit of SID θ σ∆c κ p¯i0 p¯i1
0 4 0.015 0.1 6% 4%
1 5 0.010 0.1 6% 4%
2 3 0.020 0.1 6% 4%
3 4 0.015 0.1 6% 4%
4 5 0.010 0.1 6% 4%
5 3 0.020 0.2 8% 4%
6 4 0.015 0.2 8% 4%
7 5 0.010 0.2 8% 4%
8 3 0.020 0.2 8% 4%
9 4 0.015 0.2 8% 4%
(a) Write out your SID and circle the second-to-last digit. Then write out parameter values
based on the second-last digit of your SID and the corresponding numbers in Table 2.
(1 point)
First, in terms of the cost of business cycles, consider the Lucas calculation where the rep-
resentative agent is characterized by CRRA preferences U(C) = C
1−θ
1−θ . Using a second-order
Taylor approximation of the utility function around the mean of consumption, C¯, the welfare
cost of business cycles is:
L = θ
2
(σC
C¯
)2
(b) Noting the values of θ and σ∆c, where c = lnC, and that the standard deviation of con-
sumption due to short-run fluctuations is σC = σ∆c× C¯, compute the maximum welfare
gain that could be achieved from eliminating consumption variability as a percentage of
average consumption (report percentage to 3 decimals). (3 points)
(c) Given your answer above, explain Lucas’s argument about the role of stabilization policy.
(3 points)
(d) Yellen and Akerlof (2006) argue that “By considering paths of consumption that differ
only in their volatility, Lucas implicitly assumes that the Phillips curve is linear in
unemployment.” Explain how and why the conclusion on the role of stabilization policy
would change if the Phillips curve is non-linear. (3 points)
Second, in terms of the cost of inflation, consider the Phillips curve: pit = pi
e
t + κy˜t where
piet is expected inflation. Assume that the central bank has some control of the evolution of
y˜t (by adjusting the policy rate, for example). Suppose that the central bank announces a
permanent reduction in its target or steady-state inflation rate from p¯i0 to p¯i1 at t = 1 (prior
to this, the economy was at the steady state with p¯i0 inflation and zero output gap).
(e) If the economy is characterized by an Accelerationist Phillips curve such that piet = pit−1,
what are the implications of the central bank’s disinflationary policy on the output gap?
(2 points)
Page 2 of 3
(f) In the case of the Accelerationist Phillips curve, suppose the central bank promises to
keep the output gap at a -5% level during this disinflation episode until the economy
reaches the new steady state inflation rate, but at this new steady state, the output gap
will return to its 0% level. How long does the central bank have to keep the output gap
below the 0% level? (4 points)
(g) Suppose now that the economy is characterized by a forward looking Phillips curve such
that piet = Et[pit+1] and that the central bank is fully credible. What are the implications
of the central bank’s disinflationary policy on the output gap in this case? (3 points)
4. Consider the “Q” model of investment with adjustment costs. Equilibrium suggests that
capital K(t) evolves as K˙(t) = C ′(I(t))−1(q(t)− 1) (normalizing the number of firms N = 1
and assuming no depreciation), while the marginal value of capital, q(t) evolves as q˙(t) =
rq(t) − pi(K(t)), where r is the real interest rate. Note that the capital adjustment cost
function, C(I(t)) satisfies C(0) = 0, C ′(0) = 0, and C ′′(·) > 0 and the real profit function,
pi(K(t)), satisfies pi′(·) < 0. Assume the transversality condition limt→∞e−rtq(t)κ(t) = 0,
where κ(t) is the representative firm’s capital stock. Assume initially that the economy is in
steady-state.
Table 3: Parameters for Q4
Third-last digit of SID r0 r1
0 1% 5%
1 5% 1%
2 1% 5%
3 5% 1%
4 1% 5%
5 5% 1%
6 1% 5%
7 5% 1%
8 1% 5%
9 5% 1%
At time t1 the interest rate changes unexpectedly from r0 to r1.
(a) Write out your SID and circle the third-to-last digit. Then write out parameter values
based on the third-last digit of your SID and the corresponding numbers in Table 3. (1
point)
(b) Discuss the transversality condition and explain why it is necessary to assume that
limt→∞e−rtq(t)κ(t) = 0. (2 points)
(c) If the change in the interest rate is permanent, explain both the short-run and long-run
dynamics of q(t) and K(t) and draw the transition path for the economy using a phase
diagram. (4 points)
(d) Assume now that this unexpected change in the interest rate is temporary instead of
permanent, i.e. it is expected that at some future time t2 > t1, the interest rate will
return to its original level. Explain both the short-run and long-run dynamics of q(t) and
K(t) and draw the transition path for the economy using a phase diagram. (4 points)
(e) Explain why, in the context of the “Q” model of investment, it is important to distinguish
between permanent and temporary changes in the interest rate. (2 points)
END OF ASSESSMENT