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ECON 6002 Assessment

创建日期：2024-05-29 14:35:00

所属分类：经济Economics

标签： ECON 6002

Assessment

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Final Assessment

ECON 6002
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)

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1300A ENGG 1300 OLET1139 STAT 3503 STAT 206 FEM11149 ELEN 4720 COMP20003 SOLA1070 CS574 C11CS LINB29H3 MAST90083 ECON7200 STAT 610 LINB29 DSM-5 COMP3161 EEEN40010 MATH 4431 K353 STA 3386 IERG4300 COMS W4167 ENG5298 AMME 2302 CS3910 COMPSCI 320 STATS 369 GR5242 COSC 328 CSCI435 MGTS1301 INFS2200 COMP3900 CIS 375 Module AE03 COMP3121 CS260 HAM503 MGMT5050 INT3075 COSC 285 GEOL0029 GEGE2X01 STAT1201 MATH1061 MMF1941H STAT 5060 CS 520 COMP 4320 MSIN0104 000T FINS3648 ECMT2160 ECON4003 Phys 129L CSE 142 CS 3130 MGEB01 EECS 340 Finance (20443/20444) ECMM149 COMP5310 EEEN60180 CSC 111 AT2 CSCI 4430 STAB57 MA/CSC 427 MATH322 D100 CSCI544 CITS3004 CI6227 CSE 565 APCO 1P01 852L1 ELEC S411F COMP3207 STATS330 ECON7530 FIT5149 CSI4104 CMPT 371 COMP201 SEHS4696 FI4003 MATH6182 CG1 WS MATH401 MGT 205 QTM 110 COMP 0137 MACE12201 FIT5210 ECE 544 BISM7206 HUDM 6055 ECON3203 STATS 210 MSCI 570 MATH6173 COMPSCI4039 Accounting COM3503 AOE2024 ECON213 PSYC10004 Control Data 100/200A PHIL2617 PHYS3116 MIE250 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MAT136H1 GY 6183 COMP3170 AGRI90089 PHYSICS 1002 ECON10003 IEOR E4004 ACS61012 MATH 40550 MKTG2113 TELE4653 ENSC1004 ECE 232E MK726 MTRX2700 SHEET 3 CSCA08 COMP30027 Math 2XX3 statistic MMAN3200 BISM7213 ECMM109 ECON 2022 FNCE 20005 GR5067 CSCB09 ME 3017 CS 5100 PHYS 2903 COMS 4771 COMP222 COMP 1046 CSC148H1 ISYS2038 FINS2615 OT5206 COMP2048 A6 MECH5770M MA826/20 CMPT 726 STA457 INFS6071 INFS588 integral ECON 216 IRDR 0017 MA323 PA 15213 PSYC2001 ENV222 Statistics ACCT5930 ACCT12 LAND2121 ME 5405 COMM1180 TELE3113 A7 ECE 568 ACCT2019 INFS1200 ENGG1340 CS 1400 ASST3 FINM7409 SWEN30006 INFO2222 FIN20150 SOSS1000 CSSE7231 FINS5513 COMS3200 CECN 702 ECON4060H MN3515 HW2 PSYA02H3 ECON 2112 COMP90051 CS 1652 MA30059 AF1605 MKTG7501 ECO-6003B COM4521 CTM ECON3350 COMP 3804 ELEC9762 BISM 7255 ST22 MATH20014 MNE3122 COMP343 MATH5165 ELE7029 ENGR30002 SEEM3500 ECON7350 RISK5002 FINM7405 COMP90059 MOS 3320B STAT 431 BISM7221 MATH3014 MTH783P EBA 35302 ACS133 BUS2206 IE5600 ECOS 3997 EDST2003 FIN 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