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ECON 6002 Assessment

Creation date：2024-05-29 14:35:00

Belonging category：经济Economics

Tag 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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FE 825 IERG 5130 STAT 8178 EE161 ADS2 G54FUZ CS326 113B ECN 226 QBUS6860 ELEC3202 COMP9334 MGT11B MET CS 777 STA238 00099F Python SMM306 CMT206 EC116 SP MAST90084 CS480/680 BCPM0091 CMPT 300 ECON2209 FY20 STAT 432 CVEN9625 MATH1712 CMP9771M CMP3750M CIS 325 AI506 MAT344H1S MGT7180 PSTAT 160B CSYS5010 1D STAT 453/558 ME152B STA304H1F CSCI-128 ME428 CO3002 FINE 7640 COMP3234 ECSE 223 EE497 – 3D MATH5905 ECS648U ENG5009 MATH10242 EC665 A CPI221 ISOM5220 MACE40402 MGT B456F COMP9315 AFM 113 STAT 778 CS 564 MA231 CS 230 CS 124 COMP5511 CSC317 ITEC1010 ELEC207 INFT 3019 7CCMFM06 EE 161 5G ECLT5810 MATH 7349 CS526 O2 COMP90054 ELE00063M ACCT5034 ARC1015 CSCI 40 CSCI E40 FIN 524B CS 462 389COM CMT309 MFIN703 COMP4250 STA304 STA304H1S STA 1003 FIN 448 BUFN 732 CS520 CVEN3701 ECMT6006 PHAS0100 CSIT314 MDIA 5028 CSCI 2134 MAT 451 CMPT 459 STAT 457 INFO20003 COMP4141 IELE8066 F540 ECM9 CSE 6321 FIN 430 MATH3911 BFC5916 COMP1011 EEE 6209 STATS 240 CW3 COMP206 COMP1003 4331W ISE 530 CMPT 295 MATH 239 QF5203 INFR08010 IT114105 FIT2093 ECON3124 ECON1195 MATH 337 STAT 3006 COMP202 COMP3130 MATH3609 COMP 250 CS6140 IEEE ELE00041I FIN40090 CIV 5899 MATH3066 IGNMENT MATH 2009 STAT3405 HIST 101 MATH 3281 CEGE0042 ICT532 LAB 7 LAB 5 MCO455 CSIT214 Q4 IFB104 A1 ECO220Y5Y DA5020 CMPSC473 FIN9007 DSCI553 MSCI534 COMP3308 CSE-112 CMPT 310 EE104 F 2C P20 ALY2010 BUSM060 STA258 ECO00030M R BIOSTAT 274 COS6012-B FIT3155 CMPUT 340 EC421 INFS4205 ECOM135 NATS 1740 COMP809 MBE 6005 STA465 CSSE2310 CIVL2700 DATA4700 CMPSC 473 ISE 529 CS5044 MAST30020 COMP2207 ENGG1001 COMP0046 FIT3165 STAT GR5241 MECH0007 vATHK1001 ANALYTIC ATHK1001 MATH352001 HW3 S1 BMAN 24662 COMP 636 Stat-461 STAT 302 STAT 2132 STAR534 ENG4137 CMP3752M CS3103 BISM3222 STA 135 ME155A IIMT3601 ECON3371 ECON 3371 HW4 FINA 5840 DT211C CTEC3902 MAT005 MATH2148 S261F Econ 332 MATH3734 MIS41270 7CCMFM13 SYST 664 CIS434 CENG10014 MT4111 MT4527 ECMM424 CMT219 Math 136 MATH 3120 COMP10002 MAST20009 MATH0058 BEEM117 ISYE 6420 MGMTMFE 405 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LAW3016 CS371 STAT 334 FIN0008 ACC3004 STAT 371 COMP1921 MTH201 ACCT2000 UN3412 CIV6000 MATHS 3021 MATE7014 ECON1 CIBC6035 LAW121G COMM 321 CSC8204R TTM2033 CSCI 2600 MAE 115 LNG302 CENV6175W1 ECON30019 CPS2015 BST969 DDES9015 AMATH242 CS 1151 N1592 ACCT600 EG503G SMM519 EC318 Ecstatistics EEE 471 MARK2051 Topology COM00037H ACCT3000 MTHM501 EG501V COM00055H BUSN9085 GGR273 MATH 2B ITD102 MA214 ECON0060 ECE3114 ECMM447 Mechanics CCT361H5S BSAN3210 WELF2001 Fin3001 RESP5001 STA 137 Linguistics 101 CSCI368 CMPSC497 LUBS3655 OMBA 5355 BUSM2562 BFF5902 CYBR7001 CULT2005 ECON 7720 MTRX3760 FSE598 LUE1001 MGSC 7100 CS3240 COSC7500 ACCT3091 INFOGR TRAN 2080 DESIGN CIVE215001 CIVE2360 CPSC 8430 FNCE2003 Stoichiometry INFS6023 Quantitative Method Math 21D ECE5179 Design ECON8022 Chemical DMS 213 ADM1370 BFF5902 BFF2701 AGRI10051 AMN400 ECON7322 FINC5090 MATH1052 SciComp Elec4622 FINS5516 ENG 101 MMM143 CS431CA2 BSAN2201 EBSC7070 ES9v9-10 PLIN0009 DATA 8 MATH 101 BCPM0097 MAT 237 BISM2201 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SVM. (10 points) Consider an SVM classifier using RBF kernel, and finish the following python code to search for the optimum kernel parameter γ. You are required to calculate the RBF function and search yourself, instead of using functions in Scikit-Learn (sklearn). def parameter search(gamma list ,Xtr,ytr,Xts,yts ,...): """ Parameters gamma list: A list of RBF kernel parameter gamma to search for Xtr: Training data, shape (ntr,nrow,ncol) ytr: Training labels, shape (ntr,) Xts: Test data, shape (nts,nrow,ncol) yts: Test labels, shape (nts,) ... Add other parameters as needed Returns: gamma optimum: The gamma with minimum error on Xts, yts """ ... return gamma optimum

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