AMERICAN UNIVERSITY
Department of Economics
Comprehensive Examination
Advanced Macroeconomic Theory
June 2012
Page 1 of 7
This examination has two Sections, I and II. You must answer both sections; be sure to follow
the directions in each part carefully. Each part receives equal weight in the overall grading. So,
you should plan to spend an equal amount of time (i.e., about 2 hours and 30 minutes) on each
section, I and II, regardless of the number of questions in each. Please make sure that all math is
intuitively explained, all diagrams are clearly labeled, and all answers are responsive to the
specific questions asked. The time limits should suggest the expected length and depth of your
answers. The standard for passing this exam is demonstration of mastery of the material.
SECTION I
This section has two parts A and B; answer both parts. There is choice in both parts.
Part A – Choose two (2) questions [70 minutes total; about 35 minutes each]
1. Give an intuitive and mathematical explanation of why a simple Cagan model under rational
expectations implies that the price level depends on all expected future fundamentals. Solve
the Cagan model (discrete time, rational expectations) for the price level, using the method of
undetermined coefficients. Assume the data generating process is AR(1). Do not just
provide the math; include a detailed intuitive discussion.
2. Describe in detail the model of Dosi, Fagiolo, and Roventini (2008). Your discussion should
focus on the DFR model rather than general considerations. Provide as many details about
the model as you can. What are the objectives of DFR? How well do they achieve these
objectives? What is a “stylized fact”? What stylized facts do DFR focus on? How successful
are they in matching these stylized facts? (What is the measure of success?) In what sense is
the DFR model “evolutionary”? (Be detailed and specific.) In what sense are DFR’s firms
“boundedly rational”? (Be detailed and specific.) How important are these features to the
DFR model? (Explain.)
3. What is a “New Keynesian Phillips Curve”? Why and how does it differ from Phillips’
original formulation? We can develop a New Keynesian Phillips Curve based on “Calvo
pricing”, where each firm chooses its price, zt , according to the following loss function:


Here is the firm’s optimal price at time t, 0 <  < 1, and (1 - ) is the fraction of firms that
reset prices in a given period. Derive the firm’s optimal reset price (show all your work)
and provide a detailed intuitive interpretation of it.
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4. Suppose that the central bank adjusts the nominal interest rate according to a simple
inflation-based rule, as follows:

 
Here  is inflation at time ,  is the household’s (constant) discount rate, and
  0 . The economy is also governed by the Fisher equation

where is the real interest rate and E{·} is the expectations operator.
a. Derive the steady state solution for  in the case that   1. Determine whether this
nominal interest rate rule yields a deterministic solution for the price level, or leads to
price level indeterminacy.
b. If technology follows a stationary AR(1) process such that:


where 0   1, then the equilibrium solution for the real interest rate becomes:


1

Use this equation for together with your solution from part a. to solve for equilibrium
inflation.
c. What is the “Taylor principle”? Discuss the economic intuition for it and its relevance to
this problem. How is the monetary policy rule you derived in part (a) similar or different
from the policy rule suggested by John Taylor in his well-known 1993 article? Provide a
detailed response.
5. Seigniorage is often said to be the “inflation tax.”
a. Define seigniorage and discuss its representation as a tax.
b. Use the Cagan money demand function:
ln (M/P) =  - i + lnY
where (M/P) is real money balances, i is the nominal interest rate (you may treat the real
rate as exogenous), Y is real income, and the parameters  and  are positive constants.
Derive the optimal seigniorage in the steady state.
c. What are the key assumptions about the steady state that you used to derive optimal
seigniorage above? What is hyperinflation and what is its relationship to the steady state?
d. How would you expect the holding of real money balances to change with the
announcement of credible policy reform to end hyperinflation? Why?
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Part B – Choose one (1) question [80 minutes]
1. Discuss the interbank-lending model of Gai, Haldane, and Kapadia (2011), using algebra
where appropriate to pin down concepts (e.g., the role of haircuts). Your discussion should
focus on the specifics of the GHK model rather than on general considerations.
a. Provide as many details about the model as you can.
b. What are the authors’ objectives? How well do they achieve their goals?
c. How does their study suggest that networks are important to the study of
macroeconomics?
d. How do GHK model a repo transaction and a reverse repo transaction? What do GHK
mean by a “haircut”? Why are repo transactions subject to haircuts? How are haircuts
important in the GHK model?
e. What do GHK mean by “hoarding liquidity”? When do banks hoard liquidity, and why is
it important in their model?
2. Consider the following term-structure model of a simple “Keynesian” (fix-price) economy.
M = L(i,Y)
DY = φ(Y,R,G, Yss)
i = R - DR/R
Here D is the differential operator, i is the short-term interest rate, R is the long-term interest
rate, Y is real income, Yss is the steady-state level of real income, M is the exogenous money
supply, and G is an exogenous “fiscal stance” variable.
a. Give an intuitive explanation of each of the “structural” equations, including an
explanation of the sign of each of the partial derivatives of L and φ.
b. Consider the effects of a one-time, permanent, unanticipated fiscal expansion in the short
run, intermediate run (i.e., dynamic adjustment), and long run. Include a complete
intuitive discussion supported by detailed graphs. (Analyze the case where a fiscal
expansion raises demand, but be sure to discuss the possibility that it will not.)
c. Include the complete algebra for the dynamic adjustment process, using the adjoint
matrix technique. Make sure you explain both the economic intuition and the
mathematical role of the transversality condition. (A description of what happens does
not constitute an explanation!)
d. Include the complete algebra for the long-run comparative statics (i.e., the change in the
steady-state values).
e. Discuss this model’s appropriateness for analyzing an anticipated fiscal expansion.
Contrast your results from above with the effects of a one-time, permanent, anticipated
fiscal expansion. How and why are the results different in the short run, intermediate run,
and long run. (Or are they?) Include a complete intuitive discussion supported by detailed
graphs.
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3. What is time inconsistency? Our time inconsistency results usually relies upon the existence
of a distortion. What is the nature of the distortion in the case of monetary policy? How do
Cukierman and Gerlach get around this distortion in their model?
Assume that the central banker’s loss function in a given period t is as follows:
Zt = [(a/2) (πt)²] – [b (πt – πte)]
Here π is inflation; πe is inflation rate that is expected to prevail between t and t+1 given
information available at time t; a and b are positive parameters. Assume that the policymaker
has perfect control over π and individuals set expectations.
a. If the policymaker pre-commits to a rule (and individuals believe this rule), what is the
optimal value for inflation? What is the loss associated with this rule?
b. If instead the policymaker follows a discretionary policy, what value will inflation take?
What is the loss in this case?
c. Which one of these solutions is potentially time inconsistent? Why? What is the value of
inflation under time inconsistent policy? Take the time inconsistent solution and
demonstrate that the policymaker can improve welfare by cheating.
d. Why are some central bankers critical of time-inconsistency analysis? What important
real-world concern does the model ignore that might necessitate discretionary policy?
e. Discuss solutions to the time inconsistency problem, referencing the literature.
4. Svensson describes an economy as follows:
πt+1 = πt + α yt + εt+1
yt+1 = β1 yt – β2 (it – πt) + η t+1
xt+1 = γ xt + θt+1
Here πt = pt – pt–1 is the inflation rate in year t, p is the log of the price level, y is the log of
output relative to potential, x is an exogenous variable that affects inflation, i is the nominal
policy rate, and εt, ηt, and θt are i.i.d. shocks in year t that are not known in year (t – 1).
Assume that α1 and β2 are positive, and all the other coefficients are non-negative. Assume
also that β1 < 1 and γ < 1.
The central bank’s single-period loss function is as follows:
L(πt) = ½ (πt – π*)²
Here π* is the central bank’s target for inflation.
a. What is inflation targeting? (Provide a detailed definition.)
b. Derive an expression for inflation in terms of the other variables and shocks in the model.
Define and interpret the control lag.
c. Assume that the central bank targets inflation. Given this model, derive the central bank’s
rule for the nominal policy rate.
d. Assuming the central bank sets policy as detailed above, how will actual inflation deviate
from expected inflation? How should we assess central bank success in this model?
e. If you wanted to study the empirical effects of inflation targeting, what might you look
at? What sorts of things would you expect to find in an economy with an inflationtargeting central bank relative to an economy with a central bank that does not explicitly
target inflation?
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SECTION II
This section has two parts A and B; answer both parts. There is choice in both parts.
Part A – Shorter Answers – Choose two (2) questions [70 minutes total; 35
minutes each]
These questions should be answered primarily with graphs and intuitive explanations, but
you should give any key equations or math if necessary to support your answers and
subject to the time constraints; you do not need to give complete math for each model.
1. Does the balance-of-payments-constrained growth (BPCG) model support the idea that
“mercantilist” trade policies (i.e., active export promotion combined with import restrictions)
can be successful in stimulating long-run economic growth? Why or why not? Be sure to
highlight which parameter(s) of the model have to be influenced by government policy in
order for such policies to be successful, especially in the context of a simple version of the
model in which purchasing power parity holds and there are no net capital or financial flows
in the long run.
2. Can an aggregate demand stimulus lead to more rapid long-run economic growth, and if so
under what assumptions or conditions? Analyze and explain in terms of one (1) of the
following models: Dutt’s (2006) model of “Aggregate Demand, Aggregate Supply and
Economic Growth”; or the model of export-led cumulative causation (ELCC, originally
attributed to Kaldor and later developed by Setterfield and Cornwall among others). Be sure
to explain as specifically as possible how supply-side limitations on long-run growth are
relaxed by the aggregate demand stimulus in the model you have chosen.
3. Does more rapid economic growth (represented by the rate of capital accumulation, gK+)
require a more unequal distribution of income (represented by a higher profit share, ), or
can it be achieved with greater distributional equity (a lower )? Compare and contrast the
implications of a classical-Marxian growth model (use the version with a conventional wage
share, 1   ), and a neo-Keynesian growth model (with variable capacity utilization u and the
profit share is determined by the mark-up rate  so that  = /(1+ )). What is (are) the
crucial difference(s) in assumptions that account for the different implications?
4. What are the effects of Marx-biased technological change on the profit rate in each of the
following three “closures” of a classical-Marxian model of income distribution: (a) fixed or
conventional real wage; (b) fixed or conventional wage share; (c) full employment. If there
is a case in which the profit rate can fall, what must happen to the real wage in that case, and
what solutions could be used (either by corporations or the government) to restore profitability?
(Section II, Part B begins on the next page)
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Part B – Longer Answers – Choose one (1) question [80 minutes]
1. Consider an open economy neo-Kaleckian model characterized by the following equations
(there is no government sector and no depreciation of capital for simplicity):
Mark-up pricing: P = (1 + z)Wa0 (z > 0 is the mark-up rate, W is the nominal wage, and
a0 is the labor coefficient [hours/output])
Real exchange rate: q = EP*/P (E is the nominal exchange rate in domestic/foreign
currency; P* is the foreign price level)
Wage share:  = Wa0/P
Profit rate: r = (1 – )u (where u = Y/K is a proxy for the capacity utilization rate)
Saving function:  = S/K = srr (0 < sr < 1; there are no savings out of wages)
Investment function: g = I/K = f0 + f1r
(f0, f1 > 0)
(b1, b2 > 0)
Trade balance: b = B/K = b0 + b1q – b2u
ˆ
Wage adjustment: W   ( w   ) where w is the workers’ target wage share
Price adjustment: Pˆ   (     q ) where  reflects the degree of competition in domestic markets ( is inversely related to industrial concentration) and ,  > 0.
Exchange rate adjustment (“crawling peg” managed exchange rate): Eˆ   ( q  q ) ,  > 0
a. Let  = EP*/ Wa0 be the real exchange rate in terms of unit labor costs. Demonstrate that
q = .
b. Solve mathematically for the short-run equilibrium level of u; find an explicit (reduced
form) solution for the equilibrium utilization rate u as a function of , , and other parameters. You may assume that z, W, a0, E, and P* are exogenously given in the short run.
HINT: Be sure to use q =  to substitute for q where necessary.
c. Is aggregate demand (measured by u) wage-led or profit-led, or can it be either in the
short run? Find u/ (get an explicit solution) and analyze its sign. If the sign is ambiguous, find and interpret the condition for wage-led vs. profit-led demand in terms of the
parameters of this model. Find and use the stability condition as needed.
d. Show the derivation of the two demarcation curves (isoclines) for income distribution and
the real exchange rate in the medium run, ˆ = 0 (DC curve) and q̂ = 0 (FE curve). Draw
on a diagram. Find the slopes and relate to the stability of the medium-run equilibrium
for  and q.
e. Analyze the effects of each of the following, assuming that demand is wage-led in the
short run; your answer to this part should be graphical and intuitive (math is not expected). Be sure to state if the outcome including medium-run, open economy effects is
wage-led, profit-led, or can be either.
i. A currency depreciation policy (rise in the monetary authority’s target q )
ii. An increase in the monopoly power of firms (fall in the degree of competition, )
(Section II, Part B, # 2 and 3 are on the next page)
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2. Is the NAIRU a stable equilibrium for (un)employment? And is the NAIRU unique, or is it
endogenous? Analyze using the post-Keynesian model of either Hein and Stockhammer
(chapter 5 in their 2011 edited book) or the version in Hein’s 2008 book (where he uses the
term SIRE = stable inflation rate of employment). Give a full derivation and explanation of
the model you use, including math as well as graphs and intuition. Be sure to discuss the role
of income distribution (the wage or profit share) in your model, and analyze whether (or
under what conditions) central bank monetary policy is stabilizing or destabilizing, and what
factors (if any) make the NAIRU endogenous in the medium run in your model.
3. Answer the questions below with reference to the following version of Hein’s neo-Kaleckian
model:
mark-up pricing: p = (1 + m)w/y where m is a constant (interest-inelastic) mark-up, w is
the nominal wage rate (per hour), and y is labor productivity (output/worker hour)
profit share:
h = m / (1 + m)
profit rate:
r = hu/v
saving rate:
 = S/K = (hu/v) – i(1 – sz)
investment rate: g = I/K =  + u + h – i
a. Interpret the saving function (what are the two sources of saving in this equation, and
which terms represent them?) and the investment function (what is the rational for each
term?). State briefly (and define any variables not defined above).
b. Solve for the short-run equilibrium rates of capacity utilization and capital accumulation
[growth rate], u* and g*. Be sure to find the short-run stability condition and state any
other necessary assumptions.
c. What are the effects of increasing the mark-up rate m on equilibrium utilization u* and
growth g* in the short run? Solve for the appropriate derivatives and determine whether
utilization and growth are wage-led or profit-led or can be either (if “either” then state
and interpret the sign condition).
d. During the recent financial crisis and recession, the Fed and some other central banks
adopted monetary stimulus policies consisting of reductions in interest rates. Is an
interest rate cut (reduction in i) necessarily expansionary in the short run, and how is this
related to Hein’s distinction between the “normal” and “puzzling” cases? Find the
derivatives u*/i and g*/i and interpret intuitively. Be sure to state in words the
conditions for the puzzling case to result, in terms of this specific model, and what these
imply for monetary stimulus policy. How would you determine empirically which case
applies?
e. Does this model exhibit a Keynesian “paradox of thrift” for increases in the rentiers’
saving rate, sz, either in the short run or the long run or both? First, analyze the short-run
effect on utilization by finding and interpreting the derivatives u*/sz. Second, analyze
the long-run effect on the steady-state equilibrium growth rate g (i.e., find and interpret
 g s z ). Compare and contrast your results for the short and long run and discuss. (You
may wish to discuss stability of the long-run equilibrium briefly, but a full long-run
stability analysis is not required here.)
(End of Exam)