AMERICAN UNIVERSITY
Department of Economics
Comprehensive Examination
January 2013
Advanced Macroeconomic Theory
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[Contains corrections of typos in Section I ]
This examination has two Sections, I and II. You must answer both sections; follow the directions in each section carefully. Each section receives equal weight in the overall grading. Therefore, you should plan to spend an equal amount of time (about 2 hours and 30 minutes) on each
section, I and II. Please make sure that all math and graphs are intuitively explained, all diagrams
are clearly labeled, and all answers are responsive to the specific questions asked (no credit for
extraneous material). The time limits suggest the expected length and depth of your answers. No
calculators or other electronic devices of any kind are permitted. All answers are expected to
demonstrate mastery of the material at the PhD level.
SECTION I
Directions: Choose any two (2) questions. 1 hour and 15 minutes each.
1. Answer the following questions concerning Hein and Stockhammer’s post-Keynesian “story”
for a Phillips Curve/NAIRU model:
a. On the aggregate demand side, the saving and investment functions are as follows:
hz

 hz
g  g 0  g1 z  g 2   i 
and
   i (1  sR )
v

 v
where  = S/K is the saving-capital ratio, h is the profit share, z is the utilization rate
(ratio of output/potential output), v is the capital-potential output ratio, i is the interest
rate,  is the debt-capital ratio, sR is the rentiers’ saving rate (0 < sR < 1), and g = I/K is
the investment-capital ratio (accumulation rate, or growth rate of capital stock). First,
state the assumptions and explain the rationale for each equation. Then, find the stability
condition, solve for the short-run equilibrium utilization rate z*, and find the effect of an
increase in the interest rate z*/i. What are the “normal” and “puzzling” cases for this
derivative, and what is the intuition for them? (In this part, you may ignore expected
inflation and treat i as exogenously set by central bank policy.)
b. On the aggregate supply (distribution and pricing) side of the model, p is the price level
(so p̂ is the inflation rate, with superscripts e for expected and u for unexpected), expected inflation equals one-period lagged inflation ( pˆ e  pˆ t 1 ), and e is the employment rate
(which, for simplicity, is in a constant proportion to utilization e = xz with x > 0). The
profit share is h = m/(1+m), where m is the mark-up rate on unit labor costs (there are no
raw materials costs for simplicity).
The firms’ target for the profit share is hFT  h0 , and the actual (realized) profit share
is h  h0  h2 pˆ u .
The workers’ target for the wage share is (1  h)WT  W0  W1e , and the actual (realized) wage share is 1  h  W0  W1e  W2 pˆ u .
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Solve for the short-run Phillips Curve and also find the solution for the medium-run
equilibrium NAIRU employment rate, eN. Represent these on a pair of graphs showing
income distribution (1 – h) and unexpected inflation ( pˆ u  pˆ ) on the vertical axes.
i. What is it that reconciles the distributional targets of the workers and firms when
these are inconsistent in the short run? in the long run?
ii. How does an increase in unexpected inflation p̂ u affect the distribution of income
between wages and profits, and between rentiers’ and firms shares of the profits?
c. What would be the effects of an increase in firms’ monopoly power (an increase in h0) on
(i) inflation in the short run and (ii) the NAIRU employment rate eN in the medium run?
What is the intuition for each of these effects? How would the economy adjust to the new
medium-run equilibrium? Analyze graphically and explain what must be assumed about
(1) monetary policy and (2) whether the short-run equilibrium is “normal” or “puzzling”
in order for the economy to converge to the new steady state at a higher h0 (say, h0).
d. Suppose that the firms’ target profit share is an increasing function of the interest rate,
hFT  h0  h1i . First, briefly discuss the rationale for this assumption. Then, analyze
(graphically and intuitively) how this would affect the stability of the economy’s adjustment toward the NAIRU employment rate eN.
2. Analyze and explain the effects of an increase in the saving rate (either  or s, depending on
the notation of the model) on long-run economic growth in any three (3) of the following
four models. If relevant to the model, also analyze and explain the effects on income distribution, and distinguish short-run versus long-run effects (and show adjustment dynamics).
NOTES: Mathematical solutions and graphs are expected for parts a. and b.; answers to c.
and d. can be mostly graphical and intuitive, but you should define the variables and explain
key equations as needed. For all models, be sure to discuss intuitively why the long-run equilibrium growth rate rises, falls, or remains unchanged (i.e., explain the causal mechanism).
a. A Classical-Marxian model (Foley & Michl version) with full capacity utilization (u = 1)
and full employment or a constant unemployment rate (gK = n). The saving function is
gK +  = (r +) – (1–)(1– ).
where gK is the rate of capital accumulation, 0 <  < 1is the depreciation rate, r is the net
profit rate, and 0 <  < 1 is the weight on future consumption in the capitalists’ intertemporal consumption function.
b. An investment-constrained neo-Keynesian growth model—use the Foley & Michl version, in which u < 1 is the ratio of actual output to potential or full-capacity output, the
investment function is giK +  =  + (r +),  and  are positive parameters, and the
saving function is the same as in part a. The distributional closure is w  (1   )ux . Be
sure to include an analysis of the stability condition in your solution.
c. Dutt’s (2006) model of growth determined by both aggregate demand and aggregate
supply, with endogenous “animal spirits” ˆ   (l  n) and productivity growth
aˆ   (l  n) ; the saving function is gs = su and the investment function is gi =  + u.
d. Aghion and Howitt’s model of endogenous growth with neo-Schumpeterian technological change, in which the saving function is g = s–1 –  (0 < s < 1, 0 <  < 1) and the
innovation or R&D function is g  g~ ( ) ( g~  0 ).
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3. Suppose a country’s economy is described by the following functions (with all variables in
growth rate form):
imports:
m = m(e + p*  p) + my
exports:
x = x(e + p*  p) + xy*
y   ( x x  a a)
prices:
p=+w–q
output:
labor productivity (Verdoorn’s Law):
q = q0 + y
balance-of-payments equilibrium (assuming no capital flows): p  x  p*  e  m
a. First, show how the appropriate equations can be used to solve for the export-led, cumulative causation (ELCC) growth rate yE. Which equations and what assumptions are
required to obtain this solution? Which equation(s) is (are) ignored and why?
i. Find and interpret the condition for stability of the equilibrium at y = yE.
ii. What is implicitly assumed about the balance of payments in this model? What
would have to happen if the country’s growth led to a current account deficit?
b. Second, show how the appropriate equations can be solved for the balance-of-paymentsconstrained growth (BPCG) rate yB. Again, be sure to indicate which equations and what
assumptions are required, and discuss which equation(s) is (are) ignored and why.
i. If the real exchange rate is constant in the long run (i.e., long-run relative purchasing
power parity [PPP] holds), which equations do not matter to the long-run solution and
why not?
ii. What is implicitly assumed about (the growth rate of) domestic expenditures a in this
model?
c. Suppose the country succeeds in increasing the income elasticity of its export demand x
through export-promotion efforts. What are the predicted effects on growth in each of the
two models, ELCC and BPCG (assuming PPP in the latter case)? Even if the growth
effects are similar, are the causal mechanisms different? Discuss in depth.
4. Consider a “conflicting claims” model of inflation combined with a neo-Kaleckian model of
aggregate demand. The wage share is  = a0W/P, where W is the nominal wage, a0 is the
labor coefficient (hours per unit of output), and P is the price level. The profit share is  = 1
– . The price is set via mark-up pricing: P = (1 + z)a0W (labor is the only variable cost,
there are no raw materials, and the mark-up rate is z > 0). The capacity utilization rate is
proxied by the output-capital ratio, u = Y/K. Answer the following questions:
a. First, assume that wage and price increases are governed by the reaction functions
Wˆ   ( w  )  u and Pˆ   (   f ) , where w and f are the workers’ and firms’
respective targets for the wage share, with ,, > 0. Briefly explain the behavior represented by these equations and especially the rationale for the u term.
b. Suppose that labor productivity grows at the exogenously given rate  â0   . Find the
equation for the “distribution curve” (DC, or ˆ  0 ) and determine its slope in u  
space. Does DC necessarily slope upward or downward, or can it slope either way, and if
so what is the condition for a positive or negative slope? Solve and draw all possible
cases on an appropriate graph (or graphs), given the functions as specified in part a.;
explain the intuition for each possible case.
(Question 4 continues and Question 5 is found on the next page)
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c. On the aggregate demand side, the economy is closed (no trade), and there is no government or depreciation of capital for simplicity. There are positive savings out of wages,
but at a lower rate than out of profits, so the saving function is  = S/K = [sr + sw(1)]u
with 0 < sw < sr < 1. The investment function is g = I/K =  +  + u, with , ,  > 0.
i. Solve the aggregate demand side of the model for the goods market equilibrium condition (“IS curve”). Find an explicit (reduced form) solution for the equilibrium utilization rate u as a function of the profit share .
ii. What do you have to assume for stability of the goods market and an economically
meaningful solution?
iii. Is aggregate demand (measured by u) wage-led or profit-led, or can it be either? If it
can be either, find and interpret the condition for wage-led vs. profit-led demand.
Explain your result in terms of the parameters of this specific model.
d. Combine the two curves (IS and DC) on a series of diagrams in u   space. Show all
possible cases (in terms of the relative slopes of the curves) given the functions specified
above (show only possible cases). Analyze (graphically) the conditions on the slopes of
the two curves for the economy to be stable or unstable, assuming that output (goods
market) adjustment is instantaneous but wage/price (distributional) adjustment is slow
and gradual. What is the intuition for the unstable case(s), if any are possible?
e. Suppose that the labor union movement is weakened by new legislation, so that the workers’ target for the wage share f falls. Analyze the effects using IS and DC curves for all
possible, stable cases, and explain.
SECTION II
This section has two parts A and B; answer both parts. There is choice in both parts.
Part A – Choose one (1) question [70 minutes total]
1. Solve the Cagan inflation model for the price level. (Please use the method of undetermined
coefficients model to solve the discrete time model under rational expectations. Assume the
data generating process is AR(2).) Do not just provide the math; include a detailed intuitive
discussion. Give an intuitive and mathematical explanation of why your simple Cagan model
under rational expectations implies that the price level depends on all expected future fundamentals. (You need to provide a detailed algebraic account of how we forecast the fundamentals.) Discuss how you might estimate this model and “test” its rational-expectations
assumption.
(Section II Part A continues on the next page)
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2. Consider the model of Dosi, Fagiolo, and Roventini (DFR, 2008).
Describe the model in detail. (Your discussion should focus on the DFR model rather than
general considerations. Provide as many details as you can. Be sure to carefully distinguish
the behavior of consumption goods producers and machine tool producers.)
In what sense is the DFR model “evolutionary? In what sense are DFR’s firms “boundedly
rational? What approach do DFR take to expectations? How important are these features to
the DFR model? (Be detailed and specific.)
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? (Be very specific.) How successful are
they in matching these stylized facts? (What is the measure of success? Be very specific.)
3. 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.
(Section II Part B begins on the next page)
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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 details and specifics of the GHK model rather than on general considerations.
a. Present the model. (Provide as many details about the model as you can.)
b. What are the authors’ objectives? (Be sure to provide a detailed consideration of their
experiments and policy exercises.) How well do they achieve their goals?
c. How does their study suggest that networks are important to the study of macroeconomics? (You should include a detailed and technical discussion of network formation and its
importance to the model.)
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? (You should include a detailed and technical discussion of
haircuts and repos.)
e. What do GHK mean by “hoarding liquidity”? When do banks hoard liquidity, and why is
it important in their model? (Be as detailed and specific as possible.)
2. Consider exchange-rate overshooting in a very simple “Keynesian” (fix-price) economy.
M/P = L(i,Y)
DY = φ(Y,E,G)
i = i*  DE/E
Here D is the differential operator, L is real money demand, φ is excess demand in the goods
market, i is the short-term interest rate, Y is real income, M is the exogenous money supply,
P is the exogenous price level, and G is an exogenous “fiscal stance” variable. (For
simplicity, ignore interest-rate effects on aggregate demand.)
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 monetary expansion in the
short run, intermediate run (i.e., dynamic adjustment), and long run. Include a complete
intuitive discussion supported by detailed graphs
c. Include the complete algebra for the dynamic adjustment process. (Please use 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 monetary expansion.
Contrast your results from above with the effects of a one-time, permanent, anticipated
monetary expansion. Include a complete intuitive discussion supported by detailed
graphs.
(Section II Part B continues on the next page)
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3. 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. Why might a central bank prefer inflation targeting to either a Taylor rule or a price level
target?
c. Derive an expression for inflation in terms of the other variables and shocks in the model.
Define and interpret the control lag.
d. Assume that the central bank targets inflation. Given this model, derive the central bank’s
rule for the nominal policy rate.
e. 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?
f. 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? (Be detailed and specific.)
g. Have countries adopted inflation targeting with good results? (Provide as much detail as
you can.)
(End of Exam)