Economics 607 - Core Macro

Homework 6

Homework 6 is here. It is due Friday 12/2 by 5:00 p.m.

Homework 5

Homework 5 is here.

Homework 4

Homework 4 is here.

Homework 3

Homework 3 is here.

Homework 2

Economics 607
Fall 2011
Homework #2
Due Oct. 13

1. Consider the model

y = c(y-t) + I(i-π^e)+g                 IS Curve

M(i)/P = L(y,i)                              LM Curve

dy/dt = k₁*EDG

di/dt = k₂*EDM

For what values of M_i is the model unstable? Draw the phase diagrams for an unstable case.

2. Given the model

y = c(y-t) + I(i-π^e)+g(y)            IS Curve

r = r(y, π)                                        MP Curve

dy/dt = k₁*EDG

dr/dt = k₂*(r(y, π)-r)

where government spending depends upon the level of output, characterize the conditions for stability mathematically (in terms of the admissible values of g_y) and illustrate the conditions using phase diagrams. Is countercyclical fiscal policy stable?

3. Given the model

y = c(y-t,r) + I(i-π^e)+g               IS Curve

r = r(y, π)                                         MP Curve

dy/dt = k₁*EDG

dr/dt = k₂*(r(y, π)-r)

where c_r < 0 and all other partial derivatives have their usual signs, (a) show that the model is stable. (b) Show graphically and explain intuitively how the effectiveness of fiscal policy changes when consumption becomes more responsive to changes in the interest rate.

4. Given the classical model

y* = c(y*-t,π) + I(i-π^e)+g               IS Curve

r = r(y*, π)                                            MP Curve

dπ/dt = k₁*EDG

dr/dt = k₂*(r(y*, π)-r)

where c_π < 0 and all other partial derivatives have their usual signs (the natural rate of output, y*, is assumed to be fixed), (a) show that the model is stable. (b) Show graphically (in i-π space with i on the vertical axis and π on the horizontal) how i and π change when t increases. Explain intuitively.

5. Problem 6.5 in Romer.

Homework 1

Economics 607
Fall 2011
Homework 1
Due Thursday, October 6

1. Answer the questions below based upon the following model:

y = C(y - t) + I(i- πe) + G	IS Curve
M/P = L(i, y)	LM Curve

a) Find the slope of the IS and LM curves.
b) Show graphically and mathematically how the LM curve shifts when M increases.
c) Show graphically and mathematically how the IS curve shifts when π^e increases.
d) Show graphically, mathematically, and explain intuitively how i and y change when (i) there is an increase in g, and (ii) there is an increase in M.
e) Find the slope of the aggregate demand curve (in this case, relating P and y)
f) Does an increase in the absolute values of L_i make monetary policy more or less effective? Explain graphically, mathematically, and intuitively.

2. Romer: pgs. 306-308, problems 6.1, 6.2, 6.3, 6.4 and 6.6.

3. Sargent pg. 75, problem 5 (a),(b).

4. Given the following model:

y = E(y,r,g,t)	goods market
r = r(y, P)	policy reaction function
y=F(n,k0)	production function
W=W0	labor supply

where y = real output, g = real government spending, t = real taxes, r = the real interest rate, W₀ = the fixed nominal wage, n = labor, and k₀ = the fixed capital stock, and where all partials have their usual signs:

(a) Find dy/dW₀, dP/dW₀, dr/dW₀, and d(W/P)/dW₀.

5. Given the following model:

y = E(y,r,g,t)	goods market
r = r(y, P)	policy reaction function
y=F(n,k0)	production function
W=Peg(n)	labor supply

where P^e = the (exogenous) expected price level,  y = real output, g = real government spending, t = real taxes, r = the real interest rate,  W₀ = the fixed nominal wage, n = labor, and k₀ = the fixed capital stock, and where all partials have their usual signs:

(a) Find dy/dt, dP/dt, dr/dt, dW/dt, dn/dt, and d(W/P)/dt.

Syllabus for Fall 2011

Economics 607 Core Macro I
Course Title: Seminar in Advanced Macroeconomic Theory
Instructor: Mark Thoma
Office: 471 PLC
Phone: 346-4673
Email: mthoma@uoregon.edu
Office Hours: T/Th 11:30 a.m.-12:30 p.m. and by appointment
Web Page: Core Macro Web  Page
[http://economistsview.typepad.com/economics607coremacro/]

Texts: Recursive Macroeconomic Theory, 2^nd edition, by Lars Ljungqvist and Thomas Sargent,; Advanced Macroeconomics, 4^th edition, by David Romer; and Macroeconomic Theory, 2^nd edition, by Thomas Sargent.

Tests: There will be a midterm and a final. The midterm will be given on Tuesday, November 1^st, and the final exam is scheduled for Thursday, December 8^th from 1:00 p.m. – 3:00 p.m. This is sometimes adjusted to spread the three first year Ph.D. course exams more uniformly over finals week. The final is comprehensive. No make-up exams will be given.

Homework: Homework is assigned periodically. Late homework will not be accepted.

Grading: Grades are based upon the following weights. Homework counts 15%, the midterm is worth 35%, and the final is worth 50%. Contingent upon certain minimum standards of performance, grades are based upon your relative standing in the course.

Brief Outline:

1. The Traditional Keynesian and Classical Models (Romer Ch. 6, Sargent Chapters 1 and 2)

a. The Classical Model
b. The Keynesian Model
c. Policy Effectiveness in the Short-Run and Long-Run
d. The Dornbusch exchange rate overshooting model
e. Alternative Assumptions about Wage and Price Rigidity

2. Output-Inflation Tradeoffs and the Phillips curve (Romer Ch. 6)

a. The expectations augmented Phillips curve
b. Sargent and Wallace: rational expectations, the natural rate hypothesis, market clearing, neutrality, and the Lucas Critique
c. Empirical applications: the St. Louis equation, later evidence, the behavior of real wages and other macro variables

3. Microeconomic Foundations (Romer Ch. 6)

a. A Model of Imperfect Competition and Price-Setting
b. Are Small Frictions Enough?

4. The Lucas Incomplete Information Model (Romer Ch. 6, Sargent Ch. 10, Ch. 16)

a. Signal Extraction (Sargent ch 10)
b. Perfect Information (Romer ch 6)
b. Imperfect Information (Romer ch 6, Sargent ch 16)
c. Empirical evidence and the Lucas critique once again (Romer ch 6)

5. Linear Stochastic Difference Equations (Sargent ch 9, 11, 16, Sargent and Ljungqvist ch 2, pg 40-74)

a. Difference equations and lag operators
b. Adding stochastic shocks
c. Investment under uncertainty and other examples
d. Systems of equations and state space systems
e. Impulse response functions

6. Dynamic Stochastic General Equilibrium Models of Fluctuations (Romer ch. 7)

a. Building Blocks
b. Predetermined Prices
c. Fixed Prices
d. The Caplin-Spulber Model
e. Empirical Applications

Papers: [More to be added later]

Dornbusch, Rudiger, Expectations and Exchange Rate Dynamics, Journal of Political Economy, Vol. 84, No. 6 (Dec., 1976), pp. 1161-1176.

Poole, W., "Optimal Choice of Monetary Policy Instruments in a Simple Stochastic Macro Model," Quarterly Journal of Economics, 1970, 197-216.

Sargent, T. and Wallace, N., "Rational Expectations and the Theory of Economic Policy," Journal of Monetary Economics, Vol. 2, 1976.

McCallum, B.T., "Rational Expectations and Macroeconomic Stabilization Policy: An Overview," Journal of Money, Credit, and Banking, Nov., 1980, 716-745.

Christina D. Romer and David H. Romer., 1989. "Does Monetary Policy Matter? A New Test in the Spirit of Friedman and Schwartz," NBER Macroeconomics Annual 4: 121-170.

Friedman, Milton, and Schwartz, Anna J. 1963. A Monetary History of the United States, 1867-1960. Princeton, NJ: Princeton University Press.

Lucas, R., "Some International Evidence on Output-Inflation Tradeoffs," American Economic Review 63 (June) 1973.

Lucas, R., "Econometric Policy Evaluation: A Critique," Journal of Monetary Economics, (supplement), 1976.

Lucas, Robert E., Jr. "Expectations and the Neutrality of Money." Journal of Economic Theory, 1972, 4 (2), pp. 103-24.

• Fischer, Stanley, " Long-Term Contracts, Rational Expectations, and the Optimal Money Supply Rule," Journal of Political Economy, Vol. 85, No. 1 (Feb., 1977), pp. 191-205.

Taylor, J. 1979. "Staggered Wage Setting in a Macro Model.'' American Economic Review 69:108-113.

Taylor, John, "Aggregate Dynamics and Staggered Contracts," Journal of Political Economy 88, 1-24 (1980).

Andrew Caplin and Daniel Spulber, "Menu Costs and the Neutrality of Money," Quarterly Journal of Economics, November 1987, pp. 703-725.

Caplin, Andrew & Leahy, John, 1991. "State-Dependent Pricing and the Dynamics of Money and Output," Quarterly Journal of Economics, 106 (3), 683-708.

N. Gregory Mankiw & Ricardo Reis, 2002. "Sticky Information Versus Sticky Prices: A Proposal To Replace The New Keynesian Phillips Curve," Quarterly Journal of Economics, vol. 117(4), pages 1295-1328.