Problem Sets and Exams
Problem Set 1 (due October 4)
Problem Set 2 (due October 18)
Problem Set 3 (due November 8)
Problem Set 4 (due November 29)
Problem Set 5 (due at final exam)
Midterm (Fall 2003)
Midterm (Fall 2005)
Final (Fall 2003)
Final (Fall 2005)
Programs
1.) The program bigshow.m takes AR and
MA coefficients as input, and then plots a simulated time path, an impluse
response function, and the spectral
density. It calls the programs ss.m, tf.m,
impulse.m,
dimpulse.m,
shownew.m.
and
freq.m
2.) The program ex2.m solves the simple job
search model in question #6 in problem set 1. It calls the program valit.m.
(These programs were written by
Pierre Olivier-Weill, a Stanford graduate student at the time, now an NYU
professor)
3.) The file epdata.m
contains Mehra and Prescott's (1985, JME) data. The program hanjanbnd.m
uses this
data to compute and plot Hansen-Jagannathan
bounds. These are used to answer question 5 in problem set 3.
Note, hanjanbnd.m calls the program
PTIME.M
to do some data manipulations, so you need to download this too.
Papers
Methodological Issues
These 2 papers explain why macroeconomists worry so much
about "microfoundations" (i.e., why it is so important to explain macroeconomic
aggregates
in terms of the underlying preferences and technologies
of individual agents).
Lucas (1976), "Econometric Policy Evaluation:
A Critique", Carnegie-Rochester Conference Series on Public Policy
Sargent (1980), "Rational Expectations
and the Reconstruction of Macroeconomics", Quarterly Review (Minneapolis
Fed)
The next paper discusses the tension between positive
and normative approaches to macroeconomics. It points to a potential logical
inconsistency in the Lucas Critique.
It points out that the Lucas Critique may be unimportant
from a purely positive perspective in which government policy is made endogenous.
Sargent (1984), "Autoregressions, Expectations, and Advice", American Economic Review
The next paper is Prescott's Nobel Lecture. It reviews
the dramatic changes that have taken place during the past few decades
in both the questions macroeconomists ask, and the way they
go about answering them.
Prescott (2006), "The Transformation of Macroeconomic Policy and Research", Journal of Political Economy
Dynamic Optimization and Numerical Methods
The first paper provides a relatively intuitive exposition
of continuous-time dynamic optimization. Stokey's covers the same
material but is somewhat more rigorous. The paper by Alvarex and
Stokey provides some existence and uniqueness results for a class of
unbounded return functions, of the kind often encountered in economics.
Stokey (2003), "Introduction to Optimal
Control", Unpublished notes
Alvarez & Stokey (1998), "Dynamic Programming with Homogeneous Functions", Journal of Economic Theory
Uhlig's paper shows how to linearize nonlinear Euler equations,
and applies a method of undetermined coefficients to solve them.
Sims et al. argue that first-order (ie, linear) approximation methods often
produce misleading results, especially when computing welfare and asset
prices.
The paper by Villaverde et al. contains a detailed comparison
of several alternative solution strategies for a standard stochastic growth
model. It concludes that 2nd-order
perturbation methods clearly dominated first-order linear
approximations. Projection methods are even better, but can be much more
difficult to implement.
Uhlig (1999), "A
Toolkit for Analyzing Nonlinear Dynamic Stochastic Models Easily",
book chapter
Sims et al. (2003), "Calculating
and Using Second-Order Accurate Solutions of Discrete Time Dynamic Equilibrium
Models"
Villaverde et. al. (2003), "Comparing
Solution Methods for Dynamic Equilibrium Economies", working
paper
Unemployment
The next paper surverys the influential Mortensen-Pissarides
search model of equilibrium unemployment. It points to several empirical
shortcomings of the model, and argues that
the source of the problem lies in the Nash Bargaining
wage setting assumption.
Shimer (2005), "The Cyclical Behavior of Equilibrium Unemployment and Vacancies", American Economic Review
Moen extends the Mortensen-Pissarides model by introducing
competitive wage setting, and argues that the resulting equilibrium is
efficient. Mortensen & Wright discuss the generality
of this result. Rogerson et al. provide a detailed
overview of search-theoretic models of the labor market, with an emphasis
on theory rather than empirical work. Ljungqvist & Sargent
review alternative approaches to understanding unemployment,
and question Prescott's recent contention that tax rates explain differences
between North American and European labor supply.
Moen (1997), "Competitive Search Equilibrium",
Journal
of Political Economy
Mortensen & Wright (2002), "Competitive
Pricing and Efficiency in Search Equilibrium", International Economic
Review
Rogerson, Shimer & Wright (2005), "Search-Theoretic
Models of the Labor Market", Journal of Economic Literature
Ljungqvist & Sargent (2005), "Jobs and
Unemployment in Macroeconomic Theory: A Turbulence Laboratory", mimeo
Ljungqvist & Sargent (2006), "Do
Taxes Explain European Employment?", mimeo
Growth Theory
Lucas provides some perspective on the importance of understanding
business cycles. He summarizes a research program that he initiated
in 1987 which attempts to
calculate the welfare costs of business cycles.
His original estimate suggested that business cycles have very small wefare
effects - orders of magnitude smaller than the welfare
effects of growth. The following article argues
that this original estimate is robust to a number of reasonable modifications.
Lucas (2003), "Macroeconomic Priorities", American Economic Review
The first 2 papers ignited the endogenous growth revolution.
Romer's model is based on learning-by-doing externalities. Lucas' model
is based on human capital. The third
paper is a nice survey of endogenous growth theory.
Lucas (1988), "The Mechanics of Economic
Development", Journal of Monetary Economics
Romer (1994), "The Origins of Endogenous
Growth", Journal of Economic Perspectives
The next paper points out that if the Solow model is true (with identical technologies across countries) there should be HUGE incentives for capital to flow into poor countries
Lucas (1990), "Why Doesn't Capital Flow from Rich to Poor Countries?", American Economic Review
The next two papers argue that it is impossible to explain
the cross-sectional distribution of income levels unless you assume that
technology levels differ.
Parente and Prescott offer political economy-based
models to explain why technology does not diffuse across countries.
Prescott (1998), "Needed: A Theory of
Total Factor Productivity", International Economic Review
Parente & Prescott (1999), "Monopoly
Rights: A Barrier to Riches", American Economic Review
Asset Pricing
Lucas shows that with complete markets the intertemporal
marginal rate of subsitution in consumption can be used to price assets.
Kocherlakota reviews empirical work along
these lines. He argues that asset prices are difficult
to explain from this perspective. Constantinides & Duffie show
that incomplete markets with persistent idiosyncratic labor income
risk can explain the equity premium puzzle. McGrattan
& Prescott argue that there is no equity premium puzzle if debt and
equity returns are measured correctly.
Lucas (1978), "Asset Prices in an Exchange
Economy", Econometrica
Kocherlakota (1996), "The Equity Premium:
It's Still a Puzzle", Journal of Economic Literature
Constantinides & Duffie (1996), "Asset
Pricing with Heterogeneous Consumers", Journal of Political
Economy
McGrattan & Prescott (2003), "Average
Debt and Equity Returns: Puzzling?", American Economic Review
Barro (2006), "Rare Disasters and Asset Markets in the Twentieth Century", Quarterly Journal of Economics
Dynamic Optimal Taxation
Atkeson et al review Chamley and Judd's result that the
(asymptotic) optimal tax rate on capital income is zero. They argue
that this result is more general than commonly believed.
Aiyagari et al. reconciles Barro's (1979) tax-smoothing
model with Lucas and Stokey's (1983) model. Based on Permanent-Income
logic, Barro predicted that debt and taxes should
follow random walks. Lucas and Stokey's model predicts
that tax rates should reflect the serial correlation structure of government
expenditures. The key difference between these
models is that Barro assumes only state non-contingent
debt, whereas Stokey and Lucas assume effectively complete markets. By
ruling out state-contingent debt in Lucas and
Stokey's model, Aiyagari et al show that Ramsey taxes
contain a near unit root, closely resembling the predictions of Barro's
model. However, to obtain this result, exogenous
restrictions on government asset holdings must be imposed.
Kocherlakota studies optimal taxation with private information. He
develops a so-called "Mirrlees approach" to dynamic
optimal taxation, which relaxes the Ramsey taxation literature's
(often implict) assumption that taxes are linear functions of income. He
shows that wealth taxes are zero on average, but
are higher for poorer households. Poorer households
pay higher wealth taxes purely for incentive reasons, i.e., to discourage
hidden saving.
Atkeson, Chari & Kehoe (1999), "Taxing
Capital Income: A Bad Idea", Minneapolis Fed Quarterly Review
Aiyagari, Marcet, Sargent & Seppala (2002), "Optimal
Taxation without State-Contingent Debt", Journal of Polit. Economy
Kocherlakota (2006), "Advances
in Dynamic Optimal Taxation", mimeo
Golosov, Tsyvinski, & Werning (2006), "New Dynamic Public Finance: A User's Guide", mimeo
Incomplete Markets
Aiyagari (1994), "Uninsured Idiosyncratic
Risk and Aggregate Saving", Quarterly Journal of Economics