Problem Sets and Exams
Problem Set 1 - (Due February 3)
Problem Set 2 - (Due February 19)
Problem Set 3 - (Due March 23)
Problem Set 4 - (Due April 8)
Midterm
Final
Programs
1.) Harald Uhlig's toolkit of MATLAB programs. Run the readme.m file to see what's there. - Toolkit_4.1.zip
2.) 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
3.) The program ex2.m solves the simple job
search model in question #4 in problem set 1. It calls the program valit.m.
(These programs were written by
Pierre Olivier-Weill, a Stanford graduate student.)
4.) Fackler and Miranda's toolkit of MATLAB programs. Run the
Contents.m file (in the demos subdirectory) to see
what's there. -- compecon.zip
5.) 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.
6.) The program bewley99v2.m computes equilibrium mean asset holdings for Aiyagari's (1994) model. It calls aiyagari2.m.
MORE TO COME
Papers
Numerical Methods
The first paper shows how to solve linear Rational Expectations
models by converting them to a standard eigenvalue problem. Esistence
and uniqueness are related to having the
'right number' of unstable eigenvalues. Uhlig's
paper shows how to linearize nonlinear Euler equations, and applies a method
of undetermined coefficients to solve them.
McGrattan uses projection methods to solve functional
equations. Sims et al. argue that first-order (ie, linear) approximation
methods often produce misleading results,
especially when computing welfare and asset prices.
Finally, Giordani and Soderlind show how to apply standard methods to the
robust control models of Hansen and Sargent.
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.
Blanchard & Kahn (1980), "Solution of Linear
Difference Models under Rational Expectations", Econometrica
Uhlig (1999), "A Toolkit for Analyzing Nonlinear
Dynamic Stochastic Models Easily", book chapter
McGrattan (1998), "Application of Weighted Residual
Methods to Dynamic Economic Models", working paper (book chpt).
Sims et al. (2003), "Calculating and
Using Second-Order Accurate Solutions of Discrete Time Dynamic Equilibrium
Models"
Giordani & Soderlind (2003), "Solution
of Macromodels with Hansen-Sargent Robust Policies", forthcoming
JEDC
Villaverde et. al. (2003), "Comparing
Solution Methods for Dynamic Equilibrium Economies", working
paper
Search and Matching
The first 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. Ljungqvist and Sargent try to explain the persistently
high European unemployment rate. They
note that generous welfare and unemployment insurance
is not enough, since these same policies were in place during the 1960s,
when European unemployment was much lower.
They argue that it is the combination of a generous welfare
system and aggregate shocks that is to blame for high European unemployment
rates. Moen extends the Mortensen-
Pissarides model by introducing competitive wage setting,
and argues that the resulting equilibrium is efficient. Lagos derives
a matching function from more primative assumptions
and warns that conventional matching functions may be
subject to the Lucas Critique. Finally, Rupert et al discuss how the matching
framework can be applied to various issues in
monetary theory.
Shimer (2003), "The Cyclical Behavior of
Equilibrium Unemployment and Vacancies: Evidence and Theory", working
paper
Ljungqvist & Sargent (1998), "The European
Unemployment Dilemma",
Journal of Political Economy
Moen (1997), "Competitive Search Equilibrium",
Journal
of Political Economy
Lagos (2000), "An Alternative Approach to Search
Frictions", Journal of Political Economy
Rupert, Schindler, Shevchenko & Wright (2000), "The
Search-Theoretic Approach to Monetary Economics: A Primer"
Asset Pricing
The Lucas paper develops a model that links stock returns
to the intertemporal marginal rate of substitution in consumption.
Hansen and Jagannathan develop a nonparametric
methodology that illustrates the empirical failures of
early attempts to implement Lucas' model. Constantinides and Duffie
show how introducing a particular form of
idiosyncratic risk can greatly improve the performance
of the model. Brav et al. provide some empirical evidence in support
of the Contantinides and Duffie model.
Lucas (1978), "Asset Prices in an Exchange
Economy", Econometrica
Hansen & Jagannathan (1991), "Implications
of Security Market Data for Models of Dynamic Economies", J.
Polit. Econ.
Constantinides & Duffie (1996), "Asset
Pricing with Heterogeneous Consumers", Journal of Political
Economy
Brav, Constantinides & Geczy (2002), "Asset
Pricing with Heterogenous Consumers and Limited Participation: Empirical
Evidence", Journal of Political Economy
Incomplete Markets
These first few papers analyze situations where markets
for risk-sharing and consumption smoothing are exogenously shut down, without
asking why. Chamberlain and Wilson
analyze the behavior of an individual who faces an exogensouly
imposed borrowing constraint. They show that if the interest rate
is greater than or equal to the rate of time preference
the agent's wealth will diverge to infinity with probability
one. By accumulating a 'war chest', the agent can eventually
guarantee himself that the borrowing constraint will never bind.
Aiyagari embeds Chamberlain and Wilson's borrowing constrained
agent into a market setting. He shows that in equilibrium interest
rates must be below the rate of time preference.
Krusell and Smith incorporate aggregate shocks into Aiyagari's
model. They show that wealth heterogeneity has only minor effects
on macroeconomic aggregates.
Aiyagari (1994), "Uninsured Idiosyncratic
Risk and Aggregate Saving",
Quarterly Journal of Economics
Chamberlain & Wilson (2000), "Optimal
Intertemporal Consumption under Uncertainty", Review of Economic
Dynamics
Krusell & Smith (1998), "Income and
Wealth Heterogeneity in the Macroeconomy", Journal of Political
Economy
These papers discuss how incentive and commitment problems
can produce endogenously incomplete markets. Lucas provides an intuitive
discussion of the tension between efficiency
and income distribution. He notes that in many
settings efficient allocation mechanisms may lead ex post to an ever widening
income distribution. He also highlights the
difficulties (due to limited commitment) that can arise
when attempting to decentralize these allocations.
Lucas (1992), "On Efficiency and Distribution",
Economic
Journal
Atkeson (1991), "International Lending
with Moral Hazard and Risk of Repudiation", Econometrica
Kocherlakota (1996), "Implications
of Efficient Risk Sharing without Commitment", Review of Economic
Studies
Cole & Kocherlakota (2001), "Efficient
Allocations with Hidden Income and Hidden Storage", Review
of Econ. Studies
Krueger & Uhlig (2003), "Competitive
Risk-Sharing Contracts with One-Sided Commitment", working paper
Albanesi & Sleet (2003), "Dynamic Optimal
Taxation with Private Information", working paper
Hopenhayn & Nicolini (1997), "Optimal
Unemployment Insurance",
Journal of Political Economy
Kocherlakota (2004), "The Impact of Hidden
Savings on Optimal Unemployment Insurance", Review of Econ. Dynamics
Marcet & Marimon (1998), "Recursive
Contracts", working paper
Alvarez & Jermann (2000), "Efficiency,
Equilibrium, and Asset Pricing with Risk of Default", Econometrica
Kehoe & Perri (2002), "International
Business Cycles with Endogenous Incomplete Markets", Econometrica
Bond & Park (2003), "Gradualism in
Trade Agreements with Asymmetric Countries", Review of Economic
Studies
Taub (1990), "The Equivalence of Lending
Equilibria and Signalling-Based Insurance under Asymmetric Information",
RAND
Credibility
Albanesi et al point out that it is not necessarily the
case that standard Barro-Gordon type models are subject to a time inconsistency
problem. They derive a reduced form
Barro-Gordon model from first principles, and note that
in addition to the usual benefit of surprise inflation (due to the fact
that monopoly distortions lead to inefficiently low
output), there are also efficiency costs of inflation,
and for reasonable parameter values it can easily be the case that the
costs of inflation exceed the benefits. When this is the
case, there is no time consistency problem. Alvarez
Kehoe and Neumeyer show that optimal monetary and fiscal policies are time
consistent if and only if the Friedman Rule is
optimal under commitment.
Albanesi et al. (2003), "How Severe is the Time-Inconsistency
Problem in Monetary Policy?", Quarterly Review (Minn. Fed)
Chang (1998), "Credible Monetary Policy
in an Infinite Horizon Model: Recursive Approaches", Journal of
Econ. Theory
Judd et al. (2003), "Computing Supergame
Equilibria", Econometrica
Alvarez, Kehoe & Neumeyer (2003), "The
Time Consistency of Monetary and Fiscal Policies", working paper