"I have never let my schooling interfere with my education" (Mark Twain)
Macroeconomic Theory II (G31.1026)
Heterogeneity in Macroeconomics
Professor Gianluca Violante
Room 712, Department of Economics
19 W 4th street
Tel. 212-992-9771
Download the preliminary syllabus here
General Information
Lecture Times and Location: Monday and Wednesday 9:55-11:55 in Room
517. The last class is on May 2nd.
Office Hours: Monday 12:00-1:00 in my office,
Room 712. You can always contact me
by phone at extension 29771 or
by
email
to arrange an alternative time.
TA and Tutorials: The TA is Dan Greenwald who can be reached by e-mail. He sits in room 721. Weekly tutorials are held on Friday 9:30-11:30 am in Room 517.
Homework: There will be weekly problem sets that are required for a passing grade. The problem sets are handed out on Wednesdays and are due the next Wednesday at the beginning of the class. You are allowed to cooperate with other students, but every student has to hand in his/her own uniquely written assignment.
Examination
There will be a written final examination on
May 7th, 9:30-11:30, room 517.
Summary and Objectives
Summary: This last section of the
course is devoted to studying economies where agents are heterogeneous. These
models are helpful to analyze a wide range of questions pertaining to income
distribution, asset pricing, financial markets, consumption insurance, labor
supply, the aggregate and redistributive effects of policies, etc. We will start
with some "aggregation theorems" to show that in some cases a representative
agent still exists. Next, we will move towards economies with "incomplete
markets" where agents can only borrow and save through a risk-free bond. We
begin by characterizing in detail the individual problem. Next, we proceed to
the description of the stationary equilibrium. Then, we study an
incomplete-markets model with aggregate shocks. The last set of classes are
devoted to defining economies where there is default in equilibrium, and
economies with heterogeneous firms. We may add one or two new topics, depending
on the speed at which we settle.
Objectives: The aim of this section
of the course is twofold: 1) to learn this important class of macroeconomic
models, and 2) to learn how to solve numerically for the equilibrium of these
model economies, a necessary step to use these models for quantitative research.
Reading Material
Textbook and Readings: The main textbook is Recursive
Macroeconomic Theory, by Lars Ljungqvist and Tom Sargent, MIT Press, second
edition, 2004 (denoted by LS below). You will also use Recursive Methods in
Economic Dynamics, by Stokey, Lucas and Prescott, Harvard University Press,
1989. In the recitation on March 26th, Dan will teach some basic concepts of measure
theory from SLP, chapters 7, 8.1,11.1,11.2 and 12.4. We need them from class 5
onwards.
Background readings: Two useful background readings for this course are
Jonathan Heathcote, Kjetil Storesletten, and Gianluca Violante (2008). Quantitative Macroeconomics with Heterogeneous Households, Annual Review of Economics
Guvenen, Fatih (2012). Macroeconomics with Heterogeneity: A Practical Guide
Read them once at the beginning of the course, you'll probably find many of the sections hard to follow. Read them again at the end of the course, and you will see the light.
All the papers listed below are required, with the exception of those marked with (XR) which are eXtra Readings, just for your own benefit, if you're interested in the topic.
March 19:
Aggregation (LS, 8.5.3)
We defined aggregation as a property of an economic model where the
evolution of the aggregate equilibrium quantities and prices does not depend on
the distribution of individual quantities. We briefly discussed aggregation of
CRS production functions, and aggregation of preferences when every agent is the
same along every dimension. We studied conditions under which Gorman (or demand)
aggregation holds. We studied the equilibrium of the growth model with complete markets and
household heterogeneity in endowments, where agents have (quasi) homothetic
utility. In the presentation, we followed Chatterjee's article. We showed that a
"representative agent" exists. The dynamics of aggregate
quantities and prices are independent of the distribution of wealth, and are the
same as in the representative agent economy you studied earlier. This is a stark
example of Gorman aggregation.
Gorman, William (1961) "On a class of preference fields", Metroeconomica (see also Mas Colell, ch. 4)
Chatterjee, Satyajit (1994) "Transitional dynamics and the distribution of wealth in a neoclassical growth model", Journal of Public Economics
March 21:
Aggregation (continued)
We discovered that in SS of the growth model with complete markets and
heterogeneous endowments the wealth distribution is indeterminate, but given an
initial distribution the equilibrium dynamics are unique. We then covered the Negishi method,
and derived the aggregation with complete markets result by Constantinides
(1982). The lecture notes contain an application based on the papers by Maliar-Maliar (2001, 2003).
Chatterjee, Satyajit (1994) "Transitional dynamics and the distribution of wealth in a neoclassical growth model", Journal of Public Economics
(XR) Caselli, Francesco and Jaume Ventura (2000) "A representative consumer theory of distribution" American Economic Review
(XR) Maliar, Lilia and Serguei Maliar (2001), "Heterogeneity in Capital and Skills in a Neoclassical Stochastic Growth Model", Journal of Economic Dynamics and Control
Maliar, Lilia and Serguei Maliar (2003), "The Representative Consumer in the Neoclassical Growth Model with Idiosyncratic Shocks", Review of Economic Dynamics
Constantinides, George (1982). "Intertemporal Asset Pricing with Heterogeneous Consumers and without Demand Aggregation," Journal of Business
Ogaki, Masao (2003) "Aggregation under Complete Markets", Review of Economic Dynamics
Lecture notes (updated) Homework 1 Dan's solution to Homework 1
Remember that Friday there is the Matlab recitation
March 26: Full Insurance and the Permanent Income
Hypothesis
We we talked about the dynamics of individual consumption in complete
markets and empirical tests of full insurance. We discussed the ad-hoc and micro-founded approaches to modeling market
incompleteness. We then described the budget constraint of an agent who is cut
off from all insurance markets and can only save/borrow with a non-state
contingent asset. We introduced the strict version of the PIH, quadratic utility and beta*R=1. We showed the martingale property of
consumption, certainty equivalence, we showed that consumption equals the
annuitized value of financial and human wealth, and we toyed around with a
special case (permanent-transitory income shocks). We showed that with panel or
repeated cross-section data we can identify time-varying variances of the income
shocks.
Mace, Barbara (1991); "Full Insurance in the Presence of Aggregate Uncertainty," Journal of Political Economy
Cochrane, John (1991); "A Simple Test of Consumption Insurance," Journal of Political Economy
Hall, Robert (1978); "Stochastic Implications of the Life Cycle-Permanent Income Hypothesis: Theory and Evidence", Journal of Political Economy
(XR) Friedman, Milton (1957); "The Permanent Income Hypothesis"
(XR) Blundell, Richard and Ian Preston (1998); "Consumption Inequality and Income Uncertainty," Quarterly Journal of Economics
March 28: Precautionary Saving
and the Income Fluctuation Problem (LS, 16.5-16.8, 17.3-17.5)
We have shown that borrowing constraints bind with probability one in the
PIH model if income is iid. We have introduced the notion of precautionary saving
(additional saving in the presence of uncertainty). We have related it to
the convexity of marginal utility (prudence) and to the presence of borrowing
constraints potentially binding in the future. We have defined a natural
borrowing limit for the stochastic case. We have derived necessary conditions on the
interest rate so that the optimal individual consumption sequence
is bounded above, in
the deterministic case and in the stochastic case. We have also shown, somewhat
heuristically, that when income shocks are iid and BR<1 if absolute risk aversion
declines monotonically with consumption, then the consumption sequence is
bounded.
Leland, Haynes (1968); "Saving and Uncertainty: the Precautionary Demand for Saving", Quarterly Journal of Economics
Sibley, David (1975); "Permanent and Transitory Income Effects in a Model of Optimal Consumption with Wage Income Uncertainty", Journal of Economic Theory (only section VI)
Schechtman, Jack and Vera Escudero (1977); "Some Results on an Income Fluctuation Problem", Journal of Economic Theory
(XR) Chamberlain, Gary and Charles Wilson (2000); "Optimal Intertemporal Consumption under Uncertainty", Review of Economic Dynamics
Lecture Notes Homework 2 Dan's solution to Homework 2
Derivation of Sibley's result in the multiperiod (finite-horizon) problem (thanks Dan!)
Recall that Friday there is the measure theory recitation
April 2: Numerical Techniques
to Solve the Stochastic Consumption-Saving Problem
We have discussed how to discretize an AR1 process with the Tauchen method and
the Rouwenhorst method. We have described in great detail a method to solve the
income fluctuation problem based on iterating over the Euler
equation and linearly interpolating the decision rule outside grid points.
Tauchen, George (1986); "Finite State Markov Chain Approximations to Univariate and Vector Autoregressions", Economic Letters
Kopecky, K. and R. Suen (2010); "Finite State Markov Chain Approximations to Highly Persistent Processes"
(XR) Floden, Martin (2007); "A Note on the Accuracy of Markov-Chain Approximations to Highly Persistent AR(1) Processes"
(XR) Judd, Ken (1998); Numerical Methods in Economics, MIT Press, chapters 6-10
(XR) Heer, Burkhard and Alfred Maubner (2005); "Dynamic General Equilibrium Modelling, Computational Methods and Applications," Springer, Part II
April 5: The Neoclassical
Growth Model with Incomplete Markets I (LS 17.1-17.2, 17.6-17.12)
We have kept discussing numerical solution methods for the income
fluctuation problem. We have seen the endogenous grid method and learned how to
simulate from the model. We have briefly discussed how to gauge the accuracy of
the solution. Next, we described the neoclassical growth model populated
by a continuum of agents who face idiosyncratic labor income risk and trade only
a risk-free asset (i.e., the model in Aiyagari 1994). We defined a stationary
RCE.
Carroll, Christopher (2006); "The Method of Endogenous Gridpoints for Solving Dynamic Stochastic Optimization Problems", Economic Letters
Huggett, Mark (1993); The Risk-Free Rate in Heterogeneous-Agent Incomplete-Insurance Economies, Journal of Economic Dynamics and Control
Aiyagari, Rao (1994); Uninsured Idiosyncratic Risk and Aggregate Saving, Quarterly Journal of Economics
(XR) Hopenhayn H. and E. Prescott (1992); Stochastic Monotonicity and Stationary Distributions for Dynamic Economies, Econometrica
(XR) Uhlig, Harald (1996). A Law of Large Numbers for Large Economies, Economic Theory.
Lecture Notes (updated) Dan's measure theory notes
Computational Assignment (due 5/2)
April 9: Stationary
equilibrium in the Incomplete Markets Models (continued)
We have discussed conditions for existence and uniqueness of the the equilibrium
in Aiyagari's model. We have explained how to calibrate the model and and compute the
stead-state equilibrium. Then we have illustrated how to use this class of models to analyze
questions related to precautionary saving and wealth inequality.
Cooley T, and E. Prescott , "Economic Growth and Business Cycle", chapter 1 in Frontiers of Business Cycle Research, especially section 4 on calibration that we briefly discussed.
(XR) Budria Santiago, Javier Diaz-Gimenez, Vincenzo Quadrini, Victor Rios-Rull (2002); Updated Facts on the US Distributions of Earnings, Income and Wealth, Minneapolis Fed Quarterly Review
Castaneda, Ana, Javier Diaz-Jimenez and Jose-Victor Rios-Rull (2003); Accounting for Earnings and Wealth Inequality, Journal of Political Economy
April 12: Stationary
equilibrium in the Incomplete Markets Models (continued)
We outlined a model with entrepreneurs and workers and argued that it can
generate a more skewed wealth distribution, since entrepreneurs have access to a
higher return on their investment. Next we analyzed the model with endogenous
labor supply, and explained how to compute the stationary equilibrium. We also
argued that a Ramsey planner would choose a positive level of taxation in this
model, by trading-off distortions and redistribution. We started thinking about
constrained efficiency in this class of models.
Quadrini, Vincenzo (2000); Entrepreneurship, Saving and Social Mobility, Review of Economic Dynamics
Kitao, Sagiri (2004); Entrepreneurship, Taxation and Capital Investment," Review of Economic Dynamics (Sections 1-4)
Floden Martin and Jesper Linde (2001); Idiosyncratic Risk in the U.S. and Sweden: Is there a Role for Government Insurance?, Review of Economic Dynamics
Aiyagari, Rao and Ellen Mc Grattan (1998); The Optimum Quantity of Debt, Journal of Monetary Economics
No
recitation this
Friday
Important: in the computational assignment, set
\beta=0.90 throughout the computation.
April 16:
Constrained Efficiency in the Aiyagari model & Transitional Dynamics
We began by discussing the difference between the first-best allocation and the
constrained-efficient (second-best) allocation in the Aiyagari model. We
argued that the constrained planner, through saving decisions, will manipulate
prices in order to raise wages (if the income of the poor is labor intensive),
hence redistributing from the lucky-rich to the unlucky-poor. Next we defined a RCE
of an economy undergoing a transition between two steady-states due to a tax
reform, and studied how to compute the transitional dynamics by means of a
shooting algorithm. We learned how to measure welfare changes from the tax
reform.
Hong, Jay, Julio Davila, Per Krusell, and Jose-Victor Rios-Rull (2011), Constrained Efficiency in the Neoclassical Growth Model with Uninsurable Idiosyncratic Shocks
Domeij, David and Jonathan Heathcote (2003), On the Distributional Effects of Reducing Capital Taxes, International Economic Review
Huggett (1997), The One Sector Growth Model with Idiosyncratic Shocks: Steady-States and Dynamics, Journal of Monetary Economics
(XR) Floden, Martin (2001), The Effectiveness of Government Debt and Transfers as Insurance, Journal of Monetary Economics (especially relevant is section 3 on welfare decomposition)
Lecture Notes on
constrained efficiency
Lecture Notes on
transitional dynamics
April 18: Adding Aggregate
Risk: A Near-Aggregation Result (LS 17.14.2)
We have defined different welfare criteria to study the effects of policy
reforms (conditionl and ex-ante welfare). Then we have extended the standard incomplete markets model to
incorporate aggregate fluctuations in productivity. We
have explained
how to solve for the equilibrium of this model by approximating the law of motion for the distribution.
We have explained the intuition for the "near aggregation" result: saving
policies are linear for the rich, and the rich hold the bulk of the capital
stock, so they determine its evolution.
Krusell, Per and Tony Smith (1998), Income and Wealth Heterogeneity in the Macroeconomy, Journal of Political Economy
Krusell, Per and Tony Smith (2006), Quantitative Macroeconomic Models with Heterogeneous Agents, Plenary Talk at the Econometric Society World Congress, London 2005.
Heathcote, Jonathan (2004), Fiscal Policy with Heterogeneous Agents and Incomplete Markets, Review of Economic Studies (example of a model with aggregate shocks to tax rates)
(XR) Krusell, Per, Toshi Mukoyama, Aysegul Sahin, and Tony Smith (2009), Revisiting the Welfare Effects of Eliminating Business Cycles, Review of Economic Dynamics
(XR) Levine David, and William Zame (2001), Does Market Incompleteness Matter?, Econometrica
April 23: Micro
and Macro Labor Supply Elasticity
We derived the expression for the Frisch elasticity of labor supply and
discussed issues in estimation of this magnitude from micro data. We explained
there is a tension between the small micro estimates and the large values used
by macroeconomists. We presented the Hansen-Rogerson indivisible model, where
the micro elasticity is small and the macro elasticity (i.e., the elasticity
of aggregate hours to the average wage) is infinity. We argued that even if
one relaxes the lottery/full insurance assumption and designs an economy with
indivisible labor at the household level and incomplete markets, we still find
that the aggregate elasticity is much higher than the micro elasticity.
Rogerson Richard (1998). Indivisible Labor, Lotteries and Equilibrium, Journal of Monetary Economics
Hansen, Gary (1985). Indivisible Labor and the Business Cycle. Journal of Monetary Economics.
Mike Keane and Richard Rogerson (2012). Reconciling Micro and Macro Labor Supply Elasticities: A Structural Perspective (sections 1, 2, 4.1, the rest is XR)
Chang Yongsung and S. Kim (2006). From Individual to Aggregate Labor Supply: A Quantitative Analysis Based on a Heterogeneous Agent Economy, International Economic Review
(XR) Chang Yongsung and S. Kim (2007). Heterogeneity and Aggregation: Implications for Labor-Market Fluctuations, American Economic Review
April 25:
Lifecycle Economies
Earnings inequality rises over the
life-cycle. So does consumption inequality, but by much less. Hours inequality
is flat. We argued that the complete-markets model (with separable utility) is
unable to reproduce these facts. We studied an overlapping-generations version
of the neoclassical growth model with incomplete market and we argued it can go
a long way in matching the facts. We quickly explained why the
near-aggregation result of Krusell-Smith does not carry out to life cycle
economies.
Storesletten, Kjetil, Chris Telmer and Amir Yaron (2001). How Important are Idiosyncratic Shocks? Evidence from Labor Supply, American Economic Review PP
Storesletten, Kjetil, Chris Telmer and Amir Yaron (2004). Consumption and Risk Sharing Over the Lifecycle. Journal of Monetary Economics
Kubler, Felix and Dirk Krueger (2004). Computing Equilibrium in OLG Models with Stochastic Production, Journal of Economic Dynamics and Control
April 30:
Default
We first studied an economy with collateral. Next, we have studied an incomplete-market economy where agents face borrowing
constraints that are tight enough so that they never have the incentive to
default in equilibrium. Then, we have formalized a model where agents can default
and the financial sector takes into account the default probability and
increases the prices of loans accordingly.
Fernandez-Villaverde, Jesus, and Dirk Krueger (2011). Consumption And Saving Over The Life Cycle: How Important Are Consumer Durables? Macroeconomic Dynamics
Zhang, Harold (1997), Endogenous Borrowing Constraints with Incomplete Markets, Journal of Finance
Livshits Igor, Jim McGee and Michele Tertilt (2006), Consumer Bankruptcy: A Fresh Start, American Economic Review
May 2: Industry
Dynamics
We studied the
equilibrium of an industry with firms facing shocks to their
productivity level, and with endogenous firm entry and exit. We analyzed the
impact of firing costs on the average productivity of the industry. We thought
about how to close the model in general equilibrium.
Hopenhayn, Hugo (1992). Entry, Exit and Industry Dynamics in Long-Run Equilibrium, Econometrica
Hopenhayn, Hugo ad Richard Rogerson (1993). Job Turnover and Policy Evaluation: A General Equilibrium Analysis, Journal of Political Economy
(XR) Atkeson, Andy and Pat Keohe (2006). Modeling the Transition to a New Technology, American Economic Review.
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May 7: FINAL EXAM, 9:55-11:55 am in Room 517
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Final Exam 2005
Final Exam 2006
Final Exam 2007
Final Exam 2008
Final Exam 2010