Macroeconomic Theory (First Six Weeks) Econ 504, Spring 2019

Home , Mechanism design, Nobuhiro Kiyotaki

Macroeconomic Theory (First six weeks) Econ 504, Spring 2019

Instructor: Nobuhiro Kiyotaki, O¢ce hour Wednesday 3-4pm 189 JR.Rabinowitz Preceptor: Christian Wolf, [email protected].

In this course, we will use dynamic general equilibrium models to address questions in macroeconomics. We will study asset pricing, investment, business cycles, unemployment and monetary policy, by considering Önancial frictions, labor market frictions and nominal price stickiness. The recommended (not required) textbook is Lars Ljungqvist and Thomas Sargent. Recursive Macroeconomic Theory,3rdedition,MITPress(2012)(2ndeditionisÖne). My papers are available at either Princeton E-journal or my website.

Course outline: Students are expected to read the articles with (*) in the list.

1. Consumption and Asset Pricing Models

Milton Friedman. ATheoryofConsumptionFunction. Chapters 2 and 3. (1957) Princeton University Press. (*) Rajnish Mehra and Edward Prescott. "The Equity Premium: A Puzzle." Journal of Monetary Economics (1985): 145-162. Ljungqvist-Sargent. Chapters 13 and 14. John Cochrane. "Macro-Finance." Review of Finance (March 2017): 945- 985.

2. Investment

Stephen Bond and Jason Cummins. "The Stock Market and Investment in the New Economy: Some Tangible Facts and Intangible Fictions." Brook- ings Papers on Economic Activity (2000:1):61-124. (*) Dan Cao, Guido Lorenzoni and Karl Walentin. "Financial Frictions, Investment and Tobinís q." Mimeo, (2017). Northwestern University.

3. Business Cycles and Credit

Edward Prescott. "Theory Ahead of Business Cycle Measurement." Fed- eral Reserve Bank of Minneapolis Quarterly Review (Fall 1986).

1 Ljungqvist-Sargent. Chapter 12. Takashi Kamihigashi. "Real business cycles and sunspot áuctuations are observationally equivalent." Journal of Monetary Economics (1996):105-117. Patrick Kehoe, Virgiliu Midrigan and Elena Pastorino. "Evolution of Modern Business Cycle Models." Journal of Economic Perspectives (Summer 2018). (*) Nobuhiro Kiyotaki. "Credit and Business Cycles." Japanese Eco- nomic Review (1998): 18-35. Nobuhiro Kiyotaki and John Moore. "Liquidity, Business Cycles and Monetary Policy." Journal of Political Economy, forthcoming. (*) Mark Gertler and Simon Gilchrist. "What Happened: Financial Fac- tors in the Great Recession." Journal of Economic Perspectives (Summer 2018). 4. Mechanism Design Approach to Financial Frictions Ljungqvist-Sargent. Chapters 20 and 21 (*) Nobuhiro Kiyotaki. "A Mechanism Design Approach to Financial Frictions," in Global Economy and Finance,eds.byF.Allenetal.(2016): Palgrave Macmillan. 5. Unemployment Ljungqvist-Sargent. Chapter 28. (*) Dale Mortensen and Christopher Pissarides. "Job Creation and Job Destruction in the Theory of Unemployment." Review of Economic Studies (1994): 397-415. Robert Shimer. "The Cyclical Behavior of Equilibrium Unemployment and Vacancies." American Economic Review (2005): 25-49. 6. Sticky Prices and Monetary Policy Jordi Gali. "The Basic New Keynesian Model. " Chapter 3 in Monetary Policy, Ináation, and the Business Cycle (2008) Princeton University Press. Julio Rotemberg. "Sticky Prices in the United States." Journal of Polit- ical Economy, (1982): 1187-1211. Eric Leeper, Christopher Sims and Tao Zha. "What Does Monetary Policy Do?" Brookings Papers on Economic Activity (2:1996): 1-63. Emi Nakamura and Jon Steinsson. "IdentiÖcation in Macroeconomics." Journal of Economic Perspectives (Summer 2018).

2 Macroeconomic Theory II (ECO-504) – Spring 2019

Heterogeneity and Market Incompleteness in Macroeconomics Gianluca Violante

General Information Lectures: Monday-Wednesday 10:30-12:10 in JRR 198 Office Hours: Monday 3:15-4:15 pm, 191 JRR. For alternative times, you can email meat [email protected]. Preceptor: Christian Wolf, email: [email protected]. Homework: There will be weekly problem sets that are required for a passing grade. The problem sets are handed out on Wednesday and are due the next Tuesday at precept, when Joseph will go over the solution. You are allowed to cooperate with other students, but every student has to hand in his/her own uniquely written assignment. Summary and Objectives Summary: This last section of the core macro sequence is devoted to studying economies where agents are heterogeneous. These models are helpful to analyze a wide range of questions pertain- ing to business cycles, income distribution, asset pricing, 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 (notably with complete markets) 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. Objectives: The aim of this course is to learn: 1) this important class of macroeconomic models, and 2) how to solve numerically for the equilibrium of these economies, anecessarysteptouse these models for quantitative research. Textbooks and Reading Material Textbooks: The main textbook is Recursive Macroeconomic Theory, by Lars Ljungqvist and Tom Sargent (LS), MIT Press, latest edition. You will also use Recursive Methods in Economic Dynamics, by Stokey, Lucas, and Prescott (SLP), Harvard University Press, 1989. Background readings: Three useful background readings for this course are:

• Jonathan Heathcote, Kjetil Storesletten, and Gianluca Violante (2009). Quantitative Macroeconomics with Heterogeneous Households, Annual Review of Economics

1 • Guvenen, Fatih (2012). Macroeconomics with Heterogeneity: A Practical Guide, Rich- mond Fed QR

• Quadrini, Vincenzo and Jose-Victor Rios-Rull (2014). Inequality in Macroeconomics, Handbook of Income Distribution,chapter14

Read them once at the beginning of the course, in that order. You’ll probably ﬁnd many of the sections hard to follow. Read them again at the end of the course, and you will ﬁnally see the light.

Course Outline

1. Heterogeneity in the Neoclassical Growth Model with Complete Markets (LS, 8) We discuss the assumptions on fundamentals under which, although households are heterogeneous in preferences and endowments, a representative agent exists. And we apply these results to the neoclassical growth model. We discuss the Negishi method. This methodology allows to calculate the competitive equilibrium prices and allocations of complete markets economies (in particular, economies for which the ﬁrst welfare theorem holds) with heterogeneous households. This method proves to be particularly useful for those economies where aggregation does not hold, hence we cannot use the representative agent. We present one illustration of this method based on a paper by Maliar and Maliar.

• Gorman, W.M. (1953). Community preference ﬁelds. Econometrica • Chatterjee, Satyajit (1994). Transitional dynamics and the distribution of wealth in a neoclassical growth model. Journal of Public Economics • Caselli Francesco, and Jaume Ventura (2000). A Representative Consumer Theory of Distribution. American Economic Review • Stiglitz, Joseph E. Distribution of Income and Wealth Among Individuals. Econo- metrica • Negishi, Takashi (1960). Welfare Economics and the Existence of Equilibrium for a Competitive Economy. Metroeconomica • Constantinides George (1982). Intertemporal Asset Pricing with Heterogeneous Con- sumers and Without Demand Aggregation. Journal of Business • Ogaki, Masao (2003). Aggregation under Complete Markets. Review of Economic Dynamics • 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 Neo- classical Growth Model with Idiosyncratic Shocks. Review of Economic Dynamics

2 2. The Income Fluctuation Problem I (LS, 18.14) We discuss the empirical implications of full-insurance for consumption. We review the Permanent Income Hypothesis and we apply it to characterize the consumption-saving problem of a single-agent who faces a stochastic income stream and can trade only a risk-free bond. We introduce the notion of precautionary savings and relate it to the convexity of marginal utility (prudence).

• 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 Po- litical Economy • Schulhofer-Wohl, Sam (2011). Heterogeneity and Tests of Risk Sharing. Journal of Political Economy • Hall, Robert (1978). Stochastic Implications of the Life Cycle-Permanent Income Hypothesis: Theory and Evidence. Journal of Political Economy • Leland, H. (1968). Savings and Uncertainty: The Precautionary Demand for Saving. Quarterly Journal of Economics • Sandmo Agnar (1970). The Eﬀect of Uncertainty on Saving Decisions. Review of Economic Studies. • Blundell, Richard and Ian Preston (1998). Consumption Inequality and Income Uncertainty. Quarterly Journal of Economics

3. The Income Fluctuation Problem II (LS, 17) We introduce borrowing constraints and show that precautionary savings can arise even without prudence as long as borrowing constraints may bind in some state of the world. We then derive an important condition on the interest rate that guarantees that the optimal individual consumption sequence is bounded above, in presence of income uncertainty. If time permits, we will also see the continuous time formulation of the problem and show that its solution can be characterized more completely relative to the discrete time case.

• Chamberlain, Gary and Charles Wilson (2000). Optimal Intertemporal Consump- tion under Uncertainty. Review of Economic Dynamics • Kimball, Miles (1990); Precautionary Saving in the Small and in the Large, Econo- metrica • Schechtman, J. (1976). An Income Fluctuation Problem. Journal of Economic Theory. • Schechtman J. and V. Escudero (1977). Some Results on An Income Fluctuation Problem. Journal of Economic Theory • Sibley David (1975); Permanent and Transitory Income Eﬀects in a Model of Optimal Consumption with Wage Income Uncertainty. Journal of Economic Theory

3 • Yaari, M. E. (1976). A Law of Large Numbers in the Theory of Consumer’s Choice Under Uncertainty. Journal of Economic Theory • Bewley, T. (1977). The Permanent Income Hypothesis: A Theoretical Formulation. Journal of Economic Theory. • Achdou, Yves, Jiequn Han, Jean-Michel Lasry, Pierre-Louis Lions and Benjamin Moll (2017). Income and Wealth Distribution in Macroeconomics: A Continuous Time Approach.

4. Numerical Techniques to Solve the Income Fluctuation Problem We present a set of simple numerical techniques to solve for the discrete-time consumption and saving policy functions in the recursive formulation of the income-ﬂuctuation problem for the single-agent who self-insures by saving/borrowing through a risk-free bond. In particular, we study a very fast numerical method, called endogenous grid method.

• Tauchen, George (1986). Finite State Markov Chain Approximations to Univariate and Vector Autoregressions, Economic Letters • Suen, Richard and Kopecki, Karen (2010). Finite State Markov-Chain Approxima- tions to Highly Persistent Processes. Review of Economic Dynamics • Lkhagvasuren, Damba (2012). Key Moments in the Rowenhorst Method, Mimeo. • Lkhagvasuren, Damba and N. Gospodinov (2014). A Moment-Matching Method for Approximating VAR Processes by Finite-State Markov Chains. Journal of Applied Econometrics • Carroll, Chris (2006). The Method of Endogenous Gridpoints for Solving Dynamic Stochastic Optimization Problems. Economics Letters • Judd, Ken (1998). Numerical Methods in Economics. MIT Press, chapter 6 • Miranda Mario, and Paul Fackler (2002). Applied Computational Economics and Finance. MIT Press. Chapter 6. • Heer, Burkhard and Alfred Maubner (2005). DGE Modelling, Computational Meth- ods and Applications, Springer. Chapter 6.

5. The Neoclassical Growth Model with Incomplete Markets (LS 17.1-17.2, 17.6- 17.12) We analyze the equilibrium of a neoclassical growth model populated by a continuum of agents who face idiosyncratic labor income risk and trade only a risk-free asset. We use the tools we learned to characterize (as much as possible...) the existence and uniqueness of the invariant distribution.

• Imrohoroglu, Ayse (1989). The Costs of Business Cycles with Indivisibilities and Liquidity Constraints. Journal of Political Economy • Huggett, Mark (1993). The Risk-Free Rate in Heterogeneous-Agent Incomplete- Insurance Economies. Journal of Economic Dynamics and Control

4 • Aiyagari, Rao (1994). Uninsured Idiosyncratic Risk and Aggregate Saving. Quar- terly Journal of Economics • Hopenhayn H. and E. Prescott (1992). Stochastic Monotonicity and Stationary Distributions for Dynamic Economies. Econometrica • Heer, Burkhard and Alfred Maubner (2005). DGE Modelling, Computational Meth- ods and Applications, Springer. Chapter 7. • Uhlig, Harald (1996). A Law of Large Numbers for Large Economies. Economic Theory. • Laitner, John (1992). Random Earnings Diﬀerences, Lifetime Liquidity Constraints, and Altruistic Intergenerational Transfers. Journal of Economic Theory

6. Some Applications of Bewley Models We illustrate how to use this class of self-insurance models to analyze questions related to the wealth distribution and to ﬁscal policy.

• Moritz Kuhn and Victor Rios-Rull (2015). 2013 Update on the U.S. Earnings, Income, and Wealth Distributional Facts: A View from Macroeconomic Modelers, Minneapolis Fed Quarterly Review • Benhabib, Jess and Alberto Bisin. Skewed Wealth Distributions: Theory and Em- pirics. Journal of Economic Literature • De Nardi, Mariacristina, and Giulio Fella (2017). Saving and Wealth Inequality. Review of Economic Dynamics • Hubbard, Skinner and Zeldes (1995). Precautionary saving and social insurance, Journal of Political Economy • Krusell, Per and Tony Smith (1997). Income and wealth heterogeity, portfolio choice, and equilibrium asset returns, Macroeconomic Dynamics • Castaneda, Ana, Javier Diaz-Jimenez and Jose-Victor Rios-Rull (2003). Accounting for earnings and wealth inequality, Journal of Political Economy • Quadrini Vincenzo (2000). Entrepreneurship, Saving and Social Mobility, Review of Economic Dynamics. • 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 McGrattan (1998). The Optimum Quantity of Debt, Jour- nal of Monetary Economics

7. Constrained Efficiency in the Aiyagari Model We discuss the difference between the first-best allocations and the constrained efficient allocations in the Aiyagari model with self-insurance. We argue that the planner, through saving decisions, will manipulate prices in order to raise wages (if the income of the poor

5 is labor intensive), hence redistributing from the lucky-rich to the unlucky-poor. We also debate whether macroeconomists should reﬁne the neoclassical growth model with incomplete markets by adding observed channels of insurance (family, bankruptcy laws, public insurance), or whether they should think about the fundamental reasons that limit full insurance (moral hazard, adverse selection, imperfect enforcement).

• Hong, Jay, Julio Davila, Per Krusell, and Jose-Victor Rios-Rull (2012), Constrained eﬃciency in the neoclassical growth model with uninsurable idiosyncratic shocks, Econometrica.

8. Transitional Dynamics in the Neoclassical Growth Model withIncomplete Markets We study how to compute the transitional dynamics and how to measure correctly the welfare changes associated to a tax reform.

• Benabou, R. (2003). Tax and Education Policy in a HeterogeneousAgent Economy: What Levels of Redistribution Maximize Growth and Efficiency?. Econometrica (especially, section 5 on welfare decomposition) • Domeij, David and Jonathan Heathcote (2003). On the Distributional Effects of Reducing Capital Taxes. International Economic Review • Floden, Martin (2001). The Effectiveness of Government Debt and Transfers as Insurance. Journal of Monetary Economics (especially, section 3 on welfare decomposition)

9. Adding Aggregate Risk: A Near-Aggregation Result (LS 17.14.2) We extend the model to add aggregate ﬂuctuations in productivity. We explain the original/standard way to solve this model and present the near-aggregation ﬁnding of Krusell-Smith.

• Krusell, Per and Tony Smith (1998). Income and Wealth Heterogeneity in the Macroeconomy, Journal of Political Economy • Yaari, M. (1976). A Law of Large Numbers in the Theory of Consumer’s Choice under Uncertainty. Journal of Economic Theory,12,202-217. • Levine, D., and W. Zame (2001). Does Market Incompleteness Matter? Economet- rica, vol. 70(5), 1085-1839. • Heathcote, Jonathan (2004). Fiscal Policy with Heterogeneous Agents and Incom- plete Markets, Review of Economic Studies • Boppart, Timo, Per Krusell, and Kurt Mitman (2018). Exploiting MIT Shocks in Heterogeneous-Agent Economies: The Impulse Response as a Numerical Derivative. Journal of Economic Dynamics and Control

6 • Reiter, M. (2009). Solving Heterogeneous-agent Models by Projection and Pertur- bation. Journal of Economic Dynamics and Control

10. Endogenous Insurance and Limited Commitment We ﬁrst study an incomplete-market economy where agents face a participation cost to trade state-contingent insurance contracts. Next we study an economy with limited commitment.

• Mengus, Eric and Roberto Pancrazi (2018). Endogenous Partial Insurance and In- equality. • Kocherlakota, N. (1996). Implications of Eﬃcient Risk Sharing without Commit- ment. Review of Economic Studies • Krueger, D. and F. Perri (2011). Public versus Private Risk Sharing. Journal of Economic Theory • Zhang, Y. (2013). Characterization of a Risk Sharing Contract with One-Sided Commitment. Journal of Economic Dynamics and Control • Krueger, D. and H. Uhlig. (2018). Neoclassical Growth with Long-Term One-Sided Commitment Contracts.

11. Economies with Default We ﬁrst study an incomplete-market economy where agents face borrowing constraints that are tight enough so that they never have the incentive to default in the equilibrium. Then, we formalize a model where agents can default and the ﬁnancial sector takes into account the default probability and increases the prices of loans accordingly.

• 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 • Chatterjee, Satyajit, Dean Corbae, Makoto Nakajima, Jose-Victor Rios-Rull (2007). A Quantitative Theory of Unsecured Consumer Credit with Risk of Default. Econo- metrica