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The first half of the semester is an introduction to the techniques and the applications of dynamic general equilibrium models, with particular emphasis on models of economic growth.

Syllabus The first half of the semester is an introduction to the techniques and the applications of dynamic general equilibrium models, with particular emphasis on models of economic growth. There are seven sections. The basic readings for each section are indicated by stars. The non-star items are selected articles which you may want to refer to if you get excited with the particular topic; they are not required for the course. The lectures will alternate two modes. When we introduce a benchmark paradigm, such as in the case of the Neoclassical Growth Model, the presentation of the model and the derivation of the results will be quite detailed, with emphasis on both the techniques and the economics. The presentation will instead be more "chatty" and brief when we consider applications or extensions, such as those in Sections 4 and 7.

As organized below, the material is supposed to take 14 lectures, which of course violates our budget constraint. If we are fast enough, we might be able to cover everything; otherwise, we will adjust as we proceed.

If you are an MIT Econ PhD student, you have to take the course (or pass the waiver). Otherwise, please come and see me to discuss whether this course is appropriate for you.

Lecture Notes #1: Introduction and Growth Facts

• Introduction
• The World Distribution of Income Levels and Growth Rates
• Unconditional versus Conditional Convergence
• Stylized Facts

Lecture Notes #2: The Solow Growth Model (and looking ahead)

• Centralized Dictatorial Allocations
  1. The Economy, the Households and the Social Planner
  2. Technology and Production
  3. The Resource Constraint, and the Law of Motions for Capital and Labor
  4. The Dynamics of Capital and Consumption
  5. The Policy Rule
  6. Steady State
  7. Transitional Dynamics
• Decentralized Market Allocations
  1. Households
  2. Firms
  3. Market Clearing
  4. General Equilibrium: Definition
  5. General Equilibrium: Existence, Uniqueness, and Characterization
• Shocks and Policies
  1. Productivity and Taste Shock
  2. Unproductive Government Spending
  3. Productive Government Spending
• Continuous Time and Conditional Convergence
  1. The Solow Model in Continuous Time
  2. Log-linearization and the Convergence Rate
• Cross-Country Differences and Conditional Convergence
  1. Mankiw-Romer-Weil: Cross-Country Differences
  2. Barr Conditional Convergence
• Miscellaneous
  1. The Golden Rule and Dynamic Inefficiency
  2. Poverty Traps, Cycles, etc.
  3. Introducing Endogenous Growth

Lecture Notes #3: The Neoclassical Growth Model

• The Social Planner
  1. Preferences
  2. Technology and the Resource Constraint
  3. The Ramsey Problem
  4. Optimal Control
  5. Dynamic Programming
• Decentralized Competitive Equilibrium
  1. Households
  2. Firms
  3. Market Clearing
  4. General Equilibrium: Definition
  5. General Equilibrium: Existence, Uniqueness, and Characterization
• Steady State and Transitional Dynamics
  1. Steady State
  2. Transitional Dynamics
• The Neoclassical Growth Model with Exogenous Labor
  1. Steady State and Transitional Dynamics
  2. Continuous Time
  3. Phase Diagram (Figure 1)
• Comparitive Statics and Impulse Responses
  1. Additive Endowment (Figure 2)
  2. Taxation and Redistribution (Figures 3 and 4)
  3. Productivity Shocks: A prelude to RBC (Figures 5 and 6)
  4. Government Spending (Figures 7 and 8)
• Endogenous Labor Supply, the RBC Propagation Mechanism, and Beyond
  1. The Phase Diagram with Endogenous Labor Supply
  2. Impulse Responses Revisited
  3. The RBC Propagation Mechanism, and Beyond

Lecture Notes #4: Applications

• Arrow-Debreu Markets and Consumption Smoothing
  1. The Intertemporal Budget
  2. Arrow-Debreu versus Radner
  3. The Consumption Problem with CEIS
  4. Intertemporal Consumption Smoothing, with No Uncertainty
  5. Incomplete Market and Self- Insurance
• Aggregation and the Representative Consumer
• Fiscal Policy
  1. Ricardian Equivalence
  2. Tax Smoothing and Debt Management
• Risk Sharing and CCAPM
  1. Risk Sharing
  2. Asset Pricing and CCAPM
• Ramsey Meets Tobin: Adjustment Costs and q
• Ramsey Meets Laibson: Hyperbolic Discounting
  1. Implications for Long-Run Savings
  2. Implications for Self-Insurance

Lecture Notes #5: Overlapping Generations Models

• OLG and Life-Cycle Savings
  1. Households
  2. Population Growth
  3. Firms and Market Clearing
  4. General Equilibrium
• Some Examples
  1. Log Utility and Cobb-Douglas Technology
  2. Steady State
  3. No Labor Income When Old: The Diamond Model
  4. Perpetual Youth: The Blanchard Model
• Ramsey Meets Diamond: The Blanchard Model
• Various Implications

Lecture Notes #6: Endogenous Growth I: AK, H, and G

• The Simple AK Model
  1. Pareto Allocations
  2. The Frictionless Competitive Economy
• A Simple Model of Human Capital
  1. Pareto Allocations
  2. Market Allocations
• Learning by Education (Ozawa and Lucas)
• Learning by Doing and Knowledge Spillovers (Arrow and Romer)
  1. Market Allocations
  2. Pareto Allocations and Policy Implications
• Government Services (Barro)

Lecture Notes #7: Endogenous Growth II: R & D and Technological Change

• Expanding Product Variety (Romer)
  1. Technology
  2. Final Good Sector
  3. Intermediate Good Sector
  4. The Innovation Sector
  5. Households
  6. Resource Constraint
  7. General Equilibrium
  8. Pareto Allocations and Policy Implications
  9. Introducing Skilled Labor and Human Capital
  10. International Trade, Technology Diffusion, and other implications
• Increasing Product Quality (Aghion-Howitt)

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