《Recursive Macroeconomic Theory》（货币经济学专题）

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全英文，

作者信息：
Lars Ljungqvist   Stockholm School of Economics
Thomas J. Sargent   New York University  and  Hoover Institution
目录:
Part I: The imperialism of recursive methods
1. Overview 1
1.1. A common ancestor. 1.2. The savings problem. 1.2.1. Linear-quadratic permanent income theory. 1.2.2. Precautionary savings. 1.2.3. Complete markets, insurance, and the distribution of wealth. 1.2.4. Bewley models. 1.2.5. History dependence in standard consumption models. 1.2.6. Growth theory. 1.2.7. Limiting results from dynamic optimal taxation. 1.2.8. Asset pricing. 1.2.9. Multiple assets. 1.3. Recursive methods. 1.3.1. Methodology:Dynamic programming issues a challenge. 1.3.2. Dynamic programming ischallenged. 1.3.3. Response: the imperialism of dynamic programming. 1.3.4.
History dependence and ‘dynamic programming squared’. 1.3.5. Dynamic principle-agent problems. 1.3.6. More applications.

Part II: Tools
2. Time series 24
2.1. Two workhorses. 2.2. Markov chains. 2.2.1. Stationary distributions.
2.2.2. Asymptotic stationarity. 2.2.3. Expectations. 2.2.4. Forecasting functions. 2.2.5. Invariant functions and ergodicity. 2.2.6. Simulating a Markov
chain.
2.2.7. The likelihood function.
2.3. Continuous state Markov chain.
2.4. Stochastic linear difference equations.
2.4.1.First and second moments.
2.4.2. Impulse response function.
2.4.3. Prediction and discounting.
2.4.4.Geometric sums of quadratic forms.
2.5. Population regression. 2.5.1. The
spectrum.
2.5.2. Examples.
2.6. Example: the LQ permanent income model.
2.6.1. Invariant subspace approach.
2.7. The term structure of interest rates.
2.7.1. A stochastic discount factor.
2.7.2. The log normal bond pricing model.
2.7.3. Slope of yield curve depends on serial correlation of logmt+1.
2.7.4.Backus and Zin’s stochastic discount factor.
2.7.5. Reverse engineering a stochastic discount factor.
2.8. Estimation.
2.9. Concluding remarks.
2.10.Exercises. A. A linear difference equation.

3. Dynamic Programming 78
3.1. Sequential problems.
3.1.1. Three computational methods.
3.1.2. CobbDouglas transition, logarithmic preferences.
3.1.3. Euler equations.
3.1.4. A sample Euler equation.
3.2. Stochastic control problems.
3.3. Concludingremarks.
3.4. Exercise.

4. Practical Dynamic Programming 88
4.1. The curse of dimensionality.
4.2. Discretization of state space.
4.3.Discrete-state dynamic programming.
4.4. Application of Howard improvement algorithm.
4.5. Numerical implementation.
4.5.1. Modified policy iteration.
4.6. Sample Bellman equations.
4.6.1. Example 1: Calculating expected utility.
4.6.2. Example 2: Risk-sensitive preferences.
4.6.3. Example 3: Costs of business cycles.
4.7. Polynomial approximations.
4.7.1. Recommended computational strategy.
4.7.2. Chebyshev polynomials.
4.7.3. Algorithm: summary.
4.7.4. Shape preserving splines.
4.8. Concluding remarks.

5. Linear Quadratic Dynamic Programming 101
5.1. Introduction.
5.2. The optimal linear regulator problem.
5.2.1. Value function iteration.
5.2.2. Discounted linear regulator problem.
5.2.3. Policy improvement algorithm.
5.3. The stochastic optimal linear regulator problem.
5.3.1. Discussion of certainty equivalence.
5.4. Shadow prices in the linear regulator.
5.4.1. Stability.
5.5. A Lagrangian formulation.
5.6. The Kalman filter.
5.6.1. Muth’s example.
5.6.2. Jovanovic’s example.
5.7. Concluding remarks. A. Matrix formulas. B. Linear-quadratic approximations.
5.8.1.An example: the stochastic growth model.
5.8.2. Kydland and Prescott’s method.
5.8.3. Determination of z.
5.8.4. Log linear approximation.
5.8.5.Trend removal.
5.10. Exercises.


6. Search, Matching, and Unemployment 131
6.1. Introduction. 6.2. Preliminaries. 6.2.1. Nonnegative random variables.
6.2.2. Mean-preserving spreads. 6.3. McCall’s model of intertemporal job
search. 6.3.1. Effects of mean preserving spreads. 6.3.2. Allowing quits. 6.3.3.
Waiting times. 6.3.4. Firing. 6.4. A lake model. 6.5. A model of career choice.
6.6. A simple version of Jovanovic’s matching model. 6.7. A longer horizon
version of Jovanovic’s model. 6.7.1. The Bellman equations. 6.8. Concluding remarks. A. More numerical dynamic programming. 6.A.1. Example 4:
Search. 6.A.2. Example 5: A Jovanovic model. 6.A.3. Wage distributions.
6.A.4. Separation probabilities. 6.A.5. Numerical examples. 6.10. Exercises.

Part III: Competitive equilibria and applications

7. Recursive (Partial) Equilibrium 178
7.1. An equilibrium concept.
7.2. Example: adjustment costs.
7.2.1. A planning problem.
7.3. Recursive competitive equilibrium.
7.4. Markov perfect equilibrium.
7.4.1. Computation.
7.5. Linear Markov perfect equilibria.
7.5.1.An example.
7.6. Concluding remarks.
7.7. Exercises.

8. Equilibrium with Complete Markets 194
8.1. Time- 0 versus sequential trading.
8.2. The physical setting.
8.2.1. Preferences and endowments.
8.3. Alternative trading arrangements.
8.3.1. History dependence.
8.4. Pareto problem.
8.4.1. Time invariance of Pareto weights.
8.5. Complete markets.
8.5.1. Equilibrium pricing function.
8.5.2.Optimality of equilibrium allocation.
8.5.3. Equilibrium computation.
8.5.4.Interpretation of trading arrangement.
8.6. Examples.
8.6.1. Example 1:Risk sharing.
8.6.2. Example 2: No aggregate uncertainty.
8.6.3. Example3: Periodic endowment processes.
8.7. Recursive version of Pareto problem.
8.8. Primer on asset pricing.
8.8.1. Pricing redundant assets.
8.8.2. Riskless consol.
8.8.3. Riskless strips (zero-coupon bonds).
8.8.4. Tail assets.
8.8.5.Pricing one period returns.
8.9. A recursive formulation: Arrow securities.
8.9.1. Key insight: wealth as an endogenous state variable.
8.9.2. Debt limits.
8.9.3. The sequential economy.
8.9.4. Equivalence of allocations.
8.10.j-step pricing kernel.
8.10.1. Arbitrage pricing.
8.11. Consumption strips and the cost of business cycles.
8.11.1. Consumption strips.
8.11.2. Link to business
cycle costs.
8.12. Gaussian asset pricing model.
8.13. Static models of trade.
8.14. Closed economy model.
8.14.1. Two countries under autarky.
8.14.2.Welfare measures.
8.15. Two countries under free trade.
8.15.1. Welfare under free trade.
8.15.2. Small country assumption.
8.16. A tariff.
8.16.1. Nash tariff.
8.17. Concluding remarks.
8.18. Exercises.

9. Overlapping Generations Models 244
9.1. Endowments and preferences.
9.2. Time- 0 trading.
9.2.1. Example equilibrium.
9.2.2. Relation to the welfare theorems.
9.2.3. Nonstationary equilibria.
9.2.4. Computing equilibria.
9.3. Sequential trading.
9.4. Money.
9.4.1.Computing more equilibria.
9.4.2. Equivalence of equilibria.
9.5. Deficit finance.
9.5.1. Steady states and the Laffer curve.
9.6. Equivalent setups.
9.6.1. The economy.
9.6.2. Growth.
9.7. Optimality and the existence of monetary equilibria.
9.7.1. Balasko-Shell criterion for optimality.
9.8. Within generation heterogeneity.
9.8.1. Nonmonetary equilibrium.
9.8.2. Monetary equilibrium.
9.8.3. Nonstationary equilibria.
9.8.4. The real bills doctrine.
9.9. Gift giving equilibrium.
9.10. Concluding remarks.
9.11. Exercises.

10. Ricardian Equivalence 290
10.1. Borrowing limits and Ricardian equivalence.
10.2. Infinitely lived–agent economy.
10.2.1. Solution to consumption/savings decision.
10.3. Government.
10.3.1. Effect on household.
10.4. Linked generations interpretation.
10.5. Concluding remarks.

11. Fiscal policies in the nonstochastic growth model 300
11.1. Introduction.
11.2. Economy.
11.2.1. Preferences, technology, information.
11.2.2. Components of a competitive equilibrium.
11.2.3. Competitive equilibria with distorting taxes.
11.2.4. The household: no arbitrage and asset pricing formulas.
11.2.5. User cost of capital formula.
11.2.6. Firm.
11.3.Computing equilibria.
11.3.1. Inelastic labor supply.
11.3.2. The equilibrium steady state.
11.3.3. Computing the equilibrium path with the shooting algorithm.
11.3.4. Other equilibrium quantities.
11.3.5. Steady state Rands/q.
11.3.6. Lump sum taxes available.
11.3.7. No lump sum taxes available.
11.4.A digression on ‘back-solving’.
11.5. Effects of taxes on equilibrium allocations and prices.
11.6. Transition experiments.
11.7. Linear approximation.
11.7.1. Relationship between theλi’s.
11.7.2. Once and for all jumps.
11.7.3.Simplification of formulas.
11.7.4. A one-time pulse.
11.7.5. Convergence rates and anticipation rates.
11.8. Elastic labor supply.
11.8.1. Steady state calculations.
11.8.2. A digression on accuracy: Euler equation errors.
11.9. Growth.
11.10. Concluding remarks. A. Log linear approximations.
11.12.Exercises.



12. Recursive competitive equilibria 340
12.1. Endogenous aggregate state variable.
12.2. The sequence version of the growth model.
12.2.1. Preferences, endowment, technology, and information.
12.2.2. Lagrangian formulation of the planningproblem.
12.3. Decentralization after Arrow-Debreu.
12.3.1. Household.
12.3.2. Firm of type I.
12.3.3.Firm of type II.
12.3.4. Equilibrium prices and quantities.
12.4. Recursive formulation.
12.4.1. Recursive version of planning problem.
12.5. A recursive competitive equilibrium.
12.5.1. The ‘Big K, little k’ trick.
12.5.2. Price system.
12.5.3. Household problem.
12.5.4. Firm of type I.
12.5.5. Firms of type II. 12.5.6. Financing a type II firm.
12.6. Recursive competitive equilibrium with Arrow securities.
12.6.1. Equilibrium restrictions across decision rules.
12.6.2. Using the planning problem.
12.7. Concluding remarks.
13. Asset Pricing 358
13.1. Introduction.
13.2. Asset Euler equations.
13.3. Martingale theories of consumption and stock prices.
13.4. Equivalent martingale measure.
13.5.Equilibrium asset pricing.
13.6. Stock prices without bubbles.
13.7. Computing asset prices.
13.7.1. Example 1: Logarithmic preferences.
13.7.2. Example2: A finite-state version.
13.7.3. Example 3: Asset pricing with growth.
13.8.The term structure of interest rates.
13.9. State-contingent prices.
13.9.1.Insurance premium.
13.9.2. Man-made uncertainty.
13.9.3. The ModiglianiMiller theorem.
13.10. Government debt.
13.10.1. The Ricardian proposition.
13.10.2. No Ponzi schemes.
13.11. Interpretation of risk-aversion parameter.
13.12. The equity premium puzzle.
13.13. Market price of risk.
13.14.Hansen-Jagannathan bounds.
13.14.1. Inner product representation of the pricing kernel.
13.14.2. Classes of stochastic discount factors. 13.14.3. A
Hansen-Jagannathan bound.
13.14.4. The Mehra-Prescott data.
13.15. Factor models.
13.16. Heterogeneity and incomplete markets.
13.17. Concluding remarks.
13.18. Exercises.


14. Economic Growth 410
14.1. Introduction.
14.2. The economy.
14.2.1. Balanced growth path.
14.3.Exogenous growth.
14.4. Externality from spillovers.
14.5. All factors reproducible.
14.5.1. One-sector model.
14.5.2. Two-sector model.
14.6. Research and monopolistic competition.
14.6.1. Monopolistic competition outcome.
14.6.2. Planner solution.
14.7. Growth in spite of nonreproducible factors.
14.7.1. “Core” of capital goods produced without nonreproducible inputs.
14.7.2. Research labor enjoying an externality.
14.8. Concluding comments.
14.9. Exercises.


15. Optimal Taxation with Commitment 439
15.1. Introduction. 15.2. A nonstochastic economy. 15.2.1. Government.
15.2.2. Households. 15.2.3. Firms. 15.3. The Ramsey problem. 15.3.1. Definitions. 15.4. Zero capital tax. 15.5. Limits to redistribution. 15.6. Primal
approach to the Ramsey problem. 15.6.1. Constructing the Ramsey plan.
15.6.2. Revisiting a zero capital tax. 15.7. Taxation of initial capital. 15.8.
Nonzero capital tax due to incomplete taxation. 15.9. A stochastic economy.
15.9.1. Government. 15.9.2. Households. 15.9.3. Firms. 15.10. Indeterminacy of state-contingent debt and capital taxes. 15.11. The Ramsey plan
under uncertainty. 15.12. Ex ante capital tax varies around zero. 15.12.1.
Sketch of the proof of Proposition 2. 15.13. Examples of labor tax smoothing. 15.13.1. Example 1: gt =g for all t≥0.. 15.13.2. Example 2: gt =0
for t=T,andgT >0.. 15.13.3. Example 3: gt =0 fort =T,andgT is
stochastic. 15.13.4. Lessons for optimal debt policy. 15.14. Taxation without state-contingent government debt. 15.14.1. Future values of{gt}become
deterministic. 15.14.2. Stochastic{gt}but special preferences. 15.14.3. Example 3 revisited: gt =0 fort=T,andgT is stochastic. 15.15. Zero tax on
human capital. 15.16. Should all taxes be zero?. 15.17. Concluding remarks.
15.18. Exercises.


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