Second edition - International Growth Centre

1 Recursive Macroeconomic TheorySecond editionTo our parents, Zabrina, and CarolynRecursive Macroeconomic TheorySecond editionLars LjungqvistStockholm School of EconomicsThomas J. SargentNew York UniversityandHoover InstitutionThe MIT PressCambridge, MassachusettsLondon, Englandc 2004 Massachusetts Institute of TechnologyAll rights reserved. No part of this book may be reproduced inany form by anyelectronic or mechanical means (including photocopying, recording, or informationstorage and retrieval) without permission in writing from the and bound in the United States of of Congress Cataloging-in-Publication DataLjungqvist, macroeconomic theory / Lars Ljungqvist, Thomas J.

2 Sargent. 2nd bibliographical references and 0-262-12274-X1. macroeconomics . 2. Recursive functions. 3. Statics and dynamics(Social sciences)I. Sargent, Thomas J. II..L59 2004339 .01 51135 dc22200405468810 9 8 7 6 5 4 3 2 1 ContentsAcknowledgementsxviiPreface to the Second editionxviiiPart I: The imperialism of recursivemethods1. Warning. A common ancestor. The savings Linear quadratic permanent income theory. Precaution-ary saving. Complete markets, insurance, and the distribution ofwealth. Bewley models. History dependence instandardconsumption models. Growth theory. Limitingresults fromdynamic optimal taxation.

3 Asset pricing. Multiple Recursive methods. Methodology: dynamic programmingissues a challenge. Dynamic programming challenged. Im-perialistic response of dynamic programming. History dependenceand dynamic programming squared . Dynamic principal-agentproblems. More applications. v viContentsPart II: Tools2. Time Two workhorses. Markov chains. Stationarydistribu-tions. Asymptotic stationarity. Expectations. Fore-casting functions. Invariant functions and ergodicity. Simu-lating a Markov chain. The likelihood function. Markov chain. Stochastic linear difference equations. and Second moments.

4 Impulse response function. Pre-diction and discounting. Geometric sums of quadratic forms. regression. The spectrum. Examples. Ex-ample: the LQ permanent income model. Invariant subspaceapproach. The term structure of interest rates. stochas-tic discount factor. The log normal bond pricing model. of yield curve depends on serial correlation of logmt+1. and Zin s stochastic discount factor. Reverse engineeringa stochastic discount factor. Estimation. Concluding A linear difference equation. Dynamic Sequential problems. Three computational methods. transition, logarithmic preferences.

5 Euler equa-tions. A sample Euler equation. Stochastic control Concluding remarks. Practical Dynamic The curse of dimensionality. Discretization of state space. dynamic programming. Application of Howard im-provement algorithm. Numerical implementation. Modifiedpolicy iteration. Sample Bellman equations. Example 1: cal-culating expected utility. Example 2: risk-sensitive Example 3: costs of business cycles. Polynomialapproxi-mations. Recommended computational strategy. Cheby-shev polynomials. Algorithm: summary. Shape-preservingsplines. Concluding Linear Quadratic Dynamic Introduction.

6 The optimal linear regulator problem. function iteration. Discounted linear regulator Policy improvement algorithm. The stochastic optimal lin-ear regulator problem. Discussion of certainty equivalence. prices in the linear regulator. Stability. A Lagrangianformulation. The Kalman filter. Muth s Jo-vanovic s example. Concluding remarks. A. Matrix formulas. quadratic approximations. An example: the stochasticgrowth model. Kydland and Prescott s method. of z. Log linear approximation. Trend Search, Matching, and Introduction. Preliminaries. Nonnegative random vari-ables. Mean-preserving spreads.

7 McCall s model of intertem-poral job search. Effects of mean preserving Allow-ing quits . Waiting times. Firing . A lake model. model of career choice. A simple version of Jovanovic s matchingmodel. Recursive formulation and solution. Endogenousstatistics. A longer horizon version of Jovanovic s model. Bellman equations. Concluding remarks. A. More numericaldynamic programming. Example 4: search. Example 5: aJovanovic model. III: Competitive equilibriaand applications7. Recursive (Partial) An equilibrium concept. Example: adjustment costs. Aplanning problem. Recursive competitive equilibrium.

8 Markovperfect equilibrium. Computation. Linear Markov perfectequilibria. An example. Concluding remarks. Equilibrium with Complete Time 0 versus sequential trading. The physical setting: pref-erences and endowments. Alternative trading arrangements. dependence. Pareto problem. Time invariance ofPareto weights. Time 0 trading: Arrow-Debreu securities. pricing function. Optimality of equilibrium alloca-tion. Equilibrium computation. Interpretation of tradingarrangement. Examples. Example 1: risk sharing. 2: no aggregate uncertainty. Example 3: periodic en-dowment processes. Primer on asset pricing.

9 Pricing re-dundant assets. Riskless consol. Riskless strips. assets. Pricing one-period returns. Sequential trad-ing: Arrow securities. Arrow securities. Insight: wealthas an endogenous state variable. Debt limits. Equivalence of allocations. Recursive competitiveequilibrium. Endowments governed by a Markov process. outcomes inherit the Markov property. Recursiveformulation of optimization and equilibrium. pricing ker-nel. Arbitrage-free pricing. Consumption strips and thecost of business cycles. Link to business cycle costs. Gaus-sian asset-pricing model. Recursive version of Pareto Static models of trade.

10 Closed economy model. Twocountries under autarky. Welfare measures. Two coun-tries under free trade. Small country assumption. A Nash tariff. Concluding remarks. Overlapping Generations Endowments and preferences. Time 0 trading. Exampleequilibrium. Relation to the welfare theorems. Nonstation-ary equilibria. Computing equilibria. Sequential trading. Computing more equilibria. Equivalence of equilib-ria. Deficit finance. Steady states and the Laffer curve. setups. The economy. Growth . the existence of monetary equilibria. Balasko-Shell criterionfor optimality. Within-generation heterogeneity.