Recursive macroeconomic theory:
"Recursive methods offer a powerful approach for characterizing and solving complicated problems in dynamic macroeconomics. Recursive Macroeconomic Theory provides both an introduction to recursive methods and advanced material, mixing tools and sample applications. The second edition contains...
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| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Cambridge, Mass. [u.a.]
MIT Press
2012
|
| Edition: | 3. ed. |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Summary: | "Recursive methods offer a powerful approach for characterizing and solving complicated problems in dynamic macroeconomics. Recursive Macroeconomic Theory provides both an introduction to recursive methods and advanced material, mixing tools and sample applications. The second edition contains substantial revisions to about half the original material, and extensive additional coverage appears in seven chapters new to this edition. The updated and added material covers new topics that further illustrate the power and pervasiveness of recursive methods."--BOOK JACKET. |
| Physical Description: | XXXVI, 1321 S. graph. Darst. |
| ISBN: | 9780262018746 |
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| 100 | 1 | |a Ljungqvist, Lars |d 1959- |e Verfasser |0 (DE-588)115042504 |4 aut | |
| 245 | 1 | 0 | |a Recursive macroeconomic theory |c Lars Ljungqvist ; Thomas J. Sargent |
| 250 | |a 3. ed. | ||
| 264 | 1 | |a Cambridge, Mass. [u.a.] |b MIT Press |c 2012 | |
| 300 | |a XXXVI, 1321 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 520 | 1 | |a "Recursive methods offer a powerful approach for characterizing and solving complicated problems in dynamic macroeconomics. Recursive Macroeconomic Theory provides both an introduction to recursive methods and advanced material, mixing tools and sample applications. The second edition contains substantial revisions to about half the original material, and extensive additional coverage appears in seven chapters new to this edition. The updated and added material covers new topics that further illustrate the power and pervasiveness of recursive methods."--BOOK JACKET. | |
| 650 | 4 | |a Fonctions récursives | |
| 650 | 7 | |a Macro-economie |2 gtt | |
| 650 | 4 | |a Macroéconomie | |
| 650 | 7 | |a Recursieve functies |2 gtt | |
| 650 | 4 | |a Statique et dynamique (Sciences sociales) | |
| 650 | 4 | |a aMacroeconomics | |
| 650 | 4 | |a aRecursive functions | |
| 650 | 4 | |a aStatics and dynamics (Social sciences) | |
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Record in the Search Index
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| adam_text | Contents
Acknowledgements
xix
Preface to the third edition
xx
Part I: The imperialism of recursive methods
1.
Overview
3
1.1.
Warning.
1.2.
A common ancestor.
1.3.
The savings problem.
1.3.1.
Linear quadratic permanent income theory.
1.3.2.
Precaution¬
ary saving.
1.3.3.
Complete markets, insurance, and the distribution of
wealth.
1.3.4.
Bewley models.
1.3.5.
History dependence in standard
consumption models.
1.3.6.
Growth theory.
1.3.7.
Limiting results from
dynamic optimal taxation.
1.3.8.
Asset pricing.
1.3.9.
Multiple assets.
1.4.
Recursive methods.
1.4.1.
Methodology: dynamic programming
issues a challenge.
1.4.2.
Dynamic programming challenged.
1.4.3.
Im¬
perialistic response of dynamic programming.
1.4.4.
History dependence
and ; dynamic programming squared
. 1.4.5.
Dynamic principal-agent
problems.
1.4.6.
More applications.
vi
Contents
Part II: Tools
2.
Time Series
29
2.1.
Two workhorses.
2.2.
Markov chains.
2.2.1.
Stationary distri¬
butions.
2.2.2.
Asymptotic stationarity.
2.2.3.
Forecasting the state.
2.2.4.
Forecasting functions of the state.
2.2.5.
Forecasting functions.
2.2.6.
Enough one-step-ahead forecasts determine P.
2.2.7.
Invariant
functions and ergodicity.
2.2.8.
Simulating a Markov chain.
2.2.9.
The
likelihood function.
2.3.
Continuous-state Markov chain.
2.4.
Stochas¬
tic linear difference equations.
2.4.1.
First and second moments.
2.4.2.
Summary of moment formulas.
2.4.3.
Impulse response function.
2.4.4.
Prediction and discounting.
2.4.5.
Geometric sums of quadratic forms.
2.5.
Population regression.
2.5.1.
Multiple regressors.
2.6.
Estimation
of model parameters.
2.7.
The
Kalman
filter.
2.7.1.
Estimation again.
2.8.
Vector autoregressions and the
Kalman
filter.
2.8.1.
Conditioning
on the semi-infinite past of y.
2.8.2.
A time-invariant
VAR. 2.8.3.
In¬
terpreting VARs.
2.9.
Applications of the
Kalman
filter.
2.9.1.
Muth s
reverse engineering exercise.
2.9.2.
Jovanovic s application.
2.10.
The
spectrum.
2.10.1.
Examples.
2.11.
Example: the LQ permanent in¬
come model.
2.11.1.
Another representation.
2.11.2.
Debt dynamics.
2.11.3.
Two classic examples.
2.11.4.
Spreading consumption cross sec¬
tion.
2.11.5.
Invariant subspace approach.
2.12.
Concluding remarks.
A. Linear difference equations
2.А.1.
A first-order difference equation.
2.A.
2.
A second-order difference equation. B. MCMC approximation of
Bayesian posterior
2.15.
Exercises.
3.
Dynamic Programming
103
3.1.
Sequential problems.
3.1.1.
Three computational methods.
3.1.2.
Cobb-Douglas transition, logarithmic preferences.
3.1.3.
Euler
equa¬
tions.
3.1.4.
A sample
Euler
equation.
3.2.
Stochastic control problems.
3.3.
Concluding remarks.
3.4.
Exercise.
Contents
vii
4.
Practical Dynamic Programming
113
4.1.
The curse of dimensionality.
4.2.
Discrete-state dynamic program¬
ming.
4.3.
Bookkeeping.
4.4.
Application of Howard improvement algo¬
rithm.
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.
Recom¬
mended 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
127
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 lin¬
ear 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 again.
5.7.
Concluding remarks.
A. Matrix formulas B. Linear quadratic approximations
5.В.1.
An ex¬
ample: the stochastic growth model. 5.B.2. Kydland and Prescott s
method. 5.B.3. Determination of z. 5.B.4. Log linear approximation.
5.B.5. Trend removal.
5.10.
Exercises.
6.
Search, Matching, and Unemployment
159
6.1.
Introduction.
6.2.
Preliminaries.
6.2.1.
Nonnegative
random vari¬
ables.
6.2.2.
Mean-preserving spreads.
6.3.
McCalľs
model of
intertem¬
poral
job search.
6.3.1.
Characterizing reservation wage.
6.3.2.
Effects
of mean-preserving spreads.
6.3.3.
Allowing quits.
6.3.4.
Waiting times.
6.3.5.
Firing.
6.4.
A lake model.
6.5.
A model of career choice.
6.6.
Offer
distribution unknown.
6.7.
An equilibrium price distribution.
6.7.1.
A
Burdett-Judd setup.
6.7.2.
Consumer problem with noisy search.
6.7.3.
Firms.
6.7.4.
Equilibrium.
6.7.5.
Special cases.
6.8.
Jovanovic s match¬
ing model.
6.8.1.
Recursive formulation and solution.
6.8.2.
Endogenous
statistics.
6.9.
A longer horizon version of Jovanovic s model.
6.9.1.
The
Bellman equations.
6.10.
Concluding remarks. A. More numerical dy¬
namic programming
6.А.1.
Example
4:
search. 6.A.2. Example
5:
a
Jovanovic model.
6.12.
Exercises.
viii Contents
Part III: Competitive equilibria and applications
7.
Recursive (Partial) Equilibrium
227
7.1.
An equilibrium concept.
7.2.
Example: adjustment costs.
7.2.1.
A
planning problem.
7.3.
Recursive competitive equilibrium.
7.4.
Equi¬
librium human capital accumulation.
7.4.1.
Planning problem.
7.4.2.
Decentralization.
7.5.
Equilibrium occupational choice.
7.5.1.
A plan¬
ning problem.
7.5.2.
Decentralization.
7.6.
Markov perfect equilibrium.
7.6.1.
Computation.
7.7.
Linear Markov perfect equilibria.
7.7.1.
An
example.
7.8.
Concluding remarks.
7.9.
Exercises.
8.
Equilibrium with Complete Markets
251
8.1.
Time
0
versus sequential trading.
8.2.
The physical setting: pref¬
erences 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.
Time
0
trading: Arrow-Debreu securities.
8.5.1.
Equilibrium pricing function.
8.5.2.
Optimality of equilibrium alloca¬
tion.
8.5.3.
Interpretation of trading arrangement.
8.5.4.
Equilibrium
computation.
8.6.
Simpler computational algorithm.
8.6.1.
Example
1:
risk sharing.
8.6.2.
Implications for equilibrium computation.
8.6.3.
Ex¬
ample
2:
no aggregate uncertainty.
8.6.4.
Example
3:
periodic endow¬
ment processes.
8.6.5.
Example
4. 8.7.
Primer on asset pricing.
8.7.1.
Pricing redundant assets.
8.7.2.
Riskless
consol.
8.7.3.
Riskless strips.
8.7.4.
Tail assets.
8.7.5.
One-period returns.
8.8.
Sequential trading:
Arrow securities.
8.8.1.
Arrow securities.
8.8.2.
Financial wealth as an
endogenous state variable.
8.8.3.
Financial and non-financial wealth.
8.8.4.
Reopening markets.
8.8.5.
Debt limits.
8.8.6.
Sequential trading.
8.8.7.
Equivalence of allocations.
8.9.
Recursive competitive equilib¬
rium.
8.9.1.
Endowments governed by a Markov process.
8.9.2.
Equi¬
librium outcomes inherit the Markov property.
8.9.3.
Recursive formu¬
lation of optimization and equilibrium.
8.9.4.
Computing an equilib¬
rium with sequential trading of Arrow-securities.
8.10.
j-step pricing
kernel.
8.10.1.
Arbitrage-free pricing.
8.11.
Recursive version of Pareto
problem.
8.12.
Concluding remarks. A. Gaussian asset-pricing model
B. The permanent income model revisited
8.В.1.
Reinterpreting the
single-agent model. 8.B.2. Decentralization and scaled prices. 8.B.3.
Matching equilibrium and planning allocations. 8.B.4. Interpretation.
8.15.
Exercises.
Contents ix
9.
Overlapping Generations Models
315
9.1.
Endowments and preferences.
9.2.
Time
0
trading.
9.2.1.
Example
equilibria.
9.2.2.
Relation to 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 with valued fiat currency.
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 equilib¬
ria.
9.7.1.
Balasko-Shell criterion for optimality.
9.8.
Within-generation
heterogeneity.
9.8.1.
Nonmonetary equilibrium.
9.8.2.
Monetary equi¬
librium.
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
363
10.1.
Borrowing limits and Ricardian equivalence.
10.2.
Infinitely lived
agent economy.
10.2.1.
Optimal consumption/savings decision when
bt+i
> 0. 10.2.2.
Optimal consumption/savings decision when
òt+i
>
bt+i.
10.3.
Government.
10.3.1.
Effect on household.
10.4.
Linked
generations interpretation.
10.5.
Concluding remarks.
11.
Fiscal Policies in a Growth Model
375
11.1.
Introduction.
11.2.
Economy.
11.2.1.
Preferences, technology, in¬
formation.
11.2.2.
Components of a competitive equilibrium.
11.3.
The
term structure of interest rates.
11.4.
Digression: sequential version of
government budget constraint.
11.4.1.
Irrelevance of maturity structure
of government debt.
11.5.
Competitive equilibria with distorting taxes.
11.5.1.
The household: no-arbitrage and asset-pricing formulas.
11.5.2.
User cost of capital formula.
11.5.3.
Household first-order conditions.
11.5.4.
A theory of the term structure of interest rates.
11.5.5.
Firm.
11.6.
Computing equilibria.
11.6.1.
Inelastic labor supply.
11.6.2.
The
equilibrium steady state.
11.6.3.
Computing the equilibrium path with
the shooting algorithm.
11.6.4.
Other equilibrium quantities.
11.6.5.
Steady-state
Ř.
11.6.6.
Lump-sum taxes available.
11.6.7.
No lump-
sum taxes available.
11.7.
A digression on back-solving.
11.8.
Effects
of taxes on equilibrium allocations and prices.
11.9.
Transition experi¬
ments with inelastic labor supply.
11.10.
Linear approximation.
11.10.1.
Relationship between the
Лј ѕ.
11.10.2.
Conditions for existence and
uniqueness.
11.10.3.
Once-and-for-all jumps.
11.10.4.
Simplification of
formulas.
11.10.5.
A one-time pulse.
11.10.6.
Convergence rates and
anticipation rates.
11.10.7.
A remark about accuracy:
Euler
equation
Contents
errors.
11.11.
Growth.
11.12.
Elastic labor supply.
11.12.1.
Steady-
state calculations.
11.12.2.
Some experiments.
11.13.
A two-country
model.
11.13.1.
Initial conditions.
11.13.2.
Equilibrium steady state
values.
11.13.3.
Initial equilibrium values.
11.13.4.
Shooting algorithm.
11.13.5.
Transition exercises.
11.14.
Concluding remarks. A. Log linear
approximations
11.16.
Exercises.
12.
Recursive Competitive Equilibria
455
12.1.
Endogenous aggregate state variable.
12.2.
The stochastic growth
model.
12.3.
Lagrangian formulation of the planning problem.
12.4.
Time
0
trading: Arrow-Debreu securities.
12.4.1.
Household.
12.4.2.
Firm of type I.
12.4.3.
Firm of type II.
12.4.4.
Equilibrium prices and
quantities.
12.4.5.
Implied wealth dynamics.
12.5.
Sequential trading:
Arrow securities.
12.5.1.
Household.
12.5.2.
Firm of type I.
12.5.3.
Firm
of type II.
12.5.4.
Equilibrium prices and quantities.
12.5.5.
Financing
a type II firm.
12.6.
Recursive formulation.
12.6.1.
Technology is gov¬
erned by a Markov process.
12.6.2.
Aggregate state of the economy.
12.7.
Recursive formulation of the planning problem.
12.8.
Recursive
formulation of sequential trading.
12.8.1.
A Big K, little k trick.
12.8.2.
Price system.
12.8.3.
Household problem.
12.8.4.
Firm of type
I.
12.8.5.
Firm of type II.
12.9.
Recursive competitive equilibrium.
12.9.1.
Equilibrium restrictions across decision rules.
12.9.2.
Using the
planning problem.
12.10.
Concluding remarks.
13.
Asset Pricing Theory
481
13.1.
Introduction.
13.2.
Asset
Euler
equations.
13.3.
Martingale the¬
ories 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.
Example
2:
a finite-state version.
13.7.3.
Exam¬
ple
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
Modigliani-Miller
theorem.
13.10.
Government debt.
13.10.1.
The Ricardian proposition.
13.10.2.
No
Ponzi
schemes.
14.
Asset Pricing Empirics
515
14.1.
Introduction.
14.2.
Interpretation of risk-aversion parameter.
14.3.
The equity premium puzzle.
14.4.
Market price of risk.
14.5.
Contents xi
Hansen-Jagannathan
bounds.
14.5.1.
Law of one price implies that
EmR
= 1. 14.5.2.
Inner product representation of the pricing ker¬
nel.
14.5.3.
Classes of stochastic discount factors.
14.5.4.
A Hansen-
Jagannathan bound.
14.6.
Failure of CRRA to attain HJ bounds.
14.7.
Non-expected utility.
14.7.1.
Another representation of the utility re¬
cursion.
14.7.2.
Stochastic discount factor.
14.8.
Reinterpretation of the
utility recursion.
14.8.1.
Risk aversion or model misspecification aver¬
sion.
14.8.2.
Recursive representation of probability distortions.
14.8.3.
Entropy.
14.8.4.
Expressing ambiguity.
14.8.5.
Ambiguity averse pref¬
erences.
14.8.6.
Market price of model uncertainty.
14.8.7.
Measuring
model uncertainty.
14.9.
Costs of aggregate fluctuations.
14.10.
Re¬
verse engineered consumption heterogeneity.
14.11.
Exponential
affine
stochastic discount factors.
14.11.1.
General application.
14.11.2.
Term
structure application.
14.12.
Concluding remarks. A. Riesz representa¬
tion theorem B. A log normal bond pricing model
14.
B.I. Slope of yield
curve depends on serial correlation of logmt+i. 14.B.2. Backus and
Zin s stochastic discount factor. 14.B.3. Reverse engineering a stochas¬
tic discount factor.
14.15.
Exercises.
15.
Economic Growth
583
15.1.
Introduction.
15.2.
The economy.
15.2.1.
Balanced growth path.
15.3.
Exogenous growth.
15.4.
Externality from spillovers.
15.5.
All fac¬
tors reproducible.
15.5.1.
One-sector model.
15.5.2.
Two-sector model.
15.6.
Research and monopolistic competition.
15.6.1.
Monopolistic
competition outcome.
15.6.2.
Planner solution.
15.7.
Growth in spite
of nonreproducible factors.
15.7.1.
Core of capital goods produced
without nonreproducible inputs.
15.7.2.
Research labor enjoying an ex¬
ternality.
15.8.
Concluding remarks.
15.9.
Exercises.
16.
Optimal Taxation with Commitment
613
16.1.
Introduction.
16.2.
A nonstochastic economy.
16.2.1.
Govern¬
ment.
16.2.2.
Household.
16.2.3.
Firms.
16.3.
The Ramsey problem.
16.4.
Zero capital tax.
16.5.
Limits to redistribution.
16.6.
Primal
approach to the Ramsey problem.
16.6.1.
Constructing the Ramsey
plan.
16.6.2.
Revisiting a zero capital tax.
16.7.
Taxation of initial
capital.
16.8.
Nonzero capital tax due to incomplete taxation.
16.9.
A
stochastic economy.
16.9.1.
Government.
16.9.2.
Households.
16.9.3.
Firms.
16.10.
Indeterminacy of state-contingent debt and capital taxes.
16.11.
The Ramsey plan under uncertainty.
16.12.
Ex ante capital
tax varies around zero.
16.12.1.
Sketch of the proof of Proposition
2.
xii Contents
16.13.
Examples of labor tax smoothing.
16.13.1.
Example
1:
gt
—
g
for all
t
> 0. 16.13.2.
Example
2:
gt
= 0
for
t
φ Τ
and nonstochastic
дт
> 0. 16.13.3.
Example
3:
gt
= 0
for
t
Φ Τ
,
and
дт
is stochastic.
16.14.
Lessons for optimal debt policy.
16.15.
Taxation without state-
contingent debt.
16.15.1.
Future values of {gt} become deterministic.
16.15.2.
Stochastic {gt} but special preferences.
16.15.3.
Example
3
revisited: gt
= 0
for
t
φ Γ,
and
дт
is stochastic.
16.16.
Nominal debt
as state-contingent real debt.
16.16.1.
Setup and main ideas.
16.16.2.
Optimal taxation in a nonmonetary economy.
16.16.3.
Optimal policy
in a corresponding monetary economy.
16.17.
Relation to fiscal theories
of the price level.
16.17.1.
Budget constraint versus asset pricing equa¬
tion.
16.17.2.
Disappearance of quantity theory?
16.17.3.
Price level
indeterminacy under interest rate peg.
16.17.4.
Monetary or fiscal the¬
ory of the price level?
16.18.
Zero tax on human capital.
16.19.
Should
all taxes be zero?
16.20.
Concluding remarks.
16.21.
Exercises.
Part IV: The savings problem and Bewley models
17.
Self-Insurance
699
17.1.
Introduction.
17.2.
The consumer s environment.
17.3.
Non-
stochastic endowment.
17.3.1.
An ad hoc borrowing constraint: non-
negative assets.
17.3.2.
Example: periodic endowment process.
17.4.
Quadratic preferences.
17.5.
Stochastic endowment process: i.i.d. case.
17.6.
Stochastic endowment process: general case.
17.7.
Intuition.
17.8.
Endogenous labor supply.
17.9.
Concluding remarks. A. Supermartin-
gale convergence theorem
17.11.
Exercises.
18.
Incomplete Markets Models
725
18.1.
Introduction.
18.2.
A savings problem.
18.2.1.
Wealth-employment
distributions.
18.2.2.
Reinterpretation of the distribution
λ.
18.2.3.
Ex¬
ample
1:
a pure credit model.
18.2.4.
Equilibrium computation.
18.2.5.
Example
2:
a model with capital.
18.2.6.
Computation of equilibrium.
18.3.
Unification and further analysis.
18.4.
The nonstochastic sav¬
ings problem when
ß(l + r) < 1. 18.5.
Borrowing limits: natural and
ad hoc.
18.5.1.
A candidate for a single state variable.
18.5.2.
Su-
permartingale convergence again.
18.6.
Average assets as a function
of r.
18.7.
Computed examples.
18.8.
Several Bewley models.
18.8.1.
Optimal stationary allocation.
18.9.
A model with capital and private
Contents xiii
IOUs. 18.10. Private IOUs
only.
18.10.1.
Limitation of what credit can
achieve.
18.10.2.
Proximity of
г
to p.
18.10.3.
Inside money or free
banking interpretation.
18.10.4.
Bewley s basic model of fiat money.
18.11.
A model of seigniorage.
18.12.
Exchange rate indeterminacy.
18.13.
Interest on currency.
18.13.1.
Explicit interest.
18.13.2.
The
upper bound on
—. 18.13.3.
A very special case.
18.13.4.
Implicit in¬
terest through deflation.
18.14.
Precautionary savings.
18.15.
Models
with fluctuating aggregate variables.
18.15.1.
Aiyagari s model again.
18.15.2.
Krusell and Smith s extension.
18.16.
Concluding remarks.
18.17.
Exercises.
Part V: Recursive contracts
19.
Dynamic Stackelberg Problems
775
19.1.
History dependence.
19.2.
The Stackelberg problem.
19.3.
Solv¬
ing the Stackelberg problem.
19.3.1.
Step
1:
solve an optimal linear
regulator.
19.3.2.
Step
2:
use the stabilizing properties of shadow price
Pyt
■ 19.3.3.
Stabilizing solution.
19.3.4.
Step
3:
convert implementa¬
tion multipliers into state variables.
19.3.5.
Step
4:
solve for xo and
μχο.
19.3.6.
Summary.
19.3.7.
History-dependent representation of de¬
cision rule.
19.3.8.
Digression on determinacy of equilibrium.
19.4.
A
large firm with a competitive fringe.
19.4.1.
The competitive fringe.
19.4.2.
The monopolist s problem.
19.4.3.
Equilibrium representation.
19.4.4.
Numerical example.
19.5.
Concluding remarks. A. The stabi¬
lizing
μ(
=
Pyt
В.
Matrix linear difference equations C. Forecasting
formulas
19.9.
Exercises.
20.
Insurance Versus Incentives
797
20.1.
Insurance with recursive contracts.
20.2.
Basic environment.
20.3.
One-sided no commitment.
20.3.1.
Self-enforcing contract.
20.3.2.
Recursive formulation and solution.
20.3.3.
Recursive computation of
contract.
20.3.4.
Profits.
20.3.5.
P(v) is strictly concave and contin¬
uously differentiable.
20.3.6.
Many households.
20.3.7.
An example.
20.4.
A Lagrangian method.
20.5.
Insurance with asymmetric infor¬
mation.
20.5.1.
Efficiency implies
ο,,-ι
>
6s,u s_i
<
ws.
20.5.2.
Local
upward and downward constraints are enough.
20.5.3.
Concavity of
P.
20.5.4.
Local downward constraints always bind.
20.5.5.
Coinsur¬
ance.
20.5.6.
P {v) is a martingale.
20.5.7.
Comparison to model with
xiv Contents
commitment problem.
20.5.8.
Spreading continuation values.
20.5.9.
Martingale convergence and poverty.
20.5.10.
Extension to general
equilibrium.
20.5.11.
Comparison with self-insurance.
20.6.
Insurance
with unobservable storage.
20.6.1.
Feasibility.
20.6.2.
Incentive com¬
patibility.
20.6.3.
Efficient allocation.
20.6.4.
The case of two periods
(T
= 2). 20.6.5.
Role of the planner.
20.6.6.
Decentralization in a
closed economy.
20.7.
Concluding remarks. A. Historical development
20.
A.I. Spear and Srivastava. 20.A.2. Timing. 20.A.3. Use of lotteries.
20.9.
Exercises.
21.
Equilibrium without Commitment
859
21.1.
Two-sided lack of commitment.
21.2.
A closed system.
21.3.
Recursive formulation.
21.4.
Equilibrium consumption.
21.4.1.
Con¬
sumption dynamics.
21.4.2.
Consumption intervals cannot contain each
other.
21.4.3.
Endowments are contained in the consumption intervals.
21.4.4.
All consumption intervals are
nondegenerate
(unless autarky is
the only sustainable allocation).
21.5.
Pareto frontier and ex ante divi¬
sion of the gains.
21.6.
Consumption distribution.
21.6.1.
Asymptotic
distribution.
21.6.2.
Temporary imperfect risk sharing.
21.6.3.
Per¬
manent imperfect risk sharing.
21.7.
Alternative recursive formulation.
21.8.
Pareto frontier revisited.
21.8.1.
Values are continuous in implicit
consumption.
21.8.2.
Differentiability of the Pareto frontier.
21.9.
Con¬
tinuation values
à la
Kocherlakota.
21.9.1.
Asymptotic distribution is
nondegenerate
for imperfect risk sharing (except when
5 = 2). 21.9.2.
Continuation values do not always respond to binding participation con¬
straints.
21.10.
A two-state example: amnesia overwhelms memory.
21.10.1.
Pareto frontier.
21.10.2.
Interpretation.
21.11.
A three-state
example.
21.11.1.
Perturbation of parameter values.
21.11.2.
Pareto
frontier.
21.12.
Empirical motivation.
21.13.
Generalization.
21.14.
De¬
centralization.
21.15.
Endogenous borrowing constraints.
21.16.
Con¬
cluding remarks.
21.17.
Exercises.
22.
Optimal Unemployment Insurance
913
22.1.
History-dependent unemployment insurance.
22.2.
A one-spell
model.
22.2.1.
The autarky problem.
22.2.2.
Unemployment insurance
with full information.
22.2.3.
The incentive problem.
22.2.4.
Unem¬
ployment insurance with asymmetric information.
22.2.5.
Computed
example.
22.2.6.
Computational details.
22.2.7.
Interpretations.
22.2.8.
Extension: an on-the-job tax.
22.2.9.
Extension: intermittent unem¬
ployment spells.
22.3.
A multiple-spell model with lifetime contracts.
Contents xv
22.3.1.
The setup.
22.3.2.
A recursive lifetime contract.
22.3.3.
Com¬
pensation dynamics when unemployed.
22.3.4.
Compensation dynamics
while employed.
22.3.5.
Summary.
22.4.
Concluding remarks.
22.5.
Ex¬
ercises.
23.
Credible Government Policies, I
937
23.1.
Introduction.
23.1.1.
Diverse sources of history dependence.
23.2.
The one-period economy.
23.2.1.
Competitive equilibrium.
23.2.2.
The
Ramsey problem.
23.2.3.
Nash equilibrium.
23.3.
Nash and Ram¬
sey outcomes.
23.3.1.
Taxation example.
23.3.2.
Black-box example
with discrete choice sets.
23.4.
Reputational mechanisms: general idea.
23.4.1.
Dynamic programming squared.
23.5.
The infinitely repeated
economy.
23.5.1.
A strategy profile implies a history and a value.
23.5.2.
Recursive formulation.
23.6.
Subgame
perfect equilibrium
(SPE).
23.7.
Examples of
SPE.
23.7.1.
Infinite repetition of one-period Nash equilib¬
rium.
23.7.2.
Supporting better outcomes with trigger strategies.
23.7.3.
When reversion to Nash is not bad enough.
23.8.
Values of all SPEs.
23.8.1.
The basic idea of dynamic programming squared.
23.9.
The APS
machinery.
23.10.
Self-enforcing
SPE.
23.10.1.
The quest for something
worse than repetition of Nash outcome.
23.11.
Recursive strategies.
23.12.
Examples of
SPE
with recursive strategies.
23.12.1.
Infinite rep¬
etition of Nash outcome.
23.12.2.
Infinite repetition of a better-than-
Nash outcome.
23.12.3.
Something worse: a stick-and-carrot strategy.
23.13.
The best and the worst
SPE
values.
23.13.1.
When
vi
is out¬
side the candidate set.
23.14.
Examples: alternative ways to achieve
the worst.
23.14.1.
Attaining the worst, method
1. 23.14.2.
Attaining
the worst, method
2. 23.14.3.
Attaining the worst, method
3. 23.14.4.
Numerical example.
23.15.
Interpretations.
23.16.
Extensions.
23.17.
Exercises.
24.
Credible Government Policies, II
985
24.1.
Sources of history-dependent government policies.
24.2.
The set¬
ting.
24.2.1.
The household s problem.
24.2.2.
Government.
24.2.3.
Solution of household s problem.
24.2.4.
Competitive equilibrium.
24.3.
Inventory of key objects.
24.4.
Formal analysis.
24.4.1.
Some useful
notation.
24.4.2.
Another convenient operator.
24.5.
Sustainable plans.
xvi
Contents
25.
Two Topics in International Trade
1005
25.1.
Two dynamic contracting problems.
25.2.
Lending with moral
hazard and difficult enforcement.
25.2.1.
Autarky.
25.2.2.
Investment
with full insurance.
25.2.3.
Limited commitment and unobserved invest¬
ment.
25.2.4.
Optimal capital outflows under distress.
25.3.
Gradual¬
ism in trade policy.
25.3.1.
Closed-economy model.
25.3.2.
A Ricardian
model of two countries under free trade.
25.3.3.
Trade with a tariff.
25.3.4.
Welfare and Nash tariff.
25.3.5.
Trade concessions.
25.3.6.
A
repeated tariff game.
25.3.7.
Time-invariant transfers.
25.3.8.
Grad¬
ualism: time-varying trade policies.
25.3.9.
Baseline policies.
25.3.10.
Multiplicity of payoffs and continuation values.
25.4.
Another model.
25.5.
Concluding remarks. A. Computations for Atkeson s model
25.7.
Exercises.
Part VI: Classical monetary and labor economics
26.
Fiscal-Monetary Theories of Inflation
1045
26.1.
The issues.
26.2.
A shopping time monetary economy.
26.2.1.
Households.
26.2.2.
Government.
26.2.3.
Equilibrium.
26.2.4.
Short
run versus long run .
26.2.5.
Stationary equilibrium.
26.2.6.
Initial
date (time
0). 26.2.7.
Equilibrium determination.
26.3.
Ten mone¬
tary doctrines.
26.3.1.
Quantity theory of money.
26.3.2.
Sustained
deficits cause inflation.
26.3.3.
Fiscal prerequisites of zero inflation
policy.
26.3.4.
Unpleasant monetarist arithmetic.
26.3.5.
An open
market operation delivering neutrality.
26.3.6.
The optimum quan¬
tity of money.
26.3.7.
Legal restrictions to boost demand for currency.
26.3.8.
One big open market operation.
26.3.9.
A fiscal theory of the
price level.
26.3.10.
Exchange rate indeterminacy.
26.3.11.
Determi-
nacy of the exchange rate retrieved.
26.4.
An example of exchange rate
(in)determinacy.
26.4.1.
Trading before sunspot realization.
26.4.2.
Fis¬
cal theory of the price level.
26.4.3.
A game theoretic view of the fiscal
theory of the price level.
26.5.
Optimal inflation tax: the Friedman rule.
26.5.1.
Economic environment.
26.5.2.
Household s optimization prob¬
lem.
26.5.3.
Ramsey plan.
26.6.
Time consistency of monetary policy.
26.6.1.
Model with monopolistically competitive wage setting.
26.6.2.
Perfect foresight equilibrium.
26.6.3.
Ramsey plan.
26.6.4.
Credibility
of the Friedman rule.
26.7.
Concluding remarks.
26.8.
Exercises.
Contents xvii
27.
Credit
and Currency
1093
27.1.
Credit and currency with long-lived agents.
27.2.
Preferences
and endowments.
27.3.
Complete markets.
27.3.1.
A Pareto problem.
27.3.2.
A complete markets equilibrium.
27.3.3.
Ricardian proposition.
27.3.4.
Loan market interpretation.
27.4.
A monetary economy.
27.5.
Townsend s turnpike interpretation.
27.6.
The Friedman rule.
27.6.1.
Welfare.
27.7.
Inflationary finance.
27.8.
Legal restrictions.
27.9.
A
two-money model.
27.10.
A model of commodity money.
27.10.1.
Equi¬
librium.
27.10.2.
Virtue of fiat money.
27.11.
Concluding remarks.
27.12.
Exercises.
28.
Equilibrium Search and Matching
1129
28.1.
Introduction.
28.2.
An island model.
28.2.1.
A single market
(island).
28.2.2.
The aggregate economy.
28.3.
A matching model.
28.3.1.
A steady state.
28.3.2.
Welfare analysis.
28.3.3.
Size of the
match surplus.
28.4.
Matching model with heterogeneous jobs.
28.4.1.
A steady state.
28.4.2.
Welfare analysis.
28.4.3.
The allocating role of
wages I: separate markets.
28.4.4.
The allocating role of wages II: wage
announcements.
28.5.
Matching model with overlapping generations.
28.5.1.
A steady state.
28.5.2.
Reservation productivity is increasing
in age.
28.5.3.
Wage rate is decreasing in age.
28.5.4.
Welfare analysis.
28.5.5.
The optimal policy.
28.6.
Model of employment lotteries.
28.7.
Lotteries for households versus lotteries for firms.
28.7.1.
An aggregate
production function.
28.7.2.
Time-varying capacity utilization.
28.8.
Employment effects of layoff taxes.
28.8.1.
A model of employment
lotteries with layoff taxes.
28.8.2.
An island model with layoff taxes.
28.8.3.
A matching model with layoff taxes.
28.9.
Kiyotaki-Wright
search model of money.
28.9.1.
Monetary equilibria.
28.9.2.
Welfare.
28.10.
Concluding remarks.
28.11.
Exercises.
29.
Foundations of Aggregate Labor Supply
1203
29.1.
Introduction.
29.2.
Equivalent allocations.
29.2.1.
Choosing ca¬
reer length.
29.2.2.
Employment lotteries.
29.3.
Taxation and social
security.
29.3.1.
Taxation.
29.3.2.
Social security.
29.4.
Earnings-
experience profiles.
29.4.1.
Time averaging.
29.4.2.
Employment lot¬
teries.
29.4.3.
Prescott tax and transfer scheme.
29.4.4.
No discounting
now matters.
29.5.
Intensive margin.
29.5.1.
Employment lotteries.
29.5.2.
Time averaging.
29.5.3.
Prescott taxation.
29.6.
Ben-Porath
human capital.
29.6.1.
Time averaging.
29.6.2.
Employment lotteries.
29.6.3.
Prescott taxation.
29.7.
Earnings shocks.
29.7.1.
Interpretation
xviii Contents
of wealth and substitution effects.
29.8.
Time averaging in a Bewley
model.
29.8.1.
Incomplete markets.
29.8.2.
Complete markets.
29.8.3.
Simulations of Prescott taxation.
29.9.
L
and
S
equivalence meets
С
and
K s agents.
29.9.1.
Guess the value function.
29.9.2.
Verify optimality
of time averaging.
29.9.3.
Equivalence of time averaging and lotteries.
29.10.
Concluding remarks.
Part
VII:
Technical appendices
A. Functional Analysis
1257
A.I. Metric spaces and operators. A.2. Discounted dynamic program¬
ming. A.
2.1.
Policy improvement algorithm. A.
2.2.
A search problem.
B. Linear projections and hidden Markov models
1269
B.I. Linear projections. B.2. Hidden Markov models. B.3. Nonlinear
filtering.
1.
References
1275
2.
Subject Index
1309
3.
Author Index
1315
4.
Matlab
Index
1321
|
| any_adam_object | 1 |
| author | Ljungqvist, Lars 1959- Sargent, Thomas J. 1943- |
| author_GND | (DE-588)115042504 (DE-588)118751298 |
| author_facet | Ljungqvist, Lars 1959- Sargent, Thomas J. 1943- |
| author_role | aut aut |
| author_sort | Ljungqvist, Lars 1959- |
| author_variant | l l ll t j s tj tjs |
| building | Verbundindex |
| bvnumber | BV040400032 |
| callnumber-first | H - Social Science |
| callnumber-label | HB172 |
| callnumber-raw | HB172.5 HB172.5.L59 2004 |
| callnumber-search | HB172.5 HB172.5.L59 2004 |
| callnumber-sort | HB 3172.5 |
| callnumber-subject | HB - Economic Theory and Demography |
| classification_rvk | QC 300 SK 880 |
| ctrlnum | (OCoLC)812256841 (DE-599)BVBBV040400032 |
| dewey-full | 339/.01/51135 339/.01/5113522 |
| dewey-hundreds | 300 - Social sciences |
| dewey-ones | 339 - Macroeconomics and related topics |
| dewey-raw | 339/.01/51135 339/.01/51135 22 |
| dewey-search | 339/.01/51135 339/.01/51135 22 |
| dewey-sort | 3339 11 551135 |
| dewey-tens | 330 - Economics |
| discipline | Mathematik Wirtschaftswissenschaften |
| edition | 3. ed. |
| format | Book |
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| genre | (DE-588)4123623-3 Lehrbuch gnd-content |
| genre_facet | Lehrbuch |
| id | DE-604.BV040400032 |
| illustrated | Illustrated |
| indexdate | 2024-07-10T00:23:12Z |
| institution | BVB |
| isbn | 9780262018746 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-025253238 |
| oclc_num | 812256841 |
| open_access_boolean | |
| owner | DE-384 DE-703 DE-945 DE-2070s DE-11 DE-473 DE-BY-UBG DE-523 DE-188 |
| owner_facet | DE-384 DE-703 DE-945 DE-2070s DE-11 DE-473 DE-BY-UBG DE-523 DE-188 |
| physical | XXXVI, 1321 S. graph. Darst. |
| publishDate | 2012 |
| publishDateSearch | 2012 |
| publishDateSort | 2012 |
| publisher | MIT Press |
| record_format | marc |
| spelling | Ljungqvist, Lars 1959- Verfasser (DE-588)115042504 aut Recursive macroeconomic theory Lars Ljungqvist ; Thomas J. Sargent 3. ed. Cambridge, Mass. [u.a.] MIT Press 2012 XXXVI, 1321 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier "Recursive methods offer a powerful approach for characterizing and solving complicated problems in dynamic macroeconomics. Recursive Macroeconomic Theory provides both an introduction to recursive methods and advanced material, mixing tools and sample applications. The second edition contains substantial revisions to about half the original material, and extensive additional coverage appears in seven chapters new to this edition. The updated and added material covers new topics that further illustrate the power and pervasiveness of recursive methods."--BOOK JACKET. Fonctions récursives Macro-economie gtt Macroéconomie Recursieve functies gtt Statique et dynamique (Sciences sociales) aMacroeconomics aRecursive functions aStatics and dynamics (Social sciences) Rekursive Funktion (DE-588)4138367-9 gnd rswk-swf Dynamische Makroökonomie (DE-588)4200428-7 gnd rswk-swf Makroökonomie (DE-588)4037174-8 gnd rswk-swf (DE-588)4123623-3 Lehrbuch gnd-content Makroökonomie (DE-588)4037174-8 s DE-604 Rekursive Funktion (DE-588)4138367-9 s Dynamische Makroökonomie (DE-588)4200428-7 s DE-188 Sargent, Thomas J. 1943- Verfasser (DE-588)118751298 aut Digitalisierung UB Bayreuth application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025253238&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Ljungqvist, Lars 1959- Sargent, Thomas J. 1943- Recursive macroeconomic theory Fonctions récursives Macro-economie gtt Macroéconomie Recursieve functies gtt Statique et dynamique (Sciences sociales) aMacroeconomics aRecursive functions aStatics and dynamics (Social sciences) Rekursive Funktion (DE-588)4138367-9 gnd Dynamische Makroökonomie (DE-588)4200428-7 gnd Makroökonomie (DE-588)4037174-8 gnd |
| subject_GND | (DE-588)4138367-9 (DE-588)4200428-7 (DE-588)4037174-8 (DE-588)4123623-3 |
| title | Recursive macroeconomic theory |
| title_auth | Recursive macroeconomic theory |
| title_exact_search | Recursive macroeconomic theory |
| title_full | Recursive macroeconomic theory Lars Ljungqvist ; Thomas J. Sargent |
| title_fullStr | Recursive macroeconomic theory Lars Ljungqvist ; Thomas J. Sargent |
| title_full_unstemmed | Recursive macroeconomic theory Lars Ljungqvist ; Thomas J. Sargent |
| title_short | Recursive macroeconomic theory |
| title_sort | recursive macroeconomic theory |
| topic | Fonctions récursives Macro-economie gtt Macroéconomie Recursieve functies gtt Statique et dynamique (Sciences sociales) aMacroeconomics aRecursive functions aStatics and dynamics (Social sciences) Rekursive Funktion (DE-588)4138367-9 gnd Dynamische Makroökonomie (DE-588)4200428-7 gnd Makroökonomie (DE-588)4037174-8 gnd |
| topic_facet | Fonctions récursives Macro-economie Macroéconomie Recursieve functies Statique et dynamique (Sciences sociales) aMacroeconomics aRecursive functions aStatics and dynamics (Social sciences) Rekursive Funktion Dynamische Makroökonomie Makroökonomie Lehrbuch |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025253238&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT ljungqvistlars recursivemacroeconomictheory AT sargentthomasj recursivemacroeconomictheory |