Recursive macroeconomic theory:
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Cambridge, Massachusetts ; London, England
MIT Press
[2018]
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| Edition: | Fourth edition |
| Subjects: | |
| Links: | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=030589331&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| Item Description: | Literaturverzeichnis: Seite 1391-1424 |
| Physical Description: | xxxvii, 1437 Seiten Diagramme |
| ISBN: | 9780262038669 |
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| 245 | 1 | 0 | |a Recursive macroeconomic theory |c Lars Ljungqvist, Thomas J. Sargent |
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Contents
Acknowledgments
xxi
Preface to the fourth edition
xxm
Part I: Imperialism of Recursive Methods
1. Overview
3
1.1. Warning. 1.2. A common ancestor. 1.3. The savings problem.
1.3.L 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 stan-
dard 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. Dynamic programming and the
Lucas Critique. 1.4.2. Dynamic programming challenged. 1.4.3. Impe-
rialistic 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.
- v -
VI
Contents
Part II: Tools
2. Time Series
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. 2.8. Estimation again.
2.9. Vector autoregressions and the Kalman filter. 2.9.1. Conditioning
on the semi-infinite past of y. 2.9.2. A time-invariant VAR. 2.9.3. Inter-
preting VARs. 2.10. Applications of the Kalman filter. 2.10.1. Muth’s
reverse engineering exercise. 2.10.2. Jovanovic’s application. 2.11. The
spectrum. 2.11.1. Examples. 2.12. Example: the LQ permanent in-
come model. 2.12.1. Another representation. 2.12.2. Debt dynamics.
2.12.3. Two classic examples. 2.12.4. Spreading consumption cross sec-
tion. 2.12.5. Invariant subspace approach. 2.13. Concluding remarks.
A. Linear difference equations. 2.A.I. A first-order difference equation.
2. A.2. A second-order difference equation. 2.15. Exercises.
3. Dynamic Programming
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.
4. Practical Dynamic Programming
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
Contents
vn
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 129
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. 5.9. Exercises.
6. Search and Unemployment 157
6.1. Introduction. 6.2. Preliminaries. 6.2.1. Nonnegative random vari-
ables. 6.2.2. Mean-preserving spreads. 6.3. McCall’s 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.A.I. Example 4: search. 6.A.2. Example 5: a
Jovanovic model. 6.12. Exercises.
Part III: Competitive Equilibria and Applications
7. Recursive Competitive Equilibrium: I 225
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.
Contents
viii
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
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.
8.8.1. Arrow securities. 8.8.2. Financial wealth as an endogenous state
variable. 8.8.3. Reopening markets. 8.8.4. Debt limits. 8.8.5. Sequential
trading. 8.8.6. Equivalence of allocations. 8.9. Recursive competitive
equilibrium. 8.9.1. Endowments governed by a Markov process. 8.9.2.
Equilibrium outcomes inherit the Markov property. 8.9.3. Recursive
formulation of optimization and equilibrium. 8.9.4. Computing an equi-
librium with sequential trading of Arrow-securities. 8.10. j-step pricing
kernel. 8.10.1. Arbitrage-free pricing. 8.11. Term structure of yields on
risk-free claims. 8.11.1. Constructing yields. 8.12. Recursive version
of Pareto problem. 8.13. Concluding remarks. Appendices: Departures
from key assumptions. A. Heterogenous discounting. B. Heterogenous
beliefs . 8.B.I. Example: one type’s beliefs are closer to the truth. 8.B.2.
Equilibrium prices reflect beliefs. 8.B.3. Mispricing? 8.B.4. Learning.
8. B.5. Role of complete markets. C. Incomplete markets. 8.C.I. An
example economy. 8.C.2. Asset payoff correlated with i.i.d. aggregate
endowment. 8.C.3. Beneficial market incompleteness. 8.18. Exercises.
9. Overlapping Generations
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.
Contents
IX
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 379
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 bt+\
t+i. 10.3. Government finance. 10.3.1. Effect on household. 10.4.
Linked generations interpretation. 10.5. Concluding remarks.
11. Fiscal Policies in a Growth Model 391
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 R. 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 APs. 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
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.
X
Contents
11.13.5. Transition exercises. 11.14. Concluding remarks. A. Log linear
approximations. 11.16. Exercises.
12. Recursive Competitive Equilibrium: II
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” device.
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 plan-
ning problem. 12.10. Concluding remarks. A. The permanent income
model revisited. 12.A.1. Reinterpreting the single-agent model. 12.A.2.
Decentralization and scaled prices. 12.A.3. Matching equilibrium and
planning allocations. 12.A.4. Interpretation.
13. Asset Pricing Theory
13.1. Introduction. 13.2. Euler equations. 13.3. Martingale theories
of consumption and stock prices. 13.4. Equivalent martingale mea-
sure. 13.5. Equilibrium asset pricing. 13.6. Stock prices without bub-
bles. 13.7. Computing asset prices. 13.7.1. Example 1: logarithmic
preferences. 13.7.2. Example 2: finite-state version. 13.7.3. Exam-
ple 3: growth. 13.8. Term structure of interest rates. 13.9. State-
contingent prices. 13.9.1. Insurance premium. 13.9.2. Man-made un-
certainty. 13.9.3. The Modigliani-Miller theorem. 13.10. Government
debt. 13.10.1. The Ricardian proposition. 13.10.2. No Ponzi schemes.
A. Harrison-Kreps (1978) heterogeneous beliefs. 13.A.1. Optimism and
Pessimism. 13.A.2. Equilibrium price function. 13.A.3. Comparisons of
equilibrium price functions. 13.A.4. Single belief prices. 13.A.5. Pric-
ing under heterogeneous beliefs. 13.A.6. Insufficient funds. B. Gaussian
asset-pricing model. 13.13. Exercises.
Contents
xi
14. Asset Pricing Empirics 549
14.1. Introduction. 14.2. Interpretation of risk-aversion parameter. 14.3.
The equity premium puzzle. 14.4. Market price of risk. 14.5. Hansen-
Jagannatlian bounds. 14.5.1. Law of one price implies that ErnR = 1.
14.5.2. Inner product representation of price functional. 14.5.3. Admis-
sible stochastic discount factors. 14.6. Failure of CRRA to attain HJ
bound. 14.7. Non-expected utility. 14.7.1. Another representation of
the utility recursion. 14.7.2. Stochastic discount factor. 14.7.3. Twisted
probability distributions. 14.8. Reinterpretation of the utility recursion.
14.8.1. Risk aversion versus model misspecification aversion. 14.8.2. Re-
cursive representation of probability distortions. 14.8.3. Entropy. 14.8.4.
Expressing ambiguity aversion. 14.8.5. Ambiguity averse preferences.
14.8.6. Market price of model uncertainty. 14.8.7. Measuring model
uncertainty. 14.9. Costs of aggregate fluctuations. 14.10. Reverse engi-
neered consumption heterogeneity. 14.11. Affine risk prices. 14.11.1. An
application. 14.11.2. Affine term structure of yields. 14.12. Risk-neutral
probabilities. 14.12.1. Asset pricing in a nutshell. 14.13. Distorted be-
liefs. 14.14. Concluding remarks. A. Riesz representation theorem. B.
Computing stochastic discount factors. C. A log normal bond pricing
model. 14.C.1. Slope of yield curve. 14.C.2. Backus and Zin’s stochas-
tic discount factor. 14.C.3. Reverse engineering a stochastic discount
factor. 14.18. Exercises.
15. Economic Growth 631
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 661
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. Primal approach to the Ramsey problem.
16.5.1. Constructing the Ramsey plan. 16.5.2. Revisiting a zero capital
tax. 16.6. Taxation of initial capital. 16.7. Nonzero capital tax due to
incomplete taxation, 16.8. A stochastic economy. 16.8.1. Government.
Contents
xii
16.8.2. Household. 16.8.3. Firms. 16.9. Indeterminacy of debt and cap-
ital taxes. 16.10. A Ramsey plan under uncertainty. 16.11. Ex ante
capital tax varies around zero. 16.11.1. Sketch of the proof of Proposi-
tion 2. 16.12. A stochastic economy without capital 16.12.1. Computa-
tional strategy. 16.12.2. More specialized computations. 16.12.3. Time
consistency. 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 ^ T and
nonstochastic gr 0. 16.13.3. Example 3: gt = 0 for t ^ T, and gr
is stochastic. 16.13.4. Time 0 is special with bo ^ 0. 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
but special preferences. 16.15.3. Example 3 revisited: gt — 0 for
t ^ T, and gr 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. 16.16.4. Sticky prices. 16.17. Relation to fiscal the-
ories of the price level. 16.17.1. Budget constraint versus asset pricing
equation. 16.17.2. Disappearance of quantity theory? 16.17.3. Price
level indeterminacy under interest rate peg. 16.17.4. Monetary or fis-
cal theory 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: Savings Problems and Bewley Models
17. Self-Insurance 759
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 785
18.1. Introduction. 18.2. A savings problem. 18.2.1. Wealth-employment
distributions. 18.2.2. Reinterpretation of the distribution A. 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.
Contents
18.3. Unification and further analysis. 18.4. The nonstochastic sav-
ings problem when ¡3(1 + 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
IOUs. 18.10. Private IOUs only. 18.10.1. Limitation of what credit can
achieve. 18.10.2. Proximity of r 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 delation. 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 839
19.1. History dependence. 19.2. The Stackelberg problem. 19.3. Timing
protocol. 19.4. Recursive formulation. 19.4.1. Two Bellman equations.
19.4.2. Subproblem 1. 19.4.3. Subproblem 2. 19.4.4. Timing protocol.
19.4.5. Time inconsistency. 19.5. Large firm facing a competitive fringe.
19.5.1. The competitive fringe. 19.5.2. The large firm’s problem. 19.5.3.
Numerical example. 19.6. Concluding remarks. 19.7. Exercises.
20. Two Ramsey Problems Revisited 857
20.1. Introduction. 20.2. The Lucas-Stokey economy. 20.2.1. Find-
ing the state is an art. 20.2.2. Intertemporal delegation. 20.2.3. Bell-
man equations. 20.2.4. Subproblem 1: Continuation Ramsey problem.
20.2.5. Subproblem 2: Ramsey problem. 20.2.6. First-order conditions.
20.2.7. State variable degeneracy. 20.2.8. Symptom and source of time
inconsistency. 20.3. Recursive formulation of AMSS model. 20.3.1. Re-
casting state variables. 20.3,2. Measurability constraints. 20.3.3. Bell-
man equations. 20.3.4. Martingale replaces state-variable degeneracy.
20.4. Concluding remarks.
XIV
Contents
21. Incentives and Insurance
21.1. Insurance with recursive contracts. 21.2. Basic environment.
21.3. One-sided no commitment. 21.3.1. Self-enforcing contract. 21.3.2.
Recursive formulation and solution. 21.3.3. Recursive computation of
contract. 21.3.4. Profits. 21.3.5. P(v) is strictly concave and contin-
uously differentiable. 21.3.6. Many households. 21.3.7. An example.
21.4. A Lagrangian method. 21.5. Insurance with asymmetric infor-
mation. 21.5.1. Efficiency implies bs-\ bs,ws-i ws. 21.5.2. Local
upward and downward constraints are enough. 21.5.3. Concavity of P.
21.5.4. Local downward constraints always bind. 21.5.5. Coinsurance.
21.5.6. P*(v) is a martingale. 21.5.7. Comparison to model with com-
mitment problem. 21.5.8. Spreading continuation values. 21.5.9. Mar-
tingale convergence and poverty. 21.5.10. Extension to general equilib-
rium. 21.5.11. Comparison with self-insurance. 21.6. Insurance with
unobservable storage. 21.6.1. Feasibility. 21.6.2. Incentive compatibil-
ity. 21.6.3. Efficient allocation. 21.6.4. The two-period case. 21.6.5.
Role of the planner. 21.6.6. Decentralization in a closed economy. 21.7.
Concluding remarks. A. Historical development. 21.A. 1. Spear and Sri-
vastava. 21.A.2. Timing. 21.A.3. Use of lotteries. 21.9. Exercises.
22. Equilibrium without Commitment
22.1. Two-sided lack of commitment. 22.2. A closed system. 22.3.
Recursive formulation. 22.4. Equilibrium consumption. 22.4.1. Con-
sumption dynamics. 22.4.2. Consumption intervals cannot contain each
other. 22.4.3. Endowments are contained in the consumption intervals.
22.4.4. All consumption intervals are nondegenerate (unless autarky is
the only sustainable allocation). 22.5. Pareto frontier and ex ante divi-
sion of the gains. 22.6. Consumption distribution. 22.6.1. Asymptotic
distribution. 22.6.2. Temporary imperfect risk sharing. 22.6.3. Per-
manent imperfect risk sharing. 22.7. Alternative recursive formulation.
22.8. Pareto frontier revisited. 22.8.1. Values are continuous in implicit
consumption. 22.8.2. Differentiability of the Pareto frontier. 22.9. Con-
tinuation values a la Kocherlakota. 22.9.1. Asymptotic distribution is
nondegenerate for imperfect risk sharing (except when 5 = 2). 22.9.2.
Continuation values do not always respond to binding participation con-
straints. 22.10. A two-state example: amnesia overwhelms memory.
22.10.1. Pareto frontier. 22.10.2. Interpretation. 22.11. A three-state
example. 22.11.1. Perturbation of parameter values. 22.11.2. Pareto
frontier. 22.12. Empirical motivation. 22.13. Generalization. 22.14. De-
centralization. 22.15. Endogenous borrowing constraints. 22.16. Con-
cluding remarks. 22.17. Exercises.
(Montants
xv
23. Optimal Unemployment; Insurance
987
23.1. History-dependent unemployment insurance. 23.2. A one-spell
model, 23.2.1. The autarky problem, 23.2.2. Unemployment, insurance
with full information. 23.2.3. The incentive problem. 23.2.1. Unem-
ployment insurance with asymmetric information. 23.2.3. Computed
Extension: an on-the-job tax. 23.2.9. Extension: intermittent unem-
ployment spells. 23.3, A multiple-spell model with lifetime contracts.
pensation dynamics when unemployed. 23.3.4. Compensation dynamics
24,1. Introduction. 24.1.1. Diverse sources of history dependence. 24.2.
One-period economy. 24.2.1, Competitive equilibrium. 24.2,2. Ram-
sey problem. 24.2.3. Nash equilibrium. 24.3. Nasli and Ramsey out-
comes. 24.3.1. Taxation example. 24.3.2. Black-box example with dis-
crete choice sets. 24.4. Reputational mechanisms: general idea. 24.4.1.
Dynamic programming squared. 24.4.2. Etymology of ‘dynamic pro-
gramming squared’. 24.5. The infinitely repeated economy. 24.5.1. A
strategy profile implies a history and a value. 24.5.2. Recursive formu-
lation. 24.G. Subgame perfect equilibrium (SPE). 24.7. Examples of
SPE. 24.7.1. Infinite repetition of one-period Nash equilibrium. 24.7.2.
Supporting better outcomes with trigger strategies. 24.7.3. When rever-
sion to Nash is not bad enough. 24.8. Values of all SPEs. 24.8.1. Basic
idea of dynamic programming squared. 24.9, APS machinery. 24.10.
Self-enforcing SPE. 24.10.1. The quest for something worse than rep-
etition of Nash outcome. 24.11. Recursive strategies. 24.12. Examples
of SPE with recursive strategies. 24,12.1. Infinite repetition of Nasli
outcome. 24.12.2. Infinite repetition of a better-than-Nash out conus
24.12.3. Something worse: a stick-and-carrot strategy. 24.13. Best and
worst SPE values. 24.13.1. When V\ is outside the candidate set. 24.14.
Examples: alternative ways to achieve the worst, 24.14.1. Attaining
the worst, method 1. 24.14.2. Attaining the worst, method 2. 24,14.3.
Attaining tlu? worst,, method 3. 24.14.4. Numerical example. 24.15. In-
terpretations. 24.16. Extensions. 24.17. Exercises.
24. Credible Government Policies: I
1011
XVI
Contents
25. Credible Government Policies: II
25.1. History-dependent government policies. 25.2. The setting. 25.2.1.
Household problem. 25.2.2. Government. 25.2.3. Analysis of house-
hold’s problem. 25.2.4. 9t+\ as intermediating variable. 25.3. Recur-
sive approach to Ramsey problem. 25.3.1. Subproblem 1: Continua-
tion Ramsey problem. 25.3.2. Subproblem 2: Ramsey problem. 25.3.3.
Finding set H. 25.3.4. An example. 25.4. Chang’s formulation. 25.4.1.
Competitive equilibrium. 25.5. Inventory of key objects. 25.6. Analy-
sis. 25.6.1. Notation. 25.6.2. An operator. 25.7. Sustainable plans. 25.8.
Concluding remarks.
26. Two Topics in International Trade
26.1. Two dynamic contracting problems. 26.2. Moral hazard and dif-
ficult enforcement. 26.2.1. Autarky. 26.2.2. Investment with full insur-
ance. 26.2.3. Limited commitment and unobserved investment. 26.2.4.
Optimal capital outflows under distress. 26.3. Gradualism in trade pol-
icy. 26.3.1. Closed-economy model. 26.3.2. A Ricardian model of two
countries under free trade. 26.3.3. Trade with a tariff. 26.3.4. Wel-
fare and Nash tariff. 26.3.5. Trade concessions. 26.3.6. A repeated
tariff game. 26.3.7. Time-invariant transfers. 26.3.8. Gradualism: time-
varying trade policies. 26.3.9. Baseline policies. 26.3.10. Multiplicity of
payoffs and continuation values. 26.4. Another model. 26.5. Concluding
remarks. A. Computations for Atkeson’s model. 26.7. Exercises.
Part VI: Classical Monetary and Labor Economics
27. Fiscal-Monetary Theories of Inflation
27.1. The issues. 27.2. A shopping time monetary economy. 27.2.1.
Household. 27.2.2. Government. 27.2.3. Equilibrium. 27.2.4. “Short
run” versus “long run”. 27.2.5. Stationary equilibrium. 27.2.6. Initial
date (time 0). 27.2.7. Equilibrium determination. 27.3. Ten mone-
tary doctrines. 27.3.1. Quantity theory of money. 27.3.2. Sustained
deficits cause inflation. 27.3.3. Fiscal prerequisites of zero inflation
policy. 27.3.4. Unpleasant monetarist arithmetic. 27.3.5. An “open
market” operation delivering neutrality. 27.3.6. The “optimum quan-
tity” of money. 27.3.7. Legal restrictions to boost demand for currency.
27.3.8. One big open market operation. 27.3.9. A fiscal theory of the
1059
1083
1123
Contents
price level. 27.3.10. Exchange rate indeterminacy. 27.3.11. Determi-
nacy of the exchange rate retrieved. 27.4. An example of exchange rate
(in)determinacy. 27.4.1. Trading before sunspot realization. 27.4.2. Fis-
cal theory of the price level. 27.4.3. A game theoretic view of the fiscal
theory of the price level. 27.5. Optimal inflation tax: the Friedman rule.
27.5.1. Economic environment. 27.5.2. Household’s optimization prob-
lem. 27.5.3. Ramsey plan. 27.6. Time consistency of monetary policy.
27.6.1. Model with monopolistically competitive wage setting. 27.6.2.
Perfect foresight equilibrium. 27.6.3. Ramsey plan. 27.6.4. Credibility
of the Friedman rule. 27.7. Concluding remarks. 27.8. Exercises.
28. Credit and Currency
28.1. Credit and currency with long-lived agents. 28.2. Preferences
and endowments. 28.3. Complete markets. 28.3.1. A Pareto problem.
28.3.2. A complete markets equilibrium. 28.3.3. Ricardian proposition.
28.3.4. Loan market interpretation. 28.4. A monetary economy. 28.5.
Townsend’s “turnpike” interpretation. 28.6. The Friedman rule. 28.6.1.
Welfare. 28.7. Inflationary finance. 28.8. Legal restrictions. 28.9. A
two-money model. 28.10. A model of commodity money. 28.10.1. Equi-
librium. 28.10.2. Virtue of fiat money. 28.11. Concluding remarks.
28.12. Exercises.
29. Equilibrium Search, Matching, and Lotteries
29.1. Introduction. 29.2. An island model. 29.2.1. A single market
(island). 29.2.2. The aggregate economy. 29.3. A matching model.
29.3.1. A steady state. 29.3.2. Welfare analysis. 29.3.3. Size of the
match surplus. 29.4. Matching model with heterogeneous jobs. 29.4.1.
A steady state. 29.4.2. Welfare analysis. 29.4.3. The allocating role
of wages I: separate markets. 29.4.4. The allocating role of wages II:
wage announcements. 29.5. Employment lotteries. 29.6. Lotteries for
households versus lotteries for firms. 29.6.1. An aggregate production
function. 29.6.2. Time-varying capacity utilization. 29.7. Employment
effects of layoff taxes. 29.7.1. A model of employment lotteries with lay-
off taxes. 29.7.2. An island model with layoff taxes. 29.7.3. A matching
model with layoff taxes. 29.8. Kiyotaki-Wright search model of money.
29.8.1. Monetary equilibria. 29.8.2. Welfare. 29.9. Concluding remarks.
29.10. Exercises.
xvii
1171
1207
xviii
Contents
30. Matching Models Mechanics
30.1. Introduction. 30.2. Fundamental surplus. 30.2.1. Sensitivity of
unemployment to market tightness. 30.2.2. Nash bargaining model.
30.2.3. Shimer’s critique. 30.2.4. Relationship to worker’s outside value.
30.2.5. Relationship to match surplus. 30.2.6. Fixed matching cost.
30.2.7. Sticky wages. 30.2.8. Alternating-offer wage bargaining. 30.3.
Business cycle simulations. 30.3.1. Hall’s sticky wage. 30.3.2. Hage-
dorn and Manovskii’s high value of leisure. 30.3.3. Hall and Milgrom’s
alternating-offer bargaining. 30.3.4. Matching and bargaining proto-
cols in a DSGE model. 30.4. Overlapping generations in one match-
ing function. 30.4.1. A steady state. 30.4.2. Reservation productivity
is increasing in age. 30.4.3. Wage rate is decreasing in age. 30.4.4.
Welfare analysis. 30.4.5. The optimal policy. 30.5. Directed search:
age-specific matching functions. 30.5.1. Value functions and market
tightness. 30.5.2. Job finding rate is decreasing in age. 30.5.3. Block
recursive equilibrium computation. 30.5.4. Welfare analysis. 30.6. Con-
cluding remarks.
31. Foundations of Aggregate Labor Supply
31.1. Introduction. 31.2. Equivalent allocations. 31.2.1. Choosing ca-
reer length. 31.2.2. Employment lotteries. 31.3. Taxation and social
security. 31.3.1. Taxation. 31.3.2. Social security. 31.4. Earnings-
experience profiles. 31.4.1. Time averaging. 31.4.2. Employment lot-
teries. 31.4.3. Prescott tax and transfer scheme. 31.4.4. No discounting
now matters. 31.5. Intensive margin. 31.5.1. Employment lotteries.
31.5.2. Time averaging. 31.5.3. Prescott taxation. 31.6. Ben-Porath
human capital. 31.6.1. Time averaging. 31.6.2. Employment lotteries.
31.6.3. Prescott taxation. 31.7. Earnings shocks. 31.7.1. Interpretation
of wealth and substitution effects. 31.8. Time averaging in a Bewley
model. 31.8.1. Incomplete markets. 31.8.2. Complete markets. 31.8.3.
Simulations of Prescott taxation. 31.9. L and S equivalence meets C and
K’s agents. 31.9.1. Guess the value function. 31.9.2. Verify optimality
of time averaging. 31.9.3. Equivalence of time averaging and lotteries.
31.10. Two pillars for high elasticity at extensive margin. 31.11. No
pillars at intensive margin. 31.1 LI. Special example of high elasticity
at intensive margin. 31.11.2. Fragility of the special example. 31.12.
Concluding remarks.
1269
1315
Contents
xix
Part VII: Technical Appendices
A. Functional Analysis 1373
A. l. 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 1385
B.l. Linear projections. B.2. Hidden Markov models. B.3. Nonlinear
filtering.
1. References 1391
2. Subject Index 1425
3. Author Index 1431
4. Matlab Index
1437 |
| 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- |
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| bvnumber | BV045200351 |
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| discipline | Wirtschaftswissenschaften |
| edition | Fourth edition |
| format | Book |
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| id | DE-604.BV045200351 |
| illustrated | Not Illustrated |
| indexdate | 2025-01-11T10:54:28Z |
| institution | BVB |
| isbn | 9780262038669 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-030589331 |
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| physical | xxxvii, 1437 Seiten Diagramme |
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| publisher | MIT Press |
| record_format | marc |
| spelling | Ljungqvist, Lars 1959- Verfasser (DE-588)115042504 aut Recursive macroeconomic theory Lars Ljungqvist, Thomas J. Sargent Fourth edition Cambridge, Massachusetts ; London, England MIT Press [2018] xxxvii, 1437 Seiten Diagramme txt rdacontent n rdamedia nc rdacarrier Literaturverzeichnis: Seite 1391-1424 Rekursive Funktion (DE-588)4138367-9 gnd rswk-swf Makroökonomie (DE-588)4037174-8 gnd rswk-swf Dynamische Makroökonomie (DE-588)4200428-7 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 Regensburg - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=030589331&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Ljungqvist, Lars 1959- Sargent, Thomas J. 1943- Recursive macroeconomic theory Rekursive Funktion (DE-588)4138367-9 gnd Makroökonomie (DE-588)4037174-8 gnd Dynamische Makroökonomie (DE-588)4200428-7 gnd |
| subject_GND | (DE-588)4138367-9 (DE-588)4037174-8 (DE-588)4200428-7 (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 | Rekursive Funktion (DE-588)4138367-9 gnd Makroökonomie (DE-588)4037174-8 gnd Dynamische Makroökonomie (DE-588)4200428-7 gnd |
| topic_facet | Rekursive Funktion Makroökonomie Dynamische Makroökonomie Lehrbuch |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=030589331&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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