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E-raamat: Recursive Macroeconomic Theory

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  • Formaat: 1360 pages
  • Sari: The MIT Press
  • Ilmumisaeg: 31-Aug-2012
  • Kirjastus: MIT Press
  • Keel: eng
  • ISBN-13: 9780262312011
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Recursive Macroeconomic TheorySuurem pilt
  • Formaat: 1360 pages
  • Sari: The MIT Press
  • Ilmumisaeg: 31-Aug-2012
  • Kirjastus: MIT Press
  • Keel: eng
  • ISBN-13: 9780262312011
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Recursive methods offer a powerful approach for characterizing and solvingcomplicated problems in dynamic macroeconomics. Recursive Macroeconomic Theoryprovides both an introduction to recursive methods and advanced material, mixing tools and sampleapplications. Only experience in solving practical problems fully conveys the power of the recursiveapproach, and the book provides many applications. This third edition offers substantial newmaterial, with three entirely new chapters and significant revisions to others. The new contentreflects recent developments in the field, further illustrating the power and pervasiveness ofrecursive methods. New chapters cover asset pricing empirics with possible resolutions to puzzles;analysis of credible government policy that entails state variables other than reputation; andfoundations of aggregate labor supply with time averaging replacing employment lotteries. Other newmaterial includes a multi-country analysis of taxation in a growth model, elaborations of the fiscaltheory of the price level, and age externalities in a matching model.

The book issuitable for both first- and second-year graduate courses in macroeconomics and monetary economics.Most chapters conclude with exercises. Many exercises and examples use Matlab programs, which arecited in a special index at the end of the book.

Acknowledgements xix
Preface to the third edition xx
Part I The imperialism of recursive methods
1 Overview
3(26)
1.1 Warning
1.2 A common ancestor
1.3 The savings problem
1.3.1 Lincar quadratic permanent income theory
1.3.2 Precautionary 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 Imperialistic 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
Part II Tools
2 Time Series
29(74)
2.1 Two workhorses
2.2 Markov chains
2.2.1 Stationary distributions
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 Stochastic 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 Interpreting 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 income model
2.11.1 Another representation
2.11.2 Debt dynamics
2.11.3 Two classic examples
2.11.4 Spreading consumption cross section
2.11.5 Invariant subspace approach
2.12 Concluding remarks
A Linear difference equations
2.A.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(10)
3.1 Sequential problems
3.1.1 Three computational methods
3.1.2 Cobb-Douglas transition, logarithmic preferences
3.1.3 Euler equations
3.1.4 A sample Euler equation
3.2 Stochastic control problems
3.3 Concluding remarks
3.4 Exercise
4 Practical Dynamic Programming
113(14)
4.1 The curse of dimensionality
4.2 Discrete-state dynamic programming
4.3 Bookkeeping
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
127(32)
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 again
5.7 Concluding remarks
A Matrix formulas
B Linear quadratic approximations
5.B.1 An example: 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(68)
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 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 matching 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 dynamic programming
6.A.1 Example 4: search
6.A.2 Example 5: a Jovanovic model
6.12 Exercises
Part III Competitive equilibria and applications
7 Recursive (Partial) Equilibrium
227(24)
7.1 An equilibrium concept
7.2 Example: adjustment costs
7.2.1 A planning problem
7.3 Recursive competitive equilibrium
7.4 Equilibrium human capital accumulation
7.4.1 Planning problem
7.4.2 Decentralization
7.5 Equilibrium occupational choice
7.5.1 A planning 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(64)
8.1 Time 0 versus sequential trading
8.2 The physical setting: 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 Time 0 trading: Arrow-Debreu securities
8.5.1 Equilibrium pricing function
8.5.2 Optimality of equilibrium allocation
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 Example 2: no aggregate uncertainty
8.6.4 Example 3: periodic endowment 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 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 equilibrium 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.B.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
9 Overlapping Generations Models
315(48)
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 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
363(12)
10.1 Borrowing limits and Ricardian equivalence
10.2 Infinitely lived agent economy
10.2.1 Optimal consumption/savings decision when bt+1 ≥ bt+1 ≥ 0
10.2.2 Optimal consumption/savings decision when bt+1 ≥ bt+1
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(80)
11.1 Introduction
11.2 Economy
11.2.1 Preferences, technology, information
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 lumpsum taxes available
11.7 A digression on back-solving
11.8 Effects of taxes on equilibrium allocations and prices
11.9 Transition experiments with inelastic labor supply
11.10 Linear approximation
11.10.1 Relationship between the λi's
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
11.13.5 Transition exercises
11.14 Concluding remarks
A Log linear approximations
11.16 Exercises
12 Recursive Competitive Equilibria
455(26)
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 governed 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(34)
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 Example 2: 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 Modigliani-Miller theorem
13.10 Government debt
13.10.1 The Ricardian proposition
13.10.2 No Ponzi schemes
14 Asset Pricing Empirics
515(68)
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-Jagannathan bounds
14.5.1 Law of one price implies that EmR = 1
14.5.2 Inner product representation of the pricing kernel
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 recursion
14.7.2 Stochastic discount factor
14.8 Reinterpretation of the utility recursion
14.8.1 Risk aversion or model misspecification aversion
14.8.2 Recursive representation of probability distortions
14.8.3 Entropy
14.8.4 Expressing ambiguity
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 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 representation theorem
B A log normal bond pricing model
14.B.1 Slope of yield curve depends on serial correlation of logmt+1
14.B.2 Backus and Zin's stochastic discount factor
14.B.3 Reverse engineering a stochastic discount factor
14.15 Exercises
15 Economic Growth
583(30)
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 factors 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 externality
15.8 Concluding remarks
15.9 Exercises
16 Optimal Taxation with Commitment
613(86)
16.1 Introduction
16.2 A nonstochastic economy
16.2.1 Government
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
2.16.13 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 gt > 0
16.13.3 Example 3: gt = 0 for t ≠ T, and gT 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 ≠ T, and gT 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 equation
16.17.2 Disappearance of quantity theory?
16.17.3 Price level indeterminacy under interest rate peg
16.17.4 Monetary or fiscal 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 The savings problem and Bewley models
17 Self-Insurance
699(26)
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 Supermartingale convergence theorem
17.11 Exercises
18 Incomplete Markets Models
725(50)
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 Example 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 savings problem when β(1 + r) > 1
18.5 Borrowing limits: natural and ad hoc
18.5.1 A candidate for a single state variable
18.5.2 Supermartingale 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 M/R
18.13.3 A very special case
18.13.4 Implicit interest 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(22)
19.1 History dependence
19.2 The Stackelberg problem
19.3 Solving 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 implementation multipliers into state variables
19.3.5 Step 4: solve for x0 and μx0
19.3.6 Summary
19.3.7 History-dependent representation of decision 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 stabilizing μt = Pyt
B Matrix linear difference equations
C Forecasting formulas
19.9 Exercises
20 Insurance Versus Incentives
797(62)
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 continuously differentiable
20.3.6 Many households
20.3.7 An example
20.4 A Lagrangian method
20.5 Insurance with asymmetric information
20.5.1 Efficiency implies bs-1 ≥ bs, ws-1 ≤ 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 Coinsurance
20.5.6 P'(v) is a martingale
20.5.7 Comparison to model with 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 compatibility
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.1 Spear and Srivastava
20.A.2 Timing
20.A.3 Use of lotteries
20.9 Exercises
21 Equilibrium without Commitment
859(54)
21.1 Two-sided lack of commitment
21.2 A closed system
21.3 Recursive formulation
21.4 Equilibrium consumption
21.4.1 Consumption 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 division of the gains
21.6 Consumption distribution
21.6.1 Asymptotic distribution
21.6.2 Temporary imperfect risk sharing
21.6.3 Permanent 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 Continuation values a la Kocherlakota
21.9.1 Asymptotic distribution is nondegenerate for imperfect risk sharing (except when S = 2)
21.9.2 Continuation values do not always respond to binding participation constraints
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 Decentralization
21.15 Endogenous borrowing constraints
21.16 Concluding remarks
21.17 Exercises
22 Optimal Unemployment Insurance
913(24)
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 Unemployment 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 unemployment spells
22.3 A multiple-spell model with lifetime contracts
22.3.1 The setup
22.3.2 A recursive lifetime contract
22.3.3 Compensation dynamics when unemployed
22.3.4 Compensation dynamics while employed
22.3.5 Summary
22.4 Concluding remarks
22.5 Exercises
23 Credible Government Policies, I
937(48)
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 Ramsey 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 equilibrium
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 repetition 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 v1 is outside 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(20)
24.1 Sources of history-dependent government policies
24.2 The setting
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
25 Two Topics in International Trade
1005(40)
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 investment
25.2.4 Optimal capital outflows under distress
25.3 Gradualism 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 Gradualism: 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(48)
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 monetary 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 quantity" 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 Determinacy of the exchange rate retrieved
26.4 An example of exchange rate (in)determinacy
26.4.1 Trading before sunspot realization
26.4.2 Fiscal 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 problem
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
27 Credit and Currency
1093(36)
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 Equilibrium
27.10.2 Virtue of fiat money
27.11 Concluding remarks
27.12 Exercises
28 Equilibrium Search and Matching
1129(74)
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(54)
29.1 Introduction
29.2 Equivalent allocations
29.2.1 Choosing career 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 lotteries
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 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 C 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(12)
A.1 Metric spaces and operators
A.2 Discounted dynamic programming
A.2.1 Policy improvement algorithm
A.2.2 A search problem
B Linear projections and hidden Markov models
1269(6)
B.1 Linear projections
B.2 Hidden Markov models
B.3 Nonlinear filtering
1 References 1275(34)
2 Subject Index 1309(6)
3 Author Index 1315(6)
4 Matlab Index 1321
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