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Recursive Macroeconomic Theory fourth edition [Kõva köide]

4.08/5 (77 hinnangut Goodreads-ist)
(Stockholm School of Economics), (New York University)
  • Formaat: Hardback, 1480 pages, kõrgus x laius x paksus: 229x178x56 mm
  • Sari: The MIT Press
  • Ilmumisaeg: 11-Sep-2018
  • Kirjastus: MIT Press
  • ISBN-10: 0262038668
  • ISBN-13: 9780262038669
Teised raamatud teemal:
Recursive Macroeconomic Theory fourth editionSuurem pilt
  • Formaat: Hardback, 1480 pages, kõrgus x laius x paksus: 229x178x56 mm
  • Sari: The MIT Press
  • Ilmumisaeg: 11-Sep-2018
  • Kirjastus: MIT Press
  • ISBN-10: 0262038668
  • ISBN-13: 9780262038669
Teised raamatud teemal:
Püsilink: https://www.kriso.ee/db/9780262038669.html
Märksõnad:
The substantially revised fourth edition of a widely used text, offering both an introduction to recursive methods and advanced material, mixing tools and sample applications.

The substantially revised fourth edition of a widely used text, offering both an introduction to recursive methods and advanced material, mixing tools and sample applications.

Recursive methods provide powerful ways to pose and solve problems in dynamic macroeconomics. Recursive Macroeconomic Theory offers both an introduction to recursive methods and more advanced material. Only practice in solving diverse problems fully conveys the advantages of the recursive approach, so the book provides many applications. This fourth edition features two new chapters and substantial revisions to other chapters that demonstrate the power of recursive methods.

One new chapter applies the recursive approach to Ramsey taxation and sharply characterizes the time inconsistency of optimal policies. These insights are used in other chapters to simplify recursive formulations of Ramsey plans and credible government policies. The second new chapter explores the mechanics of matching models and identifies a common channel through which productivity shocks are magnified across a variety of matching models. Other chapters have been extended and refined. For example, there is new material on heterogeneous beliefs in both complete and incomplete markets models; and there is a deeper account of forces that shape aggregate labor supply elasticities in lifecycle models.

The book is suitable for first- and second-year graduate courses in macroeconomics. Most chapters conclude with exercises; many exercises and examples use Matlab or Python computer programming languages.

Acknowledgments xxi
Preface to the fourth edition xxiii
Recursive Methods
xxiii
Dynamics
xxiii
Philosophy
xxiv
Changes in the fourth edition
xxv
New chapters
xxv
Ideas
xxvi
Theory and evidence
xxviii
Micro foundations
xxix
Road map
xxx
Alternative uses of the book
xxxiv
Computer programs
xxxv
Notation
xxxv
Brief history of the notion of the state
xxxvi
Part I: Imperialism of Recursive Methods
1 Overview
3(26)
1.1 Warning
3(1)
1.2 A common ancestor
3(1)
1.3 The savings problem
4(12)
1.3.1 Linear 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
16(13)
1.4.1 Dynamic programming and the Lucas Critique
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(76)
2.1 Two workhorses
29(1)
2.2 Markov chains
29(12)
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
41(1)
2.4 Stochastic linear difference equations
42(11)
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
53(2)
2.5.1 Multiple regressors
2.6 Estimation of model parameters
55(2)
2.7 The Kalman filter
57(4)
2.8 Estimation again
61(1)
2.9 Vector auto-regressions and the Kalman filter
62(2)
2.9.1 Conditioning on the semi-infinite past of y
2.9.2 A time-invariant VAR
2.9.3 Interpreting VARs
2.10 Applications of the Kalman filter
64(4)
2.10.1 Muth's reverse engineering exercise
2.10.2 Jovanovic's application
2.11 The spectrum
68(4)
2.11.1 Examples
2.12 Example: The LQ permanent income model
72(10)
2.12.1 Another representation
2.12.2 Debt dynamics
2.12.3 Two classic examples
2.12.4 Spreading consumption cross section
2.12.5 Invariant subspace approach
2.13 Concluding remarks
82(1)
A Linear difference equations
82(3)
2.A.1 A first-order difference equation
2.A.2 A second-order difference equation
Exercises
85(20)
3 Dynamic Programming
105(10)
3.1 Sequential problems
105(7)
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
112(2)
3.3 Concluding remarks
114(1)
Exercise
4 Practical Dynamic Programming
115(14)
4.1 The curse of dimensionality
115(1)
4.2 Discrete-state dynamic programming
115(2)
4.3 Bookkeeping
117(1)
4.4 Application of Howard improvement algorithm
118(2)
4.5 Numerical implementation
120(1)
4.5.1 Modified policy iteration
4.6 Sample Bellman equations
121(3)
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
124(4)
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
128(1)
5 Linear Quadratic Dynamic Programming
129(28)
5.1 Introduction
129(1)
5.2 The optimal linear regulator problem
130(3)
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
133(2)
5.3.1 Discussion of certainty equivalence
5.4 Shadow prices in the linear regulator
135(3)
5.4.1 Stability
5.5 A Lagrangian formulation
138(4)
5.6 The Kalman filter again
142(2)
5.7 Concluding remarks
144(1)
A Matrix formulas
144(1)
Exercises
145(12)
6 Search and Unemployment
157(68)
6.1 Introduction
157(1)
6.2 Preliminaries
158(3)
6.2.1 Nonnegative random variables
6.2.2 Mean-preserving spreads
6.3 McCall's model of intertem-poral job search
161(10)
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
171(2)
6.5 A model of career choice
173(4)
6.6 Offer distribution unknown
177(5)
6.7 An equilibrium price distribution
182(6)
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
188(9)
6.8.1 Recursive formulation and solution
6.8.2 Endogenous statistics
6.9 A longer horizon version of Jovanovic's model
197(3)
6.9.1 The Bellman equations
6.10 Concluding remarks
200(1)
A More numerical dynamic programming
201(3)
6.A.1 Example 4: search
6.A.2 Example 5: a Jovanovic model
Exercises
204(21)
Part III: Competitive Equilibria and Applications
7 Recursive Competitive Equilibrium: I
225(24)
7.1 An equilibrium concept
225(1)
7.2 Example: adjustment costs
226(5)
7.2.1 A planning problem
7.3 Recursive competitive equilibrium
231(1)
7.4 Equilibrium human capital accumulation
232(2)
7.4.1 Planning problem
7.4.2 Decentralization
7.5 Equilibrium occupational choice
234(4)
7.5.1 A planning problem
7.5.2 Decentralization
7.6 Markov perfect equilibrium
238(2)
7.6.1 Computation
7.7 Linear Markov perfect equilibria
240(4)
7.7.1 An example
7.8 Concluding remarks
244(1)
Exercises
244(5)
8 Equilibrium with Complete Markets
249(82)
8.1 Time 0 versus sequential trading
249(1)
8.2 The physical setting: preferences and endowments
249(2)
8.3 Alternative trading arrangements
251(2)
8.3.1 History dependence
8.4 Pareto problem
253(2)
8.4.1 Time invariance of Pareto weights
8.5 Time 0 trading: Arrow-Debreu securities
255(4)
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
259(4)
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
263(3)
8.7.1 Pricing redundant assets
8.7.2 Riskless console
8.7.3 Riskless strips
8.7.4 Tail assets
8.7.5 One-period returns
8.8 Sequential trading
266(8)
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
274(6)
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
280(3)
8.10.1 Arbitrage-free pricing
8.11 Term structure of yields on risk-free claims
283(2)
8.11.1 Constructing yields
8.12 Recursive version of Pareto problem
285(2)
8.13 Concluding remarks
287(2)
Appendices: Departures from key assumptions
289(15)
A Heterogenous discounting
289(1)
B Heterogenous beliefs
290(5)
8.B.1 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
295(37)
8.C.1 An example economy
8.C.2 Asset payoff correlated with i.i.d. aggregate endowment
8.C.3 Beneficial market incompleteness
Exercises
304(27)
9 Overlapping Generations
331(48)
9.1 Endowments and preferences
332(1)
9.2 Time 0 trading
332(10)
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
342(1)
9.4 Money
342(3)
9.4.1 Computing more equilibria with valued fiat currency
9.4.2 Equivalence of equilibria
9.5 Deficit finance
345(3)
9.5.1 Steady states and the Laffer curve
9.6 Equivalent setups
348(3)
9.6.1 The economy
9.6.2 Growth
9.7 Optimality and the existence of monetary equilibria
351(8)
9.7.1 Balasko-Shell criterion for optimality
9.8 Within-generation heterogeneity
359(5)
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
364(2)
9.10 Concluding remarks
366(1)
Exercises
366(13)
10 Ricardian Equivalence
379(12)
10.1 Borrowing limits and Ricardian equivalence
379(1)
10.2 Infinitely lived agent economy
380(3)
10.2.1 Optimal consumption/savings decision when bt+1 > or = to 0
10.2.2 Optimal consumption/savings decision when bt+1 > or = to bt+1
10.3 Government finance
383(4)
10.3.1 Effect on household
10.4 Linked generations interpretation
387(1)
10.5 Concluding remarks
388(3)
11 Fiscal Policies in a Growth Model
391(80)
11.1 Introduction
391(1)
11.2 Economy
392(2)
11.2.1 Preferences, technology, information
11.2.2 Components of a competitive equilibrium
11.3 The term structure of interest rates
394(1)
11.4 Digression: sequential version of government budget constraint
395(4)
11.4.1 Irrelevance of maturity structure of government debt
11.5 Competitive equilibria with distorting taxes
399(4)
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
403(6)
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
409(1)
11.8 Effects of taxes on equilibrium allocations and prices
410(1)
11.9 Transition experiments with inelastic labor supply
411(7)
11.10 Linear approximation
418(8)
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
426(4)
11.12 Elastic labor supply
430(6)
11.12.1 Steady-state calculations
11.12.2 Some experiments
11.13 A two-country model
436(11)
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
447(1)
A Log linear approximations
448(1)
Exercises
449(22)
12 Recursive Competitive Equilibrium: II
471(32)
12.1 Endogenous aggregate state variable
471(1)
12.2 The stochastic growth model
472(2)
12.3 Lagrangian formulation of the planning problem
474(1)
12.4 Time 0 trading: Arrow-Debreu securities
474(7)
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
481(5)
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
486(2)
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
488(1)
12.8 Recursive formulation of sequential trading
489(4)
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
493(3)
12.9.1 Equilibrium restrictions across decision rules
12.9.2 Using the planning problem
12.10 Concluding remarks
496(1)
A The permanent income model revisited
497(6)
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
503(46)
13.1 Introduction
503(1)
13.2 Euler equations
504(2)
13.3 Martingale theories of consumption and stock prices
506(2)
13.4 Equivalent martingale measure
508(3)
13.5 Equilibrium asset pricing
511(1)
13.6 Stock prices without bubbles
512(2)
13.7 Computing asset prices
514(2)
13.7.1 Example 1: logarithmic preferences
13.7.2 Example 2: finite-state version
13.7.3 Example 3: growth
13.8 Term structure of interest rates
516(3)
13.9 State-contingent prices
519(5)
13.9.1 Insurance premium
13.9.2 Man-made uncertainty
13.9.3 The Modigliani-Miller theorem
13.10 Government debt
524(11)
13.10.1 The Ricardian proposition
13.10.2 No Ponzi schemes
A Harrison-Kreps (1978) heterogeneous beliefs
535(6)
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 Pricing under heterogeneous beliefs
13.A.6 Insufficient funds
B Gaussian asset-pricing model
541(3)
Exercises
544(5)
14 Asset Pricing Empirics
549(82)
14.1 Introduction
549(1)
14.2 Interpretation of risk-aversion parameter
550(2)
14.3 The equity premium puzzle
552(3)
14.4 Market price of risk
555(2)
14.5 Hansen-Jagannathan bounds
557(5)
14.5.1 Law of one price implies that EmR = 1
14.5.2 Inner product representation of price functional
14.5.3 Admissible stochastic discount factors
14.6 Failure of CRRA to attain HJ bound
562(4)
14.7 Non-expected utility
566(9)
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
575(9)
14.8.1 Risk aversion versus model misspecification aversion
14.8.2 Recursive 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
584(3)
14.10 Reverse engineered consumption heterogeneity
587(4)
14.11 Affine risk prices
591(4)
14.11.1 An application
14.11.2 Affine term structure of yields
14.12 Risk-neutral probabilities
595(1)
14.12.1 Asset pricing in a nutshell
14.13 Distorted beliefs
596
14.14 Concluding remarks
59(540)
A Riesz representation theorem
599(2)
B Computing stochastic discount factors
601(1)
C A log normal bond pricing model
602(8)
14.C.1 Slope of yield curve
14.C.2 Backus and Zin's stochastic discount factor
14.C.3 Reverse engineering a stochastic discount factor
Exercises
610(21)
15 Economic Growth
631(30)
15.1 Introduction
631(2)
15.2 The economy
633(2)
15.2.1 Balanced growth path
15.3 Exogenous growth
635(2)
15.4 Externality from spillovers
637(2)
15.5 All factors reproducible
639(4)
15.5.1 One-sector model
15.5.2 Two-sector model
15.6 Research and monopolistic competition
643(5)
15.6.1 Monopolistic competition outcome
15.6.2 Planner solution
15.7 Growth in spite of nonreproducible factors
648(4)
15.7.1 "Core" of capital goods produced without nonreproducible inputs
15.7.2 Research labor enjoying an externality
15.8 Concluding remarks
652(2)
Exercises
654(7)
16 Optimal Taxation with Commitment
661(98)
16.1 Introduction
661(3)
16.2 A nonstochastic economy
664(4)
16.2.1 Government
16.2.2 Household
16.2.3 Firms
16.3 The Ramsey problem
668(1)
16.4 Zero capital tax
669(2)
16.5 Primal approach to the Ramsey problem
671(4)
16.5.1 Constructing the Ramsey plan
16.5.2 Revisiting a zero capital tax
16.6 Taxation of initial capital
675(1)
16.7 Nonzero capital tax due to incomplete taxation
676(2)
16.8 A stochastic economy
678(3)
16.8.1 Government
16.8.2 Household
16.8.3 Firms
16.9 Indeterminacy of debt and capital taxes
681(2)
16.10 A Ramsey plan under uncertainty
683(2)
16.11 Ex ante capital tax varies around zero
685(4)
16.11.1 Sketch of the proof of Proposition 2
16.12 A stochastic economy without capital
689(8)
16.12.1 Computational strategy
16.12.2 More specialized computations
16.12.3 Time consistency
16.13 Examples of labor tax smoothing
697(4)
16.13.1 Example 1: gt = g for all t > or = to 0
16.13.2 Example 2: gt = 0 for t not = to T and nonstochastic gT > 0
16.13.3 Example 3: gt = 0 for t not = to T, and gT is stochastic
16.13.4 Time 0 is special with bo not = to 0
16.14 Lessons for optimal debt policy
701(4)
16.15 Taxation without state-contingent debt
705(12)
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 not = to T, and gT is stochastic
16.16 Nominal debt as state-contingent real debt
717(10)
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 theories of the price level
727(6)
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
733(5)
16.19 Should all taxes be zero?
738(1)
16.20 Concluding remarks
739(2)
Exercises
741(18)
Part IV: Savings Problems and Bewley Models
17 Self-Insurance
759(26)
17.1 Introduction
759(1)
17.2 The consumer's environment
760(1)
17.3 Non-stochastic endowment
761(6)
17.3.1 An ad hoc borrowing constraint: non-negative assets
17.3.2 Example: periodic endowment process
17.4 Quadratic preferences
767(2)
17.5 Stochastic endowment process: i.i.d. case
769(2)
17.6 Stochastic endowment process: general case
771(1)
17.7 Intuition
772(2)
17.8 Endogenous labor supply
774(3)
17.9 Concluding remarks
777(2)
A Supermartingale convergence theorem
779(1)
Exercises
779(6)
18 Incomplete Markets Models
785(54)
18.1 Introduction
785(2)
18.2 A savings problem
787(7)
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
794(1)
18.4 The nonstochastic savings problem when β(1+r) < 1
795(2)
18.5 Borrowing limits: natural and ad hoc
797(3)
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
800(4)
18.7 Computed examples
804(2)
18.8 Several Bewley models
806(1)
18.8.1 Optimal stationary allocation
18.9 A model with capital and private IOUs
807(1)
18.10 Private IOUs only
808(3)
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
811(2)
18.12 Exchange rate indeterminacy
813(2)
18.13 Interest on currency
815(5)
18.13.1 Explicit interest
18.13.2 The upper bound on M/p
18.13.3 A very special case
18.13.4 Implicit interest through deflation
18.14 Precautionary savings
820(2)
18.15 Models with fluctuating aggregate variables
822(5)
18.15.1 Aiyagari's model again
18.15.2 Krusell and Smith's extension
18.16 Concluding remarks
827(1)
Exercises
827(12)
Part V: Recursive Contracts
19 Dynamic Stackelberg Problems
839(18)
19.1 History dependence
839(1)
19.2 The Stackelberg problem
840(3)
19.3 Timing protocol
843(1)
19.4 Recursive formulation
843(4)
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
847(4)
19.5.1 The competitive fringe
19.5.2 The large firm's problem
19.5.3 Numerical example
19.6 Concluding remarks
851(1)
Exercises
852(5)
20 Two Ramsey Problems Revisited
857(14)
20.1 Introduction
857(1)
20.2 The Lucas-Stokey economy
857(7)
20.2.1 Finding 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
864(5)
20.3.1 Recasting 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
869(2)
21 Incentives and Insurance
871(62)
21.1 Insurance with recursive contracts
871(1)
21.2 Basic environment
872(3)
21.3 One-sided no commitment
875(18)
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 continuously differentiable
21.3.6 Many households
21.3.7 An example
21.4 A Lagrangian method
893(4)
21.5 Insurance with asymmetric information
897(12)
21.5.1 Efficiency implies bs-1 > or = to bs,ws-1 < or = to 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 commitment problem
21.5.8 Spreading continuation values
21.5.9 Martingale convergence and poverty
21.5.10 Extension to general equilibrium
21.5.11 Comparison with self-insurance
21.6 Insurance with unobservable storage
909(13)
21.6.1 Feasibility
21.6.2 Incentive compatibility
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
922(1)
A Historical development
922(4)
21.A.1 Spear and Srivastava
21.A.2 Timing
21.A.3 Use of lotteries
Exercises
926(7)
22 Equilibrium without Commitment
933(54)
22.1 Two-sided lack of commitment
933(1)
22.2 A closed system
934(2)
22.3 Recursive formulation
936(2)
22.4 Equilibrium consumption
938(6)
22.4.1 Consumption 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 division of the gains
944(1)
22.6 Consumption distribution
945(3)
22.6.1 Asymptotic distribution
22.6.2 Temporary imperfect risk sharing
22.6.3 Permanent imperfect risk sharing
22.7 Alternative recursive formulation
948(2)
22.8 Pareto frontier revisited
950(5)
22.8.1 Values are continuous in implicit consumption
22.8.2 Differentiability of the Pareto frontier
22.9 Continuation values a la Kocherlakota
955(4)
22.9.1 Asymptotic distribution is nondegenerate for imperfect risk sharing (except when S = 2)
22.9.2 Continuation values do not always respond to binding participation constraints
22.10 A two-state example: amnesia overwhelms memory
959(6)
22.10.1 Pareto frontier
22.10.2 Interpretation
22.11 A three-state example
965(9)
22.11.1 Perturbation of parameter values
22.11.2 Pareto frontier
22.12 Empirical motivation
974(1)
22.13 Generalization
974(1)
22.14 Decentralization
975(1)
22.15 Endogenous borrowing constraints
976(3)
22.16 Concluding remarks
979(1)
Exercises
980(7)
23 Optimal Unemployment Insurance
987(24)
23.1 History-dependent unemployment insurance
987(1)
23.2 A one-spell model
988(9)
23.2.1 The autarky problem
23.2.2 Unemployment insurance with full information
23.2.3 The incentive problem
23.2.4 Unemployment insurance with asymmetric information
23.2.5 Computed example
23.2.6 Computational details
23.2.7 Interpretations
23.2.8 Extension: an on-the-job tax
23.2.9 Extension: intermittent unemployment spells
23.3 A multiple-spell model with lifetime contracts
997(8)
23.3.1 The setup
23.3.2 A recursive lifetime contract
23.3.3 Compensation dynamics when unemployed
23.3.4 Compensation dynamics while employed
23.3.5 Summary
23.4 Concluding remarks
1005(1)
Exercises
1005(6)
24 Credible Government Policies: I
1011(48)
24.1 Introduction
1011(2)
24.1.1 Diverse sources of history dependence
24.2 One-period economy
1013(3)
24.2.1 Competitive equilibrium
24.2.2 Ramsey problem
24.2.3 Nash equilibrium
24.3 Nash and Ramsey outcomes
1016(4)
24.3.1 Taxation example
24.3.2 Black-box example with discrete choice sets
24.4 Reputational mechanisms: general idea
1020(6)
24.4.1 Dynamic programming squared
24.4.2 Etymology of 'dynamic programming squared'
24.5 The infinitely repeated economy
1026(3)
24.5.1 A strategy profile implies a history and a value
24.5.2 Recursive formulation
24.6 Subgame perfect equilibrium (SPE)
1029(2)
24.7 Examples of SPE
1031(3)
24.7.1 Infinite repetition of one-period Nash equilibrium
24.7.2 Supporting better outcomes with trigger strategies
24.7.3 When reversion to Nash is not bad enough
24.8 Values of all SPEs
1034(2)
24.8.1 Basic idea of dynamic programming squared
24.9 APS machinery
1036(3)
24.10 Self-enforcing SPE
1039(1)
24.10.1 The quest for something worse than repetition of Nash outcome
24.11 Recursive strategies
1040(3)
24.12 Examples of SPE with recursive strategies
1043(4)
24.12.1 Infinite repetition of Nash outcome
24.12.2 Infinite repetition of a better-than-Nash outcome
24.12.3 Something worse: a stick-and-carrot strategy
24.13 Best and worst SPE values
1047(2)
24.13.1 When v1 is outside the candidate set
24.14 Examples: alternative ways to achieve the worst
1049(4)
24.14.1 Attaining the worst, method 1
24.14.2 Attaining the worst, method 2
24.14.3 Attaining the worst, method 3
24.14.4 Numerical example
24.15 Interpretations
1053(1)
24.16 Extensions
1054(1)
Exercises
1054(5)
25 Credible Government Policies: II
1059(24)
25.1 History-dependent government policies
1059(1)
25.2 The setting
1060(3)
25.2.1 Household problem
25.2.2 Government
25.2.3 Analysis of household's problem
25.2.4 0t+1 as intermediating variable
25.3 Recursive approach to Ramsey problem
1063(5)
25.3.1 Subproblem 1: Continuation Ramsey problem
25.3.2 Subproblem 2: Ramsey problem
25.3.3 Finding set Ω
25.3.4 An example
25.4 Chang's formulation
1068(1)
25.4.1 Competitive equilibrium
25.5 Inventory of key objects
1069(3)
25.6 Analysis
1072(6)
25.6.1 Notation
25.6.2 An operator
25.7 Sustainable plans
1078(3)
25.8 Concluding remarks
1081(2)
26 Two Topics in International Trade
1083(40)
26.1 Two dynamic contracting problems
1083(1)
26.2 Moral hazard and difficult enforcement
1084(10)
26.2.1 Autarky
26.2.2 Investment with full insurance
26.2.3 Limited commitment and unobserved investment
26.2.4 Optimal capital outflows under distress
26.3 Gradualism in trade policy
1094(21)
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 Welfare 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
1115(1)
26.5 Concluding remarks
1116(1)
A Computations for Atkeson's model
1117(2)
Exercises
1119(4)
Part VI: Classical Monetary and Labor Economics
27 Fiscal-Monetary Theories of Inflation
1123(48)
27.1 The issues
1123(1)
27.2 A shopping time monetary economy
1124(8)
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 monetary doctrines
1132(11)
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 quantity" 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 price level
27.3.10 Exchange rate indeterminacy
27.3.11 Determinacy of the exchange rate retrieved
27.4 An example of exchange rate (in)determinacy
1143(5)
27.4.1 Trading before sunspot realization
27.4.2 Fiscal 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
1148(5)
27.5.1 Economic environment
27.5.2 Household's optimization problem
27.5.3 Ramsey plan
27.6 Time consistency of monetary policy
1153(10)
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
1163(1)
Exercises
1164(7)
28 Credit and Currency
1171(36)
28.1 Credit and currency with long-lived agents
1171(1)
28.2 Preferences and endowments
1172(1)
28.3 Complete markets
1172(5)
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
1177(2)
28.5 Townsend's "turnpike" interpretation
1179(3)
28.6 The Friedman rule
1182(3)
28.6.1 Welfare
28.7 Inflationary finance
1185(4)
28.8 Legal restrictions
1189(4)
28.9 A two-money model
1193(3)
28.10 A model of commodity money
1196(4)
28.10.1 Equilibrium
28.10.2 Virtue of fiat money
28.11 Concluding remarks
1200(1)
Exercises
1200(7)
29 Equilibrium Search, Matching, and Lotteries
1207(62)
29.1 Introduction
1207(1)
29.2 An island model
1208(5)
29.2.1 A single market (island)
29.2.2 The aggregate economy
29.3 A matching model
1213(7)
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
1220(7)
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
1227(3)
29.6 Lotteries for households versus lotteries for firms
1230(4)
29.6.1 An aggregate production function
29.6.2 Time-varying capacity utilization
29.7 Employment effects of layoff taxes
1234(14)
29.7.1 A model of employment lotteries with layoff 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
1248(7)
29.8.1 Monetary equilibria
29.8.2 Welfare
29.9 Concluding remarks
1255(2)
Exercises
1257(12)
30 Matching Models Mechanics
1269(46)
30.1 Introduction
1269(2)
30.2 Fundamental surplus
1271(12)
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
1283(8)
30.3.1 Hall's sticky wage
30.3.2 Hagedorn and Manovskii's high value of leisure
30.3.3 Hall and Milgrom's alternating-offer bargaining
30.3.4 Matching and bargaining protocols in a DSGE model
30.4 Overlapping generations in one matching function
1291(12)
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
1303(9)
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 Concluding remarks
1312(3)
31 Foundations of Aggregate Labor Supply
1315(58)
31.1 Introduction
1315(2)
31.2 Equivalent allocations
1317(5)
31.2.1 Choosing career length
31.2.2 Employment lotteries
31.3 Taxation and social security
1322(6)
31.3.1 Taxation
31.3.2 Social security
31.4 Earnings-experience profiles
1328(4)
31.4.1 Time averaging
31.4.2 Employment lotteries
31.4.3 Prescott tax and transfer scheme
31.4.4 No discounting now matters
31.5 Intensive margin
1332(5)
31.5.1 Employment lotteries
31.5.2 Time averaging
31.5.3 Prescott taxation
31.6 Ben-Porath human capital
1337(6)
31.6.1 Time averaging
31.6.2 Employment lotteries
31.6.3 Prescott taxation
31.7 Earnings shocks
1343(4)
31.7.1 Interpretation of wealth and substitution effects
31.8 Time averaging in a Bewley model
1347(10)
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
1357(7)
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
1364(1)
31.11 No pillars at intensive margin
1364(5)
31.11.1 Special example of high elasticity at intensive margin
31.11.2 Fragility of the special example
31.12 Concluding remarks
1369(4)
Part VII: Technical Appendices
A Functional Analysis
1373(12)
A.1 Metric spaces and operators
1373(6)
A.2 Discounted dynamic programming
1379(6)
A.2.1 Policy improvement algorithm
A.2.2 A search problem
B Linear Projections and Hidden Markov Models
1385(6)
B.1 Linear projections
1385(2)
B.2 Hidden Markov models
1387(1)
B.3 Nonlinear filtering
1388(3)
References 1391(34)
Subject Index 1425(6)
Author Index 1431(6)
Matlab Index 1437