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Journal ArticleDOI

The risk-free rate in heterogeneous-agent incomplete-insurance economies

01 Sep 1993-Journal of Economic Dynamics and Control (North-Holland)-Vol. 17, pp 953-969
TL;DR: In this paper, the authors construct an economy where agents experience uninsurable idiosyncratic endowment shocks and smooth consumption by holding a risk-free asset, and calibrate the economy and characterize equilibria computationally.
About: This article is published in Journal of Economic Dynamics and Control.The article was published on 1993-09-01 and is currently open access. It has received 1293 citations till now. The article focuses on the topics: Risk-free interest rate & Interest rate.

Summary (1 min read)

2. Environment and Arrangement

  • The particular arrangement considered allows each agent to smooth consumption by holding a single asset I will use the credit balance interpretation.
  • An agent's decision problem will be described at a more technical level after setting down some notation.

Notation:

  • The decision rule a(x;q) and the transition probabilities help define a ti-ansition function P, P: S'<SxR++ -+ [0,1].
  • In the paper the dependence of the decision rules and the transition function on q will often be suppressed for notational convenience.

5. Results

  • The sensitivity of excess demand to grid size, the number of grid points and the criteria for approximate market clearing has been examined.
  • The corresponding annual interest rates are between 1.18% and 1.16%.
  • Excess demand is not sensitive to the number of grid points, other things equal.

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Citations
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Journal ArticleDOI
TL;DR: In this article, the authors present a qualitative and quantitative analysis of the standard growth model modified to include precautionary saving motives and liquidity constraints, and address the impact on the aggregate saving rate, the importance of asset trading to individuals, and the relative inequality of wealth and income distributions.
Abstract: We present a qualitative and quantitative analysis of the standard growth model modified to include precautionary saving motives and liquidity constraints. We address the impact on the aggregate saving rate, the importance of asset trading to individuals, and the relative inequality of wealth and income distributions.

2,738 citations

Journal ArticleDOI
TL;DR: In this paper, a calibrated version of the stochastic growth model with partially uninsurable idiosyncratic risk and movements in aggregate productivity is used to analyze how movements in the distribution of income and wealth affect the macroeconomy.
Abstract: How do movements in the distribution of income and wealth affect the macroeconomy? We analyze this question using a calibrated version of the stochastic growth model with partially uninsurable idiosyncratic risk and movements in aggregate productivity. Our main finding is that, in the stationary stochastic equilibrium, the behavior of the macroeconomic aggregates can be almost perfectly described using only the mean of the wealth distribution. This result is robust to substantial changes in both parameter values and model specification. Our benchmark model, whose only difference from the representative‐agent framework is the existence of uninsurable idiosyncratic risk, displays far less cross‐sectional dispersion and skewness in wealth than U.S. data. However, an extension that relies on a small amount of heterogeneity in thrift does succeed in replicating the key features of the wealth data. Furthermore, this extension features aggregate time series that depart significantly from permanent income behavior.

2,205 citations

Book
01 Jan 2000
TL;DR: In this paper, an introduction to recursive methods for dynamic macroeconomics is presented, including standard applications such as asset pricing, and advanced material, including analyses of reputational mechanisms and contract design.
Abstract: Recursive methods offer a powerful approach in dynamic macroeconomics. This book contains both an introduction to recursive tools, including standard applications such as asset pricing, and advanced material, including analyses of reputational mechanisms and contract design. The tools are presented with enough technical sophistication to get the reader started working on practical problems. When numerical simulations are called for, the book provides suggestions for how to proceed, as well as references for further reading. The applications cover many substantive issues in macroeconomics, such as equilibrium asset prices, market incompleteness, wealth distribution, fiscal-monetary theories of inflation, government debt, optimal labour and capital taxation, time consistency and credible government policies, optimal social insurance, economic growth and labour market dynamics.

1,685 citations

ReportDOI
TL;DR: In this paper, the authors formalize the concepts of self-productivity and complementarity of human capital investments and use them to explain the evidence on skill formation, and provide a theoretical framework for interpreting the evidence from a vast empirical literature, for guiding the next generation of empirical studies, and for formulating policy.
Abstract: This paper presents economic models of child development that capture the essence of recent findings from the empirical literature on skill formation. The goal of this essay is to provide a theoretical framework for interpreting the evidence from a vast empirical literature, for guiding the next generation of empirical studies, and for formulating policy. Central to our analysis is the concept that childhood has more than one stage. We formalize the concepts of self-productivity and complementarity of human capital investments and use them to explain the evidence on skill formation. Together, they explain why skill begets skill through a multiplier process. Skill formation is a life cycle process. It starts in the womb and goes on throughout life. Families play a role in this process that is far more important than the role of schools. There are multiple skills and multiple abilities that are important for adult success. Abilities are both inherited and created, and the traditional debate about nature versus nurture is scientiÞcally obsolete. Human capital investment exhibits both self-productivity and complementarity. Skill attainment at one stage of the life cycle raises skill attainment at later stages of the life cycle (self-productivity). Early investment facilitates the productivity of later investment (complementarity). Early investments are not productive if they are not followed up by later investments (another aspect of complementarity). This complementarity explains why there is no equity-efficiency trade-off for early investment. The returns to investing early in the life cycle are high. Remediation of inadequate early investments is difficult and very costly as a consequence of both self-productivity and complementarity.

1,585 citations

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TL;DR: In this article, a simple New Keynesian-style model of debt-driven slumps is presented, situations in which an overhang of debt on the part of some agents, who are forced into rapid deleveraging, is depressing aggregate demand.
Abstract: In this paper we present a simple New Keynesian-style model of debt-driven slumps – that is, situations in which an overhang of debt on the part of some agents, who are forced into rapid deleveraging, is depressing aggregate demand. Making some agents debt-constrained is a surprisingly powerful assumption: Fisherian debt deflation, the possibility of a liquidity trap, the paradox of thrift, a Keynesiantype multiplier, and a rationale for expansionary fiscal policy all emerge naturally from the model. We argue that this approach sheds considerable light both on current economic difficulties and on historical episodes, including Japan’s lost decade (now in its 18th year) and the Great Depression itself.

1,249 citations

References
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Journal ArticleDOI
TL;DR: This paper showed that an equilibrium model which is not an Arrow-Debreu economy will be the one that simultaneously rationalizes both historically observed large average equity return and the small average risk-free return.

6,141 citations

Journal ArticleDOI
TL;DR: In this article, the authors examine the stochastic behavior of equilibrium asset prices in a one-good, pure exchange economy with identical consumers, and derive a functional equation for price as a function of the physical state of the economy.
Abstract: THIS PAPER IS A THEORETICAL examination of the stochastic behavior of equilibrium asset prices in a one-good, pure exchange economy with identical consumers. The single good in this economy is (costlessly) produced in a number of different productive units; an asset is a claim to all or part of the output of one of these units. Productivity in each unit fluctuates stochastically through time, so that equilibrium asset prices will fluctuate as well. Our objective will be to understand the relationship between these exogenously determined productivity changes and market determined movements in asset prices. Most of our attention will be focused on the derivation and application of a functional equation in the vector of equilibrium asset prices, which is solved for price as a function of the physical state of the economy. This equation is a generalization of the Martingale property of stochastic price sequences, which serves in practice as the defining characteristic of market "efficiency," as that term is used by Fama [7] and others. The model thus serves as a simple context for examining the conditions under which a price series' failure to possess the Martingale property can be viewed as evidence of non-competitive or "irrational" behavior. The analysis is conducted under the assumption that, in Fama's terms, prices "fully reflect all available information," an hypothesis which Muth [13] had earlier termed "rationality of expectations." As Muth made clear, this hypothesis (like utility maximization) is not "behavioral": it does not describe the way agents think about their environment, how they learn, process information, and so forth. It is rather a property likely to be (approximately) possessed by the outcome of this unspecified process of learning and adapting. One would feel more comfortable, then, with rational expectations equilibria if these equilibria were accompanied by some form of "stability theory" which illuminated the forces which move an economy toward equilibrium. The present paper also offers a convenient context for discussing this issue. The conclusions of this paper with respect to the Martingale property precisely replicate those reached earlier by LeRoy (in [10] and [11]), and not surprisingly, since the economic reasoning in [10] and the present paper is the same. The

4,860 citations

Book
01 Jan 1989
TL;DR: In this article, a deterministic model of optimal growth is proposed, and a stochastic model is proposed for optimal growth with linear utility and linear systems and linear approximations.
Abstract: I. THE RECURSIVE APPROACH 1. Introduction 2. An Overview 2.1 A Deterministic Model of Optimal Growth 2.2 A Stochastic Model of Optimal Growth 2.3 Competitive Equilibrium Growth 2.4 Conclusions and Plans II. DETERMINISTIC MODELS 3. Mathematical Preliminaries 3.1 Metric Spaces and Normed Vector Spaces 3.2 The Contraction Mapping Theorem 3.3 The Theorem of the Maximum 4. Dynamic Programming under Certainty 4.1 The Principle of Optimality 4.2 Bounded Returns 4.3 Constant Returns to Scale 4.4 Unbounded Returns 4.5 Euler Equations 5. Applications of Dynamic Programming under Certainty 5.1 The One-Sector Model of Optimal Growth 5.2 A "Cake-Eating" Problem 5.3 Optimal Growth with Linear Utility 5.4 Growth with Technical Progress 5.5 A Tree-Cutting Problem 5.6 Learning by Doing 5.7 Human Capital Accumulation 5.8 Growth with Human Capital 5.9 Investment with Convex Costs 5.10 Investment with Constant Returns 5.11 Recursive Preferences 5.12 Theory of the Consumer with Recursive Preferences 5.13 A Pareto Problem with Recursive Preferences 5.14 An (s, S) Inventory Problem 5.15 The Inventory Problem in Continuous Time 5.16 A Seller with Unknown Demand 5.17 A Consumption-Savings Problem 6. Deterministic Dynamics 6.1 One-Dimensional Examples 6.2 Global Stability: Liapounov Functions 6.3 Linear Systems and Linear Approximations 6.4 Euler Equations 6.5 Applications III. STOCHASTIC MODELS 7. Measure Theory and Integration 7.1 Measurable Spaces 7.2 Measures 7.3 Measurable Functions 7.4 Integration 7.5 Product Spaces 7.6 The Monotone Class Lemma

2,991 citations


"The risk-free rate in heterogeneous..." refers background in this paper

  • ...In the tables interest rates (r) are annual rates whereas prices (y) are for model periods....

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Journal ArticleDOI
Philippe Weil1
TL;DR: In this paper, the authors studied the implications of general equilibnum asset pricing of a class of Kreps-Porteus nonexpected utility preferences characterized by a constant intertemporal elasticity of substitution and a constant, but unrelated, coefficient of relative risk aversion.

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"The risk-free rate in heterogeneous..." refers background in this paper

  • ...…typically require high levels of risk aversion to get a large premium on equity, but this also leads to a risk-free rate that is much too large.4 For example, Weil (1989) shows that the risk-free rate rises from about 5% to 18% when the coefficient of relative risk aversion rises from 0 to 20....

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  • ...Subsequent attempts to explain the rate of return observations within the representative-agent structure have been largely unsuccessful [see Weil (1989) for a review]....

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