Atsushi KajiiBack to index

  • Decentralizability of Efficient Allocations with Heterogenous Forecasts

    Abstract

    Do price forecasts of rational economic agents need to coincide in perfectly competitive complete markets in order for markets to allocate resources efficiently? To address this question, we define an efficient temporary equilibrium (ETE) within the framework of a two period economy. Although an ETE allocation is intertemporally efficient and is obtained by perfect competition, it can arise without the agents forecasts being coordinated on a perfect foresight price. We show that there is a one dimensional set of such Pareto efficient allocations for generic endowments.  

     

    Introduction

    Intertemporal trade in complete markets is known to achieve Pareto efficiency when the price forecasts of agents coincide and are correct. The usual justification for this coincidence of price forecasts is that if agents understand the market environment perfectly,  they ought to reach the same conclusions, and hence in particular, their price forecasts must coincide. But it is against the spirit of perfect competition to require that agents should understand the market environment beyond the market prices they commonly observe; we therefore study intertemporal trade without requiring that price forecasts of heterogenous agents coincide.  

     

    WP031

  • Efficiency, Quality of Forecasts and Radner Equilibria

    Abstract

    We study a simple two period economy with no uncertainty and complete markets where agents trade based on forecasts about the second period spot price. We propose as our solution concept a set of forecasts with the following properties: there exist (heterogenous) forecasts contained in this set that lead to efficient allocations, the set contains only those forecasts that correspond to some efficient equilibrium, and finally that the forecasts assign positive probability to the actual market clearing spot price. We call such a set of prices an efficient equilibrium with ambiguity, and interpret it as a generalization of Radner equilibrium that delivers efficient allocations under forecasts that possess a self-fulfilling property that is weaker than perfect foresight. 

    Introduction

    Walrasian trade in intertemporal economies require households to forecast prices that will prevail in spot markets at future dates. The ubiquitous nancial equilibrium model that is used to address this aspect of intertemporal economies is the one proposed by Radner (1972) (following Arrow (1963)) and is the bedrock of modern treatments of general equilibrium. This resulting Radner equilibrium (henceforth, RE), postulates that households correctly anticipate all spot prices at future dates; a RE is accordingly an equilibrium with perfect foresight (henceforth, PFE), where the forecasts of heterogenous households are perfectly aligned.

     

     

    WP024

  • Decentralizability of Efficient Allocations with Heterogenous Forecasts

    Abstract

    Do price forecasts of rational economic agents need to coincide in perfectly competitive complete markets in order for markets to allocate resources efficiently? To address this question, we define an efficient temporary equilibrium (ETE) within the framework of a two period economy. Although an ETE allocation is intertemporally efficient and is obtained by perfect competition, it can arise without the agents forecasts being coordinated on a perfect foresight price. We show that there is a one dimensional set of such Pareto efficient allocations for generic endowments.

    Introduction

    Intertemporal trade in complete markets is known to achieve Pareto efficiency when the price forecasts of agents coincide and are correct. The usual justification for this coincidence of price forecasts is that if agents understand the market environment perfectly, they ought to reach the same conclusions, and hence in particular, their forecasts must coincide. But it is against the spirit of perfect competition to require that agents should understand the market environment beyond the market prices they commonly observe; we therefore study intertemporal trade without requiring that price forecasts of heterogenous agents coincide.

     

     

    WP016

  • Notes on “Refinements and Higher Order Beliefs”

    The abstract of our 1997 survey paper Kajii and Morris (1997b) on "Refinements and Higher Order Beliefs" reads:

     

    This paper presents a simple framework that allows us to survey and relate some different strands of the game theory literature. We describe a “canonical” way of adding incomplete information to a complete information game. This framework allows us to give a simple “complete theory” interpretation (Kreps 1990) of standard normal form refinements such as perfection, and to relate refinements both to the “higher order beliefs literature” (Rubinstein 1989; Monderer and Samet 1989; Morris, Rob and Shin 1995; Kajii and Morris 1997a) and the “payoff uncertainty approach” (Fudenberg, Kreps and Levine 1988; Dekel and Fudenberg 1990).

     

    In particular, this paper provided a unified framework to relate the notion of equilibria robust to incomplete information introduced in Kajii and Morris (1997a) [Hereafter, KM1997] to the classic refinements literature. It followed Fudenberg, Kreps and Levine (1988) and Kreps (1990) in relating refinements of Nash equilibria to a "complete theory" where behavior was rationalized by explicit incomplete information about payoffs, rather than depending on action trembles or other exogenous perturbations. It followed Fudenberg and Tirole (1991), chapter 14, in providing a unified treatment of refinements and a literature on higher-order beliefs rather than proposing a particular solution concept.

     

    The primary purpose of the survey paper was to promote the idea of robust equilibria in KM1997 and we did not try to publish it as an independent paper. Since we wrote this paper, there have been many developments in the literature on robust equilibria, fortunately. But there has been little work emphasizing a unified perspective, and consequently this paper seems more relevant than ever. We are therefore very happy to publish it twenty years later. We provide some notes in the following on relevant developments in the literature and how they relate to the survey. These notes assume familiarity with the basic concepts introduced in the survey paper and KM1997.

     

     

    WP006

  • Optimal taxation and debt with uninsurable risks to human capital accumulation

    Abstract

    We consider an economy where individuals face uninsurable risks to their human capital accumulation, and analyze the optimal level of linear taxes on capital and labor income together with the optimal path of government debt. We show that in the presence of such risks it is beneficial to tax both labor and capital and to issue public debt. We also assess the quantitative importance of these findings, and show that the benefits of government debt and capital taxes both increase with the magnitude of idiosyncratic risks and the degree of relative risk aversion.

    Introduction

    Human capital is an important component of wealth both at the individual and aggregate level, and its role has been investigated in various fields in economics. In public finance, Jones, Manuelli and Rossi (1997) show that the zero-capital-tax result of Chamley (1986) and Judd (1985)1 can be strengthened if human capital accumulation is explicitly taken into account. Specifically, they demonstrate that, in a deterministic economy with human capital accumulation, in the long run not only capital but also labor income taxes should be zero, hence the government must accumulate wealth - that is, public debt be negative - to finance its expenditure.

  • Constrained Inefficiency and Optimal Taxation with Uninsurable Risks

    Abstract

    When individuals’ labor and capital income are subject to uninsurable idiosyncratic risks, should capital and labor be taxed, and if so how? In a two period general equilibrium model with production, we derive a decomposition formula of the welfare effects of these taxes into insurance and distribution effects. This allows us to determine how the sign of the optimal taxes on capital and labor depend on the nature of the shocks, the degree of heterogeneity among consumers’ income as well as on the way in which the tax revenue is used to provide lump sum transfers to consumers. When shocks affect primarily labor income and heterogeneity is small, the optimal tax on capital is positive. However in other cases a negative tax on capital is welfare improving. (JEL codes: D52, H21. Keywords: optimal linear taxes, incomplete markets, constrained efficiency)

    Introduction

    The main objective of this paper is to investigate the welfare effects of investment and labor income taxes in a two period production economy with uninsurable background risk. More precisely, we examine whether the introduction of linear, distortionary taxes or subsidies on labor income and/or on the returns from savings are welfare improving and what is then the optimal sign of such taxes. This amounts to studying the Ramsey problem in a general equilibrium set-up. We depart however from most of the literature on the subject for the fact that we consider an environment with no public expenditure, where there is no need to raise tax revenue. Nonetheless, optimal taxes are typically nonzero; even distortionary taxes can improve the allocation of risk in the face of incomplete markets. Then the question is which production factor should be taxed: we want to identify the economic properties which determine the signs of the optimal taxes on production factors.

  • Constrained Inefficiency and Optimal Taxation with Uninsurable Risks

    Abstract

    When individuals’ labor and capital income are subject to uninsurable idiosyncratic risks, should capital and labor be taxed, and if so how? In a two period general equilibrium model with production, we derive a decomposition formula of the welfare effects of these taxes into insurance and distribution effects. This allows us to determine how the sign of the optimal taxes on capital and labor depend on the nature of the shocks, the degree of heterogeneity among consumers’ income as well as on the way in which the tax revenue is used to provide lump sum transfers to consumers. When shocks affect primarily labor income and heterogeneity is small, the optimal tax on capital is positive. However in other cases a negative tax on capital is welfare improving. (JEL codes: D52, H21. Keywords: optimal linear taxes, incomplete markets, constrained efficiency)

    Introduction

    The main objective of this paper is to investigate the effects and the optimal taxation of investment and labor income in a two period production economy with uninsurable background risk. More precisely, we examine whether the introduction of linear, distortionary taxes or subsidies on labor income and/or on the returns from savings are welfare improving and what is then the optimal sign of such taxes. This amounts to studying the Ramsey problem in a general equilibrium set-up. We depart however from most of the literature on the subject for the fact that we consider an environment with no public expenditure, where there is no need to raise tax revenue. Nonetheless, optimal taxes are typically nonzero; even distortionary taxes can improve the allocation of risk in the face of incomplete markets. Then the question is which production factor should be taxed: we want to identify the economic properties which determine the signs of the optimal taxes on production factors.

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