Shurojit Chatterji ワーキングペーパー一覧に戻る

  • Rich by Accident: the Second Welfare Theorem with a Redundant Asset Under Imperfect Foresight

    Abstract

    We consider a multiperiod (T-period) model with no uncertainty where short term bonds co-exist with a long term bond. Markets are complete with just the short term bonds so that under the usual hypothesis of perfect foresight, the long term bond is redundant by no arbitrage in that it has no allocational implications. We dispense with perfect foresight, derive appropriate no arbitrage conditions and show that the presence of the long term bond has significant allocational implications. Specifically, in the model with just the short term bond, we show that a T dimensional subset of efficient allocations can arise as Walrasian equilibria whereas the dimension of efficient allocations is one less than the number of households (assumed to be much larger than T). In the model with the both types of bonds essentially all efficient allocations can arise as Walrasian equilibria; minute errors in forecasting prices can generate all income transfers that are consistent with efficiency. We argue that the beneficiaries of such unanticipated income transfers are determined not by the superiority of forecasts but rather by accident.

     

    Introduction

    What allocational role might a redundant financial asset play in an intertemporal Walrasian setting? Traditional wisdom would suggest none, since by definition, a redundant financial asset can be replicated by trading other assets dynamically at market prices so that any trader is indifferent between holding it and ignoring it, and so its presence in no way alters the possibilities of income transfers across periods/states. But notice that this conclusion might not be valid if the market prices are not correctly anticipated. That is, this conclusion relies entirely on the feature that the axiom of perfect foresight is built into the particular equilibrium concept, Radner equilibrium, used in the analysis. We dispense with perfect foresight and show that essentially all intertemporally efficient allocations can arise as Walrasian equilibria when a redundant asset is traded.

     

    WP048

     

  • On the Welfare Role of Redundant Assets with Heterogeneous Forecasts

    Abstract

    We study a multiperiod model with a nominal bond that matures in one period and identify the set of efficient allocations that can be sustained as Walrasian equilibria with heterogeneous forecasts. We next add a long maturity bond, which under perfect foresight would be a redundant asset, and show that it fundamentally expands the set of efficient allocations that can be sustained as Walrasian equilibria. Indeed all wealth transfers compatible with efficiency can arise endogenously. The key feature driving this conclusion are forecasting errors, which lead to ex post arbitrage opportunities that induce these income transfers. (JEL classification numbers: D51, D53, D61)

     

    Introduction

    No arbitrage conditions play a fundamental role in the way assets are priced and therefore are instrumental in deciding the set of allocations that can be generated by Walrasian markets. The axiom of perfect foresight is built into the methodology most frequently used to price assets. This paper investigates the allocational implications of relaxing perfect foresight in a model where a short term bond coexists with a longer maturity bond, where the latter under perfect foresight would be a redundant asset. Forecasts are required to satisfy no arbitrage conditions so that market equilibrium is well defined in each period. However, due to errors in forecasting, there may exist arbitrage possibilities in an ex post sense, which allows the presence of the long term bond to expand significantly the set of intertemporally efficient allocations that can be sustained as Walrasian equilibria.

     

    WP046

  • 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

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