Arrow-Debreu Economy Research Articles

Market selection and learning under model misspecification

This paper studies market selection in an Arrow-Debreu economy with complete markets where agents learn over misspecified models. In this setting, standard Bayesian learning loses its formal justification and biased learning processes may provide a selection advantage. Studying two cases of model misspecification and four learning processes, our analysis reveals that, differently from correctly specified settings, the ecology of traders populating the market crucially affects selection dynamics and, thus, long-run asset valuation. In fact, model misspecification implies a general difficulty in ranking learning behaviors with respect to their survival prospects. For instance, prediction averaging shows an advantage when the true data generating process belongs to the same family of models that agents use to learn. This advantage partially disappears when the true model belongs to a more general class, as a trade off emerges between approximating the projection of the true model on the space on which the agents learn and adapting to the part of the true model that cannot be represented in that space. Rules that guarantee survival are possible, but they exploit imitative mechanisms that require information about all the other market participants.

Optimal Risk Sharing in Society

We consider risk sharing among individuals in a one-period setting under uncertainty that will result in payoffs to be shared among the members. We start with optimal risk sharing in an Arrow–Debreu economy, or equivalently, in a Borch-style reinsurance market. From the results of this model we can infer how risk is optimally distributed between individuals according to their preferences and initial endowments, under some idealized conditions. A main message in this theory is the mutuality principle, of interest related to the economic effects of pandemics. From this we point out some elements of a more general theory of syndicates, where in addition, a group of people are to make a common decision under uncertainty. We extend to a competitive market as a special case of such a syndicate.

Tax Revenue Potential and Effort in Ethiopia: a Comparative Analysis of Stochastic Frontier Analysis vs Utility Maximisation Function as a New Measure of Tax Effort

This article tests the new measure of tax efforts following Dalamagas et al (2019) who argued that in the context of the Arrow-Debreu economy, with fixed labour supply and no savings, disposable income is equal to private consumption, a utility function with two arguments, income, and government spending, is maximised concerning direct and indirect tax rates. The optimal level of tax revenue is derived from a utility maximisation process and is shown to be equal to the difference between income and consumption. As a robustness check, the results of the utility maximisation function were compared to the findings of the stochastic frontier model. Each model records very near results for tax effort, tax potential, and tax gaps. The empirical findings revealed that Ethiopia has a large tax gap and poor tax effort, which is primarily due to policy choices and enforcement procedures.

Boltzmann-like income distribution in low and middle income classes: Evidence from the United Kingdom

We elucidate that a Boltzmann-like income distribution will emerge spontaneously in a long-run Arrow–Debreu economy, which is used to describe the well-functioning market economy. The emergence of such an income distribution can be regarded as a result of maximizing the entropy of the long-run Arrow–Debreu economy, which measures the extent of choice-freedom of permissible collective decisions offered to social members. By analyzing household income data of the United Kingdom from 2000 to 2015, we observe that the income structure of a market-economy country consists of three parts: super-low income class (i.e., unemployed households), low- and middle-income class, and top income class. The empirical analyses show that the low- and middle-income class (about 90%∼95% of populations) exactly obeys the Boltzmann-like income distribution. By contrast, top income class and super-low income class undermine the setting for Arrow–Debreu economy, and therefore do not conform to the Boltzmann-like distribution.

Revising the conventional tax‐effort principle

AbstractThe standard methodology on tax‐effort (i.e., the ratio of actual tax revenue to its optimal level) is to run a regression of actual tax revenue on countries’ specific (macroeconomic, demographic, geographical, political, social, and institutional) variables. The resulting predicted (fitted) values are then taken to represent the optimal (desired or maximum) level of tax revenue. The crucial issue of tracing out how the optimal tax revenue should be allocated to the fiscal objectives (equity, efficiency) does not seem to be of any interest to the researchers on tax‐effort. The present paper argues that the standard methodology is not without faults and needs revising. We demonstrate that an optimal tax system can be safely derived from maximizing a utility function with respect to (in)direct tax rates. The manipulation of the first‐order conditions, using a novel mathematical module, leads to an infinite number of optimal direct–indirect tax rates. The selection of the optimal mix of these tax rates is dependent on the country‐specific households’ preferences over equity/efficiency, as they are formulated by voters’ volition in election periods. A simulation procedure helps understanding how the optimal tax revenue is chosen and how it can be optimally allocated to fiscal objectives, in the context of a panel data set including a large number of developed and developing countries. Throughout our text, the optimal tax revenue is defined as the sum of the products of the optimal (in)direct tax rates and their corresponding tax bases. In the simple Arrow–Debreu economy, the above sum is shown to be equal to the difference between income and consumption.

Peer effects and risk sharing in experimental asset markets

We investigate the effect of introducing information about peer portfolios in an experimental Arrow–Debreu economy. Confirming the prediction of a general equilibrium model with inequality averse preferences, we find that peer information leads to reduced variation in payoffs within peer groups. Information also improves risk sharing, as the data suggests that experiencing earnings deviations from peers induces a shift to more balanced portfolios. In a treatment where we highlight the highest earner, we observe a reduction in risk sharing, while highlighting the lowest earner has no effects compared to providing neutral information. Our results indicate that the presence of social information and its framing is an important determinant of equilibrium in financial markets.

On the equivalence of rational expectations equilibrium with perfect Bayesian equilibrium

A sequential variation of the Arrow–Debreu abstract economy is developed to closely capture the timing of moves of the Walrasian general equilibrium model. Instead of inducing a pseudo- game, the extensive form game of our sequential variation is well defined. It is shown that when information is symmetric, Walrasian equilibrium allocations are equivalent to subgame-perfect equilibrium allocations. When information is asymmetric, rational expectations equilibrium allocations are shown to be equivalent to perfect Bayesian equilibrium allocations. These results are useful for understanding and characterizing Walrasian and rational expectations equilibrium allocations.

Quantum Entropy and Accounting

In a previous paper we establish the equality between accounting numbers and information in a classical Arrow-Debreu economy. One of the conditions is complete market, that is, there exists an Arrow-Debreu security for every possible state realization. In this paper, we relax this condition and establish the equality between accounting numbers and information by exploring quantum information and measurement mathematics. In the revised domain expanded relationship, von Neumann entropy replaces Shannon entropy to capture the information effect.

Competitive Equilibrium in Abstract Games: A New Interpretation

The purpose of this paper is to provide an alternative version of a generalized game, slightly different from the one provided in the seminal paper of Arrow and Debreu (1954). In this revised framework, we introduce the concept of a competitive equilibrium and show how it can be applied to a slightly modified prisoners’ dilemma and the traditional model of general equilibrium theory. A significant result that we obtain is that a strategy profile is a competitive equilibrium if and only it is a second period maximizer of every Bergson-Samuelson social welfare function. We prove existence results for the case where all the strategy sets are subsets of Euclidean spaces and for the case where all the strategy sets are non-empty and finite. The Arrow-Debreu economy is introduced in our setting as an illustration of a finite abstract economy where the preferences of the agents are independent of the strategy profile chosen in the initial period. Finally, we suggest a refinement of competitive equilibrium called an optimal competitive equilibrium and study its relationship with competitive equilibrium through some examples.

Competitive Equilibrium in Generalized Games: A New Interpretation

The purpose of this paper is to provide an alternative version of a generalized game, slightly different from the one provided in the seminal paper of Arrow and Debreu (1954). In this revised framework, we introduce the concept of a competitive equilibrium and show how it can be applied to a slightly modified prisoners’ dilemma and the traditional model of general equilibrium theory. We obtain a ‘folk theorem’ for some generalized games which are like repeated non-cooperative games. A significant result that we obtain is that a strategy profile is a competitive equilibrium if and only if it is a second period maximizer of every Bergson–Samuelson social welfare function. We prove existence results for the case where all the strategy sets are subsets of Euclidean spaces and for the case where all the strategy sets are non-empty and finite. The Arrow–Debreu economy is introduced in our setting as an illustration of a finite abstract economy where the preferences of the agents are independent of the strategy profile chosen in the initial period. Finally, we suggest a refinement of competitive equilibrium called an optimal competitive equilibrium and study its relationship with competitive equilibrium through some examples.

A Reconsideration of the Equity Premium Puzzle

This paper develops a tractable asset pricing framework based on an Arrow Debreu economy with heterogeneous agents. The model re-casts a number of well known asset pricing relationships in terms of four underlying variables. The financial relationships studied here are the risk free rate, the market risk premium, a call option, the expected returns of individual securities, and the dividend growth model. The theoretical formulations are used to measure preference parameters in three different ways. The most precise estimates yield a value of relative risk aversion of 1.27, and a time preference discount rate of 3.82% per year.

An Agent-Based Simulation of the Stolper–Samuelson Effect

We demonstrate that agent-based simulations can exhibit results in line with classic macroeconomic theory. In particular, we present an agent-based simulation of an Arrow–Debreu economy that accurately exhibits the Stolper–Samuelson effect as an emergent property. Absent of a Walrasian auctioneer or any other central coordination, we let firm and consumer agents of different types interact in an open, money-driven market. Exogenous preference shocks result in price and wage shifts that are in accordance with the general equilibrium solution, not only qualitatively but also quantitatively with high accuracy. Key to this achievement are three independent measures. First, we overcome the poor input synchronization of conventional price finding heuristics of firms in agent-based models by introducing sensor prices, a novel approach to price finding that decouples information exploitation from information exploration. Second, we improve accuracy and convergence by employing exponential search as exploration algorithm. Third, we normalize prices indirectly by fixing dividends, thereby stabilizing the system’s dynamics.

Spontaneous economic order

This paper provides attempts to formalize Hayek’s notion of spontaneous order within the framework of an Arrow-Debreu economy. Our study shows that, if a competitive economy is sufficiently fair and free, a spontaneous economic order will emerge in long-run competitive equilibria so that social members spontaneously occupy an unplanned distribution of income. Despite this, the spontaneous order may degenerate in the form of economic crises whenever an equilibrium economy approaches the extreme competition. Remarkably, such a theoretical framework of spontaneous order provides a bridge linking Austrian economics and neoclassical economics, where a truth begins to emerge: “Freedom promotes technological progress”.

Monetary equilibria and Knightian uncertainty

In the past two decades, the implications of Knightian uncertainty have been explored in several general equilibrium settings. As shown by (Econometrica 60: 197–204 (1992)) Dow and Werlang (1992), (J Econ Dyn Control 22: 357–368 (1998)) Tallon (1998), (J Math Econ 61: 953–957 (2000)) Chateauneuf et al. (2000), and (Econ Theo 23: 569–587 (2004))Dana (2004), one of the most important findings in the existing literature is that indeterminacy of equilibria can be generated in the static Arrow-Debreu economy under Knightian uncertainty when there is no aggregate uncertainty.

An alternative proof for the existence of Radner equilibria

This paper explores ‘competitive equilibrium under uncertainty’ by Radner (1968). We provide a simple proof for the existence of a Walrasian equilibrium and characterize the maximal number of markets in the extended Arrow–Debreu economy.

GENERAL PROPERTIES OF ISOELASTIC UTILITY ECONOMIES

This paper studies the class of single-good Arrow–Debreu economies in which all agents have isoelastic utility functions and homogeneous beliefs, but have possibly different cautiousness parameters and endowments. For each economy in this class, the equilibrium stochastic discount factor is an exponential function of the inverse mapping of a completely monotone function, evaluated at the aggregate consumption. This fact allows for general properties of the class to be studied analytically in terms of known properties of completely monotone functions. For example, conditions are presented under which the agents’ cautiousness parameters and a distribution of initial wealth can be recovered from an equilibrium stochastic discount factor, even if nothing is known about the agents’ endowments. This is a multiagent inverse problem since information about economic primitives is extracted from equilibrium prices. Several example economies are used to illustrate the results.

Agent-based dynamics in the general equilibrium model

We introduce agent-based dynamics in a class of Arrow-Debreu economies with capital accumulation and technological progress. In this framework we confirm the results obtained by Gintis (2006, 2007) in an exchange economy: the micro-behavior of boundedly rational agents can lead to the emergence of equilibrium at the macro-level provided some form of collective optimization takes place via evolutionary mechanisms. Sensitivity analysis hint at further properties of out-of-equilibrium dynamics which can be analyzed using agent-based models.

Equilibrium price dynamics in an overlapping-generations exchange economy

An extension to the Yaari (1965)–Blanchard (1985) continuous time overlapping generations model for an endowment Arrow–Debreu economy with an age-structured population is presented. It is proved that Arrow–Debreu equilibrium prices are represented by a double linear integral equation, and depend on the age-distributions of population and endowments. For an economy with a balanced growth, and logarithmic utility, we prove that bubbles may exist if endowments are distributed earlier than some critical age.

General equilibrium in economies with adverse selection

We model economies of adverse selection as Arrow–Debreu economies. In the spirit of Prescott and Townsend (Econometrica 52(1), 21–45, 1984a), we identify the consumption set of the individuals with the set of lotteries over net transfers. Thus, prices are linear in lotteries, but they may be non linear in commodity bundles. First, we study a weak equilibrium notion by viewing the economy of adverse selection as a pure exchange economy. The weak equilibrium set is non empty, but some of the allocations may be inefficient, and the equilibria indeterminate. Second, following Prescott and Townsend (Econometrica 52(1), 21–45, 1984a), we introduce an intermediary (firm) supplying feasible and incentive compatible measures. Equilibria are constrained efficient, but the equilibrium set is empty for an open set of economies containing the Rothschild and Stiglitz insurance economies.

Is there evidence of pessimism and doubt in subjective distributions? Implications for the equity premium puzzle

Abel (2002) shows that pessimism and doubt in the subjective distribution of the growth rate of consumption reduce the equity premium puzzle. We quantify the amount of pessimism and doubt in survey data on US consumption and income. Individual forecasters are in fact pessimistic, but show marked overconfidence rather than doubt. However, the implications for Abel's model depend on how the empirically heterogeneous beliefs are mapped into beliefs of a representative agent. We use an Arrow-Debreu economy to show that disagreement increases the equity premium. When incorporating this in our estimation, we find little empirical evidence of either overconfidence or doubt.