Theoretical Economics Volume 17, Number 1 (January 2022) is now online
Theoretical Economics
Volume 17, Number 1 (January 2022)
Table of contents
https://econtheory.org/ojs/index.php/te/issue/view/54
Articles
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Title: Information aggregation in Poisson-elections
Pages: 1-23
Authors: Mehmet Ekmekci, Stephan Lauermann
Abstract: The modern Condorcet jury theorem states that under weak conditions, when voters have common interests, elections will aggregate information when the population is large, in any equilibrium. Here, we study the performance of large elections with population uncertainty. We find that the modern Condorcet jury theorem holds if and only if the expected number of voters is independent of the state. If the expected number of voters depends on the state, then additional equilibria exist in which information is not aggregated. The main driving force is that, everything else equal, voters are more likely to be pivotal if the population is small.
Keywords: Political economy, voting, information aggregation, Poisson games
JEL classification: C72, D72, D82
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Title: Rank-optimal assignments in uniform markets
Pages: 25-55
Authors: Afshin Nikzad
Abstract: We prove that in a market where agents rank objects independently and uniformly at random, there exists an assignment of objects to agents with a constant average rank (i.e., an average rank independent of the market size). The proof builds on techniques from random graph theory and the FKG inequality (Fortuin et al., 1971). When the agents’ rankings are their private information, no Dominant Strategy Incentive Compatible mechanism can implement the assignment with the smallest average rank; however, we show that there exists a Bayesian Incentive Compatible mechanism that does so. Together with the fact that the average rank under the Random Serial Dictatorship (RSD) mechanism grows infinitely large with the market size, our findings indicate that the average rank under RSD can take a heavy toll compared to the first-best, and highlight the possibility of using other assignment methods in scenarios where average rank is a relevant objective.
Keywords: Matching, average rank, random serial dictatorship, FKG inequality
JEL classification: C78, D82
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Title: Informed intermediaries
Pages: 57-87
Authors: Paula Onuchic
Abstract: I develop a theory of intermediation in a market where agents meet bilaterally to trade and buyers cannot commit to payments. Some agents observe the past trading history of traders in the market. These informed agents can secure trades by punishing traders who previously defaulted. The punishing strategy affects equilibrium prices and determines which trades are hindered by the risk of default. Intermediation is a robust equilibrium feature, generated by asymmetric punishing strategies that yield informed agents either more effective opportunities to trade or the ability to extract more surplus in trades.
Keywords: Intermediation, limited commitment, bilateral trade, trade network
JEL classification: D83, D85
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Title: Family ties: school assignment with siblings
Pages: 89-120
Authors: Umut Dur, Thayer Morrill, William Phan
Abstract: We introduce a generalization of the school choice problem motivated by the following observations: students are assigned to grades within schools, many students have siblings who are applying as well, and school districts commonly guarantee that siblings will attend the same school. This last condition disqualifies the standard approach of considering grades independently as it may separate siblings. We argue that
the central criterion in school choice---elimination of justified
envy---is now inadequate as it does not consider siblings. We propose a new solution concept, suitability, that addresses this concern, and we introduce a new family of strategy-proof mechanisms that satisfy it. Using data from the Wake County magnet school assignment, we demonstrate the impact on families of our proposed mechanism versus the ``naive'' assignment where sibling constraints are not taken into account.
Keywords: School choice, matching theory, matching with contracts
JEL classification: C78, D47, D63, I20
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Title: Equilibrium securitization with diverse beliefs
Pages: 121-152
Authors: Andrew Ellis, Michele Piccione, Shengxing Zhang
Abstract: We study the effects of diverse beliefs on equilibrium securitization under risk neutrality. We provide a simple characterization of the optimal securities. Pooling and tranching of assets emerges in equilibrium as a consequence of the traders' diverse beliefs about asset returns. The issuer of securities tranches the asset pool, and traders sort among the tranches according to their beliefs. We show how the traders'
disagreement about the correlation of asset returns is a key factor in determining which assets are pooled.
Keywords: Securitization, heterogeneous beliefs, collateral, tranching, pooling
JEL classification: D53, G20
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Title: Choosing what to pay attention to
Pages: 153-184
Authors: Chad Fulton
Abstract: This paper studies static rational inattention problems with multiple actions and multiple shocks. We solve for the optimal signals chosen by agents and provide tools to interpret information processing. By relaxing restrictive assumptions previously used to gain tractability, we allow agents more latitude to choose what to pay attention to. Our applications examine the pricing problem of a monopolist who sells in multiple markets and the portfolio problem of an investor who can invest in multiple assets. The more general models that our methods allow us to solve yield new results. We show conditions under which the multimarket monopolist would optimally choose a uniform pricing strategy, and we show how optimal information processing by rationally inattentive investors can be interpreted as learning about the Sharpe ratio of a diversified portfolio.
Keywords: Rational inattention, information acquisition, price discrimination, portfolio choice
JEL classification: D81, D83, G11
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Title: Transparency and collateral: central versus bilateral clearing
Pages: 185-217
Authors: Gaetano Antinolfi, Francesca Carapella, Francesco Carli
Abstract: This paper studies the optimal clearing arrangement for bilateral financial contracts in which an assessment of counterparty credit risk is crucial for efficiency. The economy is populated by borrowers and lenders.
Borrowers are subject to limited commitment and hold private information about the severity of such lack of commitment. Lenders can acquire information, at a cost, about the commitment of their borrowers, which affects the assessment of counterparty risk. Clearing through a central counterparty (CCP) allows lenders to mutualize counterparty credit risk, but this insurance may weaken incentives to acquire and reveal information. If information acquisition is incentive-compatible, then lenders choose central clearing. If it is not, they may prefer bilateral clearing either to prevent strategic default or to optimize the allocation of costly collateral.
Keywords: Limited commitment, central counterparties, collateral
JEL classification: G10, G14, G20, G23
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Title: Bayesian comparative statics
Pages: 219-251
Authors: Teddy Mekonnen, René Leal Vizcaíno
Abstract: We study how changes to the informativeness of signals in Bayesian games and single-agent decision problems affect the distribution of equilibrium actions. Focusing on supermodular environments, we provide conditions under which a more precise private signal for one agent leads to an increasing-mean spread or a decreasing-mean spread of equilibrium actions for all agents. We apply our comparative statics to information disclosure games between a sender and many receivers and derive sufficient conditions on the primitive payoffs that lead to extremal disclosure of information.
Keywords: Comparative statics, supermodular order, convex order, information disclosure
JEL classification: C44, C61, D42, D81
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Title: Pseudo-Bayesian updating
Pages: 253-289
Authors: Chen Zhao
Abstract: I propose an axiomatic framework for belief revision when new information is qualitative, of the form ``Event $A$ is at least as likely as event $B$.'' My decision maker need not have beliefs about the joint distribution of the signal she will receive and the payoff-relevant states.
I propose three axioms, Exchangeability, Stationarity, and Reduction, to characterize the class of pseudo-Bayesian updating rules. The key axiom, Exchangeability, requires that the order in which the information arrives does not matter if the different pieces of information neither reinforce nor contradict each other.
I show that adding one more axiom, Conservatism, which requires that the decision maker adjust her beliefs just enough to embrace new information, yields Kullback-Leibler minimization: The decision maker selects the posterior closest to her prior in terms of Kullback-Leibler divergence from the probability measures consistent with newly received information. I show that pseudo-Bayesian agents are susceptible to recency bias, which may be mitigated by repetitive learning.
Keywords: Qualitative information, non-Bayesian updating, maximum entropy
JEL classification: D81, D83, D00
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Title: Statistical sunspots
Pages: 291-329
Authors: William A. Branch, Bruce McGough, Mei Zhu
Abstract: This paper shows that belief-driven economic fluctuations are a general feature of many determinate macroeconomic models. In environments with hidden state variables, forecast-model misspecification can break the link between indeterminacy and sunspots by establishing the existence of ``statistical sunspots'' in models that have a unique rational expectations equilibrium. To form expectations, agents regress on a set of observables that can include serially correlated non-fundamental factors (e.g. sunspots, judgment, expectations shocks, etc.). In equilibrium, agents attribute, in a self-fulfilling way, some of the serial correlation observed in data to extrinsic noise, i.e. statistical sunspots. This leads to sunspot equilibria in models with a unique rational expectations equilibrium.
Unlike many rational sunspots, these equilibria are found to be generically
stable under learning. Applications are developed in the context of a New
Keynesian and an asset-pricing model.
Keywords: Adaptive learning, animal spirits, business cycles, optimal monetary policy
JEL classification: D82, D83, E40, E50
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Title: Optimal organ allocation policy under blood-type barriers with the donor-priority rule
Pages: 331-369
Authors: Jaehong Kim, Mengling Li
Abstract: Shortages in organs for transplantation have resulted in a renewed interest in designing incentive policies to promote organ supply. The donor-priority rule, which grants priority for transplantation based on deceased organ donor registration status, has proven to be effective in both theory and practice. This study investigates the implications of the donor-priority rule for optimal deceased organ allocation policy design under a general formulation of blood-type barriers. We find that for any blood typing and organ matching technology, reserving type X organs for only type X patients maximizes the aggregate donation rate under regular distributions, which also ensures equity in organ sharing. Moreover, this is the unique optimal allocation policy if and only if the directed compatibility graph that corresponds to a given organ matching technology is acyclic.
Keywords: Market design, organ donation, priority rule, blood-type compatibility, equity
JEL classification: D47, D64, D78, H42, I11
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Title: Equilibrium contracts and boundedly rational expectations
Pages: 371-414
Authors: Heiner Schumacher, Heidi Christina Thysen
Abstract: We study a principal-agent framework in which the agent forms beliefs about the principal's project based on a misspecified subjective model. She fits this model to the objective probability distribution to predict output under alternative actions. Misspecifications in the subjective model may lead to biased beliefs. However, under mild restrictions, the agent has correct beliefs on the equilibrium path so that the optimal contract is non-exploitative. This allows for a behavioral version of the informativeness principle: The optimal contract conditions on an additional variable only if it is informative about the action according to the agent's subjective model. We further characterize when misspecifications affect the optimal contract. One implication of this characterization is that the scope for belief biases depends on the agent's job, e.g., her position in the hierarchy.
Keywords: Bayesian networks, principal-agent relationship, bounded rationality
JEL classification: D03, D82, D86
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Title: Malthusian stagnation is efficient
Pages: 415-460
Authors: Juan Carlos Cordoba, Xiying Liu
Abstract: This article studies socially optimal allocations, from the point of view of a benevolent social planner, in environments characterized by fixed resources, endogenous fertility, and full information. Individuals in our environment are fully rational and altruistic toward their descendants.
Our model allows for rich heterogeneity of abilities, preferences for children, and costs of raising children. We show that the planner's optimal allocations are efficient in the sense of Golosov et al. (2007). We also show that efficient allocations in the endogenous fertility case differ significantly from its exogenous fertility counterpart. In particular, optimal steady-state population is proportional to the amount of fixed resources and the level of technology while steady-state individual consumption is independent of these variables, a sort of a "Malthusian stagnation" result. Furthermore, optimal allocations exhibit inequality, differential fertility, random consumption, and a higher population density of poorer individuals even when the planner is fully equalitarian, and faces no aggregate risk nor frictions.
Keywords: Efficiency, optimal population, endogenous fertility, stochastic abilities, inequality
JEL classification: D04, D10, D63, D64, D80, D91, E10, E60, I30, J13, N00, 011, 040, Q01
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Title: Incomplete-information games in large populations with anonymity
Pages: 461-506
Authors: Martin Hellwig
Abstract: The paper provides theoretical foundations for models of strategic interdependence under uncertainty that have a continuum of agents and a decomposition of uncertainty into a macro component and an agent-specific micro component, with a law of large numbers for the latter. This macro-micro decomposition of uncertainty is implied by a condition of exchangeability of agents' types, which holds at the level of the prior if and only if it also holds at the level of agents' beliefs, i.e., posteriors.
Under an additional condition of anonymity in payoffs, agents' behaviours are fully determined by their macro beliefs about the cross-section distribution of types and other macro variables and about the cross-section distribution of other agents' strategies. Any probability distribution over cross-section distributions of types and other macro variables is compatible with a fully specified belief system, but not every macro belief function is compatible with a common prior. The paper gives necessary and sufficient conditions for compatibility of a macro belief function with a common prior.
Keywords: Incomplete-information games, large populations, belief functions, common priors, exchangeability, conditional independence, conditional exact law of large numbers
JEL classification: C70, D82, D83
