Theoretical Economics, Volume 16, Number 1, January 2021 is now online
Theoretical Economics
Volume 16, Number 1 (January 2021)
Table of contents
https://econtheory.org/ojs/index.php/te/issue/view/50
Articles
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Title: A model of weighted network formation
Pages: 1-23
Authors: Leonie Baumann
Abstract: The paper proposes a game of weighted network formation in which each agent has a limited resource to form links of possibly different intensities with other agents and to use for private purposes. We show that every equilibrium is either "reciprocal" or "non-reciprocal". In a reciprocal equilibrium, any two agents invest equally in the link between them. In a non-reciprocal equilibrium, agents are partitioned into "concentrated" and "diversified" agents and a concentrated agent is only linked to diversified agents and vice versa. For every link, the concentrated agent invests more in the link than the diversified agent. The unweighted relationship graph of an equilibrium, in which two agents are linked if they both invest positively in each other, uniquely predicts the equilibrium values of each agent's network investment and utility level, as well as the ratio of any two agents' investments in each other. We show that equilibria are not pairwise stable and not efficient due to the positive externalities of investing in a link.
Keywords: Weighted network, network formation, continuous link strength
JEL classification: D85, L14, C70
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Pages: 25-47
Authors: David M. Kreps, Walter Schachermayer
Abstract: We examine the connection between discrete-time models of financial markets and the celebrated Black--Scholes--Merton (BSM) continuous-time model in which ``markets are complete." Suppose that (a) the probability law of a sequence of discrete-time models converges to the law of the BSM model and (b) the largest possible one-period step in the
discrete-time models converges to zero. We prove that, under these
assumptions, every bounded and continuous contingent claim can be asymptotically synthesized, controlling for the risks taken in a manner that implies, for instance, that an expected-utility-maximizing consumer can asymptotically obtain as much utility in the (possibly incomplete) discrete-time economies as she can at the continuous-time limit. Hence, in economically significant ways, many discrete-time models with frequent trading resemble the complete-markets model of BSM.
Keywords: Market completeness, Black-Scholes-Merton model, synthesis of contingent claims
JEL classification: D0, G0
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Title: A Maximum Likelihood Approach to Combining Forecasts
Pages: 49-71
Authors: Gilat Levy, Ronny Razin
Abstract: We model an individual who wants to learn about a state of the world. The individual has a prior belief, and has data which consists of multiple forecasts about the state of the world. Our key assumption is that the decision maker identifies explanations that could have generated this data and among these focuses on the ones that maximise the likelihood of observing the data. The decision maker then bases her final prediction about the state on one of these maximum likelihood explanations. We show that in all the maximum likelihood explanations, moderate forecasts are just statistical derivatives of extreme ones. Therefore, the decision maker will base her final prediction only on the information conveyed in the relatively extreme forecasts. We show that this approach to combining forecasts leads to a unique prediction and a simple and dynamically consistent way of aggregating opinions.
Keywords: Maximum likelihood, combining forecasts, mispecified models
JEL classification: D8
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Title: Convergence in models of misspecified learning
Pages: 73-99
Authors: Paul Heidhues, Botond Koszegi, Philipp Strack
Abstract: We establish convergence of beliefs and actions in a class of one-dimensional learning settings in which the agent's model is misspecified, she chooses actions endogenously, and the actions affect how she misinterprets information. Our stochastic-approximation-based methods rely on two crucial features: that the state and action spaces are continuous, and that the agent's posterior admits a one-dimensional summary statistic. Through a basic model with a normal-normal updating structure and a generalization in which the agent's misinterpretation of information can depend on her current beliefs in a flexible way, we show that these features are compatible with a number of specifications of how exactly the agent updates. Applications of our framework include learning by a person who has an incorrect model of a technology she uses or is overconfident about herself, learning by a representative agent who may misunderstand macroeconomic outcomes, as well as learning by a firm that has an incorrect parametric model of demand.
Keywords: Misspecified model, Bayesian learning, convergence, Berk-Nash equilibrium
JEL classification: D83, D90
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Title: Voting in corporations
Pages: 101-128
Authors: Alan D. Miller
Abstract: I introduce a model of shareholder voting. I describe and provide characterizations of three families of shareholder voting rules: ratio rules, difference rules, and share majority rules. The characterizations rely on two key axioms: merger consistency, which requires consistency in voting outcomes following stock-for-stock mergers, and reallocation invariance, which requires the shareholder voting rule to be immune to certain manipulative techniques used by shareholders to hide their ownership. The paper also extends May's theorem.
Keywords: Shareholder voting, axioms, share majority rule, merger consistency, reallocation invariance, one share-one vote, difference rules, ratio rules
JEL classification: D71, G34, K22
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Title: Testable forecasts
Pages: 129-160
Authors: Luciano Pomatto
Abstract: Predictions about the future are commonly evaluated through statistical tests. As shown by recent literature, many known tests are subject to adverse selection problems and cannot discriminate between forecasters who are competent and forecasters who are uninformed but predict strategically.
We consider a framework where forecasters' predictions must be consistent with a paradigm, a set of candidate probability laws for the stochastic process of interest. The paper presents necessary and sufficient conditions on the paradigm under which it is possible to discriminate between informed and uninformed forecasters. We show that optimal tests take the form of likelihood-ratio tests comparing forecasters' predictions against the predictions of a hypothetical Bayesian outside observer. In addition, the paper illustrates a new connection between the problem of testing strategic forecasters and the classical Neyman-Pearson paradigm of hypothesis testing.
Keywords: Strategic forecasting, hypothesis testing
JEL classification: C120, D810
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Title: Information aggregation in competitive markets
Pages: 161-196
Authors: Lucas Siga, Maximilian Mihm
Abstract: We study when equilibrium prices can aggregate information in an auction market with a large population of traders. Our main result identifies a property of information---the betweenness property---that is both necessary and sufficient for information aggregation. The characterization provides novel predictions about equilibrium prices in complex, multidimensional environments.
Keywords: Auctions, betweenness, competitive markets, information aggregation, rational expectations equilibrium
JEL classification: C72, D44, D82, D83, G14
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Title: Chain stability in trading networks
Pages: 197-234
Authors: Scott Duke Kominers, John William Hatfield, Alexandru Nichifor, Michael Ostrovsky, Alexander Westkamp
Abstract: In a general model of trading networks with bilateral contracts, we propose a suitably adapted chain stability concept that plays the same role as pairwise stability in two-sided settings. We show that chain stability is equivalent to stability if all agents' preferences are jointly fully substitutable and satisfy the Laws of Aggregate Supply and Demand. In the special case of trading networks with transferable utility, an outcome is consistent with competitive equilibrium if and only if it is chain stable.
Keywords: Matching, trading networks, chain stability, stability, competitive equilibria, full substitutability, Laws of Aggregate Supply and Demand
JEL classification: C78, D85, L14
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Title: Agendas in legislative decision-making
Pages: 235-274
Authors: Sean Michael Horan
Abstract: Despite the wide variety of agendas used in legislative settings, the literature on sophisticated voting has focused on two formats, the so-called Euro-Latin and Anglo-American agendas. In the current paper, I introduce a broad class of agendas whose defining structural features, history-independence and persistence, are common in legislative settings. I then characterize the social choice rules implemented by sophisticated voting on agendas with these two features. I also characterize the rules implemented by more specialized formats (called priority agendas and convex
agendas) whose structure is closely related to the prevailing rules for order-of-voting used by legislatures. These results establish a clear connection between structure and outcomes for a wide range of legislative agendas.
Keywords: Majority voting, sophisticated voting, agendas, committees, implementation
JEL classification: C72, D02, D71, D72
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Title: Macro-financial volatility under dispersed information
Pages: 275-315
Authors: Jianjun Miao, Jieran Wu, Eric R. Young
Abstract: We provide a production-based asset pricing model with dispersed information and small deviations from full rational expectations. In the model, aggregate output and equity prices depend on the higher-order beliefs about aggregate demand and individual stochastic discount factors. We prove that equity price volatility becomes arbitrarily large as the volatility of idiosyncratic shocks diverges to infinity due to the interaction of signal-extraction with idiosyncratic trading decisions, while aggregate output volatility falls. We propose a two-step spectral factorization method that permits closed-form solutions in the frequency domain applicable to a wide range of models with more hidden states than signals. Our model can quantitatively match output and equity volatilities observed in US data.
Keywords: Dispersed information, frequency domain analysis, higher-order beliefs, asset pricing, business cycles, incomplete markets
JEL classification: E32, E44, G12, G14
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Title: A general analysis of boundedly rational learning in social networks
Pages: 317-357
Authors: Manuel Mueller-Frank, Claudia Neri
Abstract: We analyze boundedly rational learning in social networks within binary action environments. We establish how learning outcomes depend on the environment (i.e., informational structure, utility function), the axioms imposed on the updating behavior, and the network structure. In particular, we provide a normative foundation for Quasi-Bayesian updating, where a Quasi-Bayesian agent treats others' actions as if they were based only on their private signal. Quasi-Bayesian updating induces learning (i.e., convergence to the optimal action for every agent in every connected
network) only in highly asymmetric environments. In all other environments learning fails in networks with a diameter larger than four. Finally, we consider a richer class of updating behavior that allows for non-stationarity and differential treatment of neighbors' actions depending on their position in the network. We show that within this class there exist updating systems which induce learning for most networks.
Keywords: Social networks, naive inference, information aggregation, bounded rationality, agreement
JEL classification: D83, D85
