If You're So Smart, Why Aren't You Rich? Belief Selection in Complete and Incomplete Markets

This paper provides an analysis of the asymptotic properties of consumption allocations in a stochastic general equilibrium model with heterogeneous consumers. In particular we investigate the market selection hypothesis, that markets favor traders with more accurate beliefs. We show that in any Pareto optimal allocation whether each consumer vanishes or survives is determined entirely by discount factors and beliefs. Since equilibrium allocations in economies with complete markets are Pareto optimal, our results characterize the limit behavior of these economies. We show that, all else equal, the market selects for consumers who use Bayesian learning with the truth in the support of their prior and selects among Bayesians according to the size of the their parameter space. Finally, we show that in economies with incomplete markets these conclusions may not hold. Payoff functions can matter for long run survival, and the market selection hypothesis fails.Market selection hypothesis, subjective beliefs, general equilibrium, incomplete markets, complete markets

Optimality and Natural Selection in Markets

Evolutionary arguments are often used to justify the fundamental behavioral postulates of competive equilibrium. Economists such as Milton Friedman have argued that natural selection favors profit maximizing firms over firms engaging in other behaviors. Consequently, producer efficiency, and therefore Pareto efficiency, are justified on evolutionary grounds. We examine these claims in an evolutionary general equilibrium model. If the economic environment were held constant, profitable firms would grow and unprofitable firms would shrink. In the general equilibrium model, prices change as factor demands and output supply evolves. Without capital markets, when firms can grow only through retained earnings, our model verifies Friedman's claim that natural selection favors profit maximization. But we show through examples that this does not imply that equilibrium allocations converge over time to efficient allocations. Consequently, Koopmans critique of Friedman is correct. When capital markets are added, and firms grow by attracting investment, Friedman's claim may fail. In either model the long-run outcomes of evolutionary market models are not well described by conventional General Equilibrium analysis with profit maximizing firms.evolution, natural selection, equilibrium, incomplete markets

Constructive Decision Theory

Contemporary approaches to decision making describe a decision problem by sets of states and outcomes, and a rich set of acts: functions from states to outcomes over which the decision maker (DM) has preferences. Real problems do not come so equipped. It is often unclear what the state and outcome spaces would be. We present an alternative foundation for decision making, in which the primitive objects of choice are syntactic programs. We show that if the DM's preference relation on objects of choice satisfies appropriate axioms, then we can find states, outcomes, and an embedding of the programs into Savage acts such that preferences can be represented by EU in the Savage framework. A modeler can test for SEU behavior without having access to the subjective states and outcomes. We illustrate the power of our approach by showing that it can represent DMs who are subject to framing effects.Decision theory, subjective expected utility, behavioral anomalies

Tonality and drama in Verdi\u27s La Traviata

Scholars hold opposing views concerning the importance of large-scale key relations in Verdi\u27s operas. Julian Budden states that, since Verdi often allowed transpositions of his music in performance, one must take care in assigning structural importance to Verdi\u27s key schemes. Others, including David Lawton, place much significance on Verdi\u27s choice of keys. Lawton describes methods by which Verdi intensifies dramatic situations through associative tonality and recurring musical themes. In La Traviata, several recurring musical themes undergo transposition, a device that Wagner scholar Robert Bailey calls expressive tonality, which is the repetition or recall of a passage transposed by semitone or tone, either up or down to underscore dramatic intensification or relaxation. Similar in dramatic value are reactive shifts, which are abrupt modulations or tonicizations, depicting a direct response to a statement or thought. This thesis will show how Verdi uses tonality on a local and global scale to support and intensify dramatic situations throughout La Traviata. Locally, he uses reactive shifts in tonality and recurring themes to propel immediate music and dramatic action. Globally, Verdi uses expressive tonality to intensify or relax dramatic situations, which works in conjunction with a referential use of keys as well as large-scale harmonic successions to unify the work as a whole. I begin with a detailed exposition of the aforementioned analytical tools and then apply those tools to La Traviata. I will close the thesis with a discussion of the revisions made to La Traviata after its initial performances and explore some results of the musical changes Verdi made

If You\u27re So Smart, Why Aren\u27t You Rich?Belief Selection in Complete and Incomplete Markets

This paper provides an analysis of the asymptotic properties of consumption allocations in a stochastic general equilibrium model with heterogeneous consumers. In particular we investigate the market selection hypothesis, that markets favor traders with more accurate beliefs. We show that in any Pareto optimal allocation whether each consumer vanishes or survives is determined entirely by discount factors and beliefs. Since equilibrium allocations in economies with complete markets are Pareto optimal, our results characterize the limit behavior of these economies. We show that, all else equal, the market selects for consumers who use Bayesian learning with the truth in the support of their prior and selects among Bayesians according to the size of the their parameter space. Finally, we show that in economies with incomplete markets these conclusions may not hold. Payoff functions can matter for long run survival, and the market selection hypothesis fails

Time-Varying Arrival Rates of Informed and Uninformed Trades

In this paper we extend the model of Easley and O'Hara (1992) to allow the arrival rates of informed and uninformed trades to be time-varying and forecastable. We specify a generalized autoregressive bivariate process for the arrival rates of informed and uninformed trades and estimate the model on 16 actively traded stocks on the New York Stock Exchange over 15 years of transaction data. Our results show that uninformed trades are highly persistent. Uninformed order arrivals clump together, with high uninformed volume days likely to follow high uninformed volume days, and conversely. This behavior is consistent with the passive characterization of the uninformed found in the literature. But we do find an important difference in how the uninformed behave; they avoid trading when the informed are forecasted to be present. Informed trades also exhibit complex patterns, but these patterns are not consistent with the strategic behavior posited in the literature. The informed do not appear to hide in order flow, but instead they trade persistently. We also investigate the correlation between the arrival rates of trades and trade composition on market volatility, liquidity and depth. We find that although volatility increases with the forecasted arrival rates of total trades, it is relatively independent of the forecasted composition of the trade. We use the opening bid-ask spread as a measure of market liquidity. We find that as the number of trades increases over time, the relative proportion of informed trades decreases and hence, spreads become narrower and the market becomes more liquid. Finally, we compute the price impact curve of consecutive buy orders and report the half life of the price impact as a measure of market depth. We find a positive correlation between the half life and total trades indicating that the market is deeper in presence of more trades.Arrival rates; informed trades; uninformed trades; autoregressive process; market depth; liquidity; volatility.

Theories of Price Formation and Exchange in Double Oral Auctions

We provide a theory to explain the data generated by Double Oral Auctions. The primary conclusion suggested by Double Oral Auction experiments is that the quantities exchanged and the prices at which transactions take place converge to, or near to, the values predicted by the competitive equilibrium model. Our theory predicts convergence to the competitive equilibrium and provides an explanation of disequilibrium behavior. The predictions of our theory fit the data better than do the predictions of Walrasian, Marshallian or game theoretic models

Implementation of Walrasian Expectations Equilibria

In an exchange economy with differentially informed traders, Non-exclusivity of information (NEI) is the condition that each trader's private information be perfectly predictable by an outside observer who has observed the private information of all other traders. NEI is one of a set of conditions which, taken together, are sufficient for the implementability of fully revealing expectations equilibria. Here we show that this condition is in fact necessary for the weak implementation of a much broader class of Walrasian equilibria, herein called expectations equilibria.Center for Research on Economic and Social Theory, Department of Economics, University of Michiganhttp://deepblue.lib.umich.edu/bitstream/2027.42/100640/1/ECON116.pd