Constraints and non-existence of rational expectations equilibria

In this article we show that in the presence of trading constraints, such as short sale constraints, the standard definition of a Rational Expectations Equilibrium allows for equilibrium prices that reveal information unknown to any active trader in the market. We propose a new definition of the Rational Expectations Equilibrium that incorporates a stronger measurability condition than measurability with respect to the join of the information sets of the agents and give an example of non-existence of equilibrium. The example is robust to perturbations on the data of the economy and the introduction of new assets.

Nonlinear inverse dynamic models of gas sensing systems based on chemical sensor arrays for quantitative measurements

Gas sensing systems based on low-cost chemical sensor arrays are gaining interest for the analysis of multicomponent gas mixtures. These sensors show different problems, e.g., nonlinearities and slow time-response, which can be partially solved by digital signal processing. Our approach is based on building a nonlinear inverse dynamic system. Results for different identification techniques, including artificial neural networks and Wiener series, are compared in terms of measurement accuracy.

Identifying the preferred subset of enzymatic profiles in nonlinear kinetic metabolic models via multiobjective global optimization and pareto filters

Optimization models in metabolic engineering and systems biology focus typically on optimizing a unique criterion, usually the synthesis rate of a metabolite of interest or the rate of growth. Connectivity and non-linear regulatory effects, however, make it necessary to consider multiple objectives in order to identify useful strategies that balance out different metabolic issues. This is a fundamental aspect, as optimization of maximum yield in a given condition may involve unrealistic values in other key processes. Due to the difficulties associated with detailed non-linear models, analysis using stoichiometric descriptions and linear optimization methods have become rather popular in systems biology. However, despite being useful, these approaches fail in capturing the intrinsic nonlinear nature of the underlying metabolic systems and the regulatory signals involved. Targeting more complex biological systems requires the application of global optimization methods to non-linear representations. In this work we address the multi-objective global optimization of metabolic networks that are described by a special class of models based on the power-law formalism: the generalized mass action (GMA) representation. Our goal is to develop global optimization methods capable of efficiently dealing with several biological criteria simultaneously. In order to overcome the numerical difficulties of dealing with multiple criteria in the optimization, we propose a heuristic approach based on the epsilon constraint method that reduces the computational burden of generating a set of Pareto optimal alternatives, each achieving a unique combination of objectives values. To facilitate the post-optimal analysis of these solutions and narrow down their number prior to being tested in the laboratory, we explore the use of Pareto filters that identify the preferred subset of enzymatic profiles. We demonstrate the usefulness of our approach by means of a case study that optimizes the ethanol production in the fermentation of Saccharomyces cerevisiae.

Speed of convergence of recursive least squares learning with ARMA perceptions

This paper fills a gap in the existing literature on least squareslearning in linear rational expectations models by studying a setup inwhich agents learn by fitting ARMA models to a subset of the statevariables. This is a natural specification in models with privateinformation because in the presence of hidden state variables, agentshave an incentive to condition forecasts on the infinite past recordsof observables. We study a particular setting in which it sufficesfor agents to fit a first order ARMA process, which preserves thetractability of a finite dimensional parameterization, while permittingconditioning on the infinite past record. We describe how previousresults (Marcet and Sargent [1989a, 1989b] can be adapted to handlethe convergence of estimators of an ARMA process in our self--referentialenvironment. We also study ``rates'' of convergence analytically and viacomputer simulation.

Two-sided learning in new keynesian models: dynamics, (lack of) convergence and the value of information

This paper investigates the role of learning by private agents and the central bank (two-sided learning) in a New Keynesian framework in which both sides of the economy have asymmetric and imperfect knowledge about the true data generating process. We assume that all agents employ the data that they observe (which may be distinct for different sets of agents) to form beliefs about unknown aspects of the true model of the economy, use their beliefs to decide on actions, and revise these beliefs through a statistical learning algorithm as new information becomes available. We study the short-run dynamics of our model and derive its policy recommendations, particularly with respect to central bank communications. We demonstrate that two-sided learning can generate substantial increases in volatility and persistence, and alter the behavior of the variables in the model in a signifficant way. Our simulations do not converge to a symmetric rational expectations equilibrium and we highlight one source that invalidates the convergence results of Marcet and Sargent (1989). Finally, we identify a novel aspect of central bank communication in models of learning: communication can be harmful if the central bank's model is substantially mis-specified

Parameterized expectations approach; Some practical issues

We discuss some practical issues related to the use of the Parameterized Expectations Approach (PEA) for solving non-linear stochastic dynamic models with rational expectations. This approach has been applied in models of macroeconomics, financial economics, economic growth, contracttheory, etc. It turns out to be a convenient algorithm, especially when there is a large number of state variables and stochastic shocks in the conditional expectations. We discuss some practical issues having to do with the application of the algorithm, and we discuss a Fortran program for implementing the algorithm that is available through the internet.We discuss these issues in a battery of six examples.

Two-sided learning in New Keynesian models: Dynamics, (lack of) convergence and the value of information

This paper investigates the role of learning by private agents and the central bank(two-sided learning) in a New Keynesian framework in which both sides of the economyhave asymmetric and imperfect knowledge about the true data generating process. Weassume that all agents employ the data that they observe (which may be distinct fordifferent sets of agents) to form beliefs about unknown aspects of the true model ofthe economy, use their beliefs to decide on actions, and revise these beliefs througha statistical learning algorithm as new information becomes available. We study theshort-run dynamics of our model and derive its policy recommendations, particularlywith respect to central bank communications. We demonstrate that two-sided learningcan generate substantial increases in volatility and persistence, and alter the behaviorof the variables in the model in a significant way. Our simulations do not convergeto a symmetric rational expectations equilibrium and we highlight one source thatinvalidates the convergence results of Marcet and Sargent (1989). Finally, we identifya novel aspect of central bank communication in models of learning: communicationcan be harmful if the central bank's model is substantially mis-specified.

Money and prices in models of bounded rationality in high inflation economies

This paper studies the short run correlation of inflation and money growth. We study whether a model of learning can do better than a model of rational expectations, we focus our study on countries of high inflation. We take the money process as an exogenous variable, estimated from the data through a switching regime process. We findthat the rational expectations model and the model of learning both offer very good explanations for the joint behavior of money and prices.

Giffen goods and market making

This paper shows that information effects per se are not responsible forthe Giffen goods anomaly affecting competitive traders demands in multi-asset, noisy rational expectations equilibrium models. The role thatinformation plays in traders strategies also matters. In a market withrisk averse, uninformed traders, informed agents havea dual motive for trading: speculation and market making. Whilespeculation entails using prices to assess the effect of private signalerror terms, market making requires employing them to disentangle noisetraders effects in traders aggregate orders. In a correlated environment,this complicates a trader s signal-extraction problem and maygenerate upward-sloping demand curves. Assuming either (i) that competitive,risk neutral market makers price the assets, or that (ii) the risktolerance coefficient of uninformed traders grows without bound, removesthe market making component from informed traders demands, rendering themwell behaved in prices.

Inflationary expectations during Germany's great slump

Was the German slump inevitable? This paper argues that -despite thespeed and depth of Germany's deflation in the early 1930s - fear ofinflation is evident in the bond, foreign exchange, and commodity marketsat certain critical junctures of the Great Depression. Therefore, policyoptions were more limited than many subsequent critics of Brüning'spolicies have been prepared to admit. Using a rational expectationsframework, we find strong evidence from the bondmarket to suggest fearof inflation. Futures prices also reveal that market participants werebetting on price increases. These findings are discussed in the contextof reparations and related to the need for a regime shift to overcomethe crisis.

Allocative and productive efficiency in REE with asymetric information

We characterize the divergence between informational and economic efficiency in a rational expectations competitive market with asymmetric information about the costs of production. We find that prices may contain too much or too little information with respect to incentive efficient allocations depending on whether the main role of the price is, respectively, the traditional as index of scarcity or informational. Only when REE degenerate to Cournot equilibria the market solution does not show llocative inefficiency. With multidimensional uncertainty we find that the REE price does not have in general the incentive efficient information mix: It pays to sacrifice allocative efficiency at the REE to improve productive efficiency.

Asymmetries in the capacity-inflation trade-off

This paper analyzes the joint dynamics of two key macroeconomic variables for the conduct of monetary policy: inflation and the aggregate capacity utilization rate. An econometric procedure useful for estimating dynamic rational expectation models with unobserved components is developed and applied in this context. The method combines the flexibility of the unobserved components approach, based on the Kalman recursion, with the power of the general method of moments estimation procedure. A 'hyb id' Phillips curve relating inflation to the capacity utilization gap and incorporating forward and backward looking components is estimated. The results show that such a relationship in non-linear: the slope of the Phillips curve depends significantly on the magnitude of the capacity gap. These findings provide support for studying the implications of asymmetricmonetary policy rules.

Information Dispersion and Equilibrium Multiplicity

This paper studies the implications of correlation of private signals about the liquidation value of a risky asset in a variation of a standard noisy rational expectations model in which traders receive endowment shocks which are private information and have a common component. We …nd that a necessary condition to generate multiple linear partially revealing rational expectations equilibria is the existence of several sources of information dispersion. In this context equilibrium multiplicity tends to occur when information is more dispersed. A necessary condition to have strategic complementarity in information acquisition is to have mul- tiple equilibria. When the equilibrium is unique there is strategic substi- tutability in information acquisition, corroborating the result obtained in Grossman and Stiglitz (1980). JEL Classi…cation: D82, D83, G14 Keywords: Multiplicity of equilibria, strategic complementarity, asym- metric information.

Public and private learning from prices, strategic substitutability and complementarity, and equilibrium multiplicity

We study a general static noisy rational expectations model where investors have private information about asset payoffs, with common and private components, and about their own exposure to an aggregate risk factor, and derive conditions for existence and uniqueness (or multiplicity) of equilibria. We find that a main driver of the characterization of equilibria is whether the actions of investors are strategic substitutes or complements. This latter property in turn is driven by the strength of a private learning channel from prices, arising from the multidimensional sources of asymmetric information, in relation to the usual public learning channel. When the private learning channel is strong (weak) in relation to the public we have strong (weak) strategic complementarity in actions and potentially multiple (unique) equilibria. The results enable a precise characterization of whether information acquisition decisions are strategic substitutes or complements. We find that the strategic substitutability in information acquisition result obtained in Grossman and Stiglitz (1980) is robust. JEL Classification: D82, D83, G14 Keywords: Rational expectations equilibrium, asymmetric information, risk exposure, hedging, supply information, information acquisition.