Internal Rationality, Imperfect Market Knowledge and Asset Prices

We present a decision theoretic framework in which agents are learning about market behavior and that provides microfoundations for models of adaptive learning. Agents are 'internally rational', i.e., maximize discounted expected utility under uncertainty given dynamically consistent subjective beliefs about the future, but agents may not be 'externally rational', i.e., may not know the true stochastic process for payoff relevant variables beyond their control. This includes future market outcomes and fundamentals. We apply this approach to a simple asset pricing model and show that the equilibrium stock price is then determined by investors' expectations of the price and dividend in the next period, rather than by expectations of the discounted sum of dividends. As a result, learning about price behavior affects market outcomes, while learning about the discounted sum of dividends is irrelevant for equilibrium prices. Stock prices equal the discounted sum of dividends only after making very strong assumptions about agents' market knowledge.learning, internal rationality, consumption based asset pricing

Rational certificates of positivity on compact semialgebraic sets

Schm\"udgen's Theorem says that if a basic closed semialgebraic set K = {g_1 \geq 0, ..., g_s \geq 0} in R^n is compact, then any polynomial f which is strictly positive on K is in the preordering generated by the g_i's. Putinar's Theorem says that under a condition stronger than compactness, any f which is strictly positive on K is in the quadratic module generated by the g_i's. In this note we show that if the g_i's and the f have rational coefficients, then there is a representation of f in the preordering with sums of squares of polynomials over Q. We show that the same is true for Putinar's Theorem as long as we include among the generators a polynomial N - \sum X_i^2, N a natural number

Non Expectations and Adaptive Behaviours: the Missing Trade-off in Models of Innovation

We explore the modelling of the determination of the level of R&D investment of firms. This means that we do not tackle the decision of being an innovator or not, nor the adoption of a new technology. We exclude these decisions and focus on the situations where firms invest in internal R&D in order to produce an innovation. In that case the problem is to determine the level of R&D investment. Our interest is to analyse how expectation and adaptation can be combined in the modelling of R&D investment rules. In the literature both dimensions are generally split up: rational expectations are assumed in neoclassical models whereas alternative approaches (institutional and/or evolutionary) generally adopt a purely adaptive representation.Bounded rationality, learning, expectations, innovation dynamics.

Alternative Price Expectation Formulation and Information Access

Demand and Price Analysis,

The power of words in financial markets: soft versus hard communication,a strategy method experiment

The main objective of this paper is to analyze the impact of non-informative communications on asset prices. An experimental approach allows us to control for the release of non-relevant messages. We introduce the release of messages in standard experimental asset markets with bubbles (Smith, Suchanek and Williams 1988) through a strategy method experiment. We conjecture that a priori uninformative messages can significantly impact the level of asset prices. Uninformative communications may be used by boundedly rational subjects to compute the fundamental value of the asset. In addition, rational agents may anticipate such an effect and adapt their strategy to the messages received. We asked 182 subjects to construct strategies about their action in a standard experimental asset market environment. Our analysis sheds light on the possibility of manipulation and stabilization of financial markets by influential agents such as financial “gurus” or central bankers.experiment

Near-Rational Exuberance

We study how the use of judgement or “add-factors” in macroeconomic forecasting may disturb the set of equilibrium outcomes when agents learn using recursive methods. We isolate conditions under which new phenomena, which we call exuberance equilibria, can exist in standard macroeconomic environments. Examples include a simple asset pricing model and the New Keynesian monetary policy framework. Inclusion of judgement in forecasts can lead to self-fulfilling fluctuations, but without the requirement that the underlying rational expectations equilibrium is locally indeterminate. We suggest ways in which policymakers might avoid unintended outcomes by adjusting policy to minimize the risk of exuberance equilibria

Learning as a rational foundation for macroeconomics and finance

Expectations play a central role in modern macroeconomics. The econometric learning approach, in line with the cognitive consistency principle, models agents as forming expectations by estimating and updating subjective forecasting models in real time. This approach provides a stability test for RE equilibria and a selection criterion in models with multiple equilibria. Further features of learning – such as discounting of older data, use of misspecified models or heterogeneous choice by agents between competing models – generate novel learning dynamics. Empirical applications are reviewed and the roles of the planning horizon and structural knowledge are discussed. We develop several applications of learning with relevance to macroeconomic policy: the scope of Ricardian equivalence, appropriate specification of interest-rate rules, implementation of price-level targeting to achieve learning stability of the optimal RE equilibrium and whether, under learning, price-level targeting can rule out the deflation trap at the zero lower bound.cognitive consistency; E-stability; least-squares; persistent learning dynamics; business cycles; monetary policy; asset prices