Heterogeneity and learning with complete markets

We study an endowment economy with complete markets and heterogeneous agents who do not have rational expectations, but form their beliefs using adaptive learning algorithms that may differ from one individual to another. We show that market completeness allows agents to smooth consumption across states of nature, but not across time, and that the initial wealth distribution is not enough to pin down the long-run equilibrium. Consequently, initial differences in beliefs create persistent consumption imbalances that are not grounded in fundamentals. In some cases these imbalances are eventually unsustainable: the debt of one of the agents would grow without bounds, and binding borrowing limits are necessary to prevent Ponzi schemes. Finally, we find that our slight departure from rational expectations affects efficiency properties of the competitive equilibrium: if the social welfare function attaches fixed Pareto weights to the different individuals, there are configurations of individual expectations under which society is better off with financial autarky than with complete markets. The first best can be restored by introducing a distortionary tax on borrowing, which transfers consumption from the more optimistic agent to the other.learning, heterogeneous agents, complete markets

Monetary policy rules and a normative approach to the central bank’s objective function

This study attempts to explain in an understandable manner that the central bank’s effort to keep inflation low is not an end in itself, but ultimately serves the interests of social welfare. We attempt to substantiate this argument on the basis of economic theory, based on the logic of New Keynesian models, by describing loss functions that contain welfare relevant variables and interest rules that minimise them. By using this framework, we point out that – taking into account the limits of measurability, learning and potentially non-rational expectations – decision-making rules that give considerable weight to a departure from the inflation target and take into account real economy considerations generally perform well in terms of welfare and may be considered robust in New Keynesian-type models with forward looking agents. Finally, we argue that through the strategy of inflation targeting the normative implications of the above framework can be put into practice.New_keynesian model, inflation targeting, normative approach.

Behavioral Economics

Behavioral economics uses evidence from psychology and other disciplines to create models of limits on rationality, willpower and self-interest, and explore their implications in economic aggregates. This paper reviews the basic themes of behavioral economics: Sensitivity of revealed preferences to descriptions of goods and procedures; generalizations of models of choice over risk, ambiguity, and time; fairness and reciprocity; non-Bayesian judgment; and stochastic equilibrium and learning. A central issue is what happens in equilibrium when agents are imperfect but heterogeneous; sometimes firms “repair” limits through sorting, but profit-maximizing firms can also exploit limits of consumers. Frontiers of research are careful formal theorizing about psychology and studies with field data. Neuroeconomics extends the psychological data use to inform theorizing to include details of neural circuitry. It is likely to support rational choice theory in some cases, to buttress behavioral economics in some cases, and to suggest different constructs as well

STUDENTS’ CONCEPTUAL KNOWLEDGE OF LIMITS IN CALCULUS: A TWO-PART CONSTRUCTIVIST CASE STUDY

This case study investigated students’ conceptual knowledge of limits in calculus by implementing semi-structured interviews. The constructivist learning principles of Piaget and Inhelder as well as theories of understanding by Skemp guided the study. In Phase I, a pilot study was conducted with 15 students from a Calculus III class. By using 41 traditional textbook type tasks and non-traditional tasks, various ways students think about functions, limits at a point, limits at infinity and limits that do not exist were explored. Tasks included continuous and non-continuous functions; piecewise, rational and trigonometric functions, including those with oscillatory end behaviors. In Phase I, two students with different conceptions of limits and ability levels were selected for the initial analysis. The findings gave rise to a more in-depth follow-up investigation referred to as Phase II , which explored what students know about limits with respect to the definition of limit and infinity as well as knowledge of domains. Four student cases were selected out of nine based on similar emerging themes of understandings. The results are interpreted in terms of the constructivist framework and suggest that students assimilate information about limits into a variety of unique conceptual knowledge structures that ultimately develop into operational schemas. Given the nature of the content knowledge, these schemas are either appropriate or altered. Implications related to improving instructional practices, differentiating instruction for diverse learners and teaching limits in meaningful ways across the curriculum, are discussed

Conflicts in the learning of real numbers and limits

question: "Is 0.999... (nought point nine recurring) equal to one, or just less than one?". Many answers contained infinitesimal concepts: "The same, because the difference between them is infinitely small." " The same, for at infinity it comes so close to one it can be considered the same." "Just less than one, but it is the nearest you can get to one without actually saying it is one." "Just less than one, but the difference between it and one is infinitely small." The majority of students thought that 0.999... was less than one. It may be that a few students had been taught using infinitesimal concepts, or that the phrase “just less than one ” had connotations for the students different from those intended by the questioner; but it seems more likely that the answers represent the students ’ own rationalisations made in an attempt to resolve conflicts inherent in the students ’ previous experience of limiting processes. Some conscious and subconscious conflicts Most of the mathematics met in secondary school consists of sophisticated idea

(WP 2016-02) The Limits of Central Bank Forward Guidance under Learning

Central bank forward guidance emerged as a pertinent tool for monetary policymakers since the Great Recession. Nevertheless, the effects of forward guidance remain unclear. This paper investigates the effectiveness of forward guidance while relaxing two standard macroeconomic assumptions: rational expectations and frictionless financial markets. Agents forecast future macroeconomic variables via either the rational expectations hypothesis or a more plausible theory of expectations formation called adaptive learning. A standard Dynamic Stochastic General Equilibrium (DSGE) model is extended to include the financial accelerator mechanism. The results show that the addition of financial frictions amplifies the differences between rational expectations and adaptive learning to forward guidance. The macroeconomic variables are overall more responsive to forward guidance under rational expectations than under adaptive learning. During a period of economic crisis (e.g. a recession), output under rational expectations displays more favorable responses to forward guidance than under adaptive learning. These differences are exacerbated when compared to a similar analysis without financial frictions. Thus, monetary policymakers should consider the way in which expectations and credit frictions are modeled when examining the effects of forward guidance

How Models Fail. A Critical Look at the History of Computer Simulations of the Evolution of Cooperation

Simulation models of the Reiterated Prisoner's Dilemma have been popular for studying the evolution of cooperation since more than 30 years now. However, there have been practically no successful instances of empirical application of any of these models. At the same time this lack of empirical testing and confirmation has almost entirely been ignored by the modelers community. In this paper, I examine some of the typical narratives and standard arguments with which these models are justified by their authors despite the lack of empirical validation. I find that most of the narratives and arguments are not at all compelling. None the less they seem to serve an important function in keeping the simulation business running despite its empirical shortcomings