Economic Theory and Mathematical Models

Over time, the fields of economics and ethics have become more distinct with economics focusing on the rationality of actors, the incentives they face, and the outcomes of interacting within an amoral market setting. However, in the real world, economics and ethics are more interconnected. Humans are social and ethical beings regardless of setting. Recent studies have shown that individuals reward trustworthiness, punish dishonesty, and can develop meaningful social bonds within markets. Economists, seeking to better understand the world, should incorporate ethics into their economics. We argue that Adam Smith is an exemplar of pursuing a fuller approach to social science, and utilize his arguments on both economics and ethics to advance a study of ethical markets.

This chapter extends the use of integrated assessment models (IAMs) by defining rational policies based on predictive control and adaptive behavior. After a review of the main IAMs, the concept of Model Predictive Nash Equilibrium (MPNE) is introduced within a general model involving heterogeneous economic agents operating in (and interfering with) a common environment. This concept captures the fact that agents do not have a perfect foresight for several ingredients of the economy and the environment. The canonical IAM (DICE) is used as a benchmark. The concept of MPNE is then enhanced with adaptive learning about the environmental dynamics and the damages caused by global warming. The approach is illustrated by some numerical experiments in a two-region setting.

This chapter introduces the Eurace@Unibi model, one of the agent-based simulation models that are relatively new additions to the toolbox of macroeconomists, and the research that has been done within this framework. It shows how an agent-based model can be used to identify economic mechanisms and how it can be applied to spatial policy analysis. The assessment is that agent-based models in economics have passed the proof-of-concept phase and it is now time to move beyond that stage. It has been shown that new kinds of insights can be obtained that complement established modeling approaches. The chapter concludes by pointing toward some potentially fruitful areas of agent-based macroeconomic research.

This chapter discusses a step in the evolution of agent-based model (ABM) research in finance. Agent-based modeling has concentrated on the development of stylized market models, which have been extremely useful for understanding how complex macro-scale phenomena emerge from micro-rules. In order to further develop ABMs from proof of concept into robust tools for policy makers, to control and forecast complex real-world financial markets, it is essential to permit agents to behave as active data-gathering decision makers with sophisticated learning capabilities. The main focus of this chapter is to show how agent based models (ABMs) in financial markets have evolved from simple zero- intelligence agents that follow arbitrary rules of thumb into sophisticated agents described by microfounded rules of behavior. The chapter then briefly looks at the challenges posed by and approaches to model calibration and provides examples of how ABMs have been successful at offering useful insights for policy making.

With the help of two examples, this chapter illustrates the usefulness of agent-based models as tools for economic policy design. The first example applies a financial market model in which the order flow of speculators, relying on technical and fundamental analysis, generates intricate price dynamics. The second example applies a Keynesian-type goods market model in which the investment behavior of firms, relying on extrapolative and regressive predictors, generates complex business cycles. It adds a central authority to these two setups and explores the impact of simple intervention strategies on the model dynamics. On the basis of these experiments, the chapter concludes that agent-based models may help us understand how markets function and evaluate the effectiveness of various stabilization policies.

The chapter reviews the literature concerning agent-based labor market models by tracing its roots to the microsimulation literature and surveying a selection of con- tributions made since the work by Bergmann and Eliasson et al. Agent-based models have been applied to explain stylized facts of labor markets as well as labor market policy evaluations. They also constitute a major part of agent-based macroeconomic models. Besides reviewing the various results achieved, the chapter discusses modeling choices with respect to agents' behavior and the structure of interaction. The overall assessment is that agent-based labor market models have given us valuable insights into the functioning of labor markets and the consequences of labor market policies, and that they will increasingly become an essential tool of analysis, in particular, when the construction of large macro-models is involved.

The chapter discusses algorithmic trading, which refers to any automated process, consisting of a number of interconnected components, whose main aim is to perform financial transactions of any kind. Its chief advantage lies in the fact that human intervention is minimized to an acceptable extent. This is quite desirable because nowadays numerous factors affect financial decisions. Financial managers are able to deal with a limited amount of information. There are many ways to implement algorithmic trading systems. This chapter aims to highlight the efficiency of biologically inspired methodologies when incorporated in such systems. Biologically inspired intelligence comprises a range of algorithms whose common philosophy is based on the behavior of real-world, natural systems and networks. What is more, the performance of the applied nature-inspired intelligence (NII) methodologies is compared to traditional benchmark approaches such as the random portfolio construction.

This chapter reviews recent developments in the analysis of macroeconomic panel data which typically involve aggregate variables from various countries. In contrast to the large N, small T framework that characterizes microeconomic panels, the two dimensions of a macroeconomic data set are more balanced, often providing a comparable number of time periods and countries (regions). Although this is inconsequential for the analysis based on the linear static panel data framework, it becomes crucial when estimating a dynamic model. A second important feature of macroeconomic data is cross-section dependence among countries. In many cases this dependence cannot be accommodated by a simple function of the geographical distance but also depends on trade relations and the level of economic development. Furthermore, cross-country data often exhibit a much richer pattern of heterogeneity that cannot be represented just by letting the intercept vary across countries. While it is often infeasible to allow for individual specific regression coefficients in a large N, small T panel framework, this may be a reasonable option when analyzing macroeconomic data.

This chapter studies the estimation of φ in linear inverse problems Tφ = r, where r is only observed with error and T may be given or estimated. The unknown element φ belongs to a Hilbert space E. Four examples are relevant for econometrics: the density estimation, the deconvolution problem, the linear regression with an infinite number of possibly endogenous explanatory variables, and the nonparametric instrumental variables estimation. In the first two cases T is given, whereas it is estimated in the two other cases, respectively at a parametric or nonparametric rate. This chapter will recall the main results on these models: concepts of degree of ill-posedness, regularity of φ, regularized estimation, and the rates of convergence usually obtained. The main contributions are, moreover, related to the asymptotic normality of the regularized solution φ obtained with a regularization parameter α. If α → 0, we particularly consider the asymptotic normality of inner products <φ, ϕ>, where ϕ is an element of E. These results can be used to construct (asymptotic) tests on φ.

This chapter discusses the challenges raised by the inclusion of evolutionary elements in the theories of Carl Menger, Joseph Schumpeter, and Friedrich Hayek. Each adopted an idiosyncratic position in terms of method of inquiry, focus, and general message. The breadth of the topics and phenomena they cover testifies to the great variety of interpretations and potential uses of evolutionary concepts in economics. Menger, who made no reference to Darwin’s theory, advanced an “organic” view of the emergence of social institutions. Schumpeter elaborated an original theory of industrial development based on the recurrent emergence and dissemination of innovations. Hayek adopted the biological notion of group selection and made it the central element in his theory of cultural evolution and the rise of the free market. The chapter concludes with a preliminary evaluation of the possible role that evolutionary theorizing might play in the future development of Austrian economics.

This chapter offers a synthetic account of the key methodological ideas espoused by prominent Austrian economists. It focuses on the contributions of Carl Menger, Ludwig von Mises, Friedrich Hayek, Ludwig Lachmann, and Donald Lavoie, arguing that epistemological concerns fail to encapsulate their overlapping but distinctive and complementary methodological arguments. Their methodological positions are better explained as flowing from a shared and distinctive social ontology that underlies Austrian economic theory. Austrian social ontology is distinct because of its commitment to three key concepts: radical subjectivism, sheer ignorance, and spontaneous order. The chapter then presents a stylized schema of social processes that embodies these key concepts and shows that the schema both accommodates distinctively Austrian theories and allows for a synthesis of the key methodological contributions of all the Austrian economists discussed earlier.

As bettors become more sophisticated, there is an increasing focus on bankroll risk management or how much to bet on certain opportunities. Bettors often face situations where multiple games are played simultaneously. Thus, the problem of allocating capital across different games or events must be considered, much the same as an investor allocating capital to different stocks in a portfolio. In this chapter, the use of accumulator bets (parlays) as part of a portfolio betting strategy is explored.

This chapter examines the evolution of the structuralist school of economic thought in the Brazilian context. The intellectual roots of structuralism are analyzed, as is the influence this set of ideas has had on economic policy formulation in Brazil. Prominent structuralists such as Celso Furtado and Raul Prebisch influenced the governments of Getúlio Vargas and Juscelino Kubitschek, while Furtado himself played a key role in establishing the national development bank (BNDES) and the Northeast development agency, SUDENE. Furtado “historicized” CEPAL structuralism and showed how losses in the coffee sector were spread across the whole economy in the 1930s. He furthermore developed a model of internal colonialism and arguably was the first dependency theorist. The crisis of structuralism in the mid-1960s ultimately resulted in neostructuralism in 1990, a reformed version of the doctrine that emphasized the export market, technological change, and continual “learning by doing.”

The chapter focuses on the use of fuzzy logic, or soft computing, among the different methods used as supports for decision making in business applications. The processes are focused on private corporate attempts at making money or decreasing expenses; therefore, the details of applications, successful or not, are not published very often. Fuzzy logic helps in decentralization of decisionmaking processes that are to be standardized, reproduced, and documented. Fuzzy logic plays very important roles, especially in business, because it helps reduce costs. It differs from conventional (hard) computing in that it is tolerant of imprecision, uncertainty, partial truth, and approximation. In effect, the role model for fuzzy logic is the human mind. The guiding principle of fuzzy logic is to exploit this tolerance to achieve tractability, robustness, and low solution cost.

This chapter examines the interrelationships between democracy on the one hand and capitalism (or what I prefer to call “the liberal economy”) on the other. Liberal thinkers tend to maintain that the two are allies, at least as long as democracy is (constitutionally or otherwise) limited. Socialists regard them as rivals, as “true” democracy can be realized only under socialism or communism. Joseph Schumpeter stands out as the commentator who argued that there is no strong relationship at all between the two: any economic arrangement can be combined successfully with any political arrangement. I survey both the classical views on this topic and a number of more recent contributions.