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arXiv2007

Statistical properties of agent-based market area model

One dimensional stylized model taking into account spatial activity of firms with uniformly distributed customers is proposed. The spatial selling area of each firm is defined by a short interval cut out from selling space (large interval). In this representation, the firm size is directly associated with the size of its selling interval. The recursive synchronous dynamics of economic evolution is discussed where the growth rate is proportional to the firm size incremented by the term including the overlap of the selling area with areas of competing firms. Other words, the overlap of selling areas inherently generate a negative feedback originated from the pattern of demand. Numerical simulations focused on the obtaining of the firm size distributions uncovered that the range of free parameters where the Pareto's law holds corresponds to the range for which the pair correlation between the nearest neighbor firms attains its minimum.

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arXiv2007

Mixing Kohonen Algorithm, Markov Switching Model and Detection of Multiple Change-Points: An Application to Monetary History

The present paper aims at locating the breakings of the integration process of an international system observed during about 50 years in the 19th century. A historical study could link them to special events, which operated as exogenous shocks on this process. The indicator of integration used is the spread between the highest and the lowest among the London, Hamburg and Paris gold-silver prices. Three algorithms are combined to study this integration: a periodization obtained with the SOM algorithm is confronted to the estimation of a two-regime Markov switching model, in order to give an interpretation of the changes of regime; in the same time change-points are identified over the whole period providing a more precise interpretation of the various types of regulation.

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arXiv2007

Wealth distribution in a System with Wealth-limited Interactions

We model a closed economic system with interactions that generates the features of empirical wealth distribution across all wealth brackets, namely a Gibbsian trend in the lower and middle wealth range and a Pareto trend in the higher range, by simply limiting the an agents' interaction to only agents with nearly the same wealth. To do this, we introduce a parameter BETA that limits the range on the wealth of a partner with which an agent is allowed to interact. We show that this wealth-limited interaction is enough to distribute wealth in a purely power law trend. If the interaction is not wealth limited, the wealth distribution is expectedly Gibbsian. The value of BETA where the transition from a purely Gibbsian law to a purely power law distribution happens depends on whether the choice of interaction partner is mutual nor not. For a non-mutual choice, where the richer agent gets to decide, the transition happens at BETA=1.0. For a mutual choice, the transition is at BETA= 0.60. In order to generate a mixed Gibbs-Pareto distribution, we apply another wealth-based rule that depends on the parameter w_limit. An agent whose wealth is below w_limit can choose any partner to interact with, while an agent whose wealth is above w_limit is subject to the wealth-limited range in his choice of partner. A Gibbs-Pareto distribution appears if both these wealth-based rules are applied.

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arXiv2007

Kinetic Economies

We study a minimalist kinetic model for economies. A system of agents with local trading rules display emergent demand behaviour. We examine the resulting wealth distribution to look for non-thermal behaviour. We compare and contrast this model with other similar models.

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arXiv2016

Common Markets, Strong Currencies & the Collective Welfare

The so called "globalization" process (i.e. the inexorable integration of markets, currencies, nation-states, technologies and the intensification of consciousness of the world as a whole) has a behavior exactly equivalent to a system that is tending to a maximum entropy state. This globalization process obeys a collective welfare principle in where the maximum payoff is given by the equilibrium of the system and its stability by the maximization of the welfare of the collective besides the individual welfare. This let us predict the apparition of big common markets and strong common currencies. They will reach the "equilibrium" by decreasing its number until they reach a state characterized by only one common currency and only one big common community around the world.

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arXiv2007

Information, Inflation, and Interest

We propose a class of discrete-time stochastic models for the pricing of inflation-linked assets. The paper begins with an axiomatic scheme for asset pricing and interest rate theory in a discrete-time setting. The first axiom introduces a "risk-free" asset, and the second axiom determines the intertemporal pricing relations that hold for dividend-paying assets. The nominal and real pricing kernels, in terms of which the price index can be expressed, are then modelled by introducing a Sidrauski-type utility function depending on (a) the aggregate rate of consumption, and (b) the aggregate rate of real liquidity benefit conferred by the money supply. Consumption and money supply policies are chosen such that the expected joint utility obtained over a specified time horizon is maximised subject to a budget constraint that takes into account the "value" of the liquidity benefit associated with the money supply. For any choice of the bivariate utility function, the resulting model determines a relation between the rate of consumption, the price level, and the money supply. The model also produces explicit expressions for the real and nominal pricing kernels, and hence establishes a basis for the valuation of inflation-linked securities.

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arXiv2007

Financial Variables Effect on the U.S. Gross Private Domestic Investment (GPDI) 1959-2001

I studied what role the US stock markets and money markets have possibly played in the Gross Private Domestic Investment (GPDI) of the United States from the year 1959 to the year 2001, Gross Private Domestic Investment refers to the total amount of investment spending by businesses and firms located within the borders of a nation. It includes both the values of the purchases of non-residential fixed investment, which include capital goods used for production, and the values of the purchases of residential fixed investment, which include construction spending for factories or offices. And I created a Multiple Linear Regression Model of the GDPI. To see if companies and private citizens use the stock market and money markets as a way of financing capital projects (business ventures, buying commercial and noncommercial property, etc). Keywords: Gross Private Domestic Investment, Pearson Correlation, SP 500, TB3

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arXiv2007

An Economic Model of Coupled Exponential Maps

In this work, an ensemble of economic interacting agents is considered. The agents are arranged in a linear array where only local couplings are allowed. The deterministic dynamics of each agent is given by a map. This map is expressed by two factors. The first one is a linear term that models the expansion of the agent's economy and that is controlled by the {\it growth capacity parameter}. The second one is an inhibition exponential term that is regulated by the {\it local environmental pressure}. Depending on the parameter setting, the system can display Pareto or Boltzmann-Gibbs behavior in the asymptotic dynamical regime. The regions of parameter space where the system exhibits one of these two statistical behaviors are delimited. Other properties of the system, such as the mean wealth, the standard deviation and the Gini coefficient, are also calculated.

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arXiv2008

Analysing tax evasion dynamics via the Ising model

We develop a model of tax evasion based on the Ising model. We augment the model using an appropriate enforcement mechanism that may allow policy makers to curb tax evasion. With a certain probability tax evaders are subject to an audit. If they get caught they behave honestly for a certain number of periods. Simulating the model for a range of parameter combinations, we show that tax evasion may be controlled effectively by using punishment as an enforcement mechanism.

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arXiv2008

Emergence of firms in $(d+1)$-dimensional work space

Standard micro-economics concentrate on the description of markets but is seldom interested in production. Several economists discussed the concept of a firm, as opposed to an open labour market where entrepreneurs would recrute workers on the occasion of each business opportunity. Coase \cite{Coase} is one of them, who explains the existence of firms as institution because they reduce the transaction costs with respect to an open labour market. Whatever the rationale proposed by economists to account for the existence of firms, their perspective is based on efficiency and cost analysis. Little attention is paid to the dynamics of emergence and evolution of firms. The aim of the present manuscript is to check the global dynamical properties of a very simple model based on bounded rationality and reinforcement learning. Workers and managers are localised on a lattice and they choose collaborators on the basis of the success of previous work relations. The choice algorithm is largely inspired rom the observation and modeling of long term customer/sellers relationships observed on perishable goods markets discussed in Weisbuch etal\cite{Weisbuch} and Nadal etal\cite{Nadal}. The model presented here is in no way an alternative to Coase. We describe the build-up of long term relationships which do reduce transaction costs, and we deduce the dynamical properties of networks built from our simple assumptions. In conclusion, the present model explains the metastability of employment relations in the firm, but something has to be added to it to explain the more efficient workload repartition observed in real firms.

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arXiv2008

Econophysics: historical perspectives

Econophysics embodies the recent upsurge of interest by physicists into financial economics, driven by the availability of large amount of data, job shortage in physics and the possibility of applying many-body techniques developed in statistical and theoretical physics to the understanding of the self-organizing economy. This brief historical survey emphasizes that Econophysics has many historical precursors, and is in fact rooted in a continuous cross-fertilization between economics and physics that has been active in the last centuries.

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arXiv2009

The universal shape of economic recession and recovery after a shock

We show that a simple and intuitive three-parameter equation fits remarkably well the evolution of the gross domestic product (GDP) in current and constant dollars of many countries during times of recession and recovery. We then argue that this equation is the response function of the economy to isolated shocks, hence that it can be used to detect large and small shocks, including those which do not lead to a recession; we also discuss its predictive power. Finally, a two-sector toy model of recession and recovery illustrates how the severity and length of recession depends on the dynamics of transfer rate between the growing and failing parts of the economy.

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arXiv2008

Intermittency and Localization

In this paper, we show how simple logistic growth that was studied intensively during the last 200 years in many domains of science could be extended in a rather simple way and with these extensions is capable to produce a collection of behaviors widely observed in an enormous number of real-life systems in Economics, Sociology, Biology, Ecology and more.

physics.soc-ph↗

arXiv2008

Finite-time singularity in the evolution of hyperinflation episodes

A model proposed by Sornette, Takayasu, and Zhou for describing hyperinflation regimes based on adaptive expectations expressed in terms of a power law which leads to a finite-time singularity is revisited. It is suggested to express the price index evolution explicitly in terms of the parameters introduced along the theoretical formulation avoiding any combination of them used in the original work. This procedure allows to study unambiguously the uncertainties of such parameters when an error is assigned to the measurement of the price index. In this way, it is possible to determine an uncertainty in the critical time at which the singularity occurs. For this purpose, Monte Carlo simulation techniques are applied. The hyperinflation episodes of Peru (1969-90) and Weimar Germany (1920-3) are reexamined. The first analyses performed within this framework of the very extreme hyper-inflations occurred in Greece (1941-4) and Yugoslavia (1991-4) are reported. The study of the hyperinflation spiral experienced just nowadays in Zimbabwe predicts a singularity, i.e., a complete economic crash within two years.

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arXiv2008

Balance, growth and diversity of financial markets

A financial market comprising of a certain number of distinct companies is considered, and the following statement is proved: either a specific agent will surely beat the whole market unconditionally in the long run, or (and this "or" is not exclusive) all the capital of the market will accumulate in one company. Thus, absence of any "free unbounded lunches relative to the total capital" opportunities lead to the most dramatic failure of diversity in the market: one company takes over all other until the end of time. In order to prove this, we introduce the notion of perfectly balanced markets, which is an equilibrium state in which the relative capitalization of each company is a martingale under the physical probability. Then, the weaker notion of balanced markets is discussed where the martingale property of the relative capitalizations holds only approximately, we show how these concepts relate to growth-optimality and efficiency of the market, as well as how we can infer a shadow interest rate that is implied in the economy in the absence of a bank.

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arXiv2008

Quantitative analysis of privatization

In recent years, the economic policy of privatization, which is defined as the transfer of property or responsibility from public sector to private sector, is one of the global phenomenon that increases use of markets to allocate resources. One important motivation for privatization is to help develop factor and product markets, as well as security markets. Progress in privatization is correlated with improvements in perceived political and investment risk. Many emerging countries have gradually reduced their political risks during the course of sustained privatization. In fact, most risk resolution seems to take place as privatization proceeds to its later stage. Alternative benefits of privatization are improved risk sharing and increased liquidity and activity of the market. One of the main methods to develop privatization is entering a new stock to the markets for arising competition. However, attention to the capability of the markets to accept a new stock is substantial. Without considering the above statement, it is possible to reduce the market's efficiency. In other words, introduction of a new stock to the market usually decreases the stage of development and activity and increases the risk. Based on complexity theory, we quantify how the following factors: stage of development, activity, risk and investment horizons play roles in the privatization.

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arXiv2008

The virtues and vices of equilibrium and the future of financial economics

The use of equilibrium models in economics springs from the desire for parsimonious models of economic phenomena that take human reasoning into account. This approach has been the cornerstone of modern economic theory. We explain why this is so, extolling the virtues of equilibrium theory; then we present a critique and describe why this approach is inherently limited, and why economics needs to move in new directions if it is to continue to make progress. We stress that this shouldn't be a question of dogma, but should be resolved empirically. There are situations where equilibrium models provide useful predictions and there are situations where they can never provide useful predictions. There are also many situations where the jury is still out, i.e., where so far they fail to provide a good description of the world, but where proper extensions might change this. Our goal is to convince the skeptics that equilibrium models can be useful, but also to make traditional economists more aware of the limitations of equilibrium models. We sketch some alternative approaches and discuss why they should play an important role in future research in economics.

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arXiv2008

Demand forecasting for companies with many branches, low sales numbers per product, and non-recurring orderings

We propose the new Top-Dog-Index to quantify the historic deviation of the supply data of many small branches for a commodity group from sales data. On the one hand, the common parametric assumptions on the customer demand distribution in the literature could not at all be supported in our real-world data set. On the other hand, a reasonably-looking non-parametric approach to estimate the demand distribution for the different branches directly from the sales distribution could only provide us with statistically weak and unreliable estimates for the future demand. Based on real-world sales data from our industry partner we provide evidence that our Top-Dog-Index is statistically robust. Using the Top-Dog-Index, we propose a heuristics to improve the branch-dependent proportion between supply and demand. Our approach cannot estimate the branch-dependent demand directly. It can, however, classify the branches into a given number of clusters according to an historic oversupply or undersupply. This classification of branches can iteratively be used to adapt the branch distribution of supply and demand in the future.

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