Econophysics of Business Cycles: Aggregate Economic Fluctuations, Mean Risks and Mean Square Risks

1 Econophysics of Business Cycles: Aggregate Economic Fluctuations, Mean Risks and Mean Square Risks Victor Olkhov TVEL, Kashirskoe sh. 49, Moscow, 115409, Russia victor.olkhov@gmail.com Abstract This paper presents hydrodynamic-like model of business cycles aggregate fluctuations of economic and financial variables. We model macroeconomics as ensemble of economic agents on economic space and agent’s risk ratings play role of their coordinates. Sum of economic variables of agents with coordinate x define macroeconomic variables as functions of time and coordinates x. We describe evolution and interactions between macro variables on economic space by hydrodynamic-like equations. Integral of macro variables over economic space defines aggregate economic or financial variables as functions of time t only. Hydrodynamic-like equations define fluctuations of aggregate variables. Motion of agents from low risk to high risk area and back define the origin for repeated fluctuations of aggregate variables. Economic or financial variables on economic space may define statistical moments like mean risk, mean square risk and higher. Fluctuations of statistical moments describe phases of financial and economic cycles. As example we present a simple model relations between Assets and Revenue-on-Assets and derive hydrodynamic-like equations that describe evolution and interaction between these variables. Hydrodynamic-like equations permit derive systems of ordinary differential equations that describe fluctuations of aggregate Assets, Assets mean risks and Assets mean square risks. Our approach allows describe business cycle aggregate fluctuations induced by interactions between any number of economic or financial variables.

Keywords: Business cycles, Aggregate fluctuations, Risk Ratings, Economic Space
JEL: C00, E00, F00, G00 1

1 This research did not receive any specific grant or financial support from TVEL or funding agencies in the public, commercial, or not-for-profit sectors.

2 1. Introduction

Fluctuations and waves are core properties of any complex system. Macroeconomic fluctuations are the most valuable processes that have impact on all characters of economic evolution and state. Modeling and forecasting business cycles aggregate fluctuations for decades remain focal point of economic studies [1-8]. Origin and drivers of aggregate fluctuations of economic and financial variables establish the key problems of business cycles. Let quote only three statements “Theories of business cycles should presumably help us to understand the salient characteristics of the observed pervasive and persistent non seasonal fluctuations of the economy”. [3]. “Why aggregate variables undergo repeated fluctuations about trend, all of essentially the same character? Prior to Keynes’ General Theory, the resolution of this question was regarded as one of the main outstanding challenges to economic research, and attempts to meet this challenge were called business cycle theory.” [4]. “One of the most controversial questions in macroeconomics is what explains business-cycle fluctuations?” [8].

Our paper presents a general model of aggregate fluctuations of economic and financial variables and proposes further features that describe state and evolution of business cycles phases. Due to [6] “The real business cycle theory is a business cycle application of the Arrow-Debreu model, which is the standard general equilibrium theory of market economies”. Our approach to business cycles is completely different from models based on assumptions of general equilibrium [9], decisions making [10] and behavioral economics [11]. We omit review of current state of business cycles and site [1-8] for great in-depth discussion and numerous references.

We regard business cycles as essential property of economic evolution and describe aggregate fluctuations of economic and financial variables as necessary feature of economic processes. Our model of aggregate fluctuations does not require existence any external shocks and disturbances of economic variables. Aggregate fluctuations reflect hidden evolution of economic and financial variables of economic agents on economic space [12- 18]. Agent-based economic models are well known [19] but we suggest a different approach. Let assume that it is possible estimate risk rating for all agents of entire economics like huge banks and corporations and small firms and households. Let treat agent’s risk ratings as their coordinates alike to coordinates of physical particles. Each economic agent has a lot of economic and financial variables as Assets and Debts, Credits and Loans, Production Function and Consumption and so on. Huge number of economic agents of entire economics

3 can be treated alike to “economic gas”. Certain parallels to kinetic theory of gases allows establish transition fr

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