An Agent-based Computational Study of Wealth Distribution in Function of Technological Progress Using Netlogo

In this paper, we computed Gini coefficient in function of technological progress modeled using agent-based methodology in the frame of NetLogo software. We start from the simplest type of society (agrarian society), continue with the industrial one where we model the phenomenon of industrial revolution with four waves, and end with green revolution with other four waves. The conclusion is that technological progress has a negative influence on equality of wealth distribution measured by Gini coefficient and this is explained by the heterogeneity of turtle's population given by their variable vision.


Introduction
Agent-based Computational Economics applies an interdisciplinary approach that combines knowledge from Agent-based Computational Modeling and Economics with the scope to observe, to analyze and to discuss the evolution of an economic system composed by intelligent agents. Agent-based Computational Modeling involves research in areas of science where computing plays a central and essential role, emphasizing agents seen as entities that encapsulate other agents, procedures, parameters, and variables. Agent-based Computational Modeling is a branch of Applied Computational Mathematics that currently is the field of study concerned with constructing mathematical models and numerical solution techniques by using computers in order to analyze and solve scientific, social scientific and engineering problems (Damaceanu 2010).
The literature of agent-based computational economics and evolutionary economics try to create a consistent theory using the process described in Figure 1, where from using a combination of definitions and assumptions, the scientist builds a theory (an agent-based model) to be confronted with real economic phenomena. After this evaluation that uses econometric studies the theory is considered to be consistent with the observed reality or non-consistent. In the first case, there is a provisional acceptance of the theory. In the second case, is going full rejection or possibly changed assumptions as a result of observations made and the process is retaken on new forms. Figure 1 shows us clearly that the process is divided in two major parts. The first part consider what is called Normative Economics that expresses value judgments (normative judgments) about economic fairness or what the economy ought to be like or what goals of public policy ought to be. The second part enter in the sphere of Positive Economics that is the branch of Economics that describes and explains economic phenomena focusing on facts and cause-and-effect behavioral relationships and includes the development and testing of economics theories (Samuelson and Nordhaus 2004). The study done in the frame of this paper enters mostly in the sphere of Normative Economics and uses an agent-based computational model seen as a simplified image of a real economic system -see ( Figure 2). The respective figure shows us that any agent-based model is a model of a real economic system that takes input data and creates The rest of the paper is organized like this: Section 2 describes the methodology used, Section 3 and 4 are dealing with conceptual and operational validation of the model used for a number of computer experiments and the last section presents the conclusions of our study.

The Methodology
The main construction blocks of any agent-based computational model (ACM) are the following: the set of agents (A), the initializations (I) and the simulation specifications (R) -see ( Figure 3). The set of agents A contain all agents defined as artificial entities that encapsulate the following elements: parameters, variables, procedures and other sub-agents. The root agent of NetLogo software platform is called observer and this one has other three sub-agents called turtles, patches and links. Parameters have numerical values that do not modify on the entire period of simulation. Normally, parameters are initialized before simulation. However, in some situations they can be changed during the simulation. Variables are labels that have a number of values during the simulation. Procedures are a finite list of well-defined operations that are working with the passive part of an-agent based computational model (agents, parameters and variables) and with the active part (other procedures). In the frame of NetLogo there are two types of procedures: commands and reporters. A command is an action for an agent to carry out. A reporter computes a result and reports it.
Initializations I are a set of identities that have in the left side the variable or parameter name and in the right side the associated value. In the frame of NetLogo platform, these initializations are implemented inside Procedure Tab (the workspace where the code for the model is stored).
The simulation specifications R are a set of identities that have in the left side the control parameter name and in the right side the associated value. This type of specification is defined in Interface Tab (where you watch your model run) using interface items such as buttons, sliders, switchers, monitors, plotters etc. -see ( Figure 4).
Under these circumstances an agent-based computational model (ACM) can be defined as a list of three arguments: the set of agents (A), the initializations (I) and simulation specifications (R). Shortly, ACM = (A, I, R).
In order to validate ACM, we followed the following steps: (1) The analysis of real economic systems; (2) Defining the objective of research and the precise task of the model; (3) Building the conceptual model; (4) Validation of conceptual model; (5) Transformation of conceptual model in a computerized model using NetLogo software platform; (6) The operational validation of computerized model; (7) The analysis of computer experiments results and interpretation from economic point of view. Based on these, we will formulate a number of conclusions.

Conceptual Validation
Despite the fact conceptual validation is very important there is little literature that addresses this issue (Robinson 2006). According to Heath (2009), the conceptual model forms the foundation of an ABM model; an invalid conceptual model indicates the model may not be an appropriate representation of reality.

The Analysis of Real Economic Systems
In this subsection we analyze the main features of economic systems implemented by the following types of society: (i) Agrarian society is based on natural economy defined as a system where the majority of goods are produced for direct consumption (subsistence).
(ii) Industrial society implemented the process of social and economic change that transforms a human group from an agrarian type into an industrial one for the purpose of manufacturing goods not destined for direct consumption.
(iii) Green society generates a new type of economy called green economy that results in improved human well-being and social equity, with reducing environmental risks by implementing a new way of economic development based mostly on renewable resources.

Defining the Objective of Research and the Precise Task of the Model
Taking into account these three types of economic systems we defined the purpose of research as being the relation between technological progress and the distribution of wealth. The technological progress is implemented like a set of major changes in agricultural and industrial sectors. As we know both types of sectors use resources like water, food, coal, oil, gas, uranium, wind, sun, tides, and geothermal heat. To model the phenomenon of technological progress we conceived an agent-based artificial society described in Damaceanu (2011) as an evolutionary system that starts from the simplest type of economy (natural economy based only on water and food resources), continue with the industrial economy (that uses with maximum efficiency the resources of natural economy and discover nonrenewable resources such as coal, oil, gas, and uranium), and ends with the new economy (still using with maximum efficiency the resources of natural and industrial economies if they are available) based on renewable resources like wind, sun, tides, and geothermal heat. The technological progress is introduced in this model in linear way starting from agricultural technologies used in the case of natural economy, continuing with industrial technologies used for extracting nonrenewable resources in the following order coal, oil, gas, and uranium and ending with nonrenewable resources used in the following order wind, sun, tides, and geothermal heat.
The distribution of wealth is analyzed using Gini coefficient -see (Gini 1912). This coefficient is a measure of the inequality of a distribution, a value of 0 expressing total equality and a value of 1 maximal inequality. This index is defined as a ratio of the areas on the Lorenz curve diagramsee Figure 5.

Building the Conceptual Model
In section 2, we defined agent-based computational model (ACM) like a list of three arguments: the set of agents (A), the initializations (I) and the simulation specifications (R). The process of building the conceptual model can be defined like constructing the initial set of agents (A 0 ), setting the initial values of initializations (I 0 ) and specifying the initial values for simulation specifications (R 0 ) -see Figure 6, for a graphical description of the process. This figure shows us how the initial form of the ACM 0 enters in the phase of conceptual validation. If this validation fails the conceptual model is modified in a new form ACM 1 and the process is reiterated until conceptual validation is a success and the model become subject to operational validation.

Validation of Conceptual Model
The validation of conceptual model is a process that checks the integrity of all component elements of agent based model ACM k divided in three major sets: the set of agents A k , the set of initializations I k and the set of simulation specifications R k . In our case, because the model is developed in the frame of NetLogo software platform, we have the following set A k = {O, T i , P xy }, where O is the observer agent that does not have a specific location -we can imagine it like an entity that observes the world composed by its sub-agents turtles T i , and patches P xy -see    A variable owned by observer that describes the evolution in time of Gini coefficient, where At is the area between the line of perfect equality and the Lorenz curve, and Bt is the area under the Lorenz curve -see Fig. 4. A variable that keeps the value of pregnancy duration; this variable has a two possible values 0 (the initial value) and 1 when the turtle gives birth to a child.

Operational Validation
Operational validation can be defined as the transformation process of conceptual model in a model recognized by the software used (in our case NetLogo).

Transformation of Conceptual Model in a Computerized Model Using NetLogo Software Platform
In our case we used NetLogo 4.0.5 and, under these circumstances, we followed the cycles (see Figure 10  Cycle (1) is the most frequent used. In this case, the researcher uses a previous created ACM or a new one in an incipient form, modifies the simulation specifications, runs the model, evaluates the simulation results and in function of these results takes the decision to apply one of the five available cycles.
Cycle (2) starts by changing the parameter values, running ACM, evaluation of results and in function of outcomes the researcher applies one of the five cycles.
Cycle (3) modifies the initial values of variables, runs ACM, evaluates the results and in function of these the researcher takes the decision to apply one of the five cycles.
Cycle (4) modify the set of procedures, runs the model and in function of results obtained after the evaluation the researcher apply one of the five cycles.
Cycle (5) develop new agents, run the model and in function of results the researcher takes the decision to apply one of five available cycles. This cycle usually creates new ACM.
The result of operational validation is the file 3Economies. nlogo available on NetLogo User Community Models sitesee http://ccl.northwestern.edu/netlogo/ models/community/3Economies.

The Operational Validation of Computerized Model
The operational validation is a technique that facilitates a more direct correspondence between the entities in the target system and the parts of the model that represent them (Edmonds 2001). This enhances the descriptive accuracy of the modeling process, but it can also create difficulties. Under these circumstances, almost every operational validation of agent-based models may contain bugs defined as code that does something different in comparison with what you expected (Gilbert 2007). As Axelrod underlines, you have to work hard to confirm that the operational validation is really valid (Axelrod 1997). In addition, Axtell and Epstein state that "the robustness" of macrostructures to perturbations in individual agent performances is specific to agent-based models and makes very hard to identify bugs (Axtell and Epstein 1994).
Computer experiments can be seen as a branch of applied statistics, because the user must take into account the next sources of uncertainty: (i) First, the models may contain parameters whose values are not certain; (ii) Second, the models themselves are imperfect representations of the studied system; (iii) Third, data collected from the system that might be used to calibrate the models are imperfectly measured.
Taking into consideration the evolution in time of economy described in Figure 11, we will do 9 computer experiments described in Table 4.

E1
This experiment is called Agricultural Revolution and has 9 runs that describes a economy based on water and food converted in energy with the following control parameters

Conclusions
Based on data obtained after running the nine computer experiments, we computed the average value of Gini coefficient and using these averages we can describe the evolution of mean value of Gini coefficient in the case of experiments E1-E9 -see Table 5 and Figure 12.  Figure 12 shows us that the technological progress has a negative influence on wealth equality measured by Gini coefficient and this is explained by the heterogeneity of turtles' population Ti given by their variable vision Vi. On the other hand, technological progress has a positive influence on number of turtles but the distribution of wealth become more and more unequal because fewer turtles are "rich" and many others are "poor".