THEORETICAL BASIS 3.1 Introduction
3.3 Agent-based Modelling
3.3.4 Previous relevant research
EURACE was a massive endeavour to simulate the actual European economy, according to its complex nature with dynamic interacting and heterogeneous agents and was developed on the Flexible Large-scale Agent Modelling Environment (Deissenberg et al., 2008; Naciri and Tkiouat, 2016). It should be noted, however, that there is a plethora of platforms that can be utilised for the development of ACE models, these include: Swarm, NetLogo and RePast (Getchell, 2008). Some of the main components of EURACE are as follows (Deissenberg et al., 2008; Cincotti et al., 2011): time and space: EURACE is developed using the spatial boundaries that the European Statistics Office utilises for the European Union. All other regions in the world are considered as a single region. The model utilises ‘a day’ as the basis for its time construct. It is important to note that not everything occurs on a particular day, for example some activities depend on other activities while varying amounts of time controls others. Households: can fulfil various roles, such as providing labour, as an investor, or a consumer of goods. Firms: there are two types of companies that each produces a specific type of product, one produces ‘capital equipment’ which is then utilised by the other sector to manufacture ‘consumable goods’. Banks: provide loans to other agents but are made realistic in the sense that they first assess ‘credit worthiness’ and have varying degrees on interest. National government and central bank: are the only passive agents that can only operate according to narrowly defined algorithms. ‘Statistical communication agents’: essentially act as an information processing and providing agent, when information on the state of the ‘markets’ or economy is required. There are also various markets, which include: consumption goods, investment goods, labour, credit and financial assets.
It should be noted that Deissenberg et al. (2008) merely provides information on EURACE and specifically only the labour market within the model and can thus be described as a decent introductory to the overall structure of EURACE. For a more in- depth look at EURACE and some of its more salient protocols we turn to Cincotti et al. (2011). According to Cincotti et al. (2011), the following are some of the broad features of EURACE: it is an uncommon agent-based economic model that includes all the critical elements, such as financial stocks and flows that are modelled from the
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bottom-up. The agents in EURACE are modelled as ‘bounded rationally’ as opposed to having perfect knowledge and making completely rational decisions. The heuristics that are utilised as a basis to model the agents are borrowed from various other academic disciplines such as management and psychology. The algorithms that the agents are modelled according to are allowed to evolve according to the state of the entire model. There are two types of agents: the first merely makes decisions based on
‘input parameters’ received from other agents and the environment. The second actively learns and evolves and make decisions thereafter. The various markets are based on the manner in which real-life markets are structured and operate. The details of the markets will be discussed further down. A balance sheet format is utilised in EURACE to ensure that all financial flows are accounted for. Various agents’
decision making is based on time scales that are observed in real life. Interactions between agents are modelled as asynchronous to ensure that the agents do not interact in the same manner with the same agents. However, some interactions or activities are scheduled and synchronised to reflect institutional operations.
According to Cincotti et al. (2011), there are two types of manufacturers: capital manufacturers and consumption goods manufacturers, which make up the production sector. The capital manufacturers are modelled as less complex than consumption goods manufacturers. Capital manufacturers can produce unlimited goods, of one technology, in addition they don’t need to carry any inventory or require credit facilities. The only inputs required by capital manufacturers are energy and raw material. The price of the capital goods is determined by a simple percentage increase on the energy price. All of the capital manufacturers are equally owned by all of the households. Consumption goods manufacturers are modelled to utilise capital goods and labour, provided by households, according to a Cobb-Douglas production function. The quantity and price levels of stock are determined according to typical rules. Consumption goods manufacturers have the ability to access credit from banks in order to finance production and cover any other financial commitments. An important feature built into the model, is that if or when consumption goods manufacturers cannot access credit when it is needed then the manufacturer will be closed. The manufacturers financial position is based on the parameters described in Table 3.1.
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Classification Parameter Updating schedule
Assets
𝑀𝑓: Cash deposited in the bank Daily
𝐼𝑓 : Inventory Daily
𝐾𝑓 : Physical capital Monthly Liabilities Df= Σ𝑙𝜆𝑓,𝑖 : Total debt Monthly
𝐸𝑓 : Equity Monthly
Table 3.1: Parameters of manufacturers in the EURACE model Source: Cincotti et al. (2011).
𝐸𝑓 = 𝑀𝑓+ 𝑝𝐶𝐼𝑓+ 𝑝𝐾𝐾𝑓− ∑ 𝐷𝑏𝑓
𝑏∈{𝑏𝑎𝑛𝑘𝑠}
𝑝𝐶 refers to the price of consumption goods and 𝑝𝐾 is the price of capital goods.
The consumption goods manufacturer calculates the quantity of goods that is to be produced in a specific month and the corresponding price level. The planned amount of goods to be produced, taken together with inventory from the previous month determines the amount of labour and capital. If the capital held by the firm, taking depreciation into account, is less than that held by the manufacturer then an investment into capital is needed.
The manufacturer also calculates, monthly, the amount of interest to be paid for loans taken out. The equation for this is:
𝐵𝜏𝑓 = ∑ 𝑟𝑖
𝑖 12
𝜆𝜏−1𝑓,𝑖
Consumption goods manufacturers also pay Tax (T) on a monthly basis. This is calculated at a fixed percentage (𝜉) of the previous months gross profit (Π). The equation is denoted as:
𝑇𝜏𝑓= 𝜉Π𝜏−1𝑓
Revenue of the consumption goods manufacturer is calculated as price (p) multiplied by quantity (q) follows:
𝑅𝜏−1𝑓 = 𝑝𝜏−1𝑓 𝑞𝜏−1𝑓
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The cost of labour is calculated as wage per employee (𝑤) multiplied by number of employees (Ν), 𝑤𝜏−1Ν𝜏−1𝑓 .
Taking the previously mentioned parameters, we arrive at total liability of a consumption goods manufacturer by adding all debt, taxes and manufacturing costs, this is captured in the equation:
𝐿𝜏𝑓 = 𝐵𝜏𝑓+ Τ𝜏𝑓+ 𝑝 ∑ 𝜆𝜏−1𝑓,𝑖
𝑖
+ 𝐸𝑓𝐷̂𝜏𝑓+ 𝑤𝜏𝑁̂𝜏𝑓+ 𝑝𝜏𝑘𝐼̂𝜏𝑓
Cincotti et al. (2011) further discuss how the production quantity and price level decisions, for consumption goods manufacturers, are arrived at:
𝑄̃𝑓,𝑡 = {0, 𝐼𝑓,𝑡 ≥ 𝑄̂𝑓,𝑡 𝑄̂𝑓,𝑡− 𝐼𝑓,, 𝐼𝑓,𝑡 < 𝑄̂𝑓,𝑡
The quantity required for the coming month (𝑄̃𝑓,𝑡) is determined by the anticipated demand (𝑄̂𝑓,𝑡), from which current inventory level (𝐼𝑓,𝑡) is deducted.
The anticipated demand is calculated based on a simple linear regression calculation, which is as follows:
𝑄̂𝑓,𝑡 = 𝑎̂𝑓,𝑡 + (𝜏 − 1)𝑏̂𝑓,𝑡+ 𝑞̅1−𝑥∙ √𝛿̂𝑡2
where 𝑞̅1−𝑥 represents that standard distribution, where
𝑏̂𝑓,𝑡 = 𝜏Σ𝑠=1 𝜏 𝑠𝑆̂𝑓,𝑡−𝜏+𝑠−12(𝜏(𝜏 + 1))Σ𝑠=1𝜏 𝑆̂𝑓,𝑡−𝜏+𝑠
1
6(𝜏2(𝜏+1)(2𝜏+1))−14(𝜏2(𝜏+1)2)
and
𝑎̂𝑓,𝑡 =1
𝜏∑ 𝑆̂𝑓,𝑡−𝜏+𝑆
𝜏
𝑠=1
−1
2𝑏̂𝑓,𝑡(𝜏 + 1)
with the variance (𝛿2) being
𝛿2 = 1
(𝜏 − 1)∑(𝑆̂𝑓,𝑡−𝜏+𝑠− (𝑎̂𝑓,𝑡 + 𝑠 ∙ 𝑏̂𝑓,𝑡))2
𝜏
𝑠=1
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In order to prevent massive variations in the quantity produced in the current month the manufactured quantity is adjusted, this is denoted as:
𝑄̅𝑓,𝑡 = 𝜉 ∙ 𝑄̃𝑓,𝑡+ (1 − 𝜉) ∙1
𝑇∙ ∑ 𝑄𝑓,𝑘
𝑡−1
𝑘=𝑡−𝑇
The sales price of all manufactured consumption products is set according to the following calculation:
𝑝𝑓,𝜏 = 𝑐̅𝑓,𝜏−1 1 + 1/𝜀𝑓𝑒
where the cost per unit (𝑐̅𝑓,𝜏−1) is calculated taking into account the current manufacturing (𝑐̃𝑓,𝜏) and existing stock:
𝑐̅𝑓,𝜏 =𝑐̅𝑓,𝜏−1𝐼𝑓,𝜏+ 𝑐̃𝑓,𝜏𝑄𝑓,𝜏 𝐼𝑓,𝜏+ 𝑄𝑓,𝜏
The consumption goods manufacturer amasses physical capital according to the following rule:
𝐾𝑓,𝑡+𝜏 = (1 − 𝛿)𝐾𝑓,𝑡+ 𝐼𝑓,𝑡
Each individual employee has two skills sets, a general skills set (𝑏𝑤𝑔𝑒𝑛) and more specific skills set (𝑏𝑤,𝑡), which dictates how effectively an employee can utilise technology. The rule according to which an employee’s specific skills set evolves take place is:
𝑏𝑤,𝑡+1 = 𝑏𝑤,𝑡 + 𝜒(𝑏𝑤𝑔𝑒𝑛) ∙ (𝐴𝑓,𝑡 − 𝑏𝑤,𝑡)
where 𝐴𝑓,𝑡 is the average quality of capital stock.
The quantity of consumption goods manufactured by a manufacturer is calculated according to the following rule. Where 𝐵𝑓,𝑡, is the average specific skills set and 𝛼 + 𝛽 = 1
𝑄𝑓,𝑡 = min[𝐵𝑓,𝑡,𝐴𝑓,𝑡] × 𝐿𝑓,𝑡𝛼 𝐾𝑓,𝑡,𝛽
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The above rule makes use of a Cobb-Douglas production function, where the investment quality and specific skills set for utilising a specific type of technology is complimentary and where 𝐵𝑓,𝑡, represents the average specific skills set.
According to Cincotti et al. (2011), households in the EURACE model set a pre- determined consumption level for the month.
𝑐𝜏ℎ = 𝑦̅ℎ+ 𝜙𝐻(𝑊𝜏ℎ− 𝑥𝑦̅ℎ)
where: 𝑦̅ℎ is the average income of a household for the previous five month period, 𝜙𝐻 is an adjustment speed; 𝑊𝜏ℎ is the wealth of the household at the specific time. As a result households will alter consumption levels according to a specific wealth level.
The decision of households to purchase consumption goods is randomised according to a logit regression model, which is taken from standard marketing literature. Where 𝐹ℎ is all the goods that the household as sampled. The decisions to purchase a specific good is dependent on price, since there are no quality differences built into the model and where ∧ represents the level of market competition.
𝑃𝑟𝑜𝑏ℎ,𝑓= exp (−𝜆 log 𝑝𝑓) Σ𝑓∈𝐹ℎexp(− ∧ log 𝑝𝑓)
The banking sector in the EURACE model provides loans to firms and is dependent on the level of risk versus reward of that specific request. The following denotes the manner in which the probability that a firm will default on a loan (𝜋𝑓), i.e.
creditworthiness:
𝜋𝑓 = 1 − exp (−𝐷𝑓+ 𝜆𝑓 𝐸𝑓 )
where: 𝐷𝑓 is the amount of existing total debt, 𝜆𝑓 is the amount of the loan requested by the firm and 𝐸𝑓is the equity of the firm. The interest rate that the bank will then charge the firm (𝑟𝑏,𝑓) is denoted in the following equation. Where 𝑟𝑐𝑏 is the prime interest rate set by the central bank; and 𝛾𝑏 spread sensitivity which is dependent on the credit worthiness of the firm.
𝑟𝑏,𝑓 = 𝑟𝑐𝑏+ 𝛾𝑏𝜋𝑓
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As can be seen, EURACE is a comprehensive model with important agents in the normal functioning of the European economy. There are numerous important aspects that will serve as a basis for this research, especially to demonstrate precedence. The EURACE model is conceptualised from spatial and time constructs, importantly the model views all other continents and regions outside of the European economy as one agent. Agents can fulfil various roles, but belong either to active or passive classifications and it is critical for an independent agent to act as a communicator between other agents. Importantly, the model includes two types of manufacturers with one more complex than the other – which is also partly based on a standard production function. The important point that needs to be raised here is that existing functions can be utilised when developing ACE models. This will be critical if a more generalised approach is needed for certain agent’s behaviour. To date EURACE, arguably, is the most comprehensive ACE model of an actual regional economy and learning and operations from this model will be utilised for the development of the framework, to supplement primary data collection.
The Sandia National Laboratory developed the Aspen model in the mid 90’s (Pryor et al., 1996). The Aspen model utilised the Monte Carlo approach combined with time periods to model a rudimentary market economy, but not rudimentary at the time.
Households, companies in a single sector, and government form the three types of agents incorporated into the model. The agents intermingle via different types of
‘transactions’, as can be seen in Figure 3.2. At the beginning of each day, in the model, the agents’ condition are given. Throughout the day agents undertake decisions that are based on learning models or probabilities. The conditions of agents are updated at the end of the day, which is a function of all their transactions taken during the day. Government collects taxes from the other two types of agents and distributes unemployment benefits to households. The companies produce goods that are consumed by the households. Hiring and firing of employees, by companies, is a function of their stock levels. In addition, there is competition between firms, who vary their selling prices.
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Figure 3.2: Interaction between agents of Aspen Model Source: Adapted from Pryor et al. (1996, pg. 4).
Demand from households is dependent on income and size of family. Pryor et al.
(1996) conclude that the model has the ability to predict economic-like cycles.
Basu et al. (1998) further developed the Aspen simulation model. The number, type and refinement of the agents included in this model are more advanced than the previous Aspen model. The households function in the same manner, with the addition of being able to buy four different types of goods, save money or invest surplus money. Companies have been increased dramatically in this newer model, where they produce four different products, which are: cars, real estate, food and other non-durable goods. All types of goods are derived by the utilisation of labour and the addition of equipment. The government agent functions in a similar manner collecting tax and distributing unemployment benefits and now incorporates a social security system, a government administration and has the ability to issue bonds. A major inclusion in this version of the model is the financial sector which incorporates a reserve bank that is responsible for monetary policy, banks that collect households’
savings, issue loans and buy bonds and a financial agent that acts as an exchange for bonds that are bought and sold. The different agents are clustered into two groups, the first group encompasses those agents that are more than two, the second group is made up of agents where there is only one type of that agent, e.g. reserve bank. As with the initial model, the model revolves around a day and agents that belong to a
Government
Industry Individual
Savings Savings
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specific group where all utilise the same instructions. All agents are represented on nodes and have channels to communicate through, with other agents. All received messages are placed in an ‘inbox’, when a message is sent to another agent if the agent is on the same node the message is sent instantly, otherwise the message gets placed into an ‘outbox’ for sending at the end of a day. All messages in the ‘outbox’
are sent as one packet of data to specific nodes, it is then disaggregated and sent to relevant agents who then read the messages.
The Aspen model has been further utilised to model market forces on the United States of America’s electricity grid and critical infrastructure (Barton et al., 2000) and knock-on effects of terrorism on the economy (Sprigg and Ehlen, 2004).
Riccetti et al. (2015) developed a macroeconomic system modelled from the bottom- up of diverse agents. The agents include: government, central bank, firms and households. The agents interact in four specific markets, which are: goods market, labour market, credit market and the deposit market. Through the model, Riccetti et al. (2015) observes macroeconomic phenomenon that arise out of the micro complex and adaptive interaction of economic agents. These phenomenon include GDP growth and bank defaults. Due to Cincotti et al. (2011) discussing similar aspects in their research on EURACE in a more in-depth manner, the details of the research by Riccetti et al. (2015) will only be briefly discussed. The agents in the model developed by Riccetti et al. (2015) are rationally bounded and operate according to simple rules. These include: household agents buy the cheapest goods from firms, while firms try to increase profits by selling their goods to households. Household agents endeavour to supply their labour to firms that offer the highest salary, while firms try to hire the most inexpensive labour. Households deposit all surplus funds into commercial banks, banks then use those funds to offer loans to firms, where the firms look for commercial banks offering the lowest interest rates. Government hires public servants, oversees taxes and controls public debt. The central bank supplies funds to government and commercial banks, when required. Riccetti et al. (2015) utilise a ‘matching mechanism’ in the four markets that are present in the model. This mechanism functions, fundamentally, in the following manner: at the beginning a random set of two types of agents are generated, one that acts as the supplier and the other as the demand, thereafter an agent chooses a suitable agent from the opposite side, where the choice will depend on a predefined rule or parameter, thereafter, the
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second agent on the same side will repeat point two above; and point three will repeat until all agents, in at least one side, are satisfied.
Čech et al. (2013) developed an ACE model that consists of four categories of agents.
These are: consumer, manufacturer (factory), miner and transporter. All agents endeavour to either maximise profit or some type of utility. In addition, agents are allowed to form structures while seeking to maximise efficiency in terms of supply and demand. However, Čech et al. (2013) highlight that the model is a simplified version due to traditional key economic agents not being included in the model, such as banks and government. The agents operate in the following manner: consumers buy goods and services and provide labour. The wealth level of a consumer is determined by their work and qualification. Consumers also have to decide between gaining a qualification and buying goods and services. There are three types of consumers: low, middle and high income. There are also three types of goods included in the model: necessity, normal and luxurious. Manufacturers convert input to goods that is either bought by consumers or by other manufacturers. Each miner extracts one type of raw material, stored and sold to transporters. The cost of the raw material is determined by energy costs and technology utilised. The transporter procures material from the miner and sells it on to the manufacturer. The distance from the miner to the manufacturer directly relates to the transportation cost and as a result the transporter seeks to find the most efficient way to transport goods. The model is structured by Čech et al. (2013) where all the above agents, with the exception of the miner, forms a colony. Colonies have two tenets, location and population size. In addition, each colony competes with other colonies for resources (i.e. output from miners). The productivity of each colony is measured in terms of the wealth per agent, this allows the direct comparison between colonies that inherently have different population levels.
Bureš and Tučník (2014) further develop the research and model by Čech et al.
(2013). The four agents initially part of the model, as mentioned by Čech et al. (2013) i.e. consumer, manufacturer, miner and transporter. Each agent is represented as a vector that consists of a number of parameters and is described below.
Agent = (pos, w, k, s, con, e, pro, mob, a), where
‘pos’ refers to the exact physical position of the agent in the model;
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‘w’ calculates the wealth of each agent, it is important to note that it is not possible for agents in the model to accumulate debt;
‘k’ is the speed of the relevant agent;
‘s’ in essence is storage space for goods or material;
‘con’ refers to either:
consumption of end goods or services by a consumer; or utilisation of capital by miners and transporters; or
consumption of input material and labour for manufacturers.
‘e’ refers to the efficiency of each agent in its core function;
‘pro’ is relevant only for miners and manufacturers and is a production function;
‘mob’ enables mobility of an agent, i.e. transporter; and
‘a’ refers to the specific colony that an agent belongs to.
Taking the above into account, Čech et al. (2013) highlights that the parameters of each category of agent can be represented as: consumer = (pos, a, w, s, con, e), manufacturer = (pos, a, w, s, con, e, pro), miner = (pos, w, s, con, e, pro) and transporter = (pos, a, s, con, e, mob). In addition, a colony has the following parameters: Colony = (pos, s, w, cw, CP), where cw is the creditworthiness of the relevant colony and CP is the number of agents in the colony.
The research by Janssen and Vries (1998), which focuses on the economy-energy- climate nexus, and is an extension of Janssen and Rotmans (1995) that did not include an agent-based element, is undertaken with an ABM approach through a Genetic Algorithm foundation. The core focus of the research is anthropogenic climate change. The model is an elementary construct that encompasses three types of outlooks on the world: Hierarchist, Egalitarian and Individualist, which is based within a triangle, whose outlook occupies a point of the triangle. Agents in the system, depending on their outlook, are then located accordingly. In essence, Janssen and Vries (1998) demonstrate that agents ability to learn and adapt to changing