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More technically...

System dynamics (SD) is a methodology used to model and simulate complex systems to reflect real-world counter-intuitive behaviour. The first paper using this methodology was published by J Forrester in 1958, before publishing Industrial Dynamics in 1961. Forrester believed that the field of Operations Research (OR) was not addressing high-level policy problems, instead only focusing on operational problems [16]. Using computer-assisted simulation to examine complex systems around us, as based on causal loops, can help to express mental models in a more concrete manner, to improve these models and discover inconsistencies. The mathematical structure behind the simulation is a system of nonlinear, first-order differential and integral
equations used to determine the flow of information between elements of the system. By running simulated what-if scenarios we can see the real-life implications of changes in variables.

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SD has a set of characteristics that distinguish it from other methodologies. Firstly, aggregated values are used in the system instead of individual entities. The models reflect the endogenous causes regulating the system. The changes over time are generated from within the system by information feedbacks and component interactions, even though the initial stimuli may be exogenous. This aspect makes it ideal to test policy implications from policies that originate as exogenous events.

 

Mina et al. [43] argue that human history is an inevitable journey to increased complexity in all aspects of social organisation, including politics and economics. They compare the American economy to a microprocessor, which is an incredibly complicated system of millions of electronic components. They are similar in that humans construct them, but the difference is that every part of the microprocessor was precisely placed by a group of engineers, where an economy is not designed by any one human, and no one can claim to control or even fully understand an economy, but it still functions. This leads them to distinguishing between complicated and complex systems. They name the fundamental characteristic of a complex system as the property of self-organisation, described as “the spontaneous appearance of large-scale organisation through limited interactions among simple components.” The first consequence of this characteristic is that “non-trivial, large-scale order can be produced by simple processes involving interactions
operating locally on simple agents or components.” The classical engineering approach, also favoured in the field of OR, has several disadvantages when applied to complex systems.

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Practically, the process can be broken down into five steps. The first is defining the problem. A problem statement, time horizon and aims of the model must be determined for a model to be useful. Next is the exploratory phase where the key factors controlling the system should be identified. A causal loop diagram (CLD) should then be drawn based on these identified factors and other important influences. In the quantification step the CLD should then be transformed into a structured CLD and stock and flow diagram (SFD) with equations and data for all factors. Lastly, using software, the quantified model may be used to simulate scenarios and create charts to display the behaviour of the system over the desired time horizon [6].

Causal loop diagrams

Before any modelling can take place, the elements that are pertinent to the specific study should be identified and classified as exogenous or endogenous [2]. These elements need not be limited to quantitative or tangible components, but also include intangible factors that will later be quantified. Nienaber et al. [46] define endogenous variables as those who influence and are influenced by feedback loops and the behaviour of the model. Exogenous elements influence but are not influenced by the behaviour of the model, but are still important to model.

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In SD methodology, a causal loop is a simple diagram consisting of the relevant elements in the system and links between these elements, creating feedback loops in the system, which can be either balancing or reinforcing. Links have annotations about their polarity (a negative or positive correlation with the behaviour of the linked element) as well delays in feedback. Polarity is indicated with either a plus or minus sign and a delay is indicated by a double line through the link [7]. John D. Sterman [67] wrote that a complex system is equivalent to a “high-order, multiloop nonlinear feedback system.” Feedback loops arise from elements that are connected to itself through linkages between intermediary elements. Balancing loops occur when the links
in a cycle have both negative and positive polarities, where effects are neutralised [53].

 

A simple example of a balancing loop is found in classical economic theory, where economies are considered to be self-regulating in the long term. A positive supply shock in an economy that is in long-run equilibrium will require more workers to keep up with production, equivalent to real GDP in a closed economy. To attract more workers, businesses will pay higher wages. These higher wages will encourage some economically inactive people to enter the labour force, leading to a surplus in the labour market. With the classical assumption that wages are downward flexible, businesses will then lower wages again, causing people to exit the labour force and the economy to return to long-term equilibrium. These loops are formed when there is an odd number of negative links in a loop with some positive links. A reinforcing loop arises when each action reinforces the next action. This happens when all links are either positive or negative, or when there are an even number of negative links interacting with positive links. An example of a reinforcing loop in classic economics is the Keynesian multiplier effect. This is the theory that citizens in the country have some propensity to consume and to save, determining the multiplier. A liquidity injection in the economy will increase aggregate demand in the economy, leading to an increase in total expenditure, which is equivalent to an increase in GDP in a closed economy. This first-round effect of an increase in spending will produce a knock-on effect in aggregate demand that will further increase spending. These two examples are shown in Figure 1.

Real GDP

Demand for labour

Aggregate supply

Wages

+

Real GDP

Aggregate demand

Total expenditure

+

R

+

Figure 1: An example of balancing and reinforcing feedback loops.

Stock and flow diagrams

SFDs are in essence quantified CLDs. All qualitative elements present in the CLD diagram must be converted to some measurable variable for simulation to take place. First, the terminology should be defined. A stock is an element of the system whose level accumulates and depreciates over time in a way that is measurable at any one point in time. All elements that are not stocks are either flows or auxiliaries. A flow is the inflow of the unit in which its stock is measured to alter the level of the stock. System boundaries are a special type of stock that represents an anonymous source or sink, that is to say that stock units flow in or out of the system via a stock in the system. Material flows are the links between stocks where units flow from one to the other. They are defined by the derivative of the stock variable with regards to time. Information dependencies are variables that influence these flows [6].

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The left CLD in Figure 1 is transformed into an SFD in Figure 2. The stock is real GDP measured in Rand, with the inflow being aggregate supply in the economy, which comes from various sources, and the outflow is the production output flowing into the general economy with a one-to-one rate. The two auxiliary influences are the demand for labour and the wage rate. The output flow determines the demand for labour, which in turn determines the wage rate, which influences the aggregate supply in the economy that determines real GDP.

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