The Arrow That Constructs the World: The Causal Loop Diagrams Technique

Abstract

This chapter introduces the formal language through which Systems Thinking – in following the five general rules presented in Chap. 1 – builds qualitative models of dynamic systems made up of temporal variables that are connected by loops.

Appendices

Appendix 2.1 Causal Loop Diagrams for Everyone

In this Appendix I will present some Causal Loop Diagrams to stimulate the reader to practice the Systems Thinking discipline. In the choice of examples I have not followed any particular logic; their only aim is to increase the range of models already included in the text. The reader is invited to integrate the CLDs by adding new variables, thus expanding the system’s external boundaries, or by inserting other variables between the interrelated ones, thereby expanding the systems internal confines, in order to give more significance and explanatory power to the models (CLD A.2.1.1–A.2.1.8). The CLD A.2.1.9 shows a false CLD.

CLD A.2.1.1

Example of a system of diffusion: the mini-skirt craze

CLD A.2.1.2

Example of compound CLD: cost reductions

CLD A.2.1.3

Example of a balancing loop: control of demand

CLD A.2.1.4

Example of a balancing loop: stock control

CLD A.2.1.5

Example of compound CLD: co-evolution in the same habitat

CLD A.2.1.6

Compound CLD: quality control

CLD A.2.1.7

Compound CLD: the power of computer

CLD A.2.1.8

Compound CLD: research and development

CLD A.2.1.9

False CLD

Appendix 2.2 Escalation of Arms in Richardson’s Model

The arms escalation model in CLD 2.3 must be modified to include the law of dynamic instability; no growth process in arms lasts forever, since factors intervene to slow it down.

Lewis Richardson (1949), considered the founder of the scientific analysis of conflicts, analyzed the growth in arms, introducing the concepts of defense coefficient to indicate the action rates that spur X to adjust its arms to variations in those of Y, and vice-versa, and of saturation coefficient to indicate the population’s degree of tolerance (always declining) in making the sacrifices arms expenditures entail.

Not taking into account other variables introduced by Richardson, for reasons of simplicity, we can reformulate his model by assuming that Y’s arms grow due to its fear of the size of X’s arsenal, according to the defense coefficient (positive), and slow down in proportion to the size of the arsenals themselves, according to the saturation coefficient (negative).

The model in Fig. A.2.2.1 considers both the defense coefficients and the saturation coefficients.

Fig. A.2.2.1

Arms escalation. Richardson’s model simulated with Excel

We see that the arms dynamics is no longer linear, due to the change in the defense and saturation coefficients.

Since X starts with an arsenal five times larger than Y’s (200 against Y’s 50), it has a low defense coefficient (5% compared to Y’s 15%) as well as a high saturation rate (15% against Y’s 5%), since we assume the citizens in X are so sure of their superiority that they have become intolerant toward new sacrifices to increase their arsenal. The same cannot be said for Y, whose citizens, frightened by the size of their enemy’s arsenal, try to increase their defenses even if this entails considerable sacrifices. We can observe these dynamics in the recent developments in the conflicts in the Middle and Far East.

Appendix 2.3 Representation of an Economic System

An economy is not created but emerges spontaneously, a natural part of man’s essence. However, by observing the world “from a certain height”, without zooming in on the minute phenomena, we can, in my opinion, represent any economy in it, including our own, by the model in Fig. A.2.3.1.

Fig. A.2.3.1

Functioning of the economic system: synthetic view

We can start interpreting the model from the point that most interests us, but wherever we start we must always proceed by following the direction of the connected arrows.

If, for example, we assume there is an increase in production (7), then it is easy to deduce that this will lead to an increase in employment (8) and, as a result, in income – both from work (salaries (9), even in the form of pensions) or from capital (interest and profits) – thus producing higher tax revenue (11). Salaries generates resources for consumption (4) and savings (10); the monetary resources for consumption (generated by salaries (9), savings (10) and transfers (12)), taking into the account the size of consumption (3) needed to satisfy wants (1), produce a greater demand for goods (5), which translate into greater production (7), which, in turn, causes an increase in employment (8), giving rise to the reinforcing cycle, R1, which represents the basis for any economy.

The increase in savings (10) in turn frees up resources for both future consumption (homes, our children’s education, etc.), giving rise to loop R4 and to investment in production (6) through the credit system and financial markets, thus activating loop R2. The increase in investment resources increases production (7), which, in turn, regenerates the reinforcing loop R1.

Tax revenues (11) along with the public debt and new money (when possible) (11.b) allow the policy makers to transfer resources to both production (13) (government aid, social safety valves, public works, etc.) and consumption (12) (public employment, bonuses of various kinds, etc.). The initial transfers activate loop R2, and the subsequent ones activate loop R3.

Production (7), spurred by demand (5), increases the stocks of goods (0), which puts a brake to consumption (3), which reduces demand (5) and slows down production (7). Loop B1 is activated. This is the “saturation risk” that weights on all rich economies with large stocks of goods.

Starting from any other variable, the reader will find the same sequence of events, which corresponds perfectly with the important economic trends (with social implications) we observe and experience first-hand.

The model shows how the important economic variables are linked by a reinforcing loop.

It is equally clear that consumption (3) is the fundamental variable, the “prime engine” of change in the entire economy. However, consumption depends on three other variables: needs (1), which are the basis of survival, confidence (2) in the future and in a serene life, and the stock of goods (0) already possessed.

The model also illustrates the influence of taxes (11). On the one hand, these can directly increase (“s”) the transfers to production (13) and consumption (12) by activating the reinforcing loops R2 and R4, but on the other hand, they can reduce (“o”) savings (10), and as a result the monetary resources for consumption (4) and investment (6), by activating the balancing loops B2 and B3, which result in a slowing down of demand and investment. Finally, we must take into account the fact that taxes compete with salaries in the apportionment of income produced (this relationship is not illustrated in the model).

What does the model tell us about the occurrence of crises? Practically everything. The reader will know how to interpret by himself the crisis that is arriving as soon as he includes in the model the news from the TV or newspapers.

It will not be difficult to understand that when the economy contracts it is useless to save due to fear, since savings makes the crisis even more severe; useless to give incentives to firms if demand does not increase; useless to increase taxes to make more transfers to production if demand does not rise.

The model suggests the scenario for emerging from a crisis (which recent history confirms): as soon as needs (1) increase and become urgent (even with low consumer confidence (2)), consumption begins to increase (3), which uses the savings (10) that had previously accumulated, subsidies, or loans; confidence (2) grows and demand (5) starts to increase, which boosts production (7) and reduces unemployment (8), even if perhaps by only a little.

The higher incomes (8) permit greater demand (5), but also increased taxes (11), giving policy makers increased public expenditures (13) through deficit spending (11.b) in order to make transfers in favor of consumption (12) (demand stimulus) and production (13), thereby helping firms to reduce prices (15) and increase quality (14). Loops R1, R2, R5 and R6 can then do their jobs and bring the system out of the crisis.

Many readers will say the model is too simplistic and abstract, perhaps even incomplete, but “the map is not the territory”.

Appendix 2.4 Malthusian Dynamics

Fig. A.2.4.1

Ecosystem with Malthusian dynamics and scarce renewable resources

The model assumes that the population dynamics – where the initial population is specified (equal to 1,000 units) – varies yearly due to births and deaths. The simulation program also foresees the possibility that the population, having reached the resource saturation point, can initiate a production process to increase resources and continue to expand (Fig. A.2.4.1).

The expansion, however, will not continue for long, since we assume there is a limit to the expansion of the scarce resource (10,000 units); for example, due to a constraint from the other resources necessary for its production (land, water, fertilizer, etc.). Thus, the population expansion stops at t = 17.

Summarizing the situation: with the data inserted in the control panel the population expands until t = 9 with the available natural resources; a production process for the resource then starts, and the available amount increases to 10,000 units; subsequently, from t = 17 on, the population stabilizes at 2,062 units.

This simple simulation program allows us to make other hypotheses; in particular, that having reached the saturation point, there can be changes in the birth rate (it can fall) as well as the death rate (which can rise), even in individual consumption (rationing).

A limit is placed on the admissible population taking account of the scarce resource, but this limit varies with new production until the saturation point is reached.

If there were no limit to obtaining the resource, the population would continue to increase while producing ever increasing amounts of the resource, in an endless progression.

With a limit to the reproducible resource the system approaches this limit, gradually and inevitably.

Figure A.2.4.2 simulates the case where the production of the resource-food depends on the use of a depletable production resource available in a limited quantity (15,000 units).

Fig. A.2.4.2

Ecosystem with Malthusian dynamics and scarce non-renewable resources

The production starts at t = 9, when the food available to the system (reproducible each year at an amount equal to 7,500 units) is completely utilized. Food production beyond 7,500 units grows gradually until t = 19, at which time the scarce resource is completely used up (the last three columns of the table in Fig. A.2.4.1).

From then on the food production must cease and the population rapidly falls to 1,579 units.

Is humanitarian aid possible? Of course! Nevertheless, the simulation shows that this humanitarian aid (1,000) – which begins at t = 27 – has a short-term effect, being an external “disturbance”. When the aid ceases the system inevitably controls the population, which, at t = 44, returns to the maximum permitted limit of 1,579 units.

This second example shows, even in a simplified manner, that the population growth and the resulting growth in resource production, must take into account constraints involving the ecosystem’s sustainability.