System Dynamics
Causal Loop Diagrams
Morteza Bazrafshan
Causal Loop Diagrams
Feedback is one of the core concepts of system dynamics.
Yet our mental models often fail to include the critical feedbacks determining
the dynamics of our systems.
In system dynamics we use several diagramming tools to capture the structure
of systems, including causal loop diagrams (CLD) and stock and flow
maps. CLDs are excellent for:
• Quickly capturing your hypotheses about the causes of dynamics;
• Eliciting and capturing the mental models of individuals or teams;
• Communicating the important feedbacks you believe are responsible for a
problem.
CAUSAL DIAGRAM NOTATION
A causal diagram consists of
variables connected by arrows
denoting the causal influences
among the variables.
Variables are related by causal
links, shown by arrows.
Each causal link is assigned a
polarity, either positive (+) or
negative (-) to indicate how the
dependent variable changes
when the independent variable
changes.
The important loops are
highlighted by a loop identifier
which shows whether the loop is
a positive (reinforcing) or
negative (balancing) feedback.
CAUSAL DIAGRAM NOTATION
Note that the loop identifier circulates in the same direction as the loop to which it
corresponds.
A positive link means that if the cause increases, the effect increases above what it
would otherwise have been, and if the cause decreases, the effect decreases
below what it would otherwise have been.
In the previous example an increase in the fractional birth rate means the birth rate
(in people per year) will increase above what it would have been, and a decrease in
the fractional birth rate means the birth rate will fall below what it would have been.
A negative link means that if the cause increases, the effect decreases below what
it would otherwise have been, and if the cause decreases, the effect increases
above what it would otherwise have been.
In the example, an increase in the average lifetime of the population means the
death rate (in people per year) will fall below what it would have been, and a
decrease in the average lifetime means the death rate will rise above what it would
have been.
Link polarities describe the structure of the system. They do not describe the
behavior of the variables.
That is, they describe what would happen IF there were a change.
CAUSAL DIAGRAM NOTATION
They do not describe what actually happens.
The fractional birth rate might increase; it might decrease the causal diagram
doesn't tell you what will happen. Rather, it tells you what would happen if the
variable were to change.
An increase in a cause variable does not necessarily mean the effect will actually
increase.
There are two reasons:
First, a variable often has more than one input. To determine what actually
happens you need to know how all the inputs are changing.
When assessing the polarity of individual links, assume all other variables
are constant
Second, and more importantly, causal loop diagrams do not distinguish between
stocks and flows the accumulations of resources in a system and the rates of
change that alter those resources
An increase in the birth rate will increase the population, but a decrease in the
birth rate does not decrease the population.
Births can only increase the population, they can never reduce it.
CAUSAL DIAGRAM NOTATION
Similarly, the negative polarity of the link from the death rate to population
indicates that the death rate subtracts from the population.
A drop in the death rate does not add to the population.
A drop in deaths means fewer people die and more remain alive: the population
is higher than it would otherwise have been.
GUIDELINES FOR CAUSAL LOOP DIAGRAMS
Causation versus Correlation
•Every link in your diagram must represent (what you believe to be) causal
relationships between the variables.
•You must not include correlations between variables.
•A system dynamics model must mimic the structure of the real system well
enough that the model behaves the same way the real system would.
•Behavior includes not only replicating historical experience but also responding
to circumstances and policies that are entirely novel.
•Correlations among variables reflect the past behavior of a system.
• Though sales of ice cream are positively correlated with the murder rate, you
may not include a link from ice cream sales to murder in your models.
GUIDELINES FOR CAUSAL LOOP DIAGRAMS
Causation versus Correlation
•many correlations are more subtle, and it is often difficult to determine the
underlying causal structure.
•A great deal of scientific research seeks the genuine causal needles in a huge
haystack of correlations:
- Does vitamin C cure the common cold?
- Can eating oat bran reduce cholesterol, and if it does, will your
risk of a heart attack drop?
- Does economic growth lead to lower birth rates, or is the lower
rate attributable to literacy, education for women, and increasing costs of
child rearing?
- Do companies with serious quality improvement programs earn
superior returns for stockholders?
•Modelers must take extra care to consider whether the relationships in their models
are causal, no matter how strong the correlation, how high the R2, or how great the
statistical significance of the coefficients in a regression may be.
GUIDELINES FOR CAUSAL LOOP DIAGRAMS
Labeling Link Polarity
Be sure to label the polarity of every link in your diagrams.
GUIDELINES FOR CAUSAL LOOP DIAGRAMS
Determining Loop Polarity
Imagine a small disturbance in one of the variables.
-If the disturbance propagates around the loop to reinforce the original change,
then the loop is positive.
-If the disturbance propagates around the loop to oppose the original change, then
the loop is negative.
There are two methods for determining whether a loop is positive or negative:
1- Count the Number of Negative Links
- The fast method always works. . .
except when it doesn't !
- In a complex diagram it is all too easy to miscount the number of
negative links in a loop.
- And it is easy to mislabel the polarity of links when you first draw
the diagram.
- Counting the number of negative signs is unlikely to reveal these
errors.
GUIDELINES FOR CAUSAL LOOP DIAGRAMS
Determining
Identify
and label
Loopthe
Polarity
polarity of the links and loops in the examples shown.
2- Trace the Effect of a Change around the Loop
- trace the effect of a small change in one of the variables as it propagates
around the loop.
- You
Attractiveness
of Market
can start
with any
variable in the loop. The
Number of
Competitors
Profits
Market
Share
Price
be the same.
Unit
Costs
Price
Pressure to Clean
Up Environment
Environmental
Quality
Cumulative
Production
result
must
Bank Cash
Reserves
Cleanup
Effort
Net
Withdrawals
Perceived
Solvency of
Bank
GUIDELINES FOR CAUSAL LOOP DIAGRAMS
CHALLENGE
Assigning Link Polarities
Consider the attractiveness of a product to customers as it depends on various
attributes of the product. Assign link polarities.
Quality
What feedback loops might be
created as product attractiveness
changes the demand for the firm's
product?
Price
Product
Attractiveness
Delivery
Delay
Functionality
GUIDELINES FOR CAUSAL LOOP DIAGRAMS
Mathematics of Loop Polarity
When you determine loop polarity, you are calculating what is known in control
theory as the sign of the open loop gain of the loop.
The term "gain" refers to the strength of the signal returned by the loop:
- A gain of two means a change in a variable is doubled each cycle around
the loop
- A gain of negative 0.5 means the disturbance propagates around the loop
to oppose itself with a strength half as large.
The term "open loop" means the gain is calculated for just one feedback cycle
Consider an arbitrary feedback loop consisting of n variables, X1, … ,Xn.
let X1 denote the variable you choose. When you break the loop, X1 splits into an
input, X1I and output, X1O
The open loop gain is defined as the (partial) derivative of X1O with respect to X1I
GUIDELINES FOR CAUSAL LOOP DIAGRAMS
Mathematics of Loop Polarity
The polarity of the loop is the sign of the open loop gain:
Polarity of loop = SGN(∂X1O / ∂X1I)
The open loop gain is calculated by the chain rule from the gains of the individual
links:
SGN(∂X1O / ∂X1I) = SGN[(∂X1O / ∂Xn) (∂Xn / ∂Xn-1) … (∂X2 / ∂X1I)
GUIDELINES FOR CAUSAL LOOP DIAGRAMS
All Links Should Have Unambiguous Polarities
- Sometimes people say a link can be either positive or negative, depending on
other parameters or on where the system is operating.
-If demand is highly elastic, a higher price means less revenue because a 1%
increase in price causes demand to fall more than 1%.
- When you have trouble assigning a clear and unambiguous polarity to a link it
usually means there is more than one causal pathway connecting the two
variables.
GUIDELINES FOR CAUSAL LOOP DIAGRAMS
CHALLENGE
GUIDELINES FOR CAUSAL LOOP DIAGRAMS
Name Your Loops
To help your audience
navigate the network of
loops, it's helpful to give each
important feedback a number
and a name.
Numbering the loops RI, R2,
B1, B2, and so on helps your
audience find each loop as
you discuss it.
Causal diagram developed
by engineers and managers
in a workshop designed to
explore the causes of late
delivery
for
their
organization's design work.
GUIDELINES FOR CAUSAL LOOP DIAGRAMS
Variable Names
1- Variable Names Should Be Nouns or Noun Phrases
The actions (verbs) are captured by the causal links connecting the variables.
A causal diagram captures the structure of the system, not its behavior-not what
has actually happened but what would happen if other variables changed in
various ways.
Incorrect
Correct
+
Costs Rise
Price Rises
+
Costs
Price
Adding the verb "rises" to the diagram presumes costs will only rise.
It is confusing to talk of a decrease in costs rising or a fall in price increases.
Are prices rising, rising at a falling rate, or falling?
GUIDELINES FOR CAUSAL LOOP DIAGRAMS
Variable Names
2- Variable Names Must Have a Clear Sense of Direction
Choose names for which the meaning of an increase or decrease is clear,
variables that can be larger or smaller.
Without a clear sense of direction for the variables you will not be able to assign
meaningful link polarities.
GUIDELINES FOR CAUSAL LOOP DIAGRAMS
Variable Names
3- Choose Variables Whose Normal Sense of Direction Is Positive
Avoid the use of variable names containing prefixes indicating negation (non, un,
etc.)
Incorrect
Correct
-
+
Costs
Losses
Costs
+
Criticism
Unhappiness
Profit
Criticism
Happiness
Standard accounting practice is Profit = Revenue - Costs, so the better variable
name is Profit, which falls when costs rise and rises when costs fall.
criticism may make you unhappy, but it is confusing to speak of rising unhappiness
GUIDELINES FOR CAUSAL LOOP DIAGRAMS
Tips for Causal Loop Diagram Layout
To maximize the clarity and impact of your causal diagrams, you should follow
some basic principles of graphic design:
1. Use curved lines for information feedbacks. Curved lines help the reader
visualize the feedback loops.
2. Make important loops follow circular or oval paths.
3. Organize your diagrams to minimize crossed lines.
4. Don't put circles, hexagons, or other symbols around the variables in causal
diagrams.
5. Iterate. Since you often won't know what all the variables and loops will be when
you start, you will have to redraw your diagrams, often many times, to find the best
layout.
GUIDELINES FOR CAUSAL LOOP DIAGRAMS
Choose the Right Level of Aggregation
Causal loop diagrams are designed to communicate the central feedback structure
of your dynamic hypothesis.
They are not intended to be descriptions of a model at the detailed level of the
equations.
Having too much detail makes it hard to see the overall feedback loop structure
and how the different loops interact.
Having too little detail makes it hard for your audience to grasp the logic and
evaluate the plausibility and realism of your model.
If your audience doesn't grasp the logic of
a causal link, you should make some of
the intermediate variables more explicit.
GUIDELINES FOR CAUSAL LOOP DIAGRAMS
Don't Put All the Loops into One Large Diagram
Short-term memory can hold 7+- 2 chunks of information at once.
This puts a rather sharp limit on the effective size and complexity of a causal map.
Resist the temptation to put all the loops you and your clients have identified into a
single comprehensive diagram.
Build up your model in stages, with a series of smaller causal loop diagrams.
GUIDELINES FOR CAUSAL LOOP DIAGRAMS
Make the Goals of Negative Loops Explicit
All negative feedback loops have goals.
All negative loops function by comparing the actual state to the goal, then initiating
a corrective action in response to the discrepancy.
There are exceptions to
the principle of showing
the goals of negative
loops.
Consider the death rate
loop. The goal of the
death rate loop is implicit
(and equal to zero: in the
long run, we are all
dead).
GUIDELINES FOR CAUSAL LOOP DIAGRAMS
Indicate Important Delays in Causal Links
Delays are critical in creating dynamics.
Delays give systems inertia, can create oscillations, and are often responsible for
trade-offs between the short- and long-run effects of policies.
Your causal diagrams should include delays that are important to the dynamic
hypothesis or significant relative to your time horizon.
GUIDELINES FOR CAUSAL LOOP DIAGRAMS
Distinguish between Actual and Perceived Conditions
Often there are significant differences between the true state of affairs and the
perception of that state by the actors in the system.
There may be delays caused by reporting and measurement processes.
There may be noise, measurement error, bias, and distortions.
Example:
There may be significant delays in assessing quality and in changing
management's opinion about product quality.
Separating perceived and actual conditions helps prompt questions such as:
-How long does it take to measure quality?
-To change management's opinion about quality even after the data are available?
-To implement a quality improvement program?
- To realize results?
GUIDELINES FOR CAUSAL LOOP DIAGRAMS
Distinguish between Actual and Perceived Conditions
DEVELOPING CAUSAL DIAGRAMS FROM
INTERVIEW DATA
Much of the data a modeler uses to develop a dynamic hypothesis comes from
interviews and conversations with people in organizations.
There are many techniques available to gather data from members of
organizations, including:
- Surveys
- Interviews
- Participant observation
- Archival data
- And so on
Once you've done your interviews, you must be able to extract the causal structure
of the system from the statements of the interview subjects.
Formulate variable names so that they correspond closely to the actual words
used by the person you interviewed, while still adhering to the principles for proper
variable name selection described above (noun phrases, a clear and positive
sense of direction).
DEVELOPING CAUSAL DIAGRAMS FROM
INTERVIEW DATA
Process Improvement
The following two quotes are actual interview transcripts developed in fieldwork
carried out in an automobile company in the United States.
The managers, from two different component plants in the same division of the
company, describe why the yield of their lines was persistently low and why it had
been so difficult to get process improvement programs off the ground
In the minds of the [operations team leaders] they had to hit their pack counts
[daily quotas]. This meant if you were having a bad day and your yield had fallen. .
. You had to run like crazy to hit your target. You could say, "You are making 20%
garbage, stop the line and fix the problem," and they would say, "I can't hit my
pack count without running like crazy." They could never get ahead of the game. Manager at Plant A
Supervisors never had time to make improvements or do preventive maintenance
on their lines. . . they had to spend all their time just trying to keep the line going,
but this meant it was always in a state of flux. . . because everything was so
unpredictable. It was a kind of snowball effect that just kept getting worse.
DEVELOPING CAUSAL DIAGRAMS FROM
INTERVIEW DATA
Process Improvement
Develop a single causal diagram capturing the dynamics described by the
interviews.
Build your diagram around the basic physical structure shown below
Example: MANAGING YOUR WORKLOAD
Problem Definition
Consider the process of managing your workload:
-A student (imagine yourself) must balance classes and assignments with outside
activities, a personal life, and sleep.
- During the semester you attend classes, do the readings, and hand in
assignments as they are due
- You probably try to work harder if you think your grades are lower than you
desire and take more time off when you are sleepdeprived.
There are two basic policies you can follow:
(1) The ant strategy: never put off until tomorrow what you can do today
(2) the grasshopper strategy: never do today what can be put off until
tomorrow.
Example: MANAGING YOUR WORKLOAD
Problem Definition
- The ant works steadily throughout the semester as work is assigned and never
builds up a large backlog of assignments.
- As a result, the ant avoids the end of semester crunch, keeps the workweek
under control, and is able to stay well rested.
- Because the ant gets enough sleep, productivity is high, and the ant has plenty
of time to participate in outside activities.
- The ant's grades improve steadily throughout the term.
- The grasshopper, in contrast, defers the work until the last minute.
- The grasshopper's workweek is low at the beginning of the term, providing lots of
time for parties and outside activities.
- The grasshopper can stay reasonably well rested despite a heavy social
schedule because the workweek is low.
- But because the grasshopper doesn't do the work as fast as it is assigned, the
assignment backlog steadily builds up.
Example: MANAGING YOUR WORKLOAD
Problem Definition
-Eventually, it's crunch time, and the grasshopper starts putting in long hours,
perhaps pulling a few all-nighters.
- Unfortunately, as sleep suffers, energy and productivity fall.
- The rate and quality of work suffers.
-Grades plummet, and the term ends before the grasshopper can finish all the
work, perhaps leading the grasshopper to plead for extensions from the faculty.
Example: MANAGING YOUR WORKLOAD
ant strategy
Example: MANAGING YOUR WORKLOAD
grasshopper strategy
Example: MANAGING YOUR WORKLOAD
Identifying Key Variables
-Assignment rate: the rate at which professors assign work throughout the
term (tasks/week).
-Work completion rate: the rate at which tasks are completed (tasks/week).
-Assignment backlog: the number of tasks that have been assigned but not yet
completed (tasks).
-Grades: the grade received for work handed in (0-100 scale).
-Workweek: the number of hours spent on academic work, including classes,
reading, homework, projects, etc. (hours/week).
-Energy level: measures how well rested the student is. Arbitrary scale from
0-100% where 100% = fully rested and 0 = comatose).
Other variables could be added, but this set provides a reasonable starting point
for conceptualization of the feedback structure governing the dynamics.
Example: MANAGING YOUR WORKLOAD
Developing the Causal Diagrams
The Assignment Rate is assumed to be exogenous: Once a student has signed up
for a set of courses, the assignment rate is determined.
Classes can sometimes be dropped, but this possibility is ignored for now.
Example: MANAGING YOUR WORKLOAD
Developing the Causal Diagrams
Example: MANAGING YOUR WORKLOAD
Developing the Causal Diagrams
If work pressure is high, the student may choose to cut corners, skim some
reading, skip classes, or give less complete answers to the questions in
assignments.
Work pressure depends on the assignment backlog and the Time Remaining to
complete the work
Example: MANAGING YOUR WORKLOAD
Developing the Causal Diagrams
Assignment
Rate
+
-
Work
Completion
Rate
Assignment
+
The two
most basic options available
to a student faced with high
work pressure
Calendar
Backlog
+
are:
Time
B2
+
Time
Remaining
Corne r
(1) work longer hours, thus increasing
theCutting
completion rate and reducing the
+
backlog (the Midnight Oil loop B
1), or
Work
Pressure
(2) work
faster by spending less
time on eachEffort
task,
speedingProductivity
the completion rate
Devoted
Due
and reducing
the backlog (the Corner Cutting toloop
B2).
Assignments
Date
+
-
Sustained high workweeks cut into sleep and the satisfaction of other needs
B1
(eating, exercise, human companionship, etc.), causing the student's Energy Level
M idnight
R1
to fall.
Oil
Burnout
A tired student must spend longer than a well-rested one to complete a task with a
given level of quality.
+
Workweek
Delay
Energy
Level
-
Example: MANAGING YOUR WORKLOAD
Developing the Causal Diagrams
Assignment
Rate
+
-
Work
Completion
Rate
Assignment
Reducing
the
effort
devoted
to
each assignment also has side+ effects.
Calendar
Backlog
Time
-
-
B2
+
Putting less+ effort
into each task does allow assignments to be completed in less
Time
Corne r
time but reduces
the Quality- of +Work, lowering
the student's Grades.
Remaining
Cutting
Work
Pressure
When grades fall, there is pressure to boost the effort put into
each task.
Productivity
Due
Date
-
Effort Devoted
to Assignments
+
The negative Quality Control loop prevents effort
and quality
from falling too far
R1
even when work pressure is high
B1
B3
Burnout
Grades
+
M idnight
Oil
Quality
Control
+
R2
Quality of
Work
+
Too Tire d
to Think
+
Workweek
Delay
Energy
Level
-
Example: MANAGING YOUR WORKLOAD
+
Assignment
Rate
-
Work
Completion
Rate
Assignment
Developing the Causal Diagrams
Calendar
Time
Backlog
-
-
B2
+
+
If all else fails,
exhausted student can appeal to the faculty for relief,
+ the
Time
Corne r
generating Requests
for Extensions.
Remaining
Cutting
+
Work
accompanied
Pressure
B4
Usually, such requests
are
Due
beyond the student's
control:
M y Dog Ate
Date
by stories of bad luck and hardship
-
M y Hom e w ork
Effort Devoted
to Assignments
-
+"My
+
R1
dog ate my homework,"
Requests for
B3
"My hard
disk
crashed,“
+
Extensions
Grades
Quality
"My roommate had a nervous breakdown."
+
Productivity
Burnout
B1
M idnight
Oil
Control
If the faculty are moved by these tales of tragedy and
woe (a+ big if), the due date
Quality of
is slipped, making more time available and reducing Work
work pressure.
R2
Too Tire d
+
Note that slipping the deadline, because toit Think
lowers work pressure, may actually
Energy
cause the workweek to fall and the effort devoted to each
assignment to rise, both
Level
+
- to build up again.
reducing the completion rate and causing
workDelay
pressure
Workweek