The Tragedy of Overshoots
Erling Moxnes
System Dynamics Group, University of Bergen, Fosswinckelsgt.6, N-5007 Bergen, Norway,
tel: +47 55584119, fax: +47 55583099
ABSTRACT
Understanding historical overshoots is vital for policy-making, not at least when assessing
the risk of future global overshoots. For this purpose a simple, unifying theory of overshoots
is described and discussed for a variety of observed overshoots. For undesired and avoidable
overshoots, misperception at some level must be a major cause. Laboratory experiments
support this hypothesis and point to dynamics as the main complicating factor. The theory
suggests that misperceptions may cause global overshoots both because of climate change
and scarcity of cheap fossil energy. New generations of dynamic simulation models are
needed to assess the risk of overshoots, test policies for likely sustainable development, and to
aid information dissemination.
Key words: overshoot, management, resources, climate change, energy, globalization,
dynamics, welfare, simulation
Introduction
The Brundtland Commission (1987) contributed importantly to put sustainable development
on the political agenda. Consistent with their definition, sustainable development means
absence of overshoots and subsequent reductions in economic activity and welfare.
Historically, overshoots have been a recurring problem: individuals have experienced
overshoots in private affairs, asset and commodity prices have soared and fallen, businesses
have over-expanded and gone bankrupt, natural resources have been overharvested and
depleted, and the global economy has gone through expansions and depressions. Logically,
undesired and avoidable historical overshoots suggest that overshoots have not been properly
analyzed, informed about, or understood by policy-makers for them to act in time.
First, a simple, unifying theory of overshoots is discussed in light of literature dealing with
the types of overshoots mentioned above. Underlying processes are described in terms of a
funnel and glass analogy and a corresponding generic dynamic model. Observed overshoots
are seen in light of model predictions. The role of misperceptions is demonstrated by
references to laboratory experiments. With minor adaptations, the theory explains seven
important problems, suggesting generalizability of the theory. To avoid confusion, the
Tragedy of the Commons (Gordon 1954; Hardin 1968) is not a prerequisite for the type of
overshoot discussed here.
Second, when applied to problems of climate change and scarcity of cheap fossil energy, the
theory of overshoots warns about a potential for global overshoots. The theory in its
simplified form cannot produce accurate forecasts. However, it provides a tool to understand
past experiences and it raises important questions about policies for the future.
Third, it is argued that importance, complexity, and misperception call for new methods and
institutions for analysis and information dissemination.
Theory of overshoots
1. A simple analogy of filling a glass with water through a funnel illustrates the unifying
theory of overshoots. Figure | gives a graphical overview of system structure (differential
equations). There are two stocks (states): the funnel and the glass. Since the stocks
accumulate water over time, the time dimension becomes vital. Stock values change through
flows. A person controls the faucet flow; the amount of water in the funnel influences the
funnel outflow and thus the glass inflow.
Filling the glass consists of a growth phase and a goal-seeking phase. To fill the glass in a few
seconds, there must be a minimum amount of water in the funnel to get a sufficient funnel
outflow. Thus, controlling the faucet flow involves comparing the actual water in the funnel
to the desired amount of water in the funnel.
Faucet Water in funnel Water in glass
flow
Q i
Funnel outflow
Desired water Gap Goal for
in funnel water in glass
Figure 1: Stock and flow diagram of system with funnel and glass. Rectangles denote stocks,
double arrows denote flows in and out of stocks, thin arrows denote instantaneous cause and
effect relationships, and circles denote effect calculations or constants.
The growth phase ends when focus shifts from growth to goal seeking. Ideally, when the sum
of water in the funnel and the glass equals the goal for water in the glass, the faucet should be
closed. This operation requires attention to stock assessment for both funnel and glass,
summing of estimates, and comparison to the goal. Using an easier and boundedly rational
strategy, only water in the glass is considered, as illustrated in Figure 1. When water reaches
the goal, the faucet is closed. Since water is still in the funnel, an overshoot is inevitable. In
spite of the transparency of this particular system, people occasionally experience overshoots.
Repeated experiences teach individuals to start closing the faucet before the goal is reached
allowing sufficient time for the adjustment process.
The funnel and glass example illustrates the basics of a unifying theory of overshoots: a
‘funnel’ and a ‘glass’ stock, a growth process, and a boundedly rational goal seeking process.
The following cases share these basic attributes. In these cases, bounded rationality does not
necessarily follow from efforts to save on deliberations, it may also follow from
misperceptions and unconscious misrepresentations of system structure.
2. Juvenile drinking behavior frequently leads to overshoots and costly accidents including
deaths. When drinking, alcohol passes quickly into the stomach (funnel), however diffuses
only slowly into body waters (glass). Using a simulator experiment, Moxnes and Jensen
(2009) found strong indications of misperception. High school students produced an average
overshoot of 86% of an explicit goal for blood alcohol concentration of 0.8 g/l. Since alcohol
in the stomach is not observable, the growth phase had to be controlled by prior knowledge.
For both short and long stomach delay times, goal seeking was well explained by one simple
feedback strategy where drinking was simply related to the gap between goal and current
blood alcohol concentration (BAC), see Figure 2. Very few juveniles (and adults) are aware
of the stomach’s ‘funnel effect’. Still they are likely to think of their own decision rule as
rational. Lack of theory forces them to seek external explanations of overshoots, e.g. mood
and type of alcohol. Accordingly they are observed to learn only slowly from own
experiences.
‘Average long delay — Simulated long delay
BAC, giL
16 —— Average short delay ——- Simulated short delay
0 1 2 3 4 5 6 7 8
15 minute periods
Figure 2: Average and simulated BAC for short and long stomach delay time
3. Many commodity markets produce repeated over- and undershoots; i.e. cycles. Production
capacity on order (funnel) increases by ordering and decreases by delivery into the stock of
capacity (glass), which in turn decreases by scrapping, see Figure 3. To maintain the glass
analogy, imagine that water can be sucked out of the glass. In established markets, the initial
growth phase is over and goal seeking dominates. However, there is no obvious goal for
individual firms (assuming constant costs and competition). Still, at the aggregate level,
ordering of new capacity takes place in a goal seeking feedback loop — known as Adam
Smith’s invisible hand.
Capacity Production
Ordering on order capacity
o—S 8
Arrival = Scrapping
Relative
profits
Profits Price Demand
Normal profits Unit costs
Figure 3: Stock and flow diagram of commodity market
Demand serves as an implicit goal for total capacity. When capacity is insufficient, prices
stay above equilibrium levels and vice versa. Price influences profits and ordering of new
capacity. To the extent that prices and price expectations only reflect current capacity (glass)
and not poorly observed total capacity on order (funnel), overshoots can occur.
Scrapping of capacity enables undershoots and hence repeated cycles. Scrapping also means
that the long-term goal for the funnel is no longer zero; in equilibrium new orders are needed
to replace expected total scrapping. Again, data is lacking and estimates of expected total
scrapping will be uncertain or missing.
How likely is it that investment decisions are dominated by recent prices to the neglect of
capacity on order and scrapping? Using a funnel and glass model for capacity, and including
a stock for product inventory, Meadows (1970) replicated the different cycles for chicken,
hog, and cattle markets. He assumed that breeding decisions were influenced by adaptive
price expectations found in studies of farmers. By redesigning earlier Cobweb experiments to
include cohorts for capacity and capacity on order, Arango and Moxnes (2012) were finally
able to generate price and capacity cycles in a laboratory experiment. Reliance on price
increased with complexity.
Also professional forecasts tend to be strongly linked to recent observations of the variable to
be forecasted (Sterman 1987) as if they are based on anchoring and adjustment heuristics
(Tversky and Kahneman 1974). According to this heuristic, recent commodity prices
represent the anchor and capacity on order and expected scrapping represent prior
information that is insufficiently adjusted for. All this should not come as a surprise because
prediction is complicated. Accordingly, a book on forecasting recommends to “Use
extrapolations when the forecaster is ignorant about the situation.” (Armstrong 2001, p.236).
A narrow focus on reliable and easily available data is also indicated by other studies.
Insufficient adjustment for supply lines has been observed in a management experiment
(Sterman 1989) and it has been observed that people tend to underestimate both length and
importance of (funnel) delays (Brehmer 1989). Experiments have found that people tend to
focus on conspicuous problems (D6rner 1996) and that they fail to perform backward
induction (Smith 2010). Furthermore, emotions may give priority to actions (Pfister and
Bohm 1992) and these emotions may not rely on cognitive appraisal (Zajonc 1984). If so, it
seems natural to think that the heat of the moment gets too much weight.
Fishing
Investment Capacity,
@
Fish
Catch Stock Growth
Scrapping
cee)
Desired
capacity
Unit profits
Normal
unit profits Unit costs Revence per
unit effort
Fish price
Figure 4: Stock and flow diagram of a renewable resource system
4. Exploitation of renewable resources has led to overshoots in capacity and undershoots in
natural resources. In Figure 4 capacity to catch fish (funnel) increases by investments and is
reduced by scrapping. A fish stock (glass) increases through natural growth and is reduced by
catch. Similar to the water example, the funnel influences its own outflow and a flow
connected to the glass. It does not matter that there is no direct flow from the funnel to the
glass. Causation is the same while the flows are measured in different units. There is also a
difference in that the funnel influences the outflow from the glass rather than the inflow. The
sign has changed, immediately suggesting that the fish stock may undershoot rather than
overshoot. Similar to the commodity market, the long-term goal for the funnel is not zero and
growth matters but with the opposite sign of scrapping.
In the open access situation depicted in Figure 4, individual fishing firms have no obvious
long-term goal for capacity, similar to the commodity market. Desired capacity stays above
current capacity as long as unit profits exceed normal unit profits in society. Hence
investments are controlled by a reinforcing (positive) feedback loop.
As the fish stock is reduced, catch per unit effort (cpue) decreases, and so do unit profits.
When unit profits have fallen towards normal unit profits, capacity expansion stops, catch
exceeds fish growth, and the fish stock continues to decline. Capacity has overshot and the
fish stock will undershoot desirable levels.
The reinforcing loop gives rise to exponential type growth, which is often seen as problematic
because it leads to faster and faster absolute growth. Less obvious is it that the reinforcing
loop also limits early growth and gives rise to a long period where growth activities are
cultivated. A keen and institutionalized focus on growth may leave less room for attention to
long-term goal seeking and to the commons problem. History shows that fishery policies have
developed only gradually in response to experienced problems, from catch quotas to capacity
control and to sanctuaries.
In regulated waters, the Tragedy of the Commons is no longer a sufficient theory to explain
overshoots. In a laboratory experiment with private property rights (no commons problem),
Moxnes (1998) found average capacity to overshoot the optimal level by more than 60
percent; the greater the overshoot in capacity, the greater the undershoot in the fish stock.
Participants included fishing boat owners, regulators, and fishery researchers. A simple hill-
climbing heuristic for investments was not rejected; growth in profits led to investments in
new boats. At the point in time when expansion should stop, observed large and increasing
profits dominated uncertain information about fish growth.
Using a hill-climbing strategy in the funnel and glass model, it can produce just as severe
overshoots as open access. Figure 5 shows such an overshoot where model parameters are
adjusted to roughly mimic historical records of herring catch in Norway. The figure also
shows a simulated policy that limits capacity and catch to 95% of maximum sustainable yield,
clearly suggesting that the overshoot was undesirable.
Catch, 1000 tons/year
1400 7
| —— Simulated catch
2200: Historical herring catch
1000 7 ------ Simulated policy
800
1896 1916 1936 1956 1976 1996
Figure 5: Simulated overshoot in catch with private property rights. Parameters are adjusted
to mimic historical catch of Norwegian Spring-spawning Herring (1896 to 1996).
Schrank (2003) quotes great optimism in a 1980 FAO document after the introduction of 200
mile economic zones in the late 1970s: "the opportunity exists, as never before, for the
rational exploitation of marine fisheries." Schrank goes on to quote a 1992 FAO document
saying: "...the situation is generally worse than it was ten years ago. Economic waste has
reached major proportions; there has been a general increase in resource depletion..."
Schrank further describes misguided attempts by individual nations to extend the growth
phase by massive use of subsidies. Thus, public policies made capacity overshoots greater
rather than smaller, a strong indication of misperception.
Similar overshoots have been observed for many renewable resources. For instance, reindeer
management has produced overshoots in number of reindeer (funnel) and undershoots in
lichen (glass). This has been observed in laboratory experiments (Moxnes 2004) and in the
field, in spite of co-management and regulation. In 1950 the American Society of
Mammalogists (Scheffer 1951) urged planners to make thorough studies of the “problems of
integrating lichen ecology, reindeer biology, and native culture” because of “serious problems
that have not been solved to date on any workable scale on the North American continent."
Water aquifers and forest resources provide other examples of overshoots.
Production Replacement
Investment Sapacity. Customer ee
rae) units
Discards
Time to
adjust Ultimate
capacity customer
units
Desired Fraction
capacity Word of without
mouth strength unit
Figure 6: Stock and flow diagram of new durable good production
5. Overshoots also happen for manufacturing businesses. Consider a few firms being the sole
producers of a new durable consumer good, a case adapted from Paich and Sterman (1993).
Capacity (funnel) enables production and sales, Figure 6. Sales in turn lead to a build-up of
the stock of units possessed by customers (glass). Growth is guided by a reinforcing loop
where more capacity enables more sales, more word of mouth, more demand and more
desired capacity. Growth stops when a large fraction of potential customers have bought the
product. Then demand falls towards a low level of replacements for discards. A laboratory
experiment by Paich and Sterman (1993) replicated capacity overshoots and bankruptcies
observed in historical cases. In this case a certain overshoot in production and sales is
optimal; bankruptcy is not.
Capacity on order Capacity on order Capacity
consumer goods capital goods capital goods
sector sector sector
8
Ordering
a ‘Scrapping
Arrival
Capital
output Demand for price
ratio capacity
Figure 7: Stock and flow diagram of long-wave model
6. The great depression of the 1930s is probably the most well known example of over- and
ensuing undershoots in modern economic history, a case adapted from Sterman (1986; 1989).
Again consider the commodity cycle model with capacity on order (funnel) and capacity
(glass), now representing the entire capital goods producing sector of the economy, Figure 7.
In this model new capacity must be ordered from the sector itself. Self-ordering creates a
bootstrapping, reinforcing growth loop that slows down and stretches the growth period in
time. When the runaway goal for capacity expansion is reached, the capital goods sector
reduces ordering to itself. Overcapacity is revealed, which leads to further reductions in prices
and investments. Again, since the capacity stock has an outflow of scrapping, there is a
potential for cycles to occur. A laboratory experiment by Sterman (1989) produced cycles
with about 50 year long periods resembling data collected by the Russian economist
Kondratiev.
A two stock model is an overly simplified representation of the world economy; a multitude
of other mechanisms may dampen or prevent Kondratiev cycles. However, accumulation of
capital is such a central factor in modern economies that self-ordering is bound to play a role.
Since this is a recent theory, it seems highly unlikely that any policy-maker has ever reflected
over self-ordering in the capital goods sector. Shorter-term business cycles can also be
roughly described by a funnel and glass model, for instance the inventory-production
(workforce) model by Metzler (1941).
Fundamental
rice
Updating Recent page ®
i rice
recent price Pp Bree
8
Outdating j
recent price \ Updating Outdating Pee
past price past price
Price Expected
price
increase
Fixed
asset Asset
supply demand
Figure 8: Stock and flow diagram of asset market
7. The final example is asset markets, where bubbles and bursts have been frequently
observed. Asset markets differ from commodity markets mainly in that the assets themselves
10
can be easily traded and that supply is inelastic in the short run. Therefore, variations in
demand tend to cause price variations rather than changes in the total stock of assets. The two
stocks in Figure 8 are perceived recent price (funnel) and past price (glass). Both stocks are
updated with new price information and reduced by outdated information. Information is
derived from both stocks to form expectations about price growth. If price is below the
fundamental price and is expected to grow, demand exceeds supply and an inner reinforcing
loop is formed through price and recent price. As the price reaches the fundamental price,
price is still expected to grow, and this expectation pushes the price above the goal.
Eventually the gap between recent and fundamental price comes to dominate growth
expectations and demand falls below supply. Then the inner loop changes from being
reinforcing to being goal seeking and the price decays towards the fundamental price. This
model replicates bubbles and crashes produced in a laboratory experiment by Smith et al.
(1988), see Figure 9 and supplementary material.
6 ——Simulated price
Observed price
aaa Fundamental price
Figure 9: Fundamental and simulated price, together with observed price in a laboratory
experiment (Smith et al. 1988).
The above examples show that funnel and glass systems can overshoot when combined with
boundedly rational decision rules. They do not rule out that overshoots can be prevented or
that people learn from repeated experiences. However, as in the case of alcohol, theory seems
important to speed up the learning from experience. For potential future global overshoots,
there are no directly relevant repeated experiences to learn from, theory is a prerequisite in
order to transfer knowledge from history to the future.
Global natural resources
In the following, the theory of overshoots is applied to global climate change and depletion of
nonrenewable fossil energy.
A model similar to that for renewable resources in Figure 4 can be used to describe climate
change, see Figure 10. Global production capacity (funnel) increases by investments in
capital and decreases by scrapping. Production capacity enables emissions of greenhouse
gases (GHGs) that flow into the stock of GHGs in the atmosphere (glass), a stock that is only
slowly reduced by removal. The combined lifetime of these two stocks is probably close to
one hundred years. GHGs in turn influence global temperatures and climate.
GHG intensity
Production
Investment capacity GHGs in
atmosphere
8 p
Scrapping re) a. 95 ve)
Emissions Removal
Saving
roduction
Consumption Climate
Figure 10: Stock and flow diagram of climate change problem
Growth in GHGs is driven by the reinforcing growth loop of the economy involving
production capacity, production (GDP), saving, and investment. Capacity is composed of
capital, technology and population. With no theory of climate change, there would be no
announced long-term goal or upper limit for the GHG concentration. Growth would go on
until likely future climate change reverses economic growth.
A theory of climate change exists, albeit debated. The theory of overshoots suggests that
misperceptions work against the advice of theory. First, similar to forecasting of commodity
prices, representativeness heuristics lead people to seek evidence of future climate change in
recent weather observations rather than in theory. Second, people are not aware of or largely
ignore the importance of funnels, in this case the stocks of capital and GHGs. Third, even if
people know about and can name these stocks, they have a tendency to misrepresent
12
accumulating stock and flow relationships with instantaneous cause and effect relationships
(di Sessa 1993; Moxnes 1998; Sweeney and Sterman 2000; Cronin et al. 2009). For instance,
most people seem to assume that the stock of GHGs in the atmosphere changes
instantaneously and in proportion to global emissions (Sterman 2008) and this idea is not
easily influenced by information (Moxnes and Saysel 2009). This misperception helps
explain why one and the same person can both believe in the theory of climate change and
vote for ‘wait-and-see’ abatement strategies (Sterman 2008). Fourth, with general agreement
on ‘wait-and-see’ strategies, politicians and electorates may continue to focus on and spend
their energy on conspicuous problems related to economic growth. Recall the subsidies to
fishing firms in times of financial troubles.
Similar to GHG emissions, energy consumption is also driven by the reinforcing growth loop
through production capacity (funnel). Energy consumption in turn adds to the stock of
accumulated extraction of fossil energy (glass). Since fossil energy is non-renewable and non-
recyclable, the ultimate goal for fossil energy use is zero. Hence an overshoot of the ultimate
goal for fossil energy use is desirable and inevitable, recall the earlier new product case. As
accumulated extraction increases, costs increase. A crucial question is if alternative energy
sources will be developed early enough to prevent increasing energy costs from causing non-
sustainable development.
Fossil energy —_— Alternative
intensity energy production
Production
Investment capacity
S S Accumulated
rape, @ extraction
Extraction fossil energy
Saving
Production
Consumption Effect on
productivity
Figure 11: Stock and flow diagram of fossil energy scarcity
As for climate change, there is debate about what theory to believe in. Peak oil, peak gas, and
peak coal theories warn about non-sustainable development while Hotelling’s rule suggests
that resource owners will slow down production to make prices increase faster than costs and
thus encouraging the development of alternative energy sources. Similar to the climate
change case, in choosing between these ways of thinking people are likely to rely on recent
13
price observations, underestimate the importance of stocks, and focus on conspicuous
problems. When facing increasing costs of fossil energy, a first reaction is likely to be
subsidies either in financial terms or in terms of granting access to valuable land and sea
areas.
Polices to prevent global overshoots due to climate change or increasing costs of fossil energy
also involve funnel delays, only indicated in the figures. For both energy efficiency and
alternative energy it takes time: to develop new technologies, for knowledge to diffuse, and
for new technologies to replace old technologies with long lifetimes. A particular problem is
that new technologies are typically considered uneconomical as they are introduced, before
learning and scale effects bring costs down towards or below expected future costs of fossil
fuels. This is similar to the renewable resource case where stopping investing seemed less
profitable than continuing. Again, likely ignorance about inherent delays favors wait-and-see
policies. The GHG intensity of production follows energy intensity and alternative energy
production.
If delayed investments in energy intensive non-fossil energy sources have to be made over a
relatively short period, the short-term effect would be to increase demand for energy. Thus,
the underlying reinforcing loop could exacerbate overshoots in energy prices; recall the case
with self-ordering of investment goods.
Likely misperceptions make it harder to solve the commons problems involved. Doubt about
the theory of climate change and neglect of the need for early actions reduce the motivation to
reach agreements. While countries, businesses and people have incentives to take individual
actions to reduce their dependence on fossil energy, misperceptions reduce their incentives to
cooperate to bring forth technologies for alternative energy production, i.e. to produce a
public good. However, since laboratory experiments suggest that people are more willing to
contribute to a public good than to prevent an identical public bad (Andreoni 1995), it may be
politically easier to take actions to prevent a possible overshoot due to rising costs of fossil
energy than to prevent severe climate change.
Simulation
Natural resources systems, economies, businesses, and private affairs involve complicating
dynamics. Proper management requires understanding of system structure and behavior.
Simulation is well suited for this purpose for three main reasons.
First, simulation models allow for dynamics and non-linear formulations (Sterman 2000), and
thus escape some of the restrictions applied to models for econometric analysis and
optimization.
Second, in addition to time-series data, simulation models can and must benefit from prior
information about relationships and initial stock values, in accordance with Bayesian theory.
Use of prior information also opens up for a variety of additional tests to judge validity
(Forrester 1980; Zellner 1981).
Third, simulation models can be used to test popular policy suggestions and to search for
policy improvements. This can be done for different model formulations and thus reveal how
sensitive policy performance is to debated formulations and to different world-views (Moxnes
2005).
Dissemination
Misperceptions of dynamic funnel and glass systems represent a likely explanation of
important and undesired historical overshoots. Turnarounds in public opinions after
introductions of restrictions on smoking (Fong et al. 2006) and congestion charges (Leape
2006), illustrate that theory is a less effective teacher than experience, even when it comes to
policy suggestions that are of direct benefits to majorities of people. Hence, dissemination of
experience is important and not always trivial (Rogers 1995). Motivating recognition of new
problems and first time policy innovation is even more challenging.
Analyses based on complex models can influence change agents such as managers,
politicians, and activists. Simplified models that capture the essence of problems, such as
those presented here, can be useful vehicles for dissemination of model insights and for
learning from experience.
However, quite recent learning literature suggests that most people do not think in terms of
models, they operate with what di Sessa (1993) calls phenomenological primitives. People
perceive and characterize situations (pattern recognition) and this triggers predictions of
behavior patterns based on stored experience. This produces quick responses of importance
for species survival. E.g. football players develop “lookup tables” linking various types of
kicks and resulting ball trajectories. Experience is gained through trial-and-error. This points
to two essential elements in dissemination: recognition of situations and prediction of
behavior.
So how can “lookup tables” linking situations and behavior be developed when there are no
appropriate real world experiences to build on? Analogies seem essential. This is not a new
idea. It is used in narratives, parables, and illustrative examples. What science can contribute
to is to develop appropriate analogies and to unveil inappropriate analogies. An appropriate
analogy is one that captures the essence of scientific understanding, which people recognize
as representative for their problem situation, and that provides consistent predictions of
behavior. Research is also needed to test the effectiveness of analogies. For instance, is the
funnel and glass analogy effective in preventing undesired overshoots in alcohol intake and in
GHG emission? Is it effective in limiting people’s use of explanations blaming external
influences for man-made problems and reliance on ‘wait-and-see’ strategies?
Conclusion
A funnel and glass model serves as a unifying theory that seems able to explain a large set of
overshooting phenomena. Real life experiences, laboratory experiments, and simulation
models suggest that decision-makers misperceive dynamic systems and allow growth
processes to bring funnels to excessive levels before goal seeking processes set in. Clearly,
there is need for formal models and relevant analogies to judge the risks of overshoots and to
learn from history. A fishery case demonstrated the potential of better policies.
16
To reduce the risks of potential global overshoots, it seems a small investment for world
nations to invest in thorough studies of underlying dynamics. Both pessimists and optimists
seem to rely on simplified and partial arguments. Similar to studies of climate change under
the auspices of IPCC, the UN could coordinate research on potential overshoots due to
climate change, scarcity of fossil energy, and other vital resources in limited supply.
Importantly, there is need for competing models. No single institution is likely to produce
unbiased results. Because of the tendency for misperceptions, advanced information
dissemination is needed.
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Supplementary material
A model of boom and bust
Figure S1 shows a stock and flow diagram of the boom and bust model with parameter values
to replicate typical laboratory experiments where the expected fundamental price declines
linearly over periods. The model is fully described in terms of equations and parameter values
in Table S1.
Fundamental
price
Perceived
price
Updating
Perceived Qutdating
past price PPP
Outdating
PP 2 Relative
price gap
Expected
relative price
increase
Fixed asset Asset
supply demand
W increase W fundamental
Figure S1: Stock and flow diagram of asset market
Table S1: Equations and parameter values for boom and bust model (Using Euler’s method,
stocks are updated with a time step of 0.05 period).
INIT Perceived_past_price = 1.0 or 3.75
Updating_PPP = Perceived_price/Time_to_PPP
Outdating_PPP = Perceived_past_price/Time_to_PPP
INIT Perceived_price = 1.25 or 3.5
Updating_PP = Price/Time_to_PP
Outdating_PP = Perceived_price/Time_to_PP
Asset_demand = 100*(1+W_increase*Expected_relative_price_increase_in_price)*
(1+W_fundamental*Relative_price_gap)
Expected_relative_price_increase_in_price = (Perceived_price-Perceived_past_price)/
(Time_to_PPP*Perceived_past_price)
Fixed_asset_supply = 100
Fundamental_price = 3.75-0.25*time
Price = Perceived_price*(Asset_demand/Fixed {_supply)A2
Relative_price_gap = max(-1, (Fundamental_price-Perceived_price)/
max(0.0001, Fundamental_price))
SWeq =0 or 1
Time_to_PP = 0.5
Time_to_PPP = 2
W fundamental = 0.1
W increase = 0.3
20
Price formation is inspired by a formulation in (Sterman 2000). Price is based on the
perceived price (funnel) and is adjusted up if asset demand exceeds fixed asset supply and
vice versa. If the weight on expected relative price increase is set equal to zero, the price will
adjust to ensure that price follows the fundamental price since a price higher than the
fundamental price will bring demand above supply and vice versa (in experiments the
fundamental price is not certain, however is indicated by information about random dividend
payments). A minor problem is that the price will lag changes in the fundamental price such
that there will be a persistent small gap between the price and the fundamental price. When
weight is put on the expected relative price increase, perceived past price (glass or second
funnel) comes into play. This stock is needed to estimate the recent price increase. A first and
good effect of considering price changes is that the minor persistent deviation is corrected.
Figure S2 shows how Price follows Fundamental price. Behavior is clearly different from
observed price in the experiment conducted by (Smith et al. 1988).
® 1: Price 2: Observed price 3: Fundamental price
:| 6:
2
| A | |
J ibe | E | | |
4 3 5
3 i
3a
Ve
Mags,
ied
Et
)
2
3 ot r t t i
7.00 450 8.00 11:50 15.00
Page 1 Period
Untitled
i)
Figure $2: Price and fundamental price when the two stocks are initialized consistent with the
fundamental price development. Observed price comes from Figure 9 in (Smith et al. 1988).
Next consider what happens when the model is initialized outside of the equilibrium path
with initial perceived price equal to 1.25 and perceived past price equal to 1.0, consistent with
observed prices in Smith et al.’s experiment. They explain: “What we learn from the
particular experiments reported here is that a common dividend, and common knowledge
thereof is insufficient to induce initial common expectations. As we interpret it this is due to
agent uncertainty about the behavior of others.” It also seems likely that the most risk-averse
players prefer a lacking up-front payment instead of an uncertain stream of dividends. Figure
21.
S3 shows that in this case the simulation model replicates observations very well. Initially the
price is lower than the fundamental price and a positive expected relative price increase leads
to high demand and rapidly increasing prices. The feedback loop through price and perceived
price becomes a reinforcing one, leading to exponential type growth. Expected price increase
pushes the price above the fundamental price. Price growth stops when the relative price gap
becomes dominating and demand falls below supply. This turns the feedback loop through
price and perceived price into a balancing (negative) one, leading to exponential decay and
convergence towards the fundamental price.
@ 1: Price 2: Observed price 3: Fundamental price
4 od
1.00 4.50 8.00 11.50 15.00
Page 1 Period
? Untitled
Figure S3: Model development when initialized outside of equilibrium path.
Clearly, the fit is very good and the model cannot be rejected on this ground. Equally
important, the model structure represents easy to use heuristics that subjects are likely to be
able to use, albeit not as precisely and consistently executed as done by the computer code.
However, this does not mean that this is the one and only model that can explain observed
price. For instance, no initial price trend (both stocks initialized at 1.25) combined with
higher weight on the expected price increase gives approximately the same fit. Doubling of
delay times for perceived price and perceived past price, combined with higher weights on
both expected price increase and price gap, also gives a good fit to observed prices.
22,
