Asymmetric commodity cycles: Evidence from an experimental market
Santiago Arango
Decisions Science Group
Center of Complexity -CeiBA
Universidad Nacional de Colombia, Medellin
ABSTRACT
Laboratory experiments of commodity markets have used the Cobweb design to investigate market
dynamics. The predicted cycles of the Cobweb theory did not occur. Arango (2006) adds complexity and
realism to the Cobweb model and observes stronger fluctuations and autocorrelation. He shows that these
fluctuations are quite symmetric and similar to the behaviour observed in one category of markets.
However the fluctuations are different from the asymmetric price behaviour observed in other commodity
markets. We hypothesise that asymmetries could be caused by non-linear demand, different from the
linear demand curve used by Arango. Consequently we replicate his experiment using a demand structure
with constant price elasticity and dynamic adjustment. Similar to Arango, the supply side is complicated
by capacity lifetimes and investment delays across treatments. Compared to the previous results, this
experiment gives rise to larger fluctuations and stronger asymmetries.
KEY WORDS: Commodity cycles, Cournot markets, cobweb markets, bounded rationality, complexity, experimental
economics.
JEL dassification. C9 - Design of Experiments; DOI - Microeconomic Behaviour: Underlying Principles; D43 -
Oligopoly and Other Forms of Market Imperfection; D84 - Expectations; Speculations; L10 - Market Structure,
Firm Strategy, and Market Performance.
ACKNOWLEDGE: I am grateful to the Centre for Developing Studies at University of Bergen, Norway, for
providing financial support to pay the monetary rewards in the experiments, to the National University of Colombia
for providing the infrastructure and subjects required to run the experiments, and Interconexién Eléctrica S.A. for
allowing us to run a market with professionals with experience from the Colombian Electricity Market. Remarkable
thanks to the Quota program of the Norwegian government for supporting the research.
1 INTRODUCTION
It is well known that commodity markets fluctuate with certain regularities (Spraos 1990; Cuddington &
Urzua, 1989; Cashin er a/ 2002, Deaton & Laroque, 1992, 1996, and 2003), and that fluctuations have
significant negative effects for consumers, producers and developing countries (Deaton, 1999; Akiyama et
al 2001; Akiyama er al 2003). Cycles in commodity prices represent a major problem for both
microeconomic and macroeconomic policies, particularly in countries where the economy depends largely
on exports of one or two commodities (Deaton & Laroque, 1992). Therefore, the understanding of cycles
is essential for policies of national savings and consumption, monetary policy, internal inside-country
pricing policies, and for the design of risk-sharing mechanisms (Deaton & Laroque, 1992). In addition,
better market knowledge is of course of interest to producers, investors and the banking system.
Despite the importance of the problem, most modem introductory textbooks in economics either ignore
commodity cycles (e.g. Mankiw, 2004; Sloman, 2002; Samuelson & Nordhaus, 2001; and Case & Fair,
1996) or they deal with the phenomenon using the highly simplified cobweb model (e.g. Lipsey &
Chrystal, 2003). Even though the properties of the world commodity prices are well known (Deaton and
Laroque, 1992, Deaton, 1999, Cashin et al 2002), there is not agreement between economists regarding
the causes of commodity price movements (Cashin et al 2002; Deaton & Laroque, 1992; 2003; Deaton,
1999); thus, the behaviour of commodity prices is poorly understood (Cashin et al, 2002). Journal articles
dealing with commodity cycles also resort to models (e.x. Deaton & Laroque, 1992; 2003) that have not
been able to reflect the empirical evidence (Deaton & Laroque, 2003; Gilbert, 2004). Thus, the lack of
consensus and models is a problem to the extent that different models prescribe different policies. For
instance, according to Deaton (1999) some African countries have got misleading advice based on
improper models (Deaton, 1999).
Traditional economic literature attributes fluctuations in commodity prices to external shocks confronting
inelastic demand, and to the behaviour of speculators (Deaton & Laroque, 1992), factors that move the
price away from rational equilibrium and produce variability. Supply shocks normally causes temporary
shortfall in production, and they are normally thought to be large; for instance, wars, pestilence, disease,
weather, and political upheaval (Deaton, 1999). If demand is price inelastic, then variance of prices could
be a number of times the variance of the supply shock (Deaton, 1999). For instance, Brunner (2000)
presents the effect of the macroclimatic phenomenon ENSO (El Nifio South Oscillation) on some
commodities in South America. Deaton (1999) presents the case of rice in Japan, the poor harvest during
1993 lead the country to increase imports from zero in 1992 to 2.2 million tons in 1993, rice prices
doubled and fell sharply after the recovery of Japanese production in 1994. Other commodity prices that
have boomed due to extemal shocks are maize crop because of the flooding in the Midwest of the United
States, and coffee because of frost and drought in Brazil.
The use of laboratory experiments of commodity markets has been limited to very simple designs. Most
experimental markets do not include dynamic structures and are reset each period (e.g. Plott, 1982; Smith
1982). Dynamics have been considered in studies of speculative bubbles. First, Miller er al (1977) took the
simplest intertemporal possible market based on the Williams’ two season model, where carryovers were
allowed only from one season to the next one They found that the markets worked very efficiently with no
signs of instability (Miller, 2002). Following, Smith et a/ (1988) considered asset markets lasting 15
periods. These markets regularly produced bubbles followed by crashes under a variety of market
parameters. For commodity markets, dynamics have been introduced by lagged supply models (Carlson,
1967; Sonnemans er al 2004; Holt and Villamil, 1986; Sutan & Willinger, 2004) and by repeated play
Cournot models (Rassenti et a/ 2000; and Huck et a/ 2004). The predicted cycles of the Cobweb theory
did not materialize in these experiments, while some random fluctuations were sustained (Miller, 2002).
These market designs may be relevant for certain seasonal agricultural products, but it rules out the
2
capacity vintages problem. In particular, tree crop or mineral commodities require the analysis of costly
investment where several years are needed to have production from investments, and this aspect seems to
be ignored in most of commodity cycles models (Gilbert, 2006). Therefore, the obvious extension of the
Cobweb market experiment is to introduce vintages of production capacity including capacity under
construction; Arango and Moxnes (2007), step by step, introduced both vintages and capacity under
construction where cyclical tendencies and instabilities where observed.
We repeat A rango’s experiment with the following differences in the design: linear demand is replaced by
a non-linear demand curve (constant price elasticity) and the price effect on demand is lagged. As a result
(in the most complex treatment) we get stronger fluctuations than in Arango (2006), more periodic cycles,
and asymmetries characterised by sharp upward price peaks (positive skewness). Both cyclicality and
efficiency are considered.
In this experiment, we alter the demand side and observe the effects of: i. introducing a constant elasticity
demand, and ji. introducing dynamics in the demand function. This is in line with other authors who
assume constant elasticity demand and dynamic adjustment (Nerlove, 1958), for aggregate farm input in
the US (Yeh, 1976), for household driving demand (Hill, 1986), and for other economic dynamic
problems se examples in (Lewbel, 1994). We ask, will this demand formulation lead to asymmetric price
oscillations in our experiment? Will the experiment generate price cycles like the ones observed for
instance in sugar and coffee with positive skewness?
Our experiment has four treatments. Each new treatment adds complexity to the previous one. The first
experimental treatment (T1) involves a simple lagged supply model with symmetric constant marginal
costs as in Arango (2006); however we introduce a constant price elasticity of demand instead of a linear
demand function. In treatment T2 we introduce a lag in demand. In treatment T3 we introduce vintages to
reflect industries where capital lasts many years. The fourth treatment, T4, keeps the vintages and adds an
extra delivery delay for investments. Typically, capacity additions require a sequence of operations:
planning, choice of suppliers, production of parts, transportation, constructions, and testing, or time for
gestation and growth in biological production systems. In total, capacity additions take several years in
most commodity markets. In our case, the lag is such that one new investment decisions will be made
before an ordered investment is in place.
The null hypothesis is based on the rational expectations hypothesis and the standard assumption about
optimal decision making. The expected behaviour is convergence to a stable Cournot Nash equilibrium.
Minor and seemingly random variations around the equilibrium value will be consistent with this
hypothesis, but systematic cyclical tendencies will not. The alternative hypothesis is based on bounded
rationality theory. Assuming adaptive expectations and that the investment decision is approached with a
simple heuristic (Tversky & Kahneman, 1987), T4 will show cycles and possibly also T3. The alternative
hypothesis is inspired by observations of cycles in real markets and by the results of previous
experiments’. In section two we present the design and the hypotheses of the experiment. Section three
presents the results which include a general overview, hypothesis testing and comparison with relevant
empirical evidence from real markets. We observe oscillatory behaviour when complexity is increased.
The price series show sharp peaks in treatments T3 and T4 different from the more symmetric fluctuations
observed in Arango (2006). Finally, we present the conclusions.
1 More evidence of cyclical tendencies is presented in a number of one player experiments (Sterman, 1987a;
Sterman, 1989; Diehl & Sterman, 1993, and Barlas & Giinhan, 2004). Sterman (1989) and Diehl & Sterman (1995)
show oscillatory behaviour as a result of ignorance of the supply line of pending production and this is important in
all these studies. In a market setting, Kampmann (1992) observed cycles for pricing institutions with fixed and
posted prices. Using a market clearing institution, prices tended towards equilibrium over time. Different from our
experiment, Kampmann’s experiment did not include vintages, had some extra complexity and used a different
market clearing mechanism than that implied by the Cournot model
3
The next two sections present the experimental design and the hypotheses to be tested. In the last two
sections we present results and discussions. Cyclical tendencies and implications for real markets are
discussed, as well as the asymmetry in the price distribution.
2 EXPERIMENTAL DESIGN
The experiment consists of four treatments. Each new treatment builds on the preceding one. Treatments
T1 and T2 have the same supply structure as the traditional Cobweb market or Cournot Nash game. All
four treatments here have constant price elasticity while Arango uses linear demand. Furthermore, in T2,
T3 and T4 demand is lagged. Thus, T3 and T4 mimic a market where it takes some time to build new
capacity and capacity lasts for long periods. We have selected an electricity market ad hoc. The number of
periods is large enough to allow learning and eventually convergence (40 periods in all but four markets).
Following, we describe the treatments in detail, the procedures, and the hypotheses.
2.1 TREATMENT T1: STANDARD FIVE PLAYERS COURNOT MARKET
The first treatment corresponds to a computerized experiment of a Cournot market with constant marginal
cost, under Huck’s standard conditions”. There are five symmetric firms in each market, each represented
by one player. Each subject chooses production between 0 and 6 units each period. Information about the
realized price and profits is given in the next period. Thus, there is a one period production lag which
makes the experiment dynamically identical to the traditional Cobweb design or the Cournot Nash game.
The constant price elasticity of demand function is
py
D,=D,| + L
fl (2) )
Where D, and P; are demand and price at time r, Do and Py are reference points of demand and price, and «
represents the price elasticity. Total production or supply is,
5
S,= V4 Q)
Where q;, is the nonnegative production of subject i in period r. Demand D, is set equal to supply S,,
therefore the market price in period ¢ is given by an inverted demand function
Ne
S
P =P 3
1 f D, ) (3)
where q;, is the nonnegative production of subject i in period r. Note that q;, is equal to the investment
made by subject i in period +/ (q;, = x;,.;). There is a ceiling price of 500 Col $/Unit. The profit for
subject i in period ris,
? Standard conditions (Huck, 2004, p.106): a. Interaction takes place in fixed groups; b. Interaction is repeated over a
fixed number of periods; c. Products are perfect substitutes; d. Costs are symmetric; e. There is not communication
between subjects; f. Subjects have complete information about their own payoff functions; g. Subjects receive
feedback about aggregated supply, the resulting price, and band their own individual profits; h. The experimental
instructions use an economic frame.
4
Tie = (Pi- ©) Gis 3)
where the marginal cost c=85 Col $/Unit. The time step is thought 20 years per period, so that it mimics
electricity markets, where thermo generators have around 20 years of life time.
2.2 TREATMENT T2: T1 WITH DELAYED DEMAND ADJUSTMENTS
Treatment T2 is equal to treatment T1 except that demand adjusts gradually towards the long term
equilibrium demand. The adjustment process is based on the well known stock-adjustment principle
developed by Nerlove (1958) and also known as the Koyck model (1954). There is a desired level of
demand given by the long term demand curve under certain price,
py
DEsuilibrium py | At ,
| (2) (7
where D/“““""“" is the equilibrium demand for price P,. The demand is adjusted partially by the process,
D, -D,, = k(DEmorim — Day (6)
where the change from one period to the next is only a fraction x; k is known as the coefficient of stock
adjustment. The market clearance mechanism implies that D, is equal to the total production S,. Solving
equations (4) and (5), and including the same ceiling price, we set the market price as,
Pra ()
S,-(1-k)-D,,]”
k-D ,
P,=MIN| al
The coefficient of stock adjustment x is set such that the average adjustment time, z, is 10 years or half a
time period. Appendix 2 presents a comparison of parameter & across treatments, which the selections of
the parameter is selected.
2.3 TREATMENT T3: T2 WITH PRODUCTION CAPACITY LASTING FOUR PERIODS
Treatment T3 is equal to treatment T2 except that we introduce production capacity that lasts for more
than one period, resembling many production sectors of the economy. T1 and T2 represent the more
special case of agricultural products that are planted in one season and harvested the next. Capacity lasts
for four periods. Since we assume full capacity utilisation, investments can be measured in production
units. This simplifies the task for the subjects. As in T1 and T2, it takes one period before new production
capacity is in place. Thus, production is equal to the sum of capacities of all four vintages,
atl
Ge= Dy a)
j=t-4
where x;; is the investment decision made in years j=1-4 to j=t-. To be consistent with T1 and T2, the
time step is reduced from 20 years in T1 and T2 to 5 years. Hence the lifetime of capacity is still 20 years.
The parameter & is chosen such that the treatments give the same demand adjustments over time. While k
in T2 is 6.389, in T3 it is 0.649, see Appendix 2. Thus, if there is a sudden change in price, the change in
demand in one step of 20 years in T2 will be equal to the change in demand in four steps of 5 years each
inT3.
Appendix 2 presents a comparison of parameter & across treatments.
2.4 TREATMENT T4: T3 WITH A ONE PERIOD EXTRA INVESTMENT LAG
This treatment is the same as T3 except for an extra one period investment lag. In many industries the
investment lag stretches over several years. This means that there will be a period after an investment
decision has been made in which the firm is producing with the existing capacity and in which the firm
make yet another investment decision. This is captured in treatment T4 by lagging capacity by one period
such that production is given by,
Ge = VX, (3)
where x;; is the investment decision made in years j=t-5 to j=r-2.
2.5 EXPERIMENTAL PROCEDURE
The experiment follow the standard framework used in experimental economics, with the same procedures
across treatments. Subjects were recruited from the same student population and during the same time
period. The subjects were forth and fifth year students of Management Engineering, Industrial
Engineering, Master of Systems, and Economics at the National University of Colombia, Medellin. In T4
there was also one group with professors from the same faculty and one with professionals of the
electricity industry. The experiment was initially tested with System Dynamics Master students at the
University of Bergen, Norway. Treatments T1 and T2 were run with 3 markets each and treatments T3
and T4 with 6 markets each. No subject had previous experience in any related experiment and none of
them participated in more than one session. Subjects were told that they could eam between Col $ 15000
and Col $ 320000 (US$5 - US$12 at that time) in about one hour and a half (circa 1.5 to 2.5 times a
typical hourly wage for students). They knew that rewards were contingent on performance, which was
measured in cumulative profits.
Upon arrival subjects were seated behind computers. Groups were formed in a random way. There were
two or three markets per session, and subjects could not identify rivals in the market. Instructions (in
Spanish) were distributed and read aloud by the experimenter (see Appendix 1). An English translation of
the instructions of treatment T4 and the user interface can also be found in Appendix 1. Subjects were
allowed to ask questions and test out the computer interface. In all treatments, parameters of the
experiment, including the symmetry across firms, were common knowledge to all subjects.
The measurement unit for production was Mill GWh (millions of GWh), and for price Col $/kWh, both
units commonly known in electricity markets. A reference point to build the demand curve was taken from
Ford (1999), and the long term price elasticity « = -0.6. This value is also quite representative for other
commodity markets such as sugar (-0.84), coffee (-0.39), or cocoa (-0.89) (Deaton & Laroque, 2003).
There was a price ceiling of 500 Col $/kWh. The initial condition was a total industry production of 14,56
Mill GWh per 20 year period for treatment T1 and T2, and 3,64 Mill GWh per 5 year period for
treatments T3 and T4. Thus, according to eq. (6) the price started out at 70 Col $/kWh. Each period the
6
subjects received information about their own production, total production of the rest of the players, total
production in the market, market price, marginal profits, and profits. For T3 and T4 they had a capacity
vintage graph that helped them keep track of the age structure of their current capacity. The experiment
did not include a profit calculator as did the experiment of Arango (2006).
The subjects were also asked to forecast the price for the next period, except in T4, where they were asked
to forecast the price for the period after the next one. Extra reward was given for good forecasting,
measured by the accumulated forecasting error. The rewards could vary from 0 for forecast errors above
an upper limit to Col $ 8000 (around US$3) for perfect forecasts.
The experiments were run in a computer network using the simulation software Powersim Constructor
2.51. The experimental market was easily programmed; the software ran automatically and kept record of
all variables including the subjects’ decisions. Subjects were also asked to write down their decisions and
key variables on a sheet of paper to keep a record of past data and to provide a backup of the experiment.
The experiment’ s software is available upon request; the equations are shown in Appendix 1.
2.6 TESTABLE HYPOTHESIS
First, we formulate null hypotheses based on standard economic models with rational expectations.
Thereafter, we present alternative hypotheses based on bounded rationality. We consider both equilibrium
and cyclicality.
2.6.1 Rational Expectations Hypotheses
In all treatments there is a unique Courmot Nash equilibrium (CN). Table 1 shows the numbers
characterizing the CN equilibrium. Note that in T3 and T4 investments are one fourth of the investment in
T1 and T2 due to the introduction of capacity vintages. Given the market structure, the CN model leads to
acomner solution at the maximum price of 500 Col $/kWh.
Hypothesis 1: Average prices are equal across treatments and equal to Cournot Nash equilibrium
Table 1. Equilibriums of the experimental markets
Individual Investment Total production Price
[Mill Gwh] [Mill Gwh] [Col $/kWh]
T1-T2 /T3-T4 T1-T2 /T3-T4
Cournot Nash/ 0.224 / 0.056 4.48 / 1.12 500
Joint maxization
Competition 0.648 / 0.162 12.96 / 3.24 85.
Previous experiments have shown biases toward competition (Huck, 2004; Huck, er a/ 2004, Arango,
2006). To judge our results in this regard, Table 1 also presents the equilibrium values for perfect
competition. We can observe that the CN price is equal to the price to for joint maximization.
Neoclassical economic theory suggests stability and not cyclical behavior because market actors with
perfect foresight will detect any cyclical tendency and prevent it by countercyclical investments.
Accordingly, economic theory normally attributes cyclical behaviour to external shocks and particularly
so in the case of commodity markets (e.g. Cuddington & Urzua, 1989; Cuddington, 1992; Cashin et al
2002; Reinhart & Wickham, 1994; and Cashin & Patillo, 2000). We consider random shocks generated
within a market to be consistent with standard economic theory. Such random variations may occur for a
number of reasons, such as discontinuous investments, learning, strategic moves, etc. Previously,
experiments with Cournot markets have shown that outputs and prices are close to the CN equilibrium.
Typically the deviation is less than one standard deviation of the price variation over time (Huck, 2004).
7
Hypothesis 2. Market prices do not show cyclical tendencies in any of the treatments while random
variations may occur.
2.6.2 Bounded Rationality Hypotheses
Similar to Arango (2006), the alternative hypotheses are based on bounded rationality theory; where the
individual investment decision is seen as consisting of two steps. First, the subjects form expectations
about future prices, and next they deliberate on the size of their investment. For instance, Nerlove (1958)
does this by assuming adaptive expectations and by using the inverted marginal cost curve to find the
appropriate future supply (and implicit investment). Here we rely on the same assumption about adaptive
expectations; however, we formulate an explicit investment function because we assume constant
marginal costs.
Proposed heuristic
The proposed heuristic is similar to the heuristic presented in Arango (2006), which assumes that people
are not able to follow the optimal strategy (rational behaviour). Instead, they adjust capacity towards a
desired capacity. That is, we assume people use a feedback strategy, where the desired capital is indicated
by expected return on capital. The investment function is,
x, = Max{0,C, /t +a¢(C) —C,) + sc (kC! — SC,)} (9)
where the max function precludes negative investments, total capacity C, divided by the life time z denotes
depreciation, a determines how fast capacity is adjusted towards the desired capacity C*,. Finally, asc
determines how quickly the supply line is adjusted toward the desired supply line kC*,, where k=//4 since
the investment delay is one fourth of the lifetime. The latter term is only applicable in T4. The desired
capital
C. = Max{0,a—£ 7 o p'} (10)
is a linear function of expected price P*,. When P*, equals the equilibrium price P*, desired capacity C*,
equals equilibrium production q°. At the same time, the parameter a determines the intercept with the y-
axis and the slope. The parameter a is restricted to a < q* to avoid negative slopes. Also note that C*,
depends on the equilibrium price P* and not on the marginal cost c. Hence, the formulation could be used
to test different assumptions about equilibrium. Finally, the expected price is given by
Pl, = BP. +(0-f)P dy
which represents adaptive expectations (Nerlove, 1958) previously considered in related economic
experiments (e. g. Carlson, 1967; Sterman, 1987b and 1989; Frankel & Froot, 1987). The parameter / is
called the coefficient of expectations. Note that the price forecasting in T4 is two periods instead of one
larger in T4. Following, we provide a simulation analysis of the proposed heuristic.
Differences between treatments
We simulate all treatments with the proposed heuristic to observe the consequent behaviour of the market
price. The initial conditions are similar to those used in the experimental design. The coefficient of
expectations is an average of values estimated by Sterman (1989) and Carlson (1967), ie., A=0.53. The
factors for the adjustment of the supply line and the total capacity are taken from Sterman (1989), who
8
estimates parameters in an analogous heuristic with data from an inventory management problem.
Average values are asc=0.10 and a@-=0.26. Parameter a was chosen a=1.25; so that the standard deviation
of simulated prices in T4 becomes equal to those observed in T4. P° was chosen equal to the competitive
equilibrium price, since this is more appropriate according to the experimental results.
Simulations of T1 and T2 show fast convergence to the competitive equilibrium. Figure 1 presents the
simulations for T3 and T4. The simulations indicate damped oscillation for T3 and explosive oscillations
for T4. The oscillations are irregular with sharp peaks. Note that there are no external shocks in this
simulation.
50
1 ,
39
r
: :
woh AO |
i
OF
5
Price ($/kWh)
Period
Figure 1. Simulated prices for T3 (line 1) and T4 (line 2).
Sensitivity Analysis®
T1 and T2 are not sensitive to changes in parameters. Sensitivity to ac for T3 is presented in Figure 2,
where we observe that explosive oscillations emerge when the value of parameter a is increased. A
doubling of a or more (a@>0.5) leads to unstable behaviour with explosive oscillations. The effect of the
parameter a is similar to that of a. Instabilities occur for low values of a. Lower values of leads to more
stable behaviour.
500. 3
Price ($/kWh)
J
2
Period
Figure 2. Sensitivity analysis of a for T3: line 1 for a-=0.1; line 2 for @=0.3; line 3 for a=0.5.
Sensitivities in T4 are similar to those found in T3. However, explosive oscillations occur for lower values
of ac as shown in Figure 3. Additionally, T4 has the parameter asc, which could vary between 1 if there is
a full account of the supply line of capacity and 0 if the supply line of capacity is completely ignored.
5 Eigenvalue analysis could have provided insights about the stability properties of the treatments. Its use is
complicated by the non linear demand curve. Here, simulations provide enough information about the potential for
cyclical or unstable behaviour.
Simulations show that the larger asc is, the more stable the system becomes. To some extent, we expect
that people will ignore the supply line of capacity, consistent with Sterman’s observation (1989), which
should result in stronger cyclical tendencies.
i} a
ALITNAT
4: 3 3
0 5 10 15
Period
Figure 3. Sensitivity analysis of a for T4: line 1 for a-=0.1; line 2 for a=0.2; line 1 for a-=0.3.
To summarize, we present the formal hypothesis:
Hypothesis 3: Cycles will not occur in treatments TI and T2, while T3 may and T4 will show cycles with
sharp peaks.
We see that hypothesis 3 coincides with hypothesis 2 for treatments T1 and T2. The two hypotheses have
different predictions for T4 and possibly for T3. We do not state an explicit hypothesis for the equilibrium
or average price as we did in hypothesis 1. Rather we see the experiment as exploratory in this regard. The
above simulations do not provide any hypothesis since the simulations simply assume competitive
equilibrium.
3 EXPERIMENTAL RESULTS
We first present a general overview of the experimental results; next we test hypotheses and compare
cyclical behaviour to behaviour obtained in other experiments. Finally, we evaluate the performance of the
subjects.
3.1 GENERAL OVERVIEW
The main statistics for observed prices are presented in Table 2. Average prices are higher than the
competitive equilibrium (85 Col $/kWh) and far below the CN level (500 Col $/kWh) in all treatments.
Because of the large standard deviation (Sz) and the limited number of markets, we cannot distinguish
averages for the different treatments. Average standard deviations over time S increase considerable from
T1 and T2 to T3 and T4 suggesting more unstable behaviour in the latter two treatments. The tendency is
the same for autocorrelation. Statistical tests are presented in the next section.
Table 2. Summary statistics for the realized prices in the four treatments*
All periods First 20 periods Remaining periods
KX S&S S$ a X¥ S a ¥ § a
T1 157 45 50 0.34 144 48 0.16 192 42 0.23
T2 107 12 25 0.24 105 30 0.21 111 16 0.18
T3 134 46 94 0.39 137 115 0.35 134 64 0.35
T4 127 31 103 0.48 123 113 0.50 134 88 0.35
*X : mean sample of prices; Sz standard deviation of X across groups: S: average standard deviation over
time; : sample autocorrelation.
Table 2 also shows split results for the first 20 periods and the remaining ones, this enables us to look for
signs of learning over time. The divided results do not show a clear pattern for average prices. We observe
a reduction in the standard deviation from the first to the second period, especially in T3 and T4 where the
reductions were 44% and 22% respectively. We observed a reduction in average autocorrelation of T4.
Then we look in more detail at the price development over time. Figure 4 shows the realized prices. Prices
in treatments T1 and T2 are quite stable and hardly ever fall below the marginal cost (or competitive
price). Prices in T3 and T4, reach high levels in very short periods separated by long periods with prices at
or under the marginal cost. Thus, instability increases with complexity from T1 and T2 to T3 and T4.
While prices never exceed 300 Col $/kWh in T1 and T2, there are incidents where the price hits the
ceiling in 8 of the 12 markets in T3 and T4.
Treatments T1 & T2 Treatments T3 Treatment T4
500 7 7 7 500 7 0 7 7 500 7 7 7
\ ' ' ' ' ' ' ' )
1 1 t t j t I \ t
0 H H H 0 H H H 0 H H H
10 20 30 40 10 20 30 40 10 20 30 40
500 : : : 500 ; : ; 500 . ; °
\ \ \ 1 \ 1 \ \ \
\ \ ' \ \ \ ' \ \
\ ' 1 \ 1 \ 1 I 1
0 L L L 0 ier L L 0 L L L
10 20 30 40 10 20 30 40 10 20 30 40
500 : ' i 500 ' r : 500 : r '
\ \ 1 1 ' ' ' ' 1
' ' ‘ ' 1 ' ' ‘ f
0 H H H 0 i H H 0 H H H
10 20 30 40 10 20 30 40 10 20 30 40
500 j - ; 500 - ; - 500 - ; -
\ \ \ \ ‘ f \ f i
i i i \ ' 1 \ ' '
' i \ 1 4 ' ' \ \
0 H H H 0 H H H 0 H H H
10 20 30 40 10 20 30 40 10 20 30 40
500 ; ; ; 500 ; ; ; 500 ; ; ;
0 H H H 0 H H H 0 i H H
10 20 30 40 10 20 30 40 10 20 30 40
500 500 500
7 7 7 7 7 7 7 7 7
\ f \ \ f \ \ i \
\ ' ' ' ' ' ' ' '
' ' \ ' ' t \ \ '
\ ' ' ' \ ' ' ' '
' \ \ ' | ' \ ' '
\ \ \ \ ' \ \ \ \
0 H H H 0 sri H H 0 H H H
10 20 30 40 10 20 30 40 10 20 30 40
time (periods) time (periods) time (periods)
11
Figure 4. Time series for prices for all treatments together with marginal costs of 85 (all units in Col $/kWh). Left
column presents T1 in the first three plots, the other three are for T2; the middle column presents T3; and the right
column presents T4.
Note that, by design, all markets start up with overcapacity, with the corresponding price lower than the
competitive equilibrium. Still, in all groups of treatments T3 and T4 the average player start out with
investments above the equilibrium level, leading to lower prices after the delivery delay. As the subjects
observe the low prices and realize that there have been over-investments, they reduce investments. Now
they under-invest, and this leads to under-capacity and sharp price peaks due to the non-linear demand
function. The cyclical phenomenon is repeated over time.
Visual inspections of the time series confirm previous evidence of cycles and/or instabilities. We observe
that oscillations are stronger in T3 and T4 than in T1 and T2. Hence, the introduction of vintages in T3
and an extra investment lag in T4 seems to destabilise the market.
3.2 TESTING THE HYPOTHESES
Following, we perform the formal tests for the hypotheses of the experiments, first related to average
prices and second to price variations.
Hypothesis 1: Average prices are equal across treatments and equal to Cournot Nash equilibrium
Table 3 presents the confidence intervals for all average prices. In all markets, the table shows that the
predicted CN equilibrium (500 Col $/kWh) is not included in any of the 95% confidence intervals;
therefore, hypothesis 1 is rejected. Instead, average prices are closer to the competitive equilibrium (85
Col $/kWh). In four markets, the competitive price falls in the confidence interval, in one market the
average price is significantly lower.
Table 3. Confidence interval for average prices Xx
Lower — Upper
bound X bound
Treatment T1
G1 174 202 230
G2 105 111 118
G3 136 156 177
Treatment T2
G1 108 120 133
G2 94 100 106
G3 94 100 108
Treatment T3
G1 147 183 220
G2 80 108 136
G3 59 71 82
G3 123 168 212
G4 89 102 115
G6 125 171 218
Treatment T4
G1 99 127 154
G2 117 150 184
G3 134 176 217
G3 80 101 123
G4 67 100 133
G6 69 108 147
Now, we tum to test cyclicality.
12
Hypothesis 2. Market prices do not show cyclical tendencies in any of the treatments while random
variations may occur.
Hypothesis 3: cycles will not occur in T1 and T2, while T3 may and T4 will show cycles with sharp peaks.
The difference between hypotheses 2 and 3 pertains to treatments 3 and 4. If we observe cyclicality in T3
and T4, that favours hypothesis 3. No cyclicality favours hypothesis 2. We consider differences in
variance and we investigate estimated investment heuristics. We also explore cyclicality with spectral
analysis and autocorrelogram; however, we gave up this possibility because of the poor results.
Difference in variance across treatments
We pool T1 and T2 because the only difference is the delayed adjustment of demand and because both
treatments represent traditional Cobweb markets on the supply side. Table 5 shows that the standard
deviation for the pooled T1 and T2 is significantly different from the standard deviation for treatment T3
as well as from T4. There is no significant difference between the standard deviations for T3 and T4.
Table 4. Tests of differences between average standard deviations in different treatments
Ho Ss Ss tratio teritical, 0.05
Snm=Sry | 374vs.936 | 240and474 | 260 2.364
Snn=Su | 374vs1025 | 240and227 | -484] 2228
Sede 93.6vs.102.5 | 474and22.7 | -042| 2.364
S isthe average standard deviation of prices.
Test of the adaptive expectation hypothesis
The adaptive expectations hypothesis presented in eg. (11) is formulated by a linear equation restricted to
pass trough the origin of the 2D space (P,.; - P’., , P’, - P’..). We relax this constraint by postulating a
linear function of the form
(P¥i41—P*) = @+ B(P,-P*) + & (12)
where ¢; is iid random variable with zero mean and finite variance. The term @ can be interpreted as a bias
parameter. Thus, a subject might have adaptive expectations, but still retain either optimistic or pessimistic
bias. The results of estimating a and f# are presented in Table 5, for both individuals and aggregated
markets. The table also includes the arithmetic mean of the coefficients @ and f; and the r for all the
linear regressions. We define the expected price for an aggregated market to be the average of the
expected prices of the individuals participating in the particular market.
13
Table 5. Parameter estimation for the adaptive expectations hypothesis for individuals and aggregated markets across
treatments corresponding to eg. (/4).
¥
a | p [r a | p [PF a [| ps [F a | p TF
Individuals TT Individuals T2 Individuals T3 Individuals T4
TA 2.54 (0.82) 0.47 (0.05) 0.14 9.21 (0.20) -0.46 (0.06) 0.09 4.29 (0.79) 0.25 (0.11) 0.07 2.13 (0.74) 0.15 (0.09) 0.08
1/2 0.58 (0.97) 0.18 (0.67) 0.01 0.37 (0.92) 0.15 (0.16) 0.05 5.19 (0.68) -0.07 (0.59) 0.01 5.63 (0.62) 0.23 (0.35) 0.02
13 421 (0.72) 0.24 (0.26) 0.05 = 1.06 (0.73) 0.48 (0.00) 0.59 3.32 (0.88) 0.26 (0.35) 0.02, =13.77 (0.26) 0.14 (0.15) 0.06
1/4 -21.86 (0.11) 0.60 (0.04) 0.15 3.65 (0.34) 0.31 (0.01) 0.19 13.66 (0.52) 0.43 (0.06) 0.09 0.06 (0.98) 0.00 (0.94) 0.00
15, 10.33 (0.56) 0.39 (0.06) 0.13 -1.43 (0.82) 0.23 (0.29) 0.03 -9.92 (0.14) 0.08 (0.05) 0.10 12.07 (0.45) 1,02 (0.02) 0.13
2 0.22 (0.94) 0.45 (0.05) 0.13 2.56 (0.32) 0.19 (0.31) 0.03 0.68 (0.80) 0.08 (0.02) O14 24.77 (0.27) 1.06 (0.00) 0.22
2/2. 0.96 (0.77) 0.08 (0.57) 0.01 1.47 (0.30) -0.17 (0.18) 0.05 1.21 (0.75) 0.01 (0.78) 0.00 49,37 (0.02) 2.43 (0.00) 0.27
213 1.49 (0.41) 0.38 (0.00) 0.29 0.33 (0.84) 0.11 (0.34) 0.03 4.40 (0.80) 1.04 (0.02) 0.15, 3.31 (0.83) 0.59 (0.05) 0.10
24 -2.73 (0.57) 0.09 (0.50) 0.02 0.68 (0.68) 0.04 (0.48) 0.01 3.16 (0.76) 0.13 (0.53) 0.01 14.49 (0.38) 0.70 (0.03) 0.13
25 -3.60 (0.42) 0.08 (0.38) 0.03 1.07 (0.55) 0.06 (0.61) 0.01 12.79 (0.23) 0.64 (0.03) 0.13 5.71 (0.70) 0.65 (0.06) 0.10
EL 1.35 (0.88) 1.07 (0.00) 041 =1.87 (0.72) 0.29 (0.57) 0.01 0.95 (0.80) -0.08 (0.62) 0.01 1.05 (0.22) 0.01 (0.06) 0.09
3/2. 1.83 (0.05) -0.02 (0.07) 0.12 6.59 (0.30) 0.08 (0.50) 0.02 2.32 (0.67) -0.43 (0.25) 0.04 9.05 (0.51) -0.35 (0.11) 0.07
3/3 -3.61 (0.55) 0.48 (0.04) 0.15 =2.22 (0.59) 0.28 (0.23) 0.06 -4.11 (0.05) 0.08 (0.04) O11 0.91 (0.96) 0.07 (0.87) 0.00
34 =1.88 (0.82) 0.23 (0.21) 0.06 -8.44 (0.11) 0.44 (0.12) 0.09 0.60 (0.84) 0.00 (0.96) 0.00 14.96 (0.61) 0.44 (0.02) 0.14
35 13.60 (0.21) 0.93 (0.10) 0.10 3.79 (0.64) 0.56 (0.10) 0.10 2.35 (0.68) 0.30 (0.16) 0.05, 4.58 (0.74) 0.13 (0.33) 0.03
a 1.17 (0.97) 0.06 (0.85) 0.00 6.25 (0.33) 0.31 (0.05) 0.10
42 5.00 (0.81) 0.53 (0.02) 0.14 0.00 (1.00) 0.00 (0.51) 0.01
AB 12.05 (0.61) 0.45 (0.23) 0.04 0.02 (0.99) 0.02 (0.46) 0.02
aa 0.06 (0.97) 0.00 (0.94) 0.00 0.16 (0.97) 0.03 (0.78) 0.00
AS 10.55 (0.66) 0.88 (0.00) 0,22 6.25 (0.33) -0.31 (0.05) 0.10
oT 0.19 (0.96) 0.11 (0.48) 0.01 7.66 (0.64) 0.25 (0.09) 0.08
5/2 1.17 (0.47) 0.00 (0.99) 0.00 4.45 (0.86) 0.04 (0.80) 0.00
5/3 3.55 (0.48) 0.14 (0.35) 0.02, -0.91 (0.97) 0.00 (0.99) 0.00
Bt 0.06 (0.99) -0.14 (0.64) 0.01 -0.45 (0.97) 0.02 (0.84) 0.00
5/5 -0.16 (0.98) 0.23 (0.66) 0.01 -12.56 (0.65) 1.08 (0.01) 0.19
6/1 1.11 (0.96) 0.03 (0.91) 0.00. 0.22 (0.99) 0.14 (0.25) 0.04
6/2 4.15 (0.84) 0.06 (0.79) 0.00 -0.51 (0.89) 0.01 (0.85) 0.00
6/3 -4.34 (0.82) 0.56 (0.01) 0.16 18.45 (0.56) 0.62 (0.04) O11
6a 2.69 (0.87) 0.04 (0.82) 0.00 5.53 (0.73) 0.25 (0.22) 0.04
6/5 -8.60 (0.45) 0.12 (0.14) 0.06. 0.36 (0.98) 0.06 (0.79) 0.00
Avg 0.05 0.30 0.01 0.16 1.88 0.10 5.16 031
Markets T1 Markets T2 Markets T3 Markets T4
1 11.18 (0.04) 0.64 (0.00) 0.69 1.67 (0.36) 0.33 (0.00) 0.60 15.21 (0.01) 0.45 (0.00) 0.74 -7.88 (0.12) 0.41 (0.00) 0.52
2 -5.36 (0.00) 0.35 (0.00) 0.61 0.57 (0.39) 0.31 (0.00) 0.64 8.16 (0.07) 0.48 (0.00) 0.70 12.07 (0.00) 1.00 (0.00) 0.95
3 -12.54 (0.00) 0.68 (0.00) 0.74 3.86 (0.00) 0.48 (0.00) 0.76 -4.35 (0.02) 0.43 (0.00) 0.68 -14.65 (0.10) 0.47 (0.00) 0.57
a 5.22 (0.44) 0.64 (0.00) 0.84 =3.53 (0.16) 0.19 (0.00) 0.39
5 3.92 (0.02) 0.51 (0.00) 0.80 23.08 (0.00) 0.62 (0.00) 0.74
6 -16.91 (0.01) 0.52 (0.00) 0.76 -6.33 (0.35) 0.50 (0.00) 0.72
Avg 2.24 0.56 2.04 0.37 7.37 0.50 1.82 0.54
*: Market Number / Player
The coefficient of expectations fis postulated to be in a range from zero to one. All the f estimates from
aggregate markets fall in this range, and all are significant. The estimate for fis similar across treatments
and even the estimate for T2 is not significantly different from the others. Note the good fit for the
aggregated markets with r° higher than 0.50 in all markets. The average / coefficients of the aggregated
markets are all higher than the average coefficients for the individuals. Similarly, individuals present only
few significant values of # and 7? is considerable lower in almost all cases 7° of the aggregated markets.
Thus, the poor regressions may reflect different forecasting heuristics.
Now, we turn to make explicit tests of the proposed heuristics. The heuristic is constructed assuming that
individuals form expectations about future prices first, and they next deliberate on the size of their
investment. First we test the adaptive expectations and then the investment function.
Test of the heuristic
We explore the aggregated investment behaviour by performing regressions of the proposed heuristic.
Here, we regress on time-series data the linear version of the hypothesised investment heuristic, which
takes the form
X, = m3P*, + m2P, + m)SC, + b+ & (13)
where m; (i=1,2,3) and b are parameters to be estimated, and ¢; is iid random variable with zero mean and
finite variance. The expected price P* was taken as the average of individual expectations. There is no
14
supply line of capacity, SC,, in treatments T1, T2, and T3 and therefore we cannot estimate the coefficient
mz. Regressions are presented in Table 6 together with average values.
Table 6. Parameter estimation for the proposed heuristic for aggregated markets corresponding to eg.(/3) (p-value in
parenthesis).
ms; (P*) m,(P) m, (SC) b r
Treatment T1
MKtT -0.025 (0.04) 0.012 (0.23) 11.01 (0.00) 019
Mkt2 -0.010 (0.73) -0.006 (0.70) 12.51 (0.00) 0.04
Mkt3 0.006 (0.75) 0.037 (0.03) 14.35 (0.00) 0.57
Average -0.010 -0.010 12.623
Treatment T2
Mkt2 -0.057 (0.01) 0.012 (0.24) 16.04 (0.00) 0.20
Mkt 2 -0.067 (0.16) -0.002 (0.91) 18.75 (0.00) 0.18
Mkt2 0.029 (0.42) -0.034 (0.07) 12.43 (0.00) 0.20
Average 0.082 -0.008 15.740
Treatment T3
MEtI 0.000 (0.92) 0.001 (0.38) 0.53 (0.00) 0.08
Mkt2 -0.001 (0.70) 0.001 (0.42) 0.83 (0.00) 0.04
Mkt3 0.001 (0.86) 0.001 (0.68) 0.90 (0.00) 0.03
Mkt4 -0.002 (0.23) 0.002 (0.06) 0.74 (0.00) 0.12
Mkt5 -0.006 (0.10) 0.004 (0.08) 1.01 (0.00) 0.08
Mkt 6 0.004 (0.18) 0.003 (0.08), 0.74 (0.00) 0.14
Average -0.002 0.002 0.792
Treatment T4
MUI 0.005 (0.09) “0.002 (0.1) -0.12 (0.46) 0.60 (0.02) 0.09
Mkt 2 0.000 (0.91) 0.000 (0.85) 0.18 (0.28) 0.59 (0.00) 0.04
Mkt3 0.002 (0.11) 0.000 (0.94) -0.08 (0.61) 0.44 (0.00) 0.22
Mkt4 0.001 (0.77) 0.000 (0.81) 0.28 (0.05) 0.56 (0.05) O11
Mkt5 0.003 (0.36) -0.001 (0.48) -0.14 (0.43) 0.81 (0.01) 0.03
Mkt6 -0.005 (0.02) -0.001 (0.19) 0.41 (0.00) 2.98 (0.00) 0.75
Average 0.001 -0.001 0.088 0.997
Despite the potential meaning of the estimations from experiments, we should consider the poor results of
the regressions, not only in terms of the r? (only 2 out of 18 where 7? >0.25) but also in the significance of
the estimated parameters. The analysis of results does not allow us to draw conclusions to neither accept
nor reject the hypothesis. We also explore the individual investment behaviour. Even though the proposed
heuristic is built for the aggregate market, we take a similar linear form for individuals. Appendix 3 shows
the function and the results. The same puzzling and poor results dominates. Thus, the hypothesis did not
receive much support; therefore, the search for other heuristics should follow up the research, e.g. non-
linear investment functions.
Among the factors that complicate inferences about the investment decision rules are non linearity of
demand, the potential number of alternative strategies, uncertainty about other’s behaviour, etc. Since it
has been difficult to explain individual behaviour, let’s look at the other extreme, completely random
investments, we explore this possibility through simulations. We assume investments distributes normally.
Based on the experimental results, we estimate averages and standard deviations of investments for each
of the treatments.* Then we simulate the markets assuming that investments are normally distributed (iid)
with the estimated parameters. Figure 5 presents some typical behaviour. We observe that in all treatments
the simulations are quite similar to the behaviours observed in the experiment (see Figure 4) with larger
random variation in T1 compared with T2 and sharp upwards peaks in T3 and T4. Period lengths are
clearly longer in T3 and T4 than in T1 and T2, as in the results of the experiment.
* Distributions for investments are: forT1 ~N(9.39, 2.162), forT2 ~N(11.76,1.502), for T3 ~N(0.18, 0.342) and for T4
~N(0.85, 0.467).
15
400+
Price ($/kWh)
Price ($/kWh)
Period Period
T1 T2
500, + 1
1
4004 2
2 2 “
3 300} K 3 ;
Po B | 2 8
& j \ &
rn
$ 2004 ; g
a & 1
2 et
1004 iy | i 2 A
5 7 a . 3
By y _ . Vy y LY? as
0. x 2 ¥ 7]
0 5 0 1 2 2 30 3 40 o 5 1 3 2 2 30 35 40
Period Period
T3 T4
Figure 5. Stochastic simulations with normally distributed investments. Average and standard deviation from the
experimental results.
The tests and analysis of the heuristics failed to reject or support the hypotheses of investment behaviour.
Simulations have shown that a simple random investment could lead to cyclicality. Thus, systematic
investment heuristics are not necessary to produce cycles in T3 and T4. Further research is needed to
determine how investments are made. It is premature to conclude that investment decisions are not
systematic at all.
In the next section we consider in more detail the effect of assuming demand with constant elasticity and
lags.
3.3 COMPARISON WITH OTHER EXPERIMENTS AND REAL MARKETS
In this section, we compare the cyclical tendencies observed in T3 and T4 with previous experiments and
real markets. We compare cycles in terms of period lengths, autocorrelation, and degree of asymmetry
(skewness).
Visual inspection of the price time series in this experiment reveals average duration of 9.2 periods for T3
and 8.9 periods for T4, i. e., aprox. 45 years because the period length is 5 years, see Table 7. Long cycles
of 27 years are also observed in Arango (2006). These period lengths seem too long for electricity
markets, and much too long for many other commodities. For instance Cashin er al (2002) find period
lengths of 63 months for bananas, 58 months for aluminium, 50 months for beef, 56 months for cocoa, and
70 for coffee. This suggests that our choice of 5 year intervals has an important and distorting effect on
period lengths. Hence future experiments should consider using more frequent investment decisions,
preferably yearly.
16
Table 7. Number of major peaks and corresponding troughs by visual inspection of price time series for T3 and T4.
(Note: it was not possible to identify peaks for T1 and T2).
T3 | T4
Mkt1 5 Ey
Mkt 2 4 5
Mkt3 3 4
Mkt 4 5 4
Mkt5 4 4
Mkt6 5 5
“Average 43 [45
Average cycle duration 9.2 | 8.9
Cyclicality implies positive autocorrelation. Sample autocorrelation is reported positive in all the
experimental markets in both Arango (2006) and this experiment. The one-lag coefficient of
autocorrelation of our experiment is, on average, 0.39 and 0.48 for T3 and T4 respectively (see Table 2),
while and Arango (2006) shows an average of 0.73. Similarly, real commodity markets are positively
autocorrelated at yearly frequencies with autocorrelations higher than 0.8 (Cuddington & Urzua, 1989;
Deaton, 1999; Cashin et a/ 2002). Again the 5 year intervals for T3 and T4 may have caused some
distortion, and even more the 20 years of T1 and T2.
Table 8 presents the coefficient of skewness’ for both Arango (2006) and this experiment. We observe
clear price asymmetries in T3 and T4, but not in Arango. Skewness > 1 for all markets in T3 and T4,
while in Arango, skewness takes both positive and negative values. This difference in the asymmetry of
the distribution of prices around the mean implies that the demand has an important role in the price
dynamics. The price distributions support this claim.
Table 8. Coefficient of skewness for the most complex treatment (T3) in Arango (2006) and for T3 and T4.
Arango (2006) T3 T4
Mkt 1 -0.29 1.47 1.01
Mkt 2 0.15 2.72 1.57
Mkt 3 -0.73 1.42 1.32
Mkt 4 0.22 1.32 1.26
Mkt5 “1.13 119 | 2.37
Mkt 6 1.26 | 252
Lower limit -1.07 0.96 | 1.02
Average -0.36 158 | 181
Upper limit 0.36 2.17 | 233
We also compare the price distribution of T3 and T4 with that implicit in Arango (2006) (Figure 6). T3 in
Arango has a near to uniform price distribution, while the shape of T3 and T4 is close to exponential. In
T3 and T4 the highest concentration for prices is lower than the competitive equilibrium price, both cases
around 50% of the time. In Arango, the prices are distributed over a wide range that includes both the
competitive and CN equilibrium.
5 The coefficient of skewness (or third moment) indicates the degree of asymmetry of the distribution around the
mean. Positive coefficient of skewness implies that the distribution has a longer tail on the positive side of the mean,
and vice versa. For example, the coefficient of skewness for a Normal distribution is zero and exponential
distribution is positive.
17
Arango(2005)
4
0 0
0 2 4 6 0 100 200 300 400 500 0 100 200 300 400 500
Price ($/Unit) Price ($/kWh) Price ($/kWh)
Figure 6. Histograms for the realized prices of the markets in the most complex treatment in Arango (2006) and for
treatment T3 and T4.
Many commodity prices are asymmetric with positive values of skewness. For example, Deaton (1999)
show that time series for cocoa and coffee prices are punctuated by sharp upward spikes. Deaton &
Laroque (1992) find positive skewness for 13 commodities. For instance, from 1900 to 1981, sugar has
yearly autocorrelation of 0.62, a coefficient of variation of 0.60, and skewness of 1.49. These statistics are
comparable with the average observations in T3 with autocorrelation of 0.39, a coefficient of variation of
0.67, and skewness of 1.58; and they also compare with T4 with autocorrelation of 0.48, a coefficient of
variation of 0.83, and skewness of 1.81. Arango (2006) observes values of autocorrelation of 0.73 and
coefficient of variation of 0.5 on average; however, the skewness is not significantly different from zero.
Thus, constant elasticity demand with dynamic adjustment is important for the skewness, less so for
variance and not for autocorrelation.
3.4 MARKET PERFORMANCE
In this section, we are concemed with the effect of capacity lifetimes and investment lags on profits and
market performance. In Table 9 we compare the average profits across groups and treatments with
Competitive and CN equilibrium profits. We observe poor performance compared with the potential given
by the CN equilibrium. All markets produce average profits above the competitive equilibrium with the
exception of one group 3 in T3.
Table 9. Average profits across groups and treatments compared with the Competitive and CN equilibrium.
Mkt1 Mkt2 Mkt3 Mkt4 Mkt5S Mkt6 Average _ Competition CN
Tl 5057 1695 3462 3405 0 55720
T2 2677 1285 1090 1684 0 55720
T3 1968 400 -577 1569 352 1490 867 0 18573
T4 826 1328 1746 203 49 211 727 0 18573
3.5 OUTSMARTING THE MARKET
We have thus far shown that random investments lead to price behaviour that is quite similar to observed
behaviour. Simulations with a simple heuristic also produced similar behaviour. However, regressions did
not give much support to the hypothesised heuristics. Hence, we seem left with considerable uncertainty
regarding the heuristics subjects use. As a final attempt to investigate the subjects’ ability to handle the
dynamics of the market, we introduce a micro investor, MI, i.e. an atomist. The MI will either invest
nothing or a tiny amount each year, 0.046 GWh, on top of the actual investments in each of the
experimental markets. Then we see if the MI performs better or worse than the average subject in the
original experiments. The results indicate whether the original subjects could have improved at the margin
18
by changing investment behaviour. We limit the analysis to T4. We propose three rules for the timing of
the MI’s investments, increasing in sophistication.
First we assume procyclical investments, not very different from the hypothesised heuristic:
Rule 1, Invest if the ratio of price to cost is greater than 1.
The we propose a neutral strategy:
Rule 2, Invest the same amount in all periods.
The third rule is countercyclical. We define a counter that is increased by 1 if the ratio of price over costs
is less than 1, and that is reset to zero once it reaches the value 4. The rule is:
Rule 3. Invest if the counter is greater than or equal to 1.
The MI makes investment or production decisions in each of the six experimental markets for T4. The
profitability of the original subjects and of the MI is measured with a “Performance Index”, PI
SEP!
PI) =—+ ____
IC! +" ID}
d4
where EP’, is profits of subject j at time , /C is the initial capacity of subject j, and /D’, is the investment
made by subject at time ¢. Table 10, shows the results.
The average PI of the MIs is greater than the average PI for the subjects in all cases except for three cases
with rule 1. For rules 2 and 3 we find that the MIs outperform even the very best subjects in all cases but
one with rule 2.
Table 10. Performance Indices -PI- in T4: average and highest for subjects in the experiment, and micro-investor MI
with rules 1, 2 and 3.
Group Mkt1 Mkt 2 Mkt3 Mkt 4 MKt 5. Mkt6
Average 101.3 185.1 269.9 13.6 7.3 26.1
Maximum. 154.1 238.5 327.1 53.0 40.3 76.6
Micro-investor Rule 1 71.0 216.2 257.7 82.5 78.5 -37.0
Micro-investor Rule 2 151.5 238.6 330.6 59.8 55.3 83.1
Micro-investor Rule 3 164.9 262.1 339.7 65.8 58.9 96.6
When rule 1 performs just as good as the average subject, it indicates that the average subject tends to
invest procyclically. The outstanding performance of the MIs with the countercyclical rule 3, suggest that
the subjects would have benefited from using such a rule, at least at the margin.
4 CONCLUSIONS
This paper reports on a series of five players Coumot markets with groups of five seller subjects.
Analogous to Arango (2006), step by step, we add complexity (and realism) to the supply side of the
simple commodity market model: vintages in capacity and an extra investment lag. The two experiments
differ in that we introduce a constant elasticity demand with gradual dynamic adjustment, instead of the
linear static demand of Arango (2006).
19
Similar to previous experiments (e.g. Huck, 2004; Rassenti et a/ 2000; Arango, 2006) we find little
evidence of cyclical behaviour before vintages and investment lags are introduced. Similar to Arango
(2006) we find that the supply side additions lead to larger variance in price and to stronger
autocorrelation. Our results differ from those of Arango (2006) in that fluctuations become asymmetrical
measured by positive skewness. Similar to Arango (2006), average prices over all treatments are around
50 percent higher than the competitive equilibrium, respectively 45 percent and 54 percent for Arango
(2006) and the current experiment. Since the constant price elasticity and the maximum price of the
current experiment implies a much higher Coumout Nash equilibrium than the linear demand of Arango
(2006), the current experiment shows a much larger downward bias relative to the Coumot Nash
equilibrium.
Economic theory does not define any particular shape for the demand curve and leaves this as an empirical
question. Depending on the availability of close substitutes, the demand curve could be close to linear or
convex with close to constant price elasticity. Hence, one assumption is not necessarily more realistic than
the other. It is however reassuring that our simulations and experimental results with a convex demand
curve produce fluctuations similar to observations from real markets with positive autocorrelation,
positive skewness and sharp upward peaks (Deaton, 1999; Cashin, 2002). This is an important result,
given that previous models have not been able to clearly account for all of these features (He &
Westerhoff, 2005; Deaton and Laroque, 1992). Moreover, our results could be extended to different
commodities with similar market structure because, as Plott (1982) says, “The theory takes advantage of
the fact that principles of economics apply to all commodities which are valued independently of the
source of individual values or the ultimate use to which the commodities are to be put”.
Traditionally, commodity cycles have been explained by external shocks. The dynamics observed in this
experiment, by contrast, are generated endogenously by the internal structure of the market. Our
experiment does not distinguish clearly between intemally generated randomness and inappropriate
investment heuristics. A test with a micro investor, however, suggests that, at the margin, subjects could
benefit from heuristics that are countercyclical and thus are more appropriate for dynamic markets.
Further analysis is needed to settle this very interesting issue.
Subjects in Arango (2006) were availed with a profit calculator to help identify the Cournot Nash
equilibrium. Such a profit calculator was not available in this experiment. This may or may not have
influenced average prices in the two experiments. The profit calculator may also have influenced the
choice of heuristics in Arango (2006). Further research is needed to settle these issues.
Critics of experimental economics argue that real markets are inherently more complex than the markets
analysed in laboratories. Behaviour in a very complex system may be governed by different laws than
those used in simple systems (Gigerenzer et a/ 1999, Plott, 1982, p. 1522). We have responded to this
criticism by adding complexity and realism step by step. Our results clearly suggest that complexity
matters and that the subjects are not able to fully counteract the effects of complexity by altered
behaviour.
Commodity cycles are known to cause problems for consumers, producers as well as nations that depend
on a small number of commodities for their export earnings. Hence, price stabilisation is an important
policy issue (Akiyama er a/ 2001). Our study suggests that commodity price fluctuations are not only
caused by external shocks. Market actors may contribute considerably through seemingly random
behaviour and through inappropriate investment heuristics. Thus, policy focus should not be exclusively
on external events, policies should also consider the working of the market.
20
5 REFERENCES
Akiyama, T., Baffes, J., Larson, D., & Varangis, P. (2001). Commodity market reforms: lessons of two
decades. World Bank regional and Sectoral Studies, Washington, D.C.
Akiyama, T., Baffes, J., Larson, D., & Varangis, P. (2003). Commodity market reform in Africa: some
recent experience. Economic Systems, 27(1): 83-115.
Arango, S., (2006). Oscillatory behaviour as a function of market complexity: experiments on commodity
cycles, 23rd International Conference of The System Dynamics Society, Boston, Massachusetts,
USA.
Barlas, Y., & Ozevin M. G. (2004). Analysis of stock management gaming experiments and alternative
ordering formulations. Systems Research and Behavioral Science, 21(4): 439-470.
Bendat, J. S., & Piersol, A. G. (1980). Engineering Applications of Correlation and Spectral Analysis.
New Y ork : Wiley, 2/e, 458 p.
Box, G. E. P., Jenkins, G. M., & Reinsel, G. C. (1994). Time Series Analysis: Forecasting and Control.
Englewood Cliffs, N.J.: Prentice Hall, 3/e, 598 p.
Carlson, J. (1967). The Stability of an Experimental Market with a Supply-Response Lag. Southern
Economic Journal, 23(3): 305-21.
Case, K. E., & Fair, R. C., 1996. Principles of Economics, London : Prentice Hall Business Publishing,
6/e, 1014 p.
Cashin P., C. McDermott, J., & Scott, A. (2002). Booms and Slumps in World Commodity Prices. Journal
of Development Economics, 69: 277- 296.
Cashin, P., & Patillo, C. (2000). Terms of Trade Shocks in Africa: Are They Short-Lived of Long Live?
Working Paper 00/72, Washington: International Monetary Fund.
Cuddington, J. T., & Urzua, C. M., (1989). Trends and Cycles in the Net Barter Terms of Trade: A New
Apporach. The Economic Joumal, 99(396): 426-442.
Deaton, A. (1999). Commodity Prices and Growth in Africa. The Journal of Economic Perspectives,
13(3): 23-40.
Deaton, A., & Laroque, G. (1992). On the behavior of commodity prices. Review of Economic Studies, 59:
1- 24.
Deaton, A., & Laroque, G. (1996). Competitive storage and commodity price dynamics. Journal of
Political Economy, 104: 896-923.
Deaton, A., & Laroque, G. (2003). A model of commodity prices after Sir Arthur Lewis. Journal of
Development Economics, 71: 289- 310.
Diehl, E., & Sterman, J. D. (1995). Effects of Feedback Complexity on Dynamic Decision Making.
Organizational Behavior and Human Decision Processes, 62(2): 198-215.
Ford, A. (1999). Cycles in Competitive Electricity Markets: A Simulation Study of the Western United
States. Energy Policy, 29: 637-58.
Forrester, J. W. (1961). Industrial Dynamics. Productivity Press, Cambridge, Mass, 479 pages.
Gigerenzer G, Todd P. & The ABC Group (1999). Simple Heuristics that Make Us Smart. Oxford
University Press: New Y ork. 416 p.
He, X.Z., & Westerhoff, F.H. (2005). Commodity markets, price limiters and speculative price dynamics.
Journal of Economic Dynamics and Control, 29(9): 1577-1596.
Hill, D.H. (1986). Dynamics of Household Driving Demand. The Review of Economics and Statistics,
68(1): 132-141.
Holt, C., & Villamil, A. (1986). A laboratory experiment with a single person Cobweb. Atlantic Economic
Journal, 14 (2): 51-54.
Hoyck, L.M. (1954). Distributed Lags and Investment Analysis. Amsterdam: North-Holland.
Huck, S., (2004). Oligopoly. In: Economics Lab: An Intensive Course in Experimental Economics. Eds.
D. Friedman & A. Cassar, London/New Y ork: Routledge, 248 p.
Huck, S., Normann, H.-T., & Oechssler, J. (2002). Stability of the Coumot Process: Experimental
Evidence. International Journal of Game Theory, 31(1): 123-136.
21
Huck, S., Normann, H.-T., & Oechssler, J. (2004). Two are few and four are many: number effects in
experimental oligopolies. Journal of Economic Behavior and Organization: 53(4): 435-446.
Kampmann, C. E. (1992). Feedback complexity, market dynamics, and performance: Some experimental
results. Cambridge, MA, PhD thesis, MIT, 478 p.
Koutsoyiannis, A. (1979). Modern Microeconomics. Hong Kong: Macmillan Education, 2" edition, 581
p.
Lewbel, A. (1994). Aggregation and Simple Dynamics. The American Economic Review, 84 (4): 905-918.
Lipsey, R. G., & Chrystal, K. (2003). Principles of economics. Oxford : Oxford University Press, 10/e.
Mankiw, N. G. (2004). Principles of economics. Mason, Ohio : Thomson/South-W ester, 848 p.
Meadows, D. L. (1970). Dynamics of commodity production cycles. Cambridge, Mass., Wright- Allen
Press.
Miller, R.M., (2002). Experimental economics: how we can build better financial markets. Wiley, ISBN:
0471706256, 314 p.
Nerlove, M. (1958). Adaptive Expectations and Cobweb Phenomena. The Quarterly Journal of
Economics, 72(2): 227-240
Nerlove, M. (1958). Distributed Lags and Demand Analysis. Washington D.C., Agricultural Handbook,
141,
Plott, C.R. (1982). Industrial Organization Theory and Experimental Economics. Journal of Economic
Literature, 20(4): 1485-1527.
Rassenti, S., Reynolds, S. S., Smith, V. L., & Szidarovszky, F. (2000). Adaptation and Convergence of
Behavior in Repeated Experimental Coumot Games.Journal of Economic Behavior &
Organization, 41(2): 117-146.
Samuelson, P. A., & Nordhaus, W. D., (2001). Economics. McGraw-Hill: 17/e.
Sloman, J., (2002). Economics. FT Prentice Hall: Harlow, 5” edition, 762 p.
Sonnemans, J., Hommes, C., Tuinstra, J., & Velden, H. (2004). The Instability of a Heterogeneous
Cobweb Economy: A Strategy Experiment on Expectation formation. Journal of Economic
Behavior & Organization, 54 (4): 453-481.
Spraos, J. (1990). The statistical debate of the Net Barter terms of the trade between primary commodities
and manufactures. Economic Journal, 90: 107-28.
Sterman, J., (1987a). Testing Behavioral Simulation Models by Direct Experiment. Management Science,
33(12), 1572-1592.
Sterman, J., (1987b). Expectation Formation in Behavioral Simulation Models. Behavioral Science, 32,
190-211.
Sterman, J., (1989). Modeling Managerial Behavior: Misperceptions of Feedback in a Dynamic Decision
Making Experiment. Management Science, 35(3): 321-339.
Varangis, P., Akiyama, T., & Mitchel, D. (1995). Managing Commodity Booms and Busts. Directions in
Development Series, World Bank, Washington, DC.
Yeh, CJ. (1976). Prices, Farm Outputs, and Income Projections under Alternative Assumed Demand and
Supply Conditions. American Journal of Agricultural Economics, 58(4): 703-711.
Agricultural Commodity Markets And Trade
New Approaches to Analyzing Market Structure and Instability
Edited by Alexander Sarris and David Hallam, Food and Agriculture Organization of the United Nations, Italy
22
2006 480 pp Hardback 978 1 84542 444 2 £85.06 on-line discount £76.50
Gilbert, C.L. (2004), “Trends and volatility in agricultural commodity prices”, in A Sarris and D. Hallam
eds., "Agricultural Commodity Markets and Trade: New Approaches to Analyzing Market Structure and
Instability", FAO, Rome and Edward Elgar, Cheltenham (forthcoming, January 2006).
http://www.e-elgar.co.uk/Bookentry_Main.lasso?id=3910
23
Appendix 1. Instructions (with translation for T4), User interface, and Code for T4 (The
software and the rest of the material is available upon request).
INSTRUCTIONS
INSTRUCTIONES
PRECAUCION: NO TOQUE EL COMPUTADOR HASTA LA INDICACION PARA HACERLO
Este es un experimento en la economia de toma de decisiones, el caso es mercados eléctricos deregulados. Varias
instituciones han soportado financieramente para realizar el experimento. Las instrucciones son simples, si usted las
sigue cuidadosamente y toma buenas decisiones podra ganar una considerable cantidad de dinero en efectivo después
del experimento. En el experimento usted va a jugar el role de un productor de electricidad que vende la electricidad
en un mercado. Cada periodo usted decidira la produccidn futura. Su objetivo es maximizar las ganancias en todos
los periodos del experimento. A mayores ganancias, mayor sera el pago que usted recibira.
Usted es uno entre 5 productores de electricidad en un mercado. Usted no sabe quienes son los otros jugadores en su
mercado ni sobre su desempefio. Sus ganancias dependen de la produccién y del precio de la electricidad menos el
costo de produccion. La produccién no puede ser negativa y no puede ser mayor que 6 Mill GWh (T3y T4: 1.5 Mill
GWh), el cual es un limite superior para asegurar un minimo de competencia en el mercado. El costo unitario es 85
Col $/kWh para todos los productores. El costo incluye los operacionales y los costos de capital, y también el retorno
normal al capital. Esto, si usted vende electricidad a 85 Col $/kWh su exceso de ganancias seran cero, lo que
significa que usted esta haciendo las ganancias normales en la economia.
El precio de la electricidad esta dado para equilibrar la oferta y la demanda. La oferta es la suma de la produccién de
los 5 jugadores.
Para T1:; La demanda es sensitiva al precio y presenta una reaccion retardada a cambios en el precio. La curva de
demanda se muestra en la Figura 1, y tiene una elasticidad constante al precio de -0.6. Note que hay un limite
superior de 500 Col $/kWh para el precio. P
Para T2, T3 y T4: La demanda es sensitiva al precio y presenta una reaccion retardada a cambios en el precio. La
curva de demanda de largo plazo se muestra en la Figura 1, y tiene una elasticidad constante al precio de -0.6. Note
que hay un limite superior de 500 Col $/kWh para el precio. La demanda tiene un tiempo promedio de ajuste de 10
aiios. Esto significa que si hay una variacion en el precio, la demanda sera gradualmente ajustada hacia la demanda
indicada de largo plazo por la curva de demanda en la Figura 1. El proceso de ajuste es mostrado en la jError! No se
encuentra el origen de la referencia., donde usted puede ver como se ajusta la demanda después de un incremento
subito en el precio. Después de 10 afios, aproximadamente el 63% del ajuste de largo plazo ha tenido lugar.
En resumen, a mayor produccién total de electricidad, menor sera el precio. Respectivamente, a menor produccién
total de electricidad, mayor sera el precio. No hay crecimiento econdmico, lo que significa que la demanda solo
cambia por cambios en el precio. En el inicio del experimento, la produccion total de electricidad es 14.56 Mill GWh
(T3 y T4: 3.64 Mill GWh), el precio es 70 Col $/kWh, y su produccién es 2.91 Mill GWh (T3 y T4: 0.73 Mill
GWh).
600
500 4
400
300
Price (Col $/kWh)
0 25 5 15 10 125 15 175 20
Demanda (Mill GWh)
24
Figura 1. Curva de demanda.
Para Tly T2:
Usted decide cada periodo la produccién de electricidad para el proximo periodo. La longitud de cada periodo es 20 aiios. Antes
de tomar decisiones, usted obtiene informacién acerca del precio de la electricidad y de los excedentes de ganancias del periodo
actual. Cuando el proximo periodo comienza, este tendra la produccién que usted decidié en el periodo actual.
Para T3y T4:
Usted decide cada periodo su produccion adicional de electricidad para el futuro. La longitud de cada periodo es 5
afios. Antes de tomar decisiones, usted obtiene informacion acerca del precio de la electricidad y de los excedentes
de ganancias del periodo actual. Cuando el proximo periodo comienza, este tendra la produccién que usted ha
decidido los tltimos 3 periodos (T4: 4 periodos). Cada periodo usted decide la adicion (inversion) de produccién
futura (capacidad). Estas adiciones (inversiones) permaneceran toda la vida util de la capacidad de produccién. La
vida util es de 4 periodos o 20 aiios. En todos los periodos futuros su produccién sera igual a la capacidad de
produccion, la utilizacion de la capacidad no puede ser reducida. También note que es necesario un periodo (T4: dos
periodos) para construir nueva capacidad, esto es, la nueva capacidad no esta disponible hasta el proximo periodo
(T4: periodo después del siguiente periodo). La Figura 3 muestra la figura que se presenta en el experimento. Esta
muestra las decisiones que usted ha tomado los 3 (T4: 4) anteriores periodos y la decision que usted posiblemente
tomara en el periodo actual. Cuando usted haya decidido la produccion para el proximo periodo (T4: periodo
después del proximo periodo), su decisién no puede ser cambiada cuando usted esta en dicho periodo. En el primer
periodo usted vera las decisiones iniciales hechas antes de usted tomar la compaiiia.
=
Fe
g 6
S00
8
a 20
0 10 20 30 40 30 60 70 80
Afio
40
= Demanda largo plazo
8 35
2m =
= 30
z
Ba
&
20.
0 10 20 30 40 30 60 70 80
Afi
Figura 2. Reaccion dindmica del precio ante un incremento en el precio de la electricidad (T2, T3 y T4).
Produccién decidida en periodos futuros
‘Adici6n) de produccion hace tes perlodos
Mill GWh
5 Taaicion de
op lisicon de produccién en el period
a 2 3 4
Periodos Futuros
T3
25
Produccién decidida en futuros periodos
Producdién proximo perfoHo (decisiones
a fe lo 4 perfodos antes del titimo) dicién de produdcién hace tres petfodos
el ate 'Adicién de produgcién hace dos perfodos
=
© oe | (ee pe a
= 0. i ace un periodo.
03 i
tAdicién le produccién en el periodo actual
0.0. '
1 2 3 4 5
Periodos futuros
T4
Figura 3. Produccion futura decidida.
PAGOS
Usted recibira un pago segtin sea su desempefio. Su desempefio es medido por la acumulacién de excedentes de ganancias. Si
usted obtiene cero excedente de ganancias, su pago sera aprox. de Col $13 000. Si usted hace mas excedentes de ganancias
recibira un pago mayor, y si usted hace menos excedentes obtendra menos. Esto, siempre habra remuneracion para hacer lo mejor.
En cada periodo, también se le solicita hacer el prondstico del precio para el proximo periodo (T4: periodo después del
proximo). Usted ganaré pago extra dependiendo de la precisién del prondstico que haga. Si usted hace un prondstico perfecto en
todos los periodos del experimento, usted obtendra Col $6000.
CORRIENDO EL EXPERIMENTO
Todos los jugadores entran la decision de produccién y el precio pronosticado en el computador, escriben en la hoja de
papel correspondiente, y presionan “Accept Decisions”. Cuando todos han tomado sus decisiones, la ventana “Accept
Decisions” aparece de nuevo, el juego ha avanzado un periodo. El tiempo avanza, y los jugadores obtienen los
resultados del proximo periodo. Este es el momento de tomar decisiones de nuevo y asi sucesivamente.
Después de 40 periodos, el juego termina. Usted escribe su pago en la hoja de papel y se aproxima al lider del
experimento para obtener su pago.
TENGA CUIDADO DE NO PRESIONAR “Accept Decisions” A NO SER DE ESTAR SEGURO DE HACER ESTO.
Una vez presione “Accept Decisions” su decisién no puede ser cambiada.
NOTA:
De acuerdo con el propésito de los experimentos, se requiere que no compartir ninguna clase de informacion entre los jugadores
(verbal, escrita, gestual, etc.). Por favor, respete estas reglas porque son importantes para el valor cientifico de los experimento.
Gracias por participar del experimento y mucha suerte!!!
26
TREATMENT T4: Instructions (translation to English)
INSTRUCTIONS
WARNING: DO NOT TOUCH THE COMPUTER UNTIL YOU ARE TOLD TO!!!
This is an experiment in the economics of decision making, the case is a deregulated electricity market. Various foundations have
provided funds for the conduct of this experiment. The instructions are simple, and if you follow them carefully and make good
decisions you might eam a considerable amount of money which will be paid to you in cash after the experiment. In this
experiment you are going to play the role of an electricity producer who sells electricity in a market. Each period you will make a
decision regarding your future production. Y our target is to maximize the profits over all periods of the experiment. The larger
your total profits, the larger your payoff will be.
Y ou are one among five electricity producers in a market. You do not know who the other players in your market are and how
they perform. Y our profit depends on your production, and the price of electricity minus the production cost. Production can not
be negative and must be below 1,5 Mill GWh, which is an upper limit ensuring a minimum of competition in the market. The cost
per unit is 85 Col $/kWh for all the producers. The cost includes the operational and capital costs, as well as a normal return to
capital. Thus, if you sell electricity at85 Col $/kWh your excess profit will be zero, which means you are making the normal
profits in the economy.
The electricity price is set to equilibrate the supply and the demand. The supply is the sum of the production of five the players.
Demand is price sensitive and shows a delayed reaction to price changes. The long run demand curve is shown in the Figure 4,
and has a constant price elasticity of -0,6. Note that there is an upper limit of 500 Col $/kWh for the price. The demand has an
average adjustment delay of 10 years. This means that if the price is changed, the demand will gradually adjust towards the long
run demand indicated by the demand curve in Figure 4. The adjustment process is illustrated in Figure 5, where you can see the
demand adjustment after a step increase in the price. After 10 years, approximately 63% of the long run adjustment has taken
place.
To summarize, the larger the total electricity production is, the lower the price will be. Respectively, the lower the total electricity
production is, the higher the price will be. There is no economic growth, which means that demand only changes due to price
changes. When the experiment starts, the total production is 3,64 Mill GWh, the price is 70 Col $/kWh, and your production is
0,73 Mill GWh.
Precio ($/kWh)
o o5 1 415 2 25 3 35 4 45 5
Demanda (Mil GWh)
Figure 4. Long nin demand curve for the experiment.
27
4,0- T :
Demand (GWh)
3,0- ong-run demand
Price (NOK/kWh)
0 1 8620 «3040s C800
Years
Figure 5. Dynamic reaction to a step increase in the electricity price.
Once each period you decide on your additions to your future electricity production. The length of each period is 5 years. Before
you make your decision you get information about the electricity price and your profits for the period are currently in. When the
next 5 year period starts it will be with the production you have decided in the current and in the last tree periods. Each year you
decide an additions (investments) to future production (capacity).These additions (investments) will last the entire lifetime of the
production capacity. The lifetime is four periods or 20 years. In all future periods your production will equal your production
capacity, capacity utilization cannot be reduced. (Also note that it takes one period (5 years) to bu8ild new capacity, thus new
capacity will not be available in the next period, rather the one after the next). Figure 7 explains the figure that is provided in the
experiment. It shows the decisions you have made during the previous 3 periods and the decision you are about to make in the
current one. When you have decided in the production for the period after the next period, your decision cannot be changed when
you enter that period. In the first period you see the historical decision made before you take over the company.
Decided production in the future periods
Production added three perigds ago
Mill GWh
pn added one period ago
Production added in the current period
00.
1 2 3 4
Future Periods
Figure 7. Decided future production.
PAY OFF
You will receive a payoff according to your performance. Y our performance is measured by your accumulative excess profits. If
you get zero excess profit your payment will be Col $ 15000. If you make more excess profits you get a higher payoff, and if you
make less excess profits you get less. Thus, it will always pay off to do your best.
In each period, you are also asked to forecast the price of the next period (for the period after the next period). You will earn an
extra payment depending on how precise forecasts you make. If you make a perfect forecast in each and every period you get Col
$ 6000.
RUNNING THE EXPERIMENT:
All players enter their decided productions and their price forecasts in the computer, write them down in the given sheet of
paper, and press “Accept Decisions’. When everyone has made their decisions, the window “Accept Decisions” appears
again, the game has advanced to the next period and all players make new decisions, and so on.
The time advances, and the players get the results for the next period. It is time to make decisions again and so forth.
After YY periods, the game is over. You write down your payoff in the sheet of paper and approach the leader of the
experiment to get your payment.
28
BE CAREFUL NOT TO PRESS “Accept Decisions” UNLESS YOU REALLY MEAN IT. After having pressed “Accept
Decisions” your decision cannot be changed
NOTE:
According to the purpose of the experiment it is required not to share any kind of information (verbal, written, gestures, etc.).
Please, respect these rules because they are important for the scientific value of the experiment.
Thank you for joining this experiment and do your best!!!
USER INTERFACE
Informacion del mercado Decisiones
Produccién (Mill GWh)
Produccién total (Mill GWh) :
(préximo perfodo)
Precio ($/kWh) Pronéstico de precio ($/kWh)
Informacién de la firma Pago
Disponible a inal del juego
Produccién de la Firma
(Mill GWh)
Desempeiio ($)
Pronéstico del Precio ($)
Excedentes de ganancias
(Miles Mill $)
Pago total ($)
Periodo Land T2
TlandT
Informacién del mercado Decisiones
piSAceeR BEAL CH GWT Produccién adicional (millGWh) [0.00 J
: J {en los préximos 4 periodos) [0%]
Precio ($/kWh) Pronéstico de precio ($/kWh)
if Pago
Informaclonide faitrma Disponible at juego
Produccién de la Firma Desempeiio ($) Lo 7
(mill GW)
Pronéstico del Precio ($) |
Excedentes de ganancias
ae Pago tal |
Perlodo [Lo]
Produccién decidida en futuros periodos
1
13
el
3
& os
5 L__
0 =|
——
0
1 2 3 4
Periodos futuros T3
29
Informacién del mercado
Produccién total (Mill GWh)
Precio ($/kWh)
Informacién de la firma
Produccién de la Firma
Decisiones
Produccién adicional (Mill GWh)
(en los préximos 4 periodos)
P ronéstico de precio ($/kWh)
(dentro de 2 periodos)
Pago
Disponible a final del juego
Desempetio ($)
(Mill Gwen)
Pronéstico del Precio ($)
a
Excedentes de ganancias
(wites mil s)
Pago total ($)
Produccién decidida en futuros perfodos
Periodo
1
21
3
Bo
2 ost
034
00
t 2 3 a 5
Periodos futuros T4
CODE OF THE BASE PROGRAM FOR T4 (EQUATION WRITTEN IN POWERSIM
CONSTRUCTOR 2.51).
dim —_—_Acum Difference = (Players)
init Acum_Differenc
flow Acum Difference = +dt*Difference
dim Bank account = (Players)
init Bank account = 0
flow Bank account = +dt*Net_profit
dim Cap_last_0 = (Players)
init Cap_last_0 = Initial Capacity/4
flow Cap last 0 =-dt*Rate_16
4athRate_15
dim Cap_last_
init Cap_last_
flow Cap last.
4athRate 14
dim Cap_last_
init Cap_last_
flow Cap last.
4at"Rate_12
dim Cap_last_
init Cap_last
flow Cap last. 7
-dt*Rate 12
init Deman_{ minus 1=DemandReferenceX 1
flow Deman_t minus 1 = +dt*Change_in_ demand
dim ondered_capacity = (Players)
init ordered_capacity = Initial Capacity/5
flow ordered capacity =-dt*Rate 13
+dt* Investment
aux Change in demand = (Consumption-Deman t minus 1)/Demand_Adjustment Time
dim Difference = (Players)
aux Differenc
dim Investment
BS(Expected_Price-Precio_retardado)/Precio_retardado
p=Players)
30
aux Investment =
SELECTDECISION(INDEX (p),Investment_Decisions, Simulated, Simulated, Simulated) HF(TIME=0,Initial_Capacity/4,0)
doc Investment = AND INDEX(p)=p
dim Players)
aux ‘evenues-Operational_Cost
dim Players)
aux ELAY PPL(Rate_13(i),1,Rate_13(i))
dim = (i=Players)
aux ELAY PPL (Investmentti), 1 Investment(i))
dim =Players)
aux ELAY PPL(Rate_12(i),1,Rate_12(i))
dim =Players)
aux Rate 15= DELAY PPL(Rate_ 14(i),1,Rate_14())
dim =Players)
aux ELAY PPL(Rate_ 15(i),1,Rate_15(i))
dim Auxiliary 100 = (i=Players, j=1..5)
aux ‘Auxiliary 100 =IFUNDEX( ,Cap_last_1(i)+Cap_last_2(i)+Cap_last_3(i)+ordered_capacity(i),
IF(INDEX (j)=2,Cap _last_2(i)+Cap_last_3(i)+ordered_capacity (i) Hnvestment(i),
IF(INDEX (j)=3,Cap_last_3(i) +ordered_capacity(i) +Investmentti),
IF(INDEX (j)=4,ordered_capacity (i) Hnvestmentti),
IF(INDEX (j)=5 Investmentt(i),0)))))
dim Capacity = (i=Players)
aux Capacity = Cap last 3(i)+Cap_last_2(i)+Cap_last_1(i)+Cap_last_O(i)
aux Constant_ RRSUM (Production)
MAX (ARRSUM (Production),2.5)-0.65*0
p=Players)
ELECTDECISION(INDEX (p),
Decided peta price Simulated Expected price Simulated Expected_price Simulated Expected_price)
aux =EXP(-years_per_period/Demand Adjustment. Time)
dim mk Players)
aux graph_payoff = GRAPH(Bank_account,-
1000,1000,{8100, 13000,15900,17200,18300,19200,19900,20300,21000,21600,22000"Min:8000;Max:22000;Z0om"'])
dim Operational_Cost = (Players)
aux Operational Cost = Production Mill_kWh*1000000*V arable O_and_M_costs/(1000000* 1000000)
dim Payoff = (Players)
aux Payoff = IF(TIME<39,0,1)*graph_payoff
dim Payoff Price Forecasting = (Players)
aux Payoff Price Forecasting = GRAPH(Acum Difference,0,10,{6000,2790,1130,0"Min:0;Max:6000;Zoom"])*IF(TIME<39,0,1)
aux Precio_retardado = DELAY PPL (Price, 2,Price)
aux Price = MIN(PriceReferenceY 1*( (Consumption-fi*Deman_t_minus 1) / ((1-fi)*DemandReferenceX1))_ {-
1/ElasticityReference),500)
dim Production = (i=Players)
aux Production = Capacity(i)
dim Production Mill. kWh = (Players)
aux Production Mill kWh =Production*1000000
dim Revenues = (Players)
aux Revenues = Production Mill. kWh*1000000*Price/(1000000*1000000)
dim i layers)
aux Simulated = IF(TIME=0,0,.15)
aux Total_Capacity = ARRSUM (Capacity)
dim Players)
aux ayoff+Payoff_ Price Forecasting
dim Waming = (i=Players)
aux Waning =IF(Auxiliary_100(i,2)>Upper_limit_additional_production, 1,0)
dim
const
const Demand Adjustment Time = 10
const DemandReferenceX 1 = 3.64
const —_ElasticityReference = 0.6
const Initial Capacity = 3.64/5
doc Initial_Capacity = (0.9*90000/5)/1000
dim Investment_Decisions = (Players)
const —_Investment_Decisions =
const PriceReferenceY 1 = 70
dim Simulated_Expected_price = (Players)
const Simulated Expected price = 0
const Upper limit_additional_production = 1.5
const Variable O and M costs =85
const _years_per_period =5
31
Appendix 2. Selection of parameter ksuch that there is equivalence across treatments.
The delayed adjustment process of demand implies that the demand should move from an initial condition
D,-0 to the long term DE" by following equation:
D,—Dei = KD Es" Dy) ()
which can be rewritten as,
1 k
= D+ Disilibriun 2
“Uk 14k @
where and D,*“"""" is the equilibrium demand for price P,. In continuous time, eq. (1) follows the
differential equation
aD (Dé _ Did)
Sac EL CZ
dt T
where t, and t is known as the average adjustment time and it was chosen equal to 10 years. The general
solution for this differential equation is:
D(t) =e * -D(0) +(1-¢%). pes a
The eq (4) is analogous to eq. (2). If we introduce the variable ¢ = ////+k), hence, from equation
-Y
parameter ) =e “*. In T2 the time step is 20 years, while in T3 ant T4 the time step is 5 years. To make
experimental results comparable across treatments, it is required to choose an appropriate such that a
change on demand in T2 made in only one step of 20 years is the same as the change on demand in T3 and
T4 made in four steps of 5 years each.
Let's call ¢ the parameter ¢ for treatment T2 and 4; the parameter $ for treatments T3 and T4. In T2, the
change in demand from period 7 to period 7+/ (or from time t to time r + 20 years) is given by eq. (2),
hence,
Drv1 = $20 Dr + (1 ~ dry) DEMME (5)
which should be equivalent to the change in demand in T3 and T4 from period T’ to period T’ +4 (or from
time t to time t + 20 years). Thus, from the same initial demand and the same change in price, Dry =
Dy44. For T3 and T4, the adjust on demand in the first period is
Drs = $s Dr + (1 ~ gy) Deion é
The adjust in the second period is
Drag = 5 Drss + (1 = os) DPsnirom 0
Driz = $s (bs Dr + (1 ~ $s) DEM ) + (T= gs) DEaniioriom es
Dpaz = os Dy * (1-62) Dm i
The adjust in the third period is
32
Drg= 6 Das? Od: reor
Drs = 5 (bs Dry + (1 ~ $5) DEMtOr™ ) + (= gps) DEmiioriom
Drg= éé Det(l- $) pimilibrium
Finally, the adjust after four periods is
Drva = 5 Drsa + (1 - $s) DEtworm
Drs = $5 (5 Doz + (1 ~ Gs) Deer ) + (1 ~ gy DEmiioriom
Dry = Gy Dr-+ (-~o¢) Dome
(lo)
(Wl)
(12)
(13)
(14)
(15)
Since it is required that D;.; = Dr-4, the equivalence for treatments impose that ¢; = gs», which implies
that 4,4 = (e7)'4 = &* = e*"". Thus, for treatment T2 we have ¢ = e” or k = 6.389; and for treatment T3
and T4 we have g = ¢”" ork = 0.649.
33
Appendix 3. Parameter estimation for the proposed heuristic for individuals.
We explore individual behaviour with the following linear investment function
x)= m4 P*', + m3 P, +m SC,, +m, C,+b+ & (16)
where m, (j=1, ... ,4) and b are parameters to be estimated, and « is iid random variable with zero mean
and finite variance. The index i represents individuals and the variables conserve the previous names.
Parameter estimation for the proposed heuristic for individuals corresponding to eq.(/6) for treatments T1 and T2.
The p-value of each coefficient is presented in parenthesis.
Mkt/Player my, (P*) ms (P) m (QO b r
TI
ql 0.002 (0.01) 0.002 (0.01) 0.47 (0.00) 0.75 (0.00) 0.55
1/2 0.015 (0.01) 0.016 (0.03) 0.73 (0.00) 0.66 (0.48) 0.48
1/3 -0.002 (0.19) 0.001 (0.64) 0.23 (0.17) 1.56 (0.00) 0.19
1/4 0.003 (0.03) 0.003 (0.03) 0.07 (0.66) 0.87 (0.00) 0.18
15 0.006 (0.00) 0.004 (0.06) 0.07 (0.65) 2.66 (0.00) 0.31
2/1 -0.014 (0.00) 0.005 (0.00) 0.09 (0.13) 2.84 (0.00) 0.67
2/2 0.000 (0.35) 0.000 (0.49) 0,00 (0.90) 2.92 (0.00) 0.04
2/3 0.008 (0.25) 0.001 (0.88) 0.59 (0.00) 0.42 (0.46) 0.59
2/4 -0.012 (0.17) 0.005 (0.38) 0.22 (0.12) 2.18 (0.01) 0.21
2/5 0.006 (0.72) -0.007 (0.48) 0.33 (0.06) 2,99 (0.10) 0.19
3/1 0.001 (0.53) 0.005 (0.00) -0.02 (0.82) 2.65 (0.00) 0.63
3/2 0.055 (0.00) 0.003 (0.03) 0.52 (0.00) 4.81 (0.00) 0.58
3/3 0.008 (0.44) 0.005 (0.63) 0.38 (0.06) 0.90 (0.24) 0.24
3/4 -0.007 (0.01) 0.000 (0.98) 0.31 (0.02) 2.33 (0.00) 0.67
3/5 0.002 (0.82) -0.011 (0.31) 0.23 (0.13) 4.47 (0.00) 0.58
Average -0.007 0.001 0.28 2.14
T2
yi 0.003 (0.69) 0.006 (0.14) 0.18 (0.09) 1.88 (0.00) 0.30
12 0.006 (0.08) 0.003 (0.24) -0.28 (0.03) 3.99 (0.00) 0.22
1/3 -0.014 (0.00) -0.011 (0.00) 0.21 (0.04) 5.10 (0.00) 0.69
1/4 0.003 (0.33) 0.003 (0.13) -0.01 (0.96) 0.88 (0.03) 0.07
15 -0.017 (0.04) 0.013 (0.10) 0.23 (0.25) 1.52 (0.10) 0.12
2/1 -0.012 (0.03) 0.002 (0.63) 0.15 (0.14) 3.99 (0.00) 0.33
2/2 0.014 (0.27) 0.011 (0.18) 0.10 (0.53) 1,95 (0.00) 0.05
2/3 0.008 (0.45) -0.005 (0.30) 0,06 (0.72) 2.25 (0.03) 0.11
2/4 0.034 (0.13) -0.018 (0.03) 0.33 (0.01) 2.31 (0.27) 0.35,
2/5 0.005 (0.52) 0.007 (0.12) 0.41 (0.00) 0.07 (0.91) 0.43
3/1 -0.035 (0.03) 0.019 (0.07) 0.46 (0.00) 2.33 (0.01) 0.44
3/2 0.001 (0.87) 0.013 (0.00) 0.11 (0.15) 3.68 (0.00) 0.59
3/3 0.007 (0.41) 0.008 (0.03) 0.40 (0.00) 0.27 (0.74) 0.64
3/4 0.016 (0.19) 0.022 (0.01) 0.29 (0.08) 2.29 (0.08) 0.42
3/5 0.006 (0.01) 0.004 (0.24) -0.22 (0.00) 2.62 (0.00) 0.56
Average -0.003 0.000 0.17 2.32
34
Parameter estimation for the proposed heuristic for individuals corresponding to eg.(/6) for treatment T3. The p-
value of each coefficient is presented in parenthesis.
Mkt/Player: m, (P*) ms (P) m© b ta
Yl 0.000 (0.29) 0.001 (0.00) 0.06 (0.42) 0.07 (0.36) 0.27
1/2 0.000 (0.46) 0.000 (0.47) -0.17 (0.23) 0.24 (0.01) 0.06
13 0.000 (1.00) 0.000 (0.87) -0.32 (0.02) 0.35 (0.00) 0.15
a 0.000 (0.18) 0.000 (0.16) 0.02 (0.77) 0.06 (0.32) 0.08
15 0.000 (0.78) 0.000 (0.00) 0.01 (0.92) 0.08 (0.04) 0.26
2/1 0.001 (0.26) 0.001 (0.11) 0.20 (0.09) 0.15 (0.08) 0.30
2/2 0.000 (0.78) 0.000 (0.90) 0.19 (0.00) 0.00 (0.96) 0.33
2/3 0.001 (0.21) 0.000 (0.84) 0.00 (0.96) 0.24 (0.00) 0.14
2/4 0.000 (0.74) 0.000 (0.73) -0.42 (0.02) 0.53 (0.00) 0.22
2/5 0.000 (0.73) 0.000 (0.86) -0.04 (0.66) 0.29 (0.01) 0.01
3/1 0.000 (0.66) 0.001 (0.01) 0.15 (0.01) 0.09 (0.10) 0.40
3/2 0.000 (0.99) 0.000 (0.96) 0.10 (0.37) 0.10 (0.40) 0.04
3/3 0.003 (0.01) 0.000 (0.22) -0.24 (0.01) 0.74 (0.00) 0.22
3/4 0.001 (0.76) 0.000 (0.91) 0.06 (0.60) 0.12 (0.47) 0.01
3/5 0.000 (0.81) 0.001 (0.18) 0.26 (0.00) 0.10 (0.32) 0.29
4/1 -0.001 (0.14) 0.001 (0.06) 0.02 (0.85) 0.10 (0.21) 0.09
Af -0.001 (0.17) 0.001 (0.01) -0.18 (0.06) 0.36 (0.00) 0.27
AI3 0.001 (0.24) 0.001 (0.12) 0.01 (0.90) 0.06 (0.55) 0.07
Ala 0.007 (0.00) 0.000 (0.26) -0.14 (0.08) 0.88 (0.00) 0.38
4s 0.000 (0.28) 0.000 (0.22) 0.29 (0.01) 0.00 (0.99) 0.20
5/1 0.000 (0.84) 0.000 (0.50) 0.15 (0.18) 0.48 (0.00) 0.08
5/2 0.004 (0.00) 0.000 (0.06) -0.02 (0.79) 0.51 (0.00) 0.44
5/3 0.000 (0.86) 0.000 (0.08) -0.04 (0.59) 0.09 (0.00) 0.21
5/4 -0.001 (0.67) 0.001 (0.38) 0.07 (0.61) 0.05 (0.75) 0.03
5/5 0.001 (0.18) 0.001 (0.39) 0.20 (0.00) 0.02 (0.53) 0.42
6/1 -0.002 (0.00) 0.001 (0.00) 0.11 (0.19) 0.07 (0.16) 0.29
6/2 0.000 (0.42) 0.001 (0.16) -0.07 (0.51) 0.13 (0.15) 0.12
6/3 -0.001 (0.03) 0.000 (0.05) 0.12 (0.26) 0.17 (0.11) 0.12
6/4 0.001 (0.18) 0.001 (0.20) -0.02 (0.85) 0.13 (0.07) 0.06
6/5 0.000 (0.91) 0.000 (0.95) -0.10 (0.29) 0.18 (0.03) 0.04
Average 0.001 0.000 0.015, 0.199
Parameter estimation for the proposed heuristic for individuals corresponding to eg.(/6) for treatment T4. The p-
value of each coefficient is presented in parenthesis.
Mkt/Player my (P*) m; (P) m, (SL) m (C) b io
Yi 0.000 (0.77) 0.000 (0.27) 0.22 (0.18) -0.06 (0.63) 0.13 (0.35) 0.16
12 0.000 (0.19) 0.000 (0.16) 0.12 (0.49) 0.13 (0.03) 0.02 (0.51) 0.30
1/3 0.000 (0.72) 0.000 (0.83) -0.25 (0.16) 0.06 (0.79) 0.29 (0.36) 0.09
V4 0,003 (0.44) 0.000 (0.76) -0.23 (0.18) -0.05 (0.90) 0.03 (0.94) 0.08
15 0.000 (0.77) 0.000 (0.70) 0.06 (0.72) -0.19 (0.12) 0.21 (0.04) 0.13
aft 0.001 (0.06) -0.001 (0.07) 0.05 (0.78) -0.14 (0.18) 0.41 (0.01) 0.14
2/2 0.000 (0.22) 0.000 (0.14) 0.63 (0.00) 0.03 (0.41) 0.00 (0.86) 0.60
2/3 -0.001 (0.20) 0.000 (0.44) -0.22 (0.21) -0.03 (0.79) 0.29 (0.01) 0.08
2/4 -0.001 (0.05) 0,001 (0.11) 0.35 (0.03) 0.07 (0.34) 0.08 (0.12) 0.27
2/5 0.000 (0.81) 0.000 (0.39) 0.18 (0.22) -0.10 (0.19) 0.12 (0.03) 0.28
3/l 0.005 (0.01) 0.000 (0.55) 0.19 (0.26) 0.05 (0.35) -0.23 (0.08) 0.32
3/2 0.000 (0.78) 0.000 (0.97) 0.00 (0.99) 0.00 (1.00) 0.07 (0.08) 0.02
3/3 0.000 (0.72) 0.000 (0.98) -0.17 (0.30) -0.32 (0.01) 0.46 (0.00) 0.35
3/4 0,000 (0.92) 0,000 (0.54) -0.36 (0.05) -0.09 (0.69) 0.21 (0.29) 0.13
3/5 0.000 (0.06) 0.000 (0.31) 0.14 (0.45) 0.10 (0.11) -0.04 (0.33) 0.40
4/1 0.002 (0.07) -0.001 (0.06) 0.19 (0.24) -0.04 (0.63) 0.03 (0.73) 0.17
42 -0.024 (0.26) -0.001 (0.05) 0.28 (0.06) 0.03 (0.64) 2.35 (0.20) 0.27
AI3 0.000 (0.81) 0.000 (0.31) 0.35 (0.01) 0.22 (0.00) 0.33 (0.00) 0.53
4a 0,001 (0.64) 0.000 (0.48) -0.08 (0.64) -0.10 (0.51) 0.21 (0.31) 0.12
4/5, 0.002 (0.28) 0.001 (0.29) -0.10 (0.56) 0.24 (0.05) 0.36 (0.01) 0.16
5/1 0.000 (0.74) 0.000 (0.48) 0.28 (0.11) 0.02 (0.85) 0.10 (0.28) 0.10
5/2 0.000 (0.90) 0.000 (0.59) 0.35 (0.03) 0.16 (0.00) -0,02 (0.56) 0.64
5/3 0.000 (0.58) 0.000 (0.99) -0.52 (0.00) -0.36 (0.03) 0.61 (0.00) 0.28
5/4 0,003 (0.00) 0.000 (0.60) 0.12 (0.31) 0.01 (0.90) 0.15 (0.25) 0.59
5/5 0.000 (0.94) 0.000 (0.95) 0.27 (0.12) 0.18 (0.25) 0.15 (0.39) 0.10
6/1 0.000 (0.86) -0.001 (0.04) 0.84 (0.00) -0.03 (0.01) 0.32 (0.00) 0.90
6/2 0.000 (0.81) -0.001 (0.01) 0.13 (0.39) -0.01 (0.60) 1.31 (0.00) 0.28
6/3 0.001 (0.06) -0.002 (0.00) 0.78 (0.00) 0.01 (0.75) 0.22 (0.06) 0.68
6/4 0,000 (0.70) -0.001 (0.12) 0.52 (0.00) 0.02 (0.01) 0.11 (0.36) 0.65
6/5 0,000 (0.53) 0.000 (0.77) 0.86 (0.00) 0.00 (0.98) 0.10 (0.45) 0.73
Average 0.000 0.000 0.148 0.039 0.269
35
