Are storers rational? An experimental approach to testing the
competitive storage model.
Simone Pfuderer1
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School of Social Sciences, University of Trento, via Verdi 26, 38122 Trento, Italy
(phone: +39 0461 282185, fax: +39 0461 282222, email: [email protected] )
Proposal for a discussion paper
ABSTRACT
The competitive storage model has been the main workhorse of the analysis of the role of storage in
commodity price formation since Gustafson proposed his model in 1958. The main approach to testing
the competitive storage model has been the comparison of the characteristics of the predicted prices
series with actual commodity price series. This paper introduces a new approach to testing the
competitive storage model. A relatively simple model is taken to the experimental laboratory.
Participants in the experiment are asked make storage decision within a competitive storage model
framework. Their behaviour and the resulting price series are compared to the model assumptions and
predictions. The experiment pilot experiment will be run at the University of Trento in January 2014.
1. Introduction
Low stocks are one of the factors often cited as contributing factors to the 2007/08 and
2010/11 grain price peaks. Stocks-to-use ratios were low for a number of agricultural
commodities around the time of the 2007/08 price rises (European Commission, 2008;
OECD, 2008; Wiggins and Keats, 2010). Thirtle et al. (2009, p. 1) even suggested that “if a
single factor is to be identified as the cause of the recent price spikes, it has to be low stocks.”
The importance of stock-holding in price formation especially for agricultural
commodities has long been acknowledged. Models analysing the link between intertemporal
price formation and storage go back to at least the 1930s and 1940s. Working’s seminal work
on the role of storage for futures markets and intertemporal price formation is an important
example of these earlier studies (e.g. Working, 1948, 1949).
Gustafson (1958) introduced the stochastic competitive storage model by adding
uncertainty to the model of storage and price formation. In his model, harvests are subject to
yield shocks. The outcome of the shock is not known at the time production decisions are
made. However, the distribution of the harvest shocks is known to market participants.
Gustafson’s optimal storage model is basically a rational expectations model and was
published three years before Muth (1961) introduced the concept of rational expectations.
Since then, the competitive storage model has been the main workhorse of the analysis of the
role of storage in commodity price formation.
The main approach to testing the competitive storage model has been the comparison
of the characteristics of the predicted prices series with actual commodity price series (Deaton
and Laroque 1992, 1996; Cafiero et al., 2011, Miao et al., 2011, Arseneau and Leduc, 2013).
This paper introduces a new approach to testing the competitive storage model. A
relatively simple model is taken to the experimental laboratory. Participants in the experiment
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are asked make storage decision within a competitive storage model framework. Their
behaviour and the resulting price series are compared to the model assumptions and
predictions.
2. The competitive storage model
The commodity in the model is an annual crop that is storable. The model can be formulated
with one state variable, one control variable and on arbitrage equation.
In every period t, storers hold a pre-determined level of the commodity in storage,
. The quantity of the commodity available in period t, , is the state variable. It is the
quantity in storage at the beginning of t,
, plus production in period t. Production is an
exogenous random variable . Availability in period t, , can be used for consumption and
storage. The amount used for consumption, is sold to consumers at the price that clears the
market,
. The difference between availability, , and consumption, , is the
amount stored , the control variable in the model. In the next period t+1, pre-determined
storage at the beginning is which together with exogenous production,
, gives the total
amount available in period t+1,
. The transition equation of the dynamic model therefore
is:
Availability in t+1,
variable, .
depends on the exogenous variable
and the endogenous
Storers’ objective is to maximise their expected profit which leads to the storage arbitrage
equation.
[
]
] is the expected price for period t+1 in period t,
Where δ is discount rate, [
is the
price in period t, is the unit storage cost and
is expected profit. As noted before, the
amount of the commodity stored from period t to period t+1, is the control variable that the
agents in the model, the storers, adjust to maximise their profits. In a competitive market,
storers will adjust the storage level until the expected profits are zero. The arbitrage equation
can be written as a function of the state variable and the control variable .
[
]
As a whole, the economy cannot borrow production from future periods. Therefore,
storage cannot be negative. The non-negativity constraint limits arbitrage when storage is zero
and in these situations expected profits are negative.
[
]
When profits are positive, that is when the discounted expected price in period t for
period t+1 exceeds the current price minus storage costs, storers will store another unit which
will lower availability and increase the price in period t and increase availability and decrease
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the price in period t+1. Storers will continue to increase storage until expected profit is zero.
When profits are negative, that is when the discounted expected price in period t for period
t+1 is lower than the current price minus storage costs, storers will reduce storage. Reducing
storage increases availability and reduces the price in period t and at the same time lowers
availability and increases the price in period t+1. When stocks are zero, arbitrage is limited
and expected profit from storage is negative.
In a rational expectations model, agents’ expectations for variables in the next period
have to be consistent with the resultant distribution of these variables given the structure of
the model, the parameters in the model and the expectations. In the present model the
expectations are with respect to the price in the next period. In the simple version of the
model, storers are the only agents. They have to make a decision on how much of the
commodity to store from one period to the next.
3. The experiment
The experiment will be run at the experimental laboratory of the University of Trento. The
pilot is planned for January 2014 with the main experiments planned for February/March
2014.
All participants are storers. Participants will be randomly assigned to groups of eight
participants and will compete with the other participants in the group in the market for
storage. Production is subject to a shock but otherwise constant (there are no producers who
make production decisions). Consumers are implicit in a market clearing demand function
which is known to storers. Storage at the start of the period is known, the current production
becomes known at the beginning of the period and the storers will have to make a storage
decision.
To keep the experiment as simple as possible, each storer has a capacity of storage of
one unit and storage has to be in full units leading to a maximum storage capacity at the
market of eight. In each period the participants will be either a potential buyer (those
participants that do not have any storage at beginning of the period) or a potential seller (those
participants that hold one unit of storage at the beginning of the period). In each period, after
the level of production becomes known, potential buyers will be asked to place buy offers or
and potential sellers sell offers.
The market clearing mechanism consists of a pre-auction where buy and sell orders
from storers are matched. The main auction brings together the storeres’ buy and sell orders
and the demand from consumers.
The demand function in the experiment will be linear. Most studies using the
competitive storage model use a constant elasticity demand function. Here, however, a linear
function is chosen because the main aspects of the linear function will be easier to
communicate to the participants in the experiment. Gustafson (1958) used a constant elasticity
demand function (p. 23f) with price elasticity of demand of -0.5. However, he also carried out
sensitivity analysis using a linear demand function where the price elasticity of demand at the
"normal yield" is -0.5. A similar function to the linear demand function in Gustafson (1958)
will be used the the experiment. The proposed market clearing demand function in the
experiment is:
where pt is the market clearing price.
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Average production in the experiment will be 60 resulting in a price at average
production of 1.5. I propose a three point production distribution to facilitate the
communication of the stochastic distribution to the participants. Production can take three
possible outcomes, 35, 60 and 70 with probabilities of 0.2, 0.3 and 0.5, respectively.
The tables below show resulting optimal storage and price based on 2000 simulated series of
20 periods.
Table 1: Summary statistics for storage and price based on 2000 simulated series of 20
periods
Mean
storage
3.2347
% of storage at
% of storage at
maximum storage minimum storage
(8 units)
(zero units stored)
12.63%
37.58%
Mean
market
price
1.5056
Standard
deviation of the
market price
0.5461
4. Hypotheses tested
With regards to the behavioural assumptions of storers, two main hypotheses are tested.
Firstly, the competitive storage model assumes that storage decisions are only dependent on
the state variable which is availability in that period and that storage decisions are not
dependent on history. Secondly, in the model rational storers base their storage decision on
availability i.e. on the sum of storage at the beginning of the period and production in that
period. One unit in storage has exactly the same effect on the storage decision as one unit of
new production. This assumption will also be tested.
Given the production shocks, the competitive storage model predicts a price series.
The price series from the experiment will be compared to the predicted price series.
5. Results and Discussion
To be completed after the pilot/experiment.
The results will be discussed in relation to the hypotheses tested and the implications the
results for the empirical relevance of the competitive storage model for agricultural
commodity markets.
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