The pork cycle revisited with ABM
- applied to a case of Chinese pig farmers
Sjoukje A. OSINGA
Mark R. KRAMER
Gert Jan HOFSTEDE
Adrie J.M. BEULENS
Wageningen University
Logistics, Decision and Information Sciences
sjoukje.osinga@wur.nl
Pork cycle: it’s still there – China example
Increased corn prices have likely
exaggerated the shifts in supply associated
with the natural market cycle for pork. Pork
prices dropped sharply in the first half of
2006 while corn prices remained high.
Consequently, hog profitability plummeted
and many farmers reduced numbers of
hogs being reared. This led to a marked
reduction in the supply of 2007, despite
the fact that it only takes 4-6 months for
commercially produced hogs to reach
market weight. Figure 6 illustrates the
cyclical nature for both pork and poultry
over a six-year period as well as the general
upward trend for both prices.
To smoothen:
government
interferes;
buy / sell
surpluses
(indicator: hog /
grain price ratio)
Source: China National Development
and Reform Commission, Price
Information Center, chinaprice.gov.cn
Sjoukje Osinga - AE2011 - 2
Two models of the pork cycle

Basic model without
individuals (averages)

Model with individual
behaviour
Sjoukje Osinga - AE2011 - 3
From literature:
Cobweb model (1)
Basic demand and supply system (𝑄𝑑 =𝑄𝑠 ):
𝑄𝐷 = 𝐷0 − ℎ𝐷 ∗ 𝑃
𝑄𝑆 = 𝑆0 + ℎ𝑆 ∗ 𝑃
𝑃
𝑠𝑢𝑝𝑝𝑙𝑦
ℎ𝐷
𝑃2
ℎ𝑆 < ℎ𝐷
divergent
cobweb
𝑃1
ℎ𝑆
𝑑𝑒𝑚𝑎𝑛𝑑
𝑄1
𝑄2
𝑄
Sjoukje Osinga - AE2011 - 4
From literature:
Cobweb model (2)
𝑃
Basic demand and supply system (𝑄𝑑 =𝑄𝑠 ):
𝑄𝐷 = 𝐷0 − ℎ𝐷 ∗ 𝑃
𝑄𝑆 = 𝑆0 + ℎ𝑆 ∗ 𝑃
𝑠𝑢𝑝𝑝𝑙𝑦
ℎ𝐷
ℎ𝑠 > ℎ𝐷
convergent
cobweb
ℎ𝑠 = ℎ𝐷
stable
ℎ𝑆
𝑑𝑒𝑚𝑎𝑛𝑑
𝑄
Sjoukje Osinga - AE2011 - 5
Typical for over- / under supply problem:

Problem arises due to production delay


Pigs need 6 months to mature
Inaccurate price expectations


Naive expectations:
assume price will be same as current price
Adaptive / rational expectiations:
estimate price based on available information
Sjoukje Osinga - AE2011 - 6
Why model this by means of ABM?
1.
Pork cycle “still happens”:

2.
Cyclical nature of over/under supply is emergent

3.
Farmers demonstrate bounded rationality
It’s the result of many individual farmers’ decisions
Revisiting some assumptions of classical model

How valid / useful are they in an AMB?
Sjoukje Osinga - AE2011 - 7
Research questions
1.
2.
3.
Grow it to show it: can we generate “the pork
cycle” with an individual-based ABM?
Can we dampen the pork cycle through improved
information provision?
What can we learn regarding model assumptions?
Sjoukje Osinga - AE2011 - 8
Agent-based information management model




stock
pig age
info-items
estimated-price
α𝑖 =
𝑖𝑛𝑓𝑜−𝑖𝑡𝑒𝑚𝑠𝑖
𝑖 𝑖𝑛𝑓𝑜−𝑖𝑡𝑒𝑚𝑠
𝐸𝑃𝑖 = α𝑖 ∗ 𝑃𝑒𝑞 + 1 − α𝑖 ∗ 𝑃𝑡
depends on the
proportional accuracy α
of equilibrium price 𝑃𝑒𝑞
Sjoukje Osinga - AE2011 - 9

Research models
𝐸𝑃 = α ∗ 𝑃𝑒𝑞 + 1 − α ∗ 𝑃𝑡
Test 3 models (actually 1 model with 3 values for α ):



current-price-model (α = 0): 𝐸𝑃 = 𝑃𝑡
perfect-price-model (α = 1): 𝐸𝑃 = 𝑃𝑒𝑞
estimated-price-model (0 < α < 1): 𝐸𝑃 = α ∗ 𝑃𝑒𝑞 + 1 − α ∗ 𝑃𝑡
Sjoukje Osinga - AE2011 - 10
Simulation process
α𝑖
𝐸𝑃
𝑃𝑡
?
𝑆𝑡
sell
mature
pigs
(inrestock:
batches):
theon
actual
supply
𝑆𝑡 𝑃𝑡
Farmers
decide
whether
to
calculate
estimated
price based
info-items
and
Current market
price
is calculated
actual
supply:
𝑆
−𝑆𝑡1 − α ∗ 𝑃
0+
𝐸𝑃
= α𝑃∗𝑡 𝑃
𝑅𝑒𝑠𝑡𝑜𝑐𝑘
<
=𝑒𝑞𝐷𝑟𝑎𝑛𝑑𝑜𝑚
𝑡
𝑚𝑎𝑥𝑆
ℎ
𝐷
𝑆 : total supply farmers expect using their estimated price
Actual supply changes
at every time step, influencing the
𝑚𝑎𝑥𝑆 : maximum supply farmers could possibly restock
price, influencing the
decision to restock, etc.
Sjoukje Osinga - AE2011 - 11
Assumptions to this model:


Equal slopes ℎ𝐷 = ℎ𝑆 (stable model)
Farmers (fully) restock or not: discrete choice


This is what happens in reality
Farmers know the total available capacity

But they do not know individual decisions of other farmers
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Results: current price model


Current price: naive expectations
Result: periodical pattern, pork cycle
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Results: perfect price model



Perfect price: equilibrium price
Only the decision whether to restock was randomized
Result: random behaviour ?
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Results: estimated price model



Using parameter α for information accuracy (many α‘s)
This figure: α = 0.5 (varying α is consistent with expectation)
Result... periodicity or random behaviour ?
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Determine periodicity –Fourier transformation

Fourier graph shows clearly periodical frequencies
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Perfect price model results: periodical?

Fourier graph shows that there is no periodicity
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Results: estimated price model

Fourier graph shows periodicity left in frequencies
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Conclusions
1.
Grow it to show it: can we generate the pork cycle
with our individual-based ABM?

2.
Can we dampen the pork cycle through improved
information provision?

3.
Answer: yes, we can (when farmers have naive expectations).
Answer: yes, more information leads to less periodicity
What can we learn regarding model assumptions?

See next slide
Sjoukje Osinga - AE2011 - 19
Conclusions (continued) / discussion

Mapping of economic supply-demand system to an
ABM is not straightforward
The theory works with total supply quantities
 In practice, farmers will restock or find alternative income
→
40% restock (i.e. all stables 40% full)
≠
40% of the farmers (fully) restock their stables
!

Sjoukje Osinga - AE2011 - 20
Conclusions (continued) / discussion

Transition point: only periodicity when overcapacity



When farmers produce less than demand
→
problem does not appear
no periodicity
In conventional approach, 2 models:
model a for overcapacity,
model b for undercapacity
in an ABM:
the same model shows behaviour a or b
(emergent)
Sjoukje Osinga - AE2011 - 21
Conclusions (continued) / discussion

Nr of farmers involved in restocking may be limited


(depends on ratio max farmers’ supply / total demand)
Socio-economic consequences are not visible in a
conventional model

Majority of farmers may be out of business
→ not an issue in models without individual farmers
Sjoukje Osinga - AE2011 - 22
Future improvements

Experiment with alternative information diffusion
processes, or: ‘whom does it come from’



Network structures → information exchange
Nature of info-items
Include interaction mechanisms between farmers


Peer influence / imitative behaviour
(e.g. restock when your neighbour does)
Implicit interaction is already present because it is
assumed that farmers know the maximum possible supply
Sjoukje Osinga - AE2011 - 23
Future improvements (continued)

Include more heterogeneity


Personality and cultural population attributes
Include external shocks


Model government intervention based on grain price
Fall/rise of grain price → costs of pig raising change
Sjoukje Osinga - AE2011 - 24
Thank you
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