Drivers of the World Grain Price Crisis in the Short- and
Long-Run:
A Spatial-Temporal Rational Expectations Equilibrium Approach
Randall Romero-Aguilar
Mario J. Miranda
Seminar at Center for Development Research
University of Bonn
July 8-9, 2014
Outline
1
Introduction
2
The Model
The model equations
Solving the model
3
Results
Long-term results
Short-term results
4
Conclusions
Introduction
Introduction
We build a model to examine some proposed drivers of the 2007-2009 World
Food Price Crisis:
low grain stock levels;
trade restrictions by wheat exporters;
public storage by wheat importers; and
diversion of corn production to biofuels.
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Drivers of the World Grain Price Crisis
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Outline
1
Introduction
2
The Model
The model equations
Solving the model
3
Results
Long-term results
Short-term results
4
Conclusions
The Model
The model equations
The Model
Two commodities: wheat and corn
One fixed input: land
International trade
Storage
World markets
x
Corn
Exporters
1−λ
w
Corn
Corn
Importers
Romero-Aguilar, Miranda
x́
λ
ẃ
Wheat
ywm
m
Wheat
Exporters
wheat land
corn land
yẃḿ
Storage
Storage
Drivers of the World Grain Price Crisis
Wheat
Importers
ḿ
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The Model
The model equations
Supply, demand, production, consumption
Supply and demand:
Q̃i
+ Zi,−1 ≡
Ai
production
storage
availability
=
Ci
+ Zi +
Yi
consumpt.
storage
net exports
Production
Q̃i = qi,−1 · ˜i
acreage yield
Consumption demand
Ci = αi Pi
−βi
price
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The Model
The model equations
Supply, demand, production, consumption
Supply and demand:
Q̃i
+ Zi,−1 ≡
Ai
production
storage
availability
=
Ci
+ Zi +
Yi
consumpt.
storage
net exports
Production
Q̃i = qi,−1 · ˜i
acreage yield
Consumption demand
Ci = αi Pi
−βi
price
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Drivers of the World Grain Price Crisis
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The Model
The model equations
Supply, demand, production, consumption
Supply and demand:
Q̃i
+ Zi,−1 ≡
Ai
production
storage
availability
=
Ci
+ Zi +
Yi
consumpt.
storage
net exports
Production
Q̃i = qi,−1 · ˜i
acreage yield
Consumption demand
Ci = αi Pi
−βi
price
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Drivers of the World Grain Price Crisis
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The Model
The model equations
Supply, demand, production, consumption
Supply and demand:
Q̃i
+ Zi,−1 ≡
Ai
production
storage
availability
=
Ci
+ Zi +
Yi
consumpt.
storage
net exports
Production
Q̃i = qi,−1 · ˜i
acreage yield
Consumption demand
Ci = αi Pi
−βi
price
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Drivers of the World Grain Price Crisis
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The Model
The model equations
Supply, demand, production, consumption
Supply and demand:
Q̃i
+ Zi,−1 ≡
Ai
production
storage
availability
=
Ci
+ Zi +
Yi
consumpt.
storage
net exports
Production
Q̃i = qi,−1 · ˜i
acreage yield
Consumption demand
Ci = αi Pi
−βi
price
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The Model
The model equations
Trade and private storage
Trade:
0≤
yjk ≤ ȳjk
export j to k capacity
⊥


Pk − τjk − Pj



transport cost
unrestricted

min[Pk − τjk , P̄j ] − Pj



price ceiling
Private storage
0 ≤ Zi ≤ Z̄i
capacity
Romero-Aguilar, Miranda
⊥
δ E Pi0
− Pi − K
expected price
Drivers of the World Grain Price Crisis
storage cost
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The Model
The model equations
Trade and private storage
Trade:
0≤
yjk ≤ ȳjk
export j to k capacity
⊥


Pk − τjk − Pj



transport cost
unrestricted

min[Pk − τjk , P̄j ] − Pj



price ceiling
restricted
Private storage
0 ≤ Zi ≤ Z̄i
capacity
Romero-Aguilar, Miranda
⊥
δ E Pi0
− Pi − K
expected price
Drivers of the World Grain Price Crisis
storage cost
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The Model
The model equations
Trade and private storage
Trade:
0≤
yjk ≤ ȳjk
export j to k capacity
⊥


Pk − τjk − Pj



transport cost
unrestricted

min[Pk − τjk , P̄j ] − Pj



price ceiling
restricted
Private storage
0 ≤ Zi ≤ Z̄i
capacity
Romero-Aguilar, Miranda
⊥
δ E Pi0
− Pi − K
expected price
Drivers of the World Grain Price Crisis
storage cost
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The Model
The model equations
Public storage
Public storage
0 ≤ Zi ≤ Z̄i
⊥
P̄i −
interv. price
Pi
Zḿ
Z̄ḿ
alternative:
Zi = Z̄i
1 + exp [−s P̄i ]
1 + exp [−s(P̄i − Pi )]
0 ≤ Zḿ ≤ Z̄ḿ ⊥ P̄ḿ − Pḿ
Zḿ = Z̄ḿ
1+exp −sP̄ḿ
1+exp −s(P̄ḿ −Pḿ )
P̄ḿ
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Drivers of the World Grain Price Crisis
Pḿ
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The Model
The model equations
Public storage
Public storage
0 ≤ Zi ≤ Z̄i
⊥
P̄i −
interv. price
Pi
Zḿ
Z̄ḿ
alternative:
Zi = Z̄i
1 + exp [−s P̄i ]
1 + exp [−s(P̄i − Pi )]
0 ≤ Zḿ ≤ Z̄ḿ ⊥ P̄ḿ − Pḿ
Zḿ = Z̄ḿ
1+exp −sP̄ḿ
1+exp −s(P̄ḿ −Pḿ )
P̄ḿ
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Drivers of the World Grain Price Crisis
Pḿ
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The Model
The model equations
Acreage
Share of land cultivated with wheat
λmin ≤
≤ λmax
λ
E Pẃ0 − ϕ E Pw0
⊥
share wheat
wheat
corn
Acreage
qw = (1 − λ) L
Expected corn
production
Production possibilities frontier
land available
λmin
λmax
qẃ = λL
Expected wheat
production
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The Model
The model equations
Acreage
Share of land cultivated with wheat
λmin ≤
≤ λmax
λ
E Pẃ0 − ϕ E Pw0
⊥
share wheat
wheat
corn
Acreage
qw = (1 − λ) L
Expected corn
production
Production possibilities frontier
land available
λmin
λmax
qẃ = λL
Expected wheat
production
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The Model
Solving the model
Numerical solution strategy
Dynamic model, with state variable A.
Given Ai , model can be reduced to a mixed-complementarity problem with
unknowns P, Z, λ, y ; 17 or 18 variables.
P
E Pi0 is unknown ⇒ collocation methods: pi ≈ p̂i = h ch φh (A)
Inner loop iteration to solve MCP, using A0 and numerical integration to
evaluate
E Pi0
≈E
H
X
h=1
ch φh (A0 ) ≈
X
ωj
X
j
ch φh (Z + q0j )
h
Outer loop iteration to solve for collocation coeffs ch
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Drivers of the World Grain Price Crisis
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The Model
Solving the model
Numerical solution strategy
Dynamic model, with state variable A.
Given Ai , model can be reduced to a mixed-complementarity problem with
unknowns P, Z, λ, y ; 17 or 18 variables.
P
E Pi0 is unknown ⇒ collocation methods: pi ≈ p̂i = h ch φh (A)
Inner loop iteration to solve MCP, using A0 and numerical integration to
evaluate
E Pi0
≈E
H
X
h=1
ch φh (A0 ) ≈
X
ωj
X
j
ch φh (Z + q0j )
h
Outer loop iteration to solve for collocation coeffs ch
Romero-Aguilar, Miranda
Drivers of the World Grain Price Crisis
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The Model
Solving the model
Numerical solution strategy
Dynamic model, with state variable A.
Given Ai , model can be reduced to a mixed-complementarity problem with
unknowns P, Z, λ, y ; 17 or 18 variables.
P
E Pi0 is unknown ⇒ collocation methods: pi ≈ p̂i = h ch φh (A)
Inner loop iteration to solve MCP, using A0 and numerical integration to
evaluate
E Pi0
≈E
H
X
h=1
ch φh (A0 ) ≈
X
ωj
X
j
ch φh (Z + q0j )
h
Outer loop iteration to solve for collocation coeffs ch
Romero-Aguilar, Miranda
Drivers of the World Grain Price Crisis
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The Model
Solving the model
Numerical solution strategy
Dynamic model, with state variable A.
Given Ai , model can be reduced to a mixed-complementarity problem with
unknowns P, Z, λ, y ; 17 or 18 variables.
P
E Pi0 is unknown ⇒ collocation methods: pi ≈ p̂i = h ch φh (A)
Inner loop iteration to solve MCP, using A0 and numerical integration to
evaluate
E Pi0
≈E
H
X
h=1
ch φh (A0 ) ≈
X
ωj
X
j
ch φh (Z + q0j )
h
Outer loop iteration to solve for collocation coeffs ch
Romero-Aguilar, Miranda
Drivers of the World Grain Price Crisis
7 / 18
The Model
Solving the model
Numerical solution strategy
Dynamic model, with state variable A.
Given Ai , model can be reduced to a mixed-complementarity problem with
unknowns P, Z, λ, y ; 17 or 18 variables.
P
E Pi0 is unknown ⇒ collocation methods: pi ≈ p̂i = h ch φh (A)
Inner loop iteration to solve MCP, using A0 and numerical integration to
evaluate
E Pi0
≈E
H
X
h=1
ch φh (A0 ) ≈
X
ωj
X
j
ch φh (Z + q0j )
h
Outer loop iteration to solve for collocation coeffs ch
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Drivers of the World Grain Price Crisis
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The Model
Solving the model
Dealing with the “curse of dimensionality”
Collocation with Chebyshev polynomials, 9 nodes per dimension.
A has 6 dimensions ⇒ 96 = 531 441 nodes and basis functions if using
tensor product.
1
2
1
q
√
2+ 2
1 √2
2
Included
1
2
q
√
2− 2
Use Smolyak's method to
choose nodes and bases.
-1
q
√
2− 2
2
Drivers of the World Grain Price Crisis
1 √
2
2
+ √
2
2
1 q
2
−
1
2 √
2
−
1 q
2
2
− √
2
−
1 q
2
2
+ √
2
Romero-Aguilar, Miranda
-1
− √
2
√
2
−1
2
q
√
−1 2 + 2
2
1 q
−1
2
1
2
Result: only 1409 nodes
and 389 polynomials.
Not included
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The Model
Solving the model
Data sources and regions
Most parameters calibrated with historical data from PSD database (USDA).
PSD region
North America
Former Soviet Union
Oceania
South America
East Asia
Southeast Asia
Middle East
North Africa
Sub-Saharan Africa
European Union
Romero-Aguilar, Miranda
World
Corn
Exporter
Importer
X
World
Wheat
Exporter
Importer
X
X
X
X
X
X
X
X
X
X
Drivers of the World Grain Price Crisis
X
X
X
X
X
X
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Outline
1
Introduction
2
The Model
The model equations
Solving the model
3
Results
Long-term results
Short-term results
4
Conclusions
Results
The Policy Scenarios
We consider these scenarios
0: baseline
1: wheat exporters set price ceiling at baseline average
2: wheat importers set public storage, price around baseline average
3: wheat exporters and importers apply policies simultaneously
4: ethanol production increases corn demand by 20%
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Drivers of the World Grain Price Crisis
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Results
Long-term results
Long-term prices: mean and standard deviation
Scenario
World
Corn
Exporter
Importer
World
Wheat
Exporter
Importer
Mean
0: Baseline
1: Price ceiling
2: Public storage
3: Ceiling + storage
4: High demand
100.00
101.68
101.63
103.22
118.18
100.00
101.68
101.63
103.22
118.18
108.91
110.50
110.41
111.87
126.22
100.00
102.45
98.28
99.17
115.19
100.05
93.80
98.34
94.69
115.23
112.22
114.66
110.51
111.43
127.41
Normalized prices: World baseline mean=100
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Results
Long-term results
Long-term prices: mean and standard deviation
Scenario
World
Corn
Exporter
Importer
World
Wheat
Exporter
Importer
Mean
0: Baseline
1: Price ceiling
2: Public storage
3: Ceiling + storage
4: High demand
100.00
101.68
101.63
103.22
118.18
100.00
101.68
101.63
103.22
118.18
108.91
110.50
110.41
111.87
126.22
100.00
102.45
98.28
99.17
115.19
100.05
93.80
98.34
94.69
115.23
112.22
114.66
110.51
111.43
127.41
Standard Deviation
0: Baseline
1: Price ceiling
2: Public storage
3: Ceiling + storage
4: High demand
14.72
16.07
17.23
19.26
21.31
14.72
16.07
17.23
19.26
21.31
13.98
14.93
16.11
17.50
16.88
18.02
24.54
11.45
14.64
18.09
18.08
6.92
11.54
4.73
18.13
18.02
24.54
11.44
14.53
18.09
Normalized prices: World baseline mean=100
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Drivers of the World Grain Price Crisis
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Results
Long-term results
Long-term prices: mean and standard deviation
Scenario
World
Corn
Exporter
Importer
World
Wheat
Exporter
Importer
Mean
0: Baseline
1: Price ceiling
2: Public storage
3: Ceiling + storage
4: High demand
100.00
101.68
101.63
103.22
118.18
100.00
101.68
101.63
103.22
118.18
108.91
110.50
110.41
111.87
126.22
100.00
102.45
98.28
99.17
115.19
100.05
93.80
98.34
94.69
115.23
112.22
114.66
110.51
111.43
127.41
Standard Deviation
0: Baseline
1: Price ceiling
2: Public storage
3: Ceiling + storage
4: High demand
14.72
16.07
17.23
19.26
21.31
14.72
16.07
17.23
19.26
21.31
13.98
14.93
16.11
17.50
16.88
18.02
24.54
11.45
14.64
18.09
18.08
6.92
11.54
4.73
18.13
18.02
24.54
11.44
14.53
18.09
Normalized prices: World baseline mean=100
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Results
Long-term results
Long-term World prices: conditional on initial stock
World Price
(baseline average = 100)
Corn
Wheat
200
100
5
15
25
35
45
55
65
75
85
5
15
25
35
45
55
Global Initial Storage
(units of grain)
Baseline scenario
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Drivers of the World Grain Price Crisis
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Results
Long-term results
Probability of crisis: conditional on initial stock
Corn
Wheat
Probality of Price > 150
(percent)
12.5
10.0
7.5
5.0
2.5
0.0
0
25
50
75
100
0
25
50
75
100
Global Initial Storage
(units of grain)
0: Baseline
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1: Price ceiling
2: Public storage
Drivers of the World Grain Price Crisis
3: Ceiling + storage
4: High demand
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Results
Short-term results
Short-term prices: Impulse response function
We next consider the short-term adjustment to 3 different shocks
1
change of policy regime;
2
change of regime while 20% drop in Exporter wheat production; and
3
change of regime, production shock, when initial wheat stocks are low.
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Results
Short-term results
1: Regimen Change
2: [1]+Low Yields
3: [2]+Low Stocks
90
Corn
60
30
0
90
Wheat
Deviation with respect to baseline (percent)
Short-term adjustment
60
30
0
0
2
4
6 0
2
4
6 0
2
4
6
Periods after shock
0: Baseline
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1: Price ceiling
2: Public storage
3: Ceiling + storage
Drivers of the World Grain Price Crisis
4: High demand
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Results
Short-term results
1: Regimen Change
2: [1]+Low Yields
3: [2]+Low Stocks
90
Corn
60
30
0
90
Wheat
Deviation with respect to baseline (percent)
Short-term adjustment
60
30
0
0
2
4
6 0
2
4
6 0
2
4
6
Periods after shock
0: Baseline
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1: Price ceiling
2: Public storage
3: Ceiling + storage
Drivers of the World Grain Price Crisis
4: High demand
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Results
Short-term results
1: Regimen Change
2: [1]+Low Yields
3: [2]+Low Stocks
90
Corn
60
30
0
90
Wheat
Deviation with respect to baseline (percent)
Short-term adjustment
60
30
0
0
2
4
6 0
2
4
6 0
2
4
6
Periods after shock
0: Baseline
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1: Price ceiling
2: Public storage
3: Ceiling + storage
Drivers of the World Grain Price Crisis
4: High demand
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Outline
1
Introduction
2
The Model
The model equations
Solving the model
3
Results
Long-term results
Short-term results
4
Conclusions
Conclusions
Conclusions: Long-term prices
Ethanol mandate:
only policy with large effect on long-term price (both grains)
greatly increases price volatility of both grains, in all regions
Wheat Exporter price ceiling increases wheat price volatility in other regions
Public storage in Wheat Importer, despite displacing private storage,
reduces wheat price volatility in all regions
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Conclusions
Conclusions: Short-term prices
By itself, introducing price ceiling or public storage have small impact in
short-term prices
Initial grain storage is a key determinant of likelihood of crisis
An export price ceiling can worsen a crisis originated in production shock
& low stocks
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Drivers of the World Grain Price Crisis
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Conclusions
Some limitations of the model = Opportunities to improve
No disincentive to farmers from price ceiling
Stationary model: no productivity growth, no population growth
No “panic” purchases from importers
Ethanol shock as one-time permanent demand increase on corn demand
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