The Dynamics of the World Cocoa Price

Report
The Dynamics of the World Cocoa Market
Christopher L. Gilbert
(University of Trento, Italy)
[email protected]
Presentation prepared for the First Conference on the
Economics and Politics of Chocolate, University of Leuven,
Belgium, 16-18 September 2012.
Helmut Weymar and Commodities Corporation
“Most of the empirical literature on
commodity prices attempts to
explain price movements in terms of
variations of various supply and
demand variables, without any
explicit consideration of the general
theory of commodity prices”.
F. Helmut Weymar (1968), The
Dynamics of the World Cocoa Market.
Weymar said his book should be “required reading for anyone who plans to
make a killing or chooses to make his living by trading in the cocoa market”.
Weymar did make money trading cocoa, first for Nabisco and then for
Commodities Corporation, which he founded in 1969 with Paul Cootner and
Paul Samuelson. Commodities Corporation was one of the first hedge funds.
Weymar’s model
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Weymar’s model (monthly data, 1953-63) has the following structure:
The short term dynamics of the cocoa price result from shocks to the
cocoa crop – in particular, occasional crop failures.
Cocoa consumption (“grindings”) is price elastic and adapts to crop
shocks.
Storage smoothes the effects of crop shocks on prices and grindings.
Long term price expectations are constant and unaffected by shocks. (He
modified this to allow price expectations to be affected by recent prices).
A crop shortfall will therefore lead to
an immediate rise in the cocoa price,
an immediate fall in grindings,
destocking
a steady rise in stocks and fall in price as the system returns to equilibrium
at the original price level.
Summary conclusions
1.
2.
3.
4.
Weymar’s estimate of the price elasticity of demand was -0.4.
My estimate is slightly lower at -0.3.
Weymar found that the price impact of a crop shortfall would persist for
around nine years.
My model confirms this finding – production shocks have highly persistent
impacts.
Weymar’s model assumed that price variability in cocoa originates on the
supply side.
My analysis confirms that crop shocks are much larger than demand side
shocks. However, the system amplifies demand shocks more than crop shocks
so the price impact of demand shocks is comparable in size and persistence to
that of crop size shocks.
With only 11 years of monthly data, Weymar was unable to estimate an
income elasticity of demand.
It is difficult to separate a pure income effect from a general “taste-related”
tendency for cocoa consumption to rise over time. I attribute only around one
half of the trend growth in consumption to rising incomes.
Data
I have 66 years annual crop year
data from 1946-47 to 2001-12.
Source: ICCO (from 1960), IMF
(pre 1960).
Price levels and volatility both
declined after 1980.
4500
Production, consumption and
stock data are available from the
ICCO (post 1960) and FAO (from
1945).
The crop size standard deviation
(10.2%) is twice that of grindings
(5.1%) .
(000 tons)
4000
3500
Crop
3000
Grindings
2500
2000
1500
1000
500
0
Crop years
My model
• I estimate a four equation structural model of production,
grindings (consumption), stocks and price over the 62 crop
years 1950-51 to 200112.
• I compare the results with those from four equation VAR and
SVAR models using the same variables and estimated over the
same sample.
• I am interested in the Impulse Response Functions (IRFs) from
shocking crop size, grindings and world GDP growth.
• I extend the structural model to consider possible interactions
with the world coffee market.
Cocoa grindings
• Both (log) grindings and (log) crop size are non-stationary.
• I use updated Maddison’s data to construct a series for world GDP
(calendar year basis) for all those (41) countries for which Maddison gave
a continuous GDP series from 1946.
• Grindings, GDP and (real) price (all in logs) are cointegrated with or
without a time trend.
• The cointegrating vector implies an income elasticity of 0.84 if the time
trend is excluded and 0.48 if it is included.
• The AIC for the implied error correction equations prefers the model
which includes the time trend.
• The implied long run income elasticity is 0.41, the price elasticity is 0.29
and there is a 1.2% autonomous annual growth in grindings.
• The grindings response to the cocoa price is concentrated in the crop year
following a price change with a smaller contemporaneous element.
Cocoa production
Cocoa production rises at the same
trend rate as grindings.
Once planted, a tree produces
beans after three years and
remains productive for around 40
years. Presumably, production
depends on the stocks of cocoa
trees. However, there are no data
on the tree stock. I am therefore
unable to estimate an investment
relationship.
There is evidence of a rise (fall) in production three years after a rise (fall)
in the cocoa price.
Storage
Weymar analyzed storage in terms
of a Working-style “supply of
storage” model. Supply of storage
models posit a rising supply curve
for storage and were developed in
relation to grains markets in which
elevator capacity is limited.
Stockholders may be risk averse.
Modern storage theory, following
Williams and Wright (1991) and
Deaton and Laroque (1992), takes
the supply of storage to be
infinitely elastic and stockholders
to be risk-neutral (since hedged).
This theory focuses on the
consequences of stockout.
The cocoa stock-consumption ratio has
never fallen beneath two months over
the sample considered so stockout, in a
simple sense, has not been a problem.
Deaton and Laroque
• Deaton and Laroque model both storage and price as functions of a single
state variable, availability at which is the sum of the current harvest ht and
the carryover st-1 from the previous crop year. Hence the price pt = f(at)
and the carryover is st = g(at) .
• These two functions are nonlinear and depend on the crop distribution,
the functional form of the demand curve, the price elasticity of demand,
the interest rate and storage costs.
• In all cases, the storage function implies zero storage for availability less
than a critical value a*, generally slightly above the normal harvest, and
then is close to linear in a-a* for higher values of availability, so
g(at)  k(ata*)
• Market clearing gives consumption c through st + ct = ht + st-1 = at. This
gives the price as pt = f(at) = P(ct) = P(at - g(at)) where P(.) is the inverse
demand function.
The storage model applied to cocoa
a)
b)
c)
d)
e)
The Deaton-Laroque storage assumptions fit cocoa quite well:
Harvests are subject to large shocks while grindings are smooth;
The current price response to imbalance is on the demand side.
Two simple modifications are required
We need to regard 2 months as corresponding to stockout; and
We need to make production and consumption stationary by deflating
them by their (common) deterministic trend.
One major modification is required to the model :
Deaton and Laroque supposed consumption depends just on the current
price. Cocoa grindings are indeed sensitive to the price in the current
crop year, but also to that in the previous year. This may reflect
purchasing and planning behaviour of chocolate manufacturers. The
result is that the lagged price pt-1 is a second state variable.
The modified storage model
• The price and carryover functions now become price
pt = f(at,pt-1) and st = g(at,pt-1) .
• These functions are difficult to compute. I approximate them
by allowing k and a* in the approximation g(at)  k(ata*) to
depend on pt-1. In practice, a* does not appear dependent on
pt-1.
• The dependence of current grindings on the lagged price
increases the incentive to carry stocks. Suppose the current
harvest is abundant giving high availability and pushing the
price down. The low current price will stimulate increased
grindings next year increasing the incentive to carry inventory
forward. Conversely with a harvest shortfall.
Price implications
• As in the Deaton-Laroque model, the expected price rises at the rate of
interest so long as positive inventory is held with the actual price
depending on availability. Inventories smooth availability over time and
hence prices.
• Stockouts induce negative price autocorrelation. A harvest shortfall
resulting in a high price this year will depress grindings next year. This
incentivates consumption of the entire available stock. If stockout occurs,
this year’s high price will be followed by a low price next year.
• I do not find any evidence of nonlinearity in the price-availability
relationship. This may be because cocoa stocks have never gone close to
zero in the post-WW2 period. I therefore model the price as depending
on its own history (two lags are necessary) and availability.
• There is no evidence that the coefficient on lagged carryover differs from
that on the current harvest.
Price Impulse Response Functions
12.5%
A one s.d. (8.3%) crop shortfall
results in an immediate rise in the
cocoa price of nearly 4½%. The rise
in prices continues over the
following three years to peak at
11¾% in the third year following the
shortfall. The positive impact
persists through to the 9th year.
A one s.d. (3.1%) shock to grindings
reduces stocks. Because of positive
autocorrelation in grindings levels,
stocks fall over the three years
following the grindings shock. The
maximum price impact (8¾%)
comes after five years.
10.0%
Crop
Grindings
7.5%
World GDP
5.0%
2.5%
0.0%
-2.5%
-5.0%
0
2
4
6
8
10
12
14
16
Years
18
20
22
24
26
28
30
Although the size of the grindings shock
is close to one third of that of the crop
shock, the maximum price impacts are
relatively similar. A GDP growth shock is
similar to a grindings shock but there is
a permanent effect since GDP is now
permanently higher.
Grindings and stock IRFs
4%
Grindings revert to trend
within a few years of the initial
shock – see left IRF. However,
it takes stocks longer to build
back up after the grindings
shock so price remains
elevated.
3%
Crop
Grindings
2%
World GDP
1%
0%
-1%
-2%
-3%
0
2
4
6
8
10
12
14
16
Years
18
20
22
24
26
28
30 0.40
0.20
0.00
-0.20
(months)
Changes to world GDP growth
take longer to feed through into
higher grindings and hence
higher price. The stockconsumption ratio remains
permanently lower and hence
the price is permanently higher.
-0.40
-0.60
Crop
-0.80
Grindings
World GDP
-1.00
-1.20
-1.40
0
2
4
6
8
10
12
14
16
Years
18
20
22
24
26
28
30
VAR IRFs
• Many economists are distrustful
of the “incredible” assumptions
made in specifying/identifying
structural models. They prefer an
unrestricted Vector
AutoRegression (VAR) approach
to modelling.
• VAR models do not allow for
contemporaneous interactions
between variables.
• Using the same sample, I
estimate a five equation VAR(2)
linking cocoa production,
grindings, stocks and price.
• The price IRF from this VAR is
unconvincing.
4%
3%
Crop
Grindings
2%
World GDP
1%
0%
-1%
-2%
-3%
-4%
-5%
0
2
4
6
8
10
12
14
16
Years
18
20
22
24
26
28
30
Price responses to crop and GDP shocks
are incorrectly signed. The response to a
grindings shock is quite small.
Structure is necessary in some form.
A Structural VAR
• Structural VAR (SVAR) modelling is an intermediate possibility between
VAR and structural modelling.
• Here I reintroduce the possibility of contemporaneous effects within a
recursive structure – grindings are affected by the current price and
current GDP and the price is affected by the current harvest.
• I impose Granger-causal exclusion restrictions on entire lag distributions
but leave the structure of these distributions unaffected.
A0
A(L)
Δlnwgdp Δlnwq Δlnrcp Δlnwgr scr Δlnwgdp Δlnwq Δlnrcp Δlnwgr scr
Δlnwgdp
1
0
0
0
0
*
0
0
0
0
Δlnwq
0
1
0
0
0
0
*
*
0
0
Δlnrcp
0
*
1
0
0
0
0
*
0
*
Δlnwg
*
0
*
1
0
*
0
*
*
0
scr
0
*
0
*
1
0
*
0
*
*
The SVAR Price IRF
20%
Crop
Grindings
15%
World GDP
10%
5%
0%
-5%
0
2
4
6
8
10
12
14
16
Years
18
20
22
24
26
28
30
It might be possible to reconcile the
structural and SVAR models by
moving to a cointegrated SVAR but I
have not pursued this.
The pattern of responses to the
crop size and grindings shocks is
closer to that of the structural
model than to those of the
unrestricted VAR.
The impact of the grindings shock
is of similar magnitude in the two
sets of simulations but it is seen as
decaying much more slowly. The
magnitude of the impact of a crop
size shock is, however, around
double that suggested by The
structural model. Again, decay is
much slower.
A GDP growth shock has a tiny
impact.
Coffee?
•
Cocoa and coffee are produced in many of the same countries (although
typically not in the same zones of these countries) and are traded on the
same futures markets, often by the same trading companies and, until
the advent of electronic trading, in adjacent pits.
• Coffee and cocoa price movements are correlated – the correlation of
average changes in real crop year prices is 0.34 over the sample 1950-51
to 2011-12. Both cocoa and coffee prices were abnormally high in 197677 and 1977-78 following frost in the Brazilian coffee producing zone and
in 1999-2000 and 2000-01, the years of the “Coffee Crisis”..
I investigated this by adding the coffee price to the structural model.
a) There is no evidence of any coffee price effect on grindings.
b) There is evidence that a high coffee price reduces the coffee harvest in
the following year.
c) There is evidence that the current change in the coffee price directly
impacts the cocoa price. (However, identification is questionable).
The Cocoa Price IRF from a Coffee Shock
20%
Crop
15%
Grindings
World GDP
Coffee
10%
5%
0%
-5%
0
2
4
6
8
10
12
14
16
Years
18
20
22
24
26
28
30
A one s.d (21.3%) coffee price
shock is seen as having a
comparable impact on the cocoa
price as one s.d. crop shock.
However, the coffee shock has no
direct impact on cocoa stocks and
hence its price impact is short
lived and disappears after 3 years.
These results are difficult to rationalize in terms of supply and demand
fundamentals.
a) The impact of the coffee price on cocoa production may result from
governmental decisions on input allocation.
b) If confirmed, the direct contemporaneous impact of coffee on cocoa
prices may be a futures market phenomenon.
Scientific conclusions
1.
2.
3.
4.
5.
Demand side shocks are equally important as supply side shocks in
understanding movements in the cocoa price.
Shocks have highly persistent effects. It takes up to 9 years for prices to
recover from a major shock, this being the time it takes stocks to return
to their normal level.
It is difficult to disentangle income-induced rises on cocoa consumption
from autonomous taste-related rises. My estimates suggest that the
income elasticity of demand is only around 0.4 but that grindings tend to
grow at a little over 1% per year even when income growth is absent.
(The short run income elasticity exceeds unity).
There is evidence that the cocoa and coffee prices may be more closely
linked than is widely appreciated. The reasons for the existence of such
links remains unclear.
My model fails to throw light on cocoa investment decisions. Data on tree
stocks would be helpful.
Policy conclusions
1.
2.
We need to be able to explain the half of demand growth which is
unrelated to income growth. Economists talk about “taste
change” but we do not have stories about how this happens.
Many in the industry would attribute this taste change to the
efforts of the marketing divisions of the major chocolate
manufacturers. This is an important issue for research.
The apparent link between the cocoa and coffee markets suggests
that the cocoa industry may be importing price volatility from
coffee. If this turns out to be true, the cocoa authorities might
attempt to reduce cocoa volatility by weakening this link. They
could do this by educating the markets that there is no
fundamental link between coffee and cocoa.
Thank you
for your
attention

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