1. The Dynamics of the World Cocoa Market
Christopher L. Gilbert
(University of Trento, Italy)
Presentation prepared for the First Conference on the Economics and Politics of Chocolate, University of Leuven, Belgium, September 2012.

2. 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.

3. Weymar’s model
Weymar’s model (monthly data, ) 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.

4. Summary conclusions
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.

5. Data
I have 66 years annual crop year data from to Source: ICCO (from 1960), IMF (pre 1960).
Price levels and volatility both declined after 1980.
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%) .

6. My model
I estimate a four equation structural model of production, grindings (consumption), stocks and price over the 62 crop years 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.

7. 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.

8. 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.

9. 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.

10. 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.

11. The storage model applied to cocoa
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.

12. 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.

13. 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.

14. Price Impulse Response Functions
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.
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.

15. Grindings and stock IRFs
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.
Changes to world GDP growth take longer to feed through into higher grindings and hence higher price. The stock-consumption ratio remains permanently lower and hence the price is permanently higher.

16. 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.
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.

17. 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.

18. The SVAR Price IRF
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.
It might be possible to reconcile the structural and SVAR models by moving to a cointegrated SVAR but I have not pursued this.

19. 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 to Both cocoa and coffee prices were abnormally high in and following frost in the Brazilian coffee producing zone and in and , the years of the “Coffee Crisis”..
I investigated this by adding the coffee price to the structural model.
There is no evidence of any coffee price effect on grindings.
There is evidence that a high coffee price reduces the coffee harvest in the following year.
There is evidence that the current change in the coffee price directly impacts the cocoa price. (However, identification is questionable).

20. The Cocoa Price IRF from a Coffee Shock
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.
The impact of the coffee price on cocoa production may result from governmental decisions on input allocation.
If confirmed, the direct contemporaneous impact of coffee on cocoa prices may be a futures market phenomenon.

21. Scientific conclusions
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.

22. Policy conclusions
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.

23. Thank you for your attention