_COTE D’IVOIRE: Volatility, Shocks and Growth_

# **Fully Modified Least Squares Model of Cocoa Prices and Output**

**We evaluated the impact of Cote d’Ivoire’s output on world cocoa prices, to explore whether the country is a price-maker, and to find analytic evidence of a break in the time series process.** To do so, we require the use of a more sophisticated approach than is usually adopted. Traditional Ordinary Least Squares (OLS) is inefficient, and can fail, in the presence of serial auto correlation, endogenity between the explanatory and explained variables, and breaks in the statistical process generating the variables. All three problems are present in this case. In particular, we observe a serial correlation, we believe that a break in the process occurred, and we hypothesize that the country has, over time, developed market power so that prices and quantity are related.

**To properly estimate the marginal impacts of Cote d’Ivoire’s cocoa production on world cocoa price, we applied a “Fully-Modified Least Squares” (FMLS).** This procedure was first proposed in 1990F<sup>8</sup> F and recently used by CashinF<sup>9</sup> F et al when investigating commodity price impacts on the macro-economy of developing countries. Table 1 summarizes the FMLS model results. FMLS allows us to estimate this parameters in an efficient and consistent way, as it takes into account not only the structural break in the series but it also corrects the estimation for serial autocorrelation and endogeneity.F<sup>10</sup> F

**FM-OLS provides evidence that Cote d’Ivoire, indeed, has developed market power in cocoa.** In the market for cocoa regression, the FM-OLS results show that **_world cocoa prices decrease an average of 7%  when Core d’Ivoire's cocoa production increases by 10%._** F<sup>11</sup> F  The world cocoa price is, therefore, highly sensitive to changes in Cote d’Ivoire’s cocoa output. Moreover, the Cote d’Ivoire cocoa production data explains almost 50% of the variance in the world prices. Also, we find that Cote d’Ivoire’s output “Grangercauses” world prices, itself an evidence that Cote d’Ivoire has market powerF<sup>12</sup>

**The model provides clear evidence that the structural break occurred in 1976.** The estimation methodF<sup>13</sup> F is to run a series of 43 regressions, moving the dummy variable forward one year at each iteration, and identifying the break-point based on a sophisticated goodness-of-fit criteria based on the ADF testF<sup>14</sup> F.

> 8 See three articles by Hansen & Phillips, all in1990.

> 9 Cashin et al, 2002, and Cashin, 2002.

> 10 This FMLS estimation procedure is not available in econometric packages, so co-author Carlos Espina coded it in mathematical software, Gauss.

> 11 Recall that Cote d’Ivoire produced between 8% and 41% of world output over the sample period.  So a one percent increase in Cote d’Ivoire’s output corresponds to a much smaller percent increase in world output, depending on market share. In the later part of the study period, a 1.0% change in Cote d’Ivoire’s output corresponds to 0.2 to 0.4 percent increase in world output, post 1976.

> 12 That is, innovations in Cote d’Ivoire’s output “explain” subsequent world price changes.

> 13 See Phillips and Hansen, 1990.

> 14 The Hansen-Phillips tests is based on an ADF test, for which they provide a distribution.