# **4. Empirical strategy**

We test the effect of market remoteness on price volatility. To do so, we use a pooling regression of 28 markets that permits an estimation of the average effect of market remoteness on maize price volatility. Our work focuses on the empirical analysis of price volatility, which is defined as the unpredictable component of price fluctuations ( **Prakash, 2011** ). Appropriate models for this measure of volatility are ARCH family models, in which the variance of residuals is allowed to depend on the most recent residuals and other variables.

Drawing on **Shively (1996) , Barrett (1997)** and **Maître d’Hôtel et al. (2013)** , we build upon an ARCH model that displays mean and variance equations of maize prices to investigate maize price volatility in Burkina Faso. To measure this volatility, we isolate the unpredictable component of price variations from the predictable one, relying on price forecast models. To identify predictable price moves, several authors have used the conditional variance of price as an indicator of price volatility. The variance of the residuals of a price formation model typically measures the unpredictable price shifts. Thus, we use an ARCH model for two reasons. First, many storable commodity prices such as maize have an ARCH process ( **Beck, 1993** ). Second, ARCH models are particularly adaptable to the study of price volatility defined as the unpredictable part of price variations, as they enable the variance of the residual not to be constant over time, thus depicting an unpredictable dimension. The ARCH model assumes that the conditional variance depends on the lagged squared residuals of a price series over time. By including variables as regressors, the model can be used to identify potential determinants of price volatility. The ARCH model was introduced by **Engle (1982)** and generalized by **Bollerslev (1986)**<sup>12</sup> .

The ARCH structure is given by equations **(12)** and **(13)** : With εt|Ωt-1 ≈ N (0,ht) **(12)**

> 12 A General Autoregressive Conditional Heteroskedasticity (GARCH) process can also model price volatility. Some studies have used a GARCH model to analyse price volatility for different commodities ( **Yang et al., 2001** ; **Gilbert and Morgan, 2010** ). We choose ARCH model instead of GARCH, because monthly data usually do not exhibit GARCH effects ( **Baillie and Bollerslev, 1990)** . GARCH model is more appropriate for high frequency data. A robustness check is conducted in section 5.3, which relies on GARCH model. By using ARCH and GARCH processes, we assume that a quadratic relationship between the error term and the conditional variance (i.e. volatility). Series are assumed to feature high and low volatility, whatever the sign of the shock causing the volatility. Other specifications called asymmetric models exist such as Exponential-ARCH (EGARCH) model, which has been used whether the price volatility depends on the information of past shock in a non-linear fashion. The asymmetric models assumes that volatility can be spotted with clusters of amplitudes that significantly vary over time and volatility can increase or decrease depending on the information on past error terms.

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