Estimating policy effects on spatial market efficiency: an extension to the parity bounds model.

Grain markets in Ethiopia have a radial structure with the capital city of Addis Ababa being the central location. Maize and wheat typically flow from the surplus production areas in the west and south to Addis, where they are either consumed or transshipped to grain deficit areas in the east and north. Like other studies of spatial grain trade in Ethiopia, we exploit this radial structure in our choice of market pairs to investigate (see Dercon 1995; Negassa and Jayne 1997; Gabre-Madhin 2001).

Seven market pairs are investigated for maize (see figure 1). The first two of these represent flows from the maize surplus regions surrounding Jima and Nekemte in the west to the capital, Addis Ababa. The next three pairs represent flows from Addis to the maize deficit regions of Dese and Mekele in the north, and Dire Dawa in the east. The final two pairs are designed to capture the fact that there is often a considerable amount of maize that flows from the surplus region surrounding Shashemene in the south through Nazret to the deficit market of Dire Dawa, without first passing through Addis. Hence we include Shashemene-Dire Dawa and Nazret-Dire Dawa as additional market pairs.

[FIGURE 1 OMITTED]

Seven market pairs that exploit Ethiopia's radial market structure are also investigated for wheat (see figure 1). The first two of these represent flows from the wheat surplus regions surrounding Robe and Hosaina in the south to Addis. The next three pairs represent flows from Addis to the wheat deficit areas surrounding Dese and Mekele in the north, and Dire Dawa in the east. Then the final two pairings again exploit the fact that grain flows from Shashemene through Nazret to Dire Dawa without first going through Addis, leading to an examination of wheat price relationships between Shashemene and Dire Dawa, and Nazret and Dire Dawa.

A detailed description of the characteristics of wholesale grain trading firms in Ethiopia can be found in Dessalegn, Jayne, and Shaffer (1998), and in Gabre-Madhin (2001), but it may be useful to highlight some of the more important structural characteristics here. Maize-trading firms tend to be small scale and, in most cases, the owner is the sole employee and manager of the business. Traders are typically engaged in other nongrain trade activities and characterized by a low asset base. For example, only a few own their transport capital and most of them rent storage space. Major entry barriers to trading grain are lack of sufficient start-up capital, high cost of finding convenient locations, and lack of access to appropriate and adequate storage. Economies of scale are potentially important, especially in wheat trading, because of the growth of larger companies owned by regional political parties. Both farmers and merchants often lack access to high quality market information needed for making good trading decisions.

The main data required to implement the EPBM in this application are maize and wheat prices for different market pairs, interregional grain transfer costs, and the start date for the new policy regime. Weekly average wholesale maize and wheat prices for each market were obtained from the EGTE for August 1996 to August 2002. These weekly average wholesale prices were converted into monthly average prices by taking the unweighted mean of weekly prices for a given month. The main reason for converting to monthly average prices is to have the same level of aggregation for both prices and transfer costs (the minimum data frequency for the interregional truck shipment freight rates used to estimate transfer costs is monthly). Baulch (1997) has also argued that, because of the static nature of the PBM model, the observation period should be long enough to allow grain to move physically between the markets. For every month in our sample period the recorded grain price in the surplus market of each market pair was lower than the recorded price in the corresponding deficit market, which is consistent with the absence of trade reversals.

A complete time series on all interregional grain transfer costs is rarely available, particularly in developing countries like Ethiopia. However, monthly data are available on Ethiopian interregional truck shipment freight rates, an important component of total transfer cost. (5) Monthly truck freight rate data were collected from the Ministry of Economic Development and Cooperation and the Ministry of Transport Authority for the sample period and rates were found to be very similar for both inbound and outbound shipments. (6) Nominal market prices and truck freight rates are used because the arbitrage notion on which spatial efficiency is based focuses on nominal price relationships (i.e., deflating both the price differentials and the transfer costs would just rescale the arbitrage profits).

October of 1999 is used as the start date for the policy regime change because that is when the EGTE was amalgamated and reestablished as a public enterprise, which represents the major grain market policy shift over the study period.

Estimation Procedure

The EPBM is estimated for each pair of regional wholesale maize and wheat markets discussed above. Spatial price differentials are calculated as the difference between the monthly wholesale grain prices in the importing and exporting markets. Truck freight rates are an incomplete estimate of full transfer costs, and so full transfer cost is specified as

(16) T[C.sub.t] = [alpha] + T[[??].sub.t] + [e.sub.t]

where [alpha] is a parameter to be estimated, T[[??].sub.t] is the truck freight rate from the exporting to the importing market, and et is a random error.

Combining the spatial price differentials with the transfer cost model (16) leads to [[pi].sub.t] = [P.sub.it] - [P.sub.jt] - [alpha] - T[[??].sub.t] which implies the EPBM can be estimated by maximizing the log of the likelihood function (11) with respect to the parameter vector ([[lambda].sub.1], [[lambda].sub.2], [[lambda].sub.3], [[delta].sub.1], [[delta].sub.2], [[delta].sub.3], [alpha], [[sigma].sub.e], [[sigma].sub.u], [[sigma].sub.v]), making the standard assumptions that [e.sub.t] is normal and [u.sub.t] and [v.sub.t] are half normal, and imposing the probability restrictions (12) through (15). Of course, this estimation can only take place for a given end date for the policy adjustment process. Therefore, the estimation was repeated for every possible end date, starting with the date of the policy reform (i.e., assuming immediate adjustment) and ending with the last observation in the sample (i.e., assuming adjustment takes place over the entire remaining period of the sample). The end date that provides the largest log-likelihood value is then chosen as the estimated adjustment period.

There are two remaining difficulties with this estimation procedure that need to be discussed. First, the likelihood maximization is a highly nonlinear constrained optimization problem and, as with all such problems, is likely to experience convergence difficulties and have the potential for local maxima. In our application, we addressed the local maxima problem by first obtaining a converged solution and then using a grid search over a reasonable range of alternative starting values to investigate whether the converged solution was globally optimal. If the grid search led to convergence at higher likelihood values the procedure was repeated for the new parameter estimates until no higher likelihood values were obtained. (7) Despite this procedure, some parameter estimates remained at the boundary of the parameter space (i.e., some probabilities were estimated at either zero or one). In such cases we are careful to point out the corner solutions and not to provide conventionally estimated standard errors for such estimates, which would be inapplicable (see the results below).

Second, EPBM estimation still suffers from other weaknesses of the standard PBM, including the potential sensitivity of results to distributional assumptions. To evaluate this sensitivity, we undertook a Monte Carlo simulation to examine how the EPBM performs when the underlying distributions deviate from normality and half-normality. The conclusion is that deviations from normality can bias the results in the direction of underestimating the magnitude of increases in regime 3 probabilities (i.e., underestimating the increase in inefficiency resulting from a policy change), particularly when the true distribution of [e.sub.t] is skewed. However, results are more robust to deviations of [u.sub.t] and [v.sub.t] from half-normality (see Negassa and Myers 2006 for details).

Empirical Results