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

The extended PBM (EPBM) uses the PBM framework but allows gradual probability changes over time. Suppose the joint probability density function and likelihood function for the standard PBM are modified as follows:

(10) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

(11) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

where [[delta].sub.k] measures the change in the probability of being in regime k due to the policy change, and [D.sub.t] is a transition variable that characterizes the time path of adjustment in regime probabilities. The transition variable [D.sub.t] is constructed following Ohtani and Katayama (1986). Let the end date of the old marketing policy and the beginning date for realization of the full effect of the new policy be denoted by [[tau].sub.1] and [[tau].sub.2], respectively. Then [D.sub.t] takes a value of 0 for dates [[tau].sub.1] and earlier, between 0 and 1 for the period between [[tau].sub.1] and [[tau].sub.2], and 1 for [[tau].sub.2] and later dates. Hence, the [[delta].sub.k] parameters measure the full effect of the change in regime probabilities in response to the policy change, but there can be an adjustment path to that full effect.

The pattern of transition from [[tau].sub.1] to [[tau].sub.2] can be represented using alternative functional forms but in our application below we assume a simple linear time path, which imposes a constant speed of adjustment. (3) Hence, if the length of the transition period is ten months, then 1/10 (10%) of the adjustment occurs every month and by the fifth month half of the adjustment is complete. In our model, [[tau].sub.1] is known but [[tau].sub.2] is treated as a parameter to be estimated. The log-likelihood function is maximized for alternative [[tau].sub.2] values and the period that has the highest likelihood value is selected. We allow [[tau].sub.2] to be any period from the date of the policy change (instantaneous adjustment) to the last date of the sample (adjustment takes the entire sample period). The case where the effect of the policy change is instantaneous (i.e., [[tau].sub.2] = [[tau].sub.1] + 1) is a special case of the EPBM, which is essentially equivalent to estimating PBM probabilities for different subperiods (see Park et al. 2002). A joint test of no structural change in any regime probability can be conducted using a likelihood ratio (LR) test based on the restricted (no structural change) and unrestricted EPBM estimations.

In the EPBM, probabilities for the different trade regimes are determined simultaneously for the three periods: (a) before the policy change; (b) during the transition period; and (c) after the full effect of the policy change. For the period before the policy change, the probability estimates for the different trade regimes are given by the [[lambda].sub.k]. Probability estimates for the transition period and after the full effect of the policy changes is realized are given by [[lambda].sub.k] + [[delta].sub.k][D.sub.t]. Because the parameter estimates are probabilities, the probabilities should sum to one at every period, which requires the following restrictions:

(12) 0 [less than or equal to] [[lambda].sub.k] [less than or equal to] 1

(13) 0 [less than or equal to] [[lambda].sub.k] + [[delta].sub.k] [less than or equal to] 1

(14) [summation] [[lambda].sub.k] = 1

(15) [summation] [delta].sub.k] = 0

It is important to note that the EPBM outlined above allows regime probabilities to shift in response to policy changes but maintains the assumption that the parameters of the transfer cost model, [alpha] and [beta] in (4), remain constant under alternative policy regimes. (4) This is reasonable in cases where changes in marketing policy would not be expected to change the structure of transfer costs, but would be inappropriate if a policy change could reasonably be expected to influence the structure of transfer costs as well as regime probabilities (or if there were other structural changes to the transfer cost relationship which occurred around the same time as the policy change, e.g., a new road is built). If it was necessary to allow parameters other than the regime probabilities to shift in response to a policy change this could be accommodated in the EPBM by taking each of the additional parameters [[theta].sub.i] and expressing them as [[theta].sub.i] + [psi].sub.i] [D.sub.t] so that [[theta].sub.i] represent the parameter prior to the policy change and [[psi].sub.i][D.sub.t] represents the path of change in the parameter value in response to the policy change. Of course, allowing all PBM parameters to change (including the transfer cost parameters) would add additional complexity to an already highly nonlinear and complex likelihood function. In our application to Ethiopian grain marketing policy below, we explain why we think the assumption of constant transfer cost parameters is reasonable for this case.

Application to Ethiopian Grain Markets

The EPBM was applied to Ethiopian maize and wheat markets to estimate the effects of policy changes on spatial grain market efficiency. We begin with an overview of grain marketing policy changes in Ethiopia and previous research on the effects of these reforms on spatial market efficiency.

Grain Marketing Policy Changes and Previous Research

There is a long history of Government regulation and control of Ethiopian grain trade. A military coup in 1974 ushered in seventeen years of socialist control during which the government set grain prices and restricted interregional grain movements through a system of marketing parastatals and cooperatives. The negative effects of these policies on the development of grain markets, the agricultural sector, and the national economy have been well studied (e.g., Lirenso 1987, 1994; Franzel, Colburn, and Degu 1989; Dadi, Negassa, and Franzel 1992; and Gabre-Madhin 2001). In response to this poor performance, the government undertook major policy reform in 1990 by removing restrictions on interregional grain trade and abolishing price controls, forced quota delivery, and eliminating the monopoly power of the Agricultural Marketing Corporation (AMC).

Soon after the 1990 policy reform, the civil war being waged between the socialist government and a force of Tigrayan militia came to an end with the government being overthrown in May of 1991. With the socialist government ousted, many of the war-related disruptions to grain trading came to an end. Additional formal policy liberalization followed soon after. In 1992, the AMC was reorganized to operate more in the open market in competition with the private sector and its name changed to the Ethiopian Grain Trade Enterprise (EGTE). Its new stated objectives included stabilization of grain markets and prices to encourage increased output, protect consumers from unfair grain prices, earn foreign exchange through exporting grain to the world market, and maintaining a strategic grain reserve.

In October of 1999, the government amalgamated the EGTE with the Ethiopian Oil Seeds and Pulses Export Corporation and reestablished it as a public marketing enterprise designed to compete with the private sector. The amalgamated EGTE was ostensibly relieved of its grain price stabilization responsibilities and directed to focus more on exports (Bekele 2002).

Even though earlier reforms were probably more significant, the empirical application here focuses on the effects of the 1999 reorganization of the EGTE for three main reasons. First, this is the major reform that occurred during the period over which the data used in the study are available (August 1996 to August 2002--see the data discussion further below). Second, the 1999 reorganization did lead to elimination of some remaining restrictions on interregional trade that may have had important implications for spatial efficiency. Third, the effects of the earlier 1990 and 1992 reforms, and of the end to the civil war, on spatial grain trade have already been studied by Dercon (1995), by Negassa and Jayne (1997), and by Gabre-Madhin (2001), who used correlation and co-integration analysis to conclude that regional Ethiopian grain prices appear more closely connected after these reforms than before. However, the effects of the more recent 1999 reforms have not yet been studied.

The 1999 grain market reform was focused on the EGTE and the way the EGTE interacts with the private sector, so there is no reason to believe the reform would have had a significant influence of the structure of transfer costs between markets. The one possible exception is that as part of the 1999 policy reform a remaining roadblock controlling and restricting trade in the north was removed (see the discussion of results further below). One interpretation of this removal is that transfer costs were structurally reduced at this time. However, the roadblock charges could also be interpreted as a source of spatial inefficiency and the effect of their removal evaluated in terms of how much the probability of being in spatially inefficient regime 3 (price differential exceeds transfer cost) is reduced after their removal. This latter interpretation is the one that we prefer and to facilitate this interpretation we impose the identification restriction that regime probabilities may shift as a result of the policy change but transfer cost parameters are time-invariant.

Markets, Trader Characteristics, and Data