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

Early spatial price analyses examined "co-movement" among prices at different locations (e.g., simple price correlations as in Timmer 1974; and co-integration as in Goodwin and Schroeder 1991; Asche, Bremnes, and Wessells 1999; and Gonzalez-Rivera and Helfand 2001). It is now well recognized that co-movement in prices is neither necessary nor sufficient for spatial efficiency (Barrett 1996; McNew and Fackler 1997; Fackler and Goodwin 2001; Barrett and Li 2002). Correlation and co-integration analyses generally do not take explicit account of transfer costs, and so do not provide a formal test for spatial market efficiency.

More recently, two newer methods, which focus directly on spatial market efficiency, have been employed. The first is threshold autoregression, which recognizes possible "thresholds" in how spatial prices respond to shocks, depending on whether the shock is large enough to raise spatial price differentials above transfer cost (Blake and Fomby 1997; Mainardi 2001; Goodwin and Piggott 2001; Goodwin and Harper 2000). Threshold autoregressions estimate "neutral bands" associated with unobservable transfer costs and therefore pay explicit attention to the role of transfer costs in spatial market efficiency.

The second newer method is the parity bounds model (PBM), first introduced by Spiller and Huang (1986) and developed further by Sexton, Kling, and Carman (1991); Baulch (1997); Park et al. (2002); and Barrett and Li (2002). The PBM estimates the probability of being in spatial price regimes that are consistent with the equilibrium notion that all spatial arbitrage opportunities are being exploited (Enke 1951; Samuelson 1964; Takayama and Judge 1971). Transfer costs are included explicitly in the notion of spatial equilibrium underlying the PBM, and if transfer cost data are unavailable the PBM requires an assumption about the way transfer costs evolve over time.

Despite the advantages of the PBM, it has itself been subject to criticism. First, results can be sensitive to underlying distributional assumptions (Fackler 1996; Barrett and Li 2002). Second, the PBM is usually applied to just one pair of markets at a time to manage the large number of trading regimes that can emerge in a multimarket context (Fackler 2004). Third, the standard PBM assumes shocks are serially independent, and does not provide information on the path of dynamic adjustment to deviations from spatial equilibrium. Fourth, the standard PBM assumes that, while a pair of markets may switch between alternative trading regimes in different periods, the probability of being in a particular trading regime at a particular point in time is time-invariant. Put another way, the standard PBM assumes the extent of spatial efficiency (or inefficiency) between a pair of markets remains constant over time, even in the face of changes in marketing policies and new investments in marketing infrastructure. This assumption of time-invariant regime probabilities is a serious limitation because in many instances policy changes are specifically designed to improve spatial market efficiency.

This article extends the PBM by relaxing the assumption that the PBM regime probabilities (and hence the extent of spatial efficiency) are constant over time. This allows investigation of whether changes in marketing policies have increased or decreased spatial efficiency. One simple means of achieving this goal would be to identify different periods associated with different marketing policies and then estimate a different PBM for each subperiod. Differences in regime probabilities for each subperiod would indicate the effects of the alternative policies. This is essentially the approach taken in Park et al. (2002). The problem is that this approach assumes the impact of a policy change on trading regime probabilities (and hence on the extent of spatial efficiency) is discrete and instantaneous. In reality, it is likely that the effects of a policy change are gradual and evolve slowly over time as traders learn more about the effects of the policy change.

The approach introduced here allows for a gradual transition in trading regime probabilities in response to policy changes. The method also allows estimation and hypothesis testing on the length of the adjustment period. The remainder of the article is organized as follows. The next two sections introduce the PBM and then extend it to allow policy changes to have a gradual dynamic effect on trading regime probabilities. Next we provide an application to Ethiopian maize and wheat markets, which highlights the approach and provides estimates of the effect of the 1999 grain marketing reform on Ethiopian grain markets. Finally, we discuss the empirical results and provide concluding comments.

The Standard Parity Bounds Model

Consider two markets i and j located in different regions that trade a homogenous commodity. Three mutually exclusive regimes can be identified, based on the relative sizes of spatial price differentials and transfer costs. (1)

In regime 1, the spatial price differential is equal to transfer cost:

(1) [P.sub.it] - [P.sub.jt] = [TC.sub.jit]

where [P.sub.it] and [P.sub.jt] are prices in markets i and j, respectively, and [TC.sub.jit] is the transfer cost for trading from market j to market i at time t. This regime is consistent with spatial market efficiency irrespective of whether trade occurs. When trade does occur the market prices [P.sub.it] and [P.sub.jt] will differ from autarky prices and demand and supply shocks in one market will be transferred to the other market.

In regime 2, the spatial price differential is less than transfer cost:

(2) [P.sub.it] - [P.sub.jt] < [TC.sub.jit].

Here there are no profitable arbitrage opportunities between the two markets and they are spatially efficient if no trade is occurring (market prices equal autarky prices). If trade is occurring, however, then the regime is inefficient because traders are making losses. This regime emphasizes that spatial efficiency does not necessarily require physical trade flows between markets.

Finally, in regime 3 the spatial price differential is greater than the transfer cost:

(3) [P.sub.it] - [P.sub.jt] > [TC.sub.jit].

This condition violates spatial arbitrage and the markets are not spatially efficient, irrespective of whether or not trade occurs, because there are opportunities for profitable spatial arbitrage that are not being exploited. Among several conditions that may lead to regime 3 are noncompetitive pricing practices, restrictions on the amount of product that can flow between regions, government price support activities, licensing requirements, and quotas (Tomek and Robinson 1990; Baulch 1997). (2)

To derive the standard PBM, examine a particular market pair (so that the i and j subscripts can be dropped), and assume that transfer costs are unobservable but known to be explained by a vector of observable variables [Z.sub.t] according to:

(4) [TC.sub.t] = [alpha] + [Z.sub.t][beta] + [e.sub.t]

where [alpha] and [beta] are unknown parameters that can differ across market pairs, and [e.sub.t] is a random shock that is usually assumed to be normally distributed with mean zero and standard deviation [[sigma].sub.e] (which can also differ across market pairs). In practice, transfer costs are usually assumed to be a constant plus a random shock (i.e., [beta] = 0), as in Sexton, Kling, and Carman (1991); or it is assumed that transfer costs are observed with error ([Z.sub.t] = [T[??].sub.t] and [beta] = 1 where [T[??].sub.t] is the observed transfer cost estimate), as in Barrett and Li (2002).

Using (4) the conditions for the three regimes can be written:

(5) [P.sub.it] - [P.sub.jt] - [alpha] - [Z.sub.t][beta] = [e.sub.t]

(6) [P.sub.it] - [P.sub.jt] - [alpha] - [Z.sub.t][beta] = [e.sub.t] - [u.sub.t]

(7) [P.sub.it] - [P.sub.jt] - [alpha] - [Z.sub.t][beta] = [e.sub.t] + [v.sub.t]

where [u.sub.t] and [v.sub.t] are nonnegatively valued random variables that measure the negative (regime 2) and positive (regime 3) deviations (if any) between price differentials and transfer costs. The [u.sub.t] and [v.sub.t] terms are usually assumed to be half-normal and distributed independently of each other and of [e.sub.t], with standard deviations [[sigma].sub.u] and [[sigma].sub.v], respectively.

The goal of the PBM is to estimate parameters [[lambda].sub.1], [[lambda].sub.2], and [[lambda].sub.3], which represent the probabilities of being in regimes 1, 2, and 3, respectively. To derive the likelihood function, define the difference between spatial price differentials and expected transfer costs to be the random variable [[pi].sub.t] = [P.sub.it] - [P.sub.jt] - [alpha] - [Z.sub.t][beta]. Then the joint density function for [[pi].sub.t] over all trading regimes is given as the mixture distribution:

(8) [f.sub.t]([[pi].sub.t] | [theta]) = [[lambda].sub.1] [f.sub.1t] ([[pi].sub.t] | [theta]) + [[lambda].sub.2] [f.sub.2t] ([[pi].sub.t] | [theta]) + [[lambda].sub.3] [f.sub.3t] ([[pi].sub.t] | [theta])

where [f.sub.kt] (k = 1, 2, 3) are densities for regime k; and [theta] is a parameter vector ([alpha], [beta], [[sigma].sub.e], [[sigma].sub.u], [[sigma].sub.v]) to be estimated. The likelihood function for a sample of observations is:

(9) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

and estimation proceeds by maximizing the logarithm of (9) subject to the constraint that the probabilities lie between zero and one and sum to one. This is the standard PBM and does not allow for changing regime probabilities.

The Extended Parity Bounds Model