Intercommodity price transmittal : analysis of food markets in Ghana

f fi Policy Research WORKING PAPERS Agricultural Policies Western Africa Department and Agriculture and Rural Development Department The World Bank April 1992 WPS 884 Intercommodity Price Transmittal Analysis of Food Markets in Ghana Harold Alderman This dynamic model of price integration indicates functional- if not perfect - efficiency in Ghana's coarse grain markets. Policy Research Working Papers disseminate the findings of work in progrcss and encourage theexchangeof ideas smongBank staffand all others interested in deeclopment issues.Thesepapers. distribuied by the Research Advisory Stsiff,carry the names of the authors. reflect only thcirviews. and should be used and citcd accordingly. lbhefindings, intcrprctations, and conclusions are the authors'own. TheyshFould not be attributed to the World Bank, its Board of Directors, its management, or any of its member countries.  Policy Research Agricultural Policies WPS 884 This paper - a product of the Agriculture Operations Division, Westem Africa Department, and the Agricultural Policies Division, Agriculture and Rural Development Department - is part of a larger departmental study of food security in Ghana. Copies of the paper are available free from the World Bank, 1818 H Street NW, Washington, DC 20433. Please contact Cicely Spooner, room N8-039, extension 30464, or by electronic mail (April 1992, 36 pages). Aldemian expands on a dynamic model of it takes three months for the price shock to be market integration, first introduced by Ravallion fully transmitted. In the long run, this indicates (1986) to Ghana's principal maize markets, to market integration, but it is puzzling that it takes investigate how information is transmitted across so long to move commodities between markets.) commodities. He investigates onc property of an efficient market: the full usc of available infor- Second, he investigates the working of mation. commodity markets in developing countries. He notes imperfections in the way markets process Studies of spatial price integration simulta- information: the lagged price of maize conveys neously investigate the flow of informnation and information that is not contained in the past price commodities, but it is often difficult to distin- of sorghum or millet. guish between the two. A low correlation of prices between two markets may indicate either a There are several possible explanations for poor flow of information or economic ineffi- this market inefficiency. For example, traders ciency, for example - but could also indicate may set prices for other coarse grains in response competitive trade and linked markets that are to information about maize prices - requiring seasonally separated because of high transport supply changes (especially storage buildup and costs. drawdown) to bring markets into equilibrium. Another possibility is that some traders may not So Alderman also investigates the flow of deal in all grains and may therefor. .:ave differ- information within a single spatial market and ent costs for acquiring information - especially the relationship between prices in spatially for sorghum, which is both eaten and used for separate markets. making beer. Brewers, most of whom operate on a small scale, may trade and store only sorghum, He studies intercommodity price transmittal which may thus be a conceptually separate from two perspectives. First, he asks whether the (although physically contiguous) markeL But government can concentrate on a single corn- even for speculative markets in industrial modity price, yet achieve price policy objectives countries, in which information is generally in a broader arena. This is important in Ghana available electronically and trade rarely requires because no single commodity dominates con- the physical exchange of goods, perfect price sumers' food budgets, although for administra- transmittal is often rejected. tive and logistical reasons, direct intervention in all commodity markets is not feasible. He finds In short, from a practical viewpoint, that price movements for the main cereal con- Alderman's dynamic model of price integration sumed in the country (maize) are fully transmit- indicates functional - if not perfect - effi- ted to other grains and to other regions. This ciency in Ghana's coarse grain markets. simplifies any stabilization programs. (However, PThebPolicy Research Working PaperSeriesdisseminates the findings of work unda way mtheBank. Anobjectiveoftheseries| is to get these findings out quickly, even if presentations are less than fully polished. The findings. interpretations, and conclusions in these papers do not necessarily represent of ficial Bank policy. Produced by the Policy Research Dissemination Center  Intercomnodity Price Transmittal: Analysis of Food Markets in Ghana by Harold Alderman* Table of Contents I. Introductlon 1 II. Methodology for Analysis of Market Integration 4 Theoretical Considerations 4 An Interregional Two Commodity Model 7 Cointegration Models 12 III. Data and Results 15 Results of the Dynamic Interregional Model 19 Results of Tests of Integration and Cointegration 27 IV. Conclusion 31 References 34 * The author would like to thank Robert Armstrong, Meyra Mendoza, Stephen Mink, Mark Rosegrant, Alexander Sarris, Gotz Schreib-r, Gerald Shively, and Steven Younger for excellent research support, and for helpful suggestions on the topic.  INTERCOMMODITY PRICE TRANSMITTAL% ANALYSIS OF FOOD MARKETS IN GHANA 1. INTRODUCTION Since establishing a stable macroeconomic environment for long run development, the government of Ghana has explored a number of specific policies aimed at stabilizing food prices between seasons and across years. These policies have raiiged from income support and employment generation programs to improving marketing infrastructure. Options under consideration have also included the possiblity of increase government involvement in inter- and intra- year storage; in recent years government held storage capacity has been increased despite the fact that there is not yet a clearly articulated policy on the objectives of such otorage. The implementation of storage and other stabilization policies depends, in part, on the existing efficiency of trader operations. Similarly, the effectiveness of other possible interventions to guarantee food security that do not involve the government's direct handling of grain also depends on knowing which market channels operate effectively. For example, the potential for cash grants and food for work programs in districts with temporary production shortfalls to stabilize consumption is enhanced when markets in areas with low or variable levels of food consumption are linked to surplus regions via effective market channels. As part of such policy oriented analysis, a number of studies of markets in Ghana (Asante et al.) as well as other developing countries have analyzed the relationship of the price of a single commodity in various markets. With proper caveats, such studies are used to make inferences on the spatial flow of information and commodities. However, given that households in the regions of  -2- Ghana that are food insecure by a number of measures are in the northern savannah regions where sorghum and millet are primarily consumed (Alderman 1990) there is a need to know how the markets for these commodities link with the markets for maize, on which government policy is likely to focus. The current study - one component of a larger series of studies on food security in Ghana- begins with an application of a dynamic model of market integration first introduced by Ravallion (1986) to principal maize markets in Ghana. The main interest of the study, however, is to expand upon the model in order to investigatL- the transmittal of information across commodities. We investigate one property of an efficient market, the full utilization of available information. While studies of spatial price integration simultaneously investigate the flow of information and commodities, it Is often difficult to distinguish between the two. For example, while a low correlation of prices between two markets may indicate either poor flow of information or economic inefficiency, the observation may also be indicative of competitive trade and linked markets which are seasonally separated due to high transport costs (Timmer 1974). For this reason the current study also presents an investigation of the flow of information within a single spatial market. This allows a test of the principle that if a market is efficient w; -h respect to the information available, then the information conveyed by th ,rice of commodity j in period t will not improve the prediction of the price of commodity i in period t+l ovez the information already conveyed in the price of commodity _ in period t. This property has been studied mainly in regards to capital markets (Malkiel), but Granger and Escribano's study of speculative prices for silver and gold  -3- acknowledges that the concept is also valid for commodities that are close substitutes. Our purpose, however, is not solely to study the efficiency of markets. The results can be considered in the context of commodity price stabilization, using either trade or storage policies. While storage remains an expensive means to achieve a moderate amouut of stabilization (Pinckney, Siamwalla), implementation of such policies is made easier to the degree that internal markets are integrated.' Similarly, if price mover3nts are effici^ntly transmitted across commodities, stabilization policies can reduce the management burden by concentrating on one commodity. Moreover, as mentioned, since ecological conditions often dictate that regions of greatest food deficits consume different staple crops than those produced in surplus regions, even when stabilization programs are not attempted, governments may be interested in knowing the relationship of price movemeints of the surplus commodity and the staples in the deficit region. The results below are an empirical illustration of such price transmittal. 1 To a fair degree, also, such an approach to stabilization implies that internal markets are not fully integrated with external markets.  -4- II. METHODOLOGY FOR ANALYSIS OF MARKET INTEGRATION THEORETIC 'L CONSIDERATIONS As mentioneA, the analysis proceeds in three distinct stages. First, we apply a standard one commodity model of price transmittal to a West African setting. This allows for verification of earlier results of market efficiency presented in Ravallion (1986). Second, we use the same structure to investigate price transmittal across commodities. To a degree, this application is primarily statistical; theory does not give an unambiguous expectation for the magnitude the parameters of the model. Nevertheless, as discussed below, theory does indicate that the model is appropriate and day to day policy concerns indicate that it may be useful. Third, we apply a separate set of analyses, consistent with the former, which allow for testing hypotheses of information flows which are only meaningful in a multicommodity framework. While this study does not aim to modify the basic theory and, hence, aims for brevity in this section, a few points need be addressed to justify the issues intrnduced and the approach followed. In particular, before laying out a general model of market integration one needs to address both the relationship that would exist across commodities and the potential insights that can be gained by broadening the core model to a multicommodity framework. In doing so, we also reiterate some of the well known reasons for considering a dynamic structure (Hendry, Pagan and Sargan).  Ravallion (1986) as well as Faminow and Benson, attribute the underlying basis of most models of spatial price integration to Takayama and Judge. Takayama and 'udge lay out a set of optimization models to prove that when trade takes place, regional prices will differ by the transport cost. When the optimal amount of trade is zero, than the diffcrence in price is less than the transport cost. Furthermore, if supply or demand conditions in the two markets change, it is possible that trade can shift so that the p-ice differential is again the transport cost, but with the sign reversed.2 As this results holds in a multiproduct as well a single product context, a change in the price of one good, including a non-tradeable good, can change local demand such that the spatial price differential of another commodity rises to or declines from a point of equivalence to the transport cost. This result, however, does not nrovide an indication of the speed at which prices adjr-st to shocks. Intertemporal demand theory recognizes partial adjustment in a variety of models, including those which consider habit formation, stock adjustment, and delays in processing new price information (Deaton and Muellbauer, Deaton). Similarly, analysis of agricultural production virtually always is based on lagged response to price information. Moreover, if supply is taken in the broader context of stock build-up and draw-down as well as production, one can also consider the speed at which traders and other suppliers to the markets react to price information (including overreaction to such information in the short run as indicated in Ravallion, 1987). It is this 2 These points can be illustrated graphically with a standard back to back pair of supply and demand curves and a transport wedge.  -6- context that provides the underlying basis for most market integration studies, in particular, Ravallion's (1986) dynamic application. While t;Le advantage of a dynamic model pertains to any spatial models of market integration, even those which consider a single commodity, the introduction of the speculative nature of ttade and storage into a price formation model offers additional advantages in a multi-commodity model. In particular, it provides the basis for the test of the efficiency of information flows referred to in the introduction. Appeal to basic demand theory should be sufficient ti. indicate that prices of supplements and complements enter into the formation of current prices.a This, however, pertains to equilibrium values and does not say how markets forecast changes in prices. If a market is efficient with respect to some information set 0 then it is impossible to make economic profits by trading on the basis of 0. Past prices are clearly a plausible candidate for p. As such, changes in prices would be white noise; tomorrow's price change would reflect tomorrow's news but current information would be fully incorporated in today's price.' If prices of a second commodity improve the forecast of the first then they clearly provide news today and the basis for economic profits. As such, one would expect that in an efficient market the second series would be redundant. Granger and Escribano state this hypothesis in terms of drift of price series and provide the basis for the cointegration model presented below. 3 Prices of crops which are complements or supplements in production also influence market clearing prices. 4 This abstracts from any forecastable changes in risks and transaction costs (Granger and Escribano).  -7- AN INTERREGIONAL TWO COMMODITY MODEL Studies of market efficiency based on bivariate correlations are acknowledged as providing limited information (Harriss). The basic problem is that two functicnally isolated markets can appear to be synchronized if prices in each are influenced by a third market or by a common factor. A number of methodological improvements ir. recent years have gone beyond detrending (Haugh) to analyze the information contained in market price movements. For example, Delgado offers a variance components model that allows for a joint test of seasonal differences in the price integration of markets, while Ravallion (1986) places the standard model of market integration into a dynamic context. Timmer (1987) as well as Heytens offer modifications of Ravallion's model, providing intuitive interpretations on a subset of the model's parameters at a cost in terms of a simplification of the dynamic structure. Our main approach will follow from Ravallion's (1986) and Timmer's (1987) methods. The structure of Ravallion's approach is comparatively simple, although the estimation is econometrically sophisticated. He posits a central, or reference, ma_ket (denoted by subscript 1), the price in which is a function of prices in a number of n-l other markets as well as seasonal or policy variables. P1 = Ai (P2, P3, *- Pn, X1) (1) Prices in the feeder markets are functions of prices in the central market as well as policy and seasonal factors. Pi = f, (Pi, Xi) (i=2, ..., n) (2)  -8- Ravallion (1986) recognizes that the formulation above is most suited to a radial market struct'tre, although it is adaptable to alternative channels as well. In any case, the key innovation is not the model of price formation per se but tho dynamic structure of the estimation, which is indicated in eq. (3) and (4). 12 n I2 Pit = Xl c J + O lj k Pkt-j + Y1 X1e +elt t3) J.1 k=2 i-O 1 1 Pit= Eal P1t j + P fs; P2t-i + Y1 Xi eit (i=2,..., n) (4) for n $ 1 where k indicates markets; i indicates lags. Ravallion (1986) concentrates on eq. (4), recognizing that in many circumstances eq. (3) will be underidentified. If BSr = 0 for all values of i in eq. (4) then the ith market is segmented from the central market. On the other hand, if B;o = 1, then prices are immediately transmitted. Moreover. if markets are integrated in the long run, then a,j, + EBj = 1. There are, in addition, possibilities of short-run integration less immediate than instantaneous price transmittal that can be tested with this model. While simultaneous weather shocks could influence the apparent r2 values of the estimates as well as lead to a spurious value for B,o the other parameters are less susceptible to this particular proLiem that has been reported in the literature. While this model allows one to test various hypothesis about market efficiency, it doe,? not provide an esily accessible summary statistic about the degree of integration between polar cases. To deal with this issue, Timmer (1987) and Heyten'! make two modification of tnis model. First, they work in the logarithm if prices. This implies ad valorem marketing costs rather than a fee  -9- per quantity handled. This innovation is, however, not essential to their second modification which is the assumption of a single lag structure for price formation rather than the six lags that Ravallion uses. This simplifies subsequent interpretation since a little algebraic manipulation allows one to reformulate the model as: (Pit - pit-I) - (a,-3) (Pit-i - P-t-l) + 1blo (P1t - Pit-I) + (aS + Pio + P-i - 1) Ptl. + YX + l1it With this expression, one sees that the temporal change in a peripheral market is a function of the spatial price spread in the last period, the temporal change in the central, or reference, market, and the price level in the reference market in the last period. Again, seasonal and ,licy variables are included.5 This equation can be further manipulated to derive Pit = (1 + bl) Pit-, + b2 (Plt - PIt_) + (b3 -bl) Pt-, + yX + pit (6) where b1 = a1 l, b2 = Pf$o b3 = ax + Pio + Pil-l In long-run equilibrium conditions, (P,t - Pjt_j) = 0. If one assumes also that 7 = 0, then (1 + b,) and (bh - bl) are, respectively, the contributior. of local and central market price history to current prices. If the markets are well integrated, the latter will have a comparatively strong influence on the local price level. Timmer suggests that the relative magnitude of the two 6 These are bivariate dummy variables. As such, it is useful to include an intercept as well. Recently, Sexton et al. have introduced a sweitching regression alternative to model the probability of market autarky.  -10- influences can be indicated by their ratio. He defines this as the index of marKet connectedness (IMC) with values less than 1 as indicating short-run market integration .6 IMC = (b3 - bl) (7) Clearly this index is useful for comparative purposes, although it is only approximate, not only due to the above-mentioned truncation of the lag structure but also as the vector of parameters denoted by 7 may not be insi6nificant. Timmer (1987) also argues that b. is a measure of the degree to which changes in prices in the reference market are transmitted to other markets. This parameter is expected to be close to 1, although even if markets are perfectly integrated some difference from 1 could reflect a mixture of absolute and proportional marketing costs. Both Heytens and Ravallion use these models to test for the existence of any seasonal patterns in market integration.7 This is important as it is possible that in some seasons the cost of transport exceeds the difference in production or import prices between two markets. At such times, the price in one market could appear not to be linked with movements in the other.8 8 The choice of the cut-off is somewhat arbitrary although indicative. 7 In addition, Ravallion tests for the existence of a specific famine year effect. 8 One can consider this analogous to a situation in which world markets do not affect local prices of a small country when that country's market clearing price lies between import and export parity prices.  -11- An important reinterpretation of the Ravallion model is found in Faminow and Benson. They build upon Hotelling's model of locational interdependence which can be considered as spatial oligopoly. In particular, they note that short run integration as defined by Ravallion may be generated by collusive base point pricing. However, a rejection of short run integration and acceptance of long run integration is compatible with a model of market competition. Inference from such a model depends, in part, on the nature of the market structure. Ravallian assumes a radial market with few, if any, local market linkages; Faminow and Benson discuss markets in which agents are not located at a few points but are spatial disbursed. As discussed below, the spatial nature of the markets studied lend themselves to the Ravallion model employed. Moreover, if two regions or markets specialize in different commodities, so that the radial structure pertains to more than one commodity, the model discussed above can be adapted to a multicomodity frame.vork. Tests for market segmentation in such a multicommodity framework would still be appropriate. Similarly, the IMC would be a rough measure of the local versus reference market influences, albeit the influence would work through the matrix of cross price responses. There is no particular reason, however, why the price transmittal would be exactly one for one from a particular commodity to another under either short or long run integration. Nevertheless, the magnitude of 8S, and [Ea,, + s,,] would still provide information that measures the net transmittal of shocks in one market to another. Although cross price effects are generally not addressed in models of market integration they are explicitly recognized in general equilibrium and multi- market agricultural models. An understanding of the interactions of price  -12- policies in a multi-commodity environment can, for example, be gained from matrices of consumer and producer own- and cross-price responses. An illustration is found in Pinstrup-Andersen et al.. This particular application also indicates one limitation of the demand system approach, often the necessary cross-price matrix is difficult to obtain with precision.9 One advantage of the two commodity autoregressive model is that it relies on less restrictive assumptions than many complete structural models. Therefore, it provides an alternative means of modelling interactions of price policies. Moreover, although such models require a reliable time series of price information, they do not require information often unavailable from developing countries, such as data on quantities demanded or supplied over time and regions. CO-INTEGRATION MODELS Ravallion (1986) indicates that under long-run integration, the model he presents is a member of the class of error correction models. These, in turn, are related to models of co-integration (Engle and Granger, Hendry). Goodwin and Schroeder, for example, use such a model to study spatial linkages in United States cattle markets. In the present study, however, cointegration models are used within a single market to study the joint movement of two commodity prices. In particular, if a market is efficient, prices of two commodities will not be co-integrated (Granger and Escribano). This provides a test which is somewhat counterintuitive. The logic is based on the fact that if two prices are co- ' The cited study uses an assumption of additive separability in demand. While this was useful for the illustration to which it was applied, it is generally recognized as unrealistic.  -13- integrated, there will be Granger causality in at least one direction (Granger). Such causality implies that one price series can be used to forecast movement in the other. This is a violation of one property of an efficient market. Since an inter-commodity spatial model includes both the spatial flow of goods and information, this principle is best addressed withi. a single market. To illustrate the technique of testing co-integration, denote a discrete time series of a variable xt which is stationary as I(O). Alternatively, if xt must be differenced n times to be stationary, denote the series as I(n). We focus, in particular, on series that are I(1). This includes sa;ries that are random walks. Consider two such series. In general, a linear combinati6n of these series will also be I(1). If there is a stable relationship between the two series, however, there will be a linear combination of the two series that is I(O). Such series are considered co-integrated. The test of co-integration, then, first requires testing whether the different price series are I(1) using, in our case, a test introduced by Dickey and Fuller (see also Engle and Granger; Schwert; Goodwin and Schroeder). This involves regressing (xt - xt_) on xtl and testing the significance of the regression coefficient. Alternatively, one can regress (ut - ut1) on ut where u. is the residual of a regression of the price around a mean and/or time trend. In either form of the test, the test statistic is based on a t-ratio. Critical values of this test statistic, however, differ from commonly used t-statistics, but distributions based on Monte-Carlo studies are available in the literature cited. The null hypothesis is that the series are I(l); the alternative that is generally accepted (to the degree that one can ever accept an alternative hypothesis) is that the data is I(O). The underlying intuition in this test is  -14- that large absolute values of the (generally negative) coefficients of lagged residuals indicates that changes in xt or u. will be reversed over time, that is, that they are stable. If both series are I(l), one can proceed by regressing one price on the other. One then tests whether the residuals are I(1) using a Dickey-Fuller test as described above.  -15- TII. DATA AND RESULTS To reiterate the procedures used in this study. We first test the degree of market integration in the standard one commodity model. This model is then expanded to a two commodity framework. The results of this model shed some light on the relationship of commodity prices - in particular, the expected speed of price transmittal across commodities. In order to investigate the efficiency that commodity price information is utilized, however, a second approach - that of cointegration - is also employed. This is not used to model spatial integration but rather looks at the relationship of commodity prices within a single market. Each of these approaches have features that are useful for our study of Ghana. The key is to adapt the models to the specific context under investigation. The particular focus is the Upper East Region of Ghana, which is relatively poor and considered an area of food insecurity as indicated both by production variability and by higher levels of clinical malnutrition. It has the distinction of being the main millet producing and consuming region in the country, with sorghum being a secondary grain. Maize is only occasionally grown. The capital of the region (Bolgatanga) is linked to the maize exporting regions of the country (Brong-Ahafo and Ashanti) by a single trunk road (Map 1). The road is often impassable during and immediately after the rains. Long distance traders seldom stop along the route either to purchase or sell grain. Because of the linear nature of the trade link, then, and because the Upper East imports  - 16 - Bolgatanga Tamale Techiman Sunyani Kumasi Accra Cape Coast Map of Ghana indicating transport routes linking the major markets.  -17- maize, we can investigate the potential relation of other grain prices in the Upper East to maize prices using a recursive structure.10 We can take eq. (5) as explaining the tormation of maize prices in the principal maize market, Techiman. This price will be influenced by a number of markets (denoted, say, by 2 through n-l). It is not, however, determined by the price in the Upper East, which, under an analogy with standard models in international trade, can be assumed to be a "small country' price taker. It is not essential, therefore, to consider P1 (the maize price in Techiman) as simultaneously determined in estimations of Pn, (the maize price in the main market in the Upper East, Bolgatanga).11 Identification is made easier by this assumption since it also implies that under competitive conditions the local price for commodity imported from the reference market (maize) is the c.i.f. price; changes in local demand should not influence this price although they will influence the quantity traded. This assumption implies that one need not consider even local maize prices as jointly determined with millet or sorghum prices. Simultaneity, however, can also run the other way; local millet prices can be affected by local demand, hence, by local maize prices. As such millet prices must be considered jointly determined with maize prices. One needs to consider how the model structure would be affected if imports are temporarily suspended. This would not reverse the causality assumed in the 10 This is an important policy issue inasmuch as the government may intervene in the maize market, but is unlikely to do so for millet or sorghum. 11 Following Ravallion, however, we do employ an instrumental variables technique, however, as P1 may still be susceptible to errors in variables.  -18- recursive model; Techiman price3 would not be endogenous although Bolgatanga maize prices would be simultaneously determined with millet and sorghum. The underlying assumption on this market structure can be tested in the analysis. The test for market segmentation offered by Ravallion (1986) will indicate not only the degree to which local price movements are integrated with those in the exporting region, but whether there are seasonal patterns in the link. Similarly, the model can also directly test the assumption that local demand conditions do not influence the market clearing price. In the present study these conditions are indicated by the prices of millet and sorghum as well as indirectly through seasonal dummy variables. The data in this study are monthly wholesale prices from regional offices of the Ministry of Agriculture in Bolgatanga (Upper East) and Sunyani (Brong- Ahafo). Techiman, on the main north-south road in Brong-Ahafo, is taken as the reference market for maize. The data cover the period from 1977 to 1990.1 Given the high level of inflation in the period covered, all prices are deflated using a CPI deflator. Some gaps exist in the data around 1983 as drought and a severe fiscal crisis contributed to a breakdown in administration capacity in that year. Wherever there is such a gap, of course, the lag structure requires that a number of periods for which information is available should also be excluded. Apart from a loss of information, however, this should not directly affect the estimation technique. Moreover, to test the sensitivity of results, alternative specifications were run in which all observations from the drought period covering 18 u&onths in 1983 and 1984 were excluded. No change in any of the tests was observed in such explorations. The conclusions of the study also Greater detail is available in Alderman and Shively (1991).  -19- prove not to be sensitive to whether prices were specified in logarithms or levels. We, therefore, retain Ravallion's formulation in levels. RESULTS OF THE DYNAMIC INTERREGIONAL MODEL As mentioned, we also follow Ravallion in instrumenting prices in the reference market in the estimation of eq. 4. That is, the right hand side variables for Techiman prices in the subsequent analysis are predicted rather than observed prices in the reference market. This was done using Sunyani current and lagged prices with a correction for first-order serial correlation.13 Whiile more markets might improve the efficiency of the instrumenting equations, all other relevant market series contain gaps that would require a reduction in the sample size. The fit in the instrumenting equation was good, with an r2 over 0.90. Again, none of the results reported below were particularly sensitive to the use or exclusion of instrumental variable techniques. The next consideration is the appropriate length of the lag structure in the estimates of eq. 4. Test 1 in Table one indicates that adding one period lagged prices to a base model which regresses only the current price in Bolgatanga on the current Techiman price results in a significant improvement of 13 This was deemed warranted by conventional analysis of the Durbin- Watson statistic. As this test is not appropriate when lagged values of the dep3ndent variables are included on the right-hand side, Durbin's h statistic was used for initial diagnostics of a model of Bolgatanga maize price with a one-period lag (Durbin 1970). No evidence of serial correlation was revealed with this test, which used instrumented Techiman prices corrected for auto correlation as the independent price.  -20- the model.'4 Moreover, a test of the restrictions on a four-period lag (test 3) leads to a rejection of the restriction that such a model is equivalent to one with prices lagged only one period, as in Timmer (1987) and Heytens. There was, however, no significant improvement in the model when prices we:e lagged more than four periods (test 4). In none of the models was a seasonal dummy variable defined as 1 if the month was July, August or September - months during which roads are more likely to be impassable due to rain - significantly different from zero. Similarly, coefficients for a dummy variable defined as one if the observation came from the eighteen month drought period 1983-4 were not significant in any model. Complete market segmentation implies that none of the Techiman prices significantly influence Bolgatanga prices. This can be rejected for maize, millet, and sorghum in Bolgatanga. On the other hand, short-run integration (as defined by Ravallion)--indicated by the coefficient of current Techiman prices being one--is also rejected in all models.15 Test of the restrictions necessary for long-run integration--that all coefficieats of current and lagged prices sum to 1--are reported in Table 1 (tests 5, 8, and ?). These restrictions are not rejected at plausible levels of significance. This raises two questions: how long is 'long run' and how powerful is the test of this restriction? Although there is reason to be concerned that any 14 In the interest of space, the table includes only tests of restrictions. For an indication of the parameters of selected models, see the equations under Figures 1 and 2. Additional details are available from the author. is This is a necessary but not a sufficient condition. The hypothesis also implies certain restrictions on other parameters (see Ravallion 1986 and Faminow and Benson).  - 21 - Table 1 - Test Statistics for Dynamic Model of Grain Markets in Bolgatanga Model Test F-Statistic Maize Base: Maize prices as a ftunc- Significance of model: P50wZ a ptEtZ) F(4,110) * 71.23 tion of Techiman maize prices and period dummy variabtes. 1: Inclusion of 1lperiod lagged 0,OiZ r 0 8 2 1 o F(2,108) * 49.97 maize prices (Joint significance relative to base model) 2: Inclusion of 2-period lagged 8s^Z * 0, r FC2,'06) * 1.74 maize prices (Joint significance relative to Model 1) 3: Inclusion of 4-period Lagged 0, 0" =0. a, 2iZ a 0 FC6,102) a 3.39 maize prices r t, *ITUZ * 0, De"X2 a 0 ;Joint signiff;ance relative to Model 1) 4: Inclusion of 5-period lagged a! a 0, F(2.