Spatial Price Integration and Spillover Linkages Between Regional Grain Markets in Nigeria

Kassouri, Yacouba; Fofana, N' Zué Felix Article — Published Version Spatial Price Integration and Spillover Linkages Between Regional Grain Markets in Nigeria Review of Development Economics Provided in Cooperation with: John Wiley & Sons Suggested Citation: Kassouri, Yacouba; Fofana, N' Zué Felix (2025) : Spatial Price Integration and Spillover Linkages Between Regional Grain Markets in Nigeria, Review of Development Economics, ISSN 1467-9361, Wiley, Hoboken, NJ, Vol. 29, Iss. 3, pp. 1849-1862, https://doi.org/10.1111/rode.13190 This Version is available at: https://hdl.handle.net/10419/329802 Standard-Nutzungsbedingungen: Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden. Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen. 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If the documents have been made available under an Open Content Licence (especially Creative Commons Licences), you may exercise further usage rights as specified in the indicated licence. https://creativecommons.org/licenses/by-nc/4.0/ Review of Development Economics, 2025; 29:1849–1862 https://doi.org/10.1111/rode.13190 1849 Review of Development Economics REGULAR ARTICLE OPEN ACCESS Spatial Price Integration and Spillover Linkages Between Regional Grain Markets in Nigeria YacoubaKassouri1,2,3 | N' Zué FelixFofana4,5 1Biodiversity Economics Group, German Centre for Integrative Biodiversity Research (iDiv) HalleJenaLeipzig, Leipzig, Germany | 2Department of Economics, Leipzig University, Leipzig, Germany | 3Prague University of Economics and Business, Faculty of Finance and Accounting, Prague, CzechRepublic | 4Université Felix Houphouet Boigny, Abidjan, Côte d'Ivoire | 5Economic Community of West African States (ECOWAS) Commission, Abuja, Nigeria Correspondence: Yacouba Kassouri ([email protected]) Received: 24 May 2022 | Revised: 24 April 2024 | Accepted: 23 December 2024 Keywords: grain markets| law of one price| price integration| volatility spillover ABSTRACT This paper aims to characterize the spatial setup of Nigeria's grain market integration from January 2002 to December 2013 across 19 Nigerian regions. Using market price data of maize, sorghum, and millet, two hypotheses are tested: (i) the law of one price across market pairs, and (ii) the leader market hypothesis in any network of market pairs. The results suggest that integration fails to hold in many cases for over 60% of market pairs, while perfect integration is found to be considerably stronger for organized local markets such as Abuja and Lagos than for remote markets. There is evidence that Northeastern markets subject to the Boko Haram insurgency are weakly integrated with the other markets. Only three Northwest rural markets exhibit leading status in volatility prediction in different markets. The findings suggest that maize and millet markets located in Abuja and Lagos are the net receivers of price volatilities, and they are more exposed to price shocks originating from other markets. The pricing policy should mainly concentrate on leading markets as it will be efficiently transmitted to the followers. 1 | Introduction Staple food flows between spatially disconnected areas interconnect regional markets and facilitate the efficient transmission of supply/demand shocks in a given market to prices in other markets in the spatial network (Myers and Jayne2012). Research attention on the degree of market integration and the transmission of price shocks across markets in developing countries has increased markedly since the food price crisis of 2007/2008. The increasing interest in the topic is explained by the risks associated with possible instabilities in the price of staple foods in developing countries (Rlbehri etal.2013). For instance, in the subSaharan Africa region, it is established that the variation in staple food prices tends to be higher and more persistent than in other regions, severely impacting the purchasing power and food security of poor households (Gilbert, Christiaensen, and Kaminski 2017). Unlocking the intraregional market connectivity potential is at the heart of the solution to limit price increases (Abdulai and Egger1992; Jayne and Jones1997). Therefore, understanding the degree of spatial price integration and volatility transmission across staple food markets is a prerequisite for designing and implementing market interventions and food policies. Against this background, this paper aims to present a comprehensive evaluation of the law of one price from two innovative aspects in Nigeria. Firstly, we examine the degree to which staple food prices in geographically separated markets or at different levels of the value chain share common longterm price information. Secondly, we characterize the volatility dynamics involving all staple food market pairs within Nigeria to capture price spillovers among regional markets. To achieve these objectives, we focus on major staple food commodities, including sorghum, maize, and millet, which are a good illustration This is an open access article under the terms of the Creative Commons Attribution-NonCommercial License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited and is not used for commercial purposes. © 2025 The Author(s). Review of Development Economics published by John Wiley & Sons Ltd. 1850 Review of Development Economics, 2025 of thinly (domestically)- traded food commodities in Nigeria, unlike traditional export commodities (cocoa, cotton, coffee). Since the consumption patterns of these staples might vary according to regions within the same country, a comprehensive analysis of staples involves information on an acceptable spatial resolution. Thanks to the granularity of the data provided by Porteous(2019), the study focuses on 19 major staple markets for maize, sorghum, and millet in Nigeria from January 2002 to December 2013. From the empirical evidence, we select Nigeria for several reasons. Firstly, due to rapid population growth, urban expansion, and the internal conflict triggered by the insurgency of Boko Haram, food grain markets are challenged by increasing demand, short supply, and the conversion of agricultural land into settlement areas (Odozi and Omonona2012). Accordingly, domestic food grain markets need to adjust to these pressures by reducing the sensitivity of production to unforeseen events in order to improve the efficiency of the country's agricultural product markets. Secondly, in line with government policies on increasing the competitiveness of local value chains, the Federal Government of Nigeria adopted restriction measures on imports of maize and other grains. This measure can seriously alter the local market structure and equilibrium prices to work against food supplies, particularly during poor harvest season (adverse effects of climate change).1 As the crucial policy prescription for local agricultural development, market integration is a vital precondition for its effectiveness (Baulch1997). Thirdly, the underlying staple foods, including maize, sorghum, and millet, are among the leading cereal crops of the country, and their production covers more than 50% of the cultivated area (George etal.2021; Lawrence etal.2015). Despite adopting protective trade policies to prioritize domestic food and agricultural production, Nigeria is expected to face decreases in grain supplies due to conflict and economic factors. The north of Nigeria, particularly states like Kano, Kaduna, and Katsina, are known for producing grains such as maize, millet, and sorghum. However, internal security across the country's leading agricultural states poses a serious challenge to grain production. The south, including regions like Lagos, Port Harcourt, and Calabar, is more urbanized and industrialized but has a high demand for grains due to its large population. Trade between the north and south usually follows seasonal patterns dictated by agricultural cycles. The flow of grains from the north to the south increases during periods of scarcity or when prices are lower in the north during the harvesting season compared to the south (Scott, 1972; Ukwu, 2000). Traders play a crucial role in facilitating the flow of grain across Nigeria. They operate at different levels of the value chain, including wholesale and retail trading, transportation, and storage. These traders help balance supply and demand, ensuring equilibrium across grain markets (Serge, Lenis, and LiverpoolTasie 2017). In addition, the poor transport accessibility of several regions coupled with the diversity of natural conditions has limited the integration process in Nigeria. All these features make Nigeria an appealing case study, providing an essential engagement with the literature on the broader dynamics of grain prices in developing countries.2 The law of one price constitutes the primary theoretical background of this study. This law holds that, in a competitive market structure, the prices of identical commodities traded in different markets will be the same when expressed in the same currency (Baulch 1997; Stephens etal.2012). Several studies tested the law of one price by examining spatial integration in different commodity markets. Starting with the pioneering research of (Protopapadakis and Stoll1986), few studies find some support for the law of one price (Goodwin1992; Obstfeld and Taylor1997; Pippenger and Phillips2008). Another strand of the literature fails to find significant evidence for the law of one price in commodity markets (AlJabri, Boughanmi, and Omezzine 2003; Edwards and Rankin 2016; Góes and Matheson 2017). In the literature, most of the studies that explore the law of one price generally use standard unit root tests (augmented DickeyFuller, Philips and Perron), vector autoregressions of prices, and cointegration or Grangercausality analyses. Former studies have identified various market integration measures, including correlation coefficients, longterm multipliers, and times to adjust cointegration coefficients. Much empirical literature explores the law of one price in its strict version, holding that the price of a tradable good should equalize across regions if there are no impediments to trade between them. Other studies consider a more comprehensive analysis of the law of one price in its weak version form, stemming from the fact that regional markets are integrated if price differentials across regions do not exceed transportation costs. In other words, in its weak form, the law takes into account the possibility that natural trade barriers may allow some regional price differences to be no greater than transportation costs (Fackler and Goodwin2001; Gluschenko2011). In this paper, we adopt an approach that adds additional flexibility to the analysis of market integration over space. Specifically, we explore the issue of market integration by considering different grades of integration, which can be classified into (i) the perfect integration of market pairs based on the assumption of the strict law of one price, (ii) the conditional integration of market pairs assuming a weak law of one price, (iii) the intermediate grade between integration and nonintegration related to market pairs tending towards integration, (iv) the grade of neither integrated nor tendingtowardsintegration consisting of market pairs following random walk process. A similar classification of different degrees of integration has been used recently (Gluschenko 2021) to provide a comprehensive analysis of the level of integration of Russian markets. In addition, we offer further insights into volatility spillovers among regional staple food markets to gauge market interconnectedness and provide fresh perspectives on the potential risks posed by irregularities in conflictaffected areas to other markets. The current study contributes to the existing literature in two directions. First, we allow for a more flexible analysis of the degree of spatial integration by considering different dimensions of spatial integration across pairwise markets. Previous studies mainly examine the degree of integration in its strict version, where there is no room for arbitrage across markets. As discussed previously, considering different grades of integration allows us to accommodate the complex structure of local markets in a developing country like Nigeria, characterized by liquidity and availability constraints, high transaction costs, and inadequate provision of market infrastructures. 1851 These factors may yield different grades of spatial integration, which should be taken into account in order to provide more reliable outcomes. Secondly, we add to the existing literature on local market linkages and prompt regional price shock propagation across pairwise markets by considering major subsistence crops widely consumed. This is quite appealing in Nigeria, subject to the Boko Haram insurgency, where staple food markets in the affected region are likely to be less connected to other regions due to the destruction of roads and communication facilities (Adelaja and George 2019). Thirdly, we examine the strength of price comovement between each pair of provinces to provide insight into which local grain markets are most closely linked by accounting for volatility spillovers. To the best of our knowledge, this work is the first to explicitly allow for volatility spillovers in the nexus between local markets. 2 | Data, Model, and Estimation Strategy 2.1 | Data The empirical analysis relies on monthly data from January 2002 to December 2013 collected from 19 markets in all regions of Nigeria. We focus on the country's major staple crop markets, that is, Abuja, Akure, Benin city, Calabar, Enugu, Gombe, Ibadan, Ilorin, Jos, Kaduna, Kano, Katsina, Lagos, Lokoja, Maiduguri, Makurdi, Portharcourt, Sokoto, Yola. The total number of region pairs to be examined is given by N(N−1)∕2 , which is 19 ×18∕2=171 local grain markets within Nigeria. Unlike previous studies considering specific markets due to data availability (Adewopo etal.2021), it is essential to note that all Nigerian regions are represented in the sample. This allows us to have a clear overview of the pattern of crop prices for the whole country. The local market data were taken from (Porteous2019) and encompassed monthly maize, millet, and sorghum prices of each marketcatchment geography. The author identifies a market catchment geography using the minimum traveltime approach, and it is considered as the region for which the minimum travel time to the market is smaller than the minimum travel time to any other market (i.e., the region for which the market is the “closest” in terms of travel time). Following this definition, Porteous(2019) identifies 19 markets, notably Abuja, Akure, Benincity, Calabar, Enugu, Gombe, Ibadan, Ilorin, Jos, Kaduna, Kano, Katsina, Lagos, Lokoja, Maiduguri, Makurdi, Portharcourt, Sokoto, Yola. Grain prices are collected from a variety of sources, including the Living Standards Measurement Study (LSMSISA), the World Food Program's VAM unit and FAO's GIEWS project, USAID's FEWS NET project, nongovernmental organizations, and other researchers. Prices are measured in US dollars per kilogram, ensuring that price observations are standardized across each crop market.3 Basic descriptive statistics are reported in Table 1 for each crop. The average sorghum and millet prices are slightly higher than maize prices. When we look at the kurtosis and skewness results, we can make the following points: (i) all prices are positively skewed, (ii) price changes of sorghum and millet are not normally distributed, which is formally confirmed by the JarqueBera test statistics. The variability of prices given by the standard deviation is relatively higher for sorghum and millet relative to maize prices. Since we are interested in understanding price integration and transmission across local markets, we also provide information on the mean and standard deviation of the price differentials of each crop over the sample period in Figures1–3.4 We specify the mean ( cpt ) and standard deviation ( 𝜎t ) of the price differentials ( Erst ) in markets r and s as follows: The statistics depicted in Figures 1–3 provide information on the respective mean and standard deviation of the price differentials for maize, sorghum, and millet. An inspection of the price dispersion shows that prices are highly volatile with dramatic fluctuations, the maximum and minimum ratio equals almost 4.5, 5.5, and 5.3 for both mean and standard deviation of the absolute differential prices of maize, sorghum, and millet, respectively. The higher differences between maximum and minimum price values can be explained by both supply and demandside shocks, such as climatic and regional inflation. Another important observation is that the mean and standard deviation of the absolute price differential follow similar movements over the research period. However, the mean absolute price differential is relatively higher than the standard deviation. As reported in Table1, evidence of the ARCH effect at the selected lags 1 and 3 motivates us to account for volatility spillover in the market price transmission mechanism. cp t=2 N(N−1) N−1 ∑ r=1 N ∑ s=r+1|| Erst || 𝜎 t= ( 2 N(N−1) N−1 ∑ r=1 N ∑ s=r+1 (|| Erst || −cpt ) 2 )1∕2 TABLE 1 | Summary statistics. Maize Sorghum Millet Mean 0.327 0.343 0.349 Median 0.322 0.334 0.331 Maximum 0.510 0.589 0.587 Minimum 0.212 0.225 0.249 Std. Dev. 0.076 0.095 0.089 Skewness 0.717 1.077 1.287 Kurtosis 2.935 3.499 3.816 JarqueBera 4.128 9.792*** 14.597*** Probability 0.126 0.007 0.000 ARCH(1) 115.326*** 120.36*** 233.89*** ARCH(3) 271.96*** 189.63*** 144.69*** ***Indicates significance at 1% level. 1852 Review of Development Economics, 2025 2.2 | Model and Estimation Strategy As in Gluschenko(2011), the price differentials ( Erst ) across markets can be expressed as follows: where Grt and Gst represent grain prices in regions r and s ( r,s=1…,N ) at period t . The economic model of the strict law of one price can be set as follows: If Erst is stationary, then the prices in the markets can be in equilibrium in the long run, and satisfy the law of one price hypothesis. Empirically, the law of one price can be tested using the following AR(1) model with no constant: where, Δ stands for the first difference operator. The stationarity of Erst implies the validity of the law of one price. In this situation, markets r and s, are perfectly integrated. As discussed earlier, one can model the law of one price in its weak form by testing whether Erst is stationary around a nonzero constant. To do so, we can respecify price differentials across markets as Grt ∕Gst =1+qrs or Erst ≡ ln(1 + qrs) , where qrs represents timeinvariant arbitrage transaction costs in percentage terms. We respecify Equation(3) by including a constant term 𝛼=−𝜑qrs : The stationarity of Erst around a nonzero constant suggests that the weak law of one price is verified with markets r and s being conditionally integrated. The conditionality of the integration comes from the price disparity qrs stems from transportation costs. Another concept of market integration that is different from the law of one price can be tested by considering whether there could be a catchingup effect across markets. In this situation, there is a movement towards integration with an asymptotically decaying trend ( qrs(t) ), and the price differentials are given by Grt ∕Gst =1+qrs(t) or Erst ≡ln ( 1+q rs (t) ) , where qrs(t) approaches zero when t goes to infinity and d∣qrs(t)∣∕dt <0 . The concept of convergence process can be seen as a superposition of two longrun processes or deterministic convergence and shortrun or stochastic convergence, which can be written as: The difference between equations(3) and (4) and equation(5) is that the longrun paths are timeinvariant qrs(t)=0 in equation (3) and qrs(t)=− 𝛼 ∕𝜑 in equation(4). Consequently, the convergence to the law of one price or simply convergence from equations (3 & 4) is based only on shortrun features of adjustment towards the longrun path. We provide a graphical visualization of the different properties of convergence in Figure4a–c. Besides the consideration of different types of convergence, we also account for three modes of the convergence trend, including the exponential trend ( Q(t)=𝛼e𝛿t,𝛿<0 ), the logexponential trend Q (t)=ln ( 1+𝛼e𝛿 t) ,𝛿< 0 , and the fractional trend Q(t)= 𝛼 ∕(1+ 𝛿 t), 𝛿< 0 . Equations (3–5) can be modified to include the following trend when testing the law of one price. (1) Erst =ln ( G rt ∕G st) (2) Grt ∕Gst =1 or Erst =0 for t=0, . …,Tand a region pair (r, s) (3) ΔErst =𝜑Ers,t−1+vt (4) ΔErst =𝛼+𝜑Ers,t−1+vt (5) ΔErst =qrs(t)−(𝜑+1)×qrs(t−1)+𝜑Ers,t−1+vt (6a) Erst =ln ( 1+𝛼e 𝛿t) −(𝜑+1)⋅ln ( 1+𝛼e 𝛿(t−1)) +𝜑E rs,t−1 +v t FIGURE 1 | Summary statistics of the absolute price differentials of maize. [Colour figure can be viewed at wileyonlinelibrary.com] FIGURE 2 | Summary statistics of the absolute price differentials of sorghum. [Colour figure can be viewed at wileyonlinelibrary.com] FIGURE 3 | Summary statistics of the absolute price differentials of millet. [Colour figure can be viewed at wileyonlinelibrary.com] 1853 Considering the general specification displays in (6a), (6b), and (6c), one can conclude that grain price convergence holds if time series Erst is stationary about one or more of these trend models and parameter 𝛿 is well signed. However, a wrong sign of 𝛿 indicates deterministic divergence. It should be noted that all three versions of Equation (6) are estimated for each market pair, and the most suitable model is selected following the best fit (the minimal sum of squared residuals) if they turn out to be completive. Another important feature of the comovement between the series is the duration of the deviation ( 𝜋 ) of the price gap from its longrun path, which can be identified as the time it takes for the disparity to halve. In the case of logexponential trend, 𝜋=ln(0.5)∕𝛿 ; for the exponential trend 𝜋 =1 𝛿ln ( ln(0.5(ⅇ𝛼+1)) 𝛼 ) ; and for the fractional trend 𝜋 =1 𝛿 ln ( 𝛼 ln(0.5( ⅇ𝛼 +1)) −1 ) . For the sake of robustness, we employ the augmented DickeyFuller (ADF) and PhillipsPerron (P.P.) unit root tests to test the null hypothesis of unit root ( H0:𝜑=0 ) against the alternative of stationarity ( H1:𝜑<0 ). Despite a large set of unit root tests, the ADF and P.P. unit root tests are more severe in rejecting the null hypothesis. We also investigate volatility transmission between grain markets by employing a modifiedversion of the Lagrange (6b) Δ E rst =𝛼e 𝛿t −(𝜑+1)𝛼e 𝛿(t−1) +𝜑E rs,t−1 +v t (6c) Δ Erst =𝛼 1+𝛿t − (𝜑+1)𝛼 1+𝛿t +Ers,t−1+vt FIGURE 4 | Different patterns of integration across pairwise grain markets in Nigeria. [Colour figure can be viewed at wileyonlinelibrary.com] 1854 Review of Development Economics, 2025 Multiplier (L.M.) volatility spillover test developed by Hafner and Herwartz(2006). The approach is commonly used to estimate the spillover effects in variance across markets based on the univariate GARCH model approach (Atukeren, Çevik, and Korkmaz2021; Nazlioglu, Erdem, and Soytas2013). Hafner and Herwartz(2006) consider the following specification: where conditional variance 𝜎2 it =w i +𝜕 i v 2 ⅈt−1 +𝛽 i 𝜎 2 ⅈt−1 and 𝜉it represents the standardized residuals of GARCH model. The null hypothesis of nonvolatility transmission ( H0:Ψ=0 ) is tested against the alternative hypothesis of volatility transmission ( H1:Ψ ≠ 0 ). The authors propose the following L.M. statistic to test the volatility transmission between twograin markets. where V� 𝜃i � =k 4T �∑ T t=1zjtz� jt − ∑ T t=1zjtx� it �∑ T t=1xjtx� jt �−1∑ T t=1xⅈtz� jt � and k =1 T ∑ T t=1 � 𝜉2 ⅈt−1 �2 . The estimation procedure can be summarized as follows: i. Estimate a GARCH(1, 1) model for the residual vⅈt and vjt and obtain the standardized residuals 𝜉it , partial derivatives xⅈt , and the volatility process 𝜎2 jt entering zjt . ii. Regress ( 𝜉 2 ⅈt −1 ) on x′ it and z′ jt . iii. 𝜆LM is equal to T times the coefficient of explanation Rsquared of the latter regression. 3 | Empirical Findings This section estimates and discusses the empirical findings. It is divided into two parts. First, we report the pairwise crossmarket integration results and discuss Nigeria's grain market integration pattern. Second, we report the results on volatility price transmission across markets to characterize whether markets are integrated in terms of transmission of price fluctuations. 3.1 | Spatial Integration of Nigerian Grain Markets Based on Pairwise CoMovement Analysis Before interpreting the results, it should be noted that it is hardly possible to present the specific estimation for each region pair. We summarize the results obtained by displaying the percentage of regional markets with which a given individual market is integrated, converging, and diverging in Table2. These percentages are obtained as the ratio of the number of region pairs belonging to a specific type of integration to the total number of pairs. This approach allows us to identify regions strongly (or weakly) integrated with the rest of the country's regions. For the sake of brevity, we also provide an emblematic graphical visualization of the five possible integration patterns of some regions in Figure4. Figure4 shows that the evidence of different degrees of integration seems obvious across market pairs, exemplifying the econometric consideration followed in the study. As discussed earlier, one can disentangle five patterns of price differentials across market pairs. Figure 4a graphically illustrates the pattern of perfect integration across market pairs. As can be seen, the price differential between Lagos and Abuja has a mean around zero (price parity), and the series fluctuates within a band, which is consistent with a covariance stationary process. The strong version of the market integration hypothesis implies the datagenerating process of the price differential series to be covariance stationary as illustrated in Figure 4a. Deviations from the price parity take around 12.5 months to die out. The graphical illustration of the conditional integration is depicted in Figure4b. The analysis indicates that Lagos and Benincity markets are conditionally integrated, with the price differential fluctuating around 1% with 𝜋=27.3 months . There is evidence toward integration in the longrun, as shown in Figure4c. Price differentials in Ibadan and Kano grain markets display a nonlinear decreasing pattern, supporting the evidence for integration in the long run. The meanreverting process towards the longrun path occurs after 11.56 months. Figures4d,e display the nonintegration cases, where the behavior of the price differential follows a random walk process in Figure4d, whereas the presence of deterministic price divergence drives the nonintegration process observed in Figure4e. Table2 summarizes the percentage of region pairs within Nigeria that are perfectly integrated (P.I.), conditionally integrated (CI), converging (CONV), diverging (DIV), and not integrated (N.I.). Starting with all maize market pairs, the findings reveal that, on average, 30.47% (14.15% + 16.62%) are perfectly or conditionally integrated (see last row of Table2). Accounting for the market pairs moving towards convergence, a total of 37.85% is observed. Interestingly, a relatively high number of local markets tend to be perfectly integrated with the Abuja and Lagos maize markets. The data reveal that, on average, 30% of the country's markets are perfectly integrated with Abuja and Lagos. Although maize markets located in Gombe, Maiduguri, and Yola are less integrated under the perfect integration hypothesis, there is evidence for conditional convergence and movement towards convergence with the local markets. We show that nonintegration patterns are reported in nearly 61.48% of market pairs. Thus, one can infer that Nigerian maize markets display a high degree of nonintegration, providing little evidence favoring the law of one price. Concerning Nigerian sorghum markets, we report that 20.61% of market pairs are perfectly or conditionally integrated on average. Adding market pairs moving towards convergence, we have a total of 25.22%. Among individual markets, the local market of Kano seems to be highly integrated market with a perfect integration rate equal to 46.78%. Another important observation is that there are no significant patterns of perfect integration with the following markets: Gombe, Ilorin, Katsina, Maiduguri, and Yola, given that they are not perfectly integrated with any markets. However, findings support evidence that conditional and movement towards convergence, in the long run, can be reported in these markets. Again, it could be observed that there are more diverging markets, as nearly 74.75% of the sorghum price differentials are diverging and not integrated. The higher percentage rates of nonintegration and divergence patterns across market pairs imply that the law of one price is not tenable (7) v ⅈt=𝜉it √ 𝜎2 itft,ft=1+z� jtΨ,z� jt = ( v2 jt−1,𝜎2 jt−1 ) (8) 𝜆 LM =1 4T [T ∑ t=1( 𝜉2 ⅈt−1 ) z� jt ] V ( 𝜃i ) −1 [T ∑ t=1( 𝜉2 ⅈt−1 ) zjt ] ∼𝜒2(2 ) 1855 TABLE 2 | Summary of the spatial integration results. Market Maize Sorghum Millet PI CI CONV DIV NI PI CI CONV DIV NI PI CI CONV DIV NI Abuja 29.23% 17.54% 11.70% 0.00% 41.53% 11.69% 11.69% 0.00% 0.00% 76.62% 35.08% 23.39% 0.00% 0.00% 41.53% Akure 5.84% 29.23% 11.70% 0.00% 53.23% 23.39% 5.84% 11.69% 0.00% 59.08% 5.84% 0.00% 0.00% 0.00% 94.16% Benincity 5.84% 35.08% 11.70% 0.00% 47.38% 5.84% 5.84% 0.00% 0.00% 88.32% 17.54% 5.84% 0.00% 0.00% 76.62% Calabar 23.39% 11.70% 0.00% 0.00% 64.91% 17.54% 0.00% 0.00% 0.00% 82.46% 0.00% 0.00% 40.93% 0.00% 59.07% Enugu 23.39% 17.54% 0.00% 0.00% 59.07% 5.84% 0.00% 0.00% 5.84% 88.32% 0.00% 0.00% 0.00% 0.00% 100% Gombe 0.00% 29.24% 5.84% 0.00% 64.92% 0.00% 17.54% 0.00% 0.00% 82.16% 5.84% 5.84% 0.00% 0.00% 88.32% Ibadan 17.54% 29.24% 0.00% 0.00% 53.22% 5.84% 11.69% 29.23% 5.84% 47.4% 5.84% 11.69% 0.00% 0.00% 82.47% Ilorin 11.70% 23.39% 5.84% 0.00% 59.07% 0.00% 0.00% 0.00% 0.00% 100% 23.39% 17.54% 0.00% 0.00% 59.07% Jos 17.54% 29.24% 5.84% 0.00% 47.38% 5.84% 23.39% 0.00% 5.84% 64.93% 5.84% 29.23% 0.00% 0.00% 64.93% Kaduna 11.70% 0.00% 5.84% 0.00% 82.46% 11.69% 40.93% 0.00% 0.00% 47.38% 11.69% 17.54% 0.00% 0.00% 70.77% Kano 23.39% 0.00% 11.69% 0.00% 64.92% 46.78% 11.69% 11.69% 0.00% 29.84% 11.69% 23.39% 0.00% 0.00% 64.92% Katsina 17.54% 0.00% 0.00% 0.00% 82.46% 0.00% 0.00% 0.00% 5.84% 94.16% 0.00% 23.39% 11.69% 0.00% 64.92% Lagos 29.23% 29.24% 11.69% 0.00% 29.84% 23.39% 5.84% 29.23% 0.00% 41.54% 46.78% 11.69% 0.00% 0.00% 41.53% Lokoja 5.84% 0.00% 17.54% 0.00% 76.62% 11.69% 11.69% 0.00% 0.00% 76.62% 0.00% 23.39% 0.00% 0.00% 76.61% Maiduguri 0.00% 0.00% 5.84% 11.69% 82.47% 0.00% 0.00% 0.00% 5.84% 94.16% 0.00% 5.84% 0.00% 0.00% 94.16% Makurdi 5.84% 11.70% 11.70% 0.00% 70.76% 5.84% 5.84% 0.00% 0.00% 88.32% 0.00% 11.69% 0.00% 0.00% 88.31% Portharcourt 23.39% 29.24% 0.00% 0.00% 52.37% 11.69% 23.39% 0.00% 11.69% 53.23% 5.84% 0.00% 0.00% 0.00% 94.16% Sokoto 17.54% 23.39% 17.54% 0.00% 41.53% 5.84% 23.39% 0.00% 5.84% 64.93% 29.23% 35.08% 23.39% 0.00% 12.3% Yola 0.00% 0.00% 5.84% 0.00% 94.16% 0.00% 0.00% 5.84% 0.00% 94.16% 0.00% 5.84% 0.00% 0.00% 94.16% Average 14.15% 16.62% 7.38% 0.62% 61.48% 10.15% 10.46% 4.61% 2.46% 72.29% 10.77% 13.23% 4.00% 0.00% 72.00% Note: Each cell in Table2 presents the number of markets that have a given type of integration with a given market divided by 18, which represents the total number of pairs in which this market participates. Only the last row contains the average percentages of 171 pairs. Abbreviations: CI, conditional integration; CONV, movement towards convergence; DIV, divergence; NI, nonintegration; PI, perfect integration. 1856 Review of Development Economics, 2025 in Nigerian sorghum markets. By looking at the integration of the Nigerian millet market, we report that 24% of the country's markets are integrated perfectly and conditionally, while 4% of the country's millet market moves towards convergence. Most markets appear to be perfectly integrated with Abuja and Lagos, while weakly integrated markets are located in Calabar, Enugu, Katsina, Lokoja, Maiduguri, Makurdi, and Yola. We observe that a significant fraction of market pairs, about 72%, are not integrated, providing evidence against the validity of the law of one price in Nigerian millet markets. Overall, one can reject the validity of the law of one price across Nigerian grain markets, corroborating the low level of integration within African countries evidenced in previous studies (Jayne, Myers, and Nyoro2008; Pierre and Kaminski 2019). Another important observation is that allowing for different classes of integration (conditional integration and movement towards integration) substantially increases the percentage of integrated market pairs. This suggests that previous studies examining the law of one price in its strong version (perfect integration) may ignore the possibility of different forms of convergence in the long run. Furthermore, we report that markets located in northeast Nigeria (Gombe, Maiduguri, Yola), which have been in a state of Boko Haram insurgency, lack integration with the rest of the country. In contrast, most regional markets are likely to be integrated with central markets of Abuja and Lagos are likely as they tend to be perfectly integrated with a maximum number of other regional grain markets, suggesting the relative importance of the geographical location of grain markets. 3.2 | Spillover Price Transmission Across Market Pairs Having established the degree of integration across market pairs, it is appealing for policy purposes to isolate individual market(s) that play(s) leadership position(s) in the formation and transmission of prices. It is reasonable to expect the leading role of Abuja and Lagos, given that these markets are fully integrated with a relatively higher number of local markets. To address the leading market possibilities, we investigate whether there is a volatility spillover across market pairs. Tables3–5 report the volatility spillover results across market pairs of maize, sorghum, and millet, respectively. Table 3 summarizes the estimation results of the spillover price transmission across maize market pairs. The findings show that for all market pairs involving Abuja and Lagos, the null hypothesis of no volatility spillover cannot be rejected at the conventional significance level. This indicates that the causality is unidirectional, with price volatilities in individual markets Granger causing prices in Abuja and Lagos. The lack of significant reverse causality from Abuja and Lagos towards the other markets provides evidence against the leadership position of these two markets. Another interesting finding is that the null hypothesis of no volatility is frequently rejected when considering the causality from Gombe, Kano, Maiduguri, and Yola to the other markets. This finding indicates that shocks to Gombe, Kano, Maiduguri, and Yola prices significantly affect prices in all markets. Given that these markets are located in the northeast of Nigeria except Kano, one might claim that the volatility of maize prices in the conflictaffected areas could act as a signal to other markets. This provides corroborative evidence about the potential effect of conflict on the transmission of volatility shocks across markets. In the case of sorghum price transmission across markets reported in Table4, the null hypothesis of no volatility spillover is significantly rejected when considering the causation from Kaduna and Sokoto to the other markets. For instance, there is evidence of unidirectional volatility spillover stemming from Kaduna to 12 local markets, including Abuja, Akure, Benincity, Calabar, Enugu, Gombe, Ibadan, Ilorin, Kano, Katsina, Lokoja, Makurdi. A similar pattern was observed from Sokoto to 13 markets, namely Abuja, Akure, Benincity, Calabar, Enugu, Gombe, Ilorin, Kano, Katsina, Lagos, Maiduguri, Makurdi, and Portharcourt. These findings emphasize the leading role of the Kaduna and Sokoto sorghum markets in predicting volatility in other markets. However, twoway volatility spillover causalities (feedbacks) are found to exist between Kaduna and Sokoto, indicating interdependence between these two leading markets. Put differently, the price in one market reacts to any price volatility in the other market. Furthermore, bidirectional spillover volatility is more common across individual markets involving Abuja and Lagos. For instance, the results indicate that causal feedback in eight pairs (i.e., Abuja—Benincity, Abuja—Kano, Abuja—Lagos, Akure—Enugu, Lagos—Akure, Lagos—Benincity, Lagos— Calabar, Lagos—Enugu), which is an indication of increased interconnectedness across sorghum markets. Considering the volatility spillover across millet markets, the results reported in Table 5 indicate that for all pairs, including Kaduna and Kano, we report a significant unidirectional spillover stemming from Kaduna and Kano to most of the remaining markets. For instance, we observe substantial volatility spillovers from Kaduna to 13 local markets, including Abuja, Akure, Benincity, Calabar, Enugu, Ibadan, Ilorin, Katsina, Lagos, Lokoja, Maiduguri, Makurdi, Portharcourt, and Sokoto. Similarly, unidirectional volatility was observed from Kano to 12 local markets, such as Abuja, Akure, Benincity, Calabar, Enugu, Ibadan, Jos, Katsina Lagos, Maiduguri, Makurdi, and Sokoto. The unidirectional volatility connectedness from Kaduna and Kano to the remaining markets indicates the leading role of these markets in predicting volatility in Nigerian millet markets. Interestingly, the results show high bidirectional volatility connectedness among millet prices in Kano and Kaduna. This suggests the interdependence between the two central markets in terms of volatility in the Nigerian millet market. It is also expedient to note that local markets exert a greater influence on the volatilities of prices in Abuja and Lagos, given the evidence of the oneway causality from other markets to Abuja and Lagos. This simply communicates that the millet market in Abuja and Lagos are net receivers of price volatilities and are more exposed to price shocks from other markets. We also report bidirectional volatility connectedness among seven market pairs, including Akure—Calabar, Akure—Katsina, Benincity—Calabar, Calabar—Portharcourt, Sokoto—Katsina, Sokoto—Lokoja, and Sokoto—Maiduguri. The bidirectional volatility connectedness among these pairs indicates that no individual price plays a leadership role.