Examining the Regional Disparity of Agricultural Development: A Distribution Dynamics Approach

: Many scholars have argued that the increased disparity in agricultural development among countries is the crux of the regional inequality problem and exerts adverse effects on individuals’ well-being. This study thus aims to examine the distribution dynamics of global agricultural development. Speciﬁcally, it examines whether the disparity in agricultural development among countries vanishes over time and whether convergence can be achieved. On that account, a new distribution dynamics analysis method based on the stochastic kernel approach is employed at the country level. The proposed model can address the inadequacies of traditional econometric modelling methods and visualisation tools in the distribution dynamics literature. The research outcomes are as follows. Firstly, the global agricultural income disparity is primarily due to the Global South countries’ low


Introduction
The agricultural industry is a key enabler to the national socio-economic growth of a country by providing staple foods, non-staple foods, industrial raw materials, capital, and export materials for a wide range of upstream and downstream sectors.Given the rapid agricultural modernisation and technological advancements, the role of agriculture has become increasingly important in the national economy [1,2].However, the agricultural industry worldwide has been facing a host of challenges, mainly stemming from the fundamental changes in demographic and economic aspects.On the one hand, the Food and Agriculture Organisation (FAO) forecasts that the world population will increase by over one-third by 2050, reaching 10 billion people, adding substantial pressure on the food supply and posing a threat to food security.The FAO has made efforts to increase agricultural investment (Investment in this study refers to the inputs employed in a production process, usually referring to the physical capital stock such as land, equipment, machinery, storage facilities, livestock.Investment in agriculture refers to government and private expenditures investing in agricultural infrastructure, research and development (R&D) and education and training [3].) and improve the contribution of agriculture to the national economy [4][5][6][7].On the other hand, as countries worldwide are facing swift urbanisation and ageing population issues, the development of modern service and industrial sectors competes with agricultural production for investment and resource endowment [8,9].The fundamental solution to solving the structural conflicts between agriculture and the industrial and service sectors is to maintain an appropriate proportion of agricultural output value (PAOV) in the national economy, which can guarantee food security and bolster the overall development of the various economic sectors.
The PAOV is defined as the proportion of agriculture's gross output value relative to the national economy's gross output value [10].Ex post evidence from global agricultural development shows that the PAOV at different stages in different countries shows varied characteristics, dynamics, and patterns.In developed countries, the agricultural structure is usually characterised by adapting to the domestic population's consumption structure and boosting economic development.Guided by this reasonable goal of agricultural development, a reasonable PAOV would be driven by the joint forces of marketand policy-based strategies to fully consider industry-determinant factors, such as natural resource endowment, socio-economic and technological levels, population, and demand preference [1,11,12].For example, the US economy experienced a fundamental transition from an agriculturally dominant economy to an industrially dominant one and then to a service-oriented economy.PAOV was reduced substantially from nearly 90% to approximately 1% due to these transitions.However, despite its lower PAOV compared to the world average, the US remains one of the top agricultural producing and exporting countries in the world, and its agriculture industry still supports the development of the secondary and tertiary sectors [13].
Conversely, developing the agricultural industry in developing countries has been challenged by prominent problems, such as the low conversion and processing rate of agricultural products, urban-rural dual structural conflicts, and unbalanced sectoral structures.For example, in the early stages of industrial transformation, China planned to increase the weight of the secondary industry in the national economy through an array of preferential and supporting policies.This industrial-oriented development strategy stunted the growth of the agriculture industry.It resulted in an "urban-rural dual economic structure," namely slow agricultural development and a rapidly falling PAOV, compensated by rapid industrial development and modernisation.China's unreasonable agricultural structure has become one of the most concerning issues for food security due to the unbalanced agricultural product imports and backward agricultural technology, among others [14].
A reasonable PAOV ensures food security and a collaborative and sustainable national economy.It is also the core of an agricultural economic development strategy promoting agricultural production capacity and technology modernisation [15].Therefore, a systematic and in-depth review, exploration, and summary of the PAOV patterns in global countries are of great significance to shed light on the state and position of agriculture development and formulate policies to promote agricultural development and modernisation.
An increasing number of studies have investigated the determinants of PAOV or the impact of changes in PAOV.However, little focus has been placed on whether the disparity in PAOV among nations disappears and whether convergence is possible over time.The concept of convergence stems from the literature on economic growth [16].Such a concept has been applied to various research fields, such as energy economics [17,18] and development study [19].Convergence in growth refers to reducing the disparity among different groups, regions or countries [16].The subject of convergence research is essential for determining the present condition and the national policy and intergovernmental cooperation plans to rationalise the PAOV.Nevertheless, existing research does not provide policymakers with country-level estimates of the global agricultural supply market dynamics.Noting the literature gaps regarding the convergence of PAOV across countries, this study investigates the evolutionary characteristics and pattern of PAOV at the global level to better understand its dynamics.To this end, a country-level transitional dynamics analysis is performed using the distribution dynamics approach to answer the following questions: (i) How many types of PAOV evolution patterns exist worldwide?(ii) Given the different resource endowments and economic development, what is the PAOV trend for each group of countries?(iii) Finally, what is the optimal PAOV for each group of countries?The research outcomes shed light on the status of PAOV distribution across time and future PAOV evolution distribution patterns.The mechanism can be observed by MPP and understand the underlying trend of the changes in the shape of the distribution.Complementing existing studies, the information provided by this study offers another perspective from a viewpoint other than econometrics.
Convergence research is of significant policy implication, as it maps out the current status, possible trends and patterns and enables the formulation of policy to rationalise the agriculture structure in a country [16][17][18].This research is valuable, as, on the one hand, it can provide a complete and comprehensive understanding of the PAOV evolutionary patterns and characteristics.This information can help policymakers formulate development policies for the agricultural sector to prioritise preferential and supportive policies accordingly.On the other hand, this study can also depict the future trajectory of country-level PAOV.Thus, it can offer pragmatic policy suggestions to the governments for allocating resources to promote the rationalisation of PAOV transitions, particularly for those regions with outdated and imbalanced PAOV.Overall, the quantitatively based reference provided by this study helps policymakers formulate policies to assist in the development of agriculture for each group and type of country.
The contributions of this paper are twofold.First, to the best of our knowledge, this is the first systematic study to explore the dynamics and evolutionary trend of PAOV at the global level by employing distribution dynamics analysis.We use the stochastic kernel approach to provide a complete and insightful picture of the PAOV convergence and dynamics worldwide.This visualisation of the global PAOV provides an in-depth and novel understanding of its underlying dynamics.The research findings fill a crucial gap in the literature by focusing on the evolution and the changes in the shape of the distribution of agricultural output, thereby providing new evidence that traditional econometric methods cannot obtain.Second, this study estimates the effect of income on the dynamic trend of PAOV at the global level.This information can reveal the relationship between wealth and PAOV in detail, and the results can shed light on the dynamics of the changes in PAOV for all the countries in the world.Third, the novel mobility probability plots (MPPs) are used in this work.The research outcomes can pinpoint the transformation mechanism within each grouping, and thus, a well-considering policy can be designed to promote agriculture development.

Literature Review
The dynamics and adjustment of agricultural structure lay the foundation for the overall development of a country.Through adjustment, the agricultural production can adapt to market demand, improve agricultural efficiency, increase farmers' incomes, and realise sustainable development [20].Therefore, the evolution and dynamics of agricultural structures have drawn widespread concern.This work overlaps with three research areas: disparity of agricultural development and the associated causes; optimisation of agricultural structure; and the working mechanism of agricultural structural changes.
There are two definitions pertaining to agricultural structure in the literature.On the one hand, from an internal industry perspective, it refers to the proportion of the output value of various subsets of the agricultural industry, usually denoted as the change in the proportion of output value between planting and animal husbandry [10].For most countries, along with an increase in national income, the proportion of the planting industry will likely decrease, and that of animal husbandry will increase [21].An equilibrium between planting and animal husbandry ratios reflects the consumption structure, natural resource conditions, and economic development level of a country or region [22].However, there is also a reversal trend in the agricultural structure adjustment of some countries.For example, after the 1970s, to adapt to the rising demand in the global food market, the US abandoned its restrictive policy on grain production, resulting in the proportion of the planting industry slightly exceeding that of animal husbandry [13].On the other hand, the agricultural structure can also be defined from a macro perspective as the proportion of agricultural output value relative to the GDP.It is widely recognised that an effective agricultural structure should coincide with factor endowment, market maturity, scientific research level, and agricultural production technology [23][24][25][26][27][28].
Ex-post evidence of agricultural development recorded in the literature has provided mounting evidence on the vast disparity among regions, supranational and countries, particularly in the developing counties.For example, Swain et al. [29] analysed the computed agricultural development indices for different districts (i.e., Balasore, Cuttack, Puri and Ganjam) of Orissa in India and revealed that the four coastal districts are agriculturally more advanced than other districts.Ezcurra et al. [30] examined the territorial imbalances in European agriculture during the period 1980 to 2001 and found that the regional distribution of productivity is characterised by the presence of positive spatial dependence.Many methods have been used to test the convergence hypothesis in India.However, these studies provide inconclusive findings.On the one hand, the seminal works of Dholakia [31] and Cashin and Sahay [32] tested conditional convergence and absolute convergence by including many substitute variables and observed the conditional convergence of states.On the other hand, Bajpai and Sachs [33], Rao et al. [34], and Singh et al. [35] claimed that there were differences between countries in the post-independence era.Using the generalised moment method, Nayyar [36] confirmed that there is no evidence of any convergence in growth among Indian states.Apart from testing the convergence hypothesis in India, a growing number of studies have investigated the status of regional disparities in China by using different methods and indicators.For example, Wang and Yang [37] calculated and visualised the dynamic evolution characteristics of China's agricultural total factor productivity.Zhang and Ouyang [38] estimated the development level of regional agricultural and rural modernisation in China through dynamic factor analysis.They divided it into four levels, i.e., excellent, good, general and poor.The empirical results support a general consensus that China's agricultural development follows a characteristic of "adjacency dependence", which leads to a relatively small probability of the "spillover effect" to bolster the transfer and diffusion of agricultural technology and endowments across different regions [39,40].
Other works in the literature have investigated the causes of agricultural disparity, backwardness or agricultural crisis.For example, Narayanamoorthy [41] believes that the decline in wheat and rice production is not due to technical fatigue but to extensive single-crop planting, heavy use of chemical fertilisers, and incorrect agricultural pricing.Raman [42] argues that extensive cultivation has led to decreased productivity due to the intensive use of fertilisers, resulting in increased cost of inputs, ultimately leading to decreased profit margins.Ecological factors, which include decreasing land quality and water resources, adversely impact agricultural productivity due to intensive chemical and fertiliser use.Socio and cultural factors, such as the effects of globalisation and urban culture on villages, have shown an impact on health and education consciousness in rural agrarian families; to gain access to better facilities, farmers have improved their cropping pattern [42,43].To sum up, the relevant literature finds that an array of factors is the primary cause of agricultural disparity, backwardness or agricultural crisis.These include technological, ecological, socio-cultural and policy-related factors (e.g., Raman [42]; Chand [44]).
The influence of agricultural structure lies in the following two aspects.First, a reasonable or effective PAOV can guarantee food security under the unexpected impacts of natural and man-made shocks, such as natural disasters or grain trade sanctions [22,45].Simultaneously, the agricultural structure of a country must be adapted to the consumption structure of its residents.Specifically, a reasonable agricultural structure can meet market demand and adapt to the structural changes in consumption characteristics [22].Second, a reasonable PAOV is conducive to raising farmers' incomes by increasing market transactions [46,47].Moreover, a reasonable PAOV obtained by encouraging the development of the agricultural industry and narrowing the gap between agriculture and the industrial and service industry is imperative to promote the coordinated development of multiple industries [21].
Regarding how PAOV is rationalised, there are differences between countries due to their varied natural conditions and socio-economic levels [37].For countries with good resource endowment, which can be expressed as "fewer people, more land," the top priority is to transform the resource advantage into a competitive advantage and coordinate the development of multiple sectors of the economy [38].For example, the development strategy of US agriculture has undergone four historical stages: laying equal emphasis on planting and animal husbandry; the dominance of animal husbandry in agriculture; the comprehensive development of agriculture, forestry, animal husbandry, and fishery; and the export-oriented development of the planting industry [48].The evolution and structural transition of the agricultural industry lead to a reasonable PAOV, which can adequately meet domestic demand, create job opportunities, and spur agricultural product exports [15,48].Conversely, for countries with poor resource endowment, or "more people, less land," promoting an effective PAOV transition refers to fully utilising the comparative advantages of agricultural development by adopting agricultural technology innovation.Consider Japan and the Netherlands as examples.Historically, as a country with few natural resources and a lack of cultivated land, Japan has ensured a high self-sufficiency of its agriculture by restricting the import of advantageous agricultural products and improving the technical levels of greenhouse and automatic cultivation [15,49].The Netherlands has fully used the comparative advantages of its agricultural products and improved agricultural production's scientific and technological content.The Netherlands prioritises the development of animal husbandry and horticulture by encouraging the imports of grain and oil crops, which are subject to high production costs and low quality [10].The country has thus achieved agricultural structure transition, solving the problem of food shortage [10] and creating an agricultural trade surplus as a sizeable agricultural export country [25,26].
In sum, agricultural structure and PAOV have attracted substantial attention in the literature and have extensive achievements.However, there are still some limitations to be addressed.First, against economic globalisation, the evolution of the agricultural structure in various countries closely relates to the development of world agriculture.However, extant studies mainly focused on individual countries, with relatively limited research on the evolution trend of the global agricultural structure.As such, this study, as one of the first pertaining to the PAOV dynamics at the global level, expands the research on the agricultural structure dynamics and evolution patterns.Second, whether PAOVs of different countries will converge over time is an essential topic that has not been discussed in detail, and this is the question to be addressed in this study.Third, traditional models generally overlook critical information on multimodal distribution and, thus, cannot provide an informed insight into the integral shape of the distribution or its dynamics.

Data and Method
The dataset used in this study comes from the World Development Indicators provided by the World Bank.For the stand of convergence study, most research use nominal instead of real values (e.g., Bernard and Jones [50]; Cheshire and Magrini [51]; Cheong and Wu [17]).Therefore, the value added to the agricultural sector is divided by the population of each country to calculate the agricultural sector income per capita.Longitudinal data are required to perform distribution dynamics analysis, which is an important issue because the omission of a country in a given year may result in abrupt changes in the distribution, thereby providing inaccurate information on the dynamics of the distribution.Therefore, the data are collected from the same countries throughout the study period.Some countries are excluded from the study due to the unavailability of data.The research period is 18 years, from 2000 to 2017.The agricultural sector income of each country is then transformed into a relative value by first calculating the mean annual global agricultural sector income and then dividing the agricultural sector income of each country by this global average.The derived value is the country's relative agricultural sector income per capita (RAIPC).There are four stages of this study.First, a distribution dynamics analysis for the entire world is conducted.Second, data are divided into the Global North and the Global South.Distribution dynamics analysis is conducted individually to reveal the disparity between them; the findings clearly show the groups' polarisation.Third, for a more in-depth study of issues related to agricultural development, the data are divided into four income groups defined by the World Bank: low-income countries, lower-middleincome countries, upper-middle-income countries, and high-income countries.This helps reveal the relationship between income and agricultural development.Fourth, the data are separated into seven regions: East Asia and Pacific, South Asia, Europe and Central Asia, Middle East and North Africa, Sub-Saharan Africa, North America, and Latin America and the Caribbean.By conducting distribution dynamics for each of these smaller datasets, one can gain a comprehensive understanding of the characteristics of each subgroup.Moreover, the differences in the path of development of these countries can also be observed by comparing the findings derived from the distribution dynamics analysis.
This study is based on the transitional dynamics of the relative agricultural sector incomes of countries over time.Quah [52] first proposed distribution dynamic analysis to study economic problems and can be roughly divided into two related methods: the traditional Markov transition matrix analysis and the stochastic kernel method.These are useful tools for studying the evolution of distributions; therefore, they are called distribution dynamics analysis.
This approach focuses on the shapes of the distribution and the underlying trend behind the changes in shapes of the distribution across time.There are several stages in implementing distribution dynamics analysis.The distribution is first divided into several groups, and then the probability of moving from one group to another can be calculated based on historical data.After that, the probabilities of all the movements are used in the computation of the ergodic distribution, which is the steady state of the distribution in long run.
It is worth noting that while time series econometrics is often used for prediction, it can only provide single-value forecasts.Since all distributions are two-dimensional, it is not feasible to rely on time series econometrics to predict the shape of future distributions.Conversely, distribution dynamics analysis can offer crucial information on the future shape of a distribution and can show the emergence of convergence clubs and disparity in detail.Another important advantage of distribution dynamics analysis is that it can offer information on the movement of the entities within the distribution, thereby creating practical suggestions for policy formulation.Interested readers can refer to Silverman [53] for technical details.
In order to conduct the traditional Markov transition matrix analysis, one is required to separate the data into small groups so as to observe the movement of the entities amongst the groups; therefore, this procedure is plagued with the issue of demarcation of state, which is an arbitrary process.As a result, the stochastic kernel approach was developed to circumvent this problem, and thus, the grouping of the data can be carried out in an objective way.By objectively determining the grid line for the distribution dynamics analysis, the stochastic kernel approach is deemed more accurate and adopted in this study.
An estimator with a bivariate kernel was used and is represented by the following equation.
where h 1 and h 2 are the two bandwidth measures as defined by Silverman [53], K is the normal probability mass function, n is the sample size, x is a variable representing the relative agricultural income per capita for a country at time t, y is a variable representing the relative agricultural income per capita of that country at time t + 1, X i,t and X i,t+1 are the observed values at time t and time t + 1, respectively.This equation represents the kernel estimator, which can be derived by raw data; it is a three-dimensional relationship between the variables at time t and t + 1 as well as the occurrence which is represented by the height of the kernel.As a result, the higher the value of the kernel estimator, the higher the probability that the entities will move from the value of X i,t to X i,t+1 .
It is worth noting that socio-economic data are always extensive and the adaptive kernel with flexible bandwidth is used to take the sparseness of the data into consideration [53].The first-order process is assumed to be time invariant; therefore, the time t+τ distribution depends only on t but not on any other prior distribution.The relation between the distributions at time t and time t + τ can be expressed as where f t+τ (z) is the τ-period-ahead conditional density function of z conditional on x, g τ (z|x) is the transition kernel of probability that helps in mapping the distribution from time t to t + τ, and f t (x) is the kernel density function of the relative agricultural income per capita's distribution of at time t.This equation represents the evolution of the distribution from time t to time t + τ.At time t, the distribution is represented by a matrix denoted as f t (x), and then when the matrix of that distribution is multiplied by g τ (z|x), then the equation will generate f t+τ (z), which is a matrix representing the distribution at time t + τ.The ergodic density function, assuming that it exists, can be expressed as where f ∞ (z) is the probability mass function when τ is infinitely large.This reveals important insights for the evolution of distribution, as the ergodic distribution is the steadystate distribution in the long run.This equation can be derived by repeating the process of transition as shown in Equation ( 2), so it means that if the distribution as represented by a matrix f t (x) is multiplied by g τ (z|x) repeatedly, then the values of the matrix will become constant and this is f ∞ (z) which is the steady state distribution.The mobility probability plot (MPP) was proposed by Cheong and Wu [19] to display and interpret the probability of movement within a distribution.This is an important improvement of traditional display tools such as contour maps and plots in three dimensions.The net upward mobility probability of an entity, p(x), can be used to calculate the MPP as follows: The component before the minus sign, that is ∞ x g τ (z|x)dz, represents the sum of probabilities of moving upward from the current value x to other higher values, while the component x 0 g τ (z|x)dz represents the sum of probabilities of moving downward from the current value x to other lower values.Therefore, the difference between the two as represented by p(x) is the net probability of moving upward.
The MPP displays the likelihood of net upward mobility against the relative agricultural income per capita.It should be noted that a positive value indicates the country will have a higher tendency to move upwards in the future, while a negative value suggests the country has a higher tendency to move downwards within the distribution.Readers might see Cheong and Wu [19] for the technical information.
The MPP clearly observed the mechanism behind the changes in the shape of the final long-run distribution (that is the ergodic distribution).The shape of the ergodic distribution depends on the MPP since it measures the likelihood that the countries within the distribution will migrate.As a result, by observing the MPP, one can understand the movement of the countries across time and also gain relevant knowledge on the evolution and mechanism of the underlying trends.
It is worth noting that there are some differences between the distribution dynamics analysis and the traditional regression analysis.In order to observe the impacts of the variables of interest, one needs to incorporate them into the specification for the regression analysis as independent variables.However, for the distribution dynamics analysis, the impacts of the variables of interest are examined by separating the data into different groups, and comparisons are then made across the groups by observing the differences in the MPP and the shape of the ergodic distribution accordingly.

Results and Discussion
First, a distribution dynamics analysis will be conducted on the full dataset to gain an understanding of the overall trend.Then the data will be divided into several groupings to conduct a heterogeneity analysis.In order to see the heterogeneity, distribution dynamics analysis will then be carried out independently for each of these groupings.There are three kinds of groupings: the first one is the Global North and Global South, the second one is the levels of income (based on the World Bank's classification), and the last one is based on the geographical locations of each of the countries.All these analyses can reveal the heterogeneity across the groupings in detail, thereby unveiling the impacts of these factors accordingly.

All Countries
Stochastic kernel analyses are performed to derive the transitional dynamics for each country's agricultural sector.The contour maps of the transition probability kernel for the RAIPC of all nations are displayed in Figure 1a.The x-axis represents RAIPC values in period t.The y-axis represents RAIPC values at time t + 1.The width of the transition probability kernel for all countries is dispersed with the density mass concentrated along the 45-degree diagonal line, with two peaks: one at RAIPC value of 0.60 and another at RAIPC value of 1.15.While the two peaks are likely to be the clustering points for most countries in the future, the current distribution is widely dispersed from a low RAIPC of 0 to a high RAIPC of 2.5-3.0 times, as shown in Figure 1b.The RAIPC average is one since it is calculated in relation to the world average.As a result, a value less than one denotes a below-average RAIPC, whereas a value more than one denotes an above-average RAIPC.The concentration pattern in Figure 1 shows that most countries have below-average RAIPC values.In contrast, only a small number of nations have RAIPC values higher than the global average of 1.
Sustainability 2022, 14, 12779 9 of 24 average RAIPC values.In contrast, only a small number of nations have RAIPC values higher than the global average of 1.

North-South Divide
Figure 2a,b displays the contour maps of the Global North and Global South nations to compare their agricultural sectors.There is only one peak at the RAIPC value of 1.11 for Global North countries, indicating that agricultural sector income per capita tends to cluster among the level.Figure 2b shows the contour maps of Global South countries.Unlike the Global North, Global South countries' agricultural sector relative income changes may have two peaks: the first one at RAIPC of 0.64 and the second at RAIPC of 0.9.This contrast is also reflected in the range of the changes in the RAIPC values: the Global North has a wider range of income growth changes up to 3.5-4.0times, while the Global South has a narrower range of income growth changes up to 1.8-2.0times.With reference to all countries' agricultural sector income changes in Figure 1, Global North countries show productivity level increases in the agricultural sector, whereas Global South countries' patterns of productivity change vary significantly: some are higher than the world average, while the others have significantly lower relative rates.An ergodic distribution is adopted to estimate future income change trends to better understand future evolution patterns.Figure 3 shows the long-run distribution of agricultural sector income changes for all countries (see Figure 3a), Global North (see Figure 3b), An ergodic distribution is adopted to estimate future income change trends to better understand future evolution patterns.Figure 3 shows the long-run distribution of agricultural sector income changes for all countries (see Figure 3a), Global North (see Figure 3b), and Global South countries (see Figure 3c).The horizontal axis displays RAIPC values, whereas the vertical axis represents probability density.The ergodic distribution for the RAIPC of all countries with annual transitions in Figure 3 provides a side view of the three-dimensional plot of the transitional probability kernel for the RAIPC of countries' agricultural sectors.Convergence clubs can be observed for all three country types.For all countries, the highest and second highest convergence clubs are at RAIPC of 0.60 and RAIPC of 1.15, respectively.For Global North countries, there is only one convergence club at RAIPC of 1.11.For Global South countries, the three convergence clubs are situated at RAIPC values of 0.64, 1.21, and 2.39.It is noteworthy that the variations in Global South countries' convergence clubs are more significant than those of Global North countries and all countries.
Sustainability 2022, 14, 12779 11 of and Global South countries (see Figure 3c).The horizontal axis displays RAIPC value whereas the vertical axis represents probability density.The ergodic distribution for th RAIPC of all countries with annual transitions in Figure 3 provides a side view of th three-dimensional plot of the transitional probability kernel for the RAIPC of countrie agricultural sectors.Convergence clubs can be observed for all three country types.Fo all countries, the highest and second highest convergence clubs are at RAIPC of 0.  While the ergodic distribution in Figure 3 shows the emergence of convergence club the mobility of countries is not known.Although one can examine the probability ma distribution in the three-dimensional plot and the contour maps, it is difficult to discer the most significant portion of the probability mass.The new MPP framework can effe tively tackle this problem and offer a direct interpretation of the probability mass.Figu 4 displays the MPP on the distributions of the probability mass.The horizontal axis di plays RAIPC values, and the vertical axis displays net upward mobility (%).The mobilit probability plots for the RAIPC of all countries with annual transitions in Figure 4 pro vides a dynamic view of the transitional probability kernel for the RAIPC of countrie agricultural sector in evolution over time.Specifically, Figure 4a indicates that the MP for all countries is above 0 if the current relative rate is below RAIPC of 0.38.It is the below 0 for countries' agricultural sector income relative rates ranging from RAIPC of 0.3 to RAIPC of 6.18.However, for a relative rate of the agricultural sector income ratio from RAIPC of 6.18 to 9.01 times, the MPP lies above 0, which shows a net probability of movin upwards.Afterwards, it again displays a net tendency of moving downwards in the com ing periods for an agricultural sector income relative rate greater than RAIPC of 9.01.Th distribution suggests that countries will have a net probability of a downward trend While the ergodic distribution in Figure 3 shows the emergence of convergence clubs, the mobility of countries is not known.Although one can examine the probability mass distribution in the three-dimensional plot and the contour maps, it is difficult to discern the most significant portion of the probability mass.The new MPP framework can effectively tackle this problem and offer a direct interpretation of the probability mass.Figure 4 displays the MPP on the distributions of the probability mass.The horizontal axis displays RAIPC values, and the vertical axis displays net upward mobility (%).The mobility probability plots for the RAIPC of all countries with annual transitions in Figure 4 provides a dynamic view of the transitional probability kernel for the RAIPC of countries' agricultural sector in evolution over time.Specifically, Figure 4a indicates that the MPP for all countries is above 0 if the current relative rate is below RAIPC of 0.38.It is then below 0 for countries' agricultural sector income relative rates ranging from RAIPC of 0.38 to RAIPC of 6.18.However, for a relative rate of the agricultural sector income ratio from RAIPC of 6.18 to 9.01 times, the MPP lies above 0, which shows a net probability of moving upwards.Afterwards, it again displays a net tendency of moving downwards in the coming periods for an agricultural sector income relative rate greater than RAIPC of 9.01.The distribution suggests that countries will have a net probability of a downward trend if their current agricultural sector income relative rates are between RAIPC values of 0.38 and 6.18 or above RAIPC of 9.01.
times.Afterwards, it lies below the horizontal axis and goes down to RAIPC 5.70 times.should be noted that Global North countries with agricultural sector income growth from RAIPC of 5.71 to RAIPC of 8.90 times have a net tendency to move upwards before th trend turns negative again.For Global South countries, in Figure 4c, the MPP lies abov the horizontal axis from the intersection point of 0.39 until 0.61.Afterwards, the overa trend is downwards.The difference between the MPP of Global North and Global Sout countries suggests that, in the long run, more efforts are required to aid Global Sout countries, as their convergence club is more likely to be identified at the lower peak, tha is, around RAIPC of 0.6.However, they may have another convergence club at RAIPC o 1.15 because the MPP is above 0 from RAIPC of 0.82 to RAIPC of 1.19.Since the Globa North countries' convergence club is at RAIPC of 1.11, which is larger than the worl average, these countries have the responsibility to help Global South countries achiev more balanced and inclusive growth in their agricultural sectors.

Income Division
While the Global North and Global South represent developed and developing coun tries, they can be separated into various income classes to explore the source of incom disparity further.We follow the World Bank's classification and use four income group low-, lower-middle-, upper-middle-, and high-income countries.Global South countrie consist of low-income and lower-middle-income countries.Figure 5a shows the contou maps of low-income countries, with twin peaks indicating that income growth in suc countries is clustered in two groups and the stochastic transition probability kernel of in come relative rates ranging from RAIPC of 0.1 to RAIPC of 0.9. Figure 5b shows the con tour maps of the lower-middle-income countries, with the stochastic transition probabilit In Figure 4b, the MPP for Global North countries remains above the horizontal axis, with a relative rate of the agricultural sector income from RAIPC values of 0.28 to 1.08 times.Afterwards, it lies below the horizontal axis and goes down to RAIPC 5.70 times.It should be noted that Global North countries with agricultural sector income growth from RAIPC of 5.71 to RAIPC of 8.90 times have a net tendency to move upwards before the trend turns negative again.For Global South countries, in Figure 4c, the MPP lies above the horizontal axis from the intersection point of 0.39 until 0.61.Afterwards, the overall trend is downwards.The difference between the MPP of Global North and Global South countries suggests that, in the long run, more efforts are required to aid Global South countries, as their convergence club is more likely to be identified at the lower peak, that is, around RAIPC of 0.6.However, they may have another convergence club at RAIPC of 1.15 because the MPP is above 0 from RAIPC of 0.82 to RAIPC of 1.19.Since the Global North countries' convergence club is at RAIPC of 1.11, which is larger than the world average, these countries have the responsibility to help Global South countries achieve more balanced and inclusive growth in their agricultural sectors.

Income Division
While the Global North and Global South represent developed and developing countries, they can be separated into various income classes to explore the source of income disparity further.We follow the World Bank's classification and use four income groups: low-, lower-middle-, upper-middle-, and high-income countries.Global South countries consist of low-income and lower-middle-income countries.Figure 5a shows the contour maps of low-income countries, with twin peaks indicating that income growth in such countries is clustered in two groups and the stochastic transition probability kernel of income relative rates ranging from RAIPC of 0.1 to RAIPC of 0.9. Figure 5b shows the con-tour maps of the lower-middle-income countries, with the stochastic transition probability kernel of income relative rates ranging from RAIPC of 0.1 to RAIPC of 1.6.The width of the transition probability kernel for both low-income and lower-middle-income countries is dispersed, with the density mass concentrated along the 45-degree diagonal line.Hence, there is no significant difference in the clustering of agricultural income change between low-income and lower-middle-income countries, as both groups have one peak below 1 and another slightly above 1.
Sustainability 2022, 14, 12779 13 of 24 kernel of income relative rates ranging from RAIPC of 0.1 to RAIPC of 1.6.The width of the transition probability kernel for both low-income and lower-middle-income countries is dispersed, with the density mass concentrated along the 45-degree diagonal line.Hence, there is no significant difference in the clustering of agricultural income change between low-income and lower-middle-income countries, as both groups have one peak below 1 and another slightly above 1.
(a) (b)  Global North countries consist of upper-middle-income and high-income countries.Figure 6a shows the contour maps of the upper-middle-income countries, with the stochastic transition probability kernel of income relative rates ranging from RAIPC of 0.1 to RAIPC of 3.0, which is much wider than that of low-and lower-middle-income countries.Figure 6b shows the contour maps of high-income countries.The location of two peaks is similar to that of low-income countries: one peak below 1 and another above 1.This result requires further investigation of the different groups of countries' evolutionary patterns, as the stochastic transition probability kernel of income relative rates range from RAIPC of 0 to RAIPC of 4, which is the widest range.
Sustainability 2022, 14, 12779 14 of 24 Global North countries consist of upper-middle-income and high-income countries.Figure 6a shows the contour maps of the upper-middle-income countries, with the stochastic transition probability kernel of income relative rates ranging from RAIPC of 0.1 to RAIPC of 3.0, which is much wider than that of low-and lower-middle-income countries.Figure 6b shows the contour maps of high-income countries.The location of two peaks is similar to that of low-income countries: one peak below 1 and another above 1.This result requires further investigation of the different groups of countries' evolutionary patterns, as the stochastic transition probability kernel of income relative rates range from RAIPC of 0 to RAIPC of 4, which is the widest range.Figure 7 shows the long-run distribution of agricultural sector income changes for lowincome (see Figure 7a), lower-middle-income (see Figure 7b), upper-middle-income (see Figure 7c), and high-income countries (see Figure 7d).The horizontal axis displays RAIPC values, whereas the vertical axis represents probability density.The ergodic distribution by income groups with annual transitions in Figure 7 provides a side view of the threedimensional plot of the transitional probability kernel for countries' agricultural sector by income groups.For low-income countries, the twin peaks are at RAIPC of 0.50 and RAIPC of 1.08.The twin peaks for lower-middle-income countries are at RAIPC of 0.66 and RAIPC of 1.01, while that for upper-middle-income countries are at RAIPC of 1.50 and RAIPC of 2.47, both being above 1.The twin peaks for high-income countries are at RAIPC of 0.73 and RAIPC of 1.11.By comparing Figure 7a-d, the highest peaks of most income groups are situated around 1 (except for upper-middle-income countries).However, the second highest peaks (far below 1) can be found in low-income, lower-middle-income, and high-income countries; this implies that the middle-income trap seems to apply to the agricultural sector, although upper-middle-income countries may not be affected, as they have peaks that are significantly larger than 1.
Sustainability 2022, 14, 12779 15 of 24 Figure 7 shows the long-run distribution of agricultural sector income changes for low-income (see Figure 7a), lower-middle-income (see Figure 7b), upper-middle-income (see Figure 7c), and high-income countries (see Figure 7d).The horizontal axis displays RAIPC values, whereas the vertical axis represents probability density.The ergodic distribution by income groups with annual transitions in Figure 7 provides a side view of the three-dimensional plot of the transitional probability kernel for countries' agricultural sector by income groups.For low-income countries, the twin peaks are at RAIPC of 0.50 and RAIPC of 1.08.The twin peaks for lower-middle-income countries are at RAIPC of 0.66 and RAIPC of 1.01, while that for upper-middle-income countries are at RAIPC of 1.50 and RAIPC of 2.47, both being above 1.The twin peaks for high-income countries are at RAIPC of 0.73 and RAIPC of 1.11.By comparing Figure 7a-d, the highest peaks of most income groups are situated around 1 (except for upper-middle-income countries).However, the second highest peaks (far below 1) can be found in low-income, lower-middleincome, and high-income countries; this implies that the middle-income trap seems to apply to the agricultural sector, although upper-middle-income countries may not be affected, as they have peaks that are significantly larger than 1.
( Regarding future evolution trends, Figure 8 displays the MPP for distributions of the probability mass by the different income groups.The horizontal axis displays RAIPC values, and the vertical axis displays net upward mobility (%).The mobility probability plots by income groups with annual transitions in Figure 8 provide a dynamic view of the transitional probability kernel for countries' agricultural sector evolution by income groups over time.From Figure 8a-c, the MPPs of low-, lower-middle, and upper-middle-income countries initially move in similar patterns, as the three MPPs are above 0 with the relative rate of agricultural income change up to 0.35; around the values of 0.35 to 0.91, the MPP of upper-middle-income nations remains positive, while low-and lower-middle-income nations have a tendency to move down if the RAIPC is larger than 0.35.However, for Regarding future evolution trends, Figure 8 displays the MPP for distributions of the probability mass by the different income groups.The horizontal axis displays RAIPC values, and the vertical axis displays net upward mobility (%).The mobility probability plots by income groups with annual transitions in Figure 8 provide a dynamic view of the transitional probability kernel for countries' agricultural sector evolution by income groups over time.From Figure 8a-c, the MPPs of low-, lower-middle, and upper-middle-income countries initially move in similar patterns, as the three MPPs are above 0 with the relative rate of agricultural income change up to 0.35; around the values of 0.35 to 0.91, the MPP of upper-middle-income nations remains positive, while low-and lower-middle-income nations have a tendency to move down if the RAIPC is larger than 0.35.However, for income change rates falling between RAIPC of 0.35 and RAIPC of 0.64, there is a net probability of moving upwards in the distribution for both lower-and upper-middleincome countries but not for low-income countries.The distribution moves upwards again, with MPP values ranging from RAIPC of 0.65 to RAIPC of 0.84 for the three groups of countries.The MPP of low-income countries turns positive from RAIPC of 0.90 to RAIPC of 1.10 and negative afterwards.The MPP of lower-middle-income countries turns positive from RAIPC of 0.84 to RAIPC of 1.10 and falls below 0 afterwards, while that of upper middle-income countries turns positive from RAIPC of 1.04 to RAIPC of 1.21 and then turns negative from RAIPC of 1.22 to RAIPC of 1.96 and rises above 0 from RAIPC of 1.97 to RAIPC of 2.47, before finally dropping to below 0. The MPP of high-income countries has a different pattern.It is positive if the MPP ranges up to RAIPC of 0.69 and then turns negative from RAIPC of 0.70 to RAIPC of 5.95.Afterwards, it turns positive again from RAIPC of 5.96 to RAIPC of 8.97 before it falls below 0. Compared with other income groups, high-income countries have a wider range of fluctuation in their MPP values.

Division by Region
To further reveal the impact of geographical location on the distribution dynamics of the agricultural sector, Figure 9 displays the regional distributions of the seven regions, namely East Asia and Pacific, South Asia, Europe and Central Asia, Middle East and North Africa, Sub-Saharan Africa, North America, and Latin America and the Caribbean.Four regions (East Asia and Pacific, Middle East and North Africa, North America, and Latin America and the Caribbean) have three peaks, two regions (South Asia and Sub-Saharan Africa) have two peaks, and one region (Europe and Central Asia) has one peak only.Five regions (East Asia and Pacific, South Asia, Middle East and North Africa, Sub-Saharan Africa, and Latin America and the Caribbean) have peaks below 1, indicating these regions contribute to global inequality in the agricultural sector.The other two regions (Europe and Central Asia and North America) have a productivity advantage and can help bridge this gap.

Division by Region
To further reveal the impact of geographical location on the distribution dynamics of the agricultural sector, Figure 9 displays the regional distributions of the seven regions, namely East Asia and Pacific, South Asia, Europe and Central Asia, Middle East and North Africa, Sub-Saharan Africa, North America, and Latin America and the Caribbean.Four regions (East Asia and Pacific, Middle East and North Africa, North America, and Latin America and the Caribbean) have three peaks, two regions (South Asia and Sub-Saharan Africa) have two peaks, and one region (Europe and Central Asia) has one peak only.Five regions (East Asia and Pacific, South Asia, Middle East and North Africa, Sub-Saharan Africa, and Latin America and the Caribbean) have peaks below 1, indicating these regions contribute to global inequality in the agricultural sector.The other two regions (Europe and Central Asia and North America) have a productivity advantage and can help bridge this gap.
Figure 10 displays the ergodic distributions of agricultural sector income changes by region.The horizontal axis displays RAIPC values, whereas the vertical axis represents probability density.The ergodic distribution of the seven regions with annual transitions in Figure 10 provides a side view of the three-dimensional plot of the transitional probability kernel for the seven regions' agricultural sector.For East Asia and Pacific, the three convergence clubs are situated at RAIPC values of 0.71, 1.15, and 2.59.The twin convergence clubs for South Asia are located at RAIPC of 0.60 and RAIPC of 1.06.The only convergence club for Europe and Central Asia is located at RAIPC of 1.13.The three convergence clubs for the Middle East and North Africa are located at RAIPC values of 0.33, 0.93, and 1.27.The two convergence clubs for Sub-Saharan Africa are situated at RAIPC values of 0.41 and 1.17, while those for North America are at RAIPC of 1.44 and RAIPC of 1.67.The three convergence clubs for Latin America and the Caribbean are located at RAIPC values of 0.65, 1.25, and 2.26.It is worth noting that the highest convergence clubs are not from North America or Europe and Central Asia, whose agricultural sector productivity levels are generally higher than the world average, indicating that East Asia and Pacific (peak at RAIPC of 2.59) and Latin America and the Caribbean (peak at RAIPC of 2.26) have a good potential to increase their agricultural production income levels.Finally, Figure 11 displays the MPPs of agricultural sector income changes by The horizontal axis displays RAIPC values, and the vertical axis displays net upward mobility (%).The mobility probability plots of the seven regions with annual transitions in Figure 11 provide a dynamic view of the transitional probability kernel for the seven  Finally, Figure 11 displays the MPPs of agricultural sector income changes by region.The horizontal axis displays RAIPC values, the vertical axis displays net upward mobility (%).The mobility probability plots of the seven regions with annual transitions in Figure 11 provide a dynamic view of the transitional probability kernel for the seven regions' agricultural sector in evolution over time.Among the seven regions, Europe and Central Asia have the simplest form of the MPP curve: it intersects the x-axis only once such that the convergence club is clearly identified.East Asia and Pacific have the most sophisticated MPP curve, as it intersects the x-axis nine times and has wide MPP value fluctuations.The dynamic pattern of East Asia and Pacific's future evolution trend suggests that this region's agricultural productivity should be increased, which is in line with its population density as well as the projection of its economic status in the 21st century.

Conclusions
The study aims to explore the global and regional disparity of agricultural development, taking as measurable indicator.The analysis is based on country-level panel data covering global countries and spanning the period between 2000 and 2017.the novel distributional dynamics approach is introduced to the agricultural study to estimate each country's evolutionary trend and dynamic movement within the distributions in different groupings.The research findings reveal that there are remarkable divergences across countries, over time, within different groupings.
New Structural Economics "postulates that the economic structure of an economy is endogenous to its factor endowment structure and that sustained economic development is driven by changes in factor endowments and continuous technological innovation."[54].As such, the Global South/developing countries without competitive advantage in industrial/manufacturing sectors should make the best use of their existing factor endowment structure, thereby gradually upgrading its economic structure from where labour and natural resources are relatively abundant to where capital is relatively abundant [54].This study contributes to the literature by supplementing empirical evidence of the development pathways, which has implication for decision makers of countries at different development stages to upgrade their agricultural and overall economic productivity.
Several key findings have been received from this study.To reduce poverty and hunger and narrow the north-south divide, Global South countries need more fiscal and financial aid to boost their agricultural sector productivity.As Global South countries showed lower convergence clubs in their evolutionary trends, it is essential to subsidise their agricultural sectors.Global North countries should help them achieve more balanced and inclusive growth for agricultural modernisation to meet United Nations' sustainable development goals.Specifically, the agricultural sector income disparities are largely due to the Global South countries' convergence club at RAIPC of 0.64, which lowers the world average.Regarding income division, except for upper-middle-income countries, all other income groups have convergence clubs larger or smaller than 1.However, upper-middleincome countries have convergence clubs larger than 1, indicating the invalidity of the middle-income trap for these countries' agricultural sectors.This finding is interesting, as it may suggest that more investment to promote agricultural productivity can be conducive to the trap.Productivity, coming from economics, is commonly used to measure output per input unit [55].Regional disparity measures the economic difference and uneven economic progress in different regions and groupings [56].The investment may take the forms of state procurement prices to subsidise farmers, a successful experience of rural reforms and agricultural growth in China [57], or public investment such as education, agricultural research and development, rural infrastructure including roads, electricity, and telecommunications [58].Institutional reform is also conducive to the productivity growth of the agricultural sector [59,60].The findings of this research also echo the call for empirical evaluation of the most effective community-level governance mode in rural development for developing countries [61].
Geographically, Europe, Central Asia, and North America have a technological edge in the agricultural sector, with all their convergence clubs being situated above the global average.Hence, they can take more responsibility to aid the other five regions (East Asia and Pacific, South Asia, Middle East and North Africa, Sub-Saharan Africa, and Latin America and the Caribbean) in rebalancing their regional disparities.In particular, East Asia and Pacific has a significant potential to boost its agricultural sector productivity to tackle the world food supply issue and should thus be the focus of more capital inflows.
This study focuses on the changes in the shape of the distribution of agricultural output across time.This can complement existing studies by examining this issue from the perspective of distribution dynamics.However, it is also crucial to investigate the determining factors to understand the mechanism better; therefore, one future area of exploration is to conduct further empirical research based on the factors found to be important in this study.Furthermore, as this study is based on constant prices only, another angle worthy of further exploration is the impacts of purchasing power parity on the distribution dynamics if the data can be made available from the World Bank in the future.

Figure 1 .Figure 1 .
Figure 1.Contour map of the transitional stochastic kernel for RAIPC in the agricultural section of all countries (2000-2017).Source: authors' calculations.4.2.North-South Divide Figure 2a,b displays the contour maps of the Global North and Global South nations to compare their agricultural sectors.There is only one peak at the RAIPC value of 1.11 for Global North countries, indicating that agricultural sector income per capita tends to cluster among the level.Figure 2b shows the contour maps of Global South countries.Unlike the Global North, Global South countries' agricultural sector relative income

Figure 3 .
Figure 3.The ergodic distribution of RAIPC for all nations with yearly transitions (2000-2017 Source: authors' calculations.Note that the horizontal axis displays RAIPC values, whereas the ve tical axis represents probability density.(a) All countries, (b) Global North countries, (c) Glob South countries.

Figure 3 .
Figure 3.The ergodic distribution of RAIPC for all nations with yearly transitions (2000-2017).Source: authors' calculations.Note that the horizontal axis displays RAIPC values, whereas the vertical axis represents probability density.(a) All countries, (b) Global North countries, (c) Global South countries.

Figure 4 .
Figure 4. Mobility probability plots for the RAIPC of all countries with annual transitions (200 2017).Source: authors' calculations.Note that the horizontal axis displays RAIPC values, and th vertical axis displays net upward mobility (%).(a) All countries, (b) Global North countries, ( Global South countries.

Figure 4 .
Figure 4. Mobility probability plots for the RAIPC of all countries with annual transitions (2000-2017).Source: authors' calculations.Note that the horizontal axis displays RAIPC values, and the vertical axis displays net upward mobility (%).(a) All countries, (b) Global North countries, (c) Global South countries.

Figure 10 Figure 9 . 40 Figure 10 .Figure 10 .
Figure 10 displays the ergodic distributions of agricultural sector income changes by region.The horizontal axis displays RAIPC values, whereas the vertical axis represents probability density.The ergodic distribution of the seven regions with annual transitions in Figure 10 provides a side view of the three-dimensional plot of the transitional probability kernel for the seven regions' agricultural sector.For East Asia and Pacific, the three convergence clubs are situated at RAIPC values of 0.71, 1.15, and 2.59.The twin convergence clubs for South Asia are located at RAIPC of 0.60 and RAIPC of 1.06.The only convergence club for Europe and Central Asia is located at RAIPC of 1.13.The three convergence clubs for the Middle East and North Africa are located at RAIPC values of 0.33, 0.93, and 1.27.The two convergence clubs for Sub-Saharan Africa are situated at RAIPC values of 0.41 and 1.17, while those for North America are at RAIPC of 1.44 and RAIPC of 1.67.The three convergence clubs for Latin America and the Caribbean are located at RAIPC values of 0.65, 1.25, and 2.26.It is worth noting that the highest convergence clubs are not from North America or Europe and Central Asia, whose agricultural sector productivity levels are generally higher than the world average, indicating that East Asia and Pacific (peak at RAIPC of 2.59) and Latin America and the Caribbean (peak at RAIPC of 2.26) have a good potential to increase their agricultural production income levels.

Figure 10 .
Figure 10.Ergodic distributions of the seven regions (2000-2017).Source: authors' calculations.Note that the horizontal axis displays RAIPC values, whereas the vertical axis represents probability density.(a) East Asia and Pacific, (b) South Asia, (c) Europe and Central Asia, (d) Middle East and North Africa, (e) Sub-Saharan Africa, (f) North America, (g) Latin America and the Caribbean.

Figure 11 .
Figure 11.Mobility probability plots for the seven regions (2000-2017).Source: authors' calculations.Note that the horizontal axis displays RAIPC values, and the vertical axis displays net upward mobility (%).
60an RAIPC of 1.15, respectively.For Global North countries, there is only one convergenc club at RAIPC of 1.11.For Global South countries, the three convergence clubs are situate at RAIPC values of 0.64, 1.21, and 2.39.It is noteworthy that the variations in Global Sout countries' convergence clubs are more significant than those of Global North countrie and all countries.
Sustainability 2022, 14, 12779 16 of 24 income change rates falling between RAIPC of 0.35 and RAIPC of 0.64, there is a net probability of moving upwards in the distribution for both lower-and upper-middle-income countries but not low-income countries.The distribution moves upwards again, with MPP values ranging from RAIPC of 0.65 to RAIPC of 0.84 for the three groups of countries.The MPP of low-income countries turns positive from RAIPC of 0.90 to RAIPC of 1.10 and negative afterwards.The MPP of lower-middle-income countries turns positive from RAIPC of 0.84 to RAIPC of 1.10 and falls below 0 afterwards, while that of upper middleincome countries turns positive from RAIPC of 1.04 to RAIPC of 1.21 and then turns negative from RAIPC of 1.22 to RAIPC of 1.96 and rises above 0 from RAIPC of 1.97 to RAIPC of 2.47, before finally dropping to below 0. The MPP of high-income countries has a different pattern.It is positive if the MPP ranges up to RAIPC of 0.69 and then turns negative from RAIPC of 0.70 to RAIPC of 5.95.Afterwards, it turns positive again from RAIPC of 5.96 to RAIPC of 8.97 before it falls below 0. Compared with other income groups, highincome countries have a wider range of fluctuation in their MPP values.