Roads are predominantly used as mode of transport and form a strategic element for National development. Sub-Saharan African countries for example Ghana has invested in road transport infrastructure as it is a policy measure meant to revitalize regional growth and poverty reduction ( Boateng & Fricano, Adarkwa, 2015 ). Both pre and post-independence Kenya national development policies have emphasized on the need of investing in the transportation sector. The colonial policy commonly known as the Swynnerton plan ( Ministry of Agriculture and Water Resources, 1955 ) recommended investment in road sector in highlands zones mainly in central and rift valley regions which were occupied by white settlers. The settlers were mainly farmers and this policy strategy was seen as a measure of stimulating growth specifically in agriculture sector as it was the main economic activity. The first post-independence policy paper supported heavy investment on road network improvement viewed as a means a means of improving market access for most perishable goods ( Government of Kenya, 1965 ).

It is therefore imperative that there is clear link between road transport network distribution and regional growth. Road network provide good access which is the ability of citizens to interact freely with little or no friction ( Hassan, Wang, Khoo, & Foliente, 2017 ). The impact can be all economic, social or political. Economically good, reliable and affordable road transport network allows smooth flow of goods and services conveniently hence improving development ( Berg, Deichmann, Liu, & Selod, 2016 ). Socially the networks allow communities and citizens in general to move around the space and interact while creating social bonds ( Thynell, 2017 ). In the field of regional science road transport network are viewed as a means of improving spatial organization where activities are linked to each other ( Rodrigue & Ducruet, 2020 ).

Gross Domestic Product (GDP) is widely used as a measure of national development. In this study we adopt ( Frank, Bernanke, Osberg, Cross, & Macleen, 2003 ) definition of GDP which is the value of final goods and services produced by a country or region over a period of time which is mostly calculated by a given state on annual basis. The macroeconomic model used to calculate GDP is indicated in formula Equation 1 which is adopted from ( Mankiw, Kneebone, McKenzie, & Rowe, 2006 )

Equation 1: Gross Domestic Product Model

$Y=C+I+G+\left(e-i\right)$

Where Y = Gross Domestic Product

C = Consumption (expenditure goods and services)

I = Investment (expenditure on assets)

G = Governmnet Purchases

$\left(e-i\right)$ = netexport

In an empirical study using data from Russian Statistical Agency ( Sergei, Mikail, & Kudrov, 2018 ) identifies parameters used to calculate Gross Regional Product (GRP). The identified parameters are incomes from key production sectors Table 1 . These sectors are similar to the ones used to calculate Kenya’s Gross County product (GCP) which is an estimate of the size and structure of the forty-seven (47) county economies. GCP is what is international known as Gross Regional Product (GRP) ( KNBS, 2022 ) which is international used indicator of growth.

Both ( Mankiw, Kneebone, McKenzie, & Rowe, 2006 ) and ( Frank, Bernanke, Osberg, Cross, & Macleen, 2003 ) suggest that GDP is a good single measure of economic wellbeing of any society and is strongly correlated with the measure of quality of life. The GDP approach has a circular flow Figure 1 as adopted from ( Ragan & Lipsey, 2008 ). The flow indicates circulation of money which includes expenditure and income from all sectors of economy both government, households and private firms.

First we start by defining a region in the context of this study. We adopt ( Sergei, Mikail, & Kudrov, 2018 ) definition of a region which is a homogenous geographic area which has similar production factors. Regional economies which are used to measure the level of growth are quantified using Gross Regional Product (GRP) which is GDP at a lower level. In some countries for example India they use states and districts as planning regions ( Ohlan, 2012 ) and ( Kurian, 2000 ). In Kenya counties are used as regions where planning and implementation of development projects is mainly done. Kenya therefore has forty-seven (47) devolved planning regions in the name of counties ( Government of Kenya, 2010 ). The devolved units are meant to promote development and equitable sharing of national resources. The calculation of GRP is important since it used to assess revenue potential and used as an indicator of development progress over time ( KNBS, 2022 ).

In conclusion, development can be explained using regional macroeconomics models which incorporates dimension of space into analysis. Theoretical inputs of regional development are based on macroeconomics, trade theory which are expressed by mathematical formulae ( Capello, 2011 ) as shown in Equation 1. The concept of Gross Domestic Product (GDP) which is includes spending on all production sectors of a region ranging from mining, agriculture and service industry is a good denominator of regional development ( Aivazian, Afanasiev, & Kudrov, 2018 ). In this study the adoption of GCP which is GDP at the County level as an indicator was selected because the formulae used to calculate it is inclusive incorporating all sectors of development ( KNBS, 2022 ), ( Kurian, 2000 ). Using GDP to assess the impact of road infrastructure network investment which is evidenced in the network expansion is an approach which is well supported by several empirical studies ( Whittle, 2009 ), ( Nigohosyan & Vutsova, 2017 ), ( Aivazian, Afanasiev, & Kudrov, 2018 ). Supportive road infrastructure investment policy framework improves competiveness of a region by making it a locational choice. A negative loop is an outcome of unsupportive policy framework ( Figure 2 ).

Existing literature was selected specifically in studies where road transport was treated as an independent variable and regional development indicators treated as dependent variable. The reviewed documents included policy documents and scientific papers published in various journals and hardcopy textbook from the library. The first literature on attempt to calculate Kenya regions CDP was done by World Bank using night lights as proxy. The approach of using satellite data of night lights was developed by ( Henderson, Storeygard, & Weil, 2011 ) who argued that consumption of electricity is relative to disposable income by all contributors of GDP including households, firms and government entities. Areas with high intensity of night lights give an indication of a high CDP. We use the same approach where the heat map of existing road network is used as a proxy of regional development. We correlate the road infrastructure intensity data with GDP to assess the development patterns of various regions in this study the Kenya Counties and identify those that are lagging behind. This is approach is justified by ( Okrasińska & Wojewódzka-Król, 2018 ) who argues that the benefit of road infrastructure analysis should be done together with the GDP as it is a good indicator of regional growth which is combines all sectors economy of any given region ( Mankiw, Kneebone, McKenzie, & Rowe, 2006 ) and ( KNBS, 2022 ). GDP has been used to measure the growth in various regions.

The existing road network data for the year 2023 was sourced from Kenya Roads Board (KRB). The existing county boundary was sourced from Kenya Bureau of Statistics (KNBS) and later populated with macroeconomic data sourced from KNBS reports. Network density growth and distribution analysis was done using ArcGIS and Geoda mapping and visualization Apps. Supervised Self Organizing Maps (SOMs) were used to generate heat maps indicating the pattern and clustering of road density in various regions. Kernel density which is a function within Esri Armap GIS is used to calculate network density referred in this paper as Kennel density (KD) value. The formula is indicated below Equation 2 adopted from ( ESRI, 2023 ). Kernel density is used to generate a heat map indicating the general clustering of road network infrastructure on the Kenyan space. The density estimation method was pioneered by ( Siverman, 1986 ) and further published in his book ( Silverman, 1998 ).

Equation 2: Kernel Density Calculation, Source: ( ESRI, 2023 )

$\begin{array}{l}Density=\frac{1}{{\left(Radius\right)}^2}\underset{i=1}{\overset{n}{{\displaystyle \sum }}}\left\{\frac{3}{\pi }-po{p}_i{\left(1-{\left(\frac{dist{a}_i}{Radius}\right)}^2\right)}^2\right\}\\ Fordis{t}_i<radius\end{array}$

where

i = 1, …, n are the input points. only points in the sum if they are within the radius of the (x, y) location

Pop_i = the possible population field value of the point i, which is an operational parameter

dist_i = the distance between point i and the (x. y) location

To assess the spillover effect of road network infrastructure, spatial autocorrelation using Moran’s I index was applied. Spatial correlation is commonly used to assess the degree to which similar observation tend to occur near each other within regions as illustrated by ( Leitner, Glasner, & Ourania, 2018 ) in Figure 3 . This approach of describing the likelihood of a variable to relate to itself and its neighborhood in a region conforms to Tobler’s first law of geography which states ‘everything is related to everything else but near things are more related than distant things’ ( Tobler, 1970 ). Positive spatial autocorrelation is observed when similar values abuts each other. On the other hand, dispersed values are an indication of negative correlation ( Moraga, 2023 ) and ( Miller, 2004 ) as illustrated in Figure 3 .

Figure 3. Spatial autocorrelation configuration: (a) Positive correlation; (b) Negative correlation; (c) No correlation ( Leitner, Glasner, & Ourania, 2018 ).

Moran index was calculated using GIS software by converting the data into cells/grids with attribute values having the clustering of road network with Equation 2. The formula applied in Moran’s calculation is as shown in Equation 3.

Equation 3 Moran Index formula, Source: ( Leitner, Glasner, & Ourania, 2018 )

$I=\frac{{{\displaystyle \sum }}_{i=1}^n{{\displaystyle \sum }}_{j=1}^{n}wij\left(Xi-X\right)\left(X\ddot{J}-\ddot{X}\right)}{\left({{\displaystyle \sum }}_{i=1}^n{{\displaystyle \sum }}_{j=1}^{n}wij\right){{\displaystyle \sum }}_i^n\left(X-\ddot{X}\right)}$

n = number of observations (grid cells)

Xi = the grid or cell value of an attribute being

Xj = the grid or cell value of the same attribute at a different location

X = the mean value of the attribute of the cells being observed

Wij = sum of grids or grids with zero values

Wij = sum of cells/grids with zero values

A review of existing literature and theoretical frameworks gives a clear indication that there is a close relationship between road network infrastructure network distribution and regional development. A region’s total output depends positively on its infrastructure stock where road network takes a big share ( Arbues, Banos, & Mayor, 2015 ).

In summary, ( Bekisz & Kruszynski, 2021 ) observes that for any region to operate optimally, it must have a sound and reliable road transport t system. Existing studies which were reviewed have been summarized in the Table 2 below.

Table 2. Existing literature on development indicators.

Existing studies linking road transport network to development have been summarized in Table 2 . It can therefore be concluded a region’s road network infrastructure is directly correlated to its development.

In the review there are others measures of calculating regional growth but GDP is widely used.

The results from this section are for the data collected in 2023 by Kenya Roads Board. The heat map is therefore generated indicating the intensity of the road transport infrastructure network clustering within various regions. The network is clustering around central region and the white highlands which are rich agriculturally and located in lower North Rift and Mount Kenya region as indicated in Map 1 . This should have been an effect of the ( Ministry of Agriculture and Water Resources, 1955 ) policy which gave priority to investment in white

The spatial location of key contributors to the CDP econometric model is distributed randomly on the Kenyan space. The regions which are mostly homogenous in terms of natural resources are further divided into counties as administrative units. Each region is characterized by its production factors forming varied sectors ( Aivazian, Afanasiev, & Kudrov, 2018 ). The sectors are agriculture, fishing and forestry which contribute to the CDP sectors, others includes manufacturing, tourism, livestock production and mining ( KNBS, 2022 ).

Existence of reliable and accessible road transport infrastructure is an important policy tool that promotes regional growth while reducing disparity. The logic behind this argument is, existence of good road infrastructure network necessitates mobility. Mobility promotes trade while trade which is a stimulant of regional economic growth ( Elburz & Cubukcu, 2020 ). Governments formulates regional policies among them allocation of resources for road infrastructure development which enhance competiveness of region while attracting investors whose spillover effect is development ( OECD, 2009 ). This implies that areas with good road network will record a progressive regional development trend ( Rokicki & Stepniak, 2018 ).

From the above paragraph roads can be used as a good indicator of regional development, for the analyzed results which are presented here, road network density is therefore used as a proxy of regional development and disparity. Moran’s I index computation results which were calculated based on the heat map generated using Kernel Density approach will be presented. The presentation is based on how counties are distributed over Kenya classified into economic blocs ( State Department for Devolution, 2023 ). Coincidentally the economic blocs are related on the production sectors of the country ranging from agriculture, tourism, mining among others.

These are the counties which actively contribute to National GDP where agriculture, fishing and forestry are the main economic activities with a total of 20% ( KNBS, 2022 ). The counties include Meru, Nakuru, Murang’a, Nandi, Nyandarua, Kiambu, Bungoma, Kisii, Kakamega, Kericho, Bomet, Narok, Nyeri, TransNzoia, UasinGishu, Kirinyaga and Nyamira. Others include Homabay, Machokos, Migori, and Kisumu. Since Narok county is not in any of the trading blocs ( State Department for Devolution, 2023 ) it was included in lake region due its agricultural production. Agricultural products need to be transported to the market urgently since they are perishable hence require good road network.

The mountain region which is defined with Mount Kenya and Arbadare Ranges has the highest clustering of road network density. The clustering is uniform recording a maximum value of 1.690 kilometers of tarmac road per Km² spreading around Kiambu, Nakuru and Nyeri Municipalities. The intensity in heat map diminishes as you move towards Meru ( Map 2 ).

The lake region also depends on agriculture as indicated in ( KNBS, 2022 ) report on County Gross Product (CGP) report. The kernel density values ranges

The patch continuity indices for the two regions are 0.942 in Graph 4 and 0.674 in Graph 5 . Frontier region index is high and continuous patch of low network density implying there is less development.

The study contributes to the theory of regional development by giving an insight on how regional spatial metrics can be used to understand network growth and its impact on regional development. Pedagogical an integrated approach that includes geography theory, economic models and indicative maps have used which makes it easy to understand the distribution of network and add value to the lines which have always been used. We recommend more details study to link the road network work investment patterns vis-à-vis the politics and the role of executive in decision making when it comes to distribution of resources against constitutional requirements.