Micro- and Macro-Level Investigations of the Impacts of Transportation Infrastructure on Agricultural Gross Income in South Korea

Abstract

This study aims to investigate a fundamental yet largely overlooked question: “Does investing in transportation infrastructure positively impact farms’ agricultural gross income?” It is examined based on the role of transportation infrastructure in ensuring equal access to market opportunities in the context of the widening regional economic disparity in Korea. The main novelty of this study lies in its attempt to introduce an accessibility measure for evaluating the benefits of transportation infrastructure in a rural setting, which has been limitedly applied in urban-centered studies. To accomplish this task, multilevel and spatial econometric models were employed to evaluate the ex-post impact of transportation accessibility on agricultural gross income from the perspectives of farmers, primarily, and rural autonomies, subsequently. This study found that the continuation of the current direction of transportation policy—without substantial consideration for agriculture as an industry and rural areas as living spaces—can intensify the economic alienation of agriculture and rural areas. This study concludes that opportunities for market access provided by the immense public investments in transportation infrastructure should be fairly distributed to farmers and rural autonomies to promote balanced regional development in Korea.

1. Introduction

Access to reliable, well-connected transportation infrastructure is a cornerstone of economic activities. Transportation infrastructure not only facilitates a cost-effective production process by lowering transportation costs and increasing mobility but also eliminates geographic barriers to competition. Since the pioneering work by Aschauer [1], the contribution of transportation infrastructure to economic growth has long been debated; however, overall empirical findings confirm the presence of a strong association between public investment in core infrastructure and economic growth.

In recent years, the value of transportation infrastructure has been estimated from the perspective of its role in reducing income inequality through generalized access to economic opportunities and social services. Evidence shows that public investment in transportation geared toward less-affluent individuals and underdeveloped areas reduces income disparities [2,3,4]. The expansion in transportation infrastructure connects economically weaker individuals to diverse economic activities and helps lower the production and transaction costs in rural areas. Therefore, investments in transportation infrastructure are often adopted by central governments as one of their key strategies for narrowing regional economic disparities.

In the agricultural sector, adequate and efficient transportation infrastructure is an indispensable factor on which farm products rely for the creation and preservation of their value [5]. The remoteness of rural communities highlights the potential of transportation infrastructure as an effective policy instrument to resolve problems associated with the ever-declining agricultural sector. Thus, investments in transportation infrastructure in rural regions are generally expected to be highly beneficial for the farmers. Despite a common belief regarding a positive association between the expansion of transportation infrastructure and agricultural income, a thorough establishment of such an association with empirical findings remains surprisingly underinvestigated.

This study aims to explore a fundamental yet underexplored question: “Does investment in transportation infrastructure result in a positive impact on farms’ agricultural gross income?” While much of the existing literature has examined productivity, poverty, welfare, or market participation, this study distinguishes itself by evaluating the role of transportation infrastructure in shaping farms’ agricultural gross income through the integration of farm-level microdata and district-level spatial models. This question is examined in relation to the role of transportation infrastructure in ensuring fair access to market opportunities in the context of the widening regional economic disparity in South Korea (hereafter referred to as Korea). As a quantitative indicator of the economic benefits of transportation infrastructure investment, this study adopts a utility-based accessibility measure. Accessibility is not only the ultimate aim of transportation policies but also a valid indicator commonly used to measure transportation equity [6,7]. Although there exists abundant literature on the impact of transportation infrastructure investment on economic growth, only a few studies have attempted to apply the accessibility concept [8]. To our knowledge, this study is the first to apply the accessibility measure for evaluating the benefits of transportation infrastructure investment in a rural setting.

In this study, multilevel and spatial econometric models are used to evaluate the ex-post impact of improved transportation accessibility on agricultural gross income in Korea from 2005 to 2020. By using the multilevel linear model, this study aims to contribute to the limited literature that attempts to verify the impact of infrastructure on micro-level economic agents, such as households. However, concerned with methodological aspects of individual- and contextual-level sources of bias, along with a micro-level analysis on farm households, a macro-level analysis on rural districts is conducted to cross-check the results and draw broader implications at a regional level.

2. Literature Review

2.1. Economic Impacts of Transportation Infrastructure

Generally, investments in public infrastructure are known to have a positive impact on national and regional economic development by increasing productivity. Aschauer’s seminal work incorporated publicly provided infrastructure into the production function model as an input and found that core public capital, including transportation infrastructure, had made a considerable contribution to increasing national productivity in the United States [1]. Subsequent studies have investigated the contribution of transportation infrastructure to the economy of a single country or a state, with a more elaborate methodology, and confirmed a positive association between the two [9,10,11]. Similarly, numerous empirical studies have recognized transportation infrastructure as a driver of regional economic growth, as it positively affects the expanding markets by lowering their production costs and facilitating economic activities. On the demand side, transportation infrastructure improves physical accessibility, thereby increasing demand for various products and services [12]. On the supply side, transportation infrastructure lowers production costs by mitigating storage and logistics expenses [13,14]. Furthermore, the expansion of transportation infrastructure improves interregional accessibility and increases flexibility in employment opportunities, particularly by enhancing multimodal connections across regions [15].

Despite proven effects, the interaction between transportation infrastructure and economic growth is complex. Several studies have presented contrasting views with empirical results that show the negative or insignificant effects of transportation infrastructure investments. Transportation infrastructure entails so-called “network effects” that occur when increased productivity in a beneficiary region affects productivity in other locations. In this context, some studies have highlighted the positive spillover effects of transportation infrastructure in resolving regional income gaps [16], but countervailing evidence has become more prominent, with emphasis that negative externalities are generally greater than positive ones [17,18]. For example, Evans and Karras [19] and Holtz-Eakin and Schwartz [20] have found no significant correlation between highway investments and the level of regional productivity. Boarnet [18] reported that transportation infrastructure investments can lead to the emergence of an unbalanced spatial system by increasing comparative advantage in beneficiary locations at the expense of other locations. Similarly, recent studies have shown that although highway investments can contribute to regional economic growth in beneficiary areas, their effects are often spatially uneven and may accelerate the decline or economic stagnation of adjacent regions as benefits tend to concentrate locally [21,22,23].

Many studies on transportation infrastructure have focused on its aggregate contribution to the large economy, generally measured by gross domestic product (GDP) or gross regional product. Contrary to the vast literature available on the gross output contribution, studies on the impact of transportation infrastructure on specific industries are much less in number. Some existing studies with a sectoral focus are generally limited to the manufacturing sector, trying to confirm the association between transportation infrastructure and productivity or the locational choice of firms [10,24,25,26,27].

In the agricultural sector, despite transportation infrastructure being a key medium for agricultural development [5,28,29], recent research moves beyond sign-only findings to clarify how such investments affect farm outcomes. In particular, improvements in roads and highways reduce travel time and logistics costs, lower post-harvest losses, especially for perishables, widen effective market access, and reallocate labor between farm and nonfarm activities [30,31]. Antle [32] also reported positive effects of transportation infrastructure on agricultural gross domestic product in both developed and developing contexts, and subsequent work often in places with limited baseline infrastructure found gains in agricultural productivity and yields [33,34,35,36,37].

On this basis, recent studies have sought to quantify these mechanisms more explicitly. Quasi-experimental and structural approaches demonstrate that improved network access increases agricultural enterprise profits by lowering distribution costs and expanding market reach [38]. Transport investments also reduce poverty by enhancing access to nonfarm employment and services, thereby indicating an indirect income channel beyond production alone [39]. County-level structural equation analyses further show that transport development raises rural income primarily through indirect pathways such as greater nonfarm employment, higher urbanization, and improved public service access, rather than through a single direct effect [40].

The temporal dimension of these impacts is also significant. Evidence on network upgrades reveals that output responses to road investments can emerge relatively quickly, whereas accessibility gains from rail may materialize with a lag, underscoring the importance of accounting for adjustment dynamics in impact evaluation [41]. Concurrently, evaluations of road upgrading document heterogeneous short-run adjustments in prices, competition, and labor reallocation, suggesting that welfare gains may be delayed and may vary according to product perishability, market distance, and network hierarchy [30,42].

Spillover effects constitute another critical dimension of the overall impact. Earlier studies identified positive effects of road investments on agricultural productivity in both beneficiary and adjacent areas, as well as stronger transport network effects in agriculture compared to other sectors [43,44]. More recent contributions confirm these patterns while adding nuance: market thickening can diffuse benefits across space, whereas competition and spatial reallocation may generate uneven impacts across neighboring regions and over time, with incidence that can differ across income groups and by the composition of living and production-oriented investments [30,42,45].

While recent research has predominantly examined productivity, poverty, welfare, or market participation, relatively few have directly addressed agricultural gross income as the primary outcome. This study addresses this gap by integrating farm-level microdata with district-level spatial models in the Korean context, focusing specifically on agricultural gross income. We explicitly link a multimodal utility-based accessibility measure to farm revenue outcomes. Although net profit would be the welfare-relevant metric, comparable cost data are unavailable in our setting; therefore, agricultural gross income is employed as a market performance proxy, which is generally positively correlated with both profit and household income.

2.2. Korean Context: Spatial Disparities and Rural Economy

The concern for the growing regional economic disparities has become a crucial issue jeopardizing the sociopolitical cohesion in Korea. This country has achieved remarkable success in economic development, overcoming numerous challenges, including the Korean War in the 1950s. The driving force behind its rapid economic growth, particularly in the 1960s and 1970s, was the unbalanced growth strategy aimed at modernizing the postwar economy. However, the remnants of the skewed economy are the concentration of jobs and population in the capital region, along with the increasing regional income disparities that further polarize regional growth in the present era. Among the diverse forms of regional disparities, such as within urban or among rural areas, the rural–urban income gap is particularly worrisome in the context of aging and depopulation, as evident in most rural communities of Korea. A government agency forecasted that more than one-third (43.4%) of the rural administrative units of eup/myeon level in the country would go extinct in the near future [46]. Meanwhile, the capital region, which encompasses Seoul and its surrounding areas, occupies approximately 11% of the total land area in the country but accounts for 50% of the total population as of 2020 [47].

The widening rural–urban income gap in Korea is largely attributed to the decreasing agricultural gross income that accompanied the steady decline of the agricultural sector, which is losing its competitiveness to urban-centered industrial sectors [48]. On average, Korean farm household income remains at approximately 62.5% of urban household income between 2010 and 2020. When focusing solely on agricultural gross income, it has shown a consistent decline over the same period [49]. In Korea, there is a public consensus that agriculture is an indispensable industry not only for national food security but also for the virtue of preserving the rural landscape and nostalgic sense of hometowns [50]. However, the low level of income has made agriculture the least preferred industry for employment, contributing to rural flight and, subsequently, to an aging population in rural areas [51]. As in many other countries, nonfarm income has become a prevalent source of income in Korean rural households, yet agricultural income forms the foundation on which rural sustainability is based. In this context, attaining higher agricultural income is an imperative element in achieving balanced regional development.

In Korea, the central government has long attempted to reduce the ever-widening regional disparity through transportation policy [52]. The total budget allocated to transportation infrastructure had steadily increased over the period covered in this study. Granted that the low level of agricultural income is one of the key drivers of regional economic disparity, then investments in transportation infrastructure promoted with the goal of balanced regional development would need to strategically consider the agricultural sector. Therefore, this study aimed to empirically investigate the effect of transportation accessibility on the agricultural gross income of farm households in Korea. By addressing this question, the study can contribute to a deeper understanding of the role of transportation accessibility in the agricultural sector, which can, in turn, mitigate or deepen regional economic disparities.

3. Materials and Methods

3.1. Data and Variables

Three types of datasets were used in this study: (i) microdata of the Korean Agricultural Census for 2005, 2010, 2015, and 2020 containing information on household attributes and residential areas, (ii) various statistics on regional attributes at the district-level si/gun/gu of Korea, and (iii) transportation accessibility data for each si/gun/gu district. The census data and regional statistics are publicly available on the websites of the Korean National Statistics Office, and the accessibility data were obtained from the Korea Transportation Institute (KOTI).

A combination of household-level variables from the original agricultural censuses, district-level statistics, and transportation accessibility measures by districts was used for the multilevel analysis. A multilevel model was applied to analyze the effects of transportation infrastructure on agricultural gross income at the micro level of farm households, using a 20% random sample of households. To analyze the effects at the macro level of districts based on the spatial econometric modeling, variables from the agricultural census data were aggregated to derive the regional average, and such data were integrated with regional statistics and the accessibility data.

From 2005 to 2020, some municipalities had undergone administrative changes by being either integrated with neighboring municipalities or promoted to an upper tier (i.e., from a village to a city). Thus, the datasets were realigned to match the municipalities as of 2020, considering spatial conformity before and after the reorganization. Studies on rural areas in Korea commonly classify urban and rural regions by administrative units according to si/gun/gu. Si contains urban and rural areas; gun, rural areas; and gu, urban towns. Among the 226 si/gun/gu districts in Korea, all rural areas and cities where agricultural activities take place were selected for the analysis, excluding metropolitan cities and islands in the final datasets, making a total of 157 si/gun municipal districts (cities and rural autonomies) as shown in Figure 1.

Various types of factors that determine agricultural gross income were abstracted from the empirical evidence from other studies.

Table 1. Variables and definitions.

Variables				Description
		Model (1)	Model (2)
Dependent Variable
Agricultural gross income		INCOME	INCOME	Log(total amount of sales (KRW)/10,000)
Independent Variables
Demographic	Age		MIDAGE	Proportion of farmers (%) aged 35–54 yrs
		AGE		Householder’s age (linear)
		AGE_SQ		AGE $\times$ AGE (linear)
	Gender		FEMALE	Proportion of female householders
		GENDER		Male = 0, Female = 1
	Number of family members	HHNUM	HHNUM	Number of family members (linear)
		HHNUM_SQ		HHNUM $\times$ HHNUM (linear)
Socioeconomic	Level of education		LOWEDU	High school diploma or below
		SCH1		Below high school
		SCH2		High school diploma (ref.)
		SCH3		Associate degree or higher
	Experience in farming	CAREER		Years of farming experience (linear)
		CAREER_SQ		CAREER $\times$ CAREER (linear)
Agricultural	Principal income source		FARM	Earn income only from farming
		AGBIZ		Participate in agribusiness
	Computer	COMP		No computers for work
	Crop type	RICE	RICE	Cultivate rice (ref.)
		FRUIT		Cultivate fruits
		OTHER		Cultivate other types of crops
		VEGE		Cultivate vegetables
		LIVESTOCK		Raise livestock
	Marketing channel	WHOLESALE		Wholesale market, joint market
		COOP		Agricultural cooperatives (ref.)
		DISTRIBUTOR		Collector, distribution company
		DIRECT	DIRECT	Direct sales to consumers
		PROCESSING		Agricultural processing company
Regional		P_LAND	P_LAND	Land price index
		P_NET	P_NET	Number of net migrants
		UTILITY	UTILITY	Log(utility-based accessibility)

Notes: 1. Model (1) = multilevel model, Model (2) = spatial econometrics model. 2. KRW = Korean Won. 3. ref. = reference group.

describes all variables used in this study. In this table, model (1) refers to the multilevel model, whereas model (2) refers to the spatial econometric model. In both models, the dependent variable is agricultural gross income (INCOME), derived from the total sales revenue obtained from the agricultural census; as the total sales revenue is originally coded in a categorical format, the data were linearized using the median value of the sales and transformed using a natural logarithm. Although agricultural gross income serves as a proxy for agricultural income, it does not account for farm-related costs or off-farm household earnings. While agricultural gross income should not be equated with net profit or total household income, it nonetheless provides a valid indicator of farm-level market performance, as these measures are generally positively correlated.

This study focuses on a key independent variable, transportation accessibility. A fully accessible dataset obtained from KOTI includes accessibility measures in terms of roads, railroads, and utilities. This study mainly used the utility-based accessibility measure (UTILITY), also known as the logsum measure, as the indicator of enhanced transportation infrastructure. One merit of using this particular accessibility indicator is that it combines multimodal accessibility into a single measure. The application of such a measure is useful in the Korean context, where the land is densely connected and the total size of the area is relatively small. Furthermore, accessibility-based measures are capable of addressing the equity impacts of transportation policies [6,7,53]. Among various types of accessibility measures, utility accessibility is known to accurately estimate the full accessibility benefits of transportation policies reflecting transportation costs and the relative attractiveness of locations [54].

Assuming that individuals select the best alternative with the highest utility, the logsum measure computed for round trips at the individual level captures the maximum utility of all travel alternatives available to an individual, where the log form captures the decreasing marginal utility of the alternatives [6,55]. According to Geurs et al. [54], the logsum accessibility, derived from the multilogit model, can be expressed as follows:

$$L_{piz}=\log \left(\sum _j\mathrm{e}\mathrm{x}\mathrm{p}\left({\mu }_p{V}_{piz}\right)\right)$$

(1)

where p denotes the travel purpose; i, person type (segmented to income classes); z, origin zone; and ${\mu }_p$, the logsum coefficient of travel purpose p. The observed utility, $V$, can be expressed as follows:

$$V_{piz}={\beta }_p{T}_{zj}+{\chi }_{ph}\ln \left(C_{zj}\right)+{\delta }_p{D}_{pj}+\dots$$

(2)

where T denotes travel time; C, travel cost; and D, a variable representing the attractiveness of the destination zone (destination utility) for a specific activity. The cost coefficient χ differs between travel purposes and between income groups h per travel purpose [54].

In this study, logsum accessibility values were first computed for each origin–destination pair and each representative individual (segmented by travel purpose and income level), using multimodal travel time, cost data, and land-use characteristics such as employment and population. Origin zones follow the zone system used in the KOTI multimodal accessibility dataset (hereafter, transportation zones). For each origin zone, individual-level logsum values were averaged across representative individuals, and zone-level values were then combined within each si/gun/gu to obtain a district-level measure of expected maximum utility from round-trip travel opportunities. This aggregation step relies on the spatial correspondence between KOTI’s transportation zones and administrative district boundaries; where multiple zones fall within a district, the within-district mean was computed. The resulting UTILITY index, therefore, reflects the district-level average of zone-specific logsum accessibility values available to residents in each region.

In addition to transportation accessibility, demographic, socioeconomic, agricultural, and regional contextual factors were used as controlled variables. For the multilevel model analysis, the demographic-related control variables included the age of the householder (AGE) and its squared term (AGE_SQ), gender (GEDER), and number of family members (HHNUM). Meanwhile, the socioeconomic variables included the educational level of the householder (SCH1–SCH3), years of farming experience (CAREER), and its squared term (CAREER_SQ).

The agricultural characteristics of households were reflected by participation in off-farm agribusiness (AGBIZ), non-use of a computer for work (COMP), type of major farming activity (RICE, FRUIT, VEGE, LIVESTOCK, and OTHER), and the main type of marketing channel (WHOLESALE, COOP, DISTRIBUTOR, DIRECT, and PROCESSING). For district-level contextual variables, the land price index (P_LAND) and number of net migrants (P_NET) were used as indicators of the vitality of a local economy. All the continuous variables were deviated around their means for the sample to effectively perform the multilevel modeling (see [56,57]). Similarly, the control variables used in the spatial econometric analysis were designed to ensure consistency with those applied in the multilevel linear model. For the year 2020, utility accessibility was only available up to 2019. To ensure temporal consistency among district-level variables, the land price index (P_LAND) and net migrants (P_NET) were also taken from 2019, given that their year-to-year variation across districts is generally small.

3.2. Analytical Methods

3.2.1. Multilevel Linear Model for Microdata

To investigate the impact of transportation infrastructure investment on agricultural gross income of farm households, this study employed a multilevel linear model that reflects the hierarchical structure of the data, namely, the household and regional levels. Multilevel modeling is particularly appropriate when variables from different levels are simultaneously analyzed, as it helps reduce the risk of fallacious reasoning associated with cross-level inference [58]. For example, aggregating household-level variables to the regional level and then interpreting the results at the household level can result in a fallacious conclusion termed the ecological fallacy [59]. Furthermore, incorporating contextual variables using multilevel models can improve the accuracy of estimates by capturing spatial heterogeneity and acknowledging that the agricultural gross income of farm households located in nearby areas is likely to be more similar than that of farm households located in distant areas. Cohen [60] found that disregarding spatial effects may lead to biased estimates of infrastructure effects owing to omitted variables. Studies have demonstrated that multilevel modeling is almost always superior to ordinary least squares regression [56,61,62].

In this study, we have two levels of observation: the farm household level (micro) and the district (macro) level. We hypothesized that the household-level values of the response variable in some way depend on each district and that the effects of the household-level determinants potentially vary systematically as a function of idiosyncratic district characteristics. Without individual subscripts for the sake of convenience, suppose there is an $n_j$-element household-level dependent variable vector $y_{j,}$ and an explanatory variable matrix $X_j$ defined by m groups (j = 1 to m) of districts and p household-level independent variables (s = 1 to p), with the total number of observations $N=\sum _{j=1}^m{n}_j$. Define a household-level equation identically for each district as follows:

$$y_j=X_j{\beta }_j+{\epsilon }_j$$

(3)

where $\beta$ denotes a $p\times 1$ vector of unknown regression parameters, $j=1,\dots ,J$ macro-level units and districts are free to have different numbers of individual observations. Assuming ${\epsilon }_j$ is independently distributed as N($O_j,{\mathsf{\Sigma }}_j$). If we assume ${\mathsf{\Sigma }}_j$ = ${\sigma }_j^{2}I$, that is, independent and constant-variance observations, then Equation (3) is a standard linear model. As Equation (3) poses no unusual estimation or computation problems, the fixed-effects regression model has been frequently used in a multilevel situation.

A more realistic model can be developed by letting intercept and slope vary at the area level, termed a random coefficient model. Assuming ${\beta }_j$ is a random sample taken from a multivariate normal and ${\beta }_j~N_p(\beta ,\mathsf{\Xi })$ uncorrelated with ${\epsilon }_j$, this is equivalent to the random coefficient model as follows:

$$y_j=X_j\beta +Z_j{\gamma }_j+{\epsilon }_j$$

(4)

where the matrix ${{\rm Z}}_j$ is stacked by a selection of certain interests of variables (columns of $X_j$) and ${\gamma }_j={\beta }_j-\beta$ is the vector of deviations of the regression coefficients ${\beta }_j$ from the their expectation $\beta$. In this case, the matrix Z contains the intercept (=1) as its first column, and its variance is expressed by ${\sigma }_{\gamma }^2$. We denoted ${\sigma }_{\epsilon }^2$ corresponding to the household-level intercept variance term. Among the various forms of the covariance structure of variance–covariance matrices [63], we adopted a banded main diagonal covariance structure where needed.

Two special cases of the random coefficient model are worthy of attention and correspond to the analysis of our study. A random-effects analysis of variance model (ANOVA), empirically first drawn by Moellering and Tobler [64], is obtained by setting to zero all of the coefficients of $X_j$ and $Z_j$, except both levels of intercepts:

$$y_j={\beta }_1+{\gamma }_j+{\epsilon }_j$$

(5)

where ${\beta }_1$ is a constant term indicating the grand mean of y. This model is incapable of explaining variability in $y_j$ at either the household or district level, but it includes two sources of random variability in $y_j$.

Another important case where only $Z_j$ is a vector of ones, a so-called random intercept model [56], is expressed as follows:

$$y_j=X_j\beta +{\gamma }_j+{\epsilon }_j$$

(6)

This model depicts a picture as a series of parallel lines with the same fixed slope but with varying intercepts (${\beta }_1+{\gamma }_j).$

3.2.2. Spatial Econometrics Model for Aggregated Data

Despite advantages, multilevel modeling does not explicitly account for spatial autocorrelation, which refers to the interdependence between neighboring regions [65]. Although multilevel models can capture hierarchical differences across regions, they usually assume that residuals are spatially independent. Disregarding such spatial dependence can lead to biased estimates when spatial effects are present. Therefore, in addition to the multilevel model, we used a spatial econometric model to cross-check the results and draw broader implications for balanced regional development. The use of regional datasets highlights the need to account for the fact that observations in nearby regions are likely to influence each other [65]. Although the multilevel model helps address the hierarchical structure of micro-level data, spatial econometric techniques are necessary for the macro-level analysis, as they explicitly model spatial dependence across regions [65,66].

There is a class of spatial autoregressive models that captures the effects of spatial dependence and heterogeneity, which are built on the standard linear regression model. All spatial models are based on the following benchmark expressions:

$$Y=\rho W_{1}y+X\beta +u$$

(7)

$$u=\lambda W_{2}u+\epsilon$$

$$\epsilon ~N(0,{\sigma }^2{I}_n)$$

where y denotes the $n\times l$ vector of dependent variables and X denotes the $n\times k$ matrix of independent variables. $W_1$ and $W_2$ are the spatial weight matrices that formally incorporates spatial dependence into the model; $\rho$ and $\lambda$ are spatial autoregressive coefficients that express the strength of spatial interaction; and $\epsilon$ is a vector of error terms, assumed to be i.i.d.

When the spatial lag term and a spatially correlated error structure are included in the model as in Equation (7), it is referred to as the spatial autoregressive combined (SAC) model. When $\rho =0$, a spatial error model (SEM) with a spatial autocorrelation in the disturbances can be derived. When $\lambda =0$, a mixed regressive–spatial autoregressive (SAR) model can be derived.

In a spatial model, the Lagrange multiplier (LM) tests provide the general decision rule for model specification [67]. In our analysis, the LM diagnostics indicated that the spatial lag (SAR) model is appropriate for our data (c.f. Appendix A). The SAR model takes the following form:

$$Y=\rho Wy+X\beta +\epsilon$$

(8)

$$\mathsf{\epsilon }~\mathrm{N}(0,{\sigma }^2{I}_n)$$

The spatial weight matrix W is the building block of spatial econometrics, which is most commonly specified by contiguity (spatial neighbors) or distance functions. Contiguity weight matrices define the relations of two spatial units by specifying a binary relationship with weights 1 and 0. For example, if district i is contiguous to district j, then $d_{ij}=1$ and, otherwise, $d_{ij}=0$. In this case, W is expressed as follows:

$$W_{ij}={\displaystyle \frac{d_{ij}}{\sum _{j=1,i\ne j}^n{d}_{ij}}}$$

(9)

W can be constructed based on the rook, bishop, and queen contiguity matrix. There is no set of criteria for selecting the weight matrix, and it is usually selected in a manner that conforms to the data structure, applicability, and economic theory [65,68]. The row-standardized queen contiguity matrix grants $W_{ij}=1$ if two districts share a border or a corner; otherwise, $W_{ij}=0$ is used to quantify the location under study. The spatial weight matrix in this study was row-standardized.

The multilevel linear models were implemented using SAS 9.4. Moran’s I statistics and the spatial weight matrix were constructed using ArcGIS 10.7.1, and the spatial econometric models were estimated using MATLAB 2015a.

4. Results

4.1. Multilevel Linear Model

Table 2. Results of Multilevel Models.

Variable	2005		2010		2015		2020
Fixed effect
Intercept	16.3613	***	17.3858	***	17.9687	***	9.6543	***
AGE	−0.0285	***	−0.0238	***	−0.0277	***	−0.0231	***
AGE_SQ	−0.0006	***	−0.0004	***	−0.0004	***	−0.0003	***
GENDER	−0.6642	***	−0.5029	***	−0.4630	***	−0.3784	***
HHNUM	0.0616	***	0.0569	***	0.0776	***	0.0847	***
HHNUM_SQ	−0.0078	***	−0.0113	***	−0.0161	***	−0.0171	***
SCH1	−0.0490	***	0.0162		−0.0033		−0.0768	***
SCH3	−0.0569	***	−0.1207	***	−0.1123	***	−0.1263	***
CAREER	0.0081	***	0.0094	***	0.0114	***	0.0125	***
CAREER_SQ	−0.0005	***	−0.0005	***	−0.0005	***	−0.0005	***
AGBIZ	−0.2427	***	−0.9364	***	−0.6101	***	−0.7130	***
COMP	−0.5717	***	−0.4188	***	−0.3687	***	−0.3578	***
FRUIT	0.6163	***	0.6815	***	0.564	***	0.4864	***
OTHER	0.4121	***	0.5600	***	0.3282	***	0.3083	***
VEGE	−0.3671	***	−0.0571	***	−0.2206	***	−0.1918	***
LIVESTOCK	1.1252	***	1.3905	***	1.5811	***	1.5159	***
WHOLESALE	0.2395	***	0.2314	***	0.1916	***	0.2071	***
DISTRIBUTOR	−0.1135	***	−0.0610	***	−0.0329	***	−0.0250	**
DIRECT	−1.1930	***	−1.2193	***	−1.1794	***	−1.2876	***
PROCESSING	−0.1525	***	−0.6376	***	−0.7766	***	−0.2249	***
P_LAND	0.0080		−0.0410		−0.0363		0.0211
P_NET	0.0000		0.0000		0.0000		0.0000
UTILITY	0.0206		−0.0241		−0.0753	***	−0.1431	***
Random effect
Level 1
INTERCEPT (${\mathsf{\sigma }}_{\mathsf{ϵ}}^2$)	1.3351	***	1.1941	***	1.3717	***	1.4095	***
Level 2
INTERCEPT (${\mathsf{\sigma }}_{\mathsf{\gamma }}^2$)	0.1049	***	0.0858	***	0.0774	***	0.0834	***
−2RLL	671,412.1		586,324.9		562,885.7		503,083.7
BIC	671,422.2		586,335		562,895.8		503,093.8
N	214,431		194,161		178,209		157,891

Note: *** p < 0.01, ** p < 0.05.

presents the multilevel random-intercept estimates for 2005, 2010, 2015, and 2020. The household-level (${\mathsf{\sigma }}_{\mathsf{ϵ}}^2$) and district-level (${\mathsf{\sigma }}_{\mathsf{\gamma }}^2$) variance components are significant in every year (p < 0.01), indicating non-trivial clustering by district. This justifies using a multilevel specification to account for intra-district correlation and to separately identify household and contextual effects on agricultural gross income.

Regarding household characteristics, age (AGE) is negatively associated with agricultural gross income in all years, implying that older farm householders tend to earn less. The squared term (AGE_SQ) is also negative, indicating that the marginal decline accelerates with age. Gender (GENDER) has a consistently negative coefficient, meaning that female-headed households earn less agricultural gross income than their male-headed counterparts. Household size (HHNUM) has a positive effect, but its squared term (HHNUM_SQ) is negative, implying diminishing returns as household size increases. Educational attainment shows a mixed pattern: households whose heads did not complete high school (SCH1) or attained a bachelor’s degree or higher (SCH3) generally earned less than high school graduates, with the strongest and most consistent penalty observed for SCH3. Farming experience (CAREER) is positively associated with agricultural gross income, but the negative coefficient on CAREER_SQ again suggests a diminishing return to experience.

In terms of occupational and technological attributes, participation in nonfarm agribusiness (AGBIZ) is consistently negative, indicating that diversification away from farming reduces agricultural gross income, likely due to the reallocation of labor and resources. The coefficient on non-use of a computer for work (COMP) is also negative, meaning that households using computers tend to earn higher agricultural gross incomes. This may reflect improved market access and, in later years, the adoption of smart farming technologies that require computer-based operation.

The crop-type dummies reveal that producers of fruits (FRUIT), other cash crops (OTHER), and livestock (LIVESTOCK) have significantly higher agricultural gross incomes than rice farmers (reference group), while vegetable producers (VEGE) generally earn less. For marketing channels, sales via wholesale markets (WHOLESALE) are associated with higher incomes than cooperative sales, while reliance on distributors (DISTRIBUTOR), direct sales (DIRECT), or processing companies (PROCESSING) is associated with lower incomes, suggesting that economies of scale and bargaining power in wholesale markets may be more favorable to farm households.

Regional variables show weak or inconsistent effects: land price index (P_LAND) and net migration (P_NET) are generally not significant. The key variable of interest, UTILITY (utility-based transportation accessibility), is positive but not significant in 2005, and becomes increasingly negative and significant in later years, with the largest effect observed in 2020 (−0.1431, p < 0.01). This pattern indicates that while initial improvements in accessibility did not harm agricultural incomes, subsequent expansions, possibly oriented toward non-agricultural priorities, were associated with declining farm incomes. These results suggest that transportation investments in rural Korea from 2010 onward may have facilitated structural changes or competitive pressures that disadvantage farm households, rather than enhancing their market performance.

4.2. Spatial Econometric Model

To diagnose the existence of spatial patterns with respect to agricultural gross income, the global Moran’s I test was conducted (

Table 3. Global Moran’s I.

Year	Moran’s I	Z-Score
2005	0.2738 ***	5.1244
2010	0.2065 ***	3.9067
2015	0.2021 ***	3.8199
2020	0.2633 ***	6.2771

Notes: 1. Queen contiguity-based spatial weight matrix was applied. 2. *** p < 0.01.

). The global Moran’s I statistic is one of the most preferred methods to test for spatial autocorrelation in a dataset. This spatial diagnostic tool measures the level of clustering patterns across districts. Moran’s I statistic for the aggregated agricultural gross income by district presents a strong positive clustering pattern in all years. Therefore, the result confirms the need to control spatial effects owing to the presence of autocorrelation in the datasets in which the mean agricultural gross income in one district is highly likely to be influenced by that of neighboring districts.

The estimated results of the SAR, SEM, and SAC models indicate that $\rho$ (for the spatial lagged model) and $\lambda$ (for SEM) have a significant impact on agricultural gross income. The general decision rule for spatial models involves the inspection of the LM tests. The LM test was based on the estimation under the null hypothesis, that is, $H_0:\mathsf{\lambda }$ = 0 for the LM error test and $H_0:\rho =0$ for the LM lag test. We would have rejected the null hypothesis if the test statistic was greater than $X^2$(1). As shown in Appendix A, the LM statistics for both the spatial lag and spatial error models are statistically significant across all years. Given that both specifications are valid, we selected the SAR model as the main specification owing to its relatively higher explanatory power for the data.

Table 4. Results of the Spatial Econometrics Model (SAR).

Variable	2005		2010		2015		2020
CONSTANT	1.5817		4.7123	***	3.9524	***	7.9873	***
MIDAGE	0.0640	***	0.0500	***	2.3477	***	1.4553
FEMALE	−0.0022		0.0043		−0.0017		−0.0467	***
HHNUM	0.0767		−0.0028		0.6787	***	−0.0280
LOWEDU	0.0017		−0.0002		0.0116	**	0.0072
RICE	−0.0002		−0.0016		−0.0004		−0.0015
DIRECT	−0.0156	***	−0.0156	***	−0.0150	***	−0.0130	***
AGINCONLY	0.0158	***	0.0140	***	0.0167	***	0.0089	***
P_LAND	0.0027		0.0467		−0.0653	***	0.0275
P_NET	0.0000	*	0.0000	*	0.0000		0.0000	**
UTILITY	0.0019		−0.1009	***	−0.0599	***	−0.0832	***
$\rho$	0.0540	***	0.0400	**	0.0540	***	0.0704	***
Adj. R2	0.6447		0.6755		0.7120		0.7063

Note: *** p < 0.01, ** p < 0.05, * p < 0.1.

presents the results of the SAR model for 2005, 2010, 2015, and 2020. The spatial autoregressive coefficient ($\rho$) was positive and statistically significant in all years, confirming the presence of spatial dependence in agricultural income across districts. This indicates that the agricultural income of a given district is influenced by that of its neighboring districts, justifying the use of a spatial regression framework for this analysis.

Across all examined years, districts with a higher proportion of mid-aged farmers (MIDAGE) tended to have higher average agricultural gross income, with a particularly large positive coefficient in 2015. A reasonable interpretation is that the proportion of farm householders in the most economically active age group has declined owing to the acceleration of rural aging, thereby increasing their relative contribution to local agricultural outcomes.

The proportion of female-headed households (FEMALE) was largely insignificant across most years. However, in 2020, this relationship turned significantly negative, suggesting that structural disadvantages faced by female household heads have persisted and possibly intensified in recent years. The average number of household members (HHNUM) showed a substantial positive association in 2015, while no consistent trend was observed in other years; such a pattern is likely linked to the acceleration of rural aging, as more densely populated districts increasingly tended to exhibit higher agricultural incomes.

Districts with a higher proportion of farm householders with less than high school education (LOWEDU) exhibited a modest but significant positive association with agricultural income in 2015 and 2020. This may reflect the concentration of such households in regions with stronger agricultural specialization, where farming skills are acquired through experience rather than formal education. The share of rice cultivating farmers (RICE) was consistently negative but statistically insignificant, which likely reflects aggregation and composition effects at the district level, as districts contain mixed crop portfolios and heterogeneous farm sizes, while our regressor captures only the rice-oriented share, attenuating cross-sectional variation.

The proportion of farmers selling directly to consumers (DIRECT) showed a consistently significant negative effect across all years, indicating that, at the district level, direct sales are associated with lower overall agricultural income. This aligns with earlier observations that such channels are often chosen by smaller-scale producers with limited production volumes. Similarly, households solely dependent on agricultural income (AGINCONLY) exhibited a significant positive effect in all years, underscoring the income advantage of full-time over part-time farming.

The land price index (P_LAND) displayed no consistent trend, with a significant negative effect only in 2015. Land prices are generally most sensitive in centrally located areas and often follow large-scale development projects [69]. The negative shift in 2015 likely reflects the influence of national-level spatial planning policies implemented in the mid-2000s, which included the creation of innovation cities and the relocation of public agencies from the capital region to noncapital areas to promote geographically balanced development (see [70]). Such projects would have increased the price of some rural lands, affecting agricultural activities. Net migration (P_NET) was weak but significantly positive in most years, suggesting that in-migration may contribute to local agricultural vitality, although the magnitude of the effect remains limited.

The key variable of interest, utility-based accessibility (UTILITY), was positive but insignificant in 2005 and turned strongly negative and highly significant from 2010 onward. This indicates that, at the district level, public investments in transportation infrastructure had minimal effect on agricultural income in 2005 but a substantial negative effect thereafter. The results are consistent with those from the multilevel model and support the interpretation that the transportation network has been extended in a manner that is largely irrelevant to agricultural activities in rural areas. Such infrastructure may have facilitated non-agricultural economic integration or increased market competition, thereby offsetting the cost-saving benefits for local producers.

In conjunction with the results obtained at the disaggregate household level based on multilevel modeling, the aggregate district-level analysis further supports the interpretation that the expansion of the transportation network has been largely irrelevant to agricultural activities in rural areas. However, while the household-level analysis indicated a continuously deteriorating effect of transportation accessibility, the district-level estimates reveal a fluctuating but persistently negative effect in 2010, 2015, and 2020. The magnitude of the negative coefficient decreased between 2010 and 2015 but increased again in 2020, suggesting that any temporary moderation in its adverse impact was not sustained. This pattern may be related to the Korean government’s shift in infrastructure investment priorities, reducing road construction under the assumption of sufficient coverage while enhancing railroad networks to promote balanced regional development. Although expanded rail infrastructure may have begun to generate some localized economic benefits, these appear insufficient to offset the broader negative impact of reduced road investment on regional agricultural income. Notably, such dynamics were not observed at the household level, which underscores the importance of a multi-scalar analytical approach.

As aforementioned, the SAR model reflects the spatial autocorrelation of agricultural gross income across districts. In this model, the spatially lagged dependent variable, defined by the spatial weight matrix, is included as an independent variable, allowing for separate estimation of direct, indirect, and total effects. The direct effects measure the effect that a change in an independent variable in district i has on the dependent variable (average agricultural gross income) in that district. The indirect or spillover effects capture the effect of a change in an independent variable in district i on the dependent variable in all other districts. The total effects are calculated by summing the two effects.

Table 5. Direct, Indirect, and Total Effects of Utility Accessibility on Agricultural Income (SAR).

Year	Direct Effects	Indirect Effects	Total Effects
2005	0.0192	0.0011	0.0203
2010	−0.1001 ***	−0.0042 *	−0.1051 ***
2015	−0.0600 ***	−0.0034 **	−0.0634 ***
2020	−0.0833 ***	−0.0061 **	−0.0894 ***

Note: *** p < 0.01, ** p < 0.05, * p < 0.1.

presents the direct, indirect, and total effects of utility-based accessibility on district-level aggregated agricultural gross income, as estimated using the SAR model.

The results presented in Table 5 suggest that the change in utility-based accessibility in district i had a negative spillover effect on agricultural gross income in its neighboring districts; however, such an effect is more evident within its own district. For all examined years, the coefficients of direct effects were much higher than those of indirect effects. In 2010, 2015, and 2020, the direct effects demonstrated a high level of statistical significance (−0.100, −0.060, and −0.083, respectively), whereas the indirect effects were negative but much smaller in magnitude (about −0.004 to −0.006) and showed comparatively lower significance. Considering the magnitude and strength, the effects of utility-based accessibility on agricultural gross income were more closely related to the direct or within-district effects. Thus, the impact of enhanced transportation accessibility within district i on its own agricultural gross income is stronger than that of the spillover effects on adjacent districts.

The spatial regression model revealed a negative impact of transportation infrastructure investments on agricultural gross income in Korea since 2010, consistent with the results from the bivariate correlation analysis and the multilevel modeling. Overall negative results contradict the general expectation that the expansion of transportation infrastructure in rural areas would have contributed to increasing agricultural gross income by lowering production costs and securing the price competitiveness of agricultural products.

5. Discussion

This study investigated the underexplored association between transportation infrastructure investments and agricultural gross income, filling a research gap that has been largely overlooked owing to the prevailing perception of transportation infrastructure as primarily serving urban needs and the lack of compatible rural datasets. By applying a utility-based logsum measure of transportation accessibility, this study enables a more comprehensive and precise evaluation of transportation benefits in rural areas. Using data from 2005 to 2020 in Korea, the empirical analysis integrates micro- and macro-level perspectives through multilevel and spatial econometric models to thoroughly assess the impact of improved transportation accessibility on agricultural gross income.

The main findings of this study are summarized as follows. First, in the multilevel model, transportation accessibility showed a positive but statistically insignificant association with agricultural gross income in 2005, whereas the association turned negative and statistically significant in 2010, 2015, and 2020. Specifically, the coefficients of utility-based accessibility were −0.02 in 2010, −0.08 in 2015, and −0.14 in 2020, indicating that the adverse effect has strengthened over time. These results suggest that despite the continued expansion of investments in transportation infrastructure, such public investments are not efficiently contributing to the generation of agricultural gross income. Instead of providing benefits, transportation infrastructure constructed after 2010 appears to be either unrelated or hindering agricultural gross income in rural areas.

Second, the spatial econometric model analyzed at the macro level using aggregated data corroborated the results of micro-level findings. At the district level, transportation infrastructure was positive but not statistically significant in 2005, whereas in 2010, 2015, and 2020, the coefficients were negative and highly significant. The magnitude of the negative effect declined slightly from −0.10 in 2010 to −0.06 in 2015 but increased again to −0.08 in 2020. The results suggest that although the utility-based accessibility to transportation infrastructure had improved over time, the accessibility necessary for agricultural activities had deteriorated, consequently, exerting a negative effect on the sales of agricultural products.

One plausible explanation for the negative results is the shift in transportation investment planning. Efficiency-oriented planners have deemed adequately developed road infrastructure in Korea, leading to reduced road investments but increased allocations to railroads. This may facilitate the movement of labor and resources away from agriculture, potentially weakening the agricultural sector in this regard. However, in the agricultural sector, road transportation remains essential owing to its easier access, lower costs, and the ability to deliver products directly from farms. In contrast, railroads are concentrated around transportation hubs in large cities, reinforcing urban-centered land planning. This tendency has become more pronounced with the construction of satellite cities around Seoul and the so-called innovation cities in noncapital regions. If transportation policy continues without explicitly considering agriculture as an industry and rural areas as viable living spaces, the economic marginalization of farm households may deepen, partly because improving farm income is not currently an explicit objective of infrastructure policy. Incorporating considerations such as enhancing farm-to-market connectivity, upgrading rural feeder roads, and integrating cold-chain logistics into national and regional transport plans could better align transportation investments with the needs of the agricultural sector, thereby helping ensure that the benefits of large-scale infrastructure projects are more equitably shared with rural communities.

Despite valuable contributions, this study has several limitations, mainly owing to the lack of data. If regional data were available at a major granular level, such as eup/myeon instead of si/gun, more specified results exclusively focused on rural areas could have provided a clearer and more rigorous understanding of the impact of improved transportation accessibility on the agricultural gross income of farm households. Another limitation is that this study focused solely on agricultural gross income, although improved transportation accessibility may also exert potential effects on nonfarm income. Investigating this possibility could provide further insights into the comprehensive impact of transportation infrastructure investment on farm households. In addition, the possibility of reverse causality cannot be entirely ruled out. Regions with lower agricultural gross income may have been excluded from major transportation infrastructure investments, raising concerns regarding potential endogeneity. Future research incorporating panel data or more refined identification strategies would be necessary to strengthen the causal interpretation.