Econometric Modelling of the Rural Poverty, Unemployment and the Agricultural Sector Using a Truncated Spline Approach with Longitudinal Data

Abstract

Rural poverty and unemployment remain persistent challenges in Indonesia, particularly in regions where agricultural development is uneven and land conversion accelerates socio-economic disparities. These conditions are highly relevant because rural areas serve as the backbone of food security, labour supply, and national economic stability. This study aims to address these issues by developing a flexible analytical framework that simultaneously models three indicators of rural development—rural poverty, rural unemployment, and agricultural sector growth—using a truncated spline nonparametric regression approach with longitudinal data from 2015 to 2023. The methodological approach integrates this regression with panel data across five Indonesian regions, allowing the analysis to capture nonlinear relationships and regional variations that conventional parametric models may overlook. The results indicate that population migration, land use change, and village fund allocation are the dominant drivers of rural development indicators, with nonlinear and region-specific effects. Village funds consistently reduce poverty and unemployment, while excessive land conversion restricts agricultural sector growth. The findings contribute to theory by demonstrating the advantages of flexible nonparametric approaches in modelling rural development dynamics, and to practice by offering empirical evidence for more targeted and adaptive policy interventions to alleviate poverty, reduce unemployment, and strengthen rural resilience.

1. Introduction

Rural regions in emerging nations encounter various obstacles, the most significant of which are acute poverty and food scarcity (Deller et al., 2015). The economic underdevelopment of this group of countries results in insufficient agricultural advancement, thus leading to rural poverty (Zhao & Yu, 2021). This engenders a detrimental circle from which the rural populace struggles to extricate itself. Rural poverty in developing nations manifests in multiple forms. The obstacles to rural development stem from cultural, geographical, environmental, socio-economic, and various other aspects (Singh & Chudasama, 2020). A report published by the International Centre for Inclusive Development in 2019 delineates the substantial difficulties confronting rural regions that exacerbate poverty. These issues encompass the disadvantaged status of women, children, and the elderly; insufficient access to land; inadequate social protection for rural communities; human rights abuses; and the adverse circumstances faced by migrants (Đurić et al., 2023). Such conditions have slowed down the improvement in welfare of rural communities, as evidenced by the high poverty and unemployment rates in rural areas (Siregar et al., 2024). In the context of Indonesia, rural poverty and unemployment remain persistent problems that directly affect national economic performance, considering that more than 40% of Indonesia’s workforce is still dependent on agriculture and rural-based sectors. This means that rural underdevelopment not only undermines local welfare but also hampers the broader trajectory of Indonesia’s economic growth. This situation underscores the importance of conducting research that comprehensively explains the dynamics of agricultural sector growth and its connection to socio-economic issues in rural areas.

Preventing land conversion, improving agricultural productivity, and managing village funds effectively are critical strategies to reduce Indonesia’s rural poverty rate (Rahman Razak et al., 2023). Thus, issues in the agricultural sector, rural poverty, and rural unemployment are fundamentally interrelated and dynamic over time. This raises the core research problem: What are the main determinants of rural poverty, rural unemployment, and agricultural sector growth in Indonesia, and how do their interrelationships evolve over time?

Villages, as the main basis of life for the majority of Indonesia’s population, play a strategic role in supporting food security, labour supply, and national socio-economic stability (Hilmawan et al., 2023). However, various structural challenges and regional disparities remain as main obstacles to achieving rural community welfare. Therefore, analysing the dynamics of rural development is crucial as a basis for more targeted and contextual policy-making (Handoyo et al., 2021). In this regard, longitudinal or panel data analysis becomes indispensable, because it allows researchers to record variations across regions and over time, thereby providing a comprehensive picture of the dynamics of rural development and its linkages to economic performance.

However, in modelling complex and potentially nonlinear relationships between variables in longitudinal data, parametric approaches such as linear regression have limitations because they assume a fixed form of the relationship function (Eubank, 2012). Therefore, non-parametric regression approaches, particularly truncated splines offer a more flexible and adaptive alternative (Wu & Zhang, 2006). This method does not require researchers to specify the functional form of the relationship between variables from the outset but allows the data itself to form the appropriate relationship pattern (Idris & Rahman Razak, 2025; Dwi Octavanny et al., 2020).

Previous studies on rural development in Indonesia, such as the work of Handoyo et al. (2021) and Rahman Razak et al. (2023), have highlighted important determinants like Village Funds, agricultural productivity, and land use change. For instance, Rahman Razak et al. (2023) showed that Village Funds moderate the relationship between agricultural sector growth, migration, and land conversion using multigroup SEM analysis. However, such approaches are limited by their parametric assumptions and inability to capture nonlinear dynamics over time. Similarly, other Indonesian studies have often examined poverty, agriculture, or unemployment separately, and rarely within a multivariate framework that allows simultaneous modelling of their interdependencies. This indicates a methodological gap that requires a more flexible approach (Rahman Razak et al., 2023).

In this regard, truncated spline regression provides a novel and appropriate method, as it enables the identification of nonlinear relationships and temporal heterogeneity across indicators of rural development. Unlike the previous parametric models, spline regression allows the data to reveal patterns adaptively, thereby offering a more convincing explanation of rural poverty, unemployment, and agricultural sector dynamics in Indonesia.

Previous applications of spline regression in Indonesian studies have mostly focused on health data or education, while its application to multivariate rural development indicators remains largely unexplored. This highlights a methodological gap and strengthens the argument that truncated spline regression is suitable and novel for this research. Thus, truncated spline regression enables more realistic modelling of the dynamic relationships between variables that influence agricultural sector growth, poverty, and unemployment in rural areas simultaneously.

This study aims to simultaneously model three important indicators of rural development in Indonesia, namely rural poverty growth, rural unemployment rates, and agricultural sector growth, as dependent variables using a truncated spline nonparametric regression approach on longitudinal data. By combining the flexibility of nonparametric methods with the wealth of information from panel data, this study aims to identify the main factors contributing to the dynamics of these three indicators and capture changes in the patterns of relationships between variables over time in an adaptive manner.

The novelty of this study lies in its approach, which simultaneously models the three main dependent variables of rural development, agricultural sector growth, rural poverty growth, and rural unemployment using a nonparametric spline truncated regression method based on longitudinal data. This approach provides flexibility in identifying nolinear relationships and temporal heterogeneity that cannot be captured by classical linear models or conventional panel models. Unlike most previous studies that analysed these indicators separately, this study integrates them into a holistic framework, thus providing a richer understanding of rural economic dynamics. Moreover, evidence from Indonesian literature shows that while panel data has been used extensively in rural studies, the application of multivariate nonparametric regression remains scarce. This reinforces the contribution of this study in filling the research gap.

Most previous studies have focused on analysing a single rural development indicator separately, such as poverty or the agricultural sector, and have used linear approaches that assume constant relationships between variables over time. In addition, there are still few studies in Indonesia that utilise a multivariate nonparametric regression approach based on longitudinal data to examine the interrelationships between factors that simultaneously influence poverty, unemployment, and agricultural sector growth. Therefore, this study fills this gap by developing a more holistic and flexible model to capture the complex dynamics between rural development indicators in Indonesia over time.

2. Literature Review

Economic development in Indonesia is not only measured by national macroeconomic growth (Wardani & Rifa’i, 2025), but also determined by the success in creating inclusive and equitable development in rural areas (Fitrianti et al., 2022).

The agricultural industry is a crucial and significant element of the national economy, since it generates a substantial share of the country’s gross domestic product, contributes significantly to export revenues, and employs millions of individuals (Afriyanti et al., 2023). The agricultural sector is considered the backbone of the economy; hence, the state prioritises agriculture and food security for the population as they are essential for human growth (Bukhtiarova et al., 2019).

The agricultural sector supplies food and raw resources to other economic sectors to promote industrialisation (Hassoun & Abdelmadjid, 2019). Agriculture serves as the primary source of livelihood for certain individuals in developing nations, particularly for the impoverished in rural regions of low and middle-income countries who rely directly or indirectly on agriculture for their sustenance (Inomjonova, 2024). In developing nations, the agricultural sector plays a crucial role in economic growth and development, in contrast to the more established economies of wealthy countries (Brückner, 2012). Agricultural growth in a region is determined by competitive advantages, regional benefits, and the area’s agricultural potential (Pratama et al., 2023). Recent studies also indicate that agricultural performance is highly influenced by access to finance, technological adoption, and institutional support, which directly shape productivity outcomes (Ma & Li, 2025). This highlights that beyond land and labour, structural variables remain critical for rural economic growth.

In Indonesia, the agricultural sector plays a strategic role in economic development, particularly in rural areas (Khairiyakh et al., 2015). A growing body of literature shows that agricultural growth has a strong potential to reduce rural poverty by increasing labour absorption, improving productivity, and raising household income. As a sector that employs a large workforce, agriculture is not only the main source of livelihood for rural communities, but also contributes directly to local and national economic growth (Drean & Bawono, 2021). Comparable findings have been reported in Pakistan (Abedullah et al., 2023), West Africa (Osabohien et al., 2019) and the Global (Hossain et al., 2024), where agricultural expansion is significantly correlated with poverty reduction and rural employment, suggesting that Indonesia’s experience shares commonalities with other Southeast Asian economies. Strengthening the agricultural sector in rural areas is believed to boost productivity, create jobs, and reduce development gaps between regions. With the increasing demand for food and the importance of local economic resilience, agricultural development has become increasingly relevant in the context of sustainable rural development (Mehraban & Ickowitz, 2021). However, despite its great potential, there are still various challenges in developing rural agriculture in Indonesia. The growth of this sector in many areas does not show a consistent trend and tends to be stagnant (Kurnianto, 2024).

This has slowed down the improvement in welfare of rural communities, as evidenced by the high poverty and unemployment rates in rural areas (Siregar et al., 2024). Thus, agricultural performance is directly linked to poverty alleviation and job creation, but stagnation in agricultural productivity can perpetuate rural poverty and limit employment opportunities. Poverty has become a very important issue in every country (Todaro & Smith, 2012) and will always be difficult to resolve due to the low standard of living of the population, which reinforces the problem (Prasetyoningrum, 2018). In some cases, poverty is measured by considering various aspects beyond income levels, such as education levels (Ivani & Auwalin, 2024). Other studies stress that multi-dimensional poverty in rural areas also reflects structural constraints in employment opportunities, agricultural productivity, and access to markets (Moges et al., 2025); (Onyeyirichi & Deepika, 2025), which aligns with the variables explored in this study.

The significance of rural poverty and the quest for effective measures to mitigate this adverse phenomenon are underscored by the development plans used internationally, which prioritise poverty alleviation (Beltran-Peña et al., 2020). The United Nations Agenda 2030 is a document that prioritises poverty eradication among its seventeen development goals. Eliminating hunger, attaining food security, and enhancing food quality are priorities of the United Nations Sustainable Development Goals (Vos & Cattaneo, 2021).

Poverty in rural areas of Indonesia has shown a gradual decline from 2015 to 2023, but it remains higher than in urban areas. This is one of the remaining issues from the ongoing village development process. Therefore, there is still an urgent need to study the poverty problems faced by rural areas in Indonesia today in depth, especially the major factors that cause these problems, so that effective efforts can be formulated to reduce poverty in rural areas (Rahman, 2017). This is because poverty affects many aspects of community life and village administration (Widiyanto et al., 2021), indicating that rural poverty is not only a socio-economic issue but also a structural development challenge, strongly linked to limited agricultural performance and the persistence of rural unemployment.

The unemployment rate, alongside the employment rate and the count of able-bodied individuals, serves as reference indicators for delineating the labour market and the equilibrium between labour demand and supply (Ahmed et al., 2014). In addition to causing immediate adverse societal consequences, rural unemployment also instigates indirect issues by compelling individuals to migrate from rural to urban regions (Lyu et al., 2019). This phenomenon is especially evident among young adults experiencing unemployment in rural areas (van Twuijver et al., 2020). The allure of metropolitan regions contributes to the outmigration of women from rural locales, as the concentration of industry in major urban centres frequently establishes advantageous conditions for female employment (Güney Celbiş, 2023). The decline caused by the exodus of the young workforce frequently converts rural areas into enclaves of elderly residents, resulting in additional difficulties in recruiting specialised labour (Steiner et al., 2023). Such migration-driven demographic shifts have also been reported in Cambodia, where youth outmigration has deepened rural poverty and weakened agricultural labour markets (Yokying, 2025). This comparative evidence reinforces the importance of examining unemployment in Indonesia within a broader global perspective.

Unemployment constitutes a primary employment challenge encountered by developing nations, including Indonesia. Unemployment is a multifaceted issue, as it is both affected by and affects numerous interrelated causes, often exhibiting a complex and opaque pattern (Rokhim, 2023). One element is Indonesia’s substantial population, which means that a new labour force is generated year, influencing the unemployment rate (Alrakhman et al., 2022). In Indonesia, unemployment in rural areas remains a complex issue that requires serious attention in the national development agenda. Although most rural residents work in the agricultural sector, many of them are classified as underemployed or hidden unemployed due to low productivity and limited access to capital, technology, and markets (Amin & Rotinsulu, 2023). Previous research confirms that low access to finance and markets are structural barriers that exacerbate underemployment in rural settings (Huang et al., 2025), suggesting that the unemployment problem is not only demographic but also institutional.

Data from the Central Statistics Agency shows that although the open unemployment rate in rural areas is lower than in urban areas, the quality of jobs available in rural areas is generally informal, unstable, and unproductive. This disparity is exacerbated by the lack of non-agricultural employment opportunities that could serve as alternative sources of income for rural communities, especially the younger generation. As a result, many productive workers choose to migrate to cities, leaving rural areas with imbalanced demographic structures and heavy economic burdens (Rammohan & Tohari, 2023). Therefore, rural unemployment is not merely a statistical indicator, but a structural issue that limits rural economic dynamism and reinforces poverty, especially when agricultural sector growth remains stagnant.

From the literature, it can be inferred that agricultural sector growth, rural poverty, and rural unemployment are strongly interconnected. Agricultural development contributes to poverty reduction and job creation, but when agricultural growth stagnates, rural poverty remains high and unemployment persists. Conversely, high unemployment and poverty can suppress agricultural productivity by reducing labour availability and investment capacity. This triangular relationship highlights the importance of simultaneously analysing these three indicators within a unified framework.

Based on the theoretical framework and previous empirical findings, this study proposes the following hypotheses to examine the effects of migration, land use change, and village funds on rural development outcomes. The hypotheses are structured to capture their influence on agricultural sector growth, poverty, and unemployment in rural areas.

H1a. 

Migration negatively affects agricultural sector growth in rural areas.

H1b. 

Migration positively affects rural poverty rates.

H1c. 

Migration positively affects rural unemployment rates.

H2a. 

Land use change negatively affects agricultural sector growth.

H2b. 

Land use change positively affects rural poverty rates.

H2c. 

Land use change positively affects rural unemployment rates.

H3a. 

Village funds positively affect agricultural sector growth.

H3b. 

Village funds negatively affect rural poverty rates.

H3c. 

Village funds negatively affect rural unemployment rates.

3. Data and Methodology

We used cross-sectional data with longitudinal data from the variables. The scope of this study includes five major regions in Indonesia, Sumatra, Java-Bali, Kalimantan, Sulawesi, and Papua-Maluku-Nusa Tenggara with a time span 2015–2023. The details of the variables used in this study can be seen in

Table 1. Research variables.

Type of Variable	Symbol	Variable Name	Notes
Dependent Variable	$Y_1$	Growth of Agricultural Sector	Agricultural sector growth rate (Per cent)
	$Y_2$	Rural Poverty	Rural poverty rate (Per cent)
	$Y_3$	Rural Unemployment	Rural unemployment (Per cent)
Independent Variable	$X_1$	Migration	Number of rural residents who migrated (Thousands)
	$X_2$	Land Use Change	Amount of land conversion in rural areas (Hectares)
	$X_3$	Village Fund	Amount of village funds received by each village (IDR millions)

Source: Own, 2025.

below.

The longitudinal data structure used in this study can be seen in

Table 2. Research data structure.

Subject	Year	${\mathit{Y}}_1$	${\mathit{Y}}_2$	${\mathit{Y}}_3$	${\mathit{X}}_1$	${\mathit{X}}_2$	${\mathit{X}}_3$
Sumatera	2015	$Y_{111}$	$Y_{211}$	$Y_{311}$	$X_{111}$	$X_{211}$	$X_{311}$
	$⋮$	$⋮$	$⋮$	$⋮$	$⋮$	$⋮$	$⋮$
	2023	$Y_{119}$	$Y_{219}$	$Y_{319}$	$Y_{119}$	$X_{219}$	$X_{319}$
Java-Bali	2015	$Y_{121}$	$Y_{221}$	$Y_{321}$	$X_{121}$	$X_{221}$	$X_{321}$
	$⋮$	$⋮$	$⋮$	$⋮$	$⋮$	$⋮$	$⋮$
	2023	$Y_{129}$	$Y_{229}$	$Y_{329}$	$Y_{129}$	$X_{229}$	$X_{329}$
Kalimantan	2015	$Y_{131}$	$Y_{231}$	$Y_{331}$	$X_{131}$	$X_{231}$	$X_{321}$
	$⋮$	$⋮$	$⋮$	$⋮$	$⋮$	$⋮$	$⋮$
	2023	$Y_{139}$	$Y_{239}$	$Y_{339}$	$Y_{139}$	$X_{239}$	$X_{339}$
Sulawesi	2015	$Y_{141}$	$Y_{241}$	$Y_{341}$	$X_{141}$	$X_{241}$	$X_{341}$
	$⋮$	$⋮$	$⋮$	$⋮$	$⋮$	$⋮$	$⋮$
	2023	$Y_{149}$	$Y_{249}$	$Y_{349}$	$Y_{149}$	$X_{249}$	$X_{349}$
Papua-Maluku-Nusa Tenggara	2015	$Y_{151}$	$Y_{251}$	$Y_{351}$	$X_{151}$	$X_{251}$	$X_{351}$
	$⋮$	$⋮$	$⋮$	$⋮$	$⋮$	$⋮$	$⋮$
	2023	$Y_{159}$	$Y_{259}$	$Y_{359}$	$Y_{159}$	$X_{259}$	$X_{359}$

Source: Own, 2025.

, where the research subjects consist of 5 main regions in Indonesia.

where

• $Y_{1ji}$: Response 1 in Region j, observation k.
• $Y_{2ji}$: Response 2 in Region j, observation k.
• $Y_{3ji}$: Response 3 in Region j, observation k.
• $Y_{1ji}$: Independent Variable 1 in Region j, observation k.
• $Y_{2ji}$: Independent Variable 2 in Region j, observation k.
• $Y_{3ji}$: Independent Variable 3 in Region j, observation k.

Based on Table 2, there are three independent variables, so the model becomes a nonparametric two-response truncated spline regression model for longitudinal data. The following shows the models formed (Suriaslan et al., 2025):

$$Y_{1ji}=f\left(X_{11 ji}\right)+f\left(X_{21 ji}\right)+f\left(X_{31 ji}\right)+{\epsilon }_{1 ji}$$

(1)

$$Y_{2ji}=f\left(X_{12 ji}\right)+f\left(X_{22 ji}\right)+f\left(X_{32 ji}\right)+{\epsilon }_{1 ji}$$

(2)

$$Y_{3ji}=f\left(X_{13 ji}\right)+f\left(X_{23 ji}\right)+f\left(X_{33 ji}\right)+{\epsilon }_{1 ji}$$

(3)

where j = 1, 2, …, m; i = 1, 2, …, 9; and f(X) also approximated with the truncated spline function:

$$f\left(X_{skji}\right)={\sum }_{q=0}^Q{\alpha }_{kjsq}{X}_{skji}^q+{\sum }_{r=1}^R{\delta }_{kjsr}{\left(X_{skji}-K_{kjsr}\right)}_{+}^Q$$

(4)

$${\left(X_{skji}-K_{kjsr}\right)}_{+}^Q=\left\{\begin{array}{c}{\left(X_{skji}-K_{kjsr}\right)}^Q; X_{skji }\ge K_{kjsr}\\ 0; X_{skji }<K_{kjsr}\end{array}\right.$$

(5)

which will later form an equation in the form of a matrix:

$$\widehat{Y}=X\widehat{\theta }$$

(6)

The application of the truncated spline nonparametric regression model for longitudinal data in this study begins with determining the weights used in modelling (V). Next, a model is formed as in Equation (6). Then, modelling is carried out using a truncated spline nonparametric multiresponse regression approach for longitudinal data. The next step is to select the optimal knot points using the GCV method, which is determined based on the smallest GCV value obtained from Equation (7), which is as follows:

$$GCV\left(h\right)={\displaystyle \frac{MSE\left(h\right)}{{\left[\frac{1}{lmn}trace\left(I-A\left(h\right)\right)\right]}^2}}$$

(7)

where the MSE value is used to determine the best model, and the final step is to obtain the CPR and unmet need models for each region.

4. Results

Table 3. Summary statistic.

Region	Variable	Mean	Var.	Std Dev.	Kurtosis	Skewness	Minimum	Maximum
Sumatra	$Y_1$	2.75	0.91	0.95	4.84	−1.57	0.47	3.85
	$Y_2$	3.34	0.11	0.31	−1.16	0.09	2.88	3.79
	$Y_3$	18.04	0.35	0.59	0.22	0.71	17.34	19.16
	$X_1$	4708.5	5931.14	77.01	−0.28	−0.26	4585.6	4816.8
	$X_2$	4877.71	3499.89	59.16	3.95	1.48	4817.9	5016.3
	$X_3$	9199.99	27,675.89	166.36	5.78	−1.89	8707.1	9237.1
Java-Bali	$Y_1$	2.75	1.56	1.25	0.99	0.31	1.29	5.10
	$Y_2$	3.60	0.12	0.34	0.36	0.28	3.07	4.21
	$Y_3$	9.37	0.14	0.37	−0.54	0.81	8.66	9.95
	$X_1$	4980.59	1147.81	33.88	−0.84	0.11	4915.33	5015.33
	$X_2$	4731.90	2449.50	49.49	1.12	2.08	4670.33	4838.17
	$X_3$	8890.45	27,786.17	166.69	−2.25	5.61	8478.67	9015.67
Kalimantan	$Y_1$	2.34	0.74	0.86	−0.29	0.33	1.01	3.67
	$Y_2$	4.87	0.30	0.55	−0.89	0.62	4.26	5.73
	$Y_3$	12.35	0.38	0.62	−0.77	−0.32	11.40	13.20
	$X_1$	5531.64	6267.07	79.16	0.08	0.28	5420	5670.80
	$X_2$	5788.70	24,559.07	156.71	6.95	−2.50	5389.20	5931
	$X_3$	9327.03	28,947.65	170.14	5.36	−2.19	8090.60	9458.20
Sulawesi	$Y_1$	3.93	2.75	1.66	1.78	−1.26	0.39	5.69
	$Y_2$	3.19	0.08	0.29	0.63	0.11	2.71	3.72
	$Y_3$	17.14	0.14	0.37	1.04	0.89	16.71	17.90
	$X_1$	4700.35	3199.14	56.56	1.98	−1.47	4578.17	4753.33
	$X_2$	5080.17	20,858.3	144.42	7.17	−2.57	4709.83	5196.50
	$X_3$	8984.31	29,352.9	171.33	5.45	−2.22	8562.83	9108.33
Papua-Maluku-Nusa Tenggara	$Y_1$	3.80	2.067	1.437	0.379	−0.926	1.02	5.40
	$Y_2$	4.06	0.275	0.524	−0.21	0.951	3.47	4.95
	$Y_3$	8.32	0.073	0.271	−0.466	0.109	7.93	8.75
	$X_1$	4736.68	3286.78	57.33	1.87	−0.709	4621.33	4829.50
	$X_2$	4992.61	10,940.73	104.59	5.59	2.167	4899.17	5250.17
	$X_3$	8939.39	28,648.75	169.26	5.489	−2.221	8522.67	9069.17
Cumulative	$Y_1$	3.11	1.8696	1.3673	−0.60075	0.05116	0.39	5.69
	$Y_2$	3.81	0.5335	0.7304	0.3759	0.918	2.71	5.73
	$Y_3$	13.04	16.159	4.0198	−1.7178	0.13102	7.93	19.16
	$X_1$	4931.55	106,633.9	326.54	−0.0733	1.11697	45,787.17	5670.80
	$X_2$	5094.22	149,573.1	385.45	0.02178	1.09658	4670.33	5931
	$X_3$	9052.23	51179,64	226.64	0.581815	−0.3891	8478.67	9458.20

Source: Own, 2025.

shows a summary of the statistics for the variables used. The results show unique dynamics that reflect the socio-economic and geographical characteristics of each region. In the Java-Bali Region, the dependent variables tend to have lower average values for unemployment and poverty, but agricultural sector growth is also relatively low. This indicates that although relative welfare is better, the contribution of the agricultural sector in this region is no longer dominant, possibly due to the structural transition to more established industrial and service sectors. On the other hand, Sulawesi and Papua-Maluku-Nusa Tenggara Regions show high average agricultural sector growth and unemployment rates, indicating strong dependence on the primary sector but without corresponding optimisation of employment opportunities.

An interesting phenomenon is also seen in the Kalimantan Region, where the average rural poverty rate is quite high despite significant migration and land conversion. This may reflect disparities in the distribution of development outcomes or land conversion that has not fully contributed to poverty reduction. Conversely, in the Sumatra Region, despite high average migration and village fund values, the agricultural sector and unemployment show fluctuating dynamics, as evidenced by high kurtosis and skewness in some variables. This indicates an asymmetrical data distribution and the presence of outliers, reflecting districts/cities that are outliers in rural development.

Cumulatively, these results indicate that agricultural sector growth in rural areas exhibits significant variation but has a relatively low average compared to unemployment and poverty levels. This highlights the significant challenges in developing this sector as the primary driver of improved well-being. The inequality in the distribution of village funds is also quite high due to the large variation, which can impact the effectiveness of development programmes in various regions. The accumulation of these various inequalities and variations reflects that policy interventions must be tailored to the context of each region, as there is no single approach that fits all areas.

To provide an overview or preliminary information regarding the relationship between the response variable and the predictor variable for each group, a scatter plot was created (Figure 1), which provides information about the shape of the regression curve used in the modelling. The plot shows that the data points are scattered and do not form a specific pattern, so a nonparametric regression approach is a viable option.

The nonparametric regression approach is relevant because it does not require a specific function between the response variable and the predictor variable, such as linear or polynomial. When the scatter plot shows data dispersion that does not follow a specific pattern or is nonlinear, this approach can capture data variation more flexibly. In this context, nonparametric regression such as spline or kernel regression allows the formation of curves that follow the natural structure of the data without rigid assumptions, so the estimation results are more representative of the actual relationship between the variables.

In this study, nonparametric biresponse regression was used because it involved more than one response variable with a truncated spline approach for longitudinal data. The optimal knot was determined using the GCV method with one, two, and three knot points. MSE was used the model goodness criterion. Wu and Zhang (2006) was used as reference for the weight matrix models, which is the number of observations in each subject, defined as:

$$V=\left[diag\left({\displaystyle \frac{1}{n}},{\displaystyle \frac{1}{n}},\dots {\displaystyle \frac{1}{n}}\right)\right]$$

(8)

The analysis was conducted for each region with the aim of modelling each subject in that region. In the nonparametric spline truncated regression model approach, knot points are points of convergence where changes in behaviour patterns occur in the function. In a plot between the response variable and the predictor variable, several segments can be created based on the knot points. The location of the knot points and the number of knots are very important.

The GCV method is used to determine the optimal location of knot points in each variable. The number of knots used varies, ranging from one to three knot points per variable. The following are the knot points and GCV values for each variable in each subject using V weighting.

Table 4. Summary of the smallest GCV.

Region	Knot			GCV
	${\mathit{X}}_1$	${\mathit{X}}_2$	${\mathit{X}}_3$	1.541979 × 10−5
Sumatera	4595.04	4826	8728.72
Jawa-Bali	4919.41	4677.18	8500.59
Kalimantan	5430.24	5411.31	8931.99
Sulawesi	4585.32	4729.7	8585.1
Papua-Maluku-Nusa Tenggara	4629.83	4913.49	8544.97

,

Table 5. Summary of the smallest GCV for 2 knots.

Region	Knot			GCV
	${\mathit{X}}_1$	${\mathit{X}}_2$	${\mathit{X}}_3$	6.651156 × 10−8
Sumatera	4689.4	4906.98	8945.06
	4788.49	4992.01	9172.2
Jawa-Bali	4960.23	4745.69	8719.77
	5003.09	4817.62	8949.91
Kalimantan	5532.6	5632.46	9155.91
	5640.09	5864.66	9331.02
Sulawesi	4656.81	4928.34	8807.75
	4731.88	5136.91	9041.54
Papua-Maluku-Nusa Tenggara	4714.8	5056.76	8768.03
	4804.01	5207.19	9002.25

and

Table 6. Summary of the smallest GCV for 3 knots.

Region	Knot			GCV
	${\mathit{X}}_1$	${\mathit{X}}_2$	${\mathit{X}}_3$	1.071831 × 10−23
Sumatera	4741.31	4951.52	9064.04
	4779.05	4983.91	9150.74
	4793.21	4996.06	9183.02
Jawa-Bali	4982.68	4783.36	8840.32
	4999.01	4810.77	8927.99
	5005.13	4821.04	8960.87
Kalimantan	5588.91	5754.09	9279.02
	5629.85	5842.54	9368.63
	5645.21	5875.71	9402.22
Sulawesi	4696.14	5038.59	8930.21
	4724.73	5117.04	9019.27
	4735.46	5146.84	9052.67
Papua-Maluku-Nusa Tenggara	4761.53	5135.55	8890.72
	4795.51	5192.35	8979.94
	4808.26	5214.35	9013.4

Source: Own, 2025.

show the knot points formed for each smallest GCV value. Each knot point will produce many alternative knot points with various GCV values. Knot point 1 produces 48 alternative knot points with each GCV value, and it is known that the smallest GCV is 1.541979 × 10⁻⁵. Knot point 2 produces 1128 alternative knot points, with each variable possessing two knot points. From these results, it is known that the smallest GCV for two knot points is 6.651156 × 10⁻⁸. Knot point 3 produces 17,296 alternative combinations of knot points, with each variable possessing three knot points. The smallest GCV value produced for three knot points is 1.071831 × 10⁻²³.

After determining the GCV values for each knot point, the next step is to select the smallest GCV value among one, two, and three knot points. The smallest GCV is indicated by GCV for 3 knots with a value of 1.071831 × 10⁻²³, so the knot points to be used in the modelling are those listed in Table 6, where each variable for each subject has three knot points. The next step is to use the optimal knot points to perform modelling to obtain the model parameter estimates.

The model parameter estimates were obtained for all parameters to form a model for each region.

• Sumatra Region

Table 7. Parameter estimates for the Sumatra Region.

$\mathbf{Parameter} \mathbf{for} {\mathit{Y}}_1$		$\mathbf{Parameter} \mathbf{for} {\mathit{Y}}_2$		$\mathbf{Parameter} \mathbf{for} {\mathit{Y}}_3$
${\alpha }_{11}$	−1.28079	${\alpha }_{12}$	0.36572	${\alpha }_{13}$	0.12522
${\beta }_{110}$	−0.13844	${\beta }_{120}$	−0.05053	${\beta }_{130}$	−0.057781
${\beta }_{111}$	0.11633	${\beta }_{121}$	−0.095513	${\beta }_{131}$	−0.011027
${\beta }_{112}$	0.01153	${\beta }_{122}$	−0.083886	${\beta }_{132}$	0.044267
${\beta }_{113}$	−0.08044	${\beta }_{123}$	−0.145409	${\beta }_{133}$	−0.09667
${\gamma }_{110}$	−0.18262	${\gamma }_{120}$	−0.068318	${\gamma }_{130}$	−0.04492
${\gamma }_{111}$	−0.16327	${\gamma }_{121}$	−0.037542	${\gamma }_{131}$	−0.12482
${\gamma }_{112}$	−0.08013	${\gamma }_{122}$	−0.32828	${\gamma }_{132}$	−0.11841
${\gamma }_{113}$	−0.09130	${\gamma }_{123}$	−0.341591	${\gamma }_{133}$	0.084318
${\delta }_{110}$	−0.28662	${\delta }_{120}$	−0.066798	${\delta }_{130}$	−0.020638
${\delta }_{111}$	0.14035	${\delta }_{121}$	−0.320368	${\delta }_{131}$	−0.0699003
${\delta }_{112}$	−0.057067	${\delta }_{122}$	−0.213495	${\delta }_{132}$	−0.0849129
${\delta }_{113}$	0.564686	${\delta }_{123}$	−0.68305	${\delta }_{133}$	−0.44297

shows the parameter estimates generated for the model in the Sumatra Region.

Based on Table 7, the models formed for the Sumatra Region for each variable are as follows:

$$\begin{array}{c}{\widehat{Y}}_{11i}=-1.28079-0.13844X_{11i}+0.11633\left(X_{11i}+4741.31\right)\\ \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em} +0.01153\left(X_{11i}+4779.05\right)-0.08044\left(X_{11i}+4793.21\right)\\ \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em} -0.18262X_{21i}-0.16327\left(X_{21i}+4951.52\right)\\ \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}- 0.08013\left(X_{21i}+4983.91\right)-0.09130\left(X_{21i}+4996.06\right)\\ \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em} -0.28662X_{31i}+0.14035\left(X_{31i}+9064.04\right)\\ \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}- 0.057067\left(X_{31i}+9150.74\right)+0.564686\left(X_{31i}+9183.02\right)\end{array}$$

$$\begin{array}{c}{\widehat{Y}}_{21i}=0.36572-0.05053X_{11i}-0.095513\left(X_{11i}+4741.31\right)\\ \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}- 0.083886\left(X_{11i}+4779.05\right)-0.145409\left(X_{11i}+4793.21\right)\\ \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em} -0.068318X_{21i}-0.037542\left(X_{21i}+4951.52\right)\\ \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em} - 0.32828\left(X_{21i}+4983.91\right)-0.341591\left(X_{21i}+4996.06\right)\\ \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em} - 0.066798X_{31i}-0.320368\left(X_{31i}+9064.04\right)\\ \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em} -0.213495\left(X_{31i}+9150.74\right)-0.68305\left(X_{31i}+9183.02\right)\end{array}$$

$$\begin{array}{c}{\widehat{Y}}_{31i}=0.12522-0.057781X_{11i}-0.011027\left(X_{11i}+4741.31\right)\\ \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}+ 0.044267\left(X_{11i}+4779.05\right)+0.09667\left(X_{11i}+4793.21\right)\\ \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}- 0.04492X_{21i}-0.12482\left(X_{21i}+4951.52\right)\\ \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}- 0.11841\left(X_{21i}+4983.91\right)+0.084318\left(X_{21i}+4996.06\right)\\ \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em} +0.020638X_{31i}-0.0699003\left(X_{31i}+9064.04\right)\\ \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em} -0.0849129\left(X_{31i}+9150.74\right)-0.44297\left(X_{31i}+9183.02\right)\end{array}$$

Based on these models with regards on to agricultural sector growth, when there is a migration of 4741 to 4779 people, agricultural sector growth in rural areas decreases by 0.01058 per cent, while if it is more than 4779 people, growth decreases by 0.09102 per cent. Furthermore, if there is a land use change of 4951.52 to 4983.91 hectares, growth in decreases by 0.42602 percent, while if it exceeds 4983.91 hectares, growth decreases by 0.51732 percent. Finally, if the amount of village funds obtained is between IDR 9064.04 and 9150.74 million, growth decreases by 0.20337 percent, while if it exceeds IDR 9150.74 million, it will increase agricultural sector growth by 0.36109 percent.

The interpretation of the model regarding the rural poverty variable shows that when there is a migration of 4741 to 4779 people, the number of poor people in rural areas decreases by 0.229929 percent, while if it is more than 4779 people, this number decreases by 0.313317 percent. Furthermore, if there is a land use change of 4951.52 to 4983.91 hectares, the number decreases by 0.434138 percent, while if it is above 4983.91 hectares, the number decreases by 0.7757 percent. Finally, if the amount of village funds obtained is between IDR 9064.04 and 9150.74 million, the number decreases by 0.470377 percent, while if it is more than IDR 9150.74 million, the number decreases by 1.153427 percent.

The interpretation of the model regarding the rural unemployment variable, shows that when there is a migration of 4741 to 4779 people, unemployment in rural areas decreases by 0.023784 percent, while if it is more than 4779 people, unemployment decreases by 0.120454 percent. Furthermore, if there is a land use change of 4951.52 to 4983.91 hectares, unemployment decreases by 0.28821 percent, while if it is above 4983.91 hectares, unemployment decreases by 0.20383 percent. Finally, if the amount of village funds obtained is between IDR 9064.04 and 9150.74 million unemployment decreases by 0.13414 percent, while if it exceeds IDR 9150.74 million, unemployment decreases by 0.577119 percent.

2.

Java-Bali Regions

Table 8. Parameter estimates for the Java-Bali Region.

$\mathbf{Parameter} \mathbf{for} {\mathit{Y}}_1$		$\mathbf{Parameter} \mathbf{for} {\mathit{Y}}_2$		$\mathbf{Parameter} \mathbf{for} {\mathit{Y}}_3$
${\alpha }_{21}$	−0.43992	${\alpha }_{22}$	−0.314057	${\alpha }_{23}$	−1.66752
${\beta }_{210}$	−0.07927	${\beta }_{220}$	0.09732	${\beta }_{230}$	−0.08339
${\beta }_{211}$	0.07802	${\beta }_{221}$	−0.48891	${\beta }_{231}$	−0.09284
${\beta }_{212}$	−0.37767	${\beta }_{222}$	−0.21743	${\beta }_{232}$	−0.03062
${\beta }_{213}$	−0.08924	${\beta }_{223}$	−0.26431	${\beta }_{233}$	−0.01903
${\gamma }_{210}$	−0.04068	${\gamma }_{220}$	−0.12359	${\gamma }_{230}$	−0.02787
${\gamma }_{211}$	−0.68654	${\gamma }_{221}$	−0.33651	${\gamma }_{231}$	−0.02977
${\gamma }_{212}$	0.202272	${\gamma }_{222}$	−0.32156	${\gamma }_{232}$	−0.02839
${\gamma }_{213}$	0.133263	${\gamma }_{123}$	−0.05503	${\gamma }_{233}$	−0.01393
${\delta }_{210}$	−0.02837	${\delta }_{220}$	−0.55021	${\delta }_{230}$	0.02655
${\delta }_{211}$	0.13347	${\delta }_{221}$	−0.21031	${\delta }_{231}$	−0.31901
${\delta }_{212}$	−0.03351	${\delta }_{222}$	−0.82593	${\delta }_{232}$	−0.08712
${\delta }_{213}$	−0.06003	${\delta }_{223}$	−0.30685	${\delta }_{233}$	−0.01165

shows the parameter estimates generated for the model in the Java-Bali Regions.

Based on Table 8, the models formed for the Java-Bali Regions for each variable are as follows:

$$\begin{array}{c}{\widehat{Y}}_{12i}=-0.43992-0.07927X_{12i}+0.07802\left(X_{12i}+4982.68\right)\\ \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}-0.37767\left(X_{12i}+4999.01\right)-0.08924\left(X_{12i}+5005.13\right)\\ \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}-0.04068X_{22i}-0.68654\left(X_{21i}+4783.36\right)\\ \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}+0.202272\left(X_{22i}+4810.77\right)+0.133263\left(X_{22i}+4821.04\right)\\ \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}-0.02837X_{32i}+0.13347\left(X_{32i}+8840.32\right)\\ \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}-0.03351\left(X_{32i}+8927.99\right)+0.06003\left(X_{32i}+8960.87\right)\end{array}$$

$$\begin{array}{c}{\widehat{Y}}_{22i}=-0.314057+0.09732X_{12i}-0.48891\left(X_{12i}+4982.68\right)\\ \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}-0.21743\left(X_{12i}+4999.01\right)-0.26431\left(X_{12i}+5005.13\right)\\ \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}-0.12359X_{22i}-0.33651\left(X_{21i}+4783.36\right)\\ \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}-0.32156\left(X_{22i}+4810.77\right)-0.05503\left(X_{22i}+4821.04\right)\\ \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}-0.55021X_{32i}-0.21031\left(X_{32i}+8840.32\right)\\ \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}-0.82593\left(X_{32i}+8927.99\right)-0.30685\left(X_{32i}+8960.87\right)\end{array}$$

$$\begin{array}{c}{\widehat{Y}}_{32i}=-1.66752-0.08339X_{12i}-0.09284\left(X_{12i}+4982.68\right)\\ \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}-0.03062\left(X_{12i}+4999.01\right)-0.01903\left(X_{12i}+5005.13\right)\\ \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}-0.02787X_{22i}-0.02977\left(X_{21i}+4783.36\right)\\ \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}-0.02839\left(X_{22i}+4810.77\right)-0.01393\left(X_{22i}+4821.04\right)\\ \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}+0.02655X_{32i}-0.31901\left(X_{32i}+8840.32\right)\\ \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}-0.08712\left(X_{32i}+8927.99\right)-0.01165\left(X_{32i}+8960.87\right)\end{array}$$

Based on these models with regard, the agricultural sector growth variable when there is a population migration of 4982 to 4999 people, agricultural sector growth in rural areas decreases by 0.37892 per cent, while if it is more than 4999 people, growth decreases by 0.46816 per cent. Furthermore, if there is a land use change of 4783.36 to 4810.77 hectares, growth decreases by 0.929492 percent, while if it exceeds 4810.77 hectares, sector growth decreases by 1.062755 percent. Finally, if the amount of village funds obtained is between IDR 8840.32 and 8927.99 million, growth decreases by 0.07159%, while if it exceeds IDR 8927.99 million, growth decreases by 0.13162%.

The interpretation of the model regarding the rural poverty variable, shows that when there is a migration of 4982 to 4999 people, the number of poor people in rural areas decreases by 0.60902 percent, while if it is more than 4999 people, this number decreases by 0.87333 percent. Furthermore, if there is a land use change of 4783.36 to 4810.77 hectares, the number decreases by 0.78166 percent, while if it is more than 4810.77 hectares, the number decreases by 0.83669 percent. Finally, if the amount of village funds obtained is between IDR 8840.32 and 8927.99 million, the number decreases by 1.58645 percent, while if it exceeds IDR 8927.99 million, the number decreases by 1.8933 percent.

The interpretation of the model regarding the rural unemployment variable, shows that when there is a migration of 4982 to 4999 people, unemployment in rural areas decreases by 0.20685 percent, while if it is more than 4999 people, unemployment decreases by 0.22588 percent. Furthermore, if there is a land use change of 4783.36 to 4810.77 hectares, unemployment decreases by 0.08596 percent, while if it exceeds 4810.77 hectares, unemployment decreases by 0.09926 percent. Finally, if the amount of village funds obtained is between IDR 8840.32 and 8927.99 million, unemployment decreases by 0.37958 percent, while if it exceeds IDR 8927.99 million, unemployment decreases by 0.39123 percent.

3.

Kalimantan Region

Table 9. Parameter estimates for the Kalimantan Region.

$\mathbf{Parameter} \mathbf{for} {\mathit{Y}}_1$		$\mathbf{Parameter} \mathbf{for} {\mathit{Y}}_2$		$\mathbf{Parameter} \mathbf{for} {\mathit{Y}}_3$
${\alpha }_{31}$	2.72194	${\alpha }_{32}$	−0.63602	${\alpha }_{33}$	−0.09257
${\beta }_{310}$	−0.04992	${\beta }_{320}$	−0.53717	${\beta }_{330}$	−0.08799
${\beta }_{311}$	−0.09546	${\beta }_{321}$	−0.11715	${\beta }_{331}$	−0.30345
${\beta }_{312}$	−0.02721	${\beta }_{322}$	−0.30236	${\beta }_{332}$	−0.02563
${\beta }_{313}$	−0.02316	${\beta }_{323}$	−0.33962	${\beta }_{333}$	−0.06266
${\gamma }_{310}$	−0.02539	${\gamma }_{320}$	−0.05093	${\gamma }_{330}$	0.07316
${\gamma }_{311}$	−0.05145	${\gamma }_{321}$	−0.06201	${\gamma }_{331}$	−0.12366
${\gamma }_{312}$	−0.10928	${\gamma }_{322}$	−0.04278	${\gamma }_{332}$	−0.24207
${\gamma }_{313}$	−0.12699	${\gamma }_{323}$	−0.03485	${\gamma }_{333}$	−0.09138
${\delta }_{310}$	0.08762	${\delta }_{320}$	−0.07182	${\delta }_{330}$	−0.09363
${\delta }_{311}$	−0.02598	${\delta }_{321}$	−0.26742	${\delta }_{331}$	−0.01599
${\delta }_{312}$	−0.07935	${\delta }_{322}$	−0.34113	${\delta }_{332}$	−0.07601
${\delta }_{313}$	−0.05895	${\delta }_{323}$	−0.17427	${\delta }_{333}$	−0.01807

shows the parameter estimates generated for the model in the Kalimantan Region.

Based on Table 9, the models formed for the Kalimantan Region for each variable are as follows:

$$\begin{array}{c}{\widehat{Y}}_{13i}=2.72194-0.04992X_{13i}-0.09546\left(X_{13i}+5588.91\right)\\ \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}-0.02721\left(X_{13i}+5629.85\right)-0.02316\left(X_{13i}+5645.21\right)\\ \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}-0.02539X_{23i}-0.05145\left(X_{23i}+5754.09\right)\\ \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}-0.10928\left(X_{23i}+5842.54\right)-0.12699\left(X_{23i}+5875.71\right)\\ \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}+0.08762X_{33i}-0.02598\left(X_{33i}+9279.02\right)\\ \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}-0.07935\left(X_{33i}+9368.63\right)-0.05895\left(X_{32i}+9402.22\right)\end{array}$$

$$\begin{array}{c}{\widehat{Y}}_{23i}=-0.3602-0.53717X_{13i}-0.11715\left(X_{13i}+5588.91\right)\\ \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}-0.30236\left(X_{13i}+5629.85\right)-0.33962\left(X_{13i}+5645.21\right)\\ \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}-0.05093X_{23i}-0.06201\left(X_{23i}+5754.09\right)\\ \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}-0.04278\left(X_{23i}+5842.54\right)-0.03485\left(X_{23i}+5875.71\right)\\ \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}-0.07182X_{33i}-0.26742\left(X_{33i}+9279.02\right)\\ \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}-0.34113\left(X_{33i}+9368.63\right)-0.17427\left(X_{32i}+9402.22\right)\end{array}$$

$$\begin{array}{c}{\widehat{Y}}_{33i}=-0.09257-0.08799X_{13i}-0.30345\left(X_{13i}+5588.91\right)\\ \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}-0.02563\left(X_{13i}+5629.85\right)-0.06266\left(X_{13i}+5645.21\right)\\ \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}+0.07316X_{23i}-0.1236\left(X_{23i}+5754.09\right)\\ \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}-0.24207\left(X_{23i}+5842.54\right)-0.09138\left(X_{23i}+5875.71\right)\\ \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}-0.09363X_{33i}-0.01599\left(X_{33i}+9279.02\right)\\ \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}-0.07601\left(X_{33i}+9368.63\right)-0.01807\left(X_{32i}+9402.22\right)\end{array}$$

Based on these models with regards the agricultural sector growth variable, when there is a population migration of 5588 to 5629 people, agricultural sector growth in rural areas decreases by 0.17259 per cent, while if it is more than 5629 people, growth decreases by 0.19575 per cent. Furthermore, if there is a land use change of 5754.09 to 5842.54 hectares, growth decreases by 0.18612 percent, while if it exceeds 5842.54 hectares, growth decreases by 1.31311 percent. Finally, if the amount of village funds obtained is between IDR 9279.02 and 9368.63 million, growth decreases by 0.03566 percent, whereas if it exceeds IDR 9368.63 million, growth decreases by 0.02329 percent.

The interpretation of the model regarding the rural poverty variable, indicates that when migration occurs between 5588 and 5629 people, the number of poor people in rural areas decreases by 0.95661 percent, while if it exceeds 5629 people, the number decreases by 1.29623 percent. Furthermore, if there is a land use change of 5754.09 to 5842.54 hectares, the number decreases by 0.15572 percent, while if it is above 5754.09 hectares, the number decreases by 0.19057 percent. Finally, if the amount of village funds obtained is between IDR 9279.02 and 9368.63 million, the number decreases by 0.68037 percent, while if it exceeds IDR 9368.63 million, the number decreases by 0.85464 percent.

The interpretation of the model regarding the rural unemployment variable shows that when there is a population migration of 5588 to 5629 people, unemployment in rural areas decreases by 0.39174 percent, while if it is more than 5629 people, unemployment decreases by 0.47937 percent. Furthermore, if there is a land use change of 5754.09 to 5842.54 hectares, unemployment decreases by 0.29251 percent, while if it exceeds 5842.54 hectares, unemployment decreases by 0.38389 percent. Finally, if the amount of village funds obtained is between IDR 9297.02 and 9368.63 million, unemployment decreases by 0.18563%, while if exceeds IDR 9368.63 million, unemployment decreases by 0.2037%.

4.

Sulawesi Region

Table 10. Parameter estimates for the Sulawesi Region.

$\mathbf{Parameter} \mathbf{for} {\mathit{Y}}_1$		$\mathbf{Parameter} \mathbf{for} {\mathit{Y}}_2$		$\mathbf{Parameter} \mathbf{for} {\mathit{Y}}_3$
${\alpha }_{41}$	0.69345	${\alpha }_{42}$	−1.30645	${\alpha }_{43}$	−0.01093
${\beta }_{410}$	−0.02262	${\beta }_{420}$	−0.56417	${\beta }_{430}$	−0.21971
${\beta }_{411}$	−0.01228	${\beta }_{421}$	−0.10393	${\beta }_{431}$	−0.12637
${\beta }_{412}$	−0.01943	${\beta }_{422}$	−0.43784	${\beta }_{432}$	−0.14135
${\beta }_{413}$	−0.06458	${\beta }_{423}$	−0.18475	${\beta }_{433}$	−0.05709
${\gamma }_{410}$	−0.05381	${\gamma }_{420}$	−0.19427	${\gamma }_{430}$	−0.52637
${\gamma }_{411}$	−0.01861	${\gamma }_{421}$	−0.06786	${\gamma }_{431}$	−0.19458
${\gamma }_{412}$	−0.06928	${\gamma }_{422}$	−0.10761	${\gamma }_{432}$	−0.13463
${\gamma }_{413}$	−0.02691	${\gamma }_{423}$	−0.09713	${\gamma }_{433}$	−0.02631
${\delta }_{410}$	0.02241	${\delta }_{420}$	−0.24828	${\delta }_{430}$	−0.04206
${\delta }_{411}$	−0.04331	${\delta }_{421}$	−0.21725	${\delta }_{431}$	−0.04842
${\delta }_{412}$	−0.01681	${\delta }_{422}$	−0.60711	${\delta }_{432}$	−0.16449
${\delta }_{413}$	−0.06958	${\delta }_{423}$	−0.90406	${\delta }_{433}$	−0.11038

shows the parameter estimates generated for the model in the Sulawesi Region

Based on Table 10, the models formed for the Sulawesi Region for each variable are as follows:

$$\begin{array}{c}{\widehat{Y}}_{14i}=0.69345-0.02262X_{14i}-0.01228\left(X_{14i}+4696.14\right)\\ \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}-0.01943\left(X_{14i}+4724.73\right)-0.06458\left(X_{14i}+4735.46\right)\\ \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}-0.05381X_{24i}-0.01861\left(X_{24i}+5038.71\right)\\ \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}-0.06928\left(X_{24i}+5117.04\right)-0.02691\left(X_{24i}+5146.84\right)\\ \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}+0.02241X_{34i}-0.04331\left(X_{34i}+8930.21\right)\\ \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}-0.01681\left(X_{34i}+9019.27\right)-0.06958\left(X_{34i}+9052.67\right)\end{array}$$

$$\begin{array}{c}{\widehat{Y}}_{24i}=-1.30645-0.56417X_{14i}-0.10393\left(X_{14i}+4696.14\right)\\ \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}-0.43784\left(X_{14i}+4724.73\right)-0.18475\left(X_{14i}+4735.46\right)\\ \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}-0.19427X_{24i}-0.06786\left(X_{24i}+5038.71\right)\\ \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}-0.10761\left(X_{24i}+5117.04\right)-0.09713\left(X_{24i}+5146.84\right)\\ \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}-0.24828X_{34i}-0.21725\left(X_{34i}+8930.21\right)\\ \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}-0.60711\left(X_{34i}+9019.27\right)-0.90406\left(X_{34i}+9052.67\right)\end{array}$$

$$\begin{array}{c}{\widehat{Y}}_{34i}=-0.01093-0.21971X_{14i}-0.12637\left(X_{14i}+4696.14\right)\\ \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}-0.14135\left(X_{14i}+4724.73\right)-0.05709\left(X_{14i}+4735.46\right)\\ \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}-0.52637X_{24i}-0.19458\left(X_{24i}+5038.71\right)\\ \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}-0.13463\left(X_{24i}+5117.04\right)-0.02631\left(X_{24i}+5146.84\right)\\ \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}-0.04206X_{34i}-0.04842\left(X_{34i}+8930.21\right)\\ \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}-0.16449\left(X_{34i}+9019.27\right)-0.11038\left(X_{34i}+9052.67\right)\end{array}$$

Based on these models with regard to the agricultural sector growth variable, when there is a migration of 4696 to 4724 people, agricultural sector growth in rural areas decreases by 0.05433 per cent, while if more than 4724 people migrate, growth decreases by 0.11891 per cent. Furthermore, if there is a land use change of 5038.71 to 5117.04 hectares, growth decreases by 0.1417 percent, while if the change exceed 5117.04 hectares, growth decreases by 0.16861 percent. Finally, if the amount of village funds obtained is between IDR 8930.21 and 8930.21 million, growth increases by 0.03771 percent, while if it exceeds IDR 8930.12 million, growth decreases by 0.10729 percent.

The interpretation of the model regarding the rural poverty variable, shows that when there is a migration of 4696 to 4724 people, the number of poor people in rural areas decreases by 1.10594 percent, while if it is more than 4724 people, the number decreases by 1.29069 percent. Furthermore, if there is a land use change of 5038.71 to 5117.04 hectares, the number decreases by 0.36974 percent, while if there is a land use change above 5117.04 hectares, the number decreases by 0.46687 percent. Finally, if the amount of village funds obtained is between IDR 8930.21 and 9019.27 million, the number decreases by 1.07264 percent, while if it is IDR 9019.27 million, the number decreases by 1.97671 percent.

The interpretation of the model regarding the rural unemployment variable, shows that when there is a migration of 4696 to 4724 people, unemployment in rural areas decreases by 0.48743 percent, while if it is more than 4724 people, unemployment decreases by 0.54452 percent. Furthermore, if there is a land use change of 5038.71 to 5117.04 hectares, unemployment decreases by 0.85558 percent, while if there is a land use change exceeding 5117.04 hectares, unemployment decreases by 0.88189 percent. Finally, if the amount of village funds obtained is between IDR 8930.21 and 9019.27 million, unemployment decreases by 0.25497 percent, while if it exceeds 9019.27 million, unemployment decreases by 0.36535 percent.

5.

Papua-Maluku-Nusa Tenggara Regions

Table 11. Parameter estimates for the Papua-Maluku-Nusa Tenggara Region.

$\mathbf{Parameter} \mathbf{for} {\mathit{Y}}_1$		$\mathbf{Parameter} \mathbf{for} {\mathit{Y}}_2$		$\mathbf{Parameter} \mathbf{for} {\mathit{Y}}_3$
${\alpha }_{51}$	−0.22175	${\alpha }_{52}$	−1.63011	${\alpha }_{53}$	−0.19956
${\beta }_{510}$	−0.01431	${\beta }_{520}$	−0.02283	${\beta }_{530}$	−0.01294
${\beta }_{511}$	−0.01895	${\beta }_{521}$	−0.03474	${\beta }_{531}$	−0.01378
${\beta }_{512}$	−0.08712	${\beta }_{522}$	−0.08102	${\beta }_{532}$	−0.01918
${\beta }_{513}$	−0.09716	${\beta }_{523}$	−0.07915	${\beta }_{533}$	−0.22792
${\gamma }_{510}$	−0.05316	${\gamma }_{520}$	−0.07021	${\gamma }_{530}$	−0.31912
${\gamma }_{511}$	−0.13524	${\gamma }_{521}$	−0.03539	${\gamma }_{531}$	−0.04421
${\gamma }_{512}$	−0.10759	${\gamma }_{522}$	−0.34341	${\gamma }_{532}$	−0.30861
${\gamma }_{513}$	−0.83968	${\gamma }_{523}$	−0.13252	${\gamma }_{533}$	0.01596
${\delta }_{510}$	−0.20391	${\delta }_{520}$	−0.07865	${\delta }_{530}$	−0.11615
${\delta }_{511}$	−0.06724	${\delta }_{521}$	−0.19847	${\delta }_{531}$	−0.19289
${\delta }_{512}$	−0.08697	${\delta }_{522}$	−0.14732	${\delta }_{532}$	−0.09975
${\delta }_{513}$	−0.04381	${\delta }_{523}$	−0.32034	${\delta }_{533}$	−0.10283

shows the parameter estimates generated for the model in the Papua-Maluku-Nusa Tenggara Regions.

Based on Table 11, the models formed for the Papua-Maluku-Nusa Tenggara Regions for each variable are as follows:

$$\begin{array}{c}{\widehat{Y}}_{15i}=-0.22175-0.01431X_{15i}-0.01895\left(X_{15i}+4761.53\right)\\ \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}-0.08712\left(X_{15i}+4795.51\right)-0.09716\left(X_{15i}+4808.26\right)\\ \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}-0.05316X_{25i}-0.13524\left(X_{25i}+5135.55\right)\\ \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}-0.10759\left(X_{25i}+5192.35\right)-0.83968\left(X_{25i}+5214.35\right)\\ \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}-0.20391X_{35i}-0.06724\left(X_{35i}+8890.72\right)\\ \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em} -0.08697\left(X_{35i}+8979.94\right)-0.04381\left(X_{34i}+9013.4\right)\end{array}$$

$$\begin{array}{c}{\widehat{Y}}_{25i}=-1.63001-0.02283X_{15i}-0.03474\left(X_{15i}+4761.53\right)\\ \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}-0.08102\left(X_{15i}+4795.51\right)-0.07915\left(X_{15i}+4808.26\right)\\ \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}-0.07021X_{25i}-0.03539\left(X_{25i}+5135.55\right)\\ \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}-0.34341\left(X_{25i}+5192.35\right)-0.13252\left(X_{25i}+5214.35\right)\\ \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}-0.07865X_{35i}-0.19847\left(X_{35i}+8890.72\right)\\ \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em} -0.14732\left(X_{35i}+8979.94\right)-0.32034\left(X_{34i}+9013.4\right)\end{array}$$

$$\begin{array}{c}{\widehat{Y}}_{35i}=-0.19956-0.01294-0.01378\left(X_{15i}+4761.53\right)\\ \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}-0.01918\left(X_{15i}+4795.51\right)-0.22792\left(X_{15i}+4808.26\right)\\ \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}-0.31912X_{25i}-0.04421\left(X_{25i}+5135.55\right)\\ \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}-0.30861\left(X_{25i}+5192.35\right)+0.01596\left(X_{25i}+5214.35\right)\\ \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}-0.11615X_{35i}-0.19289\left(X_{35i}+8890.72\right)\\ \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em} -0.09975\left(X_{35i}+8979.94\right)-0.10283\left(X_{34i}+9013.4\right)\end{array}$$

Based on these models with regard to the agricultural sector growth variable, when there is a migration of 4761 to 4795 people, agricultural sector growth in rural areas decreases by 0.12038 per cent, while if it is more than 4795 people, growth decreases by 0.21754 per cent. Furthermore, if there is a land use change of 5135.55 to 5192.35 hectares, growth decreases by 0.29599 percent, while if his change exceeds 5192.35 hectares, growth decreases by 1.13567 percent. Finally, if the amount of village funding is between IDR 8890.72 and 8979.94 million, growth increases by 0.35812 percent, whereas if it exceeds IDR 8979.94 million, growth increases by 0.40193 percent.

The interpretation of the model regarding the rural poverty variable, shows that when there is a migration of 4761 to 4795 people, the number of poor people in rural areas decreases by 0.13859 percent, while if it is more than 4795 people, the number decreases by 0.21774 percent. Furthermore, if there is a land use change of 5135.55 to 5192.35 hectares, the number decreases by 0.44901 percent, while if it is above 5192.35 hectares, the number decreases by 0.58153 percent. Finally, if the amount of village funds obtained is between IDR 8890.72 and 8979.94 million, the number decreases by 0.42444 percent, while if it exceeds IDR 8979.94 million, the number decreases by 0.74784 percent.

The interpretation of the model regarding the rural unemployment variable, shows that when there is a migration of 4761 to 4795 people, unemployment in rural areas decreases by 0.04587 percent, while if it is more than 4795 people, unemployment decreases by 0.27379 percent. Furthermore, if there is a land use change of 5135.55 to 5192.35 hectares, unemployment decreases by 0.67194 percent, while if exceeds 5192.35 hectares, unemployment decreases by 0.65598 percent. Finally, if the amount of village funds obtained is between IDR 8890.72 and 8979.94 million, unemployment decreases by 0.40879 percent, while if it exceeds IDR 8979.94 million, unemployment decreases by 0.51162 percent.

5. Discussion

The results of this study indicate that the three dependent variables—agricultural sector growth, rural poverty, and rural unemployment—are influenced by three main factors population migration, land use change, and village funds, these factors have significantly varying effects across Indonesia’s major regions. Rather than presenting these findings in isolation, it is important to situate them within broader discussions of rural development and poverty alleviation models. Previous studies in Indonesia have highlighted the persistent role of structural transformation and agricultural modernization in reducing poverty (Drean & Bawono, 2021; Kurnianto, 2024), and our results reinforce this view by showing how migration, land conversion, and village funds interact in complex ways to shape development outcomes.

In general, all regions show that an increase in population migration to and from rural areas tends to have a negative correlation with agricultural sector growth. This phenomenon can be explained from the perspective of labour productivity and the weakening of socio-economic ties to the agricultural sector as population mobility increases. Similar findings have been documented in rural China and India, where large-scale migration reduced the agricultural labour force and undermined sectoral productivity (Lyu et al., 2019; Steiner et al., 2023). This suggests that migration, while sometimes alleviating local unemployment, may simultaneously weaken the sustainability of rural agriculture if not accompanied by complementary investment in agricultural technology and rural industries.

The relationship between village funds and agricultural sector growth tends to be nonlinear, and village funds can drive growth at certain level, but some regions no longer have a positive impact after exceeding a certain threshold. This result echoes evidence from Latin American conditional cash transfer programmes, where financial support reduced rural poverty but had limited direct impact on long-term productivity unless coupled with institutional reforms (Beltran-Peña et al., 2020). This indicates that fiscal transfers such as village funds are effective in alleviating immediate poverty, but their transformative effect depends heavily on governance capacity and alignment with local agricultural priorities.

Land conversion has a negative impact on all three main indicators. The process of land conversion, which reduces the area of agricultural land, directly impacts the decline in agricultural sector productivity and contributes to social issues such as increased household vulnerability. This is consistent with international evidence: Vos and Cattaneo (2021) show that excessive land conversion in developing countries undermines food security, while in Indonesia, it accelerates regional inequality. At the same time, our findings suggest a paradox in some regions where land conversion coincided with lower poverty and unemployment, likely due to the growth of non-agricultural activities, a pattern similar to that observed in Vietnam’s rural industrialisation (Brückner, 2012).

In terms of regional dynamics, Java-Bali exhibits an interesting characteristic, where nearly all independent variables consistently and significantly influence the three dependent variables. This reflects the relatively stable and responsive rural economic structure of Java-Bali to policy interventions. Comparable results have been reported in other middle-income countries where rural governance structures are stronger, allowing development funds to be more effectively absorbed (Ahmed et al., 2014). By contrast, Papua-Maluku-Nusa Tenggara shows a more complex and inconsistent pattern. Village funds, for example, can increase agricultural growth to a certain extent, but their impact is not sustainable and can even be counterproductive if not accompanied by good governance.

Kalimantan and Sulawesi Regions show similar patterns, with village funds contributing steadily to poverty and unemployment reduction. However, the negative impact of land conversion remains a serious issue in this region, indicating a disparity between infrastructure development and the sustainability of the agricultural sector. This again highlights the trade-off between rural industrialisation and agricultural sustainability, a dilemma also observed in Sub-Saharan Africa (Inomjonova, 2024).

Overall, village funds emerge as the most consistent factor in reducing rural poverty levels in almost all regions and have proven to be effective in expanding access to economic resources, increasing local capacity, and opening up micro-business opportunities. Meanwhile, migration plays a dominant role in reducing rural unemployment, likely due to labour redistribution to more productive areas. Land conversion, on the other hand, remains the most influential determinant of agricultural sector growth, underscoring the importance of sustainable land management. By linking these findings to international evidence, this study emphasises that rural development strategies cannot rely solely on fiscal transfers or migration dynamics; rather, they require integrated approaches that combine land-use regulation, governance reform, and local capacity building.

Based on cross-regional analysis, Java-Bali can be considered the best region in terms of the effectiveness of village policies in increasing rural economic growth, showing a balanced and stable pattern of influence. Meanwhile, Papua-Maluku-Nusa Tenggara remains the most vulnerable area, facing significant institutional and infrastructural constraints. This reinforces the argument made in the wider literature that place-based policies are essential, as uniform policy instruments may fail to deliver equitable outcomes across diverse regions (Khairiyakh et al., 2015; Mehraban & Ickowitz, 2021).

6. Conclusions

The results of this study show that the dynamics of agricultural sector growth, poverty rates, and unemployment in rural Indonesia are strongly influenced by the interaction of three main variables, namely population migration, land use change, and village fund allocation. The nonparametric truncated spline regression approach provides a flexible modelling framework, and reveals that the effects of independent variables on dependent variables are not always linear and vary across regions. These findings emphasise the importance of a regionally differentiated approach to designing more targeted policy interventions.

In general, village funds have been shown to make a significant contribution to reducing poverty and unemployment in almost all regions, while land use change remains a major factor constraining agricultural sector growth. The Java-Bali Region shows higher policy effectiveness compared to other regions, whereas the Papua-Maluku-Nusa Tenggara Region faces persistent institutional challenges and requires special attention in policy implementation.

From a policy perspective, these findings underscore the need for strengthening oversight of village fund allocation, integrating sustainable land-use planning, and balancing labour mobility with the creation of local employment opportunities. In particular, expanding the role of agriculture-based SMEs, promoting technology adoption, and improving transparency in financial governance are critical practical steps that can support more inclusive rural development.

Nevertheless, this study has several limitations that should be acknowledged. First, while the longitudinal dataset (2015–2023) enables observation of temporal patterns, it does not allow for strong causal inferences, since the analysis is based on observational rather than experimental data. Second, potential omitted variables such as education quality, health infrastructure, and regional governance capacity may also influence rural development outcomes but are not directly captured in the present model. Third, nonparametric spline regression, while flexible, may be sensitive to knot selection and model specification, which requires careful interpretation. Future research should incorporate robustness checks, such as alternative modelling strategies (e.g., dynamic panel models or instrumental variable approaches), and expand the scope of explanatory variables.

By recognising these limitations, this study contributes to both theory and practice. Theoretically, it highlights the utility of flexible modelling in capturing nonlinear and region-specific development dynamics. Practically, it offers insights for policymakers on tailoring poverty alleviation and agricultural policies according to local contexts, while also pointing to areas where governance and institutional reforms are urgently needed.