The study utilizes data collected from 2006 to 2021. The statistics on CO₂ emissions and energy consumption by sector in Vietnam are sourced from the International Energy Agency (IEA), while the data on employment and GDP in Vietnam’s agricultural sector are obtained from the General Statistics Office of Vietnam ( Table 1 ).

Initially, the study examines the decoupling between CO₂ emissions (C) and economic growth in Vietnam’s agricultural sector. The Decoupling Index (DI), as proposed by Tapio [17] , is used to differentiate economic output from environmental harm. Decoupling CO₂ emissions from economic development is crucial for environmental management [18] . The Decoupling Index (DI) is calculated for the ratio of CO₂ emissions to the GDP of the agricultural sector:

$D{I}_{GDP}=\frac{\raisebox{1ex}{$\left(C_t-C_{t-1}\right)$}\!\left/ \!\raisebox{-1ex}{$C_{t-1}$}\right.}{\raisebox{1ex}{$\left(GD{P}_t-GD{P}_{t-1}\right)$}\!\left/ \!\raisebox{-1ex}{$GD{P}_{t-1}$}\right.}=\frac{\%\Delta C}{\%\Delta GDP}$

where $C_{t-1}$ and $GD{P}_{t-1}$ represent the lagged CO₂ emissions and economic growth. These values are calculated based on the continuous chain method, such as t, (t − 1). %∆C and %∆GDP denote the growth rates of CO₂ emissions and GDP over two consecutive years.

The Decoupling Index (DI) can be classified into three categories: decoupling, negative decoupling, and coupling. Furthermore, it can be subdivided into several subcategories depending on the values of ΔC and ΔGDP.

Source: [19] Tapio (2025)

A widely used model for quantitatively analyzing CO₂ emissions was introduced by Japanese professor Yoichi Kaya during a workshop organized by the IPCC in 1989 [20] [21] . The model establishes a simple mathematical equation that relates economic, demographic, and environmental factors to estimate global CO₂ emissions from human activities as follows:

${\text{CO}}_2=P\times \frac{\text{GDP}}{P}\times \frac{E}{\text{GDP}}\times \frac{{\text{CO}}_2}{E}$ (1)

or CO₂ = P × Inc × EI × CI (2)

in which:

CO₂: Total CO₂ emissions (MtCO₂)

P: Population (people)

GDP: Gross Domestic Product (VND)

E: Total Energy consumption (GJ)

This relationship is explained by the fact that population growth (P) is one of the primary factors leading to CO₂ emissions in all countries, especially in developing nations. Income or GDP per capita is a measure of living standards and serves as a gauge for fossil fuel consumption within a society. Energy intensity (EI) (E/GDP) reflects the amount of energy required to produce one unit of economic output, serving as a measure of energy efficiency for an economy or country. Carbon intensity (CI) (CO₂/E) indicates the relative carbon emissions per unit of energy or fuel consumed. This measures how effectively countries utilize polluting energy sources such as coal, oil, and gas. Increasing the use of renewable energy will help reduce carbon intensity, whereas countries that still rely on fossil fuels to drive economic growth will have fewer opportunities to lower carbon intensity.

To align with the study, formula (1) is adjusted for application in the agricultural sector, where P is the labor force employed in agriculture, GDP is the agricultural gross product (calculated at 2010 constant prices), and E is energy consumption in agriculture. In the additive LMDI technique as guided by Ang [22] , the arithmetic change of a composite index is decomposed. This allows the study to identify and rank the causal impacts leading to trends in CO₂ emissions based on comparison. In the additive LMDI technique, the difference in CO₂ emissions between two years (year 0 and year t) can be expressed in Mt CO₂ as follows:

$\Delta C_{tot}\text{=}\Delta C_P+\Delta C_{Inc}+\Delta C_{EI}+\Delta C_{CI}$

where $\Delta C_{tot}$represents the change in total CO₂ emissions, which is decomposed into the effects of labor $\left(\Delta C_P\right)$, income effect $\left(\Delta C_{Inc}\right)$, energy intensity effect ( $\Delta C_{EI}$), and carbon intensity effect ( $\Delta C_{CI}$). The relevant formulas for these decomposing factors are as follows:

$\Delta C_P=\frac{{\text{CO}}_2^t-{\text{CO}}_2^0}{\ln {\text{CO}}_2^t-\ln {\text{CO}}_2^0}$ $\times \ln \frac{P^t}{P^0}$

$\Delta C_{Inc}=\frac{{\text{CO}}_2^t-{\text{CO}}_2^0}{\ln {\text{CO}}_2^t-\ln {\text{CO}}_2^0}$ $\times \ln \frac{In{c}^t}{In{c}^0}$

$\Delta C_{EI}=\frac{{\text{CO}}_2^t-{\text{CO}}_2^0}{\ln {\text{CO}}_2^t-\ln {\text{CO}}_2^0}$ $\times \ln \frac{E{I}^t}{E{I}^0}$

$\Delta C_{CI}=\frac{{\text{CO}}_2^t-{\text{CO}}_2^0}{\ln {\text{CO}}_2^t-\ln {\text{CO}}_2^0}$ $\times \ln \frac{C{I}^t}{C{I}^0}$

The research findings derived from the analysis of the Decoupling Index (DI) values in the agricultural sector indicate that the sector has experienced all three states: decoupling, negative decoupling, and coupling.

Based on the theoretical framework provided in Table 2 and the calculated results presented in Table 3 , some observations regarding the decoupling status during the period from 2005 to 2021 can be discussed as follows.

In 2005-2006, the agricultural sector experienced a weak decoupling status during the period from 2006 to 2009. This weak decoupling occurs when economic growth is relatively higher than the growth of CO₂ emissions. In the period from 2009 to 2014, the agricultural sector transitioned to a strong decoupling. This can be regarded as the best decoupling state, as the agricultural sector maintained economic growth while the rate of CO₂ emissions decreased ( Figure 1 ). However, in the subsequent period (2014-2017), an extended negative decoupling state emerged, reflecting growth in both GDP and CO₂ emissions in the agricultural sector, but the rate of CO₂ emissions growth significantly outpaced economic growth ( Figure 1 and Figure 2 ). The primary reason for this extended negative decoupling is the burning of fossil fuels with high carbon usage. This status was at its worst in 2014-2015, as evidenced by the significant demand for fossil fuels such as gasoline, oil, and natural gas in the agricultural sector in 2015, resulting in a marked increase in CO₂ emissions for that year ( Figure 1 ). The growth coupling status observed in the years 2017-2019 and 2020-2021 ( Figure 3 ) further indicates that both CO₂ emissions and economic growth in the agricultural sector increased together, however, adjustments have been made to ensure that economic growth outpaced the growth of emissions.

Note: The data in Table 3 is calculated by author on the 29^th of September 2024.

Using the LMDI technique. the factors affecting CO₂ emission fluctuations can be quantified. Table 4 presents the results of the LMDI analysis for CO₂ emissions in the agricultural sector from 2006 to 2021.

Note: The data in Table 4 is calculated by author on the 29^th of September 2024.

Based on the results of the decomposition analysis, we can examine the fluctuations in CO₂ emissions in the agricultural sector across different periods:

2006-2009 period: This period experienced a growing trend in CO₂ emissions, although it was at a low growth rate. During this time, the effects of income and labor contributed to increased emissions, while the effects of energy intensity and carbon intensity helped reduce them ( Figure 4 ). The agricultural sector was still largely traditional, relying on human and animal power with minimal machinery use. Intensive agricultural practices improved productivity, supporting economic growth. Land consolidation started in 2008, but fragmented land parcels significantly hindered agricultural modernization. Most farming households remained tied to agriculture due to limited non-agricultural livelihood opportunities [23] . Overall, from 2005 to 2009, the agricultural sector exhibited stable growth in terms of income and labor, with low mechanization leading to moderate energy consumption and carbon emissions.

2010-2014 period: This period saw a reduction in emissions due to improved labor efficiency ( Figure 4 ). As shown in Table 4 , in 2010, CO₂ emissions decreased by 24 Mt CO₂, primarily due to a significant reduction in the energy intensity effect (−198.24 Mt CO₂), despite an increase in income per labor. This indicates the agricultural sector’s efforts toward more efficient energy use. In the following years, the effects of carbon intensity and energy intensity played vital roles in reducing CO₂ emissions. The substantial reduction in these two effects arose from several factors. First, this period saw an increased application of scientific and technological advancements in agriculture while still maintaining reasonable scales and avoiding excessive reliance on fossil energy. Second, the impact of the agricultural restructuring policy towards increasing added value and sustainable development according to Decision 899/QD-TTg of the Vietnam Government; in addition, many localities have begun to implement organic agriculture and high-tech agriculture models such as Lam Dong, Dong Nai, Hanoi, etc. These policies encouraged farmers to reduce dependence on high-emission input materials like chemical fertilizers and pesticides, thereby decreasing carbon intensity per unit of energy consumed. Third, the fluctuation of energy prices and input costs, notably in 2011-2012, when rising fuel prices forced farmers to reduce energy consumption and operate more efficiently, contributed to lower carbon intensity. This period also saw the increased popularity of energy-saving technologies and the reuse of agricultural by-products, such as biogas.

2015-2019 period: This period was marked by unusual fluctuations, including a dramatic spike in emissions ( Figure 5 ), particularly in 2015 compared to 2014, where the CO₂ emissions gap reached 3995 Mt CO₂ largely attributed to the energy intensity effect (ΔEI = 3720.96%, as mentioned in Table 4 ). This surge likely resulted from efforts to promote mechanization in agriculture. Decision No. 68/2013/QD-TTg dated November 14, 2013 of the Vietnam Prime Minister on support policies to reduce losses in agriculture and Circular No. 08/2014/TT-BNNPTNT dated March 20, 2014 of the Ministry of Agriculture and Rural Development of Vietnam guiding the implementation of a number of articles of Decision No. 68/2013/QD-TTg have strongly promoted the process of agricultural mechanization. These initiatives enabled businesses, cooperatives, and households to receive support for purchasing agricultural machinery and equipment. As a result, the proportion of households owning various types of machinery primarily used for agricultural, forestry, and fishery production increased by 74.0% in 2016 compared to 2011 [24] . Machinery and equipment were used diversely across all stages of the production process, with significant increases in quantity. On average, for every 100 households engaged in agricultural, forestry, and fishery activities, there were 0.74 vehicles used for production purposes; 100 rice-farming households used an average of 28.87 motorized sprayers, 0.44 combined harvesters, 2.84 other types of harvesters, and 4.02 motorized rice threshers [25] . Consequently, the demand for fossil fuels to power agricultural machinery and equipment surged during this period, leading to a substantial increase in CO₂ emissions.

CO₂ emissions in the agricultural sector dropped in 2019 and 2020 ( Figure 5 ), coinciding with the global COVID-19 pandemic, which profoundly impacted the global energy system. In 2020, various lockdown measures were implemented to control the spread of COVID-19, restricting transportation, agriculture, industry, and production activities. While these measures negatively affected socio-economic activities, they had a positive impact on the environment [26] [27] . However, in the report of IEA [28] , the increase in global CO₂ emissions in 2021 compared to 2020 was the highest annual increase on record in absolute terms, as economies recovered from the pandemic through financial measures and rapid vaccine rollout. The rise in CO₂ emissions in 2021 corresponded with the global economic growth. This was also a growth coupling status between CO₂ emissions and GDP growth. The research findings align with the IEA’s conclusions regarding the increase in CO₂ emissions in Vietnam’s agricultural sector in 2021 compared to 2020, primarily driven by the income effect.

Overall, the total CO₂ emissions fluctuation from 2006 to 2021 amounted to 5,648 Mt CO₂ ( Table 4 ), driven by the income effect and energy intensity effect (with the income effect being larger). It is evident that, for Vietnam’s agricultural sector, the income effect is the primary driver of CO₂ emissions growth. This is because increased income in agriculture is often accompanied by expanded production scales, enhanced mechanization, and investment in machinery and equipment. High-energy-consuming activities such as post-harvest processing, transportation, and agricultural product processing have also been promoted to enhance the value added in the agricultural sector. These factors significantly contribute to energy consumption and the use of high CO₂ -emitting energy sources, leading to an increase in total emissions. This presents a critical concern for policymakers, as rising incomes or production values, without improvements in energy efficiency, risk making agricultural development unsustainable.

The labor effect and carbon intensity effect contribute to reducing CO₂ emissions. The labor effect reflects changes in the structure and efficiency of labor use in the agricultural sector, positively influencing CO₂ emission reductions. This is largely due to the adoption of modern farming techniques and automation, which help increase labor productivity and reduce dependence on inefficient traditional practices. Although the contribution of the carbon intensity effect is still relatively low, it indicates the potential for reducing carbon emissions in agriculture through a transition from high CO₂ -emitting energy sources, such as gasoline, oil, and coal, to cleaner energy alternatives like solar power, biomass, and biogas derived from agricultural waste.