Energy and Logistics Cost Transmission in the Dairy Market: Evidence from Kazakhstan Using a Log-Linear ARDL Model

Abstract

Background: This study aims to evaluate the impact of energy and logistics factors on the milk producer price index to support evidence-based policies that maintain price stability at an optimal level. Methods: Annual data for 2000–2023 are used, including the milk producer price index, milk production volume, transport CPI, diesel price, CO₂ emissions from agriculture, and renewable energy consumption (percentage of total energy consumption). A log-linear ARDL model is applied to examine both short- and long-run asymmetric effects of diesel prices, transport costs, and agricultural CO₂ emissions on milk production dynamics. Results: The research results indicate that energy expenses, logistics considerations, and environmental metrics have statistically significant asymmetric influences on milk production. This underscores the varying short-term adjustments and enduring long-term economic effects throughout the supply chain. Conclusions: Energy and cost factors on the supply side significantly influence the stability of milk markets. Therefore, improving transportation efficiency, encouraging the use of renewable energy sources, and addressing environmental impacts can contribute to consistent and sustainable pricing. Specific policies—including investments in transport infrastructure, subsidies for green energy targeting dairy producers, carbon pricing with support tailored to the sector, and digitalization of supply chains—can enhance resilience and ensure price stability.

1. Introduction

This study looks at milk price formation grounded in price transmission theory and cost structures in a supply chain, which both occur on agricultural land and in the course of industry. Price transmission theory can be seen as a way to understand how jolts in the price of inputs feed upstream markets—producers through processors and vendors—often in an incomplete and asymmetric fashion, partly due to market power, adjustment costs, as well as contractual inflexibility [1]. This is particularly relevant to agri-food production systems characterized by perishable foods and high transaction costs, but also with structures that do not fit well into the market concept of what needs to be accomplished if consumers purchase them later on in food. Specifically, a primary element of the upstream cost that affects farm production as well as transport is energy, specifically diesel. Higher fuel prices raise marginal costs over several phases in the dairy supply chain, causing downstream price adjustments [2]. Empirical studies have empirically demonstrated that energy price shocks are transmitted to food prices with asymmetry and lag, reflective of nonlinear mechanisms of adjustment [3,4]. This forms the theoretical backdrop for investigating the diesel price pass-through to milk price. Furthermore, they also consider CO₂ emissions as a proxy for energy intensity and environmental cost pressures in the production and distribution systems. From an energy–economics viewpoint, greater emissions corresponded with greater dependence on fossil fuels and potential regulatory costs that could be absorbed into production and logistics costs [5]. In the price transmission model, those costs then spread indirectly through the system and affect retail prices through cumulative cost effects. Finally, logistics variables (transport distance, infrastructure availability, storage capacity, and the number of intermediaries) are crucial to the cost structure of the supply chain. Higher logistics costs and inefficiencies generate frictions that reduce or delay price transmission: transaction cost economics and spatial price equilibrium theory [6,7].

They become especially amplified in geographically large and landlocked economies such as that of Kazakhstan, amplifying cost pass-through and increasing the degree of price spread by region. This serves as the groundwork for exploring the logistical determinants of milk pricing. Since such variations (nonlinear and asymmetric) can emerge in response to cost shocks, this study uses a log-linear Autoregressive Distributed Lag (ARDL) that can decompose positive and negative changes in explanatory variables and differentiate between short-run and long-run transmission dynamics [8]. This approach also captures the delicate interplay of energy costs, environmental pressure, logistics, and milk price in Kazakhstan’s dairy market.

Therefore, to assess the energy factors and other factors indirectly related to milk production, the following questions are sought:

RQ1: To what extent do diesel prices affect milk prices?

RQ2: To what extent do CO₂ emissions affect milk prices?

RQ3: To what extent do logistical factors affect milk prices?

2. Literature Review

Dairy market price formation can be analyzed in light of agricultural price transmission theory and cost structures in supply chains. Price transmission demonstrates how cost fluctuations (e.g., for energy, logistics) are communicated vertically from the producer of food products (the product and service provider) to the consumer (the final consumer) [9]. This distribution process is usually not symmetric, with market power, adjustment frictions, and so forth contributing to this process [10]. The retail prices of milk in the dairy industry are driven by input costs that consist of various energy costs (including fuel and electricity), transportation, and processing costs based on the processes in the supply chain [11]. More precisely, energy prices—especially diesel—affect both production and distribution processes, while environmental cost-related indicators (e.g., CO₂ emissions) serve as proxies for regulatory and energy intensity costs [12]. Considering that agri-food chains are not linear in nature, cost shocks propagate nonlinearly, thus lending support for the use of log-linear ARDL to more effectively model both nonlinear short- and long-run effects [13].

Rising operating costs, labor shortages, volatile milk prices, shifting consumer preferences, long hours with little relaxation, and unpredictable weather patterns brought on by climate change are just a few of the major business difficulties dairy farmers are facing [14]. Dairy farming is increasingly adopting management practices that demand more energy. Both on-farm emissions resulting from fossil fuel combustion and off-farm emissions related to the production of agricultural inputs, such as fertilizers and feed additives, play a role in exacerbating climate change when utilized in dairy operations [15]. By the year 2050, global consumption of dairy products is projected to increase by 19% per capita. However, milk production is energy-intensive. To ensure both financial viability and environmental sustainability within the dairy sector over the long term, it is crucial to align increased milk production with responsible energy resource utilization while addressing concerns regarding greenhouse gas emissions from agriculture [16]. Research by Daniel et al. [17] indicates that a significant portion (85%) of electricity used in dairy farming goes toward agricultural and processing equipment, with lighting and refrigeration being major contributors during processing, accounting for approximately 10% and 30% of total electricity usage, respectively. The food and beverage industry stands out as the largest energy user and is responsible for 67% of greenhouse gas emissions in the agro-food sector [18]. In recent years, the proportion of energy costs within overall agricultural expenditures has risen due to climbing energy prices alongside greater automation and mechanization on farms [19]. Dairy farming necessitates substantial amounts of electricity for milking processes, cooling milk, and heating and cleaning water, which underscores its high energy demand [20,21].

In order to establish baseline data for comparing the energy performance of different facilities and systems, Xu and Flapper [22] investigated energy consumption within the current global fluid milk markets. Their findings revealed that the average ultimate energy intensity of individual plants varied markedly across different facilities and countries, with values ranging from 0.2 to 12.6 MJ per kilogram of fluid milk product. Wojdalski et al. [23] analyzed four categories of dairy facilities, each characterized by distinct production profiles, to explore the relationship between two sets of parameters and energy usage. The results indicated that small dairy factories producing up to four products offered the clearest insight into variations in energy consumption per unit of final output. Furthermore, assessments of individual plants demonstrated a significant correlation between energy use per unit of final product and both the production profile and milk-processing output.

By examining a year’s worth of 30 min interval electrical data, Dew et al. [24] assessed the capacity of six large dairy farms in New Zealand to provide flexibility in electricity demand. The analysis focused on daily electricity consumption patterns to illustrate how irrigation and milking activities contribute to peak usage periods. It was found that, according to a proposed time-of-use (TOU) pricing structure, the morning peak represents 20% of the total electricity costs incurred by the dairy shed.

Implementing various conservation technologies could result in a reduction in electricity demand by one-third. Furthermore, integrating renewable energy generation with conservation efforts enables dairy farms to reach net-zero electricity consumption [25].

Moerkerken et al. [26] generated an extensive dataset concerning farm energy utilization, comprising over 25,000 observations collected from 2015 to 2018 through an online platform that systematically monitored the energy performance of dairy operations. Their research highlights three significant trends: first, the installation of solar panels emerges as the most critical element in decreasing reliance on non-renewable energy sources; secondly, ongoing mechanization—especially in automatic milking systems—counterbalances energy efficiency gains attributed to governmental policies; and thirdly, advancements in economies of scale have led to marked improvements in per-unit energy efficiency within milk production.

To explore both the prospects and constraints of a self-sustaining energy system, Höhendinger et al. [27] investigated and detailed the energy consumption associated with a milk production system. Their comprehensive assessment indicated that the total energy output could meet the consumption demands of the production process itself. Ultimately, profitability stemming from both acquisitions and sales is contingent upon prevailing energy prices. Logistics plays an important role in determining the price of any product [28,29]. Efficient logistics management helps optimize value in any supply chain.

Logistics encompasses numerous elements that influence pricing [30]. With the growing emphasis on environmental concerns, discussions surrounding diesel costs—integral to delivery expenses—and emissions within the supply chain have gained prominence in academic discourse. For dairy farmers, fluctuations in diesel prices are particularly significant [31]. These price variations exert a more substantial effect on the initial pricing within the food supply chain than on the final consumer product. A study by Chang et al. (2024) has illustrated how both diesel prices and the availability of truck drivers impact food costs [32]. Even so, whether oil prices directly correlate with milk production or the pricing structure is yet to be established [33]. However, one cannot entirely dismiss their impact. Moreover, previous research has underscored another aspect of this relationship: the emissions of CO₂ generated by dairy producers, who contribute to such emissions regardless of their operating scale [34,35]. This contribution is not only in milk production but also in fuel consumption throughout the supply chain.

Since 2012, Kazakhstan’s milk production has reached 6247.2 thousand tons across all livestock categories, reflecting a 28.7% increase from 4851.6 thousand tons in that year [36]. Data from 2019 indicate that 72.7% of households in the nation engage in milk production [37]. Despite this growth, Kazakhstan remains one of Central Asia’s leading milk importers; hence, enhancing competitiveness within its dairy sector is essential [38,39]. Limited research exists examining how energy and fuel prices intersect with food security issues [40,41]. In Kazakhstan, road transport is primarily utilized for dairy distribution; thus, gasoline costs and transportation expenses significantly affect milk pricing. Various factors influence these costs—including energy required for milk preservation, transport distance, diesel output levels, and fueling requirements for transit vehicles.

When determining pricing strategies for their products, milk producers must consider all variables present within both production and value chains comprehensively. Consequently, this research aims to assess some of the logistical and energy factors that may influence the price structure of milk.

3. Materials and Methods

3.1. Data

In this research paper, the authors aim to find out the impact of milk production volume, transport consumer price index, diesel price, CO₂ emissions, and renewable energy consumption on the milk producer price index in the Republic of Kazakhstan. This study uses data from the World Data Bank (WDI), the Bureau of National Statistics Agency for Strategic Planning and Reforms (BNSASPR) of the Republic of Kazakhstan, and Globalpetrolprices.com covering the period from 2000 to 2023.

Justification for the Use of Variables

After examining a range of studies available in the literature and applying the criteria for statistical accessibility, the subsequent variables were chosen to fulfill the research objective.

Milk production levels serve as a crucial supply-side factor that directly impacts the milk producer price index through the mechanism of market equilibrium. When production increases, the supply of raw milk grows, which, all else being equal, puts downward pressure on producer prices; conversely, reductions in supply lead to higher prices. Research indicates that fluctuations in production significantly affect farm-gate price indices due to the perishability of milk and limitations in storage [42]. Utilizing a log-linear ARDL framework, this variable accounts for both immediate supply shocks and long-term adjustments toward equilibrium that influence the milk producer price index.

The transport Consumer Price Index (CPI) is intricately connected to the milk producer price index, as it captures variations in logistics and distribution expenses throughout the dairy supply chain. Given that raw milk has a short shelf life, efficient transportation is vital for ensuring prompt delivery. When transport costs increase, transaction expenses also rise, which are partially passed back to producers, thereby affecting the producer price index. Research on price transmission indicates that distribution costs have a substantial impact on vertical pricing relationships [43,44], highlighting the transport CPI as a crucial factor influencing the fluctuations of the milk producer price index.

Diesel prices have a direct influence on the milk producer price index, primarily through their effect on both production and transportation expenses. The dairy farming sector is heavily dependent on fuel-intensive resources, including machinery, feed logistics, and the collection of milk. An increase in diesel prices raises marginal costs, which subsequently leads to higher prices for producers. Research examining the relationship between energy and food prices demonstrates notable pass-through effects from fuel costs to agricultural price indices [45,46]. Within the ARDL framework, diesel prices reflect energy cost shocks and their dynamic impact on the milk producer price index.

CO₂ emissions originating from agricultural practices are linked to the scale and intensity of livestock production, which in turn has an indirect effect on the index of milk producer prices. Elevated emissions often indicate more intensive production systems, potentially leading to changes in cost structures due to environmental regulations or carbon limitations. These elements contribute to increased production expenses, subsequently influencing producer prices. The existing literature emphasizes the strengthening connection between environmental externalities and the determination of agricultural prices [47,48]. By incorporating this variable, the ARDL model is able to reflect long-term structural relationships between environmental pressures and the index of milk producer prices.

Renewable energy use plays a role in determining the milk producer price index by impacting the cost structure associated with energy in agricultural production. An increased proportion of renewable sources lessens reliance on the volatility of fossil fuel prices, which helps stabilize input expenses and may reduce fluctuations in producer prices. Research examining the relationship between energy and agriculture indicates that shifts toward renewable energy have a considerable influence on agricultural pricing systems [49,50]. Within the ARDL framework, this factor illustrates how variations in energy sources affect both short-term and long-term trends in the milk producer price index.

The following graph shows the dynamics of changes in all indicators presented in

Table 1. Model Variables and Sources.

Variables	Definitions	Sources
MPPI	Milk producer price index	Bureau of National Statistics, Agency for Strategic Planning and Reforms of the Republic of Kazakhstan
MPV	Milk production volume, thousand tonnes	Bureau of National Statistics, Agency for Strategic Planning and Reforms of the Republic of Kazakhstan
TCPI	Transport consumer price index	Bureau of National Statistics, Agency for Strategic Planning and Reforms of the Republic of Kazakhstan
DP	Diesel price (tg/L)	Globalpetrolprices.com
CO2E	CO2 emissions from agriculture (including livestock), Mt	World Development Indicators (WDI) (2025)
REC	Renewable energy consumption (% of total energy consumption)	World Development Indicators (WDI) (2025)

for the period 2000–2023:

Figure 1 shows clear, consistent, and stable temporal patterns, indicating that the variables’ changes are suitable for further study.

3.2. Methods

Based on the literature review, we propose the following theoretical model (Equation (1)) that examines the influence of important factors on the milk producer price index in the Republic of Kazakhstan:

MPPI = f (MPV, TCPI, DP, CO2E, REC)

(1)

where all of their definitions and measurements are given in Table 1.

In the work of Bolatbek et al. (2025) [51], a block diagram was created showing the general algorithm for estimating the corresponding model. In our study, all the required procedures in that figure were carried out: the order of the lag in the model being constructed was determined, tests were performed to determine the residuals’ normalcy, normality of the residuals, serial correlation, heteroscedasticity, and to check the stability of the model, CUSUM (Cumulative sum of recursive residuals) and CUSUMSQ (Cumulative sum of squared recursive residuals) tests were used.

First, since the variables under study must satisfy certain requirements, all indicators were tested for stationarity. Not all variables under investigation were stationary at I(0) or first-difference I(1) levels, according to the ADF test results. However, this non-stationarity was removed by taking logarithms. Therefore, since the logarithms of all indicators are found to be level or first-difference stationary, it is appropriate to consider log-linear ARDL models. Consequently, a logarithmic model was estimated, and an autoregressive distributed lag (ARDL) model was deemed suitable for this situation to investigate the dynamic behavior of these variables and account for both short- and long-term impacts.

For the investigation, the log-linear power-law model (Equation (2)) that follows was created:

$$\begin{array}{ll}\mathit{\Delta }LOG\left({MPPI}_t\right)=& {\beta }_0+{\displaystyle \sum _{k=1}^m}{\beta }_1\mathit{\Delta }LOG\left({MPPI}_{t-k}\right) +{\displaystyle \sum _{k=0}^n}{\beta }_2{\mathit{\Delta }LOG(MPV}_{t-k})\\ & +{\displaystyle \sum _{k=0}^p}{\beta }_3{\mathit{\Delta }LOG(TCPI}_{ t-k})+{\displaystyle \sum _{k=0}^q}{\beta }_4{\mathit{\Delta }LOG(DP}_{ t-k})\\ & +{\displaystyle \sum _{k=0}^r}{\beta }_5{\mathit{\Delta }LOG(CO2E}_{t-k}) +{\displaystyle \sum _{k=0}^s}{\beta }_6{\mathit{\Delta }LOG(REC}_{t-k})\\ & + {\gamma }_0{LOG(MPPI}_{t-i})+{\gamma }_1{LOG(MPV}_{t-i})+{\gamma }_2{LOG(TCPI}_{t-i})\\ & + {\gamma }_3{LOG( DP}_{t-i})+{\gamma }_4{LOG(CO2E}_{t-i})+{\gamma }_{5}LOG\left({REC}_{t-i}\right)\\ & + {\epsilon }_t\end{array}$$

(2)

where operator Δ represents the differencing operation.

4. Results

4.1. Empirical Findings

Descriptive statistics facilitate a comprehensive analysis of various features within a dataset. This study employs the properties of mean, median, skewness, kurtosis, the Jarque–Bera test, and probability to evaluate the variables under consideration.

Table 2. Values of descriptive statistics of the displayed series.

Values	MPPI	MPV	TCPI	DP	CO2E	REC
Mean	108.775	4918.950	107.504	111.083	0.221	2.108
Median	108.400	5070.550	106.650	105.000	0.182	1.900
Maximum	123.700	6247.200	115.900	280.000	0.461	5.900
Minimum	94.600	3354.600	99.000	25.000	0.088	1.100
Std. Dev.	7.751	775.422	4.148	71.945	0.120	1.057
Skewness	0.128	−0.449	0.060	0.789	1.032	2.359
Kurtosis	2.559	2.518	2.484	2.818	2.734	8.652
Jarque–Bera	0.260	1.041	0.281	2.525	4.332	54.217
Probability	0.878	0.594	0.869	0.283	0.115	0.000
Sum	2610.600	118,054.80	2580.100	2666.000	5.305	50.600
Sum Sq. Dev.	1381.905	13,829,434.000	395.770	119,049.800	0.329	25.698

displays the descriptive statistics for each variable. The average values for MPPI, MPV, TCPI, DP, CO2E, and REC are 108.775, 4918.950 thousand tonnes, 107.504, 111.083 tenge/L, 0.221, and 2.108%, respectively. The standard deviations for these variables are as follows: MPPI is 7.751, MPV is 775.422 thousand tonnes, TCPI is 4.14, DP is 71.945 tenge/L, CO2E is 0.120, and REC is 1.057%. This indicates that CO2E exhibits low variability (0.120), while MPV demonstrates very high variability (775.422). All indicators except MPV display positive skewness. The mean values of MPPI and TCPI (108.775 and 107.504) are similar to their medians (108.400 and 106.650), suggesting a nearly symmetric distribution for these variables. In contrast, significant deviations can be noted in the other factors: MPV, DP, and REC; their skewness coefficients are close to zero (0.128 and 0.060), supporting this observation. There exists pronounced right skewness in both CO2E (1.032) and REC (2.359), with skewness values exceeding one indicating this trend further. The kurtosis values for the variables—MPPI (2.559), MPV (2.518), TCPI (2.484), DP (2.818), and CO2E (2.734)—are near three, suggesting they follow a normal distribution pattern; however, the kurtosis value of the REC variable at 8.652 indicates it has a heavy-tailed distribution. Notably, in our analysis, REC has undergone a logarithmic transformation for better handling of its distribution characteristics. Examining the p-values from the Jarque–Bera test criterion reveals that only the REC variable shows statistical significance with p = 0.000 < 0.05; meanwhile, the variables MPPI (p = 0.878), MPV (p = 0.594), TCPI (p = 0.869), DP (p = 0.283), and CO2E (p = 0.115) have probabilities exceeding this threshold, indicating normal distribution. These analyzed variables can be utilized within an ARDL model framework since normality is not a prerequisite; nevertheless, subsequent steps will involve testing for stationarity.

4.2. Unit Root Test

Before proceeding with the estimation of Equation (2), this study assessed the levels or differences of stationary variables using augmented Dickey–Fuller (ADF) unit root tests, as introduced by Dickey and Fuller in 1979 [52]. This assessment is crucial for identifying whether the variables are stationary prior to analyzing any long-term relationships between the series. At a significance level of 5%, it was found that the logarithms of each variable were integrated at order I(0) or I(1).

The findings from the unit root analysis (see

Table 3. ADF unit root tests.

Variables	Intercept			Trend and Intercept			None
	Level	First Diff.	Order of Integration	Level	First Diff.	Order of Integration	Level	First Diff.	Order of Integration
MPPI	−5.48 *** (0.000)	−7.02 *** (0.000)	I(0)	−5.45 *** (0.001)	−6.78 *** (0.000)	I(0)	0.650 (0.849)	−7.07 *** (0.000)	I(1)
MPV	−2.245 (0.197)	−4.70 *** (0.001)	I(1)	−1.357 (0.845)	−5.23 *** (0.002)	I(1)	−0.353 (0.546)	−4.81 *** (0.000)	I(1)
TCPI	−4.36 *** (0.003)	−6.30 *** (0.000)	I(0)	−4.24 ** (0.015)	−6.13 *** (0.000)	I(0)	−0.397 (0.789)	−6.42 *** (0.000)	I(1)
DP	2.523 (0.999)	−2.632 (0.102)	>I(1)	0.171 (0.996)	−3.237 (0.103)	>I(1)	−1.005 (0.273)	−1.652 * (0.092)	I(1)
LOGDP	−0.787 (0.804)	−4.24 *** (0.004)	I(1)	−1.729 (0.705)	−4.156 ** (0.018)	I(1)	4.104 (0.999)	−2.70 *** (0.009)	I(1)
CO2E	4.248 (1.000)	0.055 (0.952)	>I(1)	1.658 (1.000)	−1.861 (0.630)	>I(1)	2.955 (0.998)	0.971 (0.904)	>I(1)
LOGCO2E	1.959 (1.000)	−6.95 *** (0.000)	I(1)	−3.41 * (0.074)	−4.50 ** (0.011)	I(0)	−1.684 * (0.087)	−6.50 *** (0.000)	I(0)
REC	1.367 (0.998)	−2.109 (0.23)	>I(1)	1.467 (0.999)	−2.860 (0.193)	>I(1)	0.742 (0.868)	−2.010 ** (0.045)	I(1)
LOGREC	−0.021 (0.947)	−3.21 ** (0.033)	I(1)	0.044 (0.994)	−3.908 ** (0.029)	I(1)	0.662 (0.852)	−3.206 ** (0.003)	I(1)

Notes: *, **, *** denote statistically significant at the 10%, 5%, and 1% levels, respectively. p-value is inside brackets.

) align with the preliminary hypotheses, thus necessitating an examination of the ARDL logarithmic model to verify any long-term relationships between the Kazakhstan milk producer price index and its explanatory variables. The parameters derived from this logarithmic model indicate elasticity.

4.3. Lag Selection Criteria

In this research, the ARDL bounds testing approach is employed to investigate the long-term association between the chosen explanatory variables and the milk producer price index in Kazakhstan. Prior to performing the cointegration analysis, establishing an appropriate lag length criterion is crucial. The findings for the selected lag of the log-linear model are displayed in

Table 4. Selection order criteria.

ARDL(1, 1, 1, 0, 1, 0)
Lag	LogL	LR	FPE	AIC	SC	HQ
0	−0.245684	NA	1.73 × 10−5	0.385971	0.584343	0.432702
1	72.82240	112.9234 *	9.97 × 10−8 *	−4.802036 *	−3.810180 *	−4.568385 *
2	83.41671	12.52055	1.93 × 10−7	−4.310610	−2.525268	−3.890037

Notes: * denote statistically significant at the 10% level. p-value is inside brackets.

. The lag length criterion is determined based on LR, FPE, AIC, SC, and HQ. As shown in the table, the selected lag length is 1, as it has more stars and was used throughout the study. The determination of the order of an autoregression was developed by Hannan and Quinn (1979) [53].

4.4. Co-Integration Test

In this research, the logarithmic model ARDL (1, 1, 1, 0, 1, 0) (refer to Equation (2)) was utilized to analyze both long-term and short-term relationships between variables through first differences. The findings from the cointegration F-test for the ARDL presented in

Table 5. Results of the cointegration test.

Model	F Statistics	Signif.	Critical Bounds		Decision
			I(0)	I(1)
ARDL(1, 1, 1, 0, 1, 0)	19.18721 ***	10%	1.81	2.93	Cointegration
		5%	2.14	3.34
		2.5%	2.44	3.71
		1%	2.82	4.21

Critical bounds are reported at the 1% (***) level of significance.

reveal that the calculated F-statistic of 19.18721 surpasses the upper threshold of 4.21 and is statistically significant at a level of 1%. These results suggest that there is cointegration among the chosen variables, specifically for Kazakhstan, indicating that an enduring relationship exists among them.

The subsequent phase involves estimating the coefficients for both the long run and short run, as the chosen variables exhibit cointegration over time. Utilizing the log-linear ARDL(1, 1, 1, 0, 1, 0) model allows us to analyze how fluctuations in the explanatory variables influence the dependent variable across these two time frames.

4.5. Results of Long- and Short-Run Relationships

Table 6. Results of ARDL(1, 1, 1, 0, 1, 0) estimation ΔLOG(MPPI) (2000–2023).

Long Run			Short Run
Variable	Coefficient	t-Statistic	Variable	Coefficient	t-Statistic
LOG(DP)	0.096282 ***	3.587773	CointEq(−1) *	−1.246150	−12.49955
LOG(CO2E)	−0.178830 ***	−3.828803	LOG(MPPI(−1))	−1.246150 ***	−9.491030
LOG(REC)	0.103141 **	2.596667	LOG(DP(−1))	0.119982 ***	3.342298
LOG(MPV)	0.171863 *	2.123920	LOG(CO2E(−1))	−0.222849 ***	−3.755185
LOG(TCPI)	0.510803 ***	3.192311	LOG(REC)	0.128530 *	2.615056
			LOG(MPV(−1))	0.214167 **	2.190090
			LOG(TCPI)	0.636537 **	2.820620
			ΔLOG(DP)	0.553717 ***	6.094089
			ΔLOG(CO2E)	0.003987	0.086303
			ΔLOG(MPV)	−0.085795	−0.910691

(1) Coefficients are statistically significant at *** 1%, ** 5%, * 10% level of significance, in parentheses (t-values); (2) Operator D represents the differencing operation.

indicates that all estimated long-term coefficients from the chosen logarithmic model ARDL (1, 1, 1, 0, 1, 0) are statistically significant at the 10% level. The coefficient for LOG(TCPI) is notably positive and significant at the 1% level of significance. This finding confirms that the Transport Consumer Price Index has a substantial positive effect on the long-term growth of LOG(MPPI), reflected in an elasticity coefficient of 0.510803 when other factors remain constant. Additionally, the variables LOG(DP), LOG(REC), and LOG(MPV) also exert a favorable impact on LOG(MPPI) over time with respective elasticity coefficients of approximately 0.096282%, 0.103141%, and 0.171863%. Solely the logarithm of CO2E shows a sustained adverse effect on the change in the logarithm of MPPI, with an elasticity coefficient quantified at 0.178830%.

In the short term, the coefficient for the lagged variable LOG (MPPI(−1)) at period t-1 was found to be negative (−1.246150). Assuming all other variables remain constant, positive relationships were identified for LOG(DP(−1)), ΔLOG(DP), LOG(REC), LOG(MPV(−1)), LOG(TCPI), and LOG(MPPI) with corresponding elasticity coefficients of 0.119982, 0.553717, 0.128530, 0.214167, and 0.636537. The logarithm of the lagged variable LOG(CO2E(−1)) exhibited a negative correlation with ΔLOG(MPPI) (with a coefficient value of −0.222849) in the short run; this finding aligns with long-term results. The error correction factor CointEq(−1)* is −1.246 and holds statistical significance. The presence of a negative sign indicates that there is a stable long-term equilibrium among these variables. Furthermore, values exceeding one suggest an extremely rapid adjustment process concerning deviations from this equilibrium state, potentially resulting in re-regulatory effects within the system.

4.6. Diagnostic Tests

To validate the strength of the log-linear ARDL (1, 1, 1, 0, 1, 0) model, a series of diagnostic tests were conducted (see

Table 7. Short-run diagnostics.

Model—ARDL(1, 1, 1, 0, 1, 0)
Test	F-Statistics	p-Value	Conclusion
Serial correlation LM	0.671151	0.5293	No Serial Correlation
Heteroskedasticity	0.405980	0.9101	No Heteroskedasticity
Jarque–Bera	0.0844	0.9586	Normality Exists

). These assessments included evaluations for serial correlation, heteroscedasticity, and normal distribution. The results from all diagnostic procedures—Lagrange multiplier test for serial correlation, Jarque–Bera test for normality, and tests for heteroscedasticity—were favorable. This outcome confirms the robustness of the ARDL (1, 1, 1, 0, 1, 0) model. Consequently, the null hypothesis positing the absence of serial correlation or issues related to heteroscedasticity and non-normality is not rejected.

4.7. Multicollinearity Test

In this research, the variance inflation factor (VIF) is employed to assess multicollinearity. The findings from the VIF analysis are displayed in

Table 8. VIF multicollinearity test results.

Model–ARDL(1, 1, 1, 0, 1, 0)
Variable	Variable Variance	Uncentered VIF	Centered VIF
MPV	2.61 × 10−5	223.3011	5.194189
TCPI	0.198473	793.9596	1.131253
DP	0.003405	20.36329	5.838772
CO2E	1597.163	34.52757	7.559951
REC	19.17101	36.54963	7.095215
C	2510.955	867.8919	NA

, which indicates that no evidence of multicollinearity was found.

The test outcomes indicate that every VIF value remains under 10, aligning with the established empirical guidelines. Therefore, we can confirm that there are no significant issues related to multicollinearity. This finding enables us to assert that multicollinearity is not a concern in our model, allowing for the inclusion of all variables in our subsequent analysis.

4.8. The Granger Causality Test

The analysis presented in

Table 9. Granger causality test.

Null Hypothesis
Variable	Variable Variance	Uncentered VIF
LOG(DP) does not Granger cause LOG(MPPI)	1.842600	0.3980
LOG(CO2E) does not Granger cause LOG(MPPI)	2.737736	0.2544
LOG(REC) does not Granger cause LOG(MPPI)	0.767155	0.6814
LOG(MPV) does not Granger cause LOG(MPPI)	10.03167	0.0066
LOG(TCPI) does not Granger cause LOG(MPPI)	0.263475	0.8766
All do not Granger cause LOG(MPPI)	20.28139	0.0267

regarding the Granger causality test indicates a one-way causal relationship between LOG(MPV) and LOG(MPPI).

The sole notable variable with a lasting impact on MPPI is MPV. It serves as an essential element in elucidating the fluctuations of MPPI. Conversely, all other variables exhibit no substantial influence on the MPPI. Collectively, these variables provide a meaningful explanation for the changes in MPPI, indicated by p = 0.0267. Although there exists an interrelationship among them, their intrinsic importance remains minimal.

4.9. Stability Tests

To evaluate the dynamic stability of our model, we employed the CUSUM and CUSUMSQ tests. The visual outputs of these assessments, illustrated in Figure 2, demonstrate the overall stability of the ARDL (1, 1, 1, 0, 1, 0) framework.

Since the CUSUM and CUSUMSQ statistics in Figure 2 stay within the critical threshold of 5%, it indicates that the model parameters are deemed stable.

5. Discussion

5.1. Discussion of Empirical Findings

The positive influence of diesel prices and transport CPI suggests cost-push transmission, since fuel-intensive production and distribution raise marginal costs across Kazakhstan’s geographically dispersed dairy chain. The importance of lagged milk prices reflects adaptive expectations, menu costs, and contractual rigidities, generating price inertia and asymmetry. The positive association between milk volume and prices implies structural inefficiencies: fragmented smallholder production leads to increased collection, coordination, and spoilage costs that offset scale benefits [54]. The adverse effects of CO₂ emissions may reflect energy inefficiency and technological backwardness—high CO₂ emissions increase demonstrates high input usage and slow growth, which would reduce price formation [55]. Furthermore, poor market integration and long supply chains generate spatial arbitrage friction that prevents efficient price equalization [7]. Policy should:

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subsidize fuel-efficient logistics;

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invest in cold-chain and rural infrastructure;

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promote dairy cooperatives to reduce transaction costs; and

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support low-carbon technologies to enhance.

Some of the findings align with Zingbagba et al. [56] and Rose and Paparas [57]. The agricultural, logistics, and energy sectors are very closely linked [58,59]. This can be seen in the structure of milk prices. Price transmission arises from the need for energy for both milk production and milk delivery. The presence of energy elements in both milk production and delivery indicates how important they are. Energy and logistics also contribute to the environmental footprint, which is especially noticeable in terms of CO₂ emissions [60,61].

As a result, it is crucial to ensure its accessibility to the public and to reduce and improve milk prices. The dilemma is that energy sources are used in both milk production and distribution, so all aspects are interconnected and must be carefully managed to keep price fluctuations within a manageable range. Additionally, milk production and logistics affect the environment. The results of the study are similar to the results of Ortego [62], Young et al. [63], and Li and Lopez [64]. In other words, this conundrum is always pertinent. In the era of an interconnected circular economy, the influence of a factor with little to no connection to the supply chain can play a major role in the value chain.

5.2. Theoretical and Practical Implications

This research contributes to the existing body of knowledge on agricultural price transmission by examining the interplay between energy, environmental factors, and logistics in relation to milk price fluctuations in Kazakhstan. Unlike most prior studies focused solely on food prices and agricultural output, this analysis integrates diesel fuel costs, transportation expenses, renewable energy usage, and carbon dioxide emissions within a comprehensive analytical framework. The findings reveal that the dynamics of milk pricing in Kazakhstan are influenced not only by traditional supply-side factors but also by broader pressures related to energy and logistics throughout the dairy supply chain.

The study reinforces theoretical concepts regarding asymmetric and nonlinear mechanisms of price transmission within agri-food markets [9,13]. The relationships identified suggest that shocks related to energy prices and transport costs exert varying impacts on milk prices over both short and long-term periods. This variability highlights issues such as price adjustment frictions, market inflexibility, and spatial inefficiencies typical of economies characterized by geographic dispersion.

By utilizing the log-linear Autoregressive Distributed Lag (ARDL) model, this research further substantiates the significance of incorporating dynamic and nonlinear methodologies into agricultural price modeling. The findings hold considerable implications for practitioners and stakeholders within Kazakhstan’s dairy sector. Given that diesel fuel prices and transportation costs significantly influence milk pricing, enhancing rural transportation infrastructure and cold-chain logistics could mitigate supply chain inefficiencies while stabilizing market prices [56,57].

Additionally, promoting renewable energy utilization alongside energy-efficient technologies in dairy production may reduce reliance on fossil fuels and bolster sustainability at this production level [58,59,60,61]. This suggests that policies aimed at diminishing the fragmentation of supply chain operations, optimizing coordination in planning processes, and fostering low-carbon innovations could enhance competitiveness and resilience within the dairy industry.

6. Conclusions

The current research has provided confirmation that in Kazakhstan, milk prices are heavily influenced by cost-push mechanisms that are incorporated in vertically connected but spatially dispersed supply chains. It is shown that diesel prices and transport CPI greatly raise milk prices in both the short-term and the long-term from ARDL model results, confirming that energy-intensive logistics are the main component of price transmission. Lagged milk prices convey both adaptive expectations and structural price inertia; for milk production volume, it is a reflective measure of inefficiencies arising from fragmented production systems. In contrast, CO₂ emissions have a negative impact on prices, indicating that the greater the carbon intensity, the lower the productivity and technological inefficiency, rather than cost recovery. Thus, the results support the asymmetric and nonlinear nature of price transmission of a type that is expected according to theories of agricultural economics [10,11]. Logistics efficiency, low-carbon modernization, and supply-chain consolidation should be among policy interventions to bolster price stability and sectoral efficiency within Kazakhstan’s dairy market. As a result of the evaluation, the following answers were identified to the research questions posed in the Section 1.

In order to analyze, diesel fuel price and transportation-related factors have a significant positive effect on milk price for short-run and long-run periods. This highlights the importance of energy-intensive logistics in Kazakhstan’s dairy supply chain. Importantly, the quantity of milk production is shown to be linked to price fluctuations, signaling structural inefficiencies in divided production systems. On the contrary, CO₂ emissions fall in the opposite direction to the milk price. Therefore, the greater the carbon intensity, the lower the productivity and the greater the technological inefficiencies. In conclusion, the fact is revealed that three major factors influence the stability of milk prices and overall efficiency in the supply chain in Kazakhstan; they are energy issues, environmental issues, and logistics.

Our results indicate that Kazakhstan’s dairy prices have been driven significantly by cost-push transmission through energy and logistics channels. Policymakers should mitigate the effect of diesel price vulnerability by enhancing fuel-efficient transport and providing targeted subsidies for dairy logistics. Rural infrastructure and cold-chain systems should be invested in to reduce transport CPI impacts. Besides, low-carbon technologies and energy-efficiency incentives should be advocated to mitigate the adverse productivity impact of rising CO₂ emissions and help guarantee sectoral sustainability. Specific policy measures can enhance the resilience and stability of the milk market. Public entities could invest in transportation infrastructure that will reduce logistics costs and increase the efficiency of supply chains. Special targeted subsidies to try to drive farmers into renewable energy could help smooth the swings in energy prices. At the same time, effective carbon pricing strategies and industry-specific support initiatives will limit those negative environmental consequences, but not at the expense of producers. Moreover, digitizing supply chains could enhance coordination, transparency, and market efficiency.