1. Introduction
Punjab’s dairy sector contributes 70% of Pakistan’s milk production and supports 8 million rural households [
1]; it faces unprecedented challenges from climate change. Projections indicate that rising temperatures and erratic rainfall could reduce milk yields by 20–30% by 2050, threatening food security and rural livelihoods [
2,
3]. Globally, dairy farming is increasingly challenged by climate variability, with studies showing significant milk yield losses in regions experiencing prolonged heatwaves and droughts [
4]. A growing body of literature explores the link between climate change and livestock productivity, particularly in tropical and subtropical zones, where dairy animals face elevated thermal loads [
5]. Studies have revealed that heat stress reduces milk yield, reproductive performance, and animal welfare, especially in cross-bred and high-yielding dairy cattle [
6]. In Pakistan, extreme temperature spikes directly impair metabolic efficiency and feeding behavior in buffaloes and cows [
7,
8]. Moreover, globally, climate-induced disruptions, such as erratic rainfall and humidity, can reduce pasture availability and increase disease incidence, compounding risks in smallholder systems [
4]. These findings reinforce the urgency of climate-resilient livestock strategies in climate-vulnerable regions. The Intergovernmental Panel on Climate Change (IPCC), in its Sixth Assessment Report (AR6), projects global surface temperature increases of 2.1 °C to 3.5 °C under SSP2-4.5 and 2.8 °C to 4.6 °C under SSP3-7.0 by the end of the 21st century [
9,
10]. Dairy farming is particularly vulnerable due to its reliance on climate-sensitive livestock, which are highly susceptible to fluctuations in temperature and humidity [
11,
12].
In South Asia, Pakistan ranks among the most climate-vulnerable nations, with Punjab, producing 70% of the country’s milk, bearing the brunt of increasing temperatures, unpredictable rainfall, heat stress, and fodder shortages [
13]. Smallholder farmers, the backbone of Punjab’s dairy sector, are especially affected, experiencing reduced milk yields and increased livestock mortality [
14]. In dairy farming, this is commonly associated with heat stress, a physiological condition that occurs when ambient temperature and humidity exceed an animal’s thermoneutral zone, impairing its ability to dissipate heat. This leads to elevated respiration rates, reduced feed intake, hormonal imbalance, and ultimately, lower milk production, especially in high-temperature, high-humidity regions like Punjab [
15]. These challenges are compounded by the region’s reliance on rain-fed agriculture, which is increasingly disrupted by climate variability [
16].
Recent studies emphasize the importance of climate-smart agriculture (CSA) in mitigating climate risks. For example, Rojas-Downing (2022) and Sejian et al., (2015) [
4,
17] highlight the role of CSA in enhancing livestock productivity and reducing greenhouse gas emissions. Similarly, Abid [
14] stress the need for participatory approaches that involve farmers in decision-making processes, ensuring that adaptation strategies are context specific and sustainable. Farmers’ perceptions of climate risks often shape their adoption of adaptive measures, such as switching to heat-tolerant breeds or investing in improved fodder systems [
14]. These insights underscore the importance of integrating local knowledge with scientific research to develop effective climate adaptation policies. Moreover, the role of financial and institutional support cannot be overstated. Studies by Khan [
18] and Arshad [
19] reveal that access to credit, insurance, and extension services significantly enhances farmers’ adaptive capacity. For instance, microfinancing schemes have enabled smallholder farmers in Punjab to invest in heat-tolerant cattle breeds and improved fodder systems, thereby reducing their vulnerability to climate shocks. These findings highlight the need for targeted interventions that address both the economic and environmental dimensions of climate resilience.
To address this critical gap, the present study proposes a novel framework that combines perception-based insights with advanced statistical modeling. While studies highlight the impacts of heat stress on livestock, few explore how Punjab’s smallholders perceive and adapt to climate risks, a gap that limits regionally targeted policies. For instance, Abbas [
20] shows that educated farmers adopt adaptive measures; however, no study has quantified how perceptions align with empirical trends in Punjab. To bridge this gap, we employ a mixed-methods approach: Likert-scale surveys capture farmers’ subjective perceptions of climate risks; panel regression models (fixed and random effects) quantify the relationship between temperature, humidity, and milk production; and interaction regression quantifies the combined effect of climate stressors on milk production. Once these farm-level elasticities are known, a dynamic panel-data approach, specifically the Arellano–Bond (Difference GMM) model, is applied to forecast future milk production under different climate scenarios (e.g., +2 °C, +10% RH). This method incorporates both the temporal persistence in milk production (through the inclusion of lagged dependent variables) and the dynamic effects of climate variables. The GMM model is particularly suitable for forecasting with short-time-series data and is consistent with the panel regression analysis already performed. This two-step process first identifies the instantaneous impact of climate variables on milk production and then projects future trends, thus addressing both explanatory and forecasting objectives [
21]. This innovative approach integrates farmers’ subjective perceptions with robust statistical forecasting, ensuring a comprehensive understanding of climate’s impact on dairy farming.
This study aims to (1) quantify the alignment between farmers’ perceptions and empirical climate trends, (2) project milk losses under IPCC scenarios (+2 °C, +10% humidity), and (3) inform adaptive policies for Punjab’s dairy sector. The findings align with Pakistan’s National Climate Change Policy (2022), offering actionable strategies such as subsidizing heat-resistant breeds and promoting humidity-responsive cooling systems in vulnerable zones. These recommendations build on successful regional adaptations, such as the adoption of heat-tolerant cattle breeds and community-based fodder management systems, demonstrating scalable solutions for Punjab’s dairy sector [
22]. By integrating farmers’ perceptions with empirical data, this study advances both scholarly debates and on-ground resilience in Punjab’s dairy sector. To resolve the disconnect often found in the climate agriculture literature between qualitative perceptions and quantitative trends, this study integrates smallholders’ views with empirical modeling and forecasting. By bridging these two evidence streams, the study offers a comprehensive framework for understanding both current farmers’ responses and projected climatic threats to dairy systems in Punjab. This alignment ensures methodological consistency between the study’s objectives, research design, and analytical outcomes, effectively addressing both perception-based adaptation needs and climate-driven production risks.
2. Material and Research Method
2.1. Study Area
This study was conducted in Punjab, Pakistan, the largest and most agriculturally significant province in the country. Punjab contributes 54% to Pakistan’s GDP and 62% to the agricultural sector, with approximately 59% of its land under cultivation [
23]. The province is home to Pakistan’s largest dairy industry, accounting for 67% of the country’s total milk production [
1]. With a livestock population of 16.02 million buffaloes and 13.20 million cows, dairy farming is a critical component of the region’s economy and food security [
24]. The dominant farming system in Punjab follows a mixed crop–livestock model, integrating dairy farming with crop cultivation, particularly in semi-arid and irrigated zones [
25]. Faisalabad Division, a key agricultural and dairy-producing region in Punjab, was selected. Faisalabad is one of Pakistan’s largest dairy hubs, known for its extensive livestock farming and mixed cropping systems. The division comprises four districts: Faisalabad, Jhang, Chiniot, and Toba Tek Singh. Faisalabad’s semi-arid climate is characterized by extreme temperatures (often exceeding 45 °C) and variable rainfall (averaging 526 mm annually), which makes it highly vulnerable to climate-induced stressors such as heat stress and droughts [
24]. These conditions are representative of the challenges faced by dairy farmers across Punjab and other semi-arid regions.
The division’s livestock population includes 1.1 million cattle, 0.9 million buffaloes, 0.5 million sheep, and 1.3 million goats in Faisalabad District alone, highlighting its significance in Pakistan’s dairy industry [
1]. Smallholder farmers, who own fewer than five animals, account for 83% of dairy producers and manage over 50% of the dairy livestock in Punjab, making them a critical focus for climate adaptation strategies [
24]. Given Faisalabad’s climatic conditions and its prominent role in dairy production, it serves as an ideal case study for assessing the impact of climate change on milk production in the region.
2.2. Sampling Technique
A two-stage stratified probability-proportional-to-size (PPS) sampling design was adopted to select a geographically and demographically representative sample of 450 dairy farmers from the Faisalabad Division, encompassing the Faisalabad, Jhang, Chiniot, and Toba Tek Singh districts. This approach ensured that the sample reflected the proportional livestock population and regional diversity across the four districts. To reflect Faisalabad’s larger dairy sector, 150 farmers were sampled there, while 100 farmers were selected from each of the other districts.
The sampling process involved two stages:
Tehsil selection: Two tehsils (sub-district administrative unit) were randomly chosen per district, except Faisalabad, where three tehsils were selected due to its size.
Union Council and farmer selection: Five Union Councils (UCs) (smallest administrative unit and the lowest tier of local government) were randomly selected per tehsil, and 10 farmers were randomly chosen from each UC, ensuring representation across small-, medium-, and large-scale dairy farms.
Balance check: The population–sample alignment across districts is shown in
Figure 1. A χ
2 goodness-of-fit test confirms no significant difference (χ
2 = 0.59, df = 3,
p = 0.90; see
Appendix A Table A1 for full diagnostics). A parallel test across herd-size strata indicates similar balance (χ
2 = 1.24, df = 2,
p = 0.54). This demonstrates that the multi-stage stratified sample is free from geographic or herd-size bias [
26].
2.3. Climatic Risk Perception and Impact on Dairy Farming
To assess farmers’ understanding of climate change and its associated risks, structured interviews were conducted. This subsection outlines the perception survey design, directly contributing to the objective of the study: quantifying smallholders’ awareness of climate-induced dairy impacts and adaptation, focusing on their awareness of climate variability and its perceived impact on dairy farming. Respondents were asked categorical questions about climate-related extreme events and fluctuations in temperature and humidity patterns over the past decade. Farmers’ perceptions were recorded as “increasing”, “no change”, or “decreasing” to evaluate trends in climatic shifts affecting dairy production. Specific focus areas were identified to assess how climate variability influenced different aspects of dairy farming, including heat stress, relative humidity, storms, rainfall, and other relevant questions.
A Likert scale ranging from 1 (no impact at all) to 5 (very high impact) was used to determine the perceived intensity of climate stressors on dairy farming. The farmers’ responses were analyzed using descriptive statistics, and visual representations were generated by summarizing response frequencies in percentage terms. A graphical analysis provided insights into which dairy farmers most frequently reported climate-related stressors. According to farmers’ perceptions, heat stress and relative humidity had the most impact on milk production.
2.4. Milk Production Data
From the total sample of 450 farmers, 200 were selected for quantitative analysis based on the completeness and consistency of their milk production records from 2017 to 2024. These records were maintained daily by farmers and cross-validated with purchase logs kept by middlemen who bought the milk, ensuring accuracy for econometric modeling and forecasting. These farmers also participated in the perception survey, enabling the integration of subjective insights and objective milk yield data into a single, cross-linked dataset. This integration allowed for the assessment of the impact of climate stressors on milk production and enabled a dynamic modeling approach to project future milk yields under different climate scenarios. The structured questionnaire was designed and pre-tested to capture farmers’ perceptions of climate change, its impact on milk production, and the adaptation strategies they employed. This dual-dataset approach forms the empirical foundation for both the regression analysis and dynamic panel forecasting model, linking farmer-experienced stressors with observed production trends.
The survey examined multiple dimensions, including seasonal variations in milk yield and their perceived causes, the effects of extreme weather events such as heatwaves and high-humidity periods, and the various management strategies employed by farmers to mitigate climate-induced stress on dairy cattle. These management practices included the use of shading, cooling systems, and selecting more heat-tolerant cattle breeds. Additionally, the survey examined long-term adaptation measures implemented by farmers, including changes in feeding practices, modifications to herd composition, and strategic shifts in dairy farming operations aimed at enhancing resilience against climatic stressors. The collected survey responses offered valuable qualitative insights into farmers’ awareness of climate variability and their responses to changing environmental conditions.
2.5. Meteorological Data Collection
For the quantitative assessment, daily milk production records were collected from 200 farmers over an eight-year period, from 2017 to 2024. These records were meticulously maintained and later aggregated into monthly averages for analysis. Farmers with complete and reliable records were prioritized in the dataset to ensure consistency and data integrity.
The milk production data were complemented with temperature and relative humidity measurements obtained from regional meteorological stations, ensuring a precise alignment between climate conditions and fluctuations in milk yield. The meteorological dataset spanned the same eight-year period as the milk records, allowing for an accurate evaluation of seasonal and long-term climatic influences on dairy farming. The overall historical trend of climate variables in Punjab is presented in
Figure 2.
3. Empirical Analysis
The methodological design is bifurcated into a perception-based survey component and a climate response modeling component. The perception section captures how farmers subjectively assess climate risks and adaptation needs, while the modeling section quantifies the objective influence of temperature and humidity on milk production trends. To analyze the climate-induced variations in milk production, a structured empirical strategy was adopted, combining multiple regression models to capture the complex dynamics of temperature and humidity effects. The fixed effects model was initially applied to control for unobserved farm-level heterogeneity. Recognizing potential nonlinear climate responses, a quadratic model was introduced to explore threshold effects, while an interaction model assessed the combined impact of temperature and humidity. Finally, an overall regression results table unified the linear, nonlinear, and interactive terms to provide a comprehensive analytical framework. This multi-model approach strengthens the robustness of the findings and aligns with established practices in climate agriculture studies, offering greater explanatory power and deeper policy insight [
17]. It integrates farmers’ perceptions with a tiered modeling approach to balance robustness and parsimony. First, the preliminary models (fixed effects, quadratic, interaction) identify key climate response patterns, which are then consolidated into a unified dynamic panel GMM framework for forecasting. This structure minimizes redundancy while preserving critical nonlinear and spatial insights.
3.1. Baseline Panel Regression Models
We begin with a fixed effects model (FEM) to isolate the effect of temperature and humidity while controlling for time-invariant farm characteristics (e.g., breed type, management practices):
where
= Milk production for farm i at time t;
= Temperature at time t;
= Relative humidity at time t;
= Farm-specific fixed effects (controls time-invariant heterogeneity);
= Idiosyncratic error term.
Based on the Hausman test (χ
2 = 12.34,
p < 0.01), the fixed effects model was preferred over the random effects model due to its consistency [
27,
28]. However, these preliminary findings also guided the variable selection for the GMM model (
Section 3.5).
3.2. Quadratic Model
To capture nonlinear relationships, we extend the baseline model with quadratic terms for temperature and humidity. This allows us to test whether the effects of temperature and humidity exhibit diminishing or accelerating returns. Evidence suggests that agricultural productivity, including dairy production, is nonlinearly sensitive to climate extremes [
29].
where
and
are the coefficients for the squared terms of temperature and humidity, capturing nonlinear effects. This model tests for thresholds beyond which temperature and humidity significantly harm milk production [
30].
3.3. Interaction Model
To investigate the combined effects of temperature and humidity, we introduce an interaction term. This model allows us to assess whether the effect of temperature on milk production depends on humidity levels. High humidity may exacerbate heat stress, leading to greater declines in milk production than predicted by temperature alone [
31].
where
is the coefficient for the interaction term, testing whether the joint effect of temperature and humidity differs from their individual effects. A negative coefficient for
would indicate that high humidity amplifies heat stress.
3.4. Regional Model
To account for geographic heterogeneity in climate effects, we estimate region-specific coefficients. This model examines whether the impacts of temperature and humidity on milk production vary across regions due to differences in local adaptation practices, microclimates, or climate stress levels [
32].
The regional model is specified as
where
denotes the region-specific coefficients, capturing heterogeneous climate impacts across different locations. This approach acknowledges that climate impacts and adaptation practices may vary significantly by region.
3.5. Forecasting Milk Production Using Dynamic Panel Generalized Method of Moments (GMM)
Milk production exhibits both seasonal and long-term climate variability, necessitating a forecasting approach that captures the persistence of production over time. To model the temporal dependencies and climate stressors affecting milk production, we employ a dynamic panel generalized method of moments (GMM) approach for forecasting future milk production under different climate scenarios [
33].
The dynamic panel GMM approach integrates farm-level heterogeneity (fixed effects) and models the temporal persistence of milk production, accounting for both climate and farm-specific variables. This method is more suitable for the available time-series data (96 months) in this study and allows us to forecast future production more effectively. The dynamic panel GMM approach was selected over traditional time-series methods such as ARIMA due to the panel nature of the dataset, which includes both cross-sectional (farm-level) and temporal (monthly) dimensions. Unlike ARIMA, which is suited to univariate time-series forecasting, GMM effectively handles unobserved heterogeneity, endogenous regressors, and lagged dependent variables. These features make it more appropriate for modeling dynamic responses to climate stress in farm-level milk production data.
The GMM model is specified as
where
= Milk production for farm i at time t;
= Farm-specific fixed effects;
= Lagged milk production coefficient (captures persistence);
= Temperature at time t;
= Relative humidity at time t;
= Error term.
This model captures temporal dependence by including the lagged dependent variable , while controlling for time-invariant farm-specific characteristics (fixed effects). It also incorporates the effects of climate variables such as temperature and humidity on milk production.
Stationarity testing: The stationarity of the milk production series is implicitly controlled through the inclusion of lagged milk production as an independent variable, accounting for temporal dependencies (
p < 0.05) [
34].
Residual diagnostics: We test for autocorrelation in the residuals using the autocorrelation test at lag 1 and lag 2 (
p > 0.05) [
35].
Instrument validity: The Sargan test is conducted to test the validity of the instruments used in the GMM model [
36].
Model significance: The overall significance of the model is assessed using the Wald test for coefficients [
37].
3.6. Climate Scenario Modeling
To evaluate the future climate impacts on milk production, we extend the forecasting capabilities of our GMM model by conducting scenario modeling based on IPCC projections [
38]. This allows us to predict how milk production will evolve under different climate stress scenarios, incorporating both temperature and humidity changes. Three scenarios are modeled:
Scenario 1: +2 °C temperature increase;
Scenario 2: +10% relative humidity increase;
Scenario 3: Combined +2 °C temperature and +10% humidity increase.
Using the estimated coefficients from the dynamic panel GMM model, we project changes in milk production under each scenario. This approach provides insights into the vulnerability of dairy production to climate change, helping policymakers and farmers devise adaptation strategies to mitigate future risks [
30].
3.7. Robustness Checks
To ensure the reliability and validity of our regression and forecasting models, we conduct a series of robustness checks:
Log-transformed model: Addresses skewed data distributions and improves interpretability [
28].
Lagged regression models: Test for delayed climate stress impacts [
39].
Multicollinearity testing: The variance inflation factor (VIF) confirms that independent variables are not highly correlated [
40].
Heteroscedasticity and autocorrelation tests:
Breusch–Pagan test: Verifies homoskedasticity [
41].
Durbin–Watson test: Confirms no residual auto correlation [
42].
Model selection criteria: The Akaike information criterion (AIC) and Bayesian information criterion (BIC) ensure optimal model fit [
43].
Cross-validation: Tests the generalizability and predictive accuracy of the models [
44].
4. Results and Discussion
4.1. Descriptive Statistics
The descriptive statistics of milk production, temperature, and relative humidity provide valuable insights into the dairy farming environment. The mean monthly milk production was 336.37 L, with a range from 12.0 to 1710.0 L, indicating significant variability among farms (
Table 1). This variability aligns with findings from Bokharaeian (2023) [
45], who observed that environmental factors, including temperature and humidity, substantially influence milk yield and composition.
The positive skewness (1.97) and high kurtosis (3.78) in milk production suggest that while most farms have moderate production levels, a few achieve significantly higher yields mainly due to having a larger number of animals rather than higher per-animal productivity. This pattern is consistent with the effects of heat stress on dairy cows, which can lead to reduced milk yield. Bohmanova (2007) [
46] found that heat stress, indicated by temperature–humidity indices, is associated with milk production losses. The mean temperature of 32.92 °C, with a range from 17.0 °C to 45.0 °C, reflects the climatic conditions experienced by dairy farms. The negative skewness (−0.43) indicates a slight tendency toward higher temperatures. These temperature variations can influence milk production, as cows are sensitive to heat stress. In South Korea, for instance, a temperature-humidity index (THI) exceeding 70 was associated with decreased milk performance, highlighting the impact of temperature and humidity on dairy productivity [
47]. The high mean relative humidity of 92.71%, with values ranging from 47.0% to 110.0%, indicates a consistently humid environment. The positive skewness (0.49) and substantial standard deviation (26.89%) indicate significant fluctuations in humidity levels. These fluctuations can affect milk quality and cow health. Variations in humidity levels, along with temperature, influence milk composition and microbial load, emphasizing the importance of managing environmental factors in dairy farming [
45].
4.2. Dairy Farmers’ Socio-Economic and Farm Characteristics
Table 2 presents the socio-economic and farm characteristics of the farmers surveyed. On average, the farmers were 45 years old, with an average of 21 years of experience in dairy farming. This indicates that the farmers were relatively old and had substantial experience in dairy farming. The aging of the farming population in Pakistan is a growing concern for the agricultural sector [
48]. Some studies suggest that age can be used as a proxy for farming experience [
49], while others argue that with increasing farming knowledge, farmers are more likely to observe meteorological disasters [
50].
The family size of the surveyed farmers was relatively large, reflecting the typical joint family structure found in rural Pakistan. The average family size consisted of 8 members, with a standard deviation of 3.6. Dairy farming is the primary source of income for these farmers, accounting for approximately 42% of their total income. This aligns with the findings in [
1], which reports that 35% of farmers’ annual income is derived from the livestock sector. Other sources of income include crops, labor, and employment in both public and private sectors. Additionally, about 69% of the respondents had completed their education up to school level, while only 11% had attended college or university. The remaining 20% had no formal schooling.
4.3. Dairy Farmers’ Perceptions of Climatic Risks and Variability
During the interview, dairy farmers were also asked about their perceptions regarding how different sources of climate-related risks are associated with their regular farming practices, as shown in
Figure 3. The graph illustrates the farmers’ perceptions and reveals that heat stress and relative humidity are the most significant climate-related factors affecting milk production. Most farmers identified these two variables as having the most significant impact on their dairy operations. This finding aligns with previous studies, which have demonstrated a negative correlation between high environmental temperatures, elevated humidity, and milk yield. Research indicates that as temperature increases and humidity rises, milk quality declines, emphasizing the adverse effects of unfavorable environmental conditions on dairy production [
51].
Based on these findings, temperature (representing heat stress) and relative humidity were selected for further regression analysis. These factors were chosen because they were consistently identified by farmers as the most significant stressors affecting milk production. The subsequent regression models allow for more precise quantification of how temperature and humidity influence milk yield, helping to confirm the perceptions reported by farmers and to guide the development of targeted adaptation strategies. Moreover, the validity of farmers’ perceptions was supported by the regional regression analysis (
Section 4.4), wherein Region 1 (Faisalabad), reporting the highest perceived climate stress, also exhibited the most severe yield reductions. This convergence between perceptual and empirical evidence enhances the construct validity of the survey data. As most respondents were smallholder farmers, few reported the use of formal adaptation technologies, highlighting the need for low-cost, scalable resilience strategies.
4.4. Regional Differences
The analysis reveals notable regional variations in the effects of temperature and humidity on milk production. In this study, Region 1 corresponds to Faisalabad, Region 2 to Jhang, Region 3 to Toba Tek Singh, and Region 4 to Chiniot. The graph visually illustrates the regional variability in the effects of temperature and humidity on milk production. It clearly shows the negative impact of both temperature and humidity on milk production across four distinct regions. Each region is represented by two bars: one for the temperature effect (in blue) and the other for the humidity effect (in red). The graph displays the magnitude of the regression coefficients for each factor, indicating how much temperature and humidity influence milk production in the respective regions (
Figure 4).
In Region 1, the temperature effect is the most pronounced, with a coefficient of −2.179, highlighting the severe impact of temperature on milk production in this region. Similarly, the humidity effect in Region 1 is also significant (−0.812), suggesting that high humidity exacerbates the negative effects of heat stress. As we move across the regions, the temperature effect decreases, with Region 4 showing the smallest impact (−0.913). This suggests that Region 4, likely to be cooler and closer to water sources, is less impacted by high temperatures compared to the more arid and hot regions like Region 1. These findings align with previous studies highlighting the detrimental impact of high temperature–humidity indices on milk yield and quality in similar climatic regions [
52].
The humidity effect follows a similar trend, where Region 1 experiences the highest negative effect (−0.812) due to the combination of heat and humidity, while Region 4 shows the lowest negative effect (−0.322). This suggests that, while temperature plays a dominant role across all regions, humidity still plays a significant role, particularly in the hotter and more humid areas.
Overall, the graph provides a visual representation of how environmental factors such as temperature and humidity vary in their effects across different regions. It highlights the need for region-specific interventions to mitigate the adverse impacts of these climate stressors on dairy production. This also reinforces the accuracy of farmer-reported perceptions, particularly in Region 1, where perceived and actual impacts align most closely.
4.5. Regression Analysis
To comprehensively assess climate effects on milk production, we employed a stepwise regression strategy. Each model builds analytical depth: The fixed effects model controls for unobserved farm-level heterogeneity, the quadratic model detects nonlinear climate thresholds, and the interaction model captures compounding heat–humidity stress. This progression culminates in an overall regression table that unifies all effects, ensuring robust and policy-relevant insights.
Overall for the regression models, the fixed effects and random effects models (model 1 and model 2) reveal that temperature negatively influences milk production, with a coefficient of −1.722 (
p < 0.01) (
Table 3). This indicates that for every 1 °C increase in temperature, there is an approximate decrease of 1.72 L in monthly milk production. Similarly, humidity exhibits a negative effect, with a coefficient of −0.591 (
p < 0.01), suggesting that a 1% rise in relative humidity corresponds to a 0.59 L reduction in monthly milk yield. These outcomes align with findings from [
53], who reported a negative correlation between temperature–humidity index (THI) and milk yield, with higher THI values leading to reduced milk production. To determine the most appropriate model, a Hausman test was applied (χ
2 = 0.011,
p = 0.994), suggesting no significant inconsistency in the random effects model. However, due to its ability to control for unobserved time-invariant heterogeneity, the fixed effects model was retained as the preferred specification for this study.
The quadratic model (model 3) incorporates nonlinear effects, revealing that both temperature
2 (−0.199) and humidity
2 (0.012) are statistically significant (
p < 0.01). The negative coefficient for temperature
2 suggests that the detrimental effect of temperature on milk production intensifies at higher temperatures, indicating an accelerating decline in milk yield as temperatures rise beyond certain thresholds. Conversely, the positive coefficient for humidity
2 implies a complex relationship, where initial increases in humidity negatively impact milk production, but beyond a certain point, this effect may plateau or slightly reverse, potentially due to physiological adaptations in dairy animals. This complexity is echoed in the work of [
51], who observed significant variations in milk composition and somatic cell counts across different months, influenced by environmental temperature and humidity. This plateauing may reflect thermoregulatory adaptation in cattle or targeted farm interventions such as misting, shading, or timed feeding that moderate humidity-induced stress during prolonged exposure.
The interaction regression (model 4) in
Table 2 introduces the temperature × humidity interaction term (−0.068,
p < 0.01), indicating that the combined effect of high temperature and high humidity exacerbates milk production losses beyond their individual impacts. This finding aligns with studies highlighting that the interplay between temperature and humidity intensifies heat stress in dairy cattle, leading to more pronounced declines in milk yield.
Figure 5 clearly demonstrates how temperature and humidity interact to influence milk production losses. The color gradient represents milk production levels, with red indicating minimal impact and blue showing severe declines. The contour lines mark critical thresholds where milk production significantly drops, reinforcing the statistical findings from the regression analysis.
At lower temperature and humidity levels, milk production remains stable. As temperature rises beyond 30 °C, humidity’s impact becomes more pronounced, reflecting the quadratic effect (−0.199, p < 0.01) observed in the regression model. The steepest milk production declines occur in high-temperature, high-humidity conditions, aligning with the negative interaction effect (−0.068, p < 0.01) found in the interaction model. The top-right region (above 35 °C and 80% humidity) shows the most severe production losses (>200 L), emphasizing the compounding impact of heat stress on dairy cattle. These findings visually confirm that temperature and humidity interact in a nonlinear manner, accelerating milk production losses in extreme climatic conditions.
The adjusted R2 values, ranging from 0.2235 (fixed and random effects) to 0.350 (interaction model) indicate that temperature and humidity collectively explain a substantial portion of the variation in milk production. The enhanced explanatory power observed in the quadratic model (R2 = 0.3309) and interaction model (R2 = 0.3553) emphasizes the significance of considering both nonlinear and combined effects when assessing the impact of climatic factors on dairy farming. These models were applied sequentially not only to confirm robustness but also to capture distinct dimensions of the climate effects, linear, nonlinear, and synergistic, thus strengthening the theoretical and empirical rigor of the study.
4.6. Forecasting Milk Production Using Dynamic Panel GMM
In the previous empirical analysis, we utilized fixed effects, quadratic, and interaction models to examine how climate variables like temperature and humidity impact milk production. However, for accurate forecasting, particularly over longer periods and under varying climate scenarios, the dynamic panel generalized method of moments (GMM) model provides a more suitable framework [
54].
The dynamic panel GMM approach is particularly advantageous for forecasting because it accounts for temporal dependencies in milk production and farm-level heterogeneity, both essential for understanding the long-term effects of climate variability [
55]. By including fixed effects and lagged milk production, GMM captures production persistence and the evolving farm climate dynamics. This dual consideration enables more accurate scenario-based forecasts of milk yield, ensuring that farmers and policymakers can better plan for the challenges posed by future climate variability [
56].
The GMM model results reveal that lagged milk production has a strong and statistically significant positive effect (ϕ = 0.735,
p < 0.001), indicating high production persistence across time. Temperature shows a significant negative impact (β
1 = −1.600,
p < 0.001), implying that a 1 °C increase reduces monthly milk output by approximately 1.6 L per animal. Similarly, relative humidity negatively affects milk production (β
2 = −0.088,
p < 0.001), suggesting a 0.088 L loss per 1% increase in humidity (
Table 4). These results highlight the immediate and detrimental influence of climate stressors on dairy productivity, reinforcing earlier regression findings while accounting for time dependence in the milk yield [
57].
To validate the reliability of the dynamic panel GMM estimates, a series of diagnostic tests were conducted. The Sargan test for overidentifying restrictions (χ
2 = 199.97,
p = 0.229) confirms the validity of the instruments, indicating no evidence of overidentification [
58]. Autocorrelation tests show expected first-order autocorrelation (
p = 0.061), which is typical in difference GMM estimation, while second-order autocorrelation is not significant (
p = 0.116), supporting the model’s consistency [
59]. The Wald test statistic (χ
2 = 773,849,
p < 0.001) confirms that the regressors are jointly significant [
60]. Collectively, these diagnostics validate the statistical soundness and predictive adequacy of the GMM model, reinforcing its suitability for scenario-based climate impact projections on milk production.
The GMM-based projections reveal that milk production may decline by 3.2% under a +2 °C temperature rise, 0.9% with a 10% humidity increase, and 4.1% under combined stress. These results align with previous regression models and underscore the compounding effect of temperature and humidity (
Figure 6). The selected scenario deltas (+2 °C temperature and +10% relative humidity) are consistent with projected regional climate shifts under the IPCC’s Sixth Assessment Report (AR6), particularly under the Shared Socioeconomic Pathways SSP2-4.5 and SSP3-7.0. Although not modeled as complete RCP pathways, these scenarios’ increases represent realistic, mid-century projections for South Asia and serve as practical approximations for evaluating the vulnerability of dairy systems under warmer and more humid conditions [
9].
To further analyze the potential impact of climate variability, the study evaluated the effects of increased temperature and humidity on milk production (
Figure 7). A 2 °C increase in temperature resulted in a significant reduction in milk production by 1.628 L per cow (SE: 0.057,
p < 0.001), while a 10% rise in humidity led to a 0.625 L decrease (SE: 0.016,
p < 0.001). When both temperature and humidity effects were combined, the reduction reached 2.253 L (
p < 0.001), highlighting the compounding effect of these environmental stressors on dairy productivity. These findings [
61] align with previous research, such as a study conducted in Tunisia, which demonstrated that as the temperature–humidity index (THI) increased from 68 to 78, milk production declined by 21%, with dry matter intake reducing by 9.6%. This study also found that milk yield decreased by 0.41 kg per cow per day for each point increase in THI above 69, and that elevated THI levels significantly affected milk fat and protein percentages [
61]. Similarly, a decade-long study in northern Italy reported that increased THI values were strongly associated with a decline in milk yield and altered milk composition, particularly reducing protein and fat content [
62]. These insights are critical for informing climate adaptive dairy policies, including region-specific stress mitigation strategies and insurance interventions.
4.7. Robustness Checks and Sensitivity Analysis
To ensure the reliability of the regression results, robustness checks were conducted using alternative model specifications, lag structures, multicollinearity tests, and heteroskedasticity diagnostics (
Table 5). These analyses confirm that the estimated effects of temperature and humidity on milk production remain statistically significant across various model variations, reinforcing the robustness of the findings. Such methodological validation is crucial, as previous studies have shown that climatic variables often exhibit complex interactions with dairy productivity, requiring careful statistical evaluation [
63,
64].
A log-transformed model was first applied to account for potential nonlinear relationships. The estimated coefficients for temperature (−0.235,
p < 0.001) and humidity (−0.310,
p < 0.001) remain significant, confirming the negative impact of both variables on milk production. These results are consistent with prior research, which has demonstrated that rising temperatures and humidity levels tend to suppress dairy productivity due to heat stress and metabolic inefficiencies in cows [
65]. Since the log-transformed results align closely with the main regression estimates, this suggests that the original linear model provides an adequate representation of the relationship without requiring additional transformation.
To account for possible delayed climatic effects on milk production, lagged models with 2-month and 3-month delays were estimated. The 2-month lag model shows a stronger negative effect of temperature (−3.443,
p < 0.001), while humidity exhibits a positive effect (+0.427,
p < 0.001), possibly reflecting a compensatory adaptation mechanism in dairy cattle. The 3-month lag model similarly indicates a negative impact of temperature (−3.565,
p < 0.001), although the humidity effect diminishes to +0.239 (
p < 0.001). These findings suggest that temperature-related stress has a persistent and lagged impact on milk production, while the effect of humidity may be more immediate. Similar delayed effects have been observed in other climatic studies, where temperature-induced heat stress continues to influence milk yield even after the initial exposure period [
66].
Multicollinearity was assessed using variance inflation factor (VIF) scores, with values of 1.001 for both temperature and humidity, indicating no multicollinearity concerns. This confirms that the estimated coefficients are stable and independent, supporting the robustness of the regression model. The Breusch–Pagan test was used to assess whether the variance of residuals remains constant across observations, a condition known as homoskedasticity. The test result (
p = 0.2666) indicated no significant evidence of non-constant variance (heteroskedasticity), confirming that the model’s error terms are stable. This indicates that heteroskedasticity is not a concern, further validating the reliability of the regression estimates. These diagnostic tests align with previous research highlighting the importance of verifying model assumptions when analyzing climate-related agricultural data [
67].
Autocorrelation was examined using the Durbin–Watson test, which produced a DW statistic of 2.073, indicating that autocorrelation is not present in the residuals. This implies that the regression model sufficiently captures the underlying patterns in the data without serial correlation issues. Model selection criteria were evaluated using Akaike information criterion (AIC = 744.72) and Bayesian information criterion (BIC = 752.53). The relatively low values confirm that the model is well specified, without excessive complexity.
The robustness checks confirm that the estimated effects of temperature and humidity on milk production remain consistent across different model specifications, time lags, and diagnostic tests. The log transformation, lagged models, multicollinearity tests, heteroskedasticity assessments, and autocorrelation diagnostics all indicate that the original regression results are reliable. These results reinforce the broader literature on climate change and dairy productivity, which suggests that without mitigation strategies, heat stress and humidity will continue to pose significant challenges for milk production [
63,
64]. The significant temperature and humidity effects observed in the robustness models further strengthen the conclusion that climate factors play a critical role in shaping dairy productivity, necessitating adaptive management strategies to ensure the sustainability of dairy farming under changing environmental conditions.
5. Discussion
The findings of this study highlight the significant impact of climate stressors on dairy productivity, reinforcing concerns raised in the recent literature. This aligns with the growing body of climate agriculture studies that underscore the necessity of mixed-method approaches to capture both subjective perceptions and objective climate stressors. This integration of perception-based data with multi-model econometric analysis enhances methodological robustness and yields region-specific insights [
68]. The descriptive analysis and farmer perception survey indicated that heat stress and relative humidity were the primary climatic stressors affecting milk yield [
69], consistent with previous reports that prolonged exposure to high temperatures and humidity leads to physiological stress and reduced milk production in dairy cattle [
70]. Farmers overwhelmingly perceived heat stress as the dominant factor influencing their dairy operations, a sentiment echoed in recent studies linking increased ambient temperatures to reduced feed intake, altered metabolic activity, and hormonal imbalances that lower milk yields [
71], including increased respiration rates, decreased feed intake, and increased water intake.
The regression analysis provided quantitative confirmation of the detrimental effects of temperature and humidity on milk production. The fixed and random effects models indicated that a 1 °C increase in temperature reduces milk production by approximately 1.72 L per month (
p < 0.01), while a 1% rise in humidity leads to a 0.59 L decrease (
p < 0.01). These results align with earlier research demonstrating that heat stress directly impacts metabolic efficiency and reproductive performance, ultimately reducing dairy output [
72,
73]. These regression outputs, derived from both linear and nonlinear specifications, offer a robust quantification of climatic influences on milk production. Each model was purposefully selected to examine distinct hypotheses, linear trends, nonlinear thresholds, and interaction effects, thus enhancing the overall explanatory power [
74]. Furthermore, the quadratic model confirmed the nonlinear nature of these effects, indicating that the negative impact of temperature accelerates at higher temperature levels [
73,
75], an observation supported by studies showing that THI values above 72 lead to steep declines in milk productivity [
57]. The interaction model further reinforced the compounding effect of temperature and humidity, suggesting that combined heat and humidity stress worsens dairy production losses, a critical finding for future climate resilience strategies [
76]. These findings are consistent with similar patterns reported globally, such as in the Mediterranean, Southeast Asia, and North America, where climate-induced reductions in dairy productivity mirror the magnitude observed in this study.
The dynamic panel GMM model and scenario-based forecasting provided valuable insights into both short-term variability and long-term climate risks. The significant positive lagged effect (ϕ = 0.735,
p < 0.001) revealed strong persistence in milk production over time, while the negative coefficients for temperature (β
1 = −1.600,
p < 0.001) and humidity (β
2 = −0.088,
p < 0.001) underscored the adverse effects of climatic stress. Diagnostic checks confirmed the model’s robustness: the Sargan test validated instrument relevance (
p = 0.229), and the absence of second-order autocorrelation (
p = 0.116) supported model consistency. The Wald test (χ
2 = 773,849,
p < 0.001) established overall model significance [
74]. The GMM framework effectively accounts for farm-level heterogeneity and dynamic adjustment processes, crucial for understanding the nuanced, climate-driven shifts in dairy productivity. The results validate the GMM model’s suitability for analyzing temporal milk production patterns under climatic variability, aligning with recent studies on climate-induced productivity shifts in dairy systems [
77,
78].
Building on the dynamic panel GMM model climate scenario analysis, the study simulated potential future declines based on projected warming and humidity increases. The analysis revealed that a +2 °C temperature increase could reduce milk production by 1.628 L per month (
p < 0.001), while a +10% increase in humidity could result in a 0.625 L loss per month (
p < 0.001). The worst-case scenario, where both temperature and humidity increase simultaneously, could lead to a total milk production decline of 2.253 L per month. These projections are supported by global climate models indicating that dairy production is at high risk in tropical and subtropical regions due to increasing heat stress conditions (USDA Climate Report [
79]. The forecast visualization (
Figure 7) effectively illustrates the divergence between baseline GMM projections and climate-adjusted forecasts, showing that climate change will likely suppress future yields beyond historical trends. These scenarios, though based on moderate IPCC-based deltas (+2 °C, +10% RH), serve as pragmatic stress-test cases for regional adaptation [
80]. While not formal RCP pathways (e.g., RCP 8.5), these incremental simulations reflect regionally meaningful scenarios that align with gradual climate trends observed in Punjab. These projections emphasize the urgency for region-specific adaptation policies. Practical interventions such as climate-resilient infrastructure, heat-mitigation technologies, and targeted subsidies must be mainstreamed into national dairy development frameworks to ensure resilience in smallholder-dominated systems like Punjab’s.
The robustness checks further validated the findings. The lagged models (2-month and 3-month delays) demonstrated a persistent effect of temperature on milk production, indicating that climate stressors impact dairy yields beyond immediate exposure. The variance inflation factor (VIF) values (~1.001) confirmed no multicollinearity [
40], while the Breusch–Pagan test (
p = 0.2666) indicated no heteroskedasticity concerns, supporting the reliability of regression estimates [
41]. The Durbin–Watson test (DW = 2.073) ruled out autocorrelation, ensuring that the time-series model accurately captured climate impacts [
42]. These checks validated the model reliability and highlighted that even moderate climatic shifts yield measurable declines in productivity. The sequential application of log-transformed, lagged, and interaction models confirmed that milk production dynamics under climate stress cannot be captured through a single modeling approach [
4].
Implications for Dairy Farming and Adaptation Strategies
The study’s findings emphasize the urgent need for adaptation strategies to mitigate the adverse effects of climate change on dairy farming. This urgency is underscored by both empirical evidence (e.g., regression and ARIMA forecasts) and an analysis of farmers’ perceptions, which consistently highlight heat and humidity as dominant stressors in Punjab’s dairy sector [
81]. Given the projected increases in temperature and humidity, dairy farmers must adopt heat mitigation measures, such as improved ventilation, shading, water misting systems, and modified feeding strategies [
82]. Such interventions are particularly critical in high-risk tehsils, identified through our regional regression analysis, where temperature–humidity overlaps pose the greatest threats. For instance, high-risk tehsils like Faisalabad and Toba Tek Singh, identified in our regional regression model as hotspots of climate exposure, require location-specific interventions to buffer livestock from thermal extremes [
83]. Similar adaptation patterns have been observed in other climate-vulnerable regions. For example, in Ethiopia farmers commonly adopt improved livestock breeds, crop varieties, and mixed farming practices in response to climate variability [
84]. These findings reflect parallel strategies in Punjab, where smallholders are increasingly investing in heat-tolerant breeds and diversified fodder systems, indicating broader behavioral convergence in climate adaptation across developing regions. [
85]. Drawing from successful adaptation experiences in similar climatic zones such as Tunisia, Korea and northern India, Pakistan can explore cross-breeding programs and community-led breed-preservation strategies for locally adapted, heat-tolerant breeds. This includes revitalizing genetic lines such as the Sahiwal or cross-breeding with indigenous breeds that show better thermal tolerance, enhancing long-term herd resilience [
64,
86,
87]. Furthermore, precision livestock farming technologies, such as automated temperature monitoring and climate-controlled housing, wearable health trackers, automated heat stress alerts, and mobile-based advisory systems can help optimize dairy production under variable climatic conditions [
88]. However, the accessibility of such technologies remains limited for smallholders, highlighting the need for targeted public–private partnerships and subsidized innovation diffusion mechanisms. Successful models from Bangladesh and Vietnam show how village-level climate advisory hubs and livestock insurance schemes can be scaled to rural dairy systems with minimal technological access [
89].
In addition to technological solutions, well-designed policy measures are essential to support smallholder farmers, who remain most vulnerable to climate-induced productivity declines [
90]. Financial tools such as climate-indexed livestock insurance, cash transfers for adaptive investments, and credit guarantees can help de-risk climate adaptation for vulnerable producers; particularly in Pakistan’s informal dairy economy, such instruments can bridge resilience gaps where institutional capacity is limited. Subsidies for climate smart dairy infrastructure, incentives for sustainable dairy farming practices, and early-warning climate risk advisory services should be central to national dairy development policies [
25,
91]. Without proactive measures, the projected decline in milk production could severely impact small-scale farmers, threatening rural livelihoods and national dairy supply chains. The study’s simulation of region-specific yield losses provides a practical framework for targeting such interventions in the most vulnerable areas. For example, projected milk production losses up to 2.25 L per cow under combined temperature–humidity scenarios emphasize the urgency of scaling adaptation efforts.
6. Conclusions
This study provides robust evidence that both temperature and humidity significantly reduce milk production in Punjab, Pakistan, with their combined effect posing an even greater threat. By integrating farmers’ perceptions with panel regression and dynamic panel GMM forecasting, the analysis presents a comprehensive assessment of climate impacts on dairy productivity. Regression models highlight consistent declines in milk yield associated with rising temperature and humidity, while interaction and quadratic terms reveal nonlinear and synergistic stressor effects.
The GMM-based projections further signal sustained declines in milk output under moderate climate scenarios (+2 °C and +10% RH), raising serious concerns for the viability of smallholder dairy systems. Given Punjab’s economic dependence on dairy and the limited adaptive capacity of small-scale farmers, these findings underscore the urgency of targeted interventions.
This study contributes methodologically by demonstrating the added value of combining econometric modeling with farmer-based data, and practically by informing climate adaptation planning. Recommended interventions include region-specific strategies such as heat-resilient cattle breeds, climate-smart infrastructure, and localized insurance programs to enhance sectoral resilience and food security.
Future research should extend this work by examining tehsil-level adaptive capacity, incorporating RCP-based climate projections, and conducting economic evaluations of adaptation measures. Such efforts will support the development of inclusive, evidence-based policies for sustaining dairy production under increasing climate stress.