Modeling the Short- and Long-Term Impacts of Climate Change on Wheat Production in Egypt Using Autoregressive Distributed Lag Approach

Abstract

Egypt, the world’s second-largest wheat importer, has been working hard to narrow the gap between its domestic wheat production and consumption. However, these efforts have been hampered by water scarcity and the negative impact of climate change on wheat production. This study seeks to analyze the influence of climatic and technical factors on wheat production in Egypt over the long and short term. Using Egypt-specific data from 1961 to 2022 and employing the Autoregressive Distributed Lag (ARDL) model and Granger-causality, the study examines the impact of factors such as harvested area, fertilizers, technology, CO₂ emissions, seasonal temperature and precipitation patterns (winter and spring) on wheat production in Egypt. The empirical results indicate that the harvested area, level of technology, and average winter temperature significantly and positively impact wheat production. Precisely, a 1% increase in these factors leads to a 1.08%, 1.49%, and 6.89% increase in wheat production, respectively. Conversely, a 1% rise in CO₂ emissions, average spring temperature, and precipitation reduced wheat production by 1.76%, 0.52%, and 0.054%, respectively. The Granger causality results indicate a bidirectional causal relationship between wheat production and harvested area. Furthermore, the technology level exhibits a significant causal influence on wheat production, cultivated area, and CO₂ emissions, highlighting its pivotal role in both the wheat production process and its environmental impact. In conclusion, this study is crucial for Egypt’s future food security. By identifying the key climatic and non-climatic factors that impact wheat production, policymakers can gain valuable insights to address climate change and resource limitations. Improving domestic production through technological advancements, effective resource utilization, and climate-resilient practices will ensure a sustainable food supply for Egypt’s expanding population in the face of global uncertainties.

1. Introduction

Wheat plays a key role in Egypt’s economy and food security, acting as a fundamental food staple for its population. It is one of the most significant crops in the country, with bread wheat serving as a primary source of calories for most families. However, Egypt has met considerable challenges in wheat production, as domestic production has not kept up with the rising demand driven by a rapidly growing population. In 2022, Egypt produced 9.7 million tons of wheat from 1.49 million hectares of land. Notwithstanding the adoption of various production strategies, Egypt still heavily relies on imports, which account for one-fifth of its agricultural product value. As a result, Egypt is ranked as the world’s second-largest importer of seed wheat and wheat flour, after China, with an import volume of 12 million metric tons [1,2]. Therefore, Egypt must take into account the broader market dynamics in order to ensure food security for its population, as global wheat production, currently at around 789 million tons, will need to double by 2050 to meet the needs of the projected 9.5 billion global population.

The Egyptian government has introduced programs to boost wheat production and reduce reliance on imports. These programs focus on enhancing irrigation efficiency and adopting modern agricultural techniques to maximize wheat yield per acre. Additionally, the aim of these programs is to increase self-sufficiency from 47% in 2021 to 70% by 2030, proving a commitment to improving food security. However, the achievement of this ambitious target is at risk due to water scarcity, a prominent feature of Egypt’s arid climate, and the increasing effects of climate change [3]. Egypt, a country with limited rainfall, depends significantly on the Nile River for its water resources and is particularly vulnerable to the current negative effects of climate change.

Temperature, reduced precipitation in the Nile Basin and Mediterranean coastline, and increased evapotranspiration are expected to exacerbate water scarcity, which will have a direct impact on agricultural production, particularly wheat production [4]. Furthermore, increasing temperatures and erratic rainfall patterns adversely affect crop growth, especially for heat-sensitive crops like wheat, resulting in a significant reduction in their grain yield [5]. Increased mean temperature could lead to lower crop yields because changes in temperature may alter the time required for plants to reach maturity [6]. According to You et al. [7], an increase of 1 °C in the average seasonal temperature during the wheat growth stages may result in a reduction in wheat yield ranging from 3 to 10%. Most importantly, increasing temperatures during the critical growth phases of wheat, especially during the grain filling stage, result in a notable decrease in their ultimate grain yield. Additionally, elevated nighttime temperatures can lead to increased plant respiration, which in turn can reduce grain storage and ultimately lower crop yields [8]. Similarly, for C₃ plants like wheat, atmospheric CO₂ concentration plays a vital role in production. Model simulations indicate that wheat yields are projected to experience a substantial growth in the coming decades when compared to the 1961–1990 baseline. With the influence of CO₂ fertilization considered, yields could potentially increase by up to 67.8% in the 2050s and 87.2% in the 2080s. However, excluding this factor, the expected growth rates are significantly lower at 23.1% and 34.4% for the same time periods [9]. This highlights the well-established fertilization effect of rising CO₂ levels on plant growth. Increased levels of atmospheric CO₂ have been shown to enhance photosynthesis in C₃ plants, resulting in improved water use efficiency and increased biomass accumulation. Furthermore, the higher CO₂ levels lead to a reduction in stomatal conductance, which helps to decrease water loss through transpiration and makes wheat crops more resilient to water deficit. This effect is especially advantageous in arid and semiarid countries where water scarcity can hinder crop productivity [10]. However, a study by Kheir et al. [11] reported that rising atmospheric CO₂ levels, coupled with rising temperatures, decrease wheat yields in Egypt.

Several studies have examined the adverse effects of specific climatic factors—such as rising temperatures and decreased precipitation—on wheat production in Egypt [12,13,14,15,16,17,18], as well as their implications for agricultural water demand and water footprint [3,19,20,21,22]. Most of these studies, however, considered only a limited set of factors or focused exclusively on short-term effects. A key remaining question is whether—and to what extent—climate change has influenced the efficiency of wheat production in Egypt, and through what mechanisms.

Most studies investigating climate change’s impact are in natural sciences fields. Two main approaches have been used in these studies. The first is the simulation model. For instance, Gamal et al. [23] evaluated the impacts of two global warming (GW) levels (1.5 and 2.0 °C) using simulations calculated from the ISI-MIP Fast-Track archive. According to the findings, under GW1.5 and GW2.0, the national average change in wheat yield was 5.0% (0.0% to 9.0%) and 5.0% (−3.0% to 14.0%), respectively. The second model is a field experiment. As Kheir et al. [11] employed experimental data from two growing seasons in 2014–2015 and 2015–2016, to calibrate the utilization of various irrigation, planting date, and fertilization treatments. With a d-index greater than 0.80 and a root mean square deviation of less than 10%, both models accurately stood for the phenology and wheat yield. A sensitivity analysis to climate change revealed that a one to four Celsius increase in temperature reduced wheat yield by 17.6%.

In economics, researchers mostly use empirical models (regression model, panel data model, etc.). For instance, Ali [24], Abdelaal and Elsherbini [25] investigated the impact of annual minimum and maximum temperature, as well as rainfall on wheat productivity in Egypt. However, there is less evidence of empirical analysis related to climate change, wheat inputs, and technology used in wheat production. Therefore, the present study examines the impact of climatic and environmental variables associated with essential inputs on wheat production. Seasonal temperature and rainfall are considered climatic variables, while the environmental variable is the level of carbon dioxide. The main inputs analyzed are the harvested areas of wheat, fertilizers, and the number of tractors as a proxy variable for the technology level applied. To achieve this goal, an Autoregressive Distributed Lagged model (ARDL) is used to examine climate change’s short-term and long-term impact on wheat production in Egypt.

By incorporating these variables, this study provides a comprehensive understanding of the determinants of wheat production in Egypt. It will contribute to current knowledge about the economic implications associated with climate change and the importance of inputs and technology in wheat cultivation. Therefore, the results of the current research can thus lead policymakers and other stakeholders in the agricultural sector to formulate specific strategies to help increase wheat production and address the challenge of food security in the face of climate change.

Therefore, this study aims to: (1) examine the long-term and short-term impacts of climatic variables (seasonal temperatures and precipitation) on wheat production in Egypt; (2) assess the influence of environmental factors (CO₂ emissions) and agricultural inputs (harvested area, fertilizers, technology) on wheat yields; (3) determine causal relationships between these variables using Granger causality analysis; and (4) provide evidence-based policy recommendations for enhancing climate resilience in Egyptian wheat production.

2. Methodology

The current study adopts Egypt-specific time series data spanning 1961–2022. The data were extracted from the Food and Agriculture Organization FAO database [26]. FAO datasets adhere to standardized protocols for agricultural statistics, including field surveys, government reports, and satellite-based estimates, ensuring global comparability [1]. The variables harvested area of wheat, fertilizers, number of tractors, mean of winter temperature, mean of spring temperature, CO₂ emissions, and rainfall are incorporated as endogenous variables. Wheat production represents an exogenous variable, as shown in

Table 1. Abbreviation (Abb.), description, units, and data sources of different variables used in this study.

Abb.	Description	Unit	Source
WP	Wheat production	Tons	[21]
Ha	Wheat harvested area	Hectare	[21]
Fert.	Fertilizer consumption	Kilogram/hectare	[21]
Tract	Number of tractors	number	[21]
CO2	Carbon dioxide emissions	Metric tons/capita	[21]
WTEMP.	Mean winter temperature	°C	[21]
SPTEMP	Mean spring temperature	°C	[21]
Rf	Rainfall	mm	[21]

. All data are transformed into a natural logarithm before applying the ARDL bound test.

Economic analysis theoretically posits a long-term relationship among the variables being studied. However, researchers and econometricians have frequently overlooked the dynamic properties inherent in most time series when analyzing data and developing traditional regression models. It was assumed that the time series in question were stationary or at least stationary around a deterministic trend and that they exhibited a long-term relationship. Consequently, it was widespread practice to construct econometric models traditionally, presuming that the means and variances of the variables remained constant and were not time dependent. Accordingly, these estimated models were used to forecast, assess, and motivate policies and examine theories developed at an abstract level.

Recent advancements in econometrics, however, have shown that many time series are not stationary as previously believed. Thus, different time series may not share the same characteristics. Some time series may diverge from their mean over time, while others may converge. Time series that diverge from their averages are classified as non-stationary. Consequently, classical estimation methods applied to variables with this relationship often yield misleading inferences or spurious regression.

To address the issue of non-stationarity and the prior constraints on a model’s lag structure, econometric analysis of time series data has increasingly focused on co-integration. Co-integration serves as a robust method for identifying the presence of a steady-state equilibrium among variables. It has become essential for any economic model that utilizes non-stationary time series data. If the variables do not exhibit co-integration, the results may lead to spurious regression, rendering them meaningless. Conversely, if the variables do cointegrate, this indicates a meaningful long-term relationship. The data utilized in this study covers the years from 1961 to 2022, prompting the use of a time series approach.

2.1. Testing the Time Series Stationarity

In mathematics and statistics, a stationary stochastic process is one where the unconditional joint probability distribution remains unchanged over time. Consequently, parameters such as the mean and variance also stay constant. While there can be fluctuations, a line drawn through the center of a stationary process will be horizontal, showing no upward or downward trend [27].

Non-stationary data are often transformed into stationary data because stationarity is a crucial assumption in the statistical methods used for time series analysis. A common reason for violating stationarity is a trend in the mean, which can arise from either a unit root or a deterministic trend. In the case of a unit root, stochastic shocks have lasting effects, meaning the process does not revert to the mean. Conversely, when there is a deterministic trend, the process is referred to as a trend-stationary process; here, stochastic shocks only have temporary impacts, and the variable eventually trends toward a deterministically changing (non-constant) mean [28].

In statistics, the Augmented Dickey–Fuller (ADF) test assesses the null hypothesis that a unit root is present in a time series sample. The alternative hypothesis can vary depending on the test’s version but posits either stationarity or trend-stationarity. The ADF test enhances the Dickey–Fuller test, accommodating a broader and more complex range of time series models. The ADF statistic, utilized in this test, yields a negative value; the more negative the statistic, the more substantial the evidence against the null hypothesis of a unit root at a given confidence level. The extended regression framework used in the ADF test can be expressed as follows:

$$\mathsf{\Delta }{Y}_t=\mu +\gamma Y_{t-1}+{\sum }_{j=1}^p{\alpha }_j\Delta Y_{t-j}+\beta t+{\omega }_t$$

(1)

where $\mu$ is the drift term, $t$ denotes the time trend, and $p$ is the maximum lag length used. To analyze the deterministic trends, we used modified versions of the likelihood ratio tests suggested by [29]. The testing sequence suggested the following maintained regressions, test statistics, and hypotheses:

$$\Delta Y_t=\mu +\gamma Y_{t-1}+\sum ^{\underset{p}{j=1}}{\alpha }_j\Delta Y_{t-j}+\beta t+{\omega }_t$$

(2)

$${\widehat{\tau }}_{\beta },H_0:\gamma =0,H_a:\gamma <0;{\phi }_3,H_0:\gamma =0,\beta =0,H_a:\gamma \ne 0, \mathrm{and}/\mathrm{or} \beta \ne 0$$

$$\Delta Y_t=\mu +\gamma Y_{t-1}+\sum ^{\underset{p}{j=1}}{\alpha }_j\Delta Y_{t-j}+{\omega }_t$$

(3)

$${\widehat{\tau }}_{\mu },H_0:\gamma =0,H_a:\gamma <0;{\phi }_1,H_0:\mu =0,\gamma =0,\beta =0,H_a:\mu \ne 0, \mathit{and}/\mathit{or} \gamma \ne 0$$

$$\Delta Y_t=\gamma Y_{t-1}+\sum ^{\underset{p}{j=1}}{\alpha }_j\Delta Y_{t-j}+\beta t+{\omega }_t$$

(4)

$$\tau ,H_0:\gamma =0,H_a:\gamma <0$$

In practical applications, the Dickey–Fuller (DF) or Augmented Dickey–Fuller (ADF) test statistics often have a value less than its critical value, indicating that the original time series is non-stationary. Conversely, when the DF or ADF statistic exceeds the critical value, it suggests that the base series is stationary. However, it is essential to note that the ADF test has the null hypothesis of a non-stationary series. Therefore, if the test fails to reject the null hypothesis, it is interpreted as confirming that the series is non-stationary.

2.2. Autoregressive Distributed Lag (ARDL) Model

In a single-equation framework, ARDL models are frequently used to investigate dynamic relationships with time series data. ARDL Estimation Process can be summarized in the following steps in Figure 1.

Pesaran and Shin [30] were the pioneers of the ARDL technique, which was later refined by Pesaran et al. [31]. The ARDL model has advantages compared with traditional cointegration methods, such as the Engle–Granger and Johansen–Juselius approaches. One key advantage is its ability to address simultaneity biases and its suitability for small sample sizes. Traditional cointegration methods faced the limitation that all variables in the study needed to be stationary in the same order, specifically non-stationary at I(0). In contrast, the ARDL method effectively resolves this issue by allowing variables to be integrated in different orders, whether at levels I(0), first differences I(1), or a combination of both. Choosing the correct number of lags for the empirical model with flexibility is another advantage of this contemporary method. These advantageous features make the ARDL technique reliable for obtaining accurate estimations.

To examine the impact of climate change factors, for instance, temperature, CO₂ emissions, and rainfall, on wheat production in Egypt from 1961 to 2022, the model can be defined as:

$${WP}_t=f\left({Ha}_t, {Fert}_t, {{Tract}_t, {{Co}_2}_t, W_{temp}}_t, {S{P}_{temp}}_t {Rf}_t\right)$$

(5)

where WP denotes wheat production in tons, Ha is the harvested area of wheat in hectares, Fert: fertilizers consumption in tons, Tract: number of tractors used, CO₂: Carbon dioxide emissions (metric ton/capita), W_TEMP. is the mean of winter temperature in Celsius, SP_TEMP is the mean of spring temperature °C, and Rf is the rainfall in millimeters (mm). Therefore, Equation (5) can be written as:

$$\begin{array}{c}{WP}_t={\lambda }_0+{\lambda }_1{Ha}_t+ {\lambda }_2{Fert}_t+{\lambda }_3{Tract}_t+ {\lambda }_4{{CO}_2}_t+ {\lambda }_5{W}_{{TEMP}_t})\hfill \\ +{\lambda }_6{Sp}_{{TEMP}_t}+{\lambda }_7{Rf}_t+{\mu }_t\end{array}$$

(6)

All the variables are transformed to their natural logarithmic form to diminish the multicollinearity and volatility of the annual time series data. Equation (6) can be converted into a log-linear model by using the natural logarithm as follows:

$$\begin{array}{c}\hfill {LnWP}_t={\lambda }_0+{\lambda }_{1}Ln{Ha}_t+ {\lambda }_{2}Ln{Fert}_t+{\lambda }_{3}Ln{Tract}_t+ {\lambda }_{4}Ln{{CO}_2}_t\\ \hfill + {\lambda }_{5}Ln{W_{temp}}_t)+{\lambda }_{6}Ln{S{p}_{temp}}_t+{\lambda }_7{LnRf}_t+{\mu }_t\end{array}$$

(7)

To address the theoretical concern regarding the logarithmic transformation of temperature, it is noted that all log-transformed seasonal temperature values in the dataset are strictly positive and substantially above zero. Accordingly, all estimated elasticities for temperature are interpreted within this observed positive range of values.

The ARDL model encompasses two steps for assessing a long-term association. Step 1 examines the incidence of a long-term association between the study variables. Equation (8) represents the specification of the ARDL model as follows:

$$\begin{array}{c}{∆LnWP}_t={\beta }_0+{\sum }_{i=1}^p{\beta }_1{∆LnWP}_{t-k}+{\sum }_{i=0}^p{\beta }_2{∆LnHa}_{t-k}+ {\sum }_{i=0}^p{\beta }_3∆Ln{Fert}_{t-k}+{\sum }_{i=0}^p{\beta }_4∆Ln{Tract}_{t-k}+\\ {\sum }_{i=0}^p{\beta }_5∆Ln{{CO}_2}_{t-k}+{\sum }_{i=0}^p{\beta }_6∆Ln{W_{temp}}_{t-k}+{\sum }_{i=0}^p{\beta }_7∆Ln{{Sp}_{temp}}_{t-k}+ {\sum }_{i=0}^p{\beta }_8∆{LnRf}_{t-k}+{\sum }_{i=0}^p{\beta }_9∆D_{t-k}+\\ {\lambda }_1{LnWP}_{t-1}+{\lambda }_2{LnHa}_{t-1}+ {\lambda }_{3}Ln{Fert}_{t-1}+{\lambda }_{4}Ln{Tract}_{t-1}+{\lambda }_5{Ln{{CO}_2}_{t-1}+\lambda }_{6}Ln{W_{temp}}_{t-1}+{\lambda }_{7}Ln{{Sp}_{temp}}_{t-1}+\\ {\lambda }_8{LnRf}_{t-1}+ {\lambda }_9{D}_{t-1}+{\epsilon }_{t }\end{array}$$

(8)

where β₀ is the intercept, p refers to the lag order, $∆$ stands for the first difference operator, and ${\epsilon }_t$ denotes the error term. This study used the F-test to check the long-term equilibrium link among wheat production, harvested area of wheat, fertilizers, number of tractors, LnCO₂, mean of winter temperature, mean of spring temperature, and rainfall. The null hypothesis is that there is no cointegration between wheat production and other variables. The null hypothesis is H0: ${\lambda }_1$ = ${\lambda }_2$ = ${\lambda }_3$ = ${\lambda }_4$ = ${\lambda }_5$ = ${\lambda }_6$ = ${\lambda }_7$ = ${\lambda }_8$ = ${\lambda }_9=$0, against the alternative hypothesis H1: ${\lambda }_1$ ≠ ${\lambda }_2$ ≠ ${\lambda }_3$ ≠ ${\lambda }_4$ ≠ ${\lambda }_5$ ≠ ${\lambda }_6\ne$ ${\lambda }_7$ ≠ ${\lambda }_8$ ≠ ${\lambda }_9\ne$ 0. If the computed F-test is more than the upper level of the bound, the null hypothesis of no cointegration between dependent and independent variables is rejected. If the computed F-test is less than the upper level of the bound, it accepts the null hypothesis of no cointegration. However, If the computed F-test falls between the lower and upper level of the bands, the null hypothesis becomes inconclusive, which either can be testified by Johansen and Juselius [32] or by using the cumulative sum recursive residuals and cumulative of the square of recursive residuals to check the constancy of the cointegration.

Another step is needed to assess the short-term association between the dependent and independent variables above. The Error Correction Model (ECM) in ARDL formulation can be expressed as:

$$\begin{array}{c}{∆LnWP}_t={\beta }_0+{\sum }_{i=1}^p{\beta }_1{∆LnWP}_{t-k}+{\sum }_{i=0}^p{\beta }_2{∆LnHa}_{t-k}+ {\sum }_{i=0}^p{\beta }_3∆Ln{Fert}_{t-k}+\\ {\sum }_{i=0}^p{\beta }_4∆Ln{Tract}_{t-k}+{\sum }_{i=0}^p{\beta }_5∆Ln{{CO}_2}_{t-k}+{\sum }_{i=0}^p{\beta }_6∆Ln{W_{temp}}_{t-k}+\\ {\sum }_{i=0}^p{\beta }_7∆Ln{{Sp}_{temp}}_{t-k}+ {\sum }_{i=0}^p{\beta }_8∆{LnRf}_{t-k}+{\sum }_{i=0}^p{\beta }_9∆D_{t-1}+\propto {ECM}_{t-1}+{\epsilon }_t\end{array}$$

(9)

where for short-term dynamics, ∝ stands for the ECM coefficients and Δ for the first difference. ECM displays the change in speed in the long-term equilibrium following a short-term shock.

The EViews^® version 13 software was used in this study because of its robust ARDL bounds testing features, which include comprehensive diagnostic testing features and automated lag selection based on information criteria.

3. Results and Discussion

3.1. Unit Root Test Results

The Augmented Dickey–Fuller (ADF) and Phillips–Perron tests (PP) are widely utilized unit root tests in econometrics, yet they differ in their methodologies. The ADF test focuses on regressing the differenced series against its lagged values, whereas the PP test regresses the original series on a deterministic trend along with lagged differences. Moreover, the PP test is specifically designed to accommodate structural breaks in the trend function, making it particularly effective for data where the timing of breaks is unknown [33,34].

The results of the ADF and PP unit root tests are presented in

Table 2. Results of augmented Dickey–Fuller (ADF) and Phillips–Perron (PP) unit root tests.

Variables	ADF Test		PP Test		Integration Order
	Level		Level
	Constant	Constant and Trend	Constant	Constant and Trend
Production	−0.558	−2.140	−0.477	−2.146
Area	−0.373	−2.607	−0.264	−2.567
Fertilizers	−2.218	−1.414	−2.097	−1.347
Tractors	−2.016	−0.225	−1.807	−0.476
CO2	−1.152	−1.523	−1.186	−2.023
Winter temperature	−4.812 **	−5.832 ***	−6.817 ***	−7.963 ***	I(0)
Spring temperature	−3.901 *	−8.707 ***	−6.492 ***	−8.707 ***	I(0)
Rainfall	−4.694 **	−5.925 ***	−7.525 ***	−7.673 ***	I(0)
Variables	First difference		First difference
	Constant	Constant and Trend	Constant	Constant and Trend
Production	−10.113 ***	−10.030 ***	−9.899 ***	−9.790 ***	I(1)
Area	−8.490 ***	−8.497 ***	−8.488 ***	−8.497 ***	I(1)
Fertilizers	−5.040 ***	−8.585 ***	−8.237 ***	−8.584 ***	I(1)
Tractors	−5.991 ***	−6.327 ***	−6.030 ***	−6.327 ***	I(1)
CO2	−8.928 ***	−8.965 ***	−8.917 ***	−8.950 ***	I(1)
Winter temperature	−5.250 ***	−5.247 ***	−33.824 ***	−34.674 ***
Spring temperature	−5.033 ***	−5.045 ***	−51.329***	−54.420 ***
Rainfall	−11.436 ***	−11.335 ***	−15.164***	−18.030 ***

Note: *, **, and *** denote the significance level at 10%, 5%, and 1%, respectively.

. Both tests reveal that all-time series variables are non-stationary at their current levels, including wheat production, area under wheat cultivation, fertilizers usage, tractor numbers, and CO₂ emissions. However, these variables become stationary after taking their first differences, indicating that they are integrated of order one I(1). In contrast, the mean temperature during winter, mean temperature during spring, and rainfall are found to be stationary at their current levels, suggesting that they are integrated of order zero I(0).

3.2. Specifying ARDL Data Generating Process

In the context of ARDL models, accurate modeling and inference rely on selecting the appropriate form of the deterministic components (constant, trend) in the data-generating process. It assumes that the underlying data are steady in a certain way by employing a “restricted constant with no trend”.

According to Pesaran and Shin [35], if the time series data are stationary around a constant mean (without any deterministic trend), then including a restricted constant (intercept) without a trend in the ARDL model is appropriate. This situation corresponds to I(0) or stationary processes after differencing. After calculating the first differences for each variable, they are all stationary. Thus, the restricted constant with no trend specification was used.

3.3. Lag Order and Bound Test for Cointegration

The ARDL model (2, 3, 5, 4, 3, 5, 5, 3) for wheat production, the area under wheat cultivation, chemical fertilizers, number of tractors used, CO₂ emission, mean winter temperature, mean spring temperature, and rainfall, respectively, was chosen based on the estimation of the ARDL model using the Akaike info criterion (AIC) auto-selection method.

After confirming that the data are free from a unit root, a cointegration bound test was conducted to determine whether a long-term equilibrium relationship exists between the variables under consideration. The results of the bound test in

Table 3. ARDL bounds test for cointegration analysis of wheat production model (1961–2022).

Cointegration Bound Test	Value	K
F-statistics	7.301	7
Significance	At I(0)	At I(1)
At 10%	2.044	3.104
At 5%	2.373	3.540
At 1%	3.129	4.507

indicate that the F-statistic was 7.301, which exceeded the critical values for different significance levels (10%, 5%, and 1%). These results suggest a long-term equilibrium relationship among the variables in the ARDL model. This indicates that, although there may be short-term variations, the variables generally move together in the long term, indicating a long-term relationship.

3.4. ARDL Model Estimations, Both Long- and Short-Term

The long-term estimates indicate that area, tractor usage, CO₂ emissions, and winter temperature significantly influenced wheat production. In contrast, fertilizer use, spring temperature, and rainfall did not show statistically significant effects. The results highlight the importance of certain agricultural and environmental factors in determining the long-term outcomes in the ARDL model.

The empirical results underscore the critical role of agricultural inputs and climatic variables in shaping Egypt’s wheat production dynamics. The long-term positive impact of harvested area (1.08% increase per 1% expansion) aligns with findings by Chandio et al. [6] in Bangladesh, where land allocation significantly boosted cereal yields under climate stress. Similarly, the substantial elasticity of winter temperature (6.89% increase per 1 °C rise) resonates with Gamal et al. [23], who noted that moderate warming during cooler seasons can enhance wheat growth in arid regions by extending the growing period. However, this contrasts with Kheir et al. [11] who reported yield declines in Egypt’s Nile Delta under temperature increases, highlighting regional variability in climate responses

The negative long-term effect of CO₂ emissions (−1.76% per 1% increase) corroborates global studies linking elevated CO₂ to heat stress and reduced grain quality [17,36].

The long-term effects of fertilizers, average spring temperature, and rainfall were statistically insignificant, as shown in

Table 4. Long-term and short-term parameter estimates from the ARDL model for wheat production in Egypt (1961–2022).

Variable	Coefficient	Std. Error	t-Statistic	Prob.
Long-term estimation
Ln area	1.078	0.480	2.248	0.037
Ln fertilizers	0.749	0.542	1.381	0.183
Ln tractors	1.493	0.493	3.029	0.007
Ln CO2	−1.762	0.592	−2.974	0.008
Ln WTEMP	6.886	2.594	2.654	0.016
Ln SPTEMP	3.563	2.396	1.487	0.153
Ln RAIN	0.253	0.159	1.590	0.128
C	−42.309	14.091	−3.003	0.007
Short-term estimation
D(Ln area)	1.075	0.068	15.716	0.000
D(Ln fertilizers)	0.049	0.053	0.917	0.371
D(Ln tractors)	0.007	0.096	0.073	0.942
D(Ln CO2)	−0.072	0.054	−1.331	0.199
D(Ln WTEMP)	−0.096	0.099	−0.967	0.346
D(Ln SPTEMP)	−0.520	0.132	−3.927	0.001
D(Ln RAIN)	−0.054	0.018	−3.066	0.006
CointEq(−1)	−0.288	0.030	−9.663	0.000

. Wang et al. [37] found that excessive fertilizer application leads to diminishing yield returns and potential negative environmental effects, particularly when combined with intensive irrigation practices. While most Egyptian wheat production relies on irrigation systems that help stabilize yields by reducing dependence on rainfall variability, research indicates that high temperature events occurring during the critical spring grain-filling period can significantly reduce wheat yields in the short term [38].

In the short term, the effects of climatic and environmental variables differ from their long-term counterparts. Specifically, the mean spring temperature and rainfall negatively affect wheat production. A 1% increase in the mean spring temperature and precipitation is associated with a reduction in wheat production by 0.520% and 0.054%, respectively, consistent with [5] who emphasized that abrupt spring heatwaves during flowering stages disrupt pollination. The harvested wheat area continues to have a significant influence in the short term, where a 1% increase in the wheat harvested area leads to a 1.075% rise in production. However, CO₂ emissions, fertilizer use, the number of tractors, and the average winter temperature do not show significant effects in the short term.

The estimated coefficient of ECM is negative and significantly confirms the presence of cointegration among the variables. The ECM indicates the speed at which adjustments occur towards long-term equilibrium following short-term disturbances. For wheat production in Egypt, the ECM coefficient is −0.288, which is significant at the 1% level. This indicates that any deviation from the short-term equilibrium between the variables and wheat production can be corrected at 28.8% per year in the long term.

Short-term impacts of climatic variables capture the immediate response to sudden climate stress, such as heat waves or unexpected rainfall events. In contrast, long-term coefficients represent equilibrium relationships where agricultural systems have fully adapted to prevailing climatic conditions through multiple mechanisms. These adaptation mechanisms include: (1) varietal selection and breeding programs that develop crops suited to the local climate patterns; (2) infrastructure adjustments such as improved irrigation systems and storage facilities; (3) farmer learning and experience accumulation that enhances decision-making under varying climate conditions; and (4) policy interventions and institutional adaptations that support climate-resilient agricultural practices. Therefore, while short-term effects reflect vulnerability to climate shocks, long-term effects demonstrate the agricultural system’s adaptive capacity over time.

The results of various diagnostic tests conducted for the ARDL model are presented in

Table 5. Diagnostic tests and model performance statistics for ARDL wheat production model.

Diagnostic Test	Value (Probability)
R2	0.998
Adjusted R2	0.997
F-statistic	808.417 (0.000)
Ramsey RESET	1.817 (0.193)
Durbin–Watson	2.034
Breusch–Godfrey Serial Correlation	1.063 (0.316)
Heteroskedasticity Test: ARCH	0.189 (0.890)
CUSUM	Stable
CUSUM square	Stable

. The R-squared value is 0.998, indicating that the model explains 99.8% of the variation in wheat production in Egypt. The adjusted R² value is 0.997, suggesting that the model has a high goodness-of-fit even after accounting for the number of predictors. The F-statistic is 808.417 with a p-value of 0.000, which is significant at the 1% level. Thus, the model has strong explanatory power and is statistically significant. The Ramsey RESET test has a p-value of 0.193 for the ARDL residual diagnosis, which is higher than the 5% significance limit. This suggests no missing variables, and the model is adequately presented. There is no autocorrelation in the residuals, as indicated by the Durbin–Watson statistic of 2.034, which is near 2. Additionally, the p-value for the Breusch–Godfrey test is 0.316, above the 5% significance level. This confirms the residuals’ lack of serial correlation. With a p-value of 0.890 for the ARCH test, which is higher than the 5% significance level, the residuals are homoscedastic or have constant variance.

In models such as ARDL, where researchers estimate long-term relationships, verifying that these relationships remain stable over time is essential. The cumulative sum (CUSUM) and CUSUM of Squares tests (CUSUMSQ), as introduced by Brown et al. [39], are commonly used to evaluate this. As illustrated in, the CUSUM plot remains within the 5% significance limits throughout the observed period (Figure 2), indicating that the model’s parameters are stable and free from any significant structural breaks or deviations. Similarly, the CUSUMSQ test in shows that the line does not exceed the upper or lower bounds (Figure 3), suggesting no evidence of variance instability or heteroskedasticity. This confirms the stability of the model, enhancing the reliability of both the short-term and long-term ARDL results.

Conducting Granger causality after an ARDL model is meaningful, as the two approaches provide different insights. ARDL reveals long-term relationships, while Granger causality helps discover short-term causality. The categories of causal relationships are unidirectional, bidirectional, and no causal relationships. The Granger causality test results in

Table 6. Pairwise Granger causality test results between wheat production variables (1961–2022).

Null Hypothesis	F-Statistic	Prob.	Null Hypothesis	F-Statistic	Prob.
AREA ⟶ PRODUCTION	4.25 **	0.04	CO2 ⟶ FERTILIZERS	0.00	0.97
PRODUCTION ⟶ AREA	10.21 ***	0.00	FERTILIZERS ⟶ CO2	2.41	0.13
FERTILIZERS ⟶ PRODUCTION	3.83	0.06	WTEMP ⟶ FERTILIZERS	0.31	0.58
PRODUCTION ⟶ FERTILIZERS	0.01	0.93	FERTILIZERS ⟶ WTEMP	5.43 **	0.02
TRACT ⟶ PRODUCTION	6.91 ***	0.01	SPTEMP ⟶ FERTILIZERS	0.03	0.87
PRODUCTION ⟶ TRACT	1.52	0.22	FERTILIZERS ⟶ SPTEMP	11.68 ***	0.00
CO2 ⟶ PRODUCTION	2.80	0.10	RAIN ⟶ FERTILIZERS	0.51	0.48
PRODUCTION ⟶ CO2	1.88	0.18	FERTILIZERS ⟶ RAIN	1.56	0.22
WTEMP ⟶ PRODUCTION	1.23	0.27	CO2 ⟶ TRACT	0.11	0.74
PRODUCTION ⟶ WTEMP	11.78 ***	0.00	TRACT ⟶ CO2	7.34 ***	0.01
SPTEMP ⟶ PRODUCTION	0.08	0.78	WTEMP ⟶ TRACT	4.00 **	0.05
PRODUCTION ⟶ SPTEMP	19.76 ***	0.00	TRACT ⟶ WTEMP	9.25 ***	0.00
RAIN ⟶ PRODUCTION	2.22	0.14	SPTEMP ⟶ TRACT	1.26	0.27
PRODUCTION ⟶ RAIN	4.04 **	0.05	TRACT ⟶ SPTEMP	14.41 ***	0.00
FERTILIZERS ⟶ AREA	3.71	0.06	RAIN ⟶ TRACT	1.05	0.31
AREA ⟶ FERTILIZERS	0.04	0.84	TRACT ⟶ RAIN	2.63	0.11
TRACT ⟶ AREA	6.12 **	0.02	W_TEMP ⟶ CO2	0.06	0.81
AREA ⟶ TRACT	1.96	0.17	CO2 ⟶ WTEMP	11.67 ***	0.00
CO2 ⟶ AREA	5.22 **	0.03	SPTEMP ⟶ CO2	0.42	0.52
AREA ⟶ CO2	0.81	0.37	CO2 ⟶ SPTEMP	18.92 ***	0.00
W_TEMP ⟶ AREA	0.13	0.72	RAIN ⟶ CO2	0.14	0.71
AREA ⟶ WTEMP	13.69 ***	0.00	CO2 ⟶ RAIN	2.93	0.09
SPTEMP ⟶ AREA	0.02	0.89	SPTEMP ⟶ WTEMP.	2.00	0.16
AREA ⟶ SP_TEMP	18.36 ***	0.00	WTEMP ⟶ SPTEMP	0.38	0.54
RAIN ⟶ AREA	0.72	0.40	RAIN ⟶ WTEMP	15.43 ***	0.00
AREA ⟶ RAIN	5.98 **	0.02	WTEMP ⟶ RAIN	1.16	0.28
TRACT ⟶ FERTILIZERS	1.54	0.22	RAIN ⟶ SPTEMP	3.73	0.06
FERTILIZERS ⟶ TRACT	2.59	0.11	SPTEMP ⟶ RAIN	2.37	0.13

Note: **, and *** denote the significance level at 5% and 1%, respectively.

demonstrate a bidirectional causality between wheat production and wheat harvested area, indicating a robust short-term interaction between these variables. This could reflect farmers’ adaptive behavior, growing their crops in response to demand but eventually running out of land—a feedback loop seen in Nigerian farming systems [15].

Technology’s unidirectional causality with production and CO₂ emissions underscores its dual role: mechanization boosts efficiency but may exacerbate emissions if reliant on fossil fuels, a tension highlighted in Pakistani agriculture [9]. Additionally, there is a bidirectional causality between the number of tractors and the winter temperature, showing the importance of mechanization in the production process and its environmental effects. Wheat production Granger causes winter and spring temperatures, indicating potential feedback loops between agricultural activities and climate. There is no significant Granger causality between wheat production and three climatic variables, such as CO₂ emissions, rainfall, and spring temperature, but these variables could still have long-term impacts.

It is important to note that the current research emphasizes macro-level climatic and technical drivers of wheat production. Therefore, it does not address microbial dynamics (e.g., soil microbiota) due to methodological and data constraints. Investigating these interactions would require merging microbiological datasets with econometric frameworks. Future interdisciplinary efforts could advance targeted strategies, such as biofertilizer optimization, to strengthen climate resilience in arid agroecosystems.

4. Conclusions

The current research addresses the complex interaction between climate change and wheat yields in Egypt and employs the ARDL model for both the long- and short-terms. The findings reveal that agricultural inputs like the area under wheat cultivation, technology level, and weather conditions, precisely winter temperature, have a positive impact on wheat production. On the other hand, CO₂ emissions harm wheat yield; this highlights the effects of climate change on wheat production in Egypt. Because Egypt needs wheat for food security, these findings have important implications for policy development. Policymakers should develop approaches that enhance climate resilience, including adopting resilient agricultural techniques such as development and cultivation of heat- and drought-resistant wheat varieties, and investing in climate-smart technologies to minimize the risks of climate change on wheat production. This research contributes to the literature on the economic and ecological context of agricultural sustainability in Egypt. By seeking the justification for the requirement of adaptive agricultural policies and climate change adaptation measures, it aims to enhance food security as far as climate change is concerned.