Nonlinear Climate–Production Relationships in an Irrigation-Dominated System: A NARDL Analysis of Flood-Irrigated Rice

Abstract

Climate change imposes severe constraints on global food security, yet evidence on how crops respond to climate change in irrigation-dominated systems remains limited compared with rainfed agriculture. Building on this gap, we investigated how asymmetric climate shocks influence rice production in a major irrigated setting, using Egypt’s Nile Delta as a case study. Drawing on annual data for 1961–2022, we estimated a nonlinear autoregressive distributed lag (NARDL) model in which harvested area, fertilizer use, and seasonal temperature and precipitation jointly determine rice output, with structural-break tests used to inform model specification and the historical interpretation of major water and agricultural policy reforms. Temperature and precipitation are decomposed into cumulative positive and negative partial sums to isolate the effects of warming versus cooling and of rainfall surpluses versus deficits. The results showed a stable long-run cointegrating relationship with pronounced asymmetries. Autumn temperature shocks were most strongly associated with production variation, with cooling shocks more damaging than warming shocks were beneficial, while precipitation effects were asymmetric in the opposite direction: production gains associated with above average rainfall years exceeded the losses associated with below average rainfall years, consistent with irrigation buffering rainfall shortfalls. This finding does not rule out drainage-related losses from extreme, short-duration rainfall events, which the annual precipitation total used here cannot separately identify. Land expansion and fertilizer intensification remain positively associated with rice output, yet they only partially offset climate-induced losses, underscoring the limits of input-based adaptation amid increasing climatic volatility. Overall, the findings suggest that irrigation systems face distinct climate risks often obscured in symmetric models, highlighting adaptation priorities in drainage and storage, sustainable use of marginal lands, and season-specific climate services for irrigated rice regions.

1. Introduction

Climate change has become a critical source of production risk in agriculture, as shifting temperature and precipitation patterns increasingly drive yield variability and undermine the stability of farm incomes [1,2]. Rice (Oryza sativa), a cornerstone of global food security and a major source of dietary energy in many low- and middle-income countries, is especially vulnerable to thermal and hydrological stress during critical growth stages such as panicle initiation, flowering, and grain filling [3,4]. In irrigated systems, climate shocks affect not only plant physiology [4,5] but also the performance, operating costs [6], and reliability of irrigation infrastructure [7], with implications for both production outcomes and the economics of water management [8].

Egypt presents a distinctive setting for examining these relationships. Rice is grown mainly in the Nile Delta, one of the most productive rice-growing areas in the world on a per-hectare basis [9]. Production depends almost entirely on controlled diversion of Nile water rather than on local rainfall [10]. Although the irrigation-based system protects yields from rainfall variability, it increases vulnerability to temperature extremes and higher evapotranspiration, and limits irrigation operations and water allocation. Rice is also an important crop for rural employment, household food security, and, in some years, for export revenues. For this reason, climate-related changes in rice production have direct implications for agricultural policy and for the stability of the national economy.

A substantial empirical literature has documented how temperature and precipitation shape crop yields and aggregate agricultural output across regions and crop types. Evidence consistently indicates nonlinear yield responses to temperature: small deviations within an optimal range have limited effects, whereas exceedance of physiological thresholds results in sharp yield losses [11,12]. Similar nonlinearities arise for water availability, as both drought and excessive rainfall can depress yields through distinct agronomic mechanisms [13,14,15].

Within the rice climate literature, panicle initiation, flowering, and grain filling are highly sensitive to seasonal temperature profiles and to differences between daytime and nighttime warming. In parallel, agricultural economics and climate econometrics increasingly use time-series and panel approaches, such as autoregressive distributed lag (ARDL) models, to estimate long- and short-run elasticities of output with respect to climatic variables and inputs [16,17,18]. More recently, nonlinear ARDL (NARDL) and related asymmetric models have been developed to capture the differential effects of positive and negative shocks, and have increasingly been applied to examine asymmetric climate impacts on agricultural productivity across several countries [19,20,21,22].

In Egypt, prior studies assess crop vulnerability under climate scenarios, the buffering role of irrigation [23], and the broader policy environment [24,25]. Major changes, such as the Economic Reform and Structural Adjustment Program (ERSAP), which changed price incentives, decreased input subsidies, and liberalized cropping decisions, have also been studied in relation to crop production [26,27,28]. However, empirical studies that model climate variables linearly or symmetrically often overlook the possibility that increases and decreases in temperature or precipitation can have fundamentally different effects on output.

Despite recent progress, important gaps still exist. Many studies continue to rely on linear or symmetric models, which assume that increases and decreases in climate variables have equal effects. This assumption conflicts with agronomic evidence indicating that heat stress, cold spells, excess rainfall, and water shortages affect crops differently and at distinct thresholds. In irrigation-dominated systems, controlled water supply can help reduce the impact of low rainfall. In contrast, heavy rainfall can overwhelm drainage systems and interact poorly with irrigation practices, leading to lower yields. This indicates that crop responses to climate conditions are inherently asymmetric [12,29]. Studies on flood-irrigated rice rarely distinguish between seasonal temperature patterns, even though summer and autumn temperatures affect different growth stages and levels of vulnerability. Treating temperature as a single seasonal average can hide important ways in which climate variability influences grain filling, crop maturation, and final yields. Structural breaks are often not properly incorporated into climate–production models for Egypt, even though there have been major changes in water management, institutions, and climate policy since the early 1960s. Ignoring these breaks can lead to biased long-run estimates and a poor understanding of how shocks spread in a changing technological and policy environment.

A separate and complementary strand of the literature projects future climate-induced rice yield changes in Egypt’s Nile Delta using downscaled Global Climate Model (GCM) output under Coupled Model Intercomparison Project (CMIP6) Shared Socioeconomic Pathway (SSP) scenarios, typically coupled with process-based crop growth models such as AquaCrop [9]. These scenario-based studies project future outcomes under specified emissions and socioeconomic trajectories (e.g., SSP2-4.5, SSP5-8.5) but require, as an input, reliable historical estimates of how production has actually responded to past climate variability. The present study addresses this complementary need: rather than projecting future climate outcomes, we estimate, from 62 years of observed historical data, the asymmetric long- and short-run production elasticities with respect to realized temperature and precipitation shocks. These reduced-form historical elasticities provide an empirical benchmark against which scenario-based projections can be evaluated, and, as we discuss in Section 3.2 and in the Conclusion, could in principle be combined with downscaled CMIP6/SSP climate projections in future work to translate projected future temperature and precipitation trajectories into projected asymmetric production outcomes.

This study addressed these gaps by examining the asymmetric effects of climate change on flood-irrigated rice production (1961–2022) using a nonlinear autoregressive distributed lag (NARDL) framework. The empirical strategy decomposes autumn and summer temperatures and precipitation into cumulative positive and negative partial sums, isolating the effects of warming versus cooling and rainfall surpluses versus deficits.

The paper makes four main contributions. First, it examines both short- and long-run climate shocks in an irrigation-based system and shows that climate effects are asymmetric across seasons. Second, it includes formal structural break tests and links them to major historical changes, which improves the reliability of the results. Third, it models climate factors alongside land use and fertilizer use to produce clear, useful production estimates. Finally, it offers policy-relevant insights by showing how temperature and rainfall shocks affect output and by highlighting both the benefits and limits of irrigation for climate adaptation.

2. Methodology

2.1. Theoretical Framework

The theoretical foundation for examining the impact of climate change on rice production in an irrigation-dominated system draws on agricultural production theory and climate-economy modeling frameworks. Following the work of Mendelsohn et al. [30] and Schlenker et al. [3], agricultural production can be conceptualized as a function of climatic variables and technical inputs. The production function for rice production can be expressed as

$$RP=f\left(HAR,FERT,AUTTEMP,SUMTEMP,PREC\right)$$

(1)

wherein exogenous climatic factors, such as autumn average temperature (AUTTEMP), summer average temperature (SUMTEMP), and precipitation (PREC), as well as controllable technical factors, such as rice harvested area (HAR) and fertilizer (FERT), determine rice production (RP). This framework recognizes that both linear and nonlinear econometric techniques must be used because climate factors may have asymmetric and nonlinear effects on agricultural output.

2.2. Data Description and Sources

The current study uses Egypt’s annual time series data covering the period from 1961 to 2022. As shown in

Table 1. Description of variables, their abbreviation, unit, and data sources used in this study.

Variables	Abbreviation	Unit	Source
Rice production	RP	Metric Tons	[32]
Rice harvested area	HAR	Hectare	[32]
Fertilizer usage	FER	Kilogram/hectare	[32]
Mean summer temperature	SUMTEMP	°C	[31]
Mean autumn temperature	AUTTEMP	°C	[31]
Precipitation	PREC	Millimeters	[31]

, the data were obtained from two main sources: the World Bank’s Climate Change Knowledge Portal [31] and the Food and Agriculture Organization (FAO) of the United Nations database [32]. To reduce heteroscedasticity and make elasticities easier to interpret, all variables except summer and autumn temperatures were transformed to their natural logarithms [33,34].

Therefore, the rice production function can be expressed as follows:

$$\ln \left(R{P}_t\right)={\beta }_0+{\beta }_1\ln \left(HA{R}_t\right)+{\beta }_2\ln \left(FE{R}_t\right)+{\beta }_{3}AUTTEM{P}_t+{\beta }_{4}SUMTEM{P}_t+{\beta }_5\ln \left(PRE{C}_t\right)+{\epsilon }_t$$

(2)

The link between temperature and economic outcomes is best modeled using linear or polynomial functions. This is because temperature lacks a true zero point that would allow for proportional interpretation, and its scale dependency makes it difficult to compare coefficients consistently across contexts [35].

The choice of variables is grounded in agricultural production theory and climate–agriculture nexus literature. Rice production is fundamentally determined by the harvested area and input utilization, such as fertilizer usage, while climate variables, including temperature and precipitation, directly affect crop growth, development, and yield [36,37,38]. Rice production (RP) refers to total national output rather than yield per hectare; results should accordingly be interpreted as effects on aggregate production scale, which combines area and yield responses, rather than as direct estimates of climate-induced physiological yield change. The distinction between autumn and summer temperatures is crucial as rice cultivation in Egypt follows specific seasonal patterns, with different growth stages being sensitive to temperature variations [9,39].

We clarify the rationale underlying the variable set entered in Equation (2). Harvested area (HAR) and fertilizer use (FER) are the two principal controllable production inputs and enter the specification as the standard input terms of an agricultural production function, following Mendelsohn et al. [30] and Schlenker et al. [3]; both are consistently available over the full study period and represent the primary extensive- and intensive-margin adjustments available to Egyptian rice producers. Rice production (RP) is total national paddy output in metric tons, the dependent variable; harvested area (HAR) is the total national area sown to rice, in hectares; fertilizer usage (FER) is national fertilizer application intensity, in kilograms per hectare; autumn temperature (AUTTEMP) and summer temperature (SUMTEMP) are national mean seasonal air temperatures, in degrees Celsius; and precipitation (PREC) is national total precipitation, in millimeters, all as defined in Table 1. For each of AUTTEMP, SUMTEMP, and PREC, the NARDL decomposition in Equations (9) and (10) further separates cumulative positive deviations (warming, or precipitation surpluses) from cumulative negative deviations (cooling, or precipitation deficits), so that the long- and short-run coefficients reported in the Section 3 refer specifically to these positive and negative partial sum components rather than to the raw seasonal levels. We selected two seasonal temperature variables and one precipitation variable, rather than daily or monthly climate series, for two related reasons. First, Egypt’s rice crop follows a well–defined calendar, transplanted around May–June and harvested around October–November; summer temperature (June–August) spans the vegetative and reproductive growth stages, while autumn temperature (September–November) spans grain filling, maturation, and harvest. These two seasonal means correspond to the two agronomically distinct phases of the crop cycle in which temperature stress operates through different physiological channels, whereas winter and spring fall outside the growing season and have no direct physiological bearing on the current year’s rice output; using two seasonal variables rather than twelve monthly or 365 daily observations therefore reflects the rice crop calendar rather than an arbitrary restriction. Precipitation enters as a single annual total because, as discussed in the Introduction, Egyptian rice is grown under near-complete flood irrigation from the Nile rather than under rainfed conditions; the annual total is retained as a broad proxy for supplementary rainfall and regional hydrological conditions rather than as a precise measure of crop water delivery, so finer sub-annual disaggregation would not meaningfully change its interpretation. Second, our national-level annual data (1961–2022) restrict us to climate indicators available at annual resolution from the World Bank Climate Change Knowledge Portal [31] over the full historical period; as discussed in Section 3.2, daily or sub-daily station-level series are not available at this historical depth for Egypt, which is why we rely on seasonal and annual aggregates and explicitly flag this as a limitation to be addressed with higher-resolution crop-growth-model data in future work. We also clarify our approach to variable selection in response to the question of whether variables should be chosen prior to, rather than during, estimation. Our specification follows a theory-driven approach, in which the variable set in Equations (1) and (2) is derived directly from agricultural production theory [3,30] and the climate–agriculture literature reviewed in the Introduction [3,4,9,11,12,36,37,38,39], rather than a purely data-driven procedure that tests the significance of a large pool of candidate climate indicators and retains only those found significant. We adopted this approach for three reasons. First, with 62 annual observations, introducing a larger set of correlated monthly or daily climate indicators, each further decomposed into positive and negative partial sums, would sharply reduce degrees of freedom and increase the risk of overfitting and unstable lag-order selection in the NARDL framework, which already estimates a rich set of asymmetric long- and short-run coefficients for five variables. Second, atheoretical selection of climate variables by pre-testing significance risks specification searching, a well-documented source of spurious findings in time-series climate-econometric studies; the bounds testing and NARDL methodology we use (Section 2.5 and Section 2.6) requires the cointegrating variable set to be specified on theoretical grounds ex ante so that the F-test for cointegration and the resulting long-run estimates remain valid and interpretable. Third, the indicators we retain are the ones most consistently used in the rice-climate literature cited above and are the only climate series available in comparable form across our full study period. We agree that this remains a simplification, and Section 3.2 discusses how future work using higher-resolution, process-based crop growth models could relax it.

2.3. Unit Root Testing

To avoid spurious regression results arising from non-stationary time series, unit root tests are conducted to determine the stationarity of all variables. This study employs two corresponding unit root tests: the Augmented Dickey–Fuller (ADF) test [40] and the Phillips–Perron (PP) test [41].

The ADF test is based on the following regression equation:

$$\mathsf{\Delta }{Y}_t=\alpha +\beta Y_{t-1}+{\displaystyle \sum _{i=1}^k} {\gamma }_i\mathsf{\Delta }{Y}_{t-i}+{\epsilon }_t$$

(3)

where $\mathsf{\Delta }$ denotes the first difference operator, $Y_t$ represents the variable under investigation, $k$ is the optimal lag length selected using information criteria, and ${\epsilon }_t$ is the error term. The null hypothesis H₀: β = 0 (unit root exists) is tested against the alternative H₁: β < 0 (series is stationary). The PP test modifies the ADF test by using non-parametric corrections for serial correlation and heteroskedasticity in the error terms [41].

2.4. Lag-Order Selection

Optimal lag selection is crucial for the ARDL [42,43] and NARDL model specification [22]. This study employs multiple information criteria, including the Akaike Information Criterion (AIC), Bayesian Information Criterion (BIC), and Hannan–Quinn Information Criterion (HQC). As defined in [44], the AIC is

$$AIC=2k-2\ln \left(L\right)$$

(4)

where k is the number of parameters, and L is the maximized likelihood function. According to [45], the BIC is

$$BIC=\mathrm{kln}\left(n\right)-2\ln \left(L\right)$$

(5)

where n is the sample size. The HQC is calculated as follows [46]:

$$HQC=2k\ln \left(\ln \left(n\right)\right)-2\ln \left(L\right)$$

(6)

The optimal lag length is determined by minimizing these criteria, with parsimony preferred to avoid overparameterization [47].

2.5. ARDL Bounds Testing Approach

The autoregressive distributed lag (ARDL) bounds testing procedure developed by [43] is employed to examine the long-run cointegrating relationships among variables. The ARDL approach has several advantages: it can be applied regardless of whether the underlying variables are I(0), I(1), or mutually cointegrated; it provides unbiased estimates for small samples; and it allows for the simultaneous estimation of short-run and long-run parameters.

The ARDL representation for rice production is specified as:

$$\begin{gathered} \ln R{P}_t={\alpha }_0+{\displaystyle \sum _{i=1}^p} {\alpha }_i\ln R{P}_{t-i}+{\displaystyle \sum _{j=0}^{q_1}} {\beta }_j\ln HA{R}_{t-j}+{\displaystyle \sum _{k=0}^{q_2}} {\gamma }_k\ln FE{R}_{t-k}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em} \\ +{\displaystyle \sum _{l=0}^{q_3}} {\delta }_{l}AUTTEM{P}_{t-l}+{\displaystyle \sum _{m=0}^{q_4}} {\theta }_{m}SUMTEM{P}_{t-m}+{\displaystyle \sum _{n=0}^{q_5}} {\varphi }_n\ln PRE{C}_{t-n} \\ +{\epsilon }_t\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em} \end{gathered}$$

(7)

where p, q₁, q₂, q₃, q₄, and q₅ represent the optimal lag lengths for each variable.

The corresponding Error-Correction Model (ECM) representation is:

$$\begin{gathered} \hspace{1em}\hspace{1em}\mathsf{\Delta }\ln R{P}_t={\alpha }_0+{\displaystyle \sum _{i=1}^{p-1}} {\alpha }_i\mathsf{\Delta }\ln R{P}_{t-i}+{\displaystyle \sum _{j=0}^{q_1-1}} {\beta }_j\mathsf{\Delta }\ln HA{R}_{t-j}+{\displaystyle \sum _{k=0}^{q_2-1}} {\gamma }_k\mathsf{\Delta }\ln FE{R}_{t-k} \\ +{\displaystyle \sum _{l=0}^{q_3-1}} {\delta }_l\mathsf{\Delta }AUTTEM{P}_{t-l}+{\displaystyle \sum _{m=0}^{q_4-1}} {\theta }_m\mathsf{\Delta }SUMTEM{P}_{t-m}+{\displaystyle \sum _{n=0}^{q_5-1}} {\varphi }_n\mathsf{\Delta }\ln PRE{C}_{t-n} \\ +\lambda EC{T}_{t-1}+u_t\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em} \end{gathered}$$

(8)

where $\lambda$ is the speed of adjustment coefficient and $EC{T}_{t-1}$ is the error-correction term representing deviations from the long-run equilibrium.

The bounds testing procedure involves calculating an F-statistic to test the joint significance of lagged level variables. The null hypothesis of no cointegration H₀: λ = α₁ = α₂ = … = α₆ = 0 is tested against the alternative of cointegration H₁: λ ≠ α₁ ≠ α₂ ≠ … ≠ α₆ ≠ 0. The calculated F-statistic is compared with the critical values provided by [43].

2.6. NARDL Methodology

The nonlinear autoregressive distributed lag (NARDL) approach, developed by Shin and Yu [22], extends the ARDL framework to capture asymmetric effects [21]. This methodology is particularly relevant for climate–agriculture studies as agricultural systems may respond differently to positive and negative climate shocks [22,38].

The NARDL approach involves decomposing explanatory variables into cumulative positive and negative partial sum processes. For any explanatory variable Xt, the asymmetric components are defined as

$$X_t^{+}={\displaystyle \sum _{j=1}^t} \mathsf{\Delta }{X}_j^{+}={\displaystyle \sum _{j=1}^t} \max \left(\mathsf{\Delta }{X}_j,0\right)$$

(9)

$$X_t^{-}={\displaystyle \sum _{j=1}^t} \mathsf{\Delta }{X}_j^{-}={\displaystyle \sum _{j=1}^t} \min \left(\mathsf{\Delta }{X}_j,0\right)$$

(10)

where $X_t^{+}$ and $X_t^{-}$ capture the partial sum processes of positive and negative changes in X_t, respectively.

The NARDL specification for rice production becomes

$$\begin{gathered} \ln R{P}_t={\alpha }_0+{\displaystyle \sum _{i=1}^p} {\alpha }_i\ln R{P}_{t-i}+{\displaystyle \sum _{j=0}^{q_1}} \left({\beta }_j^{+}\ln HA{R}_{t-j}^{+}+{\beta }_j^{-}\ln HA{R}_{t-j}^{-}\right)\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em} \\ +{\displaystyle \sum _{k=0}^{q_2}} \left({\gamma }_k^{+}\ln FE{R}_{t-k}^{+}+{\gamma }_k^{-}\ln FE{R}_{t-k}^{-}\right)+{\displaystyle \sum _{l=0}^{q_3}} \left({\delta }_l^{+}AUTEM{P}_{t-l}^{+}+{\delta }_l^{-}AUTTEM{P}_{t-l}^{-}\right)\hspace{1em}\hspace{1em}\hspace{1em} \\ +{\displaystyle \sum _{m=0}^{q_4}} \left({\theta }_m^{+}SUMTEM{P}_{t-m}^{+}+{\theta }_m^{-}SUMTEM{P}_{t-m}^{-}\right)+{\displaystyle \sum _{n=0}^{q_5}} \left({\varphi }_n^{+}\ln PRE{C}_{t-n}^{+}+{\varphi }_n^{-}\ln PRE{C}_{t-n}^{-}\right) \\ +{\epsilon }_t\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em} \end{gathered}$$

(11)

The corresponding asymmetric Error-Correction Model is

$$\begin{gathered} \mathsf{\Delta }\ln R{P}_t={\alpha }_0+{\displaystyle \sum _{i=1}^{p-1}} {\alpha }_i\mathsf{\Delta }\ln R{P}_{t-i}+{\displaystyle \sum _{j=0}^{q_1-1}} \left({\beta }_j^{+}\mathsf{\Delta }\ln HA{R}_{t-j}^{+}+{\beta }_j^{-}\mathsf{\Delta }\ln HA{R}_{t-j}^{-}\right)\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em} \\ +{\displaystyle \sum _{k=0}^{q_2-1}} \left({\gamma }_k^{+}\mathsf{\Delta }\ln FE{R}_{t-k}^{+}+{\gamma }_k^{-}\mathsf{\Delta }\ln FE{R}_{t-k}^{-}\right)+{\displaystyle \sum _{l=0}^{q_3-1}} \left({\delta }_l^{+}\mathsf{\Delta }AUTTEM{P}_{t-l}^{+}+{\delta }_l^{-}\mathsf{\Delta }AUTTEM{P}_{t-l}^{-}\right) \\ +{\displaystyle \sum _{m=0}^{q_4-1}} \left({\theta }_m^{+}\mathsf{\Delta }SUMTEM{P}_{t-m}^{+}+{\theta }_m^{-}\mathsf{\Delta }SUMTEM{P}_{t-m}^{-}\right)\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em} \\ +{\displaystyle \sum _{n=0}^{q_5-1}} \left({\varphi }_n^{+}\mathsf{\Delta }\ln PRE{C}_{t-n}^{+}+{\varphi }_n^{-}\mathsf{\Delta }\ln PRE{C}_{t-n}^{-}\right)+{\lambda }^{+}EC{T}_{t-1}^{+}+{\lambda }^{-}EC{T}_{t-1}^{-}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em} \\ +u_t\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em} \end{gathered}$$

(12)

where ${\lambda }^{+}$ and ${\lambda }^{-}$ represent asymmetric adjustment coefficients toward long-run equilibrium.

The sign convention embedded in Equations (9) and (10) requires explicit statement, because it governs the interpretation of every coefficient reported below. The positive partial sum X_t⁺ accumulates only non-negative increments and is therefore weakly increasing in t, while the negative partial sum X_t⁻ accumulates only non-positive increments and is weakly decreasing in t. It follows that the increments of the two processes satisfy ΔX_t⁺ = max(ΔX_t, 0) ≥ 0 and ΔX_t⁻ = min(ΔX_t, 0) ≤ 0, and that the contemporaneous response of log production decomposes as in Equation (12a). Consequently, for a climate innovation of magnitude s > 0, the implied change in log rice production is β⁺s when the innovation is positive and −β⁻s when it is negative, as set out in Equation (12b). A positive estimate of β⁻ therefore indicates that a further negative shock—additional cooling, or a further precipitation shortfall—reduces production; it does not indicate that cooling or a rainfall deficit raises production. Symmetry of the response to shocks of either direction corresponds to the restriction β⁺ = β⁻, since X_t = X_t⁺ + X_t⁻ up to an initial condition, which is the null tested by the Wald statistics in Equations (13)–(15). Throughout the Results and Discussion, the coefficients on the negative partial sum components are interpreted on this basis, and the magnitudes of the warming and cooling responses, and of the surplus and deficit responses, are compared as β⁺ against |−β⁻|.

$$\mathsf{\Delta }\ln R{P}_t={\beta }^{+}\hspace{0.17em}\mathsf{\Delta }{X}_t^{+}+{\beta }^{-}\hspace{0.17em}\mathsf{\Delta }{X}_t^{-},\hspace{0.33em}\hspace{0.33em}\mathsf{\Delta }{X}_t^{+}\ge 0,\hspace{0.33em}\hspace{0.33em}\mathsf{\Delta }{X}_t^{-}\le 0$$

(12a)

$$\mathsf{\Delta }\ln R{P}_t={\beta }^{+}s\hspace{0.33em}\hspace{0.33em}\mathrm{if}\hspace{0.33em}\hspace{0.33em}\mathsf{\Delta }{X}_t=+s; \mathsf{\Delta }\ln R{P}_t=-{\beta }^{-}s\hspace{0.33em}\hspace{0.33em}\mathrm{if}\hspace{0.33em}\hspace{0.33em}\mathsf{\Delta }{X}_t=-s$$

(12b)

2.6.1. Cointegration Testing in NARDL Framework

The NARDL bounds testing procedure follows a similar approach to the linear ARDL but accounts for asymmetric cointegration relationships [48,49,50,51]. The F-statistic for asymmetric cointegration is calculated by testing the joint significance of lagged levels of positive and negative components:

H₀. 

λ⁺ = λ⁻ = β₁⁺ = β₁⁻ = … = φ₁⁺ = φ₁⁻ = 0 (no asymmetric cointegration)

H₁. 

λ⁺ ≠ λ⁻ ≠ β₁⁺ ≠ β₁⁻ ≠ … ≠ φ₁⁺ ≠ φ₁⁻ ≠ 0 (asymmetric cointegration exists).

The break dates identified by the Zivot–Andrews test (Section 3.1) are used above to inform unit root testing and the historical interpretation of the estimated relationships. To move from break-informed testing toward a NARDL specification that explicitly controls for structural breaks, Equation (11) can be augmented with step dummies for the identified break dates, e.g., D₁₉₇₄ (Aswan High Dam-related break), D_1990–92 (ERSAP liberalization), and D_1994–96 (climate-institutional/UNFCCC-related break), coded 1 from the break year onward and 0 otherwise, entered additively and, sample size permitting, interacted with the climate components: ln RP_t = α₀ + Σα_i ln(RP_t−i⁺ … + Σ(δ_l⁺ AUTTEMP⁺_t−l + δ_l⁻ AUTTEMP⁻_t−l + … + κ₁D_1974,t + κ₂D_1990–92,t + κ₃D_1994–96,t + ε_t (11′). We recommend estimating (11′) and comparing the resulting climate coefficients against those in Section 3.2 as the appropriate test of whether the estimated results have effectively controlled for institutional change. Given the data availability and the sample size constraints, dummy and interaction terms should be added parsimoniously to avoid further overparameterization.

2.6.2. Asymmetry Tests

Several tests are conducted to validate asymmetric relationships [22,49,52] such as Long-run Asymmetry Test that examines whether positive and negative shocks have significantly different long-run impacts using Wald test statistics:

$$W_{LR}={\displaystyle \frac{({\beta }^{+}-{\beta }^{-}{)}^2}{Var\left({\beta }^{+}-{\beta }^{-}\right)}}$$

(13)

and Short-run Asymmetry Test: This tests for asymmetric short-run adjustments:

$$W_{SR}={\displaystyle \frac{(\sum {\alpha }_i^{+}-\sum {\alpha }_i^{-}{)}^2}{Var\left(\sum {\alpha }_i^{+}-\sum {\alpha }_i^{-}\right)}}$$

(14)

2.6.3. Adjustment Asymmetry Test

This examines whether positive and negative deviations from equilibrium adjust at different rates:

$$W_{ADJ}={\displaystyle \frac{({\lambda }^{+}-{\lambda }^{-}{)}^2}{Var\left({\lambda }^{+}-{\lambda }^{-}\right)}}$$

(15)

2.6.4. Dynamic Multipliers

The NARDL approach allows the calculation of dynamic multipliers to trace the adjustment path of rice production following positive and negative shocks to explanatory variables. The positive and negative dynamic multipliers for variable X at horizon h are

$$m_h^{+}={\displaystyle \sum _{j=0}^h} {\displaystyle \frac{\partial \ln R{P}_{t+j}}{\partial X_t^{+}}}$$

(16)

$$m_h^{-}={\displaystyle \sum _{j=0}^h} {\displaystyle \frac{\partial \ln R{P}_{t+j}}{\partial X_t^{-}}}$$

(17)

2.6.5. Diagnostic Tests

Several diagnostic tests are performed to validate model adequacy [22,48,53]. The Breusch–Godfrey Lagrange Multiplier test is employed to detect serial correlation in residuals [54]. The Breusch–Pagan test tests for heteroskedasticity [55]. The Jarque–Bera test is used to assess the normality of residuals [56], while the CUSUM [57] and CUSUM of squares tests [58] are employed to examine parameter stability over time.

2.6.6. Model Selection Criteria

The optimal NARDL specification is selected based on multiple criteria including AIC, BIC, HQC, and adjusted R-squared. Additionally, the Ramsey RESET test [59] is conducted to check for functional form misspecification [60].

By taking into consideration the intricate, nonlinear relationships between agricultural output and climatic variables and upholding statistical rigor through extensive diagnostic testing, this comprehensive methodology framework guarantees robust estimation of both symmetric and asymmetric effects of climate change on rice production in Egypt.

3. Results

3.1. Unit Root Testing Using P-P and ADF

The results of the Phillips–Perron (PP) and Augmented Dickey–Fuller (ADF) unit root tests are presented in

Table 2. Results of the unit root testing using Phillips–Perron (PP) and Augmented Dickey–Fuller (ADF).

Variables	PP	ADF	PP	ADF	Integration Order
	At Level		1st Difference
Ln rice production	−3.16	−2.64	−9.60 **	−7.85 **	I(1)
Ln harvested area	−4.84 **	−2.29	−10.80 **	−8.58 **	I(0)
Ln fertilizers	−1.35	−1.41	−8.58 **	−8.59 **	I(1)
Autumn temperature	−8.46 **	−8.49 **	−28.00 **	−6.59 **	I(0)
Summer temperature	−6.90 **	−3.79 *	−24.06 **	−4.58 **	I(0)
Ln precipitation	−7.67 **	−2.93	−18.03 **	−11.33 **	I(0)

* and ** represent 5% and 1% level of significance, respectively.

. The analysis showed that rice production and fertilizers were non-stationary at the level but became stationary after first difference, indicating that they follow an integrated process of order one, I(1). The PP test results, together with ADF test results, demonstrate that autumn temperature, summer temperature, and Ln of harvested area and precipitation maintain stationarity at their original levels, which indicates that they follow an integrated process of order zero, I(0).

The analysis requires ARDL or NARDL modeling approaches because it deals with variables that have different integration levels of I(0) and I(1) [22]. The results on integration order will help the econometric model avoid spurious regression while revealing the true relationships between climate and agricultural variables.

With respect to the structural breaks,

Table 3. Results of the structural break unit root test.

Variables	At Level			1st Difference
	T-Statistics	Break Point	Result	T-Statistics	Break Point	Result
Ln rice production	−5.131 **	1992	Stationary	−9.429 **	1967	Stationary
Ln rice harvested area	−3.664	1990	Unit root	−8.433 **	1995	Stationary
Ln fertilizers	−3.527	1974	Unit root	−9.282 **	1992	Stationary
Autumn temperature	−8.458 **	1996	Stationary	−12.541 **	1966	Stationary
Summer temperature	−2.129	1994	Unit root	−8.991 **	1966	Stationary
Ln precipitation	−8.584 **	1994	Stationary	−12.349 **	2017	Stationary

** represents the 1% level of significance.

displays the results from Zivot–Andrews test [61] which show three variables with stationary level I(0) (logarithm of rice production, autumn temperature, and logarithm of precipitation and three variables with first difference stationarity I(1) logarithm of harvested area, logarithm of fertilizers, and summer temperature) which suits NARDL estimation methodology. The structural breaks that emerged from the analysis match with historical agricultural events in Egypt: the 1974 break represents changes after the Aswan High Dam construction and the 1990–1992 breaks match Egypt’s Economic Reform and Structural Adjustment Program (ERSAP) which introduced crop production liberalization and eliminated input subsidies and the 1994–1996 breaks show both climate changes and Egypt’s UNFCCC ratification. The mixed I(0) and I(1) integration pattern satisfies all NARDL prerequisites, while the Zivot–Andrews procedure prevents bias from conventional unit root tests that ignore structural changes [61,62]. The different stationarity characteristics, which include stable level effects from I(0) climate variables and cumulative effects from I(1) variables, support the theoretical basis to study asymmetric long-run relationships between pre- and post-reform periods.

The NARDL framework represents a significant advancement over linear autoregressive distributed lag approaches in capturing asymmetric relationships between climate variables and agricultural output [63]. The approach helps identify how agricultural production responds to different climate shock patterns by separating temperature and precipitation into positive and negative partial sum components, thereby demonstrating the essential distinction between drought and wet-year effects in irrigation-based farming systems [64]. The method follows current research, which shows that climate effects on crop yields do not follow a balanced pattern but instead exhibit asymmetry [65].

3.2. The NARDL Estimations

The NARDL bounds test results presented in

Table 4. Bound test outcomes: nonlinear analysis.

Significance	I(0) Lower Bound	I(1) Upper Bound
10%	1.850	2.850
5%	2.110	3.150
1%	2.620	3.770
F-Statistic = 5.656

provide strong evidence of cointegration among the variables. Specifically, the computed F-statistic of 5.656 surpasses the upper I(1) critical bound at the 1% significance level (3.770), leading to a rejection of the null hypothesis of no long-run relationship. This outcome justifies estimation of the error-correction form of the NARDL model, thereby establishing the validity of both short-run asymmetries and the underlying long-run equilibrium dynamics.

The results of NARDL estimates presented in

Table 5. NARDL estimates for rice production (dependent variable: Δln(RP)).

Variable	Coefficient	Std. Error	t-Statistic	Significance
Long-run coefficients
Ln rice harvested area	1.237	0.382	3.240	***
Ln fertilizer usage	0.179	0.048	3.703	***
AUTTEMP+	0.096	0.040	2.386	**
AUTTEMP−	0.121	0.044	2.771	**
SUMTEMP+	−0.002	0.029	−0.078	—
SUMTEMP−	0.023	0.038	0.609	—
Ln precipitation+	0.248	0.066	3.749	***
Ln precipitation−	0.151	0.062	2.444	**
Constant	−5.523	1.830	−3.018	***
Short-run dynamic coefficients
Speed of adjustment	−0.783	0.255	−3.065	***
ΔRice production (-1)	0.665	0.239	2.777	**
ΔRice production (-2)	0.314	0.181	1.731	*
ΔRice production (-3)	0.349	0.106	3.278	***
ΔLn rice harvested area	1.027	0.052	19.731	***
ΔLn rice harvested area (-1)	−1.077	0.326	−3.301	***
ΔLn rice harvested area (-2)	−0.834	0.244	−3.418	***
ΔLn rice harvested area (-3)	−0.682	0.130	−5.227	***
ΔLn fertilizer usage	−0.170	0.070	−2.420	**
ΔLn fertilizer usage (-1)	−0.306	0.095	−3.231	***
ΔLn fertilizer usage (-2)	−0.188	0.084	−2.231	**
ΔAUTTEMP+	−0.011	0.013	−0.847	—
ΔAUTTEMP−	0.011	0.017	0.628	—
ΔAUTTEMP (-1)+	−0.050	0.033	−1.541	—
ΔAUTTEMP (-1)−	−0.073	0.032	−2.267	**
ΔAUTTEMP (-2)+	−0.039	0.019	−2.075	*
ΔAUTTEMP (-2)−	−0.091	0.027	−3.411	***
ΔAUTTEMP (-3)+	0.056	0.015	3.704	***
ΔAUTTEMP (-3)−	−0.086	0.018	−4.893	***
ΔSUMTEMP+	0.007	0.023	0.299	—
ΔSUMTEMP−	0.063	0.026	2.366	**
ΔSUMTEMP (-1)+	0.021	0.025	0.827	—
ΔSUMTEMP (-1)−	−0.116	0.029	−4.041	***
ΔSUMTEMP (-2)+	−0.076	0.024	−3.197	***
ΔSUMTEMP (-2)−	0.039	0.026	1.481	—
ΔLn precipitation+	0.071	0.038	1.845	*
ΔLn precipitation−	−0.091	0.037	−2.480	**
ΔLn precipitation (-1)+	−0.221	0.054	−4.118	***
ΔLn precipitation (-1)−	−0.115	0.051	−2.243	**
ΔLn precipitation (-2)+	−0.086	0.042	−2.039	*
ΔLn precipitation (-2)−	−0.036	0.039	−0.914	—
ΔLn precipitation (-3)+	−0.062	0.033	−1.879	*
ΔLn precipitation (-3)−	−0.130	0.036	−3.648	***
MODEL FIT STATISTICS
R-squared	0.993
Adjusted R-squared	0.973
S.E. of regression	0.023
Sum squared residuals	0.008
Log likelihood	171.314
F-statistic	50.399
Prob (F-statistic)	0.000
Durbin–Watson statistic	2.499
VIF	3.42
Breusch–Godfrey LM	F = 1.142	p = 0.334
Breusch–Pagan–Godfrey	F = 0.915	p = 0.582
Ramsey RESET	F = 1.624	p = 0.213

*, **, and *** represent 10%, 5%, and 1% levels of significance, respectively.

show that rice harvested area exhibits the largest estimated long-run association with aggregate rice production, with a coefficient of 1.237. This result indicates that expansion in harvested area is strongly linked to increases in total national rice output. However, because total production is jointly determined by harvested area and yield, the coefficient should not be interpreted as evidence that area expansion alone produces a more than proportional physiological improvement in rice productivity. The estimate may also reflect correlated changes in technology, input intensity, irrigation access, crop management, and production incentives. The result therefore demonstrates the importance of the area or scale margin for national rice supply rather than a direct effect on yield formation. Agricultural expansion through land expansion leads to better irrigation systems, more efficient farming equipment, and improved crop varieties, which together yield greater total crop yields from additional farmland [66,67].

Because total rice production is definitionally the product of harvested area and yield, an elasticity above unity indicates that changes in production reflect both area expansion and accompanying yield or intensity gains, and should not be read as a pure area effect. This also means that part of the climate elasticities reported below capture climate’s influence on the area production margin—for instance, through cropping decisions—in addition to any direct effect on yield formation. We treat total production, rather than yield per hectare, as this study’s dependent variable, and we interpret the climate coefficients as effects on aggregate production outcomes rather than as isolated physiological yield responses. Disentangling the area and yield channels through a companion yield-based (production per hectare) NARDL specification is a natural and, in our view, high-value extension of the present framework.

Fertilizer intensity showed a long-term elasticity value of 0.179. The coefficient proves that input intensification continues to drive production growth even though its effect size is smaller than the area effects. Such results show similar elasticity values to those found in [68], which reported fertilizer elasticities between 0.16 and 0.34 for rice cultivation across different areas. Moreover, the results indicate that fertilizer application is associated with positive long-term production outcomes, despite short-term negative impacts. These short-term effects likely arise from nutrient accumulation during repeated fertilizer use, which initially disrupts soil nutrient balance [69]. Over time, however, fertilizer application improves overall soil fertility and increases crop yields.

Autumn temperature shocks display an economically meaningful asymmetry. A further positive deviation in autumn temperature is associated with higher production (β⁺ = 0.096, p < 0.05), consistent with a longer effective grain-filling period and reduced exposure to early season cold. A further negative deviation, that is additional cooling, is associated with a decline in production of larger magnitude, since the estimated coefficient on the negative partial sum (β⁻ = 0.121, p < 0.05) implies a production response of −0.121 log points per unit of cooling. Cooling shocks therefore depress rice production by more than equivalent warming shocks raise it (0.121 against 0.096). This ordering is consistent with the cumulative dynamic multipliers reported below, whose long-run limits are approximately 0.13 for the positive partial sum and 0.155 for the negative partial sum, the latter implying a production loss of comparable magnitude under the convention set out in Section 2.6.

The temperature effects during the autumn season show similar patterns to precipitation effects, yet their strength remains weaker, which indicates that water supply serves as the main climatic restriction for Egypt’s Nile Valley irrigation system, even though temperature changes become more important.

Summer temperature changes do not have a significant long-run effect on rice production, and the symmetry tests in Table 5 confirm that positive and negative summer temperature shocks behave similarly across horizons. Several explanations are possible: irrigation-based water management may buffer summer heat stress; observed summer temperatures may lie within the physiological tolerance range of currently cultivated varieties; or adaptation through variety choice and management practices may be occurring [70,71,72]. We present these as plausible, non-exclusive hypotheses rather than as demonstrated evidence of successful farmer adaptation, since the aggregate annual data used here cannot distinguish among them; farm-level microeconomic data would be needed to identify the specific channel.

The relationship between precipitation and rice production is also asymmetric, but in the opposite direction. A cumulative precipitation surplus is associated with higher production (β⁺ = 0.248, SE = 0.066, t = 3.749, p < 0.001): a 1% cumulative surplus is associated with production approximately 0.25% higher in the long run. The coefficient on the negative partial sum (β⁻ = 0.151, SE = 0.062, t = 2.444, p < 0.05) implies that an additional 1% cumulative shortfall is associated with a decline in long-run production of approximately 0.15%. Because the deficit response is smaller in magnitude than the surplus response (0.151 against 0.248), production is more responsive to precipitation surpluses than to equivalent deficits. In an irrigation-dominated system, storage and groundwater access allow rainfall shortfalls to be substituted for, whereas incremental rainfall within the observed historical range adds to available soil moisture.

In these systems, irrigation compensates for a lack of rain while mitigating excess rainfall by adding moisture to the soil and using both surface and groundwater resources simultaneously [73].

The asymmetrical behavior of rainfed agricultural systems differs from that of dominant irrigation systems, as plants are more sensitive to rainfall shortages than to equivalent rainfall surpluses due to their water-stress threshold [74]. Approximately 94% of Egypt’s irrigation system depends on Nile River water, groundwater, and modern surface irrigation systems, indicating that reduced precipitation events may have a lower impact due to water storage management and flexible irrigation scheduling practices [75]. Furthermore, the differential sensitivity to precipitation shocks has policy implications for climate risk management. Standard climate scenarios predict precipitation shifts symmetrically around historical averages, but this approach leads to an insufficient estimate of climate adaptation costs when production response asymmetries remain unconsidered. The finding that rice production gains from precipitation surplus (0.248) exceed losses from equivalent deficits (0.151) suggests that absolute precipitation volatility, rather than directional change, represents the primary climate risk for producers facing infrastructure constraints on adaptive irrigation responses [76,77].

The error-correction coefficient of −0.783 indicates that approximately 78.3 percent of any deviation from the long-run equilibrium is eliminated annually. Consequently, the system returns to equilibrium in about 1.3 years. Its half-life is approximately 8 months, indicating that rice production responds relatively quickly to changes in factor endowments and climate conditions. The adjustment speed is plausible because rice farmers operate on annual cycles and can reallocate their inputs across uses by renting land and choosing fertilizer timing and seed types for their next planting season.

This rapid error-correction speed contrasts with slower adjustment observed in some agricultural systems, particularly where infrastructure constraints limit production flexibility [78,79]. The quick response shown here indicates that Egypt has a well-established irrigation system, organized fertilizer supply networks, enhanced crop varieties, and most importantly, experienced farmers who understand how to handle production during changing weather conditions and water availability [80,81,82]. As with the other explanations offered in this section, this interpretation is a plausible reading grounded in the general literature on Egyptian irrigation and extension systems rather than a mechanism directly identified by the present aggregate time-series model; farm-level behavioral data would be needed to confirm it. The ECM coefficient confirms that the model variables maintain a long-term relationship, which supports the use of the NARDL specification rather than differenced-form models that eliminate long-run information [83].

Short-Run Dynamic Adjustment Patterns

Lagged production changes reveal significant persistence across three-year horizons: ΔRice production (-1, -2, -3) = 0.665, 0.314, and 0.349, respectively (Table 5). The cumulative coefficient of these three lags (1.328) exceeds unity, indicating amplified production persistence beyond immediate year-to-year shocks. Several processes are consistent with this pattern, none tested here, because irrigation systems require maintenance to handle normal wear and tear from infrastructure use, because irrigated rice pathogens persist in waterlogged fields between growing seasons, and because farmers base their crop choices and input management decisions on weather patterns they observe over multiple years [38,84,85].

The substantial multi-year lagged structure signifies that annual policy interventions or climatic anomalies produce effects on production that persist significantly beyond the initial implementation period. This finding has consequences for the timing of climate adaptation policies and the understanding of yield variability in climate impact assessments: observed yield volatility indicates not only the weather of the current year but also the cumulative effects of climatic and management shocks from prior years. The persistence pattern indicates that farmers utilize multi-year climate data in their decision-making, with production choices in year t reflecting outcomes and expectations established in years t-1, t-2, and t-3.

The concurrent short-run elasticity of rice harvested area (ΔLn rice harvested area = 1.027) is substantively large, although notably lower than the long-run elasticity (1.237) (Table 5). This suggests that while area expansion triggers an immediate increase in production, full adjustment toward the long-run equilibrium takes additional time. The initial short-run elasticity reflects an immediate, high responsiveness of output to cultivated area, likely driven by quick mobilization of inputs such as fertilizers, irrigation water, and labor within the current growing season.

However, the subsequent lagged short-run coefficients (ΔLn rice harvested area_-1 = −1.077, ΔLn rice harvested area_-2 = −0.834, and ΔLn rice harvested area_-3 = −0.682) show persistent negative effects that offset the initial gain (Table 5). This pattern implies an over-adjustment behavior in the short run, whereby an initial expansion in cultivated area immediately boosts output, but subsequently leads to declining productivity or contraction in cultivated area over later periods. Several underlying mechanisms can explain this transition: (1) water constraint effects, as expansion without proportional increases in irrigation inputs can reduce water availability per unit area, creating congestion effects that depress yields in subsequent years [86]; (2) soil degradation on marginal lands, as newly irrigated or reclaimed fields may experience salinization and nutrient depletion after the initial cultivation cycles [87]; (3) pest and disease buildup, as expansion into new areas can disturb ecological balance and increase pest incidence in later seasons [88]; and (4) statistical timing effects, as differencing transformations in dynamic regressions can shift the apparent temporal relationship between area decisions and realized production [89].

Fertilizer application exhibits exclusively negative short-run coefficients: ΔLn Fertilizers Usage (-1, -2, and -3) = −0.170, −0.306, and −0.188, respectively, while demonstrating significant positive long-run effects (Table 5). Soil productivity responds to nutrient buildup with a delayed response, which explains this time difference. The current increase in application rates seems to result in decreased short-term output levels because of suggested two main factors: (1) short-term decline in nutrient efficiency occurs when phosphorus and potassium move through the soil after nitrogen application leading to leaching [90]; (2) farmers reduce their employment of other inputs such as labor when they substitute human work with machines or encounter limitations in the labor market. argued that as labor and fertilizer are complements, fertilizer works best with skilled labor for proper timing, placement, and monitoring. The long-term elasticity response becomes positive because soil stock enhancements over multiple years lead to improved production outcomes. These are proposed as plausible, literature-consistent explanations for the observed short-run pattern rather than as mechanisms directly tested here; confirming them would require farm-level data on fertilizer timing, placement, and labor allocation, which are not available in the aggregate national series used in this study.

Various nonlinear adaptation processes distinct time-dependent responses to autumn temperature changes because of their short-term effects. The assessment of negative temperature shocks at intervals ΔAUTTEMP (-1, -2, -3) shows values of −0.073, −0.091, and −0.086, respectively (Table 5). The effect of positive shocks at lag 3 equals 0.056, which suggests farmers modify their production strategies according to temperature shifts across multiple years. Farmers appear to base their decisions on option values, as shown by their practice of adopting new crop varieties and modifying inputs after detecting cooler autumns three years before the actual output boost begins. This interpretation is consistent with, but not directly verified by, the general literature on variety adoption and farm management timing in Egypt; we present it as a plausible behavioral hypothesis for the observed multi-year lag structure rather than a confirmed mechanism, and we encourage future work linking this pattern to variety registration or extension service records.

Precipitation shows mainly negative short-run coefficients, although it establishes positive long-run relationships. The current period shows negative shock effects because ΔLn precipitation⁻ = −0.091, along with significant negative lagged coefficients between −0.221 and −0.036 (all at conventional significance levels), which indicate that water stress and insufficient irrigation compensation lead to output reductions during immediate precipitation shortages. The long-run positive precipitation elasticity arises from the combination of improved soil moisture storage and groundwater recharge over multiple years, along with seasonal changes in irrigation water distribution [91,92]. The short-term effects of precipitation deficits, together with the long-term consequences of precipitation surpluses, create a temporal difference, indicating that agricultural policies and climate impact evaluations should treat temporary weather disruptions differently from permanent climate alterations [93]. Of the climate variables examined, precipitation shocks are associated with the largest responses, which refers to the difference between yearly precipitation amounts and typical long-term averages, because farmers must handle both excessive and insufficient rainfall, which leads to adjustment expenses.

The temporal structure of coefficients, particularly the significant multi-lag effects for precipitation, temperature, and area, supports the NARDL specification’s capacity to capture climate adaptation processes.

To guarantee that the high explanatory power ($R^2=0.993$, Adjusted $R^2=0.973$) does not stem from multi-parameter overfitting, we conducted a comprehensive diagnostic battery. The optimal lag structure NARDL(3, 3, 2, 3, 2, 3) was strictly selected by minimizing the Schwarz Bayesian Criterion (BIC) to favor parsimony.

Multicollinearity was checked via Variance Inflation Factors (VIFs); the mean VIF was 3.42, well below the conservative threshold of 5.0, confirming that decomposing variables into partial sums did not induce catastrophic collinearity. Residual diagnostics show the following:

-

Breusch–Godfrey LM Test for Serial Correlation: $F\left(\mathrm{2,28}\right)=1.142\left(p=0.334\right)$

-

Breusch–Pagan–Godfrey Heteroskedasticity Test: $F\left(\mathrm{24,28}\right)=0.915\left(p=0.582\right)$

-

Ramsey RESET Functional Form Test: $F\left(\mathrm{1,27}\right)=1.624\left(p=0.213\right)$

The insignificance of these test statistics confirms that the model is free from serial correlation, is homoskedastic, and maintains an appropriate functional form, ruling out typical overfitting pathologies. The model demonstrates economic consistency through its coefficient signs and values, which match short-run and long-run periods, and diagnostic tests show high R² and significant F-statistic and fast adjustment convergence to confirm its usefulness for climate policy analysis and production forecasting [43].

A primary empirical limitation of this study concerns the temporal aggregation of our climate indicators. By construction, $\mathrm{AUT}\mathrm{T}\mathrm{EMP}$, $\mathrm{SUMTEMP}$, and $\mathrm{PREC}$ reflect seasonal means and annual totals. They consequently mask short-term climate anomalies, including extreme heat days, diurnal warming patterns, and intense precipitation shocks, as well as hydrological variables such as reference evapotranspiration and Nile River discharge dynamics. In Egypt’s highly managed, irrigation-dependent agricultural landscape, these finer-scale variations represent the immediate physical determinants of rice physiological stress and drainage management. Accordingly, the coefficients associated with $\mathrm{AU}\mathrm{T}\mathrm{TEMP}$ and $\mathrm{PREC}$ represent reduced-form empirical relationships between broader seasonal trends and yield outcomes, rather than direct causal evidence of distinct physiological or hydrological pathways. Future research could usefully validate and extend these reduced-form findings by coupling process-based crop growth models, such as DSSAT-CERES-Rice or ORYZA, with daily or sub-daily meteorological inputs for Egyptian rice-growing regions. Such models simulate phenology, spikelet sterility, and grain filling directly from short-term temperature extremes and diurnal temperature variation rather than seasonal means, and have been successfully calibrated and validated against field-level rice yield data under variable climate conditions elsewhere [94,95]. Combining this higher temporal resolution with the asymmetric econometric framework applied here would help disentangle whether the seasonal aggregate effects identified in this study are driven by a small number of acute extreme temperature events or by more gradual shifts in the seasonal mean, a distinction that annual and seasonal data alone cannot resolve. For reference, Figure 1 summarizes the overall analytical framework followed in this study, from the theoretical production function and data sources through unit root and structural break testing, NARDL asymmetric decomposition and estimation, diagnostic testing, and the resulting policy and future-research implications; Figure 2 situates the study area, the rice-growing governorates of the Nile Delta, within Egypt.

3.3. Asymmetric Effects and Policy Implications

The nonlinear relashionship test and The Wald asymmetry tests reported in

Table 6. Nonlinearity Dechert and Scheinkman (BDS) test statistic.

Dimension	BDS Statistic	z-Statistic	p-Value	Decision (5% Level)
2	−0.0031	−0.4426	0.6580	Fail to reject H0
3	−0.0085	−0.7506	0.4529	Fail to reject H0
4	−0.0167	−1.2241	0.2209	Fail to reject H0
5	−0.0247	−1.7122	0.0869	Fail to reject H0
6	−0.0284	−2.0076	0.0636	Fail to reject H0

and

Table 7. Wald tests for asymmetric long-run and short-run effects of climatic variables on rice production.

Variable	Horizon	F-Statistic	p-Value	Chi-Square	p-Value
AUTTEMP	Long-run	2.783	0.116	2.783	0.090
	Short-run	17.325	0.001	17.325	0.000
	Joint	8.790	0.003	17.579	0.000
Ln precipitation	Long-run	6.190	0.025	6.190	0.013
	Short-run	0.501	0.490	0.501	0.479
	Joint	5.310	0.018	10.620	0.005
SUMTEMP	Long-run	0.849	0.371	0.849	0.357
	Short-run	0.192	0.668	0.192	0.661
	Joint	0.928	0.417	1.857	0.395

, respectively. Table 7 provide the primary statistical evidence for nonlinearity in this study: for autumn temperature, symmetry is rejected in the short run (F = 17.325, p = 0.001) and in the joint test (F = 8.790, p = 0.003), but not in the long run (F = 2.783, p = 0.116). This suggests that the observed asymmetry is transitional rather than permanent, which is consistent with the near-equality of the long-run coefficients (0.096 and 0.121). For precipitation, the pattern is reversed: symmetry is rejected in the long run (F = 6.190, p = 0.025) and in the joint test (F = 5.310, p = 0.018), but not in the short run (F = 0.501, p = 0.490). Summer temperature does not provide evidence of asymmetry at any horizon.

A convincing assessment of nonlinearity should also compare the fitted NARDL model with a linear ARDL model estimated using the same variables and sample, as specified in Equations (7) and (8). This comparison should consider the Akaike Information Criterion (AIC), Bayesian Information Criterion (BIC), residual diagnostics, out-of-sample prediction errors, and long-run elasticities. Since this comparison has not yet been conducted, it remains the most important outstanding robustness check for the study.

The analysis of asymmetric climate shock responses reveals a 64-percent difference in precipitation elasticities (0.248 vs. 0.151), which is consistent with a nonlinear association, unlike the symmetric models used for agricultural impact evaluation [5]. The research results generate essential knowledge that enables organizations to create their climate risk management strategies. The estimation of climate vulnerability becomes inaccurate when linear models assume production reacts similarly to all climate variations because they do not consider the irrigation infrastructure’s protective role during dry periods and the stable output levels achieved through the combination of water systems.

The evaluation of climate risk management requires a separate assessment of deficit- and surplus shock vulnerabilities rather than treating them as equal risks. The system operates with fast error correction (0.783), indicating the production system responds quickly. Rapid convergence requires no assumption about producer sophistication. Yet short-term policies create unexpected results that need stabilization over the medium term due to complex lagged system behavior. The short-term negative effects of increased fertilizer application should not lead to the termination of multi-year input intensification programs, as these programs yield substantial long-term productivity benefits. The implementation of area expansion policies needs to follow a specific sequence with irrigation infrastructure development, as this sequence leads to congestion problems, as evidenced by the negative lagged area coefficients.

The strong positive long-run precipitation coefficient, together with a smaller magnitude deficit effect, indicates that within the range of historical variation observed in Egypt, additional seasonal rainfall has, on net, supported rather than constrained rice production, consistent with the mitigating role of irrigation storage and groundwater access in absorbing rainfall shortfalls. This should not be read as evidence against drainage risk from extreme rainfall events, which annual precipitation totals are not designed to detect (see Section 3.2); rather, it indicates that marginal increases in seasonal rainfall have, on average, been an asset rather than a liability for production during the sample period. Accordingly, the policy implications below emphasize water storage and supplemental-irrigation substitution for deficit years, alongside—rather than subordinate to—drainage-capacity investment for protection against extreme events.

The NARDL model’s ability to capture complicated nonlinear relationships between climate variables and rice yields needed validation through the Brock, Dechert, and Scheinkman (BDS) test [96], which was applied to the model’s residuals (Table 6). This finding indicates that no additional nonlinear dependence remains detectable in the residuals at conventional significance levels, providing supportive, though not definitive, evidence that the NARDL specification adequately captures the nonlinear structure of the climate–rice production relationship over the sample period.

The coefficient symmetry tests for the NARDL model, presented in Table 7, provide important insights into the relationship between climatic variables and rice production. The results show that the null hypothesis of symmetry is rejected for autumn temperature (AUTTEMP) and precipitation in both the short-run and the joint tests combining short- and long-run effects, as indicated by statistically significant F-statistics and chi-square probabilities below the 5% level. This finding suggests that positive and negative changes in autumn temperature and precipitation do not affect rice output in the same way; rather, their impacts vary in magnitude according to the direction of change. More specifically, the evidence of asymmetry in autumn temperature in the short run and in the joint specification, together with the long-run and joint asymmetry observed for precipitation, supports the use of separate positive and negative partial sum decompositions within the NARDL framework. By contrast, summer temperature (SUMTEMP) shows a symmetric relationship with rice production across all horizons, as evidenced by the consistently insignificant test statistics. This implies that increases and decreases in summer temperature generate broadly similar effects on output. Taken together, these results underscore the complexity of climatic influences on rice production and suggest that policy interventions should account for the directional nature of climate shocks, particularly for autumn temperature and precipitation.

The CUSUM test examines parameter stability by plotting the cumulative sum of recursive residuals against time [57]. As illustrated in Figure 3 (upper panel), the CUSUM statistic remains well within the 5% significance boundaries throughout the sample period (2008–2022), indicating no evidence of systematic parameter instability or structural breaks. The coefficients obtained from the NARDL model demonstrate stability and consistency when analyzed across different time intervals.

The cumulative sum of squares (CUSUMSQ) test, which is particularly sensitive to random parameter variations and changes in error variance, is presented in Figure 4 (lower panel). The cumulative sum of squared recursive residuals stays within the 5% significance boundaries during the entire estimation period, which indicates that there are no signs of parameter instability or variance heterogeneity. The results demonstrate that the estimated NARDL model is reliable and robust.

Cumulative dynamic multipliers demonstrate how rice production reacts differently to positive and negative shocks when three main climate variables are affected. For autumn temperature (Figure 5), following a positive shock, cumulative rice production rises sharply to a peak of about 0.26 around year 5, falls to a trough of about 0.05 near years 9–10, recovers to a secondary peak of about 0.20 around year 17, and eases to about 0.07 by year 20. The negative shock path rises more gradually, plateaus near 0.22–0.23 around years 6–7, eases to about 0.15 by years 10–11, rises again to about 0.20 near years 14–15, and declines to about 0.14 by year 20. Both paths show a damped cyclical adjustment that is not fully flattened by year 20, indicating that full equilibrium adjustment likely requires more than 20 years, although the bulk of the shock is absorbed within the first 10–12 years.

The Wald tests confirm this pattern: the short-run asymmetry is highly significant (F = 17.325, p = 0.001) and the joint test is significant (F = 8.790, p = 0.003), while the long-run asymmetry is not significant (F = 2.783, p = 0.116). This is directly reflected in the graph: the 95% confidence band around the asymmetry line excludes zero over approximately years 6–11, the medium-run window in which the two paths are visibly separated, but includes zero in the very short run (years 1–3) and again from around year 12 onward, as the paths converge toward long-run limits of approximately 0.13 (positive) and 0.155 (negative). Autumn temperature therefore exerts a statistically significant but transitional, medium-run asymmetric effect rather than a permanent one.

For summer temperature (Figure 6), both the positive- and negative-shock responses fluctuate at low amplitude around zero throughout the horizon. The positive response falls to a trough of about −0.07 near year 4, rises to a small peak of about 0.035 near years 8–9, and oscillates between roughly −0.07 and 0.02 thereafter; the negative response follows a similarly low-amplitude path, ranging between about −0.05 and 0.06. Because both paths hover close to zero from as early as years 6–7 onward, summer temperature shocks are effectively absorbed within about 6–7 years, with no large or persistent adjustment process extending toward the end of the horizon.

This is confirmed by the Wald tests, which are insignificant at every horizon (long-run: F = 0.849, p = 0.371; short-run: F = 0.192, p = 0.668; joint: F = 0.928, p = 0.417). The 95% confidence band around the asymmetry line contains zero for nearly the entire horizon, dipping only briefly and non-persistently below zero in narrow windows around years 3–6 and 12–15. The long-run limits are also nearly coincident (≈−0.01 for positive vs. ≈0.035 for negative shocks). Summer temperature shocks therefore produce no statistically meaningful asymmetric response at any horizon, and the relationship can reasonably be treated as symmetric, with equilibrium effectively reached within under a decade.

For precipitation (Figure 7), the positive-shock response rises steeply from about 0.07 at year 1 to a peak of approximately 0.50 around year 6, falls to a trough of about 0.18 near years 9–10, rises again to a secondary peak of about 0.42 around year 16, and eases to about 0.24 by year 20. The negative-shock response starts markedly negative (about −0.08), rises to a peak of about 0.35 around years 6–7, falls to a trough of about 0.10 near years 9–10, recovers to a secondary peak of about 0.28 near years 15–16, and declines to about 0.15 by year 20. As with autumn temperature, the adjustment follows a damped cyclical path with two waves of overshoot; by year 20 neither path has fully reached its respective long-run limit (0.31 for positive shocks; 0.19 for negative shocks), indicating that full convergence extends beyond the estimated horizon, although the narrowing oscillation amplitude across the two cycles points to eventual convergence thereafter.

The Wald tests show the reverse pattern from autumn temperature: the long-run asymmetry is significant (F = 6.190, p = 0.025), the joint test is significant (F = 5.310, p = 0.018), but the short-run asymmetry is not significant (F = 0.501, p = 0.490). This is corroborated by the graph: unlike the temperature variables, the asymmetry line for precipitation remains positive across virtually the entire 20-year horizon (about 0.07 to 0.22), and the 95% confidence band stays above zero for nearly the whole path, narrowing toward, but not clearly crossing, zero only briefly in year 1. The long-run limits are clearly separated (a gap of about 0.12 between 0.31 and 0.19), confirming that precipitation shocks generate a persistent, statistically significant long-run asymmetric effect sustained over essentially the entire 20-year period, even though the transient, year-to-year dynamics do not differ significantly by shock direction.

Taken together, the dynamic multiplier paths and the Wald tests in Table 7 jointly demonstrate that the asymmetric response of rice production to climatic shocks is variable-specific in both timing and persistence. Autumn temperature exhibits significant but transitional asymmetry, with the positive and negative shock paths statistically separated for approximately 5–6 years during the adjustment process before reconverging toward statistically similar long-run outcomes over more than 20 years. Summer temperature shows no significant asymmetry at any horizon, with shocks absorbed within roughly 6–7 years and no lasting divergence between the positive and negative responses. Precipitation, in contrast, exhibits the most persistent asymmetry: its positive and negative shock paths remain significantly separated across nearly the full 20-year horizon and converge toward long-run multipliers (0.31 vs. 0.19) that are themselves significantly different, with full equilibrium adjustment still incomplete after 20 years.

While the NARDL framework demonstrates long-run cointegration and short-run asymmetries, it establishes strong empirical associations rather than definitive causal effects due to unobserved confounders like agricultural policies, input prices, and pest pressure. Consequently, these findings should be interpreted as associations consistent with a climate channel, highlighting the need for future studies to incorporate broader control variables as data allow.

4. Conclusions and Policy Implications

The findings showed that flood-irrigated rice production responds to climate in a nonlinear, asymmetric manner, shaped by its irrigation-dominated system. Harvested area and fertilizers were the input variables most strongly associated with rice production, but short-run gains from expansion and intensification were partly offset by negative lagged effects linked to adjustment costs, resource constraints, and soil processes. Autumn temperature and precipitation shocks were most strongly associated with production outcomes and display clear asymmetries between positive and negative deviations, while summer temperature had no robust long-run impact under current management. Robust diagnostics and evidence of a stable cointegrating relationship support the credibility of these results and their relevance for policy. Climate and agricultural policies should move beyond symmetric “average climate” assumptions. They should explicitly account for the different consequences of rainfall surpluses versus deficits. They should also distinguish between moderate and extreme temperature shocks. Priorities include investing in irrigation and drainage infrastructure that buffers hydrological extremes. Another priority is to sequence land expansion with salinity control and pest management on marginal lands. A further priority is to improve fertilizer timing and nutrient balance rather than simply scaling quantities. As farmers adjust relatively quickly to shocks, adaptation measures such as heat-tolerant varieties, refined autumn planting calendars, and season-specific climate services can yield rapid benefits. However, unstable or poorly timed interventions risk amplifying production volatility. The asymmetric NARDL framework used here also offers a practical template for extending similar analyses to other key crops in Egypt’s food system.

To strengthen these findings and build on the core insights, future research can expand on several clear opportunities. Moving from annual to sub-annual or farm-level data will better capture within-season climate variation that critical crop stages rely on. Incorporating direct metrics for irrigation water volumes and extreme weather events, rather than relying solely on seasonal averages, will offer a more detailed picture of climate impacts. Shifting the focus to yield per hectare rather than aggregate production will isolate pure productivity gains from changes in land area or inputs. Additionally, accounting for extra variables like pest pressure, soil salinity, and specific policy interventions will help refine the model, while expanding the dataset over time will increase the precision of long-run estimates. A further opportunity lies in linking the asymmetric elasticities estimated here to forward-looking climate scenarios: combining our historical NARDL-based response coefficients with downscaled Global Climate Model projections under CMIP6 Shared Socioeconomic Pathways (e.g., SSP2-4.5, SSP5-8.5), following the scenario-based approach recently applied to Nile Delta rice yields [9], would allow the asymmetric production responses identified in this study to be projected forward under alternative future emissions and socioeconomic trajectories, complementing the process-based crop-model validation discussed above.