Page 116 - AJWEP-v22i3

Nabi, et al.

agriculture, precision farming, CH , N O emissions, Where CCY = Cereal crop yield; PAT = Precision
2
4
and food crop yields in Pakistan. The ARDL framework agriculture technology; TEMP = Temperature;
integrates short- and long-term influences into a single AGRI = Agriculture value-added; CH = Methane
4
estimating structure, even when variables have varied emissions; N O = Nitrous oxide emissions; DAML =
2
integration orders (I(0) and I(1)). Data irregularities Data analytics and machine learning; FAR = Farmer’s
and structural failures are common in underdeveloped adoption rate; ∆, t, and ƹ denote difference operator,
countries like Pakistan; therefore, this flexibility helps time, and error term, respectively.
to utilize this statistical technique. It can also capture The ARDL bounds testing approach developed by
complicated trade-offs between agricultural innovation Pesaran et al. is a robust method for co-integration
47
and environmental degradation since the model definition analysis. Superior to Johansen and Engle–Granger
includes emissions-technology adoption interaction tests, ARDL permits the inclusion of deterministic and
variables. This method reinforces empirical results and non-stationary variables along with their lagged values
provides a framework for policymakers to balance fast in the model. Researchers ascertain co-integration by
technological growth with environmental damage. employing least squares regression to assess the ARDL
model and comparing the F-statistic with critical values.
3.1. Econometric framework ARDL’s equations incorporate short- and long-term
The study employed the Phillips–Perron (PP) and dynamics to depict both immediate and equilibrium
Augmented Dickey–Fuller (ADF) unit root tests to interactions between variables, making it the preferred
determine stationary time-series data. These tests method for econometric analysis, especially in complex
determine if a time series is stationary, a trait that could economic systems. Equation IX shows the ARDL model
impact data predictability. The ADF test seeks a unit specification with error correction term:
root to indicate non-stationarity. Like the ADF, the PP
test finds unit roots by carefully examining the lagged p q
variable’s coefficient, but it detects heteroskedasticity ln(CCY ) = t α 0 ∑ ϕ + i ∆ ln(CCY ) t i− θ + i ∆ ln(PAT ) t i− ∑
better. Time-series data used in an economic model r i= 1 t i= 0
must fulfill both stationarity and consistency conditions. + ∑ θ i ln(TEMP ) t i− + φ ∆ i ∆ ln (n AGRI ) t i− ∑
Equations I to VIII show the estimated ADF unit root i= 0 i= 0
test equations: v w
+ φ i ln(CH 4) t i − ∑ + φ ∆ i ∆ ln( 2 )N O t i − ∑ +
∆(CCY) = ϕ + ϑ (TIME) + ζ (CCY) + ζ ∆ (CCY) +…. i= 0 i= 0
t
t-1
1
t-1
+ζ ∆ (CCY) t-p-1 + ε t (1) x φ ln(DAML ) t i − ∑ + y φ ∆ ∆ ln(FAR ) t i − ∑ +
p-1
∆ (PAT) = ϕ + ϑ (TIME) + ζ (PAT) + ζ ∆ (PAT) +…. i= 0 i i= 0 i
1
t-1
t
t-1
+ζ ∆ (PAT) + ε (II) δ 1 ln(PAT + ) t δ 2 ln(TEMP + ) t δ 3 ln(AGRI) t
p-1
t-p-1
t
+ δ 4 ln(CH 4) + t δ 5 ln( 2 ) + N O t δ 6 ln(DAML ) t
∆ (TEMP) = ϕ + ϑ (TIME) + ζ (TEMP) + ζ ∆ (TEMP) + δ ln(FAR + ) ρ (ECT ) + ε
1
t-1
t
+….+ζ ∆ (TEMP) + ε (III) 7 t t− 1 t
t-1 p-1 t-p-1 t (IX)
Where Δ denotes difference operator.
∆ (AGRI) = ϕ + ϑ (TIME) + ζ (AGRI) + ζ ∆ (AGRI)
1
t-1
t
+….+ζ ∆ (AGRI) + ε (IV) 4. Results and discussion
t-1 p-1 t-p-1 t
∆ (CH ) = ϕ + ϑ (TIME) + ζ (CH ) + ζ ∆ (CH ) +…. Table 2 shows the descriptive statistics of the variables.
4 t-1
4 t
1
4 t-1
+ζ ∆ (CH ) + ε t (V) Crop yield represents the production of cereal crops
p-1
4 t-p-1
per unit of land. In our dataset, the average yield for
∆ (N O) = ϕ + ϑ (TIME) + ζ (N O) + ζ ∆ (N O) +….
2
t
t-1
2
1
2
t-1
+ζ ∆ (N O) t-p-1 + ε t (VI) cereal crops is 1983.552 tons per hectare, ranging
from a maximum of 1429.200 tons to a minimum of
p-1
2
∆ (DAML) = ϕ + ϑ (TIME) + ζ (DAML) + ζ ∆ (DAML) 3564.900 tons. The standard deviation of 840 indicates
t
1
t-1
+….+ζ ∆ (DAML) + ε (VII) variability in cereal crop production across different
t-1 p-1 t-p-1 t
regions and time periods. Skewness and kurtosis values
∆ (FAR) = ϕ + ϑ (TIME) + ζ (FAR) + ζ ∆ (FAR) t-1 +…. of 1129.717 and 0.592 suggest a positively skewed and
t-1
1
t
+ζ ∆ (FAR) t-p-1 + ε t (VIII) flat distribution of yield data, respectively.
p-1
Volume 22 Issue 3 (2025) 110 doi: 10.36922/AJWEP025130096