Ln ðW: YieldÞ ¼ b 0t þ b 1t ðTEMP Sowing Þ þ b 2t ðTEMP Flowering Þ þ b 3t ðTEMP Harvesting Þ
þ b 4t ðPRECP Sowing Þ þ b 5t ðPRECP Flowering Þ þ b 6t ðPRECP Harvesting Þ
þ b 7t ðV: TEMP Sowing Þ þ b 8t ðV: TEMP Flowering Þ þ b 9t ðV: TEMP Harvesting Þ
þ b 10t ðV: PRECP Sowing Þ þ b 11t ðV: PRECP Flowering Þ
þ b 12t ðV: PRECP Harvesting Þ þ b 13t ðT Â P Sowing Þ þ b 14t ðT Â P Flowering Þ
þ b 15t ðT Â P Harvesting Þ þ b 16t Ln(A wheat Þ þ b 17t Ln(Fr) þ b 18t ðTimeÞ
þ b 20t ðB:AÞ þ b 20t ðSkrÞ þ b 21t ðBwpÞ þ b 22t ðMarÞ þ l t
ð4Þ
Variables in Eq. (4) are explained in Table 3.
Table 3 Description of variables
Variables
Description
TEMP Sowing
20 years moving average of temperature during November- December
TEMP Flowering
20 years moving average of temperature during January–February
TEMP Harvesting
20 years moving average of temperature during March–April
PRECP Sowing
20 years moving average of precipitation during November–December
PRECP Flowering
20 years moving average of precipitation during January–February
PRECP Harvesting
20 years moving average of precipitation during March–April
V. TEMP Sowing
Variation in climatic temperature during November–December
V. TEMP Flowering
Variation in climatic temperature during January–February
V. TEMP Harvesting Variation in climatic temperature during March–April
V. PRECP Sowing
Variation in climatic precipitation during November–December
V. PRECP Flowering Variation in climatic precipitation during January–February
V. PRECP Harvesting Variation in climatic precipitation during March–April
(P × T) Sowing
Interaction terms of climatic temperature and precipitation during
November–December
(P × T) Flowering
Interaction terms of climatic temperature and precipitation during
January–February
(P × T) Harvesting
Interaction terms of climatic temperature and precipitation during
March–April
Ln (A wheat)
Natural log of area under wheat crop
Ln (Fr)
Natural log of fertilizer used for wheat crop
Time
Technological Improvement with Time (dummy variable)
B.A
Banazir Abad (dummy variable)
Skr
Sukkur (dummy variable)
Bwp
Bahawalpur (dummy variable)
Mar
Mardan (dummy variable)
µ
Heteroscedastic error term
Author’s own
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M.H. Abdullah et al.
þ b 4t ðPRECP Sowing Þ þ b 5t ðPRECP Flowering Þ þ b 6t ðPRECP Harvesting Þ
þ b 7t ðV: TEMP Sowing Þ þ b 8t ðV: TEMP Flowering Þ þ b 9t ðV: TEMP Harvesting Þ
þ b 10t ðV: PRECP Sowing Þ þ b 11t ðV: PRECP Flowering Þ
þ b 12t ðV: PRECP Harvesting Þ þ b 13t ðT Â P Sowing Þ þ b 14t ðT Â P Flowering Þ
þ b 15t ðT Â P Harvesting Þ þ b 16t Ln(A wheat Þ þ b 17t Ln(Fr) þ b 18t ðTimeÞ
þ b 20t ðB:AÞ þ b 20t ðSkrÞ þ b 21t ðBwpÞ þ b 22t ðMarÞ þ l t
ð4Þ
Variables in Eq. (4) are explained in Table 3.
Table 3 Description of variables
Variables
Description
TEMP Sowing
20 years moving average of temperature during November- December
TEMP Flowering
20 years moving average of temperature during January–February
TEMP Harvesting
20 years moving average of temperature during March–April
PRECP Sowing
20 years moving average of precipitation during November–December
PRECP Flowering
20 years moving average of precipitation during January–February
PRECP Harvesting
20 years moving average of precipitation during March–April
V. TEMP Sowing
Variation in climatic temperature during November–December
V. TEMP Flowering
Variation in climatic temperature during January–February
V. TEMP Harvesting Variation in climatic temperature during March–April
V. PRECP Sowing
Variation in climatic precipitation during November–December
V. PRECP Flowering Variation in climatic precipitation during January–February
V. PRECP Harvesting Variation in climatic precipitation during March–April
(P × T) Sowing
Interaction terms of climatic temperature and precipitation during
November–December
(P × T) Flowering
Interaction terms of climatic temperature and precipitation during
January–February
(P × T) Harvesting
Interaction terms of climatic temperature and precipitation during
March–April
Ln (A wheat)
Natural log of area under wheat crop
Ln (Fr)
Natural log of fertilizer used for wheat crop
Time
Technological Improvement with Time (dummy variable)
B.A
Banazir Abad (dummy variable)
Skr
Sukkur (dummy variable)
Bwp
Bahawalpur (dummy variable)
Mar
Mardan (dummy variable)
µ
Heteroscedastic error term
Author’s own
48
M.H. Abdullah et al.