Universe of the study
This research was carried out in Pakistan's Khyber Pakhtunkhwa province. Khyber Pakhtunkhwa is a province in Pakistan's northwest (Khyber Pakhtunkhwa Climate Change Policy. 2016). The total area of Khyber Pakhtunkhwa is 74521 square kilometres, with mountains and rocks accounting for 70% of the land (White Paper, 2015). Extreme climatic variation is found in Khyber Pakhtunkhwa weather, northern area of Khyber Pakhtunkhwa is having extreme cold and snowy winter with a huge rate of rainfall and a pleasant summer as compared to the southern region of Khyber Pakhtunkhwa which have less severe winter, rainfall and a very hot summer. Khyber Pakhtunkhwa is divided into 4 zone namely zone A, zone B, zone C and zone D according to their climatic nature based on rainfall, temperature altitude (Khyber Pakhtunkhwa Climate Change Policy 2016) (Table 1).
Table 1
Agro ecological zones of Khyber Pakhtunkhwa with districts
Climatic zones | Description | Districts |
Northern (A) | Higher northern mountains, Northern mountain, | Chitral, Swat, Bunir, Shangla, Upper Dir, Lower Dir |
Eastern (B) | Wet mountains, Sub humid eastern mountains | Batagram, Haripur, Mansehra, Torghar, Kohistan, Abbottabad |
Central (C) | Central plain valley | Peshawar, Charsadda, Mardan, Swabi, Nowshera, Kohat |
Western (D) | Piedmont plain, Suleiman piedmont | Bannu, Karak, Lukky Marwat, Tank, D. I. Khan |
Source: Environmental Protection Agency of Khyber Pakhtunkhwa, 2016.
Zone A which are higher mountains or northern mountains consists of six districts which are Chitral, Bunir, Swat, Shangla, Upper Dir, and Lower dir. While Batagram, Haripur, Mansehra, Torghar, Kohistan and Abbottabad comes under Zone B which are sub-humid eastern mountains or wet mountains. Similarly, the Central plain valley which include Swabi, Mardan, Charsadda, Peshawar Nowshera, and Kohat lies in Zone C. while Zone D known as Piedmont plain, Suleiman piedmont include Bannu, Karak, Lakki Marwat, Tank, D. I. Khan (Fig. 1).
Data and data sources
Panel data over time and across major rice producing districts in four climatic zones of Khyber Pakhtunkhwa was used in this study. Time period and major rice producing districts across four climatic zones were selected for which data on non-climatic and climatic variables were available. Data on rice production in thousand tons, area under rice crop in thousand hectares, yield of rice in kilograms per hectare, temperature in 0C and precipitation in mm were collected. Production, area and yield of rice data was gathered from Pakistan Bureau of Statistics and Development Statistics of Khyber Pakhtunkhwa. Data on climatic variables was collected from Pakistan Meteorological Department, Peshawar.
Because of fluctuations in climatic conditions throughout in different phases of crop growth, have varied effects on crop production, the temperature and precipitation variables were computed using three phonological stages of rice crop (Auffhammer et al., 2012). Nursery growth, transplanting, and tillering are covered in the first stage, vegetative growth, blooming, and milking are covered in the second stage, and rice maturity and harvesting are covered in the third stage. The first stage of rice lasts from June to July. The second from August to September, and the third from October to November (Ahmad et al., 2016), (Segerson and Dixon, 1999), (Cabas et al. 2010) and (Cheng and Chang, 2002).
Conceptual framework
Traditionally, Influence of climate alteration was measured by many researchers. The production function which is also known as product modelling is based on empirical or experimental production, and many researcher use this model to investigate the relationship among the yield and climatic variables (Deressa et al., 2005). In the same way, The Ricardian approach is another useful tool for determining the total climatic influence on a specific geographical area. It has been used in both developed and developing countries in a variety of geographical areas (Salvo et al., 2013) Mishra and Sahu (2014), Salvo et al. (2013), Deressa and Hassan (2009), Kabubo-Mariara and Karanja (2006), Deressa et al. (2005), Gbetibouo and Hassan (2005), Mendelsohn and Dinar (2003), Mendelsohn and Dinar (2003), Mendelsohn and Dinar (2003), Mendelsohn and Dinar (2003), Mendelsohn and Din
At the global, country, and regional levels, the time series approach has been widely used to explore the impact of climate variables on crop yields (Maharjan and Joshi, 2012). Rahim and Puay (2017), Zaied and Zouabi (2015), Amponsah et al. (2015), and Alam (2013) used time series analysis to investigate the relationship between climate variables and agricultural product yield.
Advanced Ricardian (Panel Data) Approach is also used by researcher to assess the impact of rainfall and temperature change on agriculture production such as Loum and Fogarassy (2015), Sarker et al. (2014), Dasgupta (2013), Barnwal and Kotani (2013) Dell et al. (2012), Akram (2012) Lobell et al. (2011), Brown et al. (2010), Guiteras (2007). The basic advantage of this approach is that it takes into account, the fluctuations that occur randomly year-to-year in the weather conditions (Deschenes and Greenstone, 2007).
Panel data approach
Panel data is the blend of both time series and cross-sectional data. When data is collected over more than two dimensions i.e., different cross sections and over time is known as Panel data. Variables which cannot be observed or measured, and it changes over time but not across entities, these variables can be controlled through Panel data. Moreover, Panel data can include variables at different stages of analysis.
Efficiency of the panel data is more because it has variety of advantages than cross sectional and time series data. In panel data there are more observation which gives more precise estimates, more information, less collinearity issues in data. It also resolves the misspecification problem that arises from omitted variable (Jintian, 2010).
Panel data approach can be simply presented as follows:
$$Yit=\alpha + \beta xit + \epsilon it$$
1
Y = dependant variable
X = independent variable
α and β = coefficients
i and t = directories for cross section and time
εit = error term
The error (εit) component is the most important factor in the panel data method equation because it tells us whether to use a fixed effect model or a random effect model (Gardinar et al. 2009).
Three approaches are used in literature for analysis of panel data (Baltagi, 2008).
i. Pooled effect model
Pooled effect also known as common constant effect is same as simple regression. In pooled effect model no panel information are used as it is observed that every variable is uncorrelated with other, ignoring panel and time.
The simple pooled model can be expressed as follows:
$$Yit= {\beta }0+\beta xit+ \epsilon it$$
2
Pooled effect assumes, that every observation performs in the same way that never experience autocorrelation and heteroscedasticity that is why only simple regression model can be used to estimate the model. Mostly pooled effect model are restrictive than fixed effect and random effect. Pooled model should be used when fixed effect is not efficient.
ii. Fixed effect model
Deschenes and Greenstone (2007) presented the fixed model approach which removed the problems associated to hedonic approach and is considered the ideal model due to its quick response time to sudden change in weather condition and it also controls the effect of unobserved variable (Mendelsohn and Dinar, 2009).
Because fixed effect organises all time-invariant changes between entities, the projected coefficients of fixed effect cannot be skewed by excluding time invariant properties. Because it is constant for each cross section, a time-invariant feature cannot produce such a change (Torres-Reyna, 2007).
\(Yit=\alpha i + \beta xit + \epsilon it\) t = 1… T and i = 1… N (3)
Where:
\(Yit\) = Dependent variable
αi = Correlated with x and unobserved time invariant individual effect for every cross section
\(\epsilon it\) = Error term.
\(\left(\beta \right)\) Parameter representing slope (same for all cross sections, & doesn’t changeable).
For two or more than two time period data set fixed effect model is suitable. For estimation of fixed effect model least square dummy variable (LSDV) is used.
iii. Random effect model
In random effect model time variant variables are included. The logic behind random effect is that the variation across the entities are assumed to be random and are uncorrelated with the cross section or independent variables included in the models (Torres-Reyna. 2007). The constants for each part are treated as random parameters in the random effect model.
$$Yit=(\alpha i+vi)+ \beta xit + \mu it$$
4
$$Yit=\alpha i+ \beta xit + vi+\mu it$$
5
Individual effects are randomly spread crosswise in a random effect, and αi is uncorrelated with x. When the random impact is considered to be that the unit's error terms are not associated with the cross-section, time invariant variables play a function as an explanatory variable. Random effects should be employed if variations between entities have an impact on the dependent variable.
Empirical model
Yield of rice across districts and over time is expected to be a function of area under rice crop, minimum and maximum temperature and precipitation during the crop season. Model for panel data estimation is given as:
LNYIELDit = \(\beta 0\)+ \({\beta }_{1}\)LNAREAit + \({\beta }_{2}\)LNTmax_Sit + \({\beta }_{3}\)LNTmax_Vit + \({\beta }_{4}\)LNTmax_Mit + \({\beta }_{5}\)(LNTmax_Sit)² + \({\beta }_{6}\)(LNTmax_Vit)² + \({\beta }_{7}\)(LNTmax_Mit)² + \({\beta }_{8}\)LNRain_Sit + \({\beta }_{9}\)LNRain_Vit + \({\beta }_{10}\)LNRain_Mit + \({\beta }_{11}\)(LNRain_Sit)² + \({\beta }_{12}\)(LNRain_Vit)² + \({\beta }_{13}\)(LNRain_Mit)² + \({\beta }_{14}T+\) \(Uit\) (6)
Where:
LNYIELD = Natural log of rice yield (kg/ha)
LNAREA = Natural log of area (000 ha)
LNTmax_S = Natural log of maximum temperature for sowing stage
LNTmax_V = Natural log of max. temperature for vegetative stage
LNTmax_M = Natural log of max. temperature in maturity stage
(LNTmax_S)² = Natural log of max. temperature square in sowing stage
(LNTmax_V)² = Natural log of max. temperature square in vegetative stage
(LNTmax_M)² = Natural log of max. temperature square in maturity stage
LNRain_S = Natural Log of rainfall in sowing stage
LNRain_V = Natural Log of rainfall in vegetative stage
LNRain_M = Natural Log of rainfall in maturity stage
(LNRain_S)² = Natural Log of rainfall square in sowing stage
(LNRain_V)² = Natural Log of rainfall square in vegetative stage
(LNRain_M)² = Natural Log of rainfall square in maturity stage
β1–13 = Estimated parameters
T = Trend (Time in years)
U = Error term
i = Cross section
t = Time period
Model selection
Following test was conducted for the selection of appropriate model.
1. Durbin Wu Hausman test
For selection between random and fixed effect model Durbin Wu Hausman test was conducted (Gardinar et al. 2009). Durbin Wu Hausman test construct the following hypothesis
HO: The random effect model is efficient
H1: The fixed effect model is efficient
Following static are used in Hausman test:
H = (β^FE - β^RE) ̸ - [Var (β^FE) – Var (β^RE)] −1 (β^FE - β^RE) ͠ χ2 (k) (7)
Hausman test follows chi square distribution. If the chi square value is found insignificant then null hypothesis of random effect model will be accepted and vice versa.
2. Breusch-Pagan Lagrange Multiplier (LM) test
Breusch-Pagan Lagrange Multiplier (LM) test assists in deciding between pooled effects and random effects model. The LM test's hypothesis:
H0: Variance of the random effect is zero: Var[ui] = 0
H1: Variance of the random effect is not zero: Var[ui] ≠ 0
LM test follows chi square distribution
Critical temperature and its impact on yield
Critical temperature is the temperature where the yield is maximum or minimum. This temperature can be calculated using the formula provided below.
Critical temperature = exp (-(β2/2* β3)) (8)