Empirical Model
Though several studies used Ricardian model to estimate climate change impact, Deschênes and Greenstone (2007) proposed an alternative to cross-sectional Ricardian approach by using random, year-to-year variability in weather parameters such as precipitation and temperature on farm profits. Consequently, this approach allows the use of panel data model, to estimate the effect of weather on farm profits, conditional on locations by year fixed effects. Kumar (2011) used this approach in his analysis of 271 Indian districts over a period of 20 years to estimate the impact of climate change on farm net revenue. Following these studies, the empirical, panel data econometric model of our study consists of a set of two equations—the first one concerning the impact of climate and non-climate factors on groundwater table and the second one concerning the impact of climate, water and other economic factors affecting farm income.
$$\begin{aligned} {\text{Watlev}}_{{{\text{it}}}} & = \alpha_{0} + \alpha_{1} \; {\text{Lwatlev}} + \alpha_{2} \; {\text{Rain}} + \alpha_{3} \; {\text{Lrain}} \\ & \quad + \alpha_{4} \; {\text{Tmax}} + \alpha_{5} \; {\text{Watint}} + \alpha_{6} \; {\text{Lwatint}} \\ & \quad + \alpha_{7} \; {\text{Elecdum}} + \alpha_{8} \; {\text{Tankgia}} + \alpha_{9} \; {\text{Canalgia}} + \alpha_{10} \; {\text{Time}} \\ \end{aligned}$$
(10.1)
Equation (10.1) was estimated using dynamic panel data approach in view of the presence of lagged dependent variable as one of the regressors.
The equation for net returns is specified as shown below, and it was estimated using aggregate district-level data rather than farm-level data. In the net returns equation, we use the estimated depth to water table from Eq. 10.1. In addition to the depth to water table, climate variables, dummy for districts (coastal and non-coastal), dummy for electricity price, well density, indices of input and output prices were also used as explanatory variables.
$$\begin{aligned} {\text{Return}} & = \gamma_{0} + \gamma_{1} \; {\text{Rain}}_{{{\text{it}}}} + \gamma_{2} \; {\text{Rain}}^{2} + \gamma_{3} \; {\text{Tmax}} \\ & \quad + \gamma_{4} \; {\text{Tmax}}^{2} + \gamma_{5} \; {\text{Distdum}} + \gamma_{6} \; {\text{Wellden}} \\ & \quad + \gamma_{7} \; {\text{Wellden}}^{2} + \gamma_{8} \; {\text{Elecdum}} + \gamma_{9} \; {\text{Ewatlev}} \\ & \quad + \gamma_{10} \; {\text{Inprice}} + \gamma_{11} \; {\text{Outprice}} + \gamma_{12} \; {\text{Time}} + \gamma_{13} \; {\text{Surfgia}} \\ \end{aligned}$$
(10.2)
where
Return = Net farm income from crop production
Rain = Rainfall (mm)
Tmax = Max. temperature (°C)
Distdum = District dummy (0= Coastal district; 1= Non-coastal district)
Wellden = Well density (total number of wells per ha of geographical area of the ith district)
Elecdum = Dummy for electricity price (= 0 for pro-rata tariff; = 1 for flat rate or full subsidy)
Ewatlev = Estimated water level from Eq. 10.1
Inprice = Weighted average of input prices
Outprice = Weighted average of output prices
Time = Time (Trend variable)
Surfgia = Proportion of surface irrigated area to gross irrigated area by all sources
Tankgia = Gross irrigated area by tanks (ha)
Canalgia = Gross irrigated area by canals (ha)
Watlev = Groundwater level (in metres below surface)
Lwatlev = One-period lag of groundwater level
Watint = Share of water-intensive crops to gross cropped area
Lwatint = One-period lag of share of water-intensive crops to gross cropped area.
Estimation Strategy
The first equation was estimated using spatial dynamic panel method due to the presence of lagged dependent variable as one of the explanatory variables in the model. The model was estimated with two-period lag structure, using Arellano–Bond estimators for spatial dynamic panel model (Arellano & Bond, 1991). The net revenue equation was estimated using panel-corrected standard errors regression model using estimated water level from the first equation as one of the explanatory variables. Descriptive statistics of the variables are presented in Table 10.1.
Table 10.1 Definition of variables and their descriptive statistics