Integrated model shows that atmospheric brown clouds and greenhouse gases have reduced rice harvests in India

Auffhammer et al. 10.1073/pnas.0609584104.

Supporting Information

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Supporting Table 3
Supporting Table 4
Supporting Table 5
Supporting Table 6
Supporting Text




Table 3. Variables in the production function and the area demand function

All variables are annual and are measured at the state level except solar radiation (two regions, north and south) and rice and jowar prices (same for all states).

Table 4. Estimation results for the production function

Sample consists of annual observations during 1972-98 for 9 Indian states (panel data). All variables are in natural logarithms. Dependent variable is wet-season rice harvest. All models include fixed effects for states, and model I also includes fixed effects for years. Models I and II correct for endogeneity of area harvested; model III corrects for endogeneity of area harvested, fertilizer, and labor. Robust standard errors are shown in parentheses below the coefficient estimates; ^* = significant at 10%, ^** significant at 5%, ^*** significant at 1%. Results for model I provide the basis for the analysis reported in the text.

Table 5. Estimation results for the area demand function

Sample consists of annual observations during 1972-98 for 9 Indian states (panel data). All variabes are in natural logarithms. Dependent variable is area of rice harvested during the wet season. Both models include fixed effects for states, and model IV also includes fixed effects for years. Robust standard errors are shown in parentheses below the coefficient estimates; * = significant at 10%, ** significant at 5%, *** significant at 1%. Results for model IV provide the basis for the analysis reported in the text.

Table 6. Characteristics of PCM output used in study

Variables were constructed by averaging the original PCM output across grid cells corresponding to the 9 states in our sample and, in the case of the GHG+SO4_1998 scenario, across multiple runs. The sample period was 1961-98. Difference tests were conducted using paired t tests. The mean of observed October-November minimum temperature during 1930-60 was 18.0°C.

Supporting Text

Regression Models. We specified the production function as

,

where i denotes state, t denotes year, y_it is rice harvest, a_it is area harvested, X_it is a set of variables for other agricultural inputs (labor, fertilizer, high-yielding varieties, irrigation), Z_it is a set of climate variables (rainfall, radiation, temperature), b₁, b, and g are parameters, and e_it is the error term. c_i and q_t are fixed effects for states and years, respectively. All variables are in natural logarithms except the fixed effects. Table 3 provides detail on the variables. Data sources were as follows: rice harvest and area harvested, official statistics in the online database, www.indiastat.com; labor inputs, the Census of India (Census Commissioner, Office of the Registrar General, New Delhi, various years); fertilizer inputs, the Fertiliser Statistics Yearbook (Fertiliser Association of India, New Delhi, various years); high-yielding varieties, and irrigation, the International Rice Research Institute's online database, World Rice Statistics (http://irri.org/science/ricestat/); rainfall, the IITM Indian regional/subdivisional monthly rainfall data set (Indian Institute of Tropical Meteorology, Pune, www.tropmet.res.in/); radiation, the database described in Gilgen, H. & Ohmura, A. (1999) Bull. Am. Meteorol. Soc. 80, 831-850; and temperature, the database described in Mitchell, T. D. & Jones, P. D. (2005) Int. J. Climatol. 25, 693-712.

We specified the input demand function for area harvested as

,

where a_it-1is area harvested during the previous year, W is a set of exogenous economic variables (inflation-adjusted prices of agricultural outputs and inputs) (1, 4, 8), Z is the same set of climate variables as in the production function, d₁, d, and j are parameters, and m_it is the error term.

and

are again fixed effects for states and years, and all continuous variables are again in natural logarithms. To correct for the endogeneity between rice harvest and area harvested, we used the fitted values from this regression, , in place of the observed values of a_it when we estimated the production function. We obtained data on prices from www.indiastat.com, World Rice Statistics, and the Indian government report Farm (Harvest) Prices of Principal Crops (Directorate of Economics and Statistics, New Delhi, various years).

Regression coefficients on the climate variables were shown in Table 1. Other regression results are shown in Tables 4 and 5. Coefficients on the nonclimate variables generally had the expected signs, were statistically significant (P < 0.05), and were comparable to estimates reported by other agricultural production studies. Correcting the production function for the potential endogeneity of labor and fertilizer in addition to area harvested did not change the coefficient estimates on the area and climate variables much. The yearly fixed effects in the production function (not shown) trended downward, suggesting that they proxied for factors associated with the deceleration of harvest growth that we did not model explicitly (e.g., soil degradation). Trial regressions not shown here, but available upon request, indicated that: (i) unlike lagged area, lagged yield did not have a significant impact on area harvested, which indicates that lagged area captures the most important dynamic effects in the area demand function; and (ii) dropping the fertilizer price variable, which was available only from 1972 onward, and estimating the two equations for 1966-98 instead of 1972-98 had little impact on the predicted impacts of reducing ABCs and GHGs.

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