India provides rich within-district variation to study the impact of temperature on agriculture

The data I use to investigate how temperature shocks affect output value span half a century, as the district-year observations begin in 1966 and end in 2015. This large span of time provides me with rich within-district variation, especially in a country such as India that has developed tremendously over the course of the past fifty to sixty years. Notably, the Green Revolution steadily increased crop yields and boosted crop production across the world beginning in the 1950s (Schlenker Reference Schlenker2019).

In addition to the large number of years that the data provides, there are also a very large number of districts across the country. The data I use have around 313 apportioned districts; essentially, these districts follow 1966 boundaries, and the data for the new districts are apportioned back to the parent districts. Both the large number of years and the large number of districts provide me with rich within-district variation to study the impact of temperature shocks on agriculture.

Figure 1 depicts the change in temperature, rainfall, and rice yields from 1966 to 2015 for districts across the country. It appears that the majority of the districts have had an increase in temperature from 1966 to 2015, which is expected given global warming. However, a sizable amount of districts have had a decrease in temperature from 1966 to 2015. This is not necessarily surprising, however, because this map captures the raw difference in temperature between the years 2015 and 1966. It does not capture the trend in temperature over time. Therefore, districts where temperature decreased from 1966 to 2015 could still have an increasing trend in temperature.

Figure 1. Change in temperature, rainfall, and log output value, 1966–2015.

In contrast to the change in temperature, the change in rainfall from 1966 to 2015 follows less of a clear pattern. Some districts appear to have had an increase in rainfall from 1966 to 2015, while other districts appear to have had a decrease in rainfall in the same time span. Once again, there is a distinction between the trend in rainfall and the raw difference in rainfall from 1966 to 2015; this map captures the latter. Nevertheless, it is not clear whether rainfall is trending upward or downward over time. This suggests that the change in rainfall from 1966 to 2015 is highly location-varying.

The change in log output value from 1966 to 2015 follows a relatively clear pattern: most districts have experienced an increase – although not all districts. Over the past fifty to sixty years, agricultural technology has drastically improved, especially in developing countries such as India. The Green Revolution in the 1950s and 1960s in particular is what spurred large boosts in crop yields (Schlenker Reference Schlenker2019). From the figure, it is clear that output value has trended upward over time.

Temperature is trending upward over time

One of the features of global warming is that land surface temperatures are increasing over time, and estimates indicate that global land surface temperatures have increased by around 0.9°C over the past fifty years (Rohde and Hausfather Reference Rohde and Hausfather2020).

Figure 2 depicts the temperature trend line for twenty states. The solid line represents the actual annual average temperature in degrees Celsius, and the dotted line represents the trend line of temperature in degrees Celsius. The trend line was constructed by taking the moving average of temperature over the past 5 years.

Figure 2. State-level temperature trends ( $^ \circ {\rm{C}}$ ).

From examining the moving average line for each state, it is indeed the case that temperature is trending over time. However, some states have experienced faster warming than other states. For instance, states such as Tamil Nadu, Uttarakhand, and Bihar display a clear upward trend in temperature, while states such as Orissa, Jharkhand, and Madhya Pradesh display a weaker (although still increasing) trend in temperature. The takeaway is that state-level temperature trends seem to be universally increasing, with some states experiencing greater warming than others.

How does climate change make farmers worse off?

My hypothesis for how climate change makes farmers worse off is depicted below:

climate change $ \Rightarrow $ greater temperature fluctuations $ \Rightarrow $ higher probability of negative income shock for farmers

The first part of the proposed mechanism is that climate change leads to greater fluctuations in average temperature. Climate patterns are rapidly shifting across the world due to climate change. Moreover, climate scientists claim that extreme weather events, such as storms and heat waves, may occur more often in the future as a result of climate change (Coumou and Rahmstorf Reference Coumou and Rahmstorf2012; Katz and Brown Reference Katz and Brown1992; Rahmstorf and Coumou Reference Rahmstorf and Coumou2011; Schär et al. Reference Schär, Vidale, Lüthi, Frei, Häberli, Liniger and Appenzeller2004). This implies that not only will the average temperature level rise over time but the average temperature level will become more volatile over time. Nonetheless, there is mixed evidence of this. Huntingford et al. (Reference Huntingford, Jones, Livina, Lenton and Cox2013) find that there is significant geographic variation in annual temperature fluctuations over the past few decades, but the time-evolving standard deviation of globally averaged temperature has remained fairly constant. On the other hand, Bathiany et al. (Reference Bathiany, Dakos, Scheffer and Lenton2018) show that climate models consistently predict that temperature variability will increase in the coming decades, particularly in tropical countries, and that this is driven by large increases in the time-evolving standard deviation over tropical land in the summer season.

To check whether average annual temperature is indeed becoming more volatile over time, I compute the state-level rolling standard deviation. This computation is done by taking the moving average of the standard deviation of temperature over the past five years. After plotting the rolling standard deviation over time (the results of which can be checked in Figure A1 in the appendix), the trend in the standard deviation of average annual temperature appears to be mixed. Some states exhibit an increase in the standard deviation of temperature, while others exhibit a decrease or no trend at all. States such as West Bengal have an upward trend in temperature volatility, while states such as Kerala have a downward trend in temperature volatility. States like Telangana and Karnataka have no discernible trend. Overall, the trend in temperature volatility is mixed.

The second part of the proposed mechanism is that greater temperature fluctuations lead to a higher probability that farmers face a negative income shock. Crops are not fully resistant to large fluctuations in temperature, so increases in temperature fluctuation would directly decrease crop output (Schlenker and Roberts Reference Schlenker and Roberts2009). In addition, weather is stochastic in the short-run from the perspective of farmers, and they thus find it difficult to anticipate the timing and intensity of temperature fluctuations (Dell, Jones, and Olkens Reference Dell, Jones and Olken2014). Moreover, given that India is a country with scarce formal insurance networks in rural areas, it is difficult for farmers to fully insure themselves against the risk of an unexpected heat shock or low rainfall (Aditya and Kishore Reference Aditya and Kishore2018). Taraz (Reference Taraz2018) finds that higher yields significantly harm yields in all Indian districts; for example, an additional day in the 27–30°C range reduces yields by 0.99%, relative to a day in the 12–15°C range. Even after taking adaptation into account, farmers are only able to recover a small portion of their lost profits, no more than 9% (Taraz Reference Taraz2017). Other studies find qualitative similar results, although the magnitude of their estimates differs. Guiteras (Reference Guiteras2009) predicts that the yields of crops in India would fall by 25 percent in the long-run (2070–2099), in the absence of adaptation. Birthal et al. (Reference Birthal, Khan, Negi and Agarwal2014) conclude long-run (2100) impacts of a 16 percent fall in yields. Blakeslee and Fishman (Reference Blakeslee and Fishman2018) estimate that positive temperature shocks are associated with nearly a 5% fall in wages during the monsoon season, and Burgess et al. (Reference Burgess, Deschenes, Donaldson and Greenstone2014) find that one standard deviation increase in high-temperature days within a given year reduces wages by 9.8%. This suggests the presence of direct temperature impacts on wages – in addition to direct temperature impacts on yields.

Growth and level effects

The literature on the impact of weather shocks on aggregate output makes the distinction between growth effects and level effects (Burke, Hsiang, and Miguel Reference Burke, Hsiang and Miguel2015; Burke and Tanutama, Reference Burke and Tanutama2019; Dell, Jones, and Olken Reference Dell, Jones and Olken2012). The “level effects” of weather shocks on output represent instances where the shock affects output solely in the initial period; that is, the effect is transitory and reverses itself. On the other hand, the “growth effects” of weather shocks on output represent instances where the shock affects output both in the initial period and in future periods. This distinction is important because the presence of these effects depends on the channel through which the weather shock affects aggregate output. Growth and level effects on output are present when temperature shocks impact institutional quality, which is linked to productivity growth (Dell, Jones, and Olken Reference Dell, Jones and Olken2012). However, only level effects on output are present when temperature shocks reduce agricultural yields (Dell, Jones, and Olken Reference Dell, Jones and Olken2012).

My study focuses solely on the agricultural channel, so I am only concerned with level effects on output. Prior studies that investigate the effect of weather shocks on aggregate output estimate distributed lag models to capture level and growth effects on output (Burke, Hsiang, and Miguel Reference Burke, Hsiang and Miguel2015; Burke and Tanutama Reference Burke and Tanutama2019; Dell, Jones, and Olken Reference Dell, Jones and Olken2012). Contrarily, the main dependent variable in my study is crop output value, and weather shocks only affect crop yields in the same period; that is, there are no growth effects present. This motivates me to construct my main estimating equation closely to the production function of Burke and Tanutama (Reference Burke and Tanutama2019), where the temperature and rainfall terms in time $t$ only affect crop output value in time t.

Determinants of agricultural production

Temperature and rainfall are indirect, albeit significant, inputs in the production of crops (Auffhammer, Ramanathan, and Vincent Reference Auffhammer, Ramanathan and Vincent2012; Lobell and Burke Reference Lobell and Burke2008; Schlenker and Roberts Reference Schlenker and Roberts2009). Moreover, temperature has nonlinear effects on crop production, with the hottest days driving the majority of the negative effect on output (Burgess et al. Reference Burgess, Deschenes, Donaldson and Greenstone2014; Guiteras Reference Guiteras2009; Moore and Lobell Reference Moore and Lobell2015; Schlenker and Lobell Reference Schlenker and Lobell2010; Schlenker and Roberts Reference Schlenker and Roberts2009). Prior studies show that temperature impacts outweigh rainfall impacts, yet very high and low levels of rainfall indeed damage yields (Fishman Reference Fishman2016; Schlenker and Roberts Reference Schlenker and Roberts2009), and that this effect is driven primarily by rainfall patterns in the growing season.

Agricultural production is broadly a function of weather, quality of the land, farmer technologies, capital, and labor. Two significant inputs in agricultural production include irrigated area and fertilizer use (Birthal et al. Reference Birthal, Khan, Negi and Agarwal2014; Deschênes and Greenstone Reference Deschênes and Greenstone2007). Fertilizer mixtures are often a combination of nitrogen, phosphate, and potash. Irrigation systems vary across India, although most irrigation in India is groundwater well based, serving around 60% of irrigated agriculture (Jain et al. Reference Jain, Fishman, Mondal, Galford, Bhattarai, Naeem, Lall, Balwinder-Singh and DeFries2021), where water pumps are used to extract groundwater for irrigation. Soil quality and soil characteristics, such as temperature, pH, and depth, are also important inputs that promote crop growth, as well as elevation of the farm location (Birthal et al. Reference Birthal, Khan, Negi and Agarwal2014; Deschênes and Greenstone Reference Deschênes and Greenstone2007). Of course, seeds are needed to plant the crops as well, in addition to pesticides and insecticides to protect the crops from invasive organisms. Technologies such as tractors are inputs which farmers have direct control over, and which affect crop production – these technologies are part of the stock of capital inputs, which include machinery that are central to the farm’s operations. Agricultural laborers perform numerous tasks related to cultivating crops, and they work out on the fields (Barton and Cooper Reference Barton and Cooper1948) – a larger number of laborers may increase crop production. The total population within a district may also affect crop production, as a larger population demands higher food consumption.

Data source

The data sets I use to conduct my analysis come from the District-Level Database for Indian Agriculture and Allied Sectors. This database was constructed by the Tata-Cornell Institute and the International Crops Research Institute for the Semi-Arid Tropics, with the intent to provide access to agriculture and nutrition data in India. Before the release of this database, there was no single platform that contained this India-specific data.

This database contains data on nearly thirty crops, spans the years 1966 to 2015, and covers 313 apportioned districts; that is, the districts follow 1966 boundaries but the data for the new districts are apportioned back to the parent districts. Moreover, it contains all the agriculture and climate-related data I need to carry out my analysis, including yields, prices, temperature, and rainfall. The data for all the variables (excluding temperature) are structured annually at the district level. Thus, each observation represents a unique district-year combination.

Data construction

In the database, temperature is recorded monthly. And the temperature data consist of only two variables: the monthly maximum and the monthly minimum temperature. To construct the annual temperature variable, I first compute the monthly average temperature by averaging the monthly maximum and the monthly minimum temperature. Then, I average over the monthly average temperatures within a particular year to obtain the average annual temperature for that year.

The database does not have variables for the crop revenues or the amount of crops sold, so I construct revenue estimates for thirteen out of the thirty crops. These 13 crops include rice, wheat, sorghum, pearl millet, maize, finger millet, barley, chickpea, pigeon pea, groundnut, sesamum, linseed, and sugarcane. I focus the analysis solely on these crops, as they are major staple crops both in India and across the globe. To construct revenue estimates, I first adjust the crop prices at harvest for inflation using the India Consumer Price Index. Then, I take the product of crop price and crop production to obtain the estimated crop revenue. The main assumption here is that all crops that were produced within district d in year t were sold at the harvest price. To compute the output value of the thirteen crops, I simply sum over the revenues of each crop.

One of the shortcomings with the database is that about half of the crop price data is missing. To address this, I adopt an imputation strategy to fill in the missing crop price observations. In particular, I employ predictive mean matching using crop-specific variables to fill in the missing crop price observations. I also employ a similar imputation strategy for control variables, including fertilizer usage and the average proportion of crop area irrigated to increase the statistical power and accuracy of my estimates. I explain in greater detail the imputation strategy as well as the data construction steps in the appendix.

Summary statistics

Table 1 shows the number of observations, mean, and standard deviation for each of the variables used in the main estimation, over the course of the entire sampling period. Panel A displays the summary statistics for the key explanatory and outcome variables, including annual average temperature, annual rainfall, and total output value. Each observation represents a unique district-year combination. The mean of annual average temperature is 25.06°C, and the standard deviation is 4.05°C. The mean of annual rainfall (in 1000 mm/year) is 1.3, and the standard deviation is 0.72. And the mean of total output value (measured in 10,000,000 Indian Rupees), which is a composite variable constructed from 13 crops ^{Footnote 1} , is 1,364.10, and the standard deviation is 1,263.62. As indicated by the standard deviation, there is significant variation in total output value.

Table 1. Summary statistics, 1966–2015

Note: The estimation is based on 313 districts and 49 years, and the table only includes district-year observations where the average yearly temperature variable is not missing.

Panel B displays the summary statistics for the control variables. The mean of fertilizer usage (measured in 100,000 tons) is 0.40, and the standard deviation is 0.49. Additionally, the mean of average proportion of area irrigated is 0.31 while the standard deviation is 0.19. Other controls employed in the analysis include total population, agricultural laborers, the area of operational holdings within districts, and the area of source-wise irrigation. Source-wise irrigation serves as a proxy for the stock of capital inputs, and the area of operational holdings proxies for characteristics of the land and the wealth of districts.

Estimating the trend in temperature over time

To quantify the aggregate trend in average annual temperature at the district level, I estimate the following equation using OLS:

(1) $${T_{dt}} = {\beta _0}yea{r_t} + {\varepsilon _{dt}}$$

On the left-hand side of the equation is ${T_{dt}}$ , which is the average annual temperature at district d in year t. On the right-hand side of the equation is $yea{r_t}$ , which spans from 1966 to 2015. Assuming a statistically significant estimate, ${\hat \beta _0} \gt 0$ would imply that average annual temperature is increasing over time at the district level.

From Table A2, the estimated coefficient is ${\hat \beta _0} = 0.013$ . Because the sampling period ranges from 1966 to 2015, the average annual temperature has trended upward by approximately 0.64°C within this span of time. This is a little lower than the estimates that indicate that land surface temperatures have increased by around 0.9°C over the past fifty years (Rohde and Hausfather Reference Rohde and Hausfather2020). Nevertheless, this estimated trend is still significantly positive and suggests that the temperature level has increased over time.

Estimating the effect of temperature on output value

To estimate the effect of temperature on output value, I use the annual mean temperature and rainfall within each district to compute simple differences, or deviations, from the mean. That is, I specify weather shocks as deviations from the annual, district-specific mean. The annual mean temperature is the average temperature over all the years within a particular district (annual mean rainfall is computed in a similar fashion), and the rest of the variables represent their respective annual values. To quantify the effect of temperature shocks on output value, I estimate the following equation using OLS:

(2) $$ln{y_{dt}} = {\beta _1}{T_{dt}} + {\beta _2}T_{dt}^2 + {\gamma _1}{P_{dt}} + {\gamma _2}P_{dt}^2 + \rho {{\bf{X}}_{dt - 1}} + {\alpha _s} + {\delta _t} + {\varepsilon _{dt}}$$

The outcome variable is $ln{y_{dt}}$ , or log output value at district d in year t. Output value is a composite variable, as it is the sum of the revenue of 13 crops. Formally, output value is expressed as follows: ${y_{dt}} = \sum\nolimits_{c \in C} productio{n_{cdt}} \times pric{e_{cdt}}$ , where c represents the crop and C is the set of all 13 crops. Production is measured in quintals, and the harvest price is measured in rupees per quintal (thus output value is measured in rupees). On the right-hand side of the equation are ${T_{dt}}$ and $T_{dt}^2$ , which represent the deviation from the annual mean in temperature and the deviation from the annual mean in temperature squared, respectively. Likewise, ${P_{dt}}$ and $P_{dt}^2$ represent the deviation from the annual mean in rainfall and the deviation from the annual mean in rainfall squared. The interpretation of my estimates is that a 1 $^ \circ $ C deviation above the annual mean temperature leads to a $({\beta _1} + 2{\beta _2})$ % change in output value. ${\alpha _s}$ and ${\delta _t}$ represent state fixed effects and year fixed effects, respectively. By employing state fixed effects, I control for the time-invariant characteristics within states that affect output value (such as the persistence of institutions, soil characteristics, and elevation). Moreover, employing state fixed effects permits me to estimate the within-state effect. By employing year fixed effects, I control for time-varying characteristics that are common across all districts. Lastly, ${{\bf{X}}_{dt - 1}}$ is a vector of time-varying characteristics that are plausibly correlated with weather shocks and output value. Using the prior year, values of the variables in this vector mitigates reverse causality.

Estimating the efficacy of mitigation mechanisms

The effect of temperature deviations from the annual mean on output value is likely varying according to the amount of irrigation and fertilizer usage within a district. I hypothesize that heat shocks decrease output value more in districts with less irrigation and fertilizer usage relative to districts with more of these two. To test this hypothesis, I estimate the following equation (separately for irrigation and fertilizer usage) using OLS:

(3) \begin{align}ln{y_{dt}} &= {\beta _1}{T_{dt}} + {\beta _2}T_{dt}^2 + {\phi _1}[1{(MitigationMechanism < x)_{dt - 1}}]\\ &\quad + {\phi _2}[{T_{dt}} \times 1{(MitigationMechanism < x)_{dt - 1}}]\\ &\quad + {\phi _3}[T_{dt}^2 \times 1{(MitigationMechanism < x)_{dt - 1}}]\\ &\qquad \quad + {\gamma _1}{P_{dt}} + {\gamma _2}P_{dt}^2 + {\alpha _s} + {\delta _t} + {\varepsilon _{dt}}\end{align}

My outcome of interest is once again log output value in district d in year t, and I once again include ${T_{dt}}$ , ${P_{dt}}$ , and their quadratic terms. To capture the differential effect of heat shocks on output value, I include interaction terms between the deviation from the annual mean in temperature at district d in year t and an indicator for if the amount of a mitigation mechanism is less than some threshold x at district d in year $t - 1$ . I use the prior year value of the mitigation mechanism to mitigate reverse causality, as it could be the case that farmers respond to poor harvests by employing more of a certain mitigation mechanism. The interpretation of the estimates here is that a 1 $^ \circ $ C deviation above the annual mean in districts below the threshold leads to a $({\phi _2} + 2{\phi _3})$ % change in output value, relative to districts above the threshold.