The impact of climate change on wheat yields
in India
Ridhima Gupta∗ E. Somanathan† Sagnik Dey‡
January 15, 2014
Abstract
Regression analysis on data from all major wheat growing districts of India
was conducted to examine the effect of temperature, solar radiation (affected
by pollution from aerosols), and rainfall on wheat yields in India. Estimates
for the model with district fixed effects and year fixed effects indicate that
a 1◦ C increase in average daily maximum temperature tends to lower yields
by 4 ± 2.7%. Solar radiation in turn had a positive effect on wheat yields.
We found a one to one relationship between a percentage increase in solar
radiation and a percentage increase in yields. The estimated weather parameter from these regressions were used to assess the impact of recent climate
trends and the impact of future climate change on wheat yields. The maximum temperature during the wheat-growing season has increased by 0.7◦ C
over the period 1981-2009. Wheat yields in India would have been higher in
2009 by 3± 1.9% if this temperature increase had not occurred. Results of the
estimation of the impact of future climate change predict even higher losses
ranging from 7± 4.7% for mid-term climate change (2010-2040) and up to
18.3± 10.6% by the end of the century.
PRELIMINARY AND INCOMPLETE DRAFT-DO NOT CITE OR QUOTE
∗
Indian Statistical Institute
Indian Statistical Institute
‡
Indian Institute of Technology
†
1
1
Introduction
With current annual production at over 92 million tonnes, India is the world’s second largest producer of wheat and wheat is the second largest crop in India. Thus,
impacts on wheat yields in India due to climate change are linked to food security
and poverty of a large population. Yet, how climate change will affect wheat yields
remains imperfectly understood. In this paper, we therefore focus on estimating
the effect of climate change on wheat yields in India. Relationships between wheat
yield and daily maximum temperature and daily minimum temperature and solar
radiation were evaluated by analysing district-level data covering the period 19812009.
Although current agronomic research on wheat has analysed the impact of high
temperature on wheat growth, it is largely based on field trials and controlled experiments (Sofield et al., 1977; Wardlaw and Moncur, 1995; Stone and Nicolas, 1998;
Rane and Nagarajan, 2004). These studies indicate that high temperatures that prevail towards the end of the growing season (grain filling stage) reduce wheat yield.
Such studies do not take into account the adaptive behaviour of farmers. Typically,
farmers respond to year to year changes in weather and adjust their practices for
example by applying more irrigation in a dry year. Responses have indeed tended
to be less severe in the field as the wheat plant was exposed to higher temperatures
in glasshouse experiments than those observed in the field (Asseng et al., 2011). A
better understanding of this relationship in real world agricultural settings is therefore required to avoid over-estimating the effect of weather on crop yields.
Previously Lobell et al. (2011) have used non-experimental data to study the impact of past climate trends on wheat yields, they have analysed aggregated data at
the country level. Thus, their estimated parameter of mean temperature is the same
over all countries. The estimate on wheat in India may be different from that elsewhere for several reasons. One important one being that Indian wheat production
is largely irrigated. Their analysis does not control for solar radiation, an important
confounder Lobell et al. (2005).
This is the first study of the impact of global warming on Indian wheat using
observational data from farms. We analyse district-level data on weather and yields
from 168 districts of India. These districts are located in the seven major wheat
producing states of the country that contribute more than 90% to the national output
and span an agricultural area of more than 200 million hectares. This region is a part
of the fertile Indo-Gangetic plains, one of the most intensely farmed and populated
2
areas in the world, where rice and wheat are grown in rotation each year.
Our findings indicate that high daily maximum temperatures reduce wheat yield.
Although the literature emphasises on the negative effects of high temperatures during grain filling, we found that the impact of high temperature on crop productivity
did not vary by the growth phase of the plant. On the contrary, the absence of temperature extremes in the data did not permit us to examine the effect of heat stress
on yields. Minimum temperature was not significant in the estimated regressions.
Solar radiation had a positive effect on wheat yields. There was a one to one relationship between a percentage increase in solar radiation and a percentage increase
in yields. This result was not robust across specifications, we attribute this to the
limited variation in solar radiation in the sample and not to the absence of an effect
of solar radiation on yields.
The estimated weather parameter from these regressions were used to assess the
impact of recent climate trends and the impact of future climate change on wheat
yields. We found that maximum temperature during the wheat-growing season has
increased by 0.7◦ C over the period 1981-2009. Wheat yields in India would have
been higher in 2009 by 3% if this temperature increase had not occurred.
Climate change predictions were derived from the Reg CM4.3 model for the
high emission scenario. The model estimates predict yield losses of 7± 4.7% for
mid-term (2010-2040) climate change and yield losses of 18.3± 10.6% by the end
of the century.
Wheat yield was regressed on district-level weather measures and district fixed
effects and year fixed effects. The weather parameters are therefore identified from
deviations from district specific variations in yearly weather from the district mean
weather. Since variations in weather between years in a district are mostly random,
they are uncorrelated with other unobserved determinants of yields thereby avoiding
the bias caused by omitted variables. The year fixed effects control for unobserved
factors such as technical progress that were common to all districts in a given year.
The rest of the paper is organised as follows. The following section describes
the data sources and summary statistics. Results of the effects of weather on wheat
yields are presented in section 3. Section 4 discusses the impact of past temperature
trend on wheat yields. Section 5 contains the predicted impacts of climate change
on future yields and section 6 concludes with policy implications.
3
2
Data and Summary Statistics
2.1
Agricultural Data
We use district-level data on agricultural outcomes primarily from two sources,
the Indian Harvest database from the Centre for Monitoring the Indian Economy
(CMIE) and the statistics released by the Directorate of Economics, Ministry of
Agriculture (MOA) 1 . The MOA reports district-level area, production and yield
and irrigated area for all major crops beginning from the year 1999. Hence prior to
1999 the observations are from the CMIE database. These data are a compilation of
the official statistics published by the state governments and the Ministry of Agriculture. Other data sources are the ICRISAT VDSA (Village Dynamics in South
Asia) unapportioned Meso database2 and the statistics complied by the Fertilizer
Association of India. These data are from the same original sources. Thus missing
data from either MOA or the CMIE was replaced by data from these sources.
The states of Punjab, Haryana, Uttar Pradesh, Bihar, Rajasthan,Madhya Pradesh,
Maharashtra and Gujarat comprise the study area. We exclude districts that were a
part of the newly created states of Chattisgarh and Jharkhand. This is because data
on the area of the wheat crop that is irrigated was largely missing for these 2 states.
Indian district boundaries change periodically as larger districts have been split
into smaller ones making it difficult to compare districts over time. To circumvent
this, any changes occurring in district boundaries after 1981 have been accounted
for. We use the 1981 districts in order to have a balanced panel so that withindistrict variation is preserved. Original district boundaries have been preserved by
merging new districts into their ‘parent’ districts. The criterion used for determining
the apportioning percent was based on the geographical area of the ‘parent’ district
transferred to the new district.
2.2
Weather Data
Daily gridded (1◦ × 1◦ ) resolution data on temperature and rainfall was obtained
from the Indian Meteorological Department (IMD). To create daily district-level
data, we construct the area-weighted average temperature and rainfall of all the grid
cells intersecting a 1981 district.
1
2
http://eands.dacnet.nic.in/LUS_1999_2004.htm
http://www.icrisat.org/vdsa/vdsa-index.htm
4
To the best of our knowledge, reliable data on surface solar radiation for most
of India is not available. Ground based measurements of solar radiation are available from as few as 12 weather stations across the country. The Surface Radiation
Budget (SRB) datasets3 too suffers from a wide data gap. To overcome this, we
collected daily-level reanalysis data on surface solar radiation from the MERRA
database4 . This data is available at the (2/3◦ ×1/2◦ ) resolution. Creation of districtlevel solar radiation data proceeds in the same way as for temperature and rainfall.
The daily temperature and solar radiation variables are then averaged over the
growing season in each year and the rainfall data is summed up over the growing
season in each year. The growing season of wheat varies across the states. It is
slightly longer in the Northwest Indo-Gangetic plains (Punjab, Haryana and Western Uttar Pradesh) than in the eastern Indo-Gangetic plains (Eastern Uttar Pradesh,
Bihar). Wheat is also planted earlier, by a month or so, in the Northwest IndoGangetic plains. Information on sowing dates and the length of the growing season
was obtained from a variety of sources such as the crop calendars published by the
Agricultural Meteorological Division of the IMD and data provided by the regional
centres of the Indian Agricultural Research Institute.
3
Results
Table 1 reports the summary statistics of the key variables of interest. Following the
literature our dependent variable is the log of yield of wheat in tonnes per hectare.
We specify linear controls for average daily maximum and average daily minimum
temperature measured in celsius and total rainfall in centimetres and take the natural log of average solar radiation in hectowatt per meter. Pairwise residual correlations after removing district and year fixed effects and scatterplots of the control
variables are shown in Appendix (Figure 2). Log solar radiation’s correlation with
maximum temperature was 0.18 and with minimum temperature was -0.255 . Both
these variables were positively and moderately correlated with each other and negatively correlated with rainfall. Solar radiation’s correlation with rainfall was smaller
in absolute value than its correlation with the temperature variables. The correlation
of the share of the wheat crop that is irrigated with the weather variables under the
study was small. These correlations suggest that we can uniquely identify the ef3
http://www.gewex.org/srbdata.htm
http://disc.sci.gsfc.nasa.gov/mdisc/
5
These refer to season averages of daily variables.
4
5
fect of maximum temperature, minimum temperature and solar radiation on wheat
yields and that a failure to account for solar radiation would bias the estimates on
the temperature variables.
All the models contain district fixed effects and year fixed effects to control for
unobserved factors that were unique to each district or year. The model is of the
form
log(Yit ) = ci + γt + β1 MaxTit + β2 MinTit + β3 log(SRit )
+ β4 Rainit + β5 ShareIrrigatedit + µit
where ci is a district fixed effect, γt is a year fixed effect, M axTit and M inTit
is the daily maximum and minimum temperature in district i in year t averaged
over the growing season, logSRit is the average log solar radiation in district i in
year t averaged over the growing season, rainit is the total rainfall in a district-year
averaged over the growing season, ShareIrrigatedit is the fraction of the wheat
crop that is irrigated and µit is the error term.
Error terms may be spatially correlated across districts within a state in a year.
This is because time varying unobserved factors such as varietal choice are spatially
correlated. Geographic regions may also have similar errors across nearby years.
Thus, we adjust the standard errors to allow for both the spatial and time-series dependence 6 following the methodology of Conley (2008) as implemented by Hsiang
(2010).
Multiple regression estimates for different specifications of the regression model
are shown in Table 2. Column 1 of Table 2 shows the results for the full model.
Maximum temperature and the log of solar radiation had opposing impacts on yield
growth. A 1◦ C increase in maximum temperature tends to lower yields by 4%.
By analysing country-level data over the period 1980-2008, Lobell et al. (2011)
found that wheat yields in India declined by 9% in response to a 1◦ C increase in
maximum temperature. As mentioned before, this estimate is biased because the
authors’ do not control for solar radiation. As the data is aggregated at the county
level, the authors’ control for country-specific quadratic time trends and country
fixed effects.
6
Spatial dependence between two observations vanishes as the distance between two districts
reaches a specified cut-off. Similarly, observations across time cease to be dependent as the temporal
period between the observations equals a specified cut-off. Throughout the analysis, we fix the
distance at 300 Kilometres and the temporal period at 2.
6
The model estimates suggest a one to one relationship between a percentage
increase in solar radiation and a percentage increase in yields. It is possible that
the lower significance of log solar radiation with year fixed effects is owing to its
limited variation over time and not because it does not influence wheat yields. The
estimated parameter on maximum temperature in absolute terms was 2 times higher
than that of minimum temperature. Minimum temperature was highly insignificant
in all specifications. The overall greater importance of maximum temperature is in
agreement with the simulation and observational studies on wheat (Rosenzweig and
Tubiello, 1996; Dhakhwa and Campbell, 1998; Lobell and Ortiz-Monasterio, 2007;
Lobell et al., 2011).
Exclusion of solar radiation caused the parameter estimate on maximum temperature and minimum temperature to decrease in absolute terms by 1.26 and 1.82
times (Column 2 of Table 1). The last column of Table 2 reports the estimates for
the sub-sample of irrigated wheat. Since unirrigated wheat can respond differently
to weather shocks than irrigated wheat, we re-estimate our models for the subsample of irrigated wheat. A district in a given year is defined as irrigated if at least 80%
of the wheat area is irrigated. Results were nearly identical for maximum temperature. Solar radiation was no longer significant in this smaller sub-sample. Although
rainfall was significant in this subsample its estimated impact was close to zero.
Next, we estimate a model controlling for mean temperature instead of maximum and minimum temperature (Table 3). Mean temperature tended to have a
negative effect on yield but the impacts were not significant across specifications.
Thus, including maximum and minimum temperature separately is more appropriate than including their mean. The estimated impact of mean temperature although
is not far removed from those reported by recent simulation studies on wheat yields
in India. These studies suggest a 2 to 5% decrease in yield potential of wheat for a
mean temperature rise of 0.5◦ C to 1.5◦ C in India (Parry, 2007).
So far the yield response to temperature has been restricted to be linear. To allow
for a non-linear relationship between temperature and yields, we model maximum
temperature using restricted cubic splines (RCS). Stone (1986) has shown that the
location of knots in a restricted cubic spline model is not very crucial, the fit is
influenced much more by the number of knots. For large sample sizes (Harrell,
2001) recommends using 5 knots and placing them at equally spaced quantiles of
the predictor’s marginal distribution. We follow this approach and run the following
specification.
7
log(Yit ) = ci + γyeart + β1 RCS(MaxTit ) + β2 MinTit + β3 log(SRit )
+ β4 Rainit + β5 ShareIrrigatedit
where ci is a district fixed effect and yeart is a year fixed effect. The underlying
relationship is indeed almost linear (Figure 1). Robustness checks indicated that the
fit was not sensitive to a change in the number or location of knots.
Temperatures exceeding a cutoff (about 30◦ C) are found to be harmful for wheat
productivity (Rane and Nagarajan, 2004; Jenner, 1991). In order to test whether the
temperature response function is different beyond a certain threshold, we model
temperature as a piece-wise linear function as in Schlenker and Roberts (2009).
The temperature variables therefore have been converted to growing degree days
(GDD) and heating degree days (HDD). Growing degree days measure accumulated
exposure to heat through out the growing season. They are calculated by integrating
the temperature time (measured in days) above a lower threshold and below a upper
threshold. Thus, if the baseline threshold is 10◦ C, a day with a temperature below
10◦ C contributes 0 growing degree days. Here we use a lower bound of 5◦ C and a
upper bound of 27◦ C. Growing degree days therefore are determined as follows:
g(h) =



0
if h ≤ 5
h − 8 if 5 < h < 27


22
if 27 ≤ h
Heating degree days (HDD) measure growing degree days above a certain lower
threshold but no upper threshold. Agricultural scientists suggest a baseline temperature of 5◦ C for Indian wheat7 . Following Schlenker and Roberts (2009), the upper
threshold of 27◦ C was determined by looping over several possible thresholds, estimating the least squares slope for each one and choosing the one with the highest R
squared. We estimate three specifications that differ in the way we model temporal
heterogeneity. The F test for testing the equality of coefficients on GDD and HDD
did not reject the null hypothesis of equality. The absence of too many observations in the extreme right of the temperature distribution may explain this finding.
Results are shown in Table 4.
7
Source: Conversations with scientists that specialise in wheat breeding.
8
An important assumption made in all our models is the time separability of the
weather effects. Thus, the effect of a very hot day on yields is independent of the
timing of its occurrence over the growing season. For checking the validity of this
assumption, we implement the approach of Welch et al. (2010). The growing season
is hence divided into three sub-seasons i.e. vegetative, reproductive and ripening.
We allowed for the weather estimates to vary across each of the three growth phases.
But we could not reject the null hypothesis of equality of the effects of the weather
variables across the plant’s different growth stages (Table 5).
So far the models do not control for fixed effects that vary by state. A countrywide year fixed effect fails to capture unobservables that are specific to each state.
However state-by-year fixed effects are too restrictive as they absorb a significant
amount of variation in weather. Alternatively, we replicate the analysis controlling
for linear and quadratic state-specific trends (Table 6). The estimated impact on
maximum temperature although significant decreases in magnitude. Results were
nearly identical when the linear state-specific trend was replaced by a quadratic
state-specific trend or by including overall trends rather than by state. Solar radiation regained significance in the models with the overall time trends. This again
reflects the limited variation in log solar radiation overtime that may lead to its
insignificance in models that allow for state-specific trends. Further, these results
indicate that time-varying unobservables that are specific to each state are uncorrelated with the weather variables. Year fixed effects impose less structure on the
model so that bias is reduced. Hence the estimates with year fixed effects are preferred to the estimates obtained after controlling for time trends.
4
Impact of Temperature trends on Wheat Yields
Over the study period, the production weighted maximum temperature in the wheat
growing region increased by 0.7◦ C. This section assesses the impact of this increase
in maximum temperature on wheat yields. Thus, we attempt to answer the question
of how wheat growth would have evolved without this trend. Maximum temperature
was de-trended by fitting a linear time trend separately for each district. For each
district-year observation, we compute the difference between predicted yields with
observed weather and predicted yields with de-trended temperature for the year
2009. To arrive at the national effect, we take a production weighted average of
these differences. The results indicate that by the year 2009 wheat yields may have
declined by 3± 1.9% relative to what would have been achieved without the trend
9
in maximum temperature over 1981-2009.
5
Climate Change Predictions
Climate change predictions are made from the Reg CM4.3 model. This is the latest
version of the regional climate model of International centre for Theoretical Physics
(ICTP). As the name suggests, regional climate models provide climate simulations
over a finer spatial resolution, therefore they are sufficiently accurate for assessing the impact of climate change. Details of the model physics and dynamics are
discussed in Giorgi et al. (2012).
We obtained monthly model output on both maximum temperature and solar
radiation. The gridded data was converted to the district-level data using the approach employed to convert the historical gridded data. We considered the (RCP)
8.5 emission scenario for climate change. This is a high emission scenario. We
compute climate change impacts for three time periods, near-future (2040), midfuture (2070) and distant future (i.e. end of the century).
One caveat of this analysis is that the district fixed effects and year fixed effects used to control for unobservable factors wipe out a great deal of variation in
weather. Hence the predicted impacts for large changes in climate that are expected
to occur in the coming decades depend on functional form assumptions. Another
consideration is the absence of days with maximum temperature exceeding 33◦ C in
the data. If days with temperatures exceeding this bound are expected to occur with
climate change then the estimated parameter of the impact of maximum temperature can no longer be applied to infer about the effect of such hot days on wheat
yields.
Climate change predictions were made as follows. We calculated the production
weighted predicted yield per acre for each district-year observation after climate
change and at the observed weather. These yield outcomes were summed across all
the districts in the sample for each year. We then computed the percentage change
in average yield per acre after climate change and at the current climate (i.e. average
over the 1981-2009 period). Results are shown in Table 7.
The aggregate impact though positive is not significant, with significant impacts
of maximum temperature being outweighed by insignificant impacts of log solar
radiation. The estimated impacts of maximum temperature predicts yield losses
of 7± 4.7% for near-future and mid-future climate change. In the absence of any
adaptation, wheat yields are expected to be lower by 18.3± 10.6% by the end of the
10
century.
6
Conclusion
In this paper we analysed the impact of climate change on wheat yields in India.
First, regression analysis on data from all major wheat growing districts of India was
conducted to examine the effect of temperature, solar radiation (affected by pollution from aerosols), and rainfall on wheat yields in India. The estimated weather
parameter from these regressions were then used to assess the impact of recent climate trends and the impact of future climate change on wheat yields.
Consistent with previous literature we conclude that high day-time temperatures
reduce yield whereas high solar radiation increases it. The latter finding was not
robust across specifications. The impact of high temperature on crop productivity
did not vary by the growth phase of the plant. Further, the absence of temperature
extremes in the data did not permit us to examine the effect of heat stress on yields.
Minimum temperature was not significant in the estimated regressions.
We found that trend in maximum temperature over the period 1981-2009 reduced wheat yields by 3± 1.9%. Results of the estimation of the impact of future
climate change predict even higher losses ranging from 7% for medium-term climate change (2010-2040) and up to 18% by the end of the century.
Although wheat yields in India have been growing over the period 1961-2008,
the rate of increase is only 1.1% per year. In many parts of the country such as
Madhya Pradesh and Uttaranchal yields are declining (Ray et al., 2013). This rate
of increase is lower than the rate of increase in population of India of 1.35% over
the period 2005-20108 . Given that wheat constitutes a major part of the diet in
India, yield needs to increase further to meet the rising demand from a growing
population.
Our results show that the past trend in maximum temperature has already led to
a significant decline in wheat production in India and future changes in maximum
temperature are predicted to be even more harmful. They signal the importance of
accelerating measures to tackle climate change such as the development of heatresistant varieties. Such developments would have a huge pay-off whereas a failure
to adapt would lead to significant shortages in wheat supply.
8
Source: United Nations, Department of Economics and Social Affairs,Population Division
(2013). World Population Prospects. The 2012 Revision, DVD Edition.
11
Table1: Descriptive Statistics
Variable
yield ( tonnes per hectare )
log yield
maxt (◦ C)
mint (◦ C)
meant (◦ C)
log solar radiation
rain (cm)
share irrigated
Number of Districts
Number of Observations
Mean
2.19
0.69
26.15
10.88
18.51
0.56
5.47
0.82
168
4866
Std. Dev
0.91
0.44
2.31
1.56
1.84
0.11
6.49
0.25
168
4866
Min
0.23
-1.48
17.44
6.01
12.03
0.16
0
0.01
168
4866
Max
5.73
1.75
32.52
15.37
23.94
0.83
73.04
1
168
4866
Notes: Values were calculated across the period 1981-2009 and the growing season. Standard deviations in parentheses.
12
Table 2: Results of Weather Variables Effect on Wheat Yields
Dependent Variable-log of yield of wheat in tonnes per hectare
maxt
log sr
mint
rain
share irrigated
Observations
R-squared
District Fixed Effects
Year Fixed Effects
Full
Model
(1)
Solar Radiation
excluded
(2)
Sub-sample of
Irrigated wheat
(3)
-0.04117***
(0.014)
0.82900*
(0.463)
0.02034
(0.015)
0.00173
(0.001)
0.30689***
(0.049)
-0.03270***
(0.012)
-0.04638***
(0.014)
0.65999
(0.472)
0.01611
(0.016)
-0.00288**
(0.001)
4,866
0.962
Yes
Yes
4,866
0.962
Yes
Yes
0.01118
(0.015)
0.00115
(0.001)
0.30263***
(0.049)
3,448
0.975
Yes
Yes
Notes: Standard errors have been corrected for spatial and auto-correlation. Figures in
parentheses are standard errors. *** indicates significance at the 1% level, ** indicates
significance at the 5% level, * indicates significance at the 10% level
13
Table 3: Results of Weather Variables Effect on Wheat Yields Controlling for
Mean Temperature
Dependent Variable-log of yield of wheat in tonnes per hectare
meant
log sr
rain
share irrigated
Observations
R-squared
District Fixed Effects
Full
Model
(1)
Solar Radiation
excluded
(2)
Sub-sample of
Irrigated wheat
(3)
-0.02571
(0.018)
0.36470
(0.442)
0.00222*
(0.001)
0.28834***
(0.048)
-0.02535
(0.018)
0.00185
(0.001)
0.28889***
(0.048)
-0.03582*
(0.019)
0.21152
(0.433)
-0.00230*
(0.001)
4,866
0.962
Yes
4,866
0.962
Yes
3,448
0.975
Yes
Notes: Standard errors have been corrected for spatial and auto-correlation. Figures in
parentheses are standard errors. *** indicates significance at the 1% level, ** indicates
significance at the 5% level, * indicates significance at the 10% level
14
0
.5
fitted log yield
1
1.5
2
Figure 1 : Fitted log yield against maximum temperature
18
20
22
24
26
28
maxt in growing season (in celsius)
30
32
Notes: The shaded region denotes the 95% confidence intervals. The model controls for
district and year fixed effects. Standard errors have been clustered by agro-climatic zones.
15
Table 4: Results of Degree Day Variables Effect on Wheat Yields
Dependent Variable-log of yield of wheat in tonnes per hectare
Linear
Trend
(1)
Quadratic
Trend
(2)
Year Fixed
Effects
(3)
-0.20382
(0.136)
-0.91537*
(0.483)
0.89776**
(0.381)
0.00014
(0.000)
0.00388***
(0.001)
-0.11954
(0.125)
-0.43751
(0.426)
0.59413*
(0.356)
0.00015
(0.000)
0.00288***
(0.001)
-0.15870
(0.159)
-0.17486
(0.453)
0.36601
(0.438)
0.00023*
(0.000)
0.00286***
(0.000)
F statistic for testing gdd = hdd
Prob > F
1.58
0.21
0.40
0.53
0.00
0.98
Observations
R-squared
District Fixed Effects
4,866
0.956
Yes
4,866
0.959
Yes
4,866
0.962
Yes
gdd
hdd
log sr
rain
share irrigated
Notes: Growing and Heating degree days are measured in 1000 days. Standard errors
have been corrected for spatial and auto-correlation. Figures in parentheses are standard
errors. *** indicates significance at the 1% level, ** indicates significance at the 5% level,
* indicates significance at the 10% level
16
Table 5: Equality tests of weather coefficients across the three growth stages
P values
Null Hypothesis
w\ linear
trend
w\ quadratic
trend
Year Fixed
Effects
(1)
(2)
(3)
maxt equal for all 3 stages
log sr equal for all 3 stages
mint equal for all 3 stages
rain equal for all 3 stages
0.25
0.64
0.71
0.17
0.98
0.98
0.73
0.52
0.17
0.18
0.19
0.49
Observations
4,866
4,866
4,866
Yes
Yes
Yes
District Fixed Effects
17
Table 6: Results of Weather Variables Effect on Wheat Yields Controlling for
State-specific trends
Dependent Variable-log of yield of wheat in tonnes per hectare
maxt
log sr
mint
rain
share irrigated
State-specific Linear
Trend
(1)
State-specific Quadratic
Trend
(2)
-0.02552***
(0.009)
0.59911
(0.402)
-0.01771
(0.013)
0.00006
(0.001)
0.53589***
(0.057)
-0.02140***
(0.008)
0.55135
(0.371)
-0.00004
(0.011)
0.00002
(0.001)
0.39299***
(0.053)
4,866
0.958
Yes
4,866
0.961
Yes
Observations
R-squared
District Fixed Effects
Notes: Standard errors have been corrected for spatial and auto-correlation. Figures in
parentheses are standard errors. *** indicates significance at the 1% level, ** indicates
significance at the 5% level, * indicates significance at the 10% level
18
Table 7: Impact of Climate Change on Wheat Yields
Percentage change in Yield
Near Future- 2040
Maximum
Temperature Effect
(1)
Solar Radiation
Effect
(2)
Total
Effect
(3)
High Emission Scenario
-7.41∗∗∗
(2.37)
Mid Future- 2070
52.19
(35.70)
40.90
(31.57)
High Emission Scenario
-7.37∗∗∗
(2.35)
Distant Future- 2099
52.54
(35.98)
41.29
(31.85)
High Emission Scenario
-18.30∗∗∗
(5.48)
52.55
(35.99)
24.64
(26.64)
Notes: Predicted impacts of climate change have been calculated as the percentage change
in average yield per acre after climate change and at the current climate (i.e. average over
the 1981-2009 period. Standard errors have been corrected for spatial and auto-correlation.
Figures in parentheses are standard errors. Sample:4866 observations from 168 districts
over the period 1981-2009 *** indicates significance at the 1% level, ** indicates significance at the 5% level, * indicates significance at the 10% level
19
7
Appendix
Figure 1: Correlations among the variables
0.0
1.0
−20 0
20 40 60
r= 0.32
r= −0.27
r= 0.079
p= <0.01
p= <0.01
p= <0.01
r= −0.25
r= 0.035
r= −0.063
p= <0.01
p= 0.014
p= <0.01
r= −0.29
r= 0.014
p= <0.01
p= 0.33
−1
r= 0.18
p= <0.01
−2
maxt
0
1
−1.0
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share.irrigated
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Notes: Correlations were calculated using residual variation in the variables after removing
the influence of district fixed effects and year fixed effects. Number of observations = 4,866.
P values are listed below the correlation coefficients.
20
−0.2
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