Working Paper on Social-Ecological Resilience SeriesNo. 2009-008
Quantifying the Impact of Climatic Change on Yields and Yield
Variability of Major Crops and Optimal Land Allocation for
Maximizing Food Production in Different Agro-Climatic Zones ofTamil Nadu, India: An Econometric Approach
By

C.R. Ranganathan
Tamil Nadu Agricultural University, Coimbatore, Tamil Nadu, India
August 2009

Vulnerability and Resilience of Social-Ecological Systems
RIHN Research Project E-04

Research Institute for Humanity and Nature (RIHN)Inter-University Research Institute Corporation, National Institutes for the Humanities

大学共同利用機関法人 人間文化研究機構
総合地球環境学研究所

Working Paper on Social-Ecological Resilience SeriesNo. 2009-008
Quantifying the Impact of Climatic Change on Yields and Yield Variabilityof Major Crops and Optimal Land Allocation for Maximizing Food
Production in Different Agro-Climatic Zones of Tamil Nadu, India:
An Econometric Approach
By

C.R. Ranganathan
Tamil Nadu Agricultural University, Coimbatore, Tamil Nadu, India
E-mail: crr_nathan@yahoo.co.in
August 2009

Vulnerability and Resilience of Social-Ecological Systems
RIHN Research Project E-04

Research Institute for Humanity and Nature (RIHN)Inter-University Research Institute Corporation, National Institutes for the Humanities

大学共同利用機関法人 人間文化研究機構
総合地球環境学研究所

Abstract
This paper provides a framework for optimal land use planning in the context of climatechange. All agricultural activities are very sensitive to climate change resulting invariability in crop yields. Hence it becomes necessary to study the effect of climatechange not only on mean yield but also on variability in yield. The quantitative
information so obtained should be used for optimal land allocation in order to utilize
natural resources in a judicious way. Previous studies using regression techniques
concentrated on the estimation of average productivity only but little attention wasgiven for optimal land allocation to competing crops with climate change induced
productivities. The problem becomes more important in the context of gradual decline inavailable land area for agriculture due to urbanization. The present study focuses onthese issues for major crops grown in Tamil Nadu State. It employs econometricmodelling for estimating the mean yield and yield variability and also covariance
between yields of different crops. The mean yields so obtained which reflect the impact
of climate change are then used in multi-objective linear programming models formeeting objectives like maximum food grain production, maximum paddy production
and minimization of agricultural land area for maintaining at least the current level ofproduction of crops etc. Finally the study attempts to link the optimal food grain
production with the projected population of Tamil Nadu for 2021 and 2026 to determine
the quantum of food grain availability per individual. The study shows thatprecipitation and temperature have varying effect on productivity and variability ofcrops. Trend has positive impact on most of the crops. Also, climate change, as dictatedby HADCM3A2a scenario, will have modest impact on crop productivities across the fivezones of Tamil Nadu. Zones where paddy is grown traditionally may witness modest
increase in productivity followed by increase in variability while many other crops may
have decrease in productivity and there is no uniformity in changes in their variability.
The study indicates that when land is the only constraint, with climate change induced
productivities, optimal allocation of crop area will result in increased production of foodgrain. These results will be useful for policy makers in finding the gap between supply
and demand of food grain for projected population.
Key words:

Impact; Climate Change; productivity; Just-Pope Production function;mean yield; yield variability; optimization

要旨

本研究では、気候変動下での最適土地利用計画のフレームワークを提供する。気候変動が農業生産へ与える影響は多方面にわたる。すべての農業生産活動は非常に気候変動に対して敏感であり、作物収量の変動を伴う。よって、気候変動の影響を平均収量のみではなく、変動について研究することが必要である。定量的な情報は自然資源の賢明な利用と土地配分の最適化のために利用されるべきである。回帰分析を使った過去の研究では、平均生産性にのみ注目し、気候変動にともなう作物生産性の競合による最適土地配分にはあまり注目していなかった。都市化によって農業用地が減少している状況では、この問題はさらに重要度を増している。本研究では、この問題をタミルナドゥ州で生産されている主要穀物について検討する。計量経済分析
により、平均収量と変動収量、そして異なる作物収量の共分散を推計する。気候変動の影響を反映している推計された平均収量は、多目的線形計画モデルによって最大穀物収量、最大米収量、現在の作物生産を維持するための最小農業用地などの目的を達成するために利用される。
最後に、本研究では、２０２１年と２０２６年のタミルナドゥ州の人口予測と最適食料穀物生産をリンクさせて、一人当たりの可能食料穀物量を決定する。研究の結果、降雨量と温度は生産性と穀物の変動にさまざまな影響を与え、また HADCM3A2a シナリオによる気候変動は、タミ
ルナドゥ州の５区域での作物生産性への影響は小さかった。伝統的な稲作地区では変動の増加と共に生産性も増加した。一方、多くの他の穀物の生産性は減少し、同一的な変化はなかった。
土地のみが制約である場合、気候変動による生産性の変化により、作物の最適配分により食料穀物の生産は増加する。これらの結果は政策決定者にとって人口予測下での穀物の供給と需要のギャップを知るために有効である。
キーワード：影響、気候変動、生産性、Just‐Pope 生産関数、平均収量、収量変動、最適化

1

1. Introduction
Climate change or global warming is an important issue on which
research is being carried out globally. It threatens to have far reachingenvironmental changes that could have severe impacts on societies throughout
the world. Climate change will have multi-dimensional effect on humanity interms of several socio-economic parameters. It could affect many sectors ofhuman life including agriculture, human health, natural disasters and sea levelrise. Of these, agriculture is prone to be affected very much due to climate change
because its input variables, viz., precipitation and temperature are mainly
climate related variables. It puts agriculture at great risk. If population growth
remains high and economic growth in the developing world is low, the impact ofclimate change will add to the number of undernourished people in the world(IIASA, 2002). Globally several studies focus on the effect of climate change on
agricultural production (Kurukulasuriya and Rosenthal, 2003; Carraro andSgobbi, 2008; Kameyama et al., 2008).
There are many studies to estimate the effects of environmental changes
on crop productivity levels using agro-economic models or regression analysis.
Assuming that climate change affects the area and productivity of crops three
approaches have been widely used in the literature to measure the sensitivity ofagricultural production to climate change; agronomic-economic models, crosssectional models and agro-ecological zone models.
The agronomic-economic method begins with a crop model that has beencalibrated from carefully controlled agronomic experiments (FAO, 2000; Kumar
and Parikh, 1998a). Crops are grown in field or laboratory settings under
different possible future climates and carbon dioxide levels keeping all farming
methods across experimental conditions fixed so that all differences in outcomescan be attributed to the climate variables, viz., temperature, precipitation, or
carbon dioxide.
In cross-sectional approach, also known as Ricardian method, farm
performances are examined across climate zones (Mendelsohn et al., 1994; 1996;

2
Kumar and Parikh, 1998b). Ricardo observed that land values would reflect land
productivity at a site (under competition). In this approach land value isregressed on a set of environmental inputs to measure the marginal contributionof each input to farm income. The approach has been applied to the United States(Mendelsohn et al., 1994; 1996). In the Ricardian analysis, prices of both inputs
and outputs are assumed to remain proportionately constant. Climateparameters are precipitation, minimum, maximum and diurnal temperature.
Usually climate normals, based on time series averages over a fairly long periodof time are considered.
The third approach to measure the impact of climate change utilizes agroecological zones (AEZ) (FAO, 1996). The main advantage associated with theagro-ecological zones is that they have been measured and published for all
developing countries (FAO, 1992). Detailed information is available about theclimate and soil conditions, crops, and technologies being used throughout thetropical zone. The AEZ model develops a detailed eco-physiological process model.
Factors such as length of growing cycle, yield formation period, leaf area index,
and harvest index etc that explain plant growth are inputs to the model. Existing
technology, soil, and climate are combined to predict Land Utilization Types(LUT). Combining these variables, the model determines which crops are
suitable for each cell. The impact of changes in climate variables on potential
agricultural output and cropping patterns are thus simulated.
In India several research studies are being done now on the effect ofclimate change on agriculture. The Indian Council of Agricultural Research has
set up a Network project to focus on the issue at various locations. India ranks
fifth among the top 25 Green House Gas(GHG) emitting countries with a share of
5.5% world GHG and it is projected to increase its emissions by 70% from theyear 2000 to 2025 (Baumert et al., 2004). Agronomic studies of India suggested
that extensive warming could cause significant reduction in yield. If temperaturerose by 4 degree centigrade, grain yield would fall 25- 40 percent, rice yields will
fall by 15-25 percent and wheat yields by 30-35 percent (Kumar and Parikh,
1998b). Mendelsohn, et al. (1994) indicated that the global warming would

3decrease net income by 8 percent. In this context, it is important to address this
impact of climate change on future crop area, production and productivity ofcrops using the available data. The agronomic studies indicate that higher
temperature are likely to be harmful in many developing countries where theclimate is marginal, water is inadequate and temperature are high. Thus theagronomic studies suggest that the countries of the temperate and polar regions
could gain productivity whereas developing countries in the subtropical andtropical zones are likely to lose productivity (IPCC, 1990).
There are studies based on Ricardian approach to quantify the impact of
global warming on crop production in Tamil Nadu State, India. For example,
Palanisami et al. (2009) employed Ricardian type analysis to study the effect ofclimate variables on area and production of three major crops of Tamil Nadu,
State India. The crops selected for study were paddy, groundnut and sugarcanethat account for major cultivated area of the state besides being grown in almost
all districts. Dependent variables considered for analysis were area and yield of
the crops. To account for Ricardian type climate variables, 30 year averages ofprecipitation, minimum and maximum temperatures and diurnal variations were
included as the independent variables. Data from HADCM3 climate change
projections for Tamil Nadu region downloaded and extracted from the GCM
outputs of IPCC SCENARIOS subdirectory available from the internet site

http://www.ipcc-data.org/sres/hadcm3_download.html were used in the Ricardian
type regressions to estimate the impact of climate change on the area, yield andproduction levels of the crops analyzed. The results show that there will be a
reduction in both area and yields of major crops by about 3.5 to 12.5 percent due
to impact of climate change. Consequently overall production will decrease
between 9 to 22 percent for these crops.
Many studies focus on the effect of climate variables on mean yield. But
fluctuation in crop yields is also important because agricultural production isvery sensitive to changes in precipitation and temperature both of which areclimate variables. This aspect has been studied only to a much lesser extent(Bindi et al. 1996, Mearns et al., 1997). In the recent past econometric models are
employed to study the impact of climate change on yield and yield variability.

4
Chen et al. (2004) and Isik and Devadoss (2006) have used regression analysis byapplying a Just-Pope (1978) production functional form to simultaneously
estimate the mean and variability in crop productivity. Chen et al. (2004) showedthat changes in climate modify crop yield levels and variances in a crop-specificfashion. For sorghum, rainfall and temperature increases are found to increase
yield level and variability. On the other hand, precipitation and temperature areindividually found to have opposite effects on corn yield levels and variability.
Isik and Devadoss (2006) employed Just-Pope production function to
analyze the impacts of projected climate change on the yield of wheat, barley,
potato and sugar bees in Idaho, USA. The explanatory variables used were total
precipitation, temperature and trend. Their results showed that climate change
will have modest effects on the mean crop yields, but will significantly reduce thevariance and covariance for most of the crops studied.
The main thrust of quantifying the impact of climate variables on crop
production is for formulating optimal allocations of agricultural land among crops
and for crop production mix. It seems this aspect has not been studied in depth sofar. Optimal allocation of land area in the light of climate change will definitely
help to use the natural resources in a judicious way. The climate change induced
productivities can be used to estimate maximum possible production under
different climate change scenarios by formulating suitable optimization models.
It will help for optimal land use planning and allocation. The optimality isachieved by selecting suitable objective functions. Possible objectives are
maximizing food grain production, maximizing paddy production (because paddy
is the staple food grain for majority of people in the study area of the present
paper) and minimizing agricultural area. This becomes a multi goal linear
programming problem with constraints on land area, water, labour and otherresources. It is a suitable tool to predict the possible changes in the food grain
production and utilization of resources under different climate change scenarios.
This model has been used in several studies for land use planning at the statelevel (Aggarwal et al., 2001), sub-regional and regional level (Schipper et al.,
1995; Veeneklaas et al., 1991), village level (Huizing and Bronsveld, 1994) and5farm level (Schans, 1991). In all these studies climate change was not taken into
account to project the optimal land allocation.
Accordingly the purpose of the present study is three fold, viz.
 to quantify the mean and variability in agricultural production in Tamil
Nadu State, India due to climate change.
 to use the climate change induced crop productivities for optimal land
allocation during 2020 with multiple goals (such as) i) maximization of foodgrain production ii) maximization of paddy production and iii) minimum
agricultural land area required to maintain at least the current level ofproduction
 to examine the food security by linking the projected production of crops
and population levels of Tamil Nadu for the years 2021 and 2026.
Thus the results presented in the study will help to formulate methods forresilience from the effects of climate change.
This study contributes to the literature in three ways, viz., it employs an econometric model to examine the impact of climate variables
not only on mean yield but also on the variability in yield.
 it uses the climate induced productivities for optimal land allocation withseveral objectives.
 it links food security with population projection in the light of climatechange.
The outline of the paper is as follows: Section 2 describes the econometricmodel employed to estimate the mean, variance and covariance in productivity ofcrops. Section 3 describes the study area, crops and variables included for the
study. Empirical analysis results which include estimated production functions
their properties, elasticities of production and covariance between productivities

6of crops are presented in section 4. Section 5 describes the effects of climatechange on mean and variance of crop productivities. Optimal land allocations
among competing crops in the context of climate change induced productivities
using multi-goal linear programming are presented in section 6. A brief analysis
linking population projection and food grain availability is included in section 7
whereas section 8 presents conclusions and last section presents the limitationsof the present study and scope for future research.

2. Econometric modelling and multi-goal linear programming
In the present study we focus on the impact of climate change on major
crops production in Tamil Nadu using an econometric approach. Following Chenet al. (2004) and Isik and Devadoss (2006), we assume that the relation between
productivity (production per hectare) yit of a crop at agro-ecological zone i during
year t and the climatic variables xit viz., precipitation and temperature is givenby the Just–Pope stochastic production function (Just and Pope, 1978):yit  f  xit ;    it h xit ;  0.5

(1)

where it is the stochastic term with mean zero and variance  2 and  and are the production function parameters to be estimated using historical data.
The independent variables (xit) used for the estimations include a constant,annual precipitation (P), temperature (T), trend (t) and 4 zonal dummy variables.
The expected crop productivity is given by E  yit   f  xit ;   and crop variability
is given by V  y it     h xit ;   . Hence the functions f  xit ;   and h xit ;   are2

called mean and variance functions respectively. The derivatives of the variancefunction h xit ;   w.r.t. the input variables, viz., precipitation and temperature
can be used to identify whether a climate variable increases or decreases crop
variability. So if, hx  0 , it indicates that the corresponding input variable x is
risk increasing , if hx  0 implies risk decreasing. Thus by employing Just-Popeproduction function, not only the mean yield but also yield variability and effectof an input variable on risk also can be simultaneously estimated.

7
Estimation of the above production function can be considered as
estimation with heteroscedastic errors as in the following equation (Saha et al.,
1997; Kumbhakar, 1997)yit  f  xit ;    uit
where uit  it h xit ;  

0.5

(2)

with E uit   0 and Var uit    2 h xit ;   . There are

two approaches suggested in many studies to estimate the mean and variancefunctions of the Just-Pope production function. They can be estimated using
feasible generalized least squares or the maximum likelihood method. However,
Saha et al. (1997) have shown that the estimators under the maximum likelihood
method are consistent and more efficient than the feasible generalized leastsquares method. Hence in our study maximum likelihood method was used toestimate the Just-Pope production function.
Before that, the forms of the mean and variance functions have to be
explicitly specified. For this it was assumed that the zonal effects are fixed. Thisin turn implied the use of zonal dummy variables. Following Isik and Devadoss(2006), the following two specific forms are assumed for the mean functionf  xit ;   . i) linear form:f xit ;  , d    0  1P   2T   3t i  R 1

 di Di(3)i 1and ii) quadratic form:f  xit ;  , d    0  1P   2T   3t   4 P 2   5T 2   6 PT i  R 1

 di Di(4)

i 1

where Di, i=1, 2,...,4 are the zonal dummy variables taking values 1 and 0. The
variance function  2 h xit ;  ,  with  2  1 was assumed to have exponential
form
i  R 1hxit ; ,   expxit  D   exp  0  1P   2T   3t  i Di 


i 1



(5)

8
This form was introduced first by Harvey (1976) and subsequently
employed by several studies (Isik and Devadoss (2006), Isik and Khanna (2003),
Asche and Tveteras, (1999)). The main advantage of this form is that it ensurespositive output variance. Another advantage is that the riskiness of an input
variable can be readily obtained by the sign of the coefficient of that variable in
the function. For example, with the above functional form, it can be easily
checked thath
 1h . Since the variance function h is always positive,P

precipitation will be risk increasing if 1 >0 and it will be risk decreasing if 1 < 0.

Estimation of the parameters
Under the assumption that  it ~ N 0,1 the Likelihood function is given by
1

N





T R 
1  2
 1  22
L     
 exp  yit  f xit ;   / 2h xit ;   2  t 1 i 1  hxit ;   (6)where R is the number of zones and T is the number of time periods and N=RT.
So the log likelihood function is given by
T R
T Ry  f xit ;  2 
1
ln L    N ln 2    ln hxit ;     it



2 
h
x
;


it
t 1i 1t 1i 1

(7)

which has to be maximised to estimate the parameter vectors β and δ.

Estimation of covarianceFarmers usually produce more than one crop in a given year. So it isimportant to determine how the covariance among crops is affected by theclimate variables. For this, after estimating the production functions, we
computed the residuals for the kth and jth crops: uitk  yitk  f  xitk ;  k  ;uitj  yitj  f xitk ;  j where βk and βj are the parameter vectors corresponding to
kth and jth crop respectively. Then the observed covariance between kth and jthcrops is given by uitk uitj and it is assumed that, for simplicity, this product islinearly related to the climate variables and so we run the following regression

9line u k u j   0  1P   2T   3t   to estimate the effect of climate variables on
the covariance between crops.

Multi-Goal Linear Programming:
Multi-Goal Linear Programming (MGLP) is an effective tool in addressing
the situations where multiple goals are to be handled when the resources areconstrained.

In this study, after estimating the climate change induced

productivities of crops, they were used for obtaining optimum land area to satisfy
the following objectives and constraints:

I. Objective Functions:a)Maximization of food grain production during 2020b)

Maximization of paddy production during 2020c)

Minimization of agricultural area needed for normal production during
2020.

a) Maximization of food grain production (this includes paddy, sorghum , maizeand pulses) in the five agro-ecological zones of Tamil Nadu
The objective function coefficients are the productivities of food grain
crops (in tonnes/ha) in five agro-ecological zones in three seasons. The following
constraints were imposed:i)total land area used in each season in each agro-ecological zone by eachone of the nine food crops is less than or equal to maximum land area
availableii)

areas under annual crops viz., sugarcane and banana are same in all
the three seasonsiii) production of each one of the five crops(viz., cotton, chillies, sugarcane,banana and groundnut) should be at least equal to their normal levelof productioniv) share of paddy area in North Eastern, Cauvery and Southern zones ineach season should be maintained (these are traditionally ricecultivating zones).

10
An analysis of percentage share of paddy area in each season in each zoneshows that out of the five zones, North East, Cauvery Delta and Southern zones
occupy major share as shown in the following table:
Percentage share of each zone in paddy area
Zone
Season 1 Season 2
Season 3
NE
48
25
69
NW
12
7
8
W
5
4
2
CD
22
33
8
SZ
13
31
13
Total
100
100
100
It is likely that these shares of the zones should be continued in futurealso. Hence constraints were added to reflect the above percentages for the threemajor zones, viz., NEZ, CDZ and SZ. For example, the constraint for NEZ for firstseason will be
0.52NEZarea – 0.48NWZarea -0.48WZarea-0.48CDZarea-0.48SZarea ≥0
andv)

total cropped area under all crops is less than or equal to normal croparea.

b) Maximization of paddy production:
The objective function is sum of productivities of paddy in 5 zones in eachseason and all the constraints that were imposed for maximizing food grain
production were applied here also.
c) Minimization of agricultural area for maintaining at least normal production
This objective ensures that at least the normal productions of all crops aremaintained with minimum agricultural area. So the objective function is the sumof agricultural area allotted to each crop in each season in each zone and all theconstraints used for maximizing food grain production were used here also.

3. Study area, data used, variables and their trends
The study area is Tamil Nadu State, India. Based on precipitation
distribution, irrigation pattern, soil characteristics and other physical, economic

11and social characteristics, India is classified into 93 agro-climatic regions andTamil Nadu falls into seven agro climatic zones: North East, North West, West,South, Cauvery Delta, High Precipitation and High Altitude (Fig.1)

Fig.1. Agro-Climatic Zones of India and Tamil Nadu Statea) Crop Area
Table 1 summarises the districts and geographical area falling under eachzone of Tamil Nadu. The present study focuses on the first five zones of Tamil
Nadu and it excludes high precipitation and hilly zones which occupy less than
4% of the geographic area. Of the five zones, the Southern zone and North Eastzone rank the first two places with 31.8% and 24% of the total area. The study
aims to quantify the impact of CC on the major nine crops viz., paddy, sorghum,
maize, cotton, chillies, pulses, sugarcane, groundnut and banana. Historical dataon area and production of these crops for the 30 years period, 1976-77 to 2005-06
were collected from the Government of Tamil Nadu publication, Season and Crop

Report for the above periods. The data are available district wise only. So zone
wise area and production were estimated by aggregating the figures for the
districts which correspond to each zone. Fig.2 provides average percentage shareof area of these crops in each zone during the last five years viz., 2001-02 to 200506. Paddy is the major crop in the three zones North East, Cauvery Delta, North
East and Southern with shares in the respective zones being 67%, 50% and48%.Groundnut and Sorghum are respectively predominant crops in North West

12
and Western zones with shares 24% and 29%. In all zones combined, paddy isgrown in about 44% of the total cropped area followed by groundnut and pulses
each grown at 15% of the cropped area.
Table 1. Agro-Ecological Zones and Districts of Tamil Nadu
Zone

North East

North West

WesternCauvery Delta

Southern

High Precipitation
Hilly

Districts
Kancheepuram
Thiruvallur
VelloreThiruvannamalai
Cuddalore
Villupuram
Total
Salem
Namakkal
Dharmapuri
Krishnagiri
Perambalur
Total
Erode
Coimbatore
Karur
Total
Thanjavur
Nagapattinam
Thiruvarur
TrichyTotal
Pudukkottai
MaduraiDindugul
Theni
RamnadSivagangai
Virudhunagar
Thirunelveli
Thoothukudi
Total
Kanniyakumari
The Nilgiris

Geographical area
(sq.km.)
4481
3550
6077
6190
3706
7190
31194
5245
3404
4498
5124
3694
21965
8209
7469
2901
18579
3476
2417
2377
4511
12781
4651
3696
6058
2869
4175
4143
4283
6810
4621
41306
1684
2549

Percentage shareto total area

24.0

16.9

14.3

9.8

31.8
1.3
2.0

13

Fig.2. Shares of crop areas in different agro-ecological zones of Tamil Nadu
The total cropped area in Tamil Nadu has declined gradually over years.
Table 2 presents the difference between normal area in ‘000ha (average
agricultural area for the last five years viz., 2001-02 to 2005-06) and the base line
area (average agricultural area for the last thirty years viz., 1976-77 to 2005-06).
It shows that except for maize, sugarcane and banana, area under all other crops

14
have decreased and the total cropped area has also decreased from 4808.15‘000ha to 3922.67 ‘000 ha, a decrease of 18.4%. This decrease in cropped area
coupled with demand for higher productivity and production due to population
explosion, imply that land area has to be optimally allocated to meet the targets
of production.
Table 2. Difference between normal and baseline cropped area (‘000ha)
Zone

Paddy

Sorghum

Maize

Sugarcane

CottonGnut

Chillies

BananaPulses

Total

NEZone-126.35-24.99

4.18

20.76

-3.12

-97.86

-1.48

1.19

23.07

-204.59

NWZone1.65-28.17

38.55

8.20

-6.88

-37.521.18

0.23-30.21-52.98Wzone-31.40-37.10

13.10

4.16

-13.97-40.19

-1.54

7.21

-11.46-111.19

CDZone-136.92-62.75

3.66

-6.71

-4.43

-50.66

-7.61

-2.31

-27.27-295.01

Szone-100.77-39.07

35.87

7.13

-74.42-55.01

4.27

4.69

-4.40

-221.71

Total-393.79-192.08

95.35

33.53

-102.83-281.24

-5.19

11.01

-50.26-885.48b)

Crop Production
Crops productions exhibit wide variation between the zones. Table 3

exhibits the normal productions, viz., average agricultural production for the last
five years viz., 2001-02 to 2005-06. North East zone produces 1726.3 kilotons of
paddy followed by Southern and Cauvery Delta zones with 1252.9 and 1088.5
kilotons respectively. These are respectively 37, 27 and 23 percentages of thetotal production of paddy. Similarly Southern zone produces 39% of sorghum,
Table 3. Normal production of crops in different agro-ecological zones ofTamil Nadu (in kilotons)
Zone

Paddy

Sorghum Maize Sugarcane Cotton Groundnut Chillies Banana

PulsesNE Zone1726.317.3

9.1

12852.4

19.3

523.8

1.9

403.3

50.6

NW Zone

359.4

73.1

61.8

4724.9

44.5

212.2

3.3

177.3

53.1

W Zone

209.5

39.6

44.3

4901.1

20.8

94.2

2.2

605.3

21.1

CD Zone1088.518.6

8.1

2364.6

16.8

45.9

2

580.7

33.9

S Zone1252.994.4

96.1

3980.2

56.6

121.5

30.3

1436.4

53.6

Total

4636.6

243

219.4

28823

158

997.6

39.7

3202.9212.2

North West zone (30%) and Western zone (16%). Again, Southern zone produces
maximum percentage of maize (44%), followed by North Western zone (28%) and15
Western zone (20%). The first three percentages of production of other crops indifferent zones are provided in the Fig.3.

Fig.3 Shares of Agro-Ecological Zones in crop production in Tamil Naduc) Crop Productivity
Table 4 gives the descriptive statistics of the crop productivity for eachcrop in each zone. West zone has the highest productivity of paddy with anaverage of 3.507 tons/ha followed by North West zone with productivity of 2.964
tons/ha. It should be noted that these two zones rank the last two places among
the five zones in terms of area under paddy. Among the other three major zones
for paddy production, North Eastern zone has a productivity of 2.768 tons/ha.
The average productivity of all the five zones is 2.863 tons/ha. Both North
Western zone and Cauvery Delta zone have high variability in productivity withstandard deviations of 0.743 and 0.741 tons/ha. Southern zone has the highest
mean productivity of 1.222 tons/ha for Sorghum and Western zone has the lowest
mean productivity of 0.516 tons/ha. Cauvery Delta zone has the highest mean
productivity of 2.027 tons/ha for Maize with a standard deviation of 0.618
tons/ha. Among the five zones, the productivity of cotton by Western zone ismaximum followed by North Eastern zone. But the Western zone has highest
variability in productivity with a standard deviation of 0.735 tons/ha. The
highest productivity of Chillies is 1.034 tons/ha by North Eastern zone.

16
Table 4. Descriptive statistics of the crop productivity
Zone
Paddy (tons/ha)
Mean
Std.
Min
Max
Sorghum (tons/ha)
Mean
Std.
Min
Max
Maize (tons/ha)
Mean
Std.
Min
Max
Cotton (bales/ha) (inbales of 170 Kg lint each)
Mean
Std.
Min
Max
Chillies (tonnes/ha)
Mean
Std.
Min
Max
Pulses (tonnes/ha)
Mean
Std.
Min
Max
Sugarcane (tonnes/ha)
Mean
Std.
Min
Max
Groundnut (tonnes/ha)
Mean
Std.
Min
Max
Banana (tonnes/ha)
Mean
Std.
Min
Max

NEast

NWest

West

Cauvery
Delta

Southern

Tamil
Nadu

2.768
0.575
1.692
3.608

2.964
0.743
1.81
4.994

3.507
0.727
2.229
4.792

2.613
0.741
1.647
4.983

2.463
0.668
1.442
3.73

2.863
0.775
1.442
4.994

1.17
0.228
0.787
1.68

1.035
0.275
0.504
1.63

0.516
0.14
0.303
0.784

0.758
0.238
0.361
1.329

1.222
0.26
0.74
1.845

0.94
0.353
0.303
1.845

1.564
0.374
0.784
2.606

1.55
0.384
0.977
2.754

1.297
0.231
0.958
2.056

2.027
0.618
1.072
2.952

1.789
0.53
0.994
3.211

1.645
0.506
0.784
3.211

2.041
0.705
1.181
4.123

1.831
0.478
0.859
2.958

2.363
0.735
1.004
4.701

1.701
0.461
0.896
2.78

1.293
0.275
0.826
1.847

1.846
0.656
0.826
4.701

1.034
0.287
0.597
1.91

0.636
0.305
0.306
1.916

0.784
0.459
0.177
2.895

0.708
0.272
0.262
1.499

0.653
0.304
0.3
2.111

0.763
0.359
0.177
2.895

0.452
0.070
0.309
0.590

0.434
0.096
0.234
0.597

0.354
0.077
0.219
0.582

0.339
0.087
0.153
0.509

0.384
0.061
0.237
0.472

0.392
0.090
0.153
0.597

99.5589.097
77.463115.198103.266
13.50944.369119.356112.641
8.460
93.833131.298

104.955
8.488
82.780119.322106.153
12.22982.263144.227105.315
11.27744.369144.227

1.419
0.376
0.827
2.133

1.313
0.338
0.583
1.893

1.402
0.269
0.733
1.842

1.417
0.340
0.945
2.162

1.304
0.327
0.857
1.889

1.371
0.332
0.583
2.162

29.0558.977
14.09054.77531.74510.08215.92950.89031.4159.242
16.44748.44834.9169.353
19.87953.23133.882
11.39416.56256.34832.2039.930
14.09056.34817d) Trends in Crop Productivity
Fig.4 gives a graphical representation of the trends in productivity ofcrops zone wise and Table 5 gives the growth rates of productivities in different
agro-ecological zones of Tamil Nadu. The results show that in all the zones
productivity of paddy has registered an increasing trend. The Southern zone has
the highest growth rate of 1.91% and the Cauvery Delta zone has the lowest
growth rate of 0.82% during the past thirty years. The positive growth rate inproductivity of paddy in all the five zones can be attributed to the adoption of new
hybrid varieties and new technologies by the farmers. Sorghum (also known as
cholam), cotton and chillies had slightly decreasing productivity trend over years
while all other crops showed increase in productivity. The overall growth rate ofproductivity of banana was highest with 2.83% followed by groundnut with 2.28%.

Fig.4. Trends in zone wise productivity of different crops

18
Table 5. Growth Rates (%) of productivity of crops in different Agro-EcologicalZones of Tamil Nadu
Paddy Sorghum Maize Sugarcane Cotton Groundnut Chillies Banana Pulses
NE Zone

1.82

-0.58

0.83

0.63

0.11

2.66

-1.79

2.50

1.82

NW Zone

1.84

1.38

0.54

0.49

-0.22

2.05

0.73

3.09

1.84

W Zone

1.76

-2.35

0.68

0.26

-2.26

1.57

1.00

2.51

1.76

CD Zone

0.82

-0.88

0.92

0.20

1.06

2.33

1.14

2.48

0.82

S Zone

1.91

0.07

0.89

0.63

0.04

2.19

-1.66

3.53

1.91

Tamil Nadu

1.59

-0.28

0.82

0.44

-0.15

2.28

-1.28

2.83

1.59

e) Crop growing months
The crop growing seasons and months vary over zones. However, for the
purpose of the present study, based on the common growing seasons andrecommendations from Tamil Nadu Agricultural University and Department ofAgriculture, Government of Tamil Nadu (Crop Production Guide), Table 6 was
prepared showing the months in which various crops are grown.
Table 6. Growing months of crops in Tamil Nadu
Crop

Jan

Feb

Mar

Apr

May

Jun

Jul

Aug

Sep

Oct

Nov

Dec

Paddy

0

0

0

0

0

1

1

1

1

1

0

0

Sorghum

0

0

0

0

0

1

1

1

1

0

0

0

Maize

0

0

0

0

0

0

0

1

1

1

1

0

Cotton

1

0

0

0

0

0

0

1

1

1

1

1

Chillies

1

1

1

1

0

0

0

0

0

0

0

0

Pulses

0

0

0

0

0

0

1

1

1

1

1

0

Sugarcane

1

1

1

1

1

1

1

1

1

1

0

0

Groundnut

0

0

0

0

0

1

1

1

1

0

0

0

Banana
1
1
1
1
1
1
1
1
1
1
1
1
An entry 1 in a cell means that the crop in the row is grown in the month specified in
the columnf) Climate variables
The present study aims to quantify the impact of the climate related
variables, viz, precipitation and temperature on the productivity of crops. The
precipitation data are the time series of the total precipitation within a year, that
is, annual precipitation and it reflects both precipitation falling directly on a cropand inter-seasonal water accumulation within a year. These data were obtained
from India Meteorological Department, Pune for the thirty year period. Data for19
stations that belonged to each zone were pooled and average precipitations were
worked out to estimate the precipitation for each zone. Table 7 provides asummary of the descriptive statistics related to precipitation used in the present
study. It shows that Cauvery Delta Zone had the highest mean annual
precipitation of 11.291 cm with a standard deviation of 1.89 cm. The Western
Zone had the highest variability in precipitation with a standard deviation of
3.39 cm. It had the lowest mean precipitation of 6.84 cm. On the average, Tamil
Nadu had an average precipitation of 9.59 cm during the period under study.
Table 7. Average precipitation (in cm) in different zones

Precipitation(cm)

VariableZone
N EastN WestWest
Cauvery Delta
Southern
Tamil Nadu

Mean
11.0298.985
6.839
11.291
9.813
9.591

Std.
2.314
1.660
3.390
1.887
1.467
2.745

Min
6.799
5.365
4.201
7.155
7.189
4.201

Max
17.29912.55322.71615.29913.80422.716

Temperature data for each crop were worked out for each zone as theaverage of the observations for the growing season of the crop. The summary
statistics for the temperature data used in the presented study are reported inTable 8. The trends in average temperature during growing seasons of different
crops in the five zones are depicted graphically in Fig.5.
The mean precipitation and temperature of the observed data for theperiod 1976-77 to 2005-06 for each zone constitute the baseline scenario climate
variables.
To project the mean and variance of crop productivity due to climatechange, data for the period 2010-2039 from HADCM3 climate change projections
for Tamil Nadu region were downloaded and extracted from the GCM outputs of
IPCC SCENARIOS subdirectory available from the internet site http://www.ipcc-

data.org/sres/ hadcm3_download.html. This website provides the values for a
combination of 7008 grids with 96 longitudes starting from 0.00o E to 356.25o E

20Table 8. Descriptive statistics of the Temperature (oC) Data
Zone
Paddy
Mean
Std.
Min
Max
Sorghum
Mean
Std.
Min
Max
Maize
Mean
Std.
Min
Max
Cotton
Mean
Std.
Min
Max
Chillies
Mean
Std.
Min
Max
Pulses
Mean
Std.
Min
Max
Sugarcane
Mean
Std.
Min
Max
Groundnut
Mean
Std.
Min
Max
Banana
Mean
Std.
Min
Max

N EastN WestWest

Cauvery
Delta

Southern

Tamil
Nadu

29.61
0.38
28.83
30.33

28.44
0.34
27.74
29.21

27.05
0.46
25.91
28.17

29.55
0.49
28.28
30.51

26.29
0.26
25.74
26.92

28.19
1.39
25.74
30.51

30.09
0.41
29.31
30.88

28.74
0.39
27.89
29.66

27.09
0.47
25.81
28.29

29.94
0.49
28.65
30.87

26.62
0.30
26.03
27.42

28.50
1.49
25.81
30.88

28.08
0.35
27.40
28.76

27.42
0.33
26.81
28.10

26.66
0.41
25.79
27.60

28.39
0.49
26.99
29.39

25.28
0.23
24.82
25.73

27.17
1.18
24.82
29.39

26.85
0.28
26.17
27.44

26.57
0.31
26.11
27.18

25.92
0.37
25.13
26.70

27.34
0.44
26.17
28.09

24.43
0.24
24.06
24.89

26.22
1.06
24.06
28.09

27.28
0.42
26.12
28.40

28.15
0.46
27.07
29.17

27.55
0.50
26.45
28.63

27.78
0.54
26.01
28.75

24.70
0.38
23.70
25.88

27.09
1.32
23.70
29.17

28.51
0.38
27.76
29.23

27.71
0.34
27.09
28.42

26.68
0.41
25.75
27.68

28.74
0.48
27.41
29.72

25.57
0.25
25.07
26.16

27.44
1.24
25.07
29.72

28.95
0.29
28.12
29.45

28.59
0.27
28.01
29.07

27.49
0.42
26.54
28.39

29.01
0.48
27.74
29.84

25.80
0.25
25.15
26.54

27.97
1.27
25.15
29.84

30.09
0.41
29.31
30.88

28.74
0.39
27.89
29.66

27.09
0.47
25.81
28.29

29.94
0.49
28.65
30.87

26.62
0.30
26.03
27.42

28.50
1.49
25.81
30.88

28.32
0.26
27.63
28.75

28.05
0.26
27.48
28.55

27.06
0.39
26.14
27.89

28.48
0.46
27.27
29.22

25.36
0.24
24.79
26.03

27.45
1.21
24.79
29.22

21

Fig. 5 Average temperature during growing seasons of different crops
at an increment of 3.75o and 73 latitudes starting from 90.0oN to 90.0oS with anincrement of 2.5o. Tamil Nadu has six regions falling in the grid range 75o to
82.5o longitude and 7.5o to 12.5o latitude (Fig.6).
The mean precipitation and temperature so computed are called projectedvalues. Table 9 below gives the baseline and projected climate variables andexpected percentage increases. Thus the HADCM3 climate change projections
predict that there will be an 8% increase in precipitation in Cauvery Delta zone.
Similarly Southern zone will have an increase of 6.1% in precipitation during
2010-39. In other zones the increase will be comparatively less. The percentage
increase in temperature will be between 2.8 to 3.5 in the five zones withmaximum percentage increase of 3.5% in North East zone.

22
Fig.6 Climate change scenario - Regionalization
Based on HADCM3 runs
Latitude : 2.5 degLongitude : 3.75 degree
Tamilnadu has 6 regions
Region 1: Northeast(78.75 to 82. l on x 12.5 to 15 lat)
Region 2: Northwest(75 to 78.5 lon x 12.5 to 15 lat)
Region 3: Centraleast(78.75 to 82.5 lon x 10 to 12.5 lat)
Region 4: Centralwest(75 to 78.75 lon x 10 to 12.5 lat)
Region 5: Southeast(78.75 to 82.5 lon x 7.5 to 10 lat)
Region 6: Southwest(75 to 78.75 lon x 7.5 to 10 lat)

Table 9 Baseline and projected climate variables
zone

Baseline
Precipitation(in cm)2010-39
Precipitation(in cm)Percentage
Increase

Baseline
Temperature(oC)

2010-39
Temperature(oC)

Percentage
Increase

NEZ

11.0

11.3

2.1

28.3

29.3

3.5

NWZ

9.0

9.0

0.2

28.0

28.8

2.8

WZ

6.8

6.9

1.6

27.1

27.8

2.6

CDZ

11.3

12.2

8.0

28.5

29.4

3.2

SZ

9.8

10.4

6.1

25.4

26.0

2.6

4. Empirical Analysis
Before fitting the production functions, it is important to test whether
there exists significant differences between zones in productivity of crops.
Introduction of dummy variables for the zones in the empirical model describedin section 2 is justified only if the crop productivities differ significantly acrossthe zones. This was tested by performing analysis of variance for each crop withzones as treatments and crop productivities for each year as observations with
the null hypothesis that there is no difference between the five agro-ecologicalzones w.r.t. productivity of the crops under study. The tests showed that except
for Sugarcane, Groundnut and Banana for all other crops the productivities differ

23
significantly and so for all these six crops introduction of dummy variables forthe zones was justified.
Next for each crop, the Just-Pope production function was estimated by
maximizing the log-likelihood function (equation 7) separately for linear andquadratic mean functions. Table 10 provides the estimated coefficients for themean functions and variance function, standard errorsof the coefficients, log-

likelihood function, Wald’s chi-square statistic and the root mean square error.
The sign and significance of the estimated coefficients for the precipitationin the mean function for paddy differ between the two alternative functional
forms. In the linear form, precipitation had strong (1%) negative influence on
productivity whereas it had weak (10%) positive effect for the quadratic form. For
temperature the sign of the coefficient is positive for both forms but the level ofsignificance is different; it is not significant in the linear form but strongly
significant in quadratic form. The square terms of precipitation and temperatureand their interaction terms all have negative effect on mean paddy productivity.
Trend has positive and significant impact on productivity at 1% level for bothlinear and quadratic forms. The Western zone dummy variable was strongly
significant for both forms. All other dummy variable coefficients are notstatistically significant. For the variance function of paddy productivity,
precipitation had significant negative impact and the impact of temperature issignificant and positive. This means that precipitation is a risk decreasing input
variable and temperature is a risk increasing input. That is, higher the
precipitation lower will be the variability in productivity of paddy and higher thetemperature, higher will be the variability. For both linear and quadratic models,trend had positive and significant impact on variability as in the case of meanfunction. Since time variable is used as a proxy for technology, this implies that
paddy productivity increases over time because of the technological progress butat the same time yield variability also increases. This finding confirms theresults of Isik and Devadoss (2006) and that of Anderson and Hazell (1987) who
found that improved technology augments both the mean and variability of crop

24

Table 10. Just and Pope Production Function – Parameter Estimates
Mean
Productivity
Precipitation(R) (in Cm)
Temperature(T)(in oC)
Trend(year)
R2
T2
R*T
NE zoneNW zoneW zoneCD zoneConstant
Variability in
Productivity
Precipitation(R)
Temperature
(T)
Trend
NE zoneNW zoneW zoneCD zoneConstant
Wald'sChiSq.
Likelihood
Fun.
RMSE~

Paddy
LinearQuadratic
Coefficient Std.Err. Coefficient Std.Err.

Sorghum
LinearQuadratic
Coefficient Std.Err. Coefficient Std.Err.

Maize
LinearQuadratic
Coefficient Std.Err. Coefficient Std.Err.

-0.0198***

0.007

0.5776*0.322

0.0076*0.004

0.08790.124-0.0135

0.012

0.04410.333

0.1501

0.094

5.9877***1.524-0.0135

0.038-0.78120.724

0.00610.074

2.74592.350

0.0569***

0.006

0.002

0.147
0.108
0.058
0.145
0.983

0.002
0.001
0.013
0.005
0.157
0.110
0.064
0.152
9.963

0.004

-0.0404-0.1186-0.7109***-0.4638***
1.6819*-0.0098***-0.00080.0142-0.0023-0.0843-0.1039-0.6791***-0.4948***
11.96780.0033

0.315
0.230
0.119
0.285
2.435

0.005
0.002
0.028
0.012
0.311
0.218
0.122
0.275
21.125-0.0094***-0.15420.09030.6535***-0.2786-2.0747

0.0569***-0.0020-0.1009***-0.0203*-0.1616-0.2356
0.5788***-0.4242-86.2056***-0.1656-0.2424-0.4855***
0.26451.6797

0.221
0.176
0.128
0.261
1.870

0.0023-0.0033-0.05020.0001-0.3108-0.4306*-0.6326***
0.1587-35.7227

0.004
0.002
0.044
0.013
0.256
0.235
0.206
0.279
31.576-0.1534**

0.077-0.2645***0.095-0.04610.086-0.0104

0.102

0.1586*0.093

0.1503*0.087

0.9893**0.412

1.3852***0.440

0.15320.320

0.25640.353

1.0827**0.538

1.0642**0.522

0.0655***-3.3830**-1.8485**-1.4253***-2.3839*-26.9652**
230.36

0.019
1.461
0.921
0.525
1.409
10.9550.0685***-4.5724***-2.6501***-2.2595***-3.4830**-36.4321***377.3000

0.019
1.574
0.986
0.617
1.509
11.708-0.0381*-1.0335-0.0517-2.4051***-0.7115-5.6882472.8300

0.021
1.226
0.770
0.463
1.220
8.590

-0.0482**-1.4339-0.2376-2.3474***-1.1592-8.6318496.9600

0.023
1.340
0.832
0.473
1.348
9.500

-0.1195***-4.0140**-2.6326**-2.6117***-2.6810-28.9359**
93.9800

0.017
1.669
1.177
0.829
1.812
13.966-0.1242***-3.9433**-2.7335**-2.7433***-2.6955-28.2762**
106.4600

0.017
1.636
1.187
0.854
1.779
13.490-112.08-103.7191

26.8400

27.8000-44.5600-42.4600

0.59700.58140.23780.23800.43450.4404

25

Table 10 Just and Pope Production Function – Parameter Estimates-Contd..
Mean Productivity
Precipitation (R) (inCm)

CottonChillies
PulsesLinearQuadratic
LinearQuadratic
LinearQuadratic
Coefficient Std.Err. Coefficient Std.Err. Coefficient Std.Err. Coefficient Std.Err. Coefficient Std.Err. Coefficient Std.Err.
0.37200.419

0.0230**0.011

0.18010.189-0.0033

0.003

0.0036

0.060

0.127

-1.2780

2.813-0.06140.037-1.0036*0.590-0.0363*

0.019

0.5056

0.452

0.005

-0.0142***0.005-0.0029

0.002-0.00240.002

0.00140.001

0.00080.001-0.0075*0.004-0.0006

0.003-0.0006

0.001

T2

0.02290.053

0.01860.011-0.0099

0.008

R*T

-0.00640.017-0.00540.007

0.00030.002

Temperature (T) (in oC)
Trend(year)

0.0406**0.019-0.1436-0.0138***

R2

NE zone0.9768***0.332

1.0665***0.340

0.6137***0.108

0.6627***0.109

0.1720***0.059

0.1431**

0.064

NW zone0.8260***0.290

0.8929***0.311

0.2394*0.139

0.2316*0.134

0.1290***0.046

0.0966*

0.055

W zone1.1025***0.239

1.2772***0.292

0.4914***0.142

0.5042***0.137-0.0051

0.028-0.0196

0.042

CD zone0.8361**0.383

0.8823**0.375

0.2613**0.122

0.2936**0.121

0.06520.064

0.0382

0.068

Constant

4.68503.092

17.7459

37.0801.9310**0.892

13.6887*

7.719

1.3275***0.495-6.1268

6.183

Variability in
Productivity
Precipitation (R)-0.0349

0.071-0.0175

0.068

0.01750.047

0.00530.070-0.0173

0.073-0.02220.090

Temperature (T)-0.48970.455-0.64470.484-2.0504***

0.341-2.0258***

0.331

0.10340.428

0.0002

0.471
0.020

Trend

-0.0733***

0.019-0.0805***

0.019-0.01760.020-0.0194

0.021-0.0335*0.019-0.0460**

NE zone2.8179**1.144

3.0680**1.190

6.3657***1.017

6.4029***0.983

0.13871.216

0.43151.328

NW zone1.7280*1.044

2.0770*1.105

7.8240***1.304

7.9407***1.281

0.64760.920

0.8407

1.001

W zone2.1832***0.782

2.6322***0.826

7.0375***

1.139

6.9414***1.107

0.29690.542

0.3067

0.616

CD zone2.4244*1.308

2.8295**

1.411

7.5496***1.075

7.6187***1.042

0.60441.399

0.97771.511

Constant

10.9152

11.19614.6080

11.89646.9411***8.131

46.3753***

7.919-7.7280

11.281-4.850912.324Wald'sChiSq.

100.6800

116.8900

97.3100

121.3600

59.2900

66.7000

Likelihood Fun.

-95.3954-93.5302

8.9953

10.3917180.0243

181.5673

RMSE

0.55720.57100.32750.32410.07600.0766

26

Table 10 Just and Pope Production Function – Parameter Estimates-Contd..
Mean Productivity
Precipitation (R) (in Cm)
Temperature (T) (in oC)
Trend(year)
R2
T2
R*T
NE zoneNW zoneW zoneCD zoneConstant
Variability in
Productivity
Precipitation (R)Temperature (T)Trend
NE zoneNW zoneW zoneCD zoneConstant
Wald'sChiSq.
Likelihood Fun.
RMSE

Sugarcane
Groundnut
BananaLinearQuadratic
LinearQuadratic
LinearQuadratic
Coefficient Std.Err. Coefficient Std.Err. Coefficient Std.Err. Coefficient Std.Err. Coefficient Std.Err. Coefficient Std.Err.
-0.42410.345
2.897010.1660.02450.006-0.26260.127
0.23750.162
4.65394.719-1.4906
0.717
61.552144.850-0.00690.012
0.3041
0.563-0.3408
0.371
38.6218*
22.6390.48740.100
0.51820.098
0.0291
0.002
0.02890.002
0.8991***0.059
0.9006***0.058
0.07270.057
0.00210.001-0.0625*** 0.022-1.1163
0.819-0.00690.010-0.7063*0.421-0.1647
0.355
0.00850.004-0.10330.167

143.5190

19.629-739.9345

620.949

0.88190.326-2.17697.971

25.4913**10.097-519.7368* 307.617

0.0175-0.0632
0.0037

0.047
0.101
0.016

-0.02400.04200.0104

0.063
0.103
0.017

-0.0519-0.0200
0.0331

0.053
0.092
0.014

-0.07310.05180.0391

0.058
0.097
0.013

-0.0761
0.1658*0.0519***

0.051
0.095
0.015

-0.1154**0.2122**0.0588***

0.052
0.093
0.016

6.197928.5800-562.0291
10.2774

2.859

3.509136.4100-559.0880
10.08072.844-2.6071229.2200
24.1708
0.21192.522-4.5904
253.7000
27.8782
0.2091

2.583-0.9804
235.3000-486.2497
6.60092.612-2.0315
268.7000-482.8500
6.56002.521***, **,* respectively denote significance at 1%, 5% and 10%.
~ This is calculated as the square root of the mean of the squares of the deviations of observed productivities from their corresponding
estimated mean values.

27
yields. The root mean square error for the linear and quadratic mean functions
are respectively 0.5970 and 0.5814 implying the quadratic mean function isslightly better than linear mean function in prediction.
In the case of sorghum, precipitation had positive effects on mean yield forthe two functional forms and temperature had negative but non-significant
effect. Trend coefficients in the two models are negative and significant at 1%
level, implying that mean productivity of sorghum decreases over time. The sameconclusion can be derived by observing the graph of the productivity of sorghumin Fig.4. Also as shown in Table 5, its overall growth rate for Tamil Nadu is-.28%. Sorghum is purely a rain fed crop and majority of the farmers grow it for
fodder only. They switch over to other crops when sufficient water is available
and hence its production shows a declining trend. As in the case of paddy, thecoefficient of precipitation is negative in variance function for linear andquadratic forms but the coefficient of temperature is positive. But the coefficientsof both variables are not statistically significant. The trend coefficient in variancefunction is negative and significant for the two alternative functional forms
which means that as technology advances, variability in sorghum productivity
decreases. This emphasizes that risk due to productivity differences may also
reduce over years. The root mean square errors for both linear and quadraticmodels are equal and so any model can be used.
For maize, coefficients of most of the variables including climate related
variables viz., precipitation, and temperature and trend in the mean function, forthe two functional forms are insignificant. In the variance function, precipitationand temperature both have positive and significant effect implying that these twovariables are risk increasing. All the coefficients for the dummy variables are
significant except for Cauvery Delta zone. The root mean square errors for thetwo models do not differ much.
For cotton precipitation had positive and significant effect for the linear
form of mean function. Temperature has non-significant effect for both forms.
Trend effect is strongly significant but negative for the two functional forms

28
implying that the cotton productivity declines over years. This result is confirmed
by noting that the overall growth rate of cotton productivity is -0.15% (Table 5),in the case of variance function, the coefficients of the climate related variables
are all negative for the two functional forms. The trend coefficients are negative
but statistically significant at 1% level and this in turn means that variability incotton productivity also decreases over years. The root mean square error for the
linear model is 0.5572 and quadratic model is 0.571 and hence linear model isbetter than the quadratic model as mean function.
For chillies coefficient of precipitation is positive and significant for the
linear model but coefficient of temperature is negative and significant for
quadratic model. All other coefficients of climate variables are non-significant.
Further trend coefficient is negative but insignificant for both models and this
implies that productivity of chillies has not changed over time. The coefficients ofthe two climate variables in the variance function suggest that precipitation isrisk increasing whereas temperature is risk decreasing. Trend has insignificant
negative effect on the variance. All the coefficients of the dummy variables arestrongly significant at 1% implying that the variance in productivity differs verymuch between the zones. The root mean square errors for the two models do notdiffer much.
For pulses most of the coefficients in both models are not significant. Only
temperature is negatively significant at 10% level for the linear form of the meanfunction. Coefficients of precipitation and trend are not significant. Similarly forthe variance function, coefficient of trend is significant and all other coefficientsare not statistically significant. Further the root mean square errors are almost
equal for both functional forms.
In the case of sugarcane and groundnut none of the coefficient for any variable
is significant for both mean and variance functions. For banana, trend is positive andstrongly significant implying that technological progress increases banana
productivity. Also both precipitation and temperature are risk increasing inputs.

29
In summary, the climate variables viz., precipitation and temperature
have similar effect on paddy and maize productivity; precipitation decreases the
productivity for the linear form and it increases the productivity for the quadratic
form and temperature increases the mean function for the two alternative
functional forms. Similarly for sorghum, cotton and chillies, for both forms,
precipitation increases and temperature decreases the mean function.
Table 11 gives a summary of the effect of the climate variables on themean productivity for the two different functional forms.
Table 11 Signs of the coefficients of precipitation and temperature in the meanfunction
Paddy and
Maize
Mean Function
Precipitation
Temperature

L
+

Q
+
+

Sorghum,
CottonandChillies
L
Q++-

Pulses andSugarcane
L-

Groundnut

Q
+
+

L
+
-

Banana

Q
+

L
+
-

Q
+
+

As far as trend is concerned, it has positive effect on the productivities of six
crops, viz., paddy, maize, pulses, sugarcane, groundnut and banana. It has negative
effect in the case of the other three crops, viz., Sorghum, cotton and chillies.
The risk increasing (↑) / decreasing (↓) effects of climate variables on the
productivity are summarised in Table 12.
Table 12 Effect of climate variables on the variability (risk) in productivity
Crop

Paddy,
Sorghum,
Pulses, Banana

Maize

Chillies

Sugarcane Groundnut

CottonForm of Mean
Function

L

Q

L

Q

L

Q

L

Q

L

Q

L

Q

Precipitation

↓

↓

↑

↑

↑

↑

↑

↓

↓

↓

↓

↓

Temperature

↑

↑

↑

↑

↓

↓

↓

↓

↓

↑

↓

↓

Table 13 provides a summary of the estimated elasticities calculated at
the mean values of precipitation and average temperature for the two meanfunction forms. Elasticities which are unit free can be used to evaluate and30compare the impacts of explanatory variables. A brief discussion on theestimated elasticities is given below:
The elasticities of precipitation in the mean crop yield function are all
numerically less than 1 for all crops. They vary from -0.289 to +0.563 and this
implies that the response of mean productivities of all crops to the changes in the
precipitation level is inelastic. An increase in the precipitation level generally
reduces the mean precipitation in the case of paddy, maize, pulses and sugarcane
crops while it increases the mean productivity of all other crops. The elasticities
of temperature vary from -5.512 to +4.884. The estimated elasticities of thetemperature for the mean productivities for both linear and quadratic functional
forms are greater than one in most of the zones for paddy, cotton, chillies andpulses and therefore are elastic. In the case of other crops except groundnut theelasticities of temperature are less than 1 for linear form and greater than 1 forquadratic form. For groundnut, for both functional forms, all the elasticities oftemperature are less than 1 and so inelastic. A similar discussion can be given in
the case of variance function (see Table 14). The elasticities for precipitation varyfrom -2.987 to + 26.008 and that of temperature vary from -57.714 to 41.020.
The impact of climate change variables on the covariance between all
combinations of crops (there were 36 combinations) were worked out and Table
15 reports the results for selected crops only. The estimated coefficients ofprecipitation

are

not

statisticallysignificant

whereastemperaturehadsignificant effect in most of the covariance models. Trend had strong significant
effect in all combinations except for cotton and groundnut.
5. Effect of climate change on yield and yield variability
The estimated production functions have been used to study the effect ofclimate change on productivities of the nine crops for the long term climatechange scenario (HADCM3 A2a) for the period 2010-39. For this, as alreadystated, the projected values of precipitation and temperature for Tamil Nadu
State

were

downloaded

hadcm3_download. html.

from

the

websitehttp://www.ipcc-data.org/sres/

31
Table 13 Elasticities of precipitation and temperature: Mean productivity

Paddy
Precipitation
Temperature
Sorghum
Precipitation
Temperature
Maize
Precipitation
Temperature
CottonPrecipitation
Temperature
Chillies
Precipitation
Temperature
Total Pulses
Precipitation
Temperature
Sugarcane
Precipitation
Temperature
Groundnut
Precipitation
Temperature
BananaPrecipitation
Temperature

NEzoneNWzoneLinearWzone CDzone

Szone

OverallNEzoneNWzoneQuadratic
Wzone
CDzoneSzone

Overall-0.0761.543-0.0591.428-0.0401.199-0.0811.618-0.0761.541-0.0651.453-0.257-2.175-0.104
0.653

0.004
3.044

-0.289-2.306

0.021
4.884

-0.1061.036

0.072-0.3470.062-0.3540.102-0.7160.114-0.5370.060-0.2880.076-0.402

0.029
1.181

0.075
0.327

0.218
-1.551

0.045
1.629

0.100
-1.043

0.089
0.129

-0.0940.107-0.0790.108-0.0700.123-0.0760.085-0.0760.087-0.0790.100-0.189-1.314-0.079-0.151

0.004
1.389

-0.161-1.483-0.1082.997-0.1030.289

0.220-1.891

0.198-2.0680.130-1.7500.249-2.1350.293-2.5770.211-2.0440.184-1.5250.327-1.6900.342-1.6710.167-1.4240.490-3.9390.313-1.9530.235-1.5510.342-2.8560.187-2.0030.370-2.4270.379-2.5440.289-2.1730.206-1.2240.276-0.2370.199-0.5300.278-1.2440.563-5.5120.290-1.703-0.082-2.304-0.068-2.275-0.065-2.747-0.113-3.131-0.084-2.392-0.081-2.535-0.034-3.5150.016-2.5090.059-1.562-0.056-5.194-0.0200.148

0.000-2.428-0.045-0.418-0.036-0.407-0.027-0.382-0.046-0.420-0.038-0.355-0.039-0.396-0.029-1.378-0.043-1.024-0.040-0.241-0.027-1.440

0.007
0.564

-0.029-0.6570.193-0.1480.162-0.1460.127-0.1420.197-0.1470.173-0.1320.171-0.1430.304-0.3230.123-0.294-0.022-0.1870.309-0.230

0.029
0.439

0.132
-0.1110.081-0.2980.067-0.2990.051-0.2900.083-0.3000.070-0.2610.070-0.2890.118-2.1920.176-1.6700.220-0.2720.105-2.453

0.239
1.361

0.184
-0.97932
Table 14 Elasticities of precipitation and temperature : Variability in productivity

Paddy
Precipitation
Temperature
Sorghum
Precipitation
Temperature
Maize
Precipitation
Temperature
CottonPrecipitation
Temperature
Chillies
Precipitation
Temperature
Total Pulses
Precipitation
Temperature
Sugarcane
Precipitation
Temperature
Groundnut
Precipitation
Temperature
BananaPrecipitation
Temperature

Linear
Wzone
CDzoneSzone

OverallNEzoneNWzone-1.37928.134-1.04926.759-1.73229.233-1.50626.008-1.47227.886-2.91741.020-2.37739.393-1.80937.468-0.5094.610-0.4154.404-0.3164.151-0.5214.588-0.4534.080-0.4434.367-0.1147.713-0.0937.368

1.749
30.3981.425
29.6901.084
28.8691.790
30.7351.556
27.3671.521
29.412

1.658
29.879-0.385-13.149-0.314-13.011-0.239-12.694-0.394-13.387-0.343-11.961-0.335-12.8400.193-55.940

0.157-57.7140.120-56.4850.197-56.9600.172-50.647-0.1902.948-0.1552.865-0.1182.759-0.1952.972

0.193-1.8300.157-1.8070.120-1.738-0.572-0.600-0.466-0.574-0.8394.694-0.6844.649

NEzoneNWzone-1.69229.296

Quadratic
Wzone
CDzoneSzone

Overall-2.98740.932-2.59536.415-2.53739.046-0.071
6.946-0.1177.676-0.1026.826-0.1007.306

1.351
29.1841.028
28.3771.697
30.211

1.475
26.9001.442
28.910-0.193-17.311-0.157-17.131-0.119-16.713-0.197-17.625-0.171-15.748-0.168-16.906

0.168-55.5490.058-55.2690.048-57.0220.036-55.8070.060-56.2760.052-50.0390.051-54.883-0.1692.644-0.1652.837-0.2440.006-0.1990.006-0.1520.006-0.2500.006-0.2170.005-0.2130.006

0.198-1.8340.172-1.6310.168-1.768-0.2641.217-0.2151.202-0.1641.156-0.2701.219-0.2351.084-0.2301.176-0.355-0.541-0.585-0.598-0.509-0.531-0.497-0.569-0.8071.558-0.6571.488-0.5001.403-0.8261.551-0.7181.379-0.7021.476-0.5204.486-0.8594.722-0.7474.204-0.7304.551-1.2736.010-1.037
5.952-0.7895.743-1.3036.045-1.1325.383-1.107
5.827

33
Table 15 Impact of precipitation and temperature on covariance of selected crops
Crop Names

Paddy & Pulses

Intercept

Precipitation

Temperature

Time

D1

D2

D3

D4

-0.404*0.000

0.016*

0.001**-0.051*-0.018-0.021*-0.021

0.216

0.001

0.008

0.000

0.028

0.020

0.012

0.029

Intercept

Precipitation

Temperature

Time

D1

D2

D3

D4

Regression Coefficients-1.033-0.0060.041

0.004***-0.166-0.075-0.032-0.221*

Standard Errors

0.883

0.006

0.033

0.002

0.121

0.080

0.046

0.118

Intercept

Precipitation

Temperature

Time

D1

D2

D3

D4

-0.0190.003-0.008-0.011

Regression Coefficients
Standard Errors
R-Square0.197

Crop Names

Paddy & Groundnut

R-Square0.147

Crop Names

Sorghum & Pulses

Regression Coefficients
Standard Errors
R-Square0.148

Crop Names

Maize & Cotton-0.122

0.000

0.005

0.000***

0.111

0.001

0.004

0.000

0.015

0.010

0.006

0.015

Intercept

Precipitation

Temperature

Time

D1

D2

D3

D4

Regression Coefficients

2.591*

0.010-0.103*-0.008***0.307*

0.282**

0.189**

0.469**

Standard Errors

1.413

0.008

0.057

0.002

0.160

0.132

0.096

0.182

Intercept

Precipitation

Temperature

Time

D1

D2

D3

D4

-0.726-0.006*

0.031

0.001

-0.150**-0.106**-0.018-0.116

0.566

0.003

0.022

0.001

0.070

0.052

0.032

0.074

Intercept

Precipitation

Temperature

Time

D1

D2

D3

D4

Regression Coefficients-31.075**-0.427***1.365**

0.057**-3.515*-4.959**-5.675***-3.410Standard Errors

15.660

0.100

0.623

0.028

1.928

2.066

1.597

2.093

R-Square0.223

Crop Names

Cotton & Groundnut

Regression Coefficients
Standard Errors
R-Square0.169

Crop Names

Chillies & Sugaracne

R-Square

0.215

34
The projected values of precipitation and temperature were then plugged
into the estimated production functions to project the productivities of the crops
during 2020. The baseline productivities are the mean of the observed
productivities for the 30 year period 1976-77 to 2005-06. Table 16 presents theinfluence of HADCM3A2a scenario on crop productivity and its variability. For
each crop, the base line productivity, its coefficient of variation, climate change
induced productivity, its coefficient of variation and percentage change inproductivity due to climate change are presented. In view of similarity indiscussion, we shall present the results for the linear form of the mean function
only and these productivities have been used in the optimisation models.
Table 16 shows that the productivity of paddy may increase in all thezones except in Western region. Both North East and Cauvery Delta zones may
experience an increase of 9.6% in productivity. This result is surprising because
it is generally believed that increase in temperature due to climate change will
normally reduce the productivity. But this result is in agreement with a similarfinding reported for Tamil Nadu (ICAR,2008). As per the report, the productivityof paddy will increase up to 10% during Northeast monsoon period (September toDecember). This might be due to the positive effect of slight increase intemperature during this period and increase of 1 to 2 degree Celsius temperature
Table 16Impact of HADCM3A2a scenario on productivity (tonnes/ha) of cropslinear mean function
zone

Crop : Paddy
Baseline Productivity
CV (%)CC Productivity
CV (%)
Change in Productivity (%)
Crop : Sorghum
Baseline Productivity
CV (%)CC Productivity
CV (%)
Change in Productivity (%)

North
East

North
West

West

Cauvery
Delta

Southern

2.77
21
3.03
23
9.6

2.96
25
3.11
28
4.8

3.51
21
3.49
18
-0.4

2.61
28
2.87
34
9.6

2.46
27
2.65
25
7.7

1.17
19
1.16
19
-0.8

1.04
27
1.09
30
5.0

0.52
27
0.50
19
-2.6

0.76
31
0.75
33
-1.3

1.22
21
1.25
22
2.0

35

Table 16Impact of HADCM3A2a scenario on productivity (tonnes/ha) of crops:
linear mean function (Contd...)zone

Crop:Maize
Baseline Productivity
CV (%)CC Productivity
CV (%)
Change in Productivity (%)
Crop:Cotton
Baseline Productivity
CV (%)CC Productivity
CV (%)
Change in Productivity (%)
Crop:Chillies
Baseline Productivity
CV (%)CC Productivity
CV (%)
Change in Productivity (%)
Crop:Pulses
Baseline Productivity
CV (%)CC Productivity
CV (%)
Change in Productivity (%)
Crop:Sugarcane
Baseline Productivity
CV (%)CC Productivity
CV (%)
Change in Productivity (%)
Crop:Groundnut
Baseline Productivity
CV (%)CC Productivity
CV (%)
Change in Productivity (%)
Crop:Banana
Baseline Productivity
CV (%)CC Productivity
CV (%)
Change in Productivity (%)

North
East

North
West

West

Cauvery
Delta

Southern

1.56
24
1.59
29
1.6

1.55
25
1.54
31
-0.8

1.30
18
1.32
20
1.5

2.03
30
2.01
54
-0.9

1.79
30
1.75
34
-2.3

2.04
35
1.91
26
-6.3

1.83
26
1.74
19
-4.9

2.36
31
2.03
26
-13.9

1.70
27
1.75
21
3.0

1.29
21
1.29
18
0.0

1.03
28
1.03
9
-0.8

0.64
48
0.56
17
-12.4

0.78
59
0.80
16
2.3

0.71
38
0.67
17
-5.5

0.65
47
0.57
13
-12.8

0.45
15
0.41
18
-8.8

0.43
22
0.41
22
-4.5

0.35
22
0.33
22
-7.7

0.34
26
0.30
31
-12.3

0.38
16
0.36
16
-5.8

99.56
10
101.6310
2.1

103.2713103.469
0.2

112.648
106.069-5.8

104.968
101.2910-3.5

106.15
12
107.19
10
1.0

1.42
26
1.39
14
-1.8

1.31
26
1.35
15
2.8

1.40
19
1.31
17
-6.5

1.42
24
1.42
13
0.1

1.30
25
1.40
15
7.3

35.09
31
45.15
21
28.7

39.55
32
44.78
22
13.2

35.39
29
44.65
22
26.2

42.05
27
45.34
20
7.8

47.83
34
46.06
16
-3.7

may create a positive impact during 2020. It can be noticed that this increase inproductivity may also be accompanied by increase in variability. For example, inNorth East and Cauvery Delta zones which are important regions for paddy

36
production, the coefficient of variation will increase from 21% and 28% to 23%
and 34% respectively.
In the case of sorghum crop, in all zones except in North West and Southernzones there will be decrease in productivity and the coefficient of variation may
remain at the same level as that of base line values in these zones. In the case ofmaize most of the regions may register a slight marginal change in productivity
with a significant increase in variation. For example, in the Cauvery delta zone,
the mean productivity will decrease from 2.03 tonnes/ha to 2.01 tonnes per ha but
the coefficient of variation will increase from 30% to 54%. Cotton crop may registera decrease in productivity with a reduction in variability. In North East, NorthWest and Western zones there will be significant decline in productivity and inWestern zone the productivity of cotton may fall by 13.9%. In Cauvery Delta zone
there will be a marginal increase in productivity of 3% whereas in Southern zone
there may not be any change in productivity.
HADCM3A2a scenario will produce a decrease in productivity of chilly
crop. There may be a maximum reduction of about 12 to 13% reduction in
productivity at North West and Southern zones but a significant reduction invariability is possible. For example, the coefficient of variation of the productivityof North West zone will drastically decrease from 48% to 17%. Similarly the
productivity of pulses crop will decrease in all the zones with maximum reductionof 12.3% occurring at Cauvery Delta zone and the fluctuation in productivity may
remain at the base line level.
Sugarcane may register marginal change in productivity and the
maximum change will be a reduction of 5.8% productivity with a coefficient ofvariation of 9% in Western zone. Groundnut crop may experience very moderatechanges in productivity. The maximum decline in productivity will be about 6.5%
in Western zone and in Southern zone the productivity may go up by 7.3% and in
all the zones there will be a significant reduction in coefficient of variation in
productivity. Banana will have significant increase in productivities ranging from
7.8% to 28.7% and there will be significant reduction in the variability.

37
The impact of HADCM3 scenario can be analysed zone wise also. Table
below presents a summary of the effect of climate change on the five zones. It
provides the number of crops with increase/decrease in productivity. It showsthat in western zone out of 9 crops, 6 crops will have decrease in productivity.
Similarly North East and Cauvery Delta zones will have each 5 crops withdecrease in productivity and southern zone will have equal number of crops in
the two categories.

NE

NW

zone
W

CD

S

Increase in productivity

4

5

3

4

4

Decrease in productivity

5

4

6

5

4

Number of Crops with

To summarise, HADCM3 A2a scenario may have both positive and negative
effects on crop productivities in all the five zones. It appears that slightly morenumber of crops will have decrease in productivity in all the zones. Further thevariability in productivity may increases/decreases across crops and zones.

6. Optimum land area allocation using multi-goal-linear programming
The climate change induced productivities were used to allocate crop area
to the nine competing crops to satisfy the objectives and constraints specified in
Section 3. Tables 17 to 21 summarise the results for each objective. They provide
the crop area and also increase/decrease in production.
i. Maximization of food grain productiona) Area
Table 17a. Optimal area (‘000ha)
zone

Paddy

CholamMaize

Sugarcane

CottonGroundnut

Chillies

BananaPulses

Total

NEZ

691.5

0.0

0.0

0.0

0.0

259.7

38.7

0.0

0.0

990.0

NWZ

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

512.2

512.2

WZ

250.0

0.0

0.0

0.0

77.7

0.0

0.0

0.0

0.0

327.7

CDZ

612.2

0.0

128.7

0.0

0.0

174.6

0.0

0.0

0.0

915.5

SZ

561.4

0.0

0.0

268.9

0.0

277.4

0.0

69.5

0.0

1177.2

Total

2115.1

0.0

128.7

268.9

77.7

711.7

38.7

69.5

512.2

3922.7

38
Table 17b. Shift in area (‘000ha) allocation (optimal area-normal area)
zone

Paddy

Sorghum

Maize Sugarcane Cotton

Groundnut Chillies Banana Pulses

Total

NEzone

120.3

-16.2

-5.9

-120.6

-11.3

-27.8

36.4

-11.1

-124.8 -161.0

NWzone-119.6

-82.2

-48.3

-44.8

-28.3

-147.5

-5.2

-4.4

382.5

Wzone

194.5

-119.5

-30.9

-42.2

64.2

-62.3

-2.9

-16.7

-63.7

-79.6

CDzone

126.8

-35.6

122.9

-22.1

-10.1

150.2

-2.0

-13.8

-128.8

187.4

Szone

66.0

-92.8

-58.5

232.2

-52.2

200.9

-53.9

39.7

-130.4

150.9

Total

388.0

-346.3

-20.6

2.5

-37.6

113.5

-27.8

-6.3

-65.3

0.0

-97.8

The above tables show that in order to achieve maximum food grain (which
includes paddy, sorghum, maize and pulses) production, total paddy area in thefive zones should be increased from the 1727 ‘000ha to 2115.1 ‘000ha, an increaseof 388 ‘000 ha. This increase can be achieved by increasing the paddy area inNorth East zone by 120.3 ‘000ha, Western zone by 194.5 ‘000ha, Cauvery Delta
zone by 126.8 ‘000ha and Southern zones area by 66.0 ‘000 ha. Also the current
paddy area in North Western zone should be reduced by 119.6 ‘000 ha. Also area
under sorghum should be completely removed and area under maize should be
reduced by 20.6 ‘000 ha. There should be a reduction in pulses area by 65.3 ‘000 ha.
In order to main at least the normal level of production of other crops (viz.,sugarcane, cotton, chillies, groundnut, chillies and banana), area under sugarcane
has to be increased by 2.5 ‘000 ha, area under groundnut should be increased by
113.5 ‘000ha ha whereas areas under cotton, chillies and banana should be
respectively reduced by 37.6 ‘000ha, 27.8 ‘000 ha and 6.3 ‘000 ha. Of course there is
no change in the total area under all crops. Thus the above analysis implies
reallocation of existing crop areas only without requiring additional crop area.
With this reallocation, the optimum production of each crop and change inproduction can be worked out and they are presented in the following tables:b) Production
Table 18a. Optimum production (in kilotons)
zone

Paddy

Sorghum

Maize

Sugarcane

CottonGroundnut

Chillies

BananaPulses

Total

NEZ

2098

0

0

0

0

362

40

0

0

2499

NWZ

0

0

0

0

0

0

0

0

212

212

WZ

873

0

0

0

158

0

0

0

0

1031

CDZ

1754

0

258

0

0

248

0

0

0

2260

SZ

1489

0

0

28823

0

388

0

3203

0

33903

Total

6214

0

258

28823

158

998

40

3203

212

39906

39
Table 18b. Change in production (kilotons) (optimum production – normal
production)
Paddy
371
-359
664
666
236
1577

NEzoneNWzoneWzone
CDzoneSzone
Total

Sorghum
-17
-73
-40
-19
-94
-243

Maize
-9
-62
-44
250
-96
39

Sugarcane-12852
-4725
-4901
-2365
24843
0

Cotton
-19
-45
137
-17
-57
0

Gnut
-162
-212
-94
202
267
0

Chillies
38
-3
-2
-2
-30
0

Banana
-403
-177
-605
-581
1767
0

Pulses
-51
159
-21
-34
-54
0

The above analysis shows that with reallocation of land area, theproduction of paddy can be increased from the current level of 4637 kilotons to6214 kilotons tonnes, an increase by 1577 kilo tons. There won’t be any sorghum
production and maize production will go up by 39 kilotons and all other crops will
maintain their current level of production. Finally the total food grain production
will go up from the current level of 5311 kilotons to 6685 kilotons.
ii. Maximization of paddy production
For this objective, the production of all other crops is maintained at least attheir current level. The optimal area under each crop and the change fromnormal area are summarized in the tables below:a) Area
Table 19a Optimal area (‘000ha)
zone

Paddy

Sorghum

Maize

Sugarcane

CottonGroundnut

Chillies

BananaPulses

Total

NEzone

647.8

0.0

0.0

0.0

0.0

322.6

38.7

0.0

0.0

1009.2

NWzone

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

512.2

512.2

Wzone

230.8

0.0

0.0

0.0

77.7

0.0

0.0

0.0

0.0

308.5

CDzone

554.6

0.0

109.3

0.0

0.0

251.7

0.0

0.0

0.0

915.5

Szone

507.2

195.0

0.0

268.9

0.0

136.6

0.0

69.5

0.0

1177.2

Total

1940.4

195.0

109.3

268.9

77.7

710.9

38.7

69.5

512.2

3922.7

Table 19b Shift in area (‘000ha) (optimal area – normal area)
zone

Paddy

Sorghum

Maize

Sugarcane

CottonGroundnut

Chillies

BananaPulses

Total

NEzone

76.6

-16.2

-5.9

-120.6

-11.3

35.1

36.4

-11.1

-124.8-141.8NWzone-119.6

-82.2

-48.3

-44.8

-28.3

-147.5

-5.2

-4.4

382.5

-97.8

Wzone

175.3

-119.5

-30.9

-42.2

64.2

-62.3

-2.9

-16.7

-63.7

-98.8

CDzone

69.1

-35.6

103.5

-22.1

-10.1

227.3

-2.0

-13.8

-128.8

187.4

Szone

11.9

102.2

-58.5

232.2

-52.2

60.1

-53.9

39.7

-130.4

150.9

Total

213.3

-151.3

-40.1

2.5

-37.6

112.7

-27.8

-6.3

-65.3

0.0

40
The analysis of the shifts in area shows that in order to have maximum
paddy production, there should be an overall increase of 213.3 ‘000 ha of area
under paddy. To achieve this, area under paddy in all zones except north westernzone wherein the productivity is low should be increased. Areas under othercrops except sugarcane and groundnut have to be decreased. Of course these are
net changes. The optimum production and the change from normal production
are presented in the next two tables:b) Production
Table 20a. Optimum production ( in kilotons)
zone
NEZ
NWZ
WZ
CDZ
SZ
Total

Paddy

Sorghum

Maize

Sugarcane

CottonGroundnut

Chillies

BananaPulses

1965
0
806
1589
1346
5706

0
0
0
0
243
243

0
0
0
219
0
219

0
0
0
0
28823
28823

0
0
158
0
0
158

450
0
0
357
191
998

40
0
0
0
0
40

0
0
0
0
3203
3203

0
212
0
0
0
212

Paddy Sorghum Maize Sugarcane Cotton Gnut Chillies Banana
239
-17
-9
-12852
-19
-74
38
-403
-359
-73
-62
-4725
-45
-212
-3
-177
597
-40
-44
-4901
137
-94
-2
-605
500
-19
211
-2365
-17
311
-2
-581
93
149
-96
24843
-57
70
-30
1767
1069
0
0
0
0
0
0
0

Pulses
-51
159
-21
-34
-54
0

Table 20b. Change in production (in kilotons)
zone
NEZ
NWZ
WZ
CDZ
SZ
Total

So there can be a net increase of 1069 kilotons of paddy due to optimum
allocation. There will not be any change in the production of other crops.
iii. Minimum agricultural area needed for normal production
The problem of finding the minimum agricultural area needed to produce
at least the current level of production assumes special importance in the context
of change in productivity and gradual decline in cropped area over years due tourbanization and other factors. On one hand these factors try to reduce the total
production and on the other hand population explosion demands increased
production. In order to meet these two opposing forces, a balance must be struck.
One way of achieving this is to find what should be the minimum cropped area

41
needed for meeting the required level of production and how much excess area isused or available now. Table 21 below presents the optimisation results. The
normal levels of productions of the nine crops are set as the target levels.
Table 21a Optimal area ( ‘000ha)
zone

Paddy

Sorghum

Maize

Sugarcane

CottonGroundnut

Chillies

BananaPulsesNEzone

556.0

0.0

0.0

0.0

0.0

85.0

38.7

0.0

0.0

Total
679.7

NWzone

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

512.2

512.2

Wzone

190.4

0.0

0.0

0.0

77.7

0.0

0.0

0.0

0.0

268.1

CDzone

433.4

0.0

109.3

0.0

0.0

372.9

0.0

0.0

0.0

915.5

Szone

393.3

195.0

0.0

268.9

0.0

250.5

0.0

69.5

0.0

1177.2

Total

1573.1

195.0

109.3

268.9

77.7

708.3

38.7

69.5

512.2

3552.8

Table 21b Surplus area used for normal production (normal area-optimal area)
zone

Paddy

Sorghum

Maize

Sugarcane

CottonGroundnut

Chillies

BananaPulses

Total

NEzone

15.2

16.2

5.9

120.6

11.3

202.5

-36.4

11.1

124.8

471.3

NWzone

119.6

82.2

48.3

44.8

28.3

147.5

5.2

4.4

-382.5

97.8

Wzone

-134.9

119.5

30.9

42.2

-64.2

62.3

2.9

16.7

63.7

139.2

CDzone52.1

35.6-103.522.1

10.1-348.5

2.0

13.8

128.8

-187.4

Szone

102.0

-102.258.5-232.252.2-173.9

53.9

-39.7

130.4

-150.9

Total

154.0

151.3

40.1

-2.5

37.6

-110.1

27.8

6.3

65.3

369.9

Negative sign indicates deficiency
The total crop area needed in all the five zones for producing the normal
production is 3922.7 ‘000 ha and the optimization results show that it is possible
to generate the same production with 3552.8 ‘000ha only and so there is anexcess of 369.9 ‘000 ha of land currently used. The results also show that except
for groundnut and sugarcane, areas under all crops are used in excess.

7. Linking the results of optimisation with per capita food grain
availability in 2021 and 2026
Food security implies a state of affairs in which every human being canhave access to sufficient nutritious food to maintain a happy and healthy living.
This is possible only if food production keeps pace with population. But natural
resources such as arable land and fresh water for production are fixed. Further
about 43% of the population of the world depends on agriculture and this sector
dominates economies of 25% of the world’s countries. The problem becomes moresignificant in the context of climate change which threatens to decrease
agricultural production. Hence an estimate of food grain availability when crop

42
production is limited by climate change will help policy makers not only toidentify the quantum of gap between supply and demand but also to takeappropriate steps to fill the gap.

Projected population of Tamil Nadu
Fig.7 presents the population trend of Tamil Nadu. The projected
population for the year 2021 and 2026 are given in Table 22. The food grain
production and crop area required to meet the three objectives are as given in
Table 23.

Fig.7 Decennial growth of population in Tamil Nadu ( persons in lakhs)
Table 22. Population Projection (in ‘000) for Tamil Nadu for 2021 and 2026
Sex
Male
Female
Total

Year
2021
35482
35383
70865

2026
35931
35920
71859

(Source: Census of India 2001 – Population projection for India and States
2001-2026, Exhibit 3.4: Population projection for Tamil Nadu state)43
Table 23. Food grain production (tonnes) under three goals

Paddy

Sorghum

Maize

Pulses

Total
Food
Grain

Crop Area
Required(‘000ha)Max Food Grain

621409102584672122426684800

3922.7

Max Paddy production

5705563

24299921940721224263802113922.7Min Agrl.Area463664824299921940721224253112963552.8

Goal

With these data available, the projected food grain availability per capita
per day can be worked out and the results are presented in Table 24.
Table 24a. Food grain availability ( in gms) per capita per day in 2021
Objective
Max Food Grain
Max Paddy production
Min Agrl.Area

Paddy
240.2
220.6
179.3

Sorghum
0.0
9.4
9.4

Maize
10.0
8.5
8.5

Pulses
8.2
8.2
8.2

Total Food Grain
258.4
246.7
205.3

Table 24b. Food grain availability ( in gms) per capita per day in 2026
Goal

Paddy

Sorghum

Maize

PulsesTotal Food Grain

Max Food Grain
Max Paddy production
Min Agrl.Area

236.9
217.5
176.8

0.0
9.3
9.3

9.9
8.4
8.4

8.1
8.1
8.1

254.9
243.3
202.5

The current level of food grain availability, assuming a population level of
651.35 lakhs works out 223.4 gms which includes 195 gms of paddy, 10.2 gms ofsorghum, 9.2 gms of maize and 8.9 gms of pulses. The results presented in Table
24 show that the decrease in per cap food grain availability during 2026 ascompared to that of 2021 will range from 3.5 gms to 2.8 gms for the three goals.
Fig.8 provides a comparison of projected food grain availability under different
goals. It shows that the per capital food grain availability under maximum foodgrain/maximum paddy production will be higher than the current level and alsothat obtained by minimizing agricultural area. Thus optimal land allocation will
ensure increased food grain availability even under increased population
explosion and changes in crop productivities due to climate change.

44

Fig.8 Per-capita per day food grain availability(in grams) under different goals

8

Conclusions
Climate change induces increase in the temperature and changes inprecipitation. These changes will have wide impact on agricultural production interms of average yield and yield variability because all agricultural operations
are climate dependent. This paper presents a framework for quantifying theimpact of climate change on the mean and variance of productivities of crops
simultaneously. Specifically it employs econometric modelling to estimate
stochastic production functions. The estimated production functions and theirparameters are then used to estimate the change in agricultural production in
Tamil Nadu. Further, it uses the climate change induced productivities to findoptimum land allocation for crop mix to meet maximum food production. Lastly,
it provides a link between the projected food grain production and population forthe year 2021. Thus this paper provides a complete modelling framework toresilience of agriculture from the impact of climate change.
The study shows that precipitation and temperature have varying effect on
productivity and variability of crops. Trend has positive impact on paddy, maize,
pulses, sugarcane, groundnut and banana for the two alternative functional
forms of the mean function whereas for the other three crops, viz, sorghum,
cotton and chillies it has negative impacts.

45
Similarly the climate variables have different impact on risk in crop
productivity. For paddy, sorghum, pulses and banana, under both forms of meanfunction, precipitation is a risk decreasing climate variable whereas temperature
is a risk increasing input. The two climate variables are risk increasing inputs
for maize and for cotton they are risk decreasing inputs. For chillies,
precipitation increases the variability in productivity whereas temperature
decreases the variability. For sugarcane, temperature decreases risk

while

precipitation decreases variability in groundnut productivity.
HADCM3A2a scenario of climate change will have modest impacts in crop
productivities across the five zones of Tamil Nadu. zones where traditionally
paddy is cultivated, may witness modest increase in productivity accompanied byincrease in variability also. Other crops except banana may have decrease inproductivity in most of the zones. There is no uniformity in changes in theirvariability across the five zones.
With climate change induced productivities, it is possible find out optimum
allocation of crop area for meeting multiple objectives. When land is the only
constraint, food grain production can be increase by 26% without decrease in the
outputs of other crops, by optimally reallocating the crop area. To achieve this,total area under paddy, sugarcane and groundnut have to be increased whileareas under the remaining crops may have to be decreased. This will not result indemand for additional agricultural area.
When the objective is to produce maximum paddy without reduction in the
production levels of all other crops, it is possible to increase the production by
23% of the current level with productivity of all crops governed by climatechange. To achieve this, area under paddy in all zones except north western zone
wherein the productivity is low should be increased by 12.4% and area underother crops have to be modified and there will not be any net change in
agricultural area and it will remain at the current level only.
Total agricultural area can be brought down by 9% without change incurrent level of production of all crops when productivities are dictated by

46
climate change and land is the only constraint. This will involve decrease in area
under all crops except sugarcane and groundnut.
Estimation of food grain availability is an important step towards foodsecurity with increase in population. The present study provides a link between
food grain availability per capita per day with projected population of Tamil
Nadu for 2021 and 2026. It shows that optimal land use planning can overcome
the negative effects of climate change and population increase.
As stated in the next section, the results of the present study have
limitations. With constraints on other resources for agriculture, there will bechanges in total production and area under crops. Nevertheless, this study
provides a framework for future studies on optimum land use planning in thecontext of climate change.

9 Limitations of the Study
The present study and the results reported have certain limitations. The
area and production of crops which have been collected from various issues of

Season and Crop Report of government of Tamil Nadu are available annually andnot for each season except for paddy. Hence it was not possible to estimate season
wise productivities (which would have been more useful) of crops due to climatechange and the productivities reported are average productivities during theyear. So there will be a difference in the estimated productions. Second, theresults of multi-goal linear programming model suffer due to non-inclusion of
constraints on resources like water, labour etc. In the absence of good estimation
for the availability of these resources due to climate change, it was assumed thatstatus quo availabilities of all resources will continue in future period, viz., 201020039 also. Probably when constraints on these resources are included in themodel, there will be decrease in area and production. This issue can be taken up
in future studies. Third, the variability in productivities of crops estimated via
Just-Pope production function has not be incorporated in the linear programming
models. When they are included, it is possible to compute not only the mean
production but also its variance. This issue can be solved by formulating risk

47
optimisation models like expected value-variance model of Markowitz or Freund’s(Freund,1956) M-V model,

MOTAD model of Hazell (Hazell,1971) or Tauer’s(Tauer,1983) Target MOTAD model etc. This will also be taken up in futurestudies.
ACKNOWLEDGEMENT
I express my sincere thanks to Dr. Chieko Umetsu and all her colleagues
in the ‘Vulnerability and Resilience of Socio-Ecological Systems’ Project and the
Director General Professor Narifumi Tachimoto of Research Institute for
Humanity and Nature for having invited me as a Visiting Research Fellow
during the period 20th April to 19th July 2009. Also I thank Professor K.
Palanisami, Director, IWMI-TATA Policy Research Program, International
Water Management Institute (IWMI), ICRISAT, Hyderabad, India, for his
encouragement and support . I thank all staff at RIHN who made my stay
comfortable.
I thank Tamil Nadu Agricultural University, Coimbatore, Tamil Nadu,
India for providing me necessary leave to undertake the fellowship. I thank all
my colleagues at Tamil Nadu Agricultural University who helped me in many
ways.

48

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List of Working Paper

No. 2008-001

Moses Mwale, Synthesis of Soil Management Options for Better
Targeting of Technologies and Ecological Resilience under Variable
Environmental Conditions

No. 2008-002

Thamana Lekprichakul, Impact of 2004/2005 Drought on Zambia’s
Agricultural Production and Economy: Preliminary Results

No. 2008-003

Gear M. Kajoba, Vulnerability and Resilience of Rural Society in
Zambia: From the View Point of Land Tenure and Food Security

No. 2008-004

Lawrence S Flint, Socio-Ecological Vulnerability and Resilience inan Arena of Rapid Environmental Change: Community Adaptation to
Climate Variability in the Upper Zambezi Floodplain

No. 2008-005

Tetsuya Nakamura, The Livelihood of ‘Escarpment Tonga’: A Case
Study of One Village, Southern Zambia

No. 2008-006

Chihiro Ito, Re-thinking Labour Migration in Relation to Livelihood
Diversity in African Rural Area: A Case Study in Southern Province,
ZambiaNo. 2009-007

Matheaus Kioko Kauti, Rural Livelihood Security Assessment for
Smallholders Undergoing Economic Changes and Agro-Climatic
Events in Central Kenya

No. 2009-008

C.R. Ranganathan, Quantifying the Impact of Climatic Change on
Yields and Yield Variability of Major Crops and Optimal Land
Allocation for Maximizing Food Production in Different AgroClimatic Zones of Tamil Nadu, India: An Econometric ApproachVulnerability and Resilience of Social-Ecological Systems
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