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Appendix G: A description of the economic model.

The structure of the economic model has been determined by the outputs, sequence and constraints imposed by the agronomic model EPIC. The approach in this report extends and draws upon previous work where EPIC has been linked to economic models to determine the impacts of agricultural policy in the EU. (67)

Following the steps in EPIC it is assumed that once land area has been allocated to different crops, farmers make farm management decisions in response to the observed weather pattern, by altering fertilization, watering etc to optimize payoffs. This suggests a two stage modeling process: in the first stage, the crop mix is determined based on the anticipated weather outcomes and expected profits from each crop. Once crop choices and land allocation decisions are made, planting, fertilizing and irrigation occurs and is adjusted in response to the actual weather.

Accordingly, by backward induction, the second stage of the model, where farm techniques are determined, is solved first. Specifically, for any given crop i [member of] (1, n), the farmer varies farm management techniques to maximize the per hectare payoffs from the crop:

1. [[pi].sub.i] = [p.sub.i][y.sub.i]([z.sub.i], [GAMMA]) - [c.sub.i]([Z.sub.i])

where [[pi].sub.i] is per hectare profits from crop i, [p.sub.i] is price of crop i, [y.sub.i]([Z.sub.i], T) is yields from EPIC based on farm management strategy Zi and a vector representing climate event [GAMMA]. The properties of [y.sub.i]([Z.sub.i], [GAMMA])are determined by EPIC and typically appear to exhibit single peaked behavior. Specifically: for some [z.sub.k] [member of] [Z.sub.i] [there exists] a [bar.z] such that for z < [bar.z], [partial derivative][y.sub.i]/[partial derivative][z.sub.k] > 0 and for z > [bar.z], [partial derivative][y.sub.i]/[partial derivative][z.sub.k] < 0. [c.sub.i]([Z.sub.i]) are the corresponding costs of farm strategy [Z.sub.i]. Costs are linear in inputs and are expressed as: [c.sub.i]([Z.sub.i]) = [h.summation over (k=1)][c.sup.k][V.sup.k], where [c.sup.k] is the cost coefficient of input [V.sup.k], k [member of] (1, h). [GAMMA] represents the many dimensions of climate incorporated in EPIC and includes among other factors the daily level and distribution of temperature, rainfall, soil moisture and carbon dioxide. Thus for an element [[GAMMA].sup.j] [member of] [GAMMA], [partial derivative][y.sub.i]/[partial derivative][[GAMMA].sup.j] > [less than or equal to] 0 and [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. Since the focus is on the farm household at the district level it is natural to assume that all prices are exogenous.

For purposes of the simulations a range of discrete farm management strategies are used covering variations and different combinations of (a) seeding, (b) fertilization, (c) irrigation and (d) tillage techniques. Let * denote the optimum value of inputs from the maximization of equation (1), then in stage two farmers determine land allocation based on the expected profits from each crop:

2. [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

where [[PI].sub.i] = E([[pi].sup.*.sub.i]), E is the expectations operator with expectations defined over climate events that determine yields for any given farm management strategy, [L.sub.i] is land devoted to crop i, and D([[PI].sup.i]) is the sum of negative deviation of payoffs from crop i and [sigma] is a risk aversion parameter. Together these terms capture risk taking behavior in a simple way using the familiar mean-variance approach. Other more complex methods are left for future extensions of the framework. Equation (2) is maximized subject to a series of technical constraints. The key among these are a land availability constraint:

3. [n.summation over (i=1)] [L.sub.i] [less than or equal to] [bar.L] land availability constraint

where [bar.L] is the given endowment of land. And a water supply constraint:

4. [n.summation over (i=1)] [w.sub.i][L.sub.i] [less than or equal to] [bar.W] water supply constraint

where [w.sub.i] is water consumption coefficient for crop i, and [bar.W] is total water supply. For completeness a number of additional constraints are incorporated into the spreadsheet for seeds, fertilizer and labor but are not allowed to bind since there is little evidence of quantity constraints of these inputs on farms.

In Andhra Pradesh, an additional constraint is imposed requiring a minimum of 0.5 hectares is devoted to rice. This captures survey evidence showing that rice is grown on these farms to meet subsistence needs for fodder and consumption.

5. [L.sub.r] > [[??].sub.r] subsistence rice consumption constraint

where [[??].sub.r] = 0.5 ha, and subscript r denotes rice crop.

Since not all farmers are identical, the analysis distinguishes between three types of cultivators, depending on the availability of land. Subsistence farmers are classified as those with landholdings up to 2 hectares. They are driven by subsistence needs and the imperative to survive takes precedence over commercial considerations. This is modeled as a safety-first constraint where the primary objective is to earn a threshold amount of Rs. 12,000, which is the subsistence threshold in the National Sample Survey (NSS). Medium farmers have holdings between 2 and 3.5 hectares and large farmers have holdings in excess of 4.5 hectares. The farmers attempt to maximize the commercial payoffs from farming, as defined in equations (2) (5). To capture subsistence behavior an additional simple constraint is imposed for small land holders:

6. [n.summation over (i=1)]{[[PI].sub.i][L.sub.i]} > [bar.[PSI]] small farm subsistence constraint where [bar.[PSI]] = Rs. 12,000. The simulations allow for rational expectations where expectations are based on the known distribution of events and adaptive expectation where there is learning and expectations are based on past series of events.

Sensitivity Analysis of the Farm Economic Model

The results of quantitative assessments are dependent on key modeling decisions and assumptions. It is therefore important to assess the robustness of the results to various plausible changes. This section describes sensitivity assessments of the results presented in the main report. The focus is on (a) crop and input prices bi) levels of farmer's attitude towards risk (c) assumptions on farmer's knowledge of climate events and (d) levels of water availability/shortage.

The farm economic model finds that in Andhra Pradesh, irrespective of farm size, the bulk of the cropped area is devoted to groundnut. Under climate change scenarios, groundnut still remains the most profitable crop, and consequently there is no change in the planting mix. Table A.1 assesses the extent to which changes in input parameters (including price of crops, total labor cost, and fertilizer cost) would be required to alter the current findings. Table A.1 reports critical percentage changes that make rice and jowar competitive to groundnut.

Table G.1 suggests, for example, that under the baseline scenario the price of rice has to increase by 27% (from 5.7 to 7.3 Rs/kg) to induce farmers to start growing rice, while this is 44% (from 5.3 to 7.6 Rs/kg) for jowar. Fertilizer cost for rice needs to be reduced by as much as 107% to make rice competitive--an unrealistic situation even if subsidized.

Turning next to variations in the risk aversion parameter, the degree of risk aversion is likely to be negatively associated with farm size--asset holdings and wealth, so results are presented for medium farmers as an illustration of the insensitivity of the cropping mix results. (68)

Table G.2 gives an example of medium farmers cropping patterns with varying levels of attitude towards risk. Higher risk coefficient implies a higher degree of risk aversion. Under all climate scenarios, the crop mix is not sensitive to whether farmers are risk-neutral or risk-averse (69).

Turning next to Maharashtra. The economic assessment finds that, on farms where there is adequate water, sugarcane is the dominant crop due to its significantly higher profits. Table G.3 shows the levels of crop prices, fertilizer costs, and user charge of water necessary to make bajra and jowar competitive to sugarcane. For this, bajra and jowar prices have to be increased more than three fold. The level of user charge of water for sugarcane farmer is assumed to be minimal (1.2 Rs/mm) to reflect simply costs of irrigation without water charges. If water charges were increased to the levels shown in Table G.4, the area of land allocated to sugarcane would shrink and farmers would start growing less water-intensive crops. The analysis with variations in risk aversion shows that sugarcane remains dominant regardless of whether farmers are risk-neutral or risk-averse (Table G.4).

The Role of Expectations: Expectations on climate events also play a significant role in determining how farmers respond to climate change. The main analysis presented is with the case where farmers hold rational expectations--based on the actual distribution of climate events. Further analysis shows that, even when farmers are not as well-informed, the relative profitability among the crops under consideration remains unchanged--groundnut being the most profitable in Andhra Pradesh and sugarcane in Maharashtra. Thus, the findings are not contingent on whether the farmers have full knowledge of climate change or make planting decision based on year-by-year past experience of weather events (table G.5). This reflects the extreme conditions in these areas.

According to EPIC model, farmers are expected to deal with weather events that are more extreme more frequently compared to the past. Although higher returns are possible, the farmers will encounter undesirable outcomes in A2 that lie outside their experience (figure Gl). It is important to note that the assessment so far is based on the optimistic notion that water and irrigation supplies are unaffected by climate change. With warmer conditions and higher rates of evapotranspiration, water demand is likely to increase and water tables, which are already in decline, may deplete even further. So, it is important to assess how growing water shortages, combined with climate change, affect farm incomes.

[FIGURE G.1 OMITTED]

Significant water shortages lead to shifts in cropping patterns, a decline in cropped area and lower incomes. With shrinking water availability the balance shifts towards jowar, (figure G.2). Figure G.3 shows the consequences of water shortages on farm incomes. Even medium-sized farms fall below the "survival threshold" of Rs 12,000 in the A2 scenario, when the constraint binds sufficiently. Though these results are illustrative rather than predictive, the implied magnitudes highlight the importance of strengthening water conservation initiatives across the state.

[FIGURE G.3 OMITTED]

Farmers in these arid areas are typically water constrained, and a similar pattern emerges for both millets and sugarcane farmers in Maharashtra. Corresponding to the declining water availability is a decline in farm income. Figure G.4 shows that a 30% water shortage results in an 11% decline in income.

[FIGURE G.4 OMITTED]

Overall, the sensitivity assessment finds that the predicted cropping patterns are relatively robust to the various assumptions that potentially affect farm practices. However, the level of water availability/shortages has a significant implication on farmers' planting decisions and associated levels of their incomes.

Econometric Analysis and Results

This section reports detailed findings of the analysis of determinants of household vulnerability to drought in Andhra Pradesh and Maharashtra. It is aimed to supplement the discussion in chapters 3 and 4. The organization is as follows. First, key statistics for Andhra Pradesh are summarized in table G.6, then table G.7 presents those for Maharashtra. A summary of statistics and pair-wise correlation coefficients are given from table G.8-11, with the description of variables provided in table G.12.

The econometric exercise utilizes cross-sectional, household-level survey data from the two states, and uses the Ordinary Least Square (OLS) technique with linear specifications. Standard errors are corrected for heteroskedasticity. Multicollinearity is a possible concern; however, it is unlikely to present in the analysis--correlation coefficients among the explanatory variables are low (see tables G.10 and G.12) and there is no evidence of substituting impacts.

Estimated coefficients should be interpreted with care. The low explanatory power of some regressions suggests the potential of omitted variable bias. Keeping in mind the cautions, messages and implications for the study are drawn from key determinants that are highly significant and that the direction and magnitude of impacts are stable across various specifications. Table G.8-12 provide a summary of data and variable used in the analysis.
Table G.1 Critical Percentage Changes for Diversification out of
Groundnut in Andhra Pradesh

 Rice

 Price Total Labor Cost Fertilizer Cost

Baseline 27 -57 -107
A2 23 -23 -60
B2 25 -50 -103

 Jowar

 Price Total Labor Cost Fertilizer Cost

Baseline 44 -229 -188
A2 29 -151 -108
B2 47 -246 -186

Table G.2 Risk Aversion and Cropping Mix in Andhra Pradesh

risk Baseline A2 B2
aversion
coefficient Rice GN Jowar Rice GN Jowar Rice GN Jowar

0 0.5 3 0 0.5 3 0 0.5 3 0
1 0.5 3 0 0.5 3 0 0.5 3 0
2 0.5 3 0 0.5 3 0 0.5 3 0

Table G.3 Competitive Crop Prices, Fertilization Cost, and User Charge
of Water in Maharashtra (Rs/kilogram and Rs/mm)

 Price Bajra Price Jowar User
 of Fertilizer of Fertilizer Charge of
 Bajra Cost Jowar Cost Water

Baseline 24 -82 28.5 -123 59.3
A2 17.8 -50 20.2 -80 43.8
B2 19.5 -55 21.3 -85 41.8

Note: current price of bajra and jowar is 5.25 Rs/kg, while their
fertilization cost is 12 Rs/kg

Table G.4 Risk Aversion and Cropping Mix in Maharashtra

risk Baseline A2
aversion
coefficient Bajra Jowar Sugarcane Bajra Jowar Sugarcane

0 0 0 3.5 0 0 3.5
1 0 0 3.5 0 0 3.5
2 0 0 3.5 0 0 3.5

risk B2
aversion
coefficient Bajra Jowar Sugarcane

0 0 0 3.5
1 0 0 3.5
2 0 0 3.5

Table G.5 Farmers' Knowledge of Climate Events and Cropping Mix

Knowledge Andhra Pradesh Maharashtra
Base of Climate
Events Rice Groundnut Jowar Bajra Jowar Sugarcane

Rational
Expectations 0.5 3 0 0 0 3.5
Past 20 years 0.5 3 0 0 0 3.5
Past 10 years 0.5 3 0 0 0 3.5
Past 1 year 0.5 3 0 0 0 3.5

Table G.6 Andhra Pradesh--OLS Regressions

 (1)

Variable Income in Normal Year

District dummy 386.04 ***
 (145.14)
Landholding size 528.47 ***
 (82.47)
Infrastructure development 493.14 ***
 (148.39)
Water needs 0.11 ***
 (0.02)
Education 48.68 ***
 (16.39)
Tubewell irrigation access 1190.68 **
 (560.84)
Canal irrigation access 344.28 *
 (234.73)
Diversified income in drought year

Indebtedness

Non-agricultural occupation 367.05 **
 (187.82)
Observations 505
[R.sup.2] 0.37

 (2)

Variable Income Volatility

District dummy 0.074 ***
 (0.02)
Landholding size 0.064 ***
 (0.009)
Infrastructure development -0.02
 (0.02)
Water needs 4.10e-06 ***
 (1.30e-06)
Education -0.001
 (0.001)
Tubewell irrigation access -0.004
 (0.04)
Canal irrigation access 0.015
 (0.03)
Diversified income in drought year -1.9e-04 ***
 (1.8e-05)
Indebtedness 4.9e-04 **
 (2.8e-04)
Non-agricultural occupation

Observations 505
[R.sup.2] 0.35

 (3)

Variable Diversified income
 in drought year

District dummy -89.26 **
 (53.42)
Landholding size

Infrastructure development 127.28 **
 (54.69)
Water needs -0.008 **
 (0.003)
Education 6.47 **
 (3.49)
Tubewell irrigation access 64.04
 (87.07)
Canal irrigation access 146.99 **
 (83.08)
Diversified income in drought year

Indebtedness

Non-agricultural occupation

Observations 505
[R.sup.2] 0.03

Notes: Constants are not reported. Standard errors in parenthesis and
are corrected for heteroskedasticity. ***, **, and * indicate
statistical significance at the 1,5, and 10% level, respectively.

Table G.7 Maharashtra--OLS Regressions

 (4) (5)

Variable Income in Income Volatility
 Drought Year

District dummy -1022.90 ** 0.36 ***
 (509.07) (0.05)
Landholding size 261.15 *** -0.05 ***
 (98.07) (0.01)
Infrastructure development 540.60 **
 (236.36)
Tubewell irrigation access 659.55 ** 0.09 ***
 (373.97) (0.03)
Canal irrigation access -187.58 0.05
 (332.88) (0.07)
Diversified income in drought year -3.0e-05 **
 (1.6e-05)
Education

Indebtedness

Observations 409 409
[R.sup.2] 0.06 0.29

 (6)

Variable Diversified income
 in drought year

District dummy -980.99 ***
 (179.67)
Landholding size

Infrastructure development 393.63 **
 (181.05)
Tubewell irrigation access

Canal irrigation access

Diversified income in drought year

Education 26.95 **
 (11.97)
Indebtedness -102.44 ***
 (39.47)
Observations 409
[R.sup.2] 0.09

Notes: Tubewell and canal access used for (4) are in drought year,
while those for (5) are in normal year. Constants are not reported.
Standard errors in parenthesis and are corrected for
heteroskedasticity. ***, **, and * indicate statistical significance
at the 1, 5, and 10% level, respectively.

Table G.8 Descriptive Statistics for Andhra Pradesh

Variable Obs Mean Std. Dev. Min Max

Landholding size 509 2.51 1.06 1 4
Infrastructure development 509 0.6 0.49 0 1
Water needs 509 2870 5980 0 58750
Education 509 6.71 8 1 54.6
Tubewell irrigation access 505 0.08 0.26 0 1
Canal irrigation access 505 0.1 0.3 0 1
Diversified income in drought
 year 509 303.8 493.2 0 1200
Indebtedness 509 7.48 24.36 0 500
Non-agricultural occupation 509 0.83 0.37 0 1

Table G.9 Correlation Matrix for Andhra Pradesh

Landholding size 1
Infrastructure development -0.08 1
Water needs 0.49 -0.08 1
Education 0.18 0.18 0.21 1
Tubewell irrigation access 0.23 -0.01 0.26 0.14
Canal irrigation access 0.18 -0.28 0.12 -0.03
Diversified income in drought year -0.04 0.08 -0.05 0.09
Indebtedness -0.09 -0.02 -0.03 0.01
Non-agricultural occupation -0.16 0.13 -0.11 0.06

Landholding size
Infrastructure development
Water needs
Education
Tubewell irrigation access 1
Canal irrigation access -0.09 1
Diversified income in drought year 0.01 0.06 1
Indebtedness -0.02 -0.01 -0.01 1
Non-agricultural occupation -0.09 -0.1 0.25 -0.05 1

Table G.10 Descriptive Statistics for Maharashtra

 Std.
Variable Obs Mean Dev. Min Max

Landholding size 409 2.09 1.01 1 4
Infrastructure development 409 0.57 0.50 0 1
Tubewell irrigation access in
 normal year 409 0.41 0.49 0 1
Canal irrigation access in
 normal year 409 0.03 0.18 0 1
Tubewell irrigation access in
 drought year 409 0.17 0.37 0 1
Canal irrigation access in
 drought year 409 0.02 0.15 0 1
Diversified income in drought
 year 409 680.14 1601.18 0 20000
Education 409 14.64 10.67 1 54.598
Indebtedness 409 0.41 1.38 0 21.505

Table G.11 Correlation Matrix for Maharashtra

Landholding size 1
Infrastructure development 0.06 1
Tubewell irrigation access in
 normal year 0.38 0.36 1
Canal irrigation access in normal
 year 0.08 0.16 -0.05 1
Tubewell irrigation access in
 drought year 0.20 0.15 0.53 -0.05
Canal irrigation access in drought
 year 0.05 0.13 -0.09 0.80
Diversified income in drought year 0.10 0.05 0.07 -0.04
Education 0.20 0.10 0.18 -0.01
Indebtedness 0.05 -0.04 0.05 0.05

Landholding size
Infrastructure development
Tubewell irrigation access in
 normal year
Canal irrigation access in normal
 year
Tubewell irrigation access in
 drought year 1
Canal irrigation access in drought
 year -0.02 1
Diversified income in drought year 0.09 -0.02 1
Education 0.09 0.00 0.17 1
Indebtedness -0.08 -0.02 -0.08 0.16 1

Table G.12 Description of Variables

Variable Description

Landholding size An index measuring the size of land
 ownership: landless (1), marginal (2),
 medium (3), and large (4)

Infrastructure A village-level index capturing the
development availability of health and education
 facilities, electricity, drinking
 water, banks, agricultural
 cooperatives, and communication
 linkages, classified into low (0),
 moderate (1), and high (2)

Water needs Total water needs of the households in
 normal years (in millimeters),
 calculated by multiplying water
 requirement of crops grown by the area
 cultivated for each crop

Education The level of education based on the
 number of schooling years with the
 assumption of increasing return to
 education, captured through an
 exponential function

Tubewell irrigation A dummy variable capturing whether a
access household has access to tubewell
 irrigation, with 1 and 0 value
 indicating access and no access,
 respectively

Canal irrigation A dummy variable capturing whether a
access household has access to canal
 irrigation, with 1 and 0 value
 indicating access and no access,
 respectively

Diversified income in The total level of non-agricultural
drought year incomes (Rs) including non-agricultural
 labor, petty and diary businesses, and
 remittances that a household derives in
 drought year

Indebtedness The ratio of credit/loan amount taken
 by a household to total yearly income

Non-agricultural A dummy variable reflecting whether a
occupation household is engaged in cultivation,
 with 0 indicating cultivation and 1
 otherwise

Figure G.2 Area Allocation and Water Supply, Medium Farm,
Andhra Pradesh

 Rice Groundnut Jower

240 3 0
230 2.33 0.67
220 1.67 1.33
210 1 2
200 0.33 2.67
195 0 3

Note: Table made from bar graph.
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Title Annotation:Climate Change Impacts in Drought and Flood Affected Areas: Case Studies in India
Publication:Climate Change Impacts In Drought and Flood Affected Areas: Case Studies In India
Date:Jun 1, 2008
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Previous Article:Appendix F: Program for stakeholder consultations.
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