Report No. 22171-IN INDIA POWER SUPPLY TO AGRICULTURE VOLUME 4 METHODOLOGICAL FRAMEWORK AND SAMPLING PROCEDURES REPORT June 15, 2001 Energy Sector Unit South Asia Regional Office Document of the World Bank -2 - Contents Page No. Introduction ................................................................. ........................... .. 3 PART I A. Characteristics of Power Supply: Definitions and Impacts on Farmers .3 B. Cost Structure of Alternative Irrigation Options .......................... .... ....................... 5 C. Proposed Policy Reforms ................. 8 D. Review of Altemative Approaches and Justification for Proposed Approach. 9 E. Questions to be addressed ........0.... ............................................................... l0 F. The Conceptual Model ............................ ........................... 12 Appendix I.1 - The Econometric Model ..22 Appendix 1.2 - Availability and Reliability of Power Supply at Feeder Level . .24 PART II A. Sampling and Survey Procedures .25 B. Sampling Design for the Study............ . . ....... ....... 27 C. Sample Size ....................... ................................ 28 D. Haryana ............ ....... ... ..................2......... . 29 E. Andhra Pradesh ........................................................ . .................... 33 Appendix 11.1 - Irrigation Technology Options, Sample Description and Sample Size ...... ...... .39 Appendix 11.2 - Procedure For Estimation of Mean and Estimate of its Variance . . 40 Figures Figure I - Marginal Value Product of Water and Cost of Water from various Sources .. .. ............................................................. . ...... 6 Figure 2 - Policy Matrix Showing Alternative Reform Scenarios .......................... ........... 7 Figure 3 - Determinants of Technology Choice and Farm Incomes ..................................... 15 Figure 4 - Relation between Quality of Power Supply and Farm Income .............................. 20 Tables Table 1 - Effects of Irrigation Technology Choice on the Upper Bound on Water Available ............... ...................................... 16 Table 2 - Sample Size for different values of CV and relative error of 'r' .......... . ............ .... 29 Table H-1 - Formation of regions based on agro-climatic and irrigation parameters - Haryana ...................................................... 35 Table H-2 - Connected Load and Sample Size for metering and Survey - Haryana ...................3.6. . ...................................................... 36 Table A-1 - Formation of regions based on agro-climatic and irrigation parameters - Andhra Pradesh ........................... 37 Table A-2 - Connected Load and Sample Size for metering and Survey - Andhra Pradesh ............................ 38 -3 - METHODOLOGICAL FRAMEWORK AND SAMPLING PROCEDURES USED TO ANALYZE THE POWER SECTORS IN HARYANA AND ANDHRA PRADESH Introduction 1.1 In the past, state governments have primarily relied on anecdotal information and selected data to analyze the power sector. For the first time statistically significant primary data on power supply and usage in the agriculture sector has been collected in the states of Haryana and Andhra Pradesh. This new data has allowed for the development of econometric models than can help predict the impact of power reforms policies on farmers over time. 1.2 The collection of data included extensive metering at farm and feeder levels to quantify electricity usage and supply and recall and attidunal surveys that focussed on farmers perceptions of power supply and reasons for different irrigation choices. 1.3 Part I of this report looks in detail at the characteristics of power supply and how, for the purposes of constructing an econometric model, these are defined. It looks at the relationship between power supply and irrigation methods used in the field and why there is a need for reforms of the power sector. It also describes the questions that needed to be addressed to build the model and provides details of the conceptual model used. 1.4 Part II deals with sampling and survey procedures describes how pumpsets were chosen and then metered and what information was collected PART I A. Characteristics of Power Supply: Definitions and Impacts on Farmers 1.5 As a result of overall shortages, power supply to agriculture is heavily rationed. There is a long waiting period (often as long as 3-5 years) for farmers to get an electricity connection. Moreover, the three-phase power supply to the agriculture sector is typically rostered amongst the various feeders for a specified number of hours every day. The three-phase supply during the scheduled timings of the roster is referred to as the "scheduled supply." The actual availability of three-phase supply to farmers differs from the scheduled supply on two accounts. First, there are frequent power cuts during the scheduled hours of supply (due to transformer burnouts or otherwise). Second, it is also common for power to be available outside the scheduled hours. Accordingly, the following indicators of power supply have been defined. 1. Availability per day in each season: is defined as the average number of hours per day for which power was available at the farm level during time periods when the transformer and the pump motor were in working condition. It should be noted that availability as defined here includes the total number of hours of available supply per day at the farm level irrespective of whether that supply occurred during scheduled or unscheduled periods. When either the transformer or the motor is not working then power is not available at the farm level for several days at a stretch until necessary repairs are undertaken The effect of such continuous periods of lack of power, which is almost entirely random, is likely to be different from the effect of interruption of power that occurs as a result of regular power rostering. Therefore the effect of availability when transformer and motor is in working condition is defined and analyzed separately from the effect of interruption of power supply -4 - due to motor and transformer failures. For the econometric modeling, it makes sense to look at availability at the farm level which, in general, is different from availability at the substation level. Availability at the farm level, depends on availability at the substation level plus a host of other factors related to the transmission and distribution system. From a policy perspective, this suggests that availability at the farm level can be increased even if availability at the substation level stays constant provided improvements are made in the transmission and distribution system. 2. Unreliability of scheduled supply Average hours of power cuts (hours/day) during scheduled hours of supply in the different seasons, during time periods when motor and transformer was in working condition. In the attitude survey, farmers reported that on average, power was cut for two hours every day during scheduled hours of supply in Haryana. 3. Average frequency of transformer burnouts in the different seasons and the average time it took for rectification. In the attitude survey, farmers reported that on average a total of 16 days were lost due to transformer burnouts every year in Haryana. 4. Quality of supply: no precise measurements of voltage imbalance or voltage fluctuations were carried out at the farms of the sample farmers. In the attitude survey, sample farmers were just asked whether problems with voltage fluctuations occurred always, frequently, sometimes or never. Around 73% of sample farmers reported that voltage fluctuations occurred "frequently" or "always" in Haryana However, this is a very rough measure of the quality of supply and does not show much variation across the sample. One of the ways that voltage imbalance and voltage fluctuations affect farmers is through frequent motor burnouts. In the farmers' recall survey, farmers were asked about the number of times during each season that their motor bumt out. This measure is taken as a proxy for poor quality of supply. 1.6 To understand the impact of limited availability and unreliability of supply on farmers, it is important to bear in mind that unlike the case of households, electricity demand for water pumping is a seasonal phenomenon. The demand for pumped water depends on a variety of complex factors including rainfall; availability of canal irrigation; cost of purchasing water from other farmers; cropping pattern; evapotranspiration requirements and soil type etc. Further, storage of water is costly and using excess water results in damage to the crop and reduced yields in many cases. Uncertainty about the supply of electricity imposes high costs on farmers because the yields of many irrigated crops (such as high yielding varieties of wheat) are very sensitive to the timing of irrigation. To insure themselves against the risk of not having electricity when needed, farmers often invest in several back-up strategies such as diesel pumps and tractors. The use of these backup strategies substantially increases the effective costs of irrigation. 1.7 The magnitude of voltage and its variability, often referred to as the quality of power supply, increases farmers' costs for three reasons. First, low voltage implies that water delivered by the pump per unit of time is reduced (generally @square of voltage), other things remaining the same. Second, low voltage compared to the standard agreed by the utility, leads to motor bumouts. Apart from the costs of getting the motor rewound, production activities need to be readjusted and there is potential loss of output in the time period it takes to get the motor reinstalled. Low voltage may also cause the utility transformer to fail, further interrupting the supply of power until the time it takes to repair it. Third there is also some evidence to suggest that given the poor quality of supply, farmers tend to select robust motors that have thicker armature coil windings. These motors reduce the frequency of motor burnouts but have a lower overall efficiency. Moreover, to ensure that the flow rate of water is not reduced due to low voltage, farmers often over-invest in pumps with higher capacity rating. From the farmer's viewpoint, a 10 hp motor operating under low voltage conditions is likely to perform as well as a 5 hp motor (Padmanabhan and Govindarajalu). - 5 - 1.8 Finally an important characteristic of current conditions of supply, is the price the utility charges farmers. Although farmers in Haryana have the option of paying for electricity on the basis of a flat rate (per unit of installed horsepower) or on the basis of metered rate (per unit of consumption), the majority of sample farmers (around 94 per cent) in the attitude survey reported paying for electricity on the basis of a flat rate. In Andhra Pradesh, all farmers are charged for electricity consumption on the basis of a flat rate, also based on the horsepower level of pumpsets. The above discussion leads one to conclude that although the price charged for electricity is highly subsidized, farmers face a number of constraints in the current situation which raise the real costs of pumping.. B. Cost Structure of Alternative Irrigation Options 1.9 In this subsection, the costs and benefits of irrigation through electric pumps are compared to other irrigation options available to farmers. In most regions where surface water is available for irrigation purposes, it is the lowest cost alternative for irrigation (see Fig. 1). The costs associated with canal irrigation include the cost of digging and maintaining field channels and a highly subsidized payment to the irrigation department in terms of crop and area cultivated. However, there are quotas or other kinds of quantitative limits on the total amount of canal water that is available per season. Farmers also have very little flexibility with respect to the timing of supply because a fixed rotation schedule is followed. -6 - Figure 1 - Marginal value product of water and cost of water from various sources D Marginal Value Product \ \ ^~ ~ ~~~~~ Of Water Cost of pumping using diesel pump Cost of water C Co[ usinig hi h HP Electiic pump) CotofuprsintowHPe / Canal Water A B C Quantity of water (1000 cubic meters per season) - 7 - 1 10 Thus in most cases, farmers use whatever surface water is available and supplement it with other sources. Investment in an irrigation well is a large and risky investment in most areas, and particularly so, in the hard rock areas of Andhra Pradesh. As pointed out earlier, in most areas a fixed tariff per unit of installed capacity is charged irrespective of the volume of water pumped out. Thus, the variable costs associated with electric pump operation are very low and consist primarily of cost incurred in motor repair and maintenance. As opposed to this, the variable cost associated with operation of diesel pumps are much higher (as shown by the much steeper slope of the diesel cost line in Fig. 1). 1.11 Given the poor availability and reliability of electricity supply, however, diesel pumps are often used as a backup strategy to meet the shortfalls in supply of electric power. In addition, in some areas where canal is the main source of irrigation but a supplemental source is needed, farmers may prefer to use diesel pumps rather than electric pumps if groundwater table is high. This is because for electric pumps they have to pay a fixed tariff irrespective of use, whereas for a diesel pump they pay per unit of diesel consumption. Thus a diesel pump may be more profitable at low levels of consumption. 1.12 For those farmers who do not own wells, use of canal water or purchase of water from well-owners are the only two options for irrigation. Evidence from several studies suggests that markets for water tend to be very thin and fragmented for several reasons (Shah, 1993 provides a survey). First, because of the physical costs of transporting water over large distances, transactions in groundwater tend to be limited between neighboring farmers. Second, farmers in a given region generally grow very similar crops and hence their demand for water tends to be synchronous. Given this synchronicity in demand and uncertainty regarding the dynamics of groundwater stock, transaction costs are generally quite high and so water markets tend to be very thin. Third, in many areas, there is also an underlying social belief that water is a natural, common pool resource that belongs to everyone and therefore charging a price for it is immoral (Wood, Aggarwal). In the attitude survey conducted in Haryana, it was found that of the 600 pumpset owners covered under the survey, only 3 per cent (around 22 farmers) reported selling water to other farmers. Thus for those farmers who do not own wells, the options for irrigation are rather limited. 1.13 Thus to sum up, from a farmer's perspective, in areas where canal water is available, it is the lowest cost altemative for irrigation. However, there are quotas and farmers have very little control on the timing of irrigation applications from canal water. For those farmers who can invest in wells, electricity is much less costlier than diesel as an energy source. However, given the poor availability and quality of electricity supply, farmers often use diesel pumps as a backup or a supplemental source of power. The growing use of diesel pumps is a rough indicator of the fact that the current supply of electricity is inadequate for the needs of the farmers and that they are willing to pay a much higher price for additional and more reliable supply. 1.14 From the society's perspective, since electricity supply is not priced at its true scarcity value, there is a loss in overall social efficiency. Moreover, with a flat rate there are very limited incentives at the margin to conserve either water or power, through the use of more efficient pumps or water conserving technologies. As discussed earlier, uncertainty about availability of electricity supply leads to production losses and forces farmers to adopt various kinds of coping strategies which are highly inefficient, such as the use of diesel operated tractors to pump water when electricity is not available. All this raises the question of whether at the margin it is more efficient for the utility to improve the reliability of supply and charge a somewhat higher price or to let the farmers evolve their own private mechanisms to deal with this situation. 1.15 In this context, it is also worth noting that in the present situation where there is no explicit regulation of groundwater pumping, the allocative effects of electricity rates on water extraction are also very important. Although it is true that the scarce value of the groundwater resource can be better addressed by other more direct policies such as pumping limits and pump spacing, the potential for - 8 - electricity rate structures to encourage or discourage groundwater extraction cannot be ignored. Shah (1992) conducted a survey of studies on groundwater use in areas where a switch was made from per unit to flat tariffs in the late 1970s/early 1980s. His main conclusion was that this switch resulted in an increase of 40 to 60% in pumping of water by existing well owners. This finding reinforces the need for revisions in the current tariff structure, particularly in areas where water table is declining rapidly or where there is an imminent danger of saline intrusion. C. Proposed Policy Reforms 1.16 As discussed above, the current situation regarding electricity supply results in low revenues for the utility and high real costs borne by the farmers and the society. Thus, the overall result is a situation where all the major stakeholders find themselves in a situation of a "low equilibrium trap". This calls for the need for policy reforms which can help the economy emerge out of this trap. 1.17 The policy reform process proposed in this study consists of a combination of some or all of the following changes: 1.18 Increase in number of hours for which electricity is supplied to the agricultural sector. Improvements in reliability of supply: reduction in the frequency and duration of unscheduled power cuts. An important component of policy here is the reduction in the frequency of transformer burnouts and time taken to repair it. Improvements in quality of supply. Reduction in magnitude (how high or low compared to the standard agreed by the utility), frequency and duration of voltage fluctuations Increase in tariff: This could take the form of increase in the current fixed rates charged per horsepower of pump or a move towards pro-rata tariff with installation of meters. 1.19 An important objective of this project is to estimate the impact of these policies on input (in particular, water and electricity) demands, cropping patterns and farm costs and incomes. The purpose is to estimate these impacts both over the short run (when the capital stock, particularly in the form of installed irrigation capacity is held constant) and the medium to long run (when capital stock is allowed to adjust). The sequencing and pace of the reform process is likely to be very important. Thus for instance, increasing the rates without improvements in quality of supply is not likely to be politically feasible. Hence one of the objectives of this study is to shed light on these aspects by simulating the impact under alternative policy reform scenarios as shown in Figure 2. Figure 2 - Policy matrix showing alternative reform scenarios Policy Scenario Option 1 2 3 4 5 69 Increase tariff X X X X X Increase hours of supply X X Reduce power interruptions X X X Reduce voltage fluctuations _ __ _ __ X X _ _ O thers9 _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ -9 - D. Review of Alternative Approaches and Justification for Proposed Approach 1 20 As discussed above, the main purpose of this study is to evaluate the impact of policy reforms in the power sector on agriculture. The study has two broad components. The first one relates to the micro aspects (pertaining to farm level behavior) and the other relates to the macro aspects (at the region or state level). For now only the micro level is complete. This analysis is conducted within a partial equilibrium framework and the focus here is to examine the impact of policy reforms on costs of production, yields, cropping patterns, demand for electricity and farm incomes for different categories of farmers classified as marginal, small, medium and large. 1.21 To evaluate the impact of policy reform quantitatively at the micro level, an econometric model based on data on observed choices of farmers in the current situation is used. This predicts what farmers are likely to do when the policy change occurs. 1.22 Another method would have been to use a contingent valuation survey (CV) elicits farmer's responses and willingness to pay for the changes in policiy. The advantage of the CV approach is that it can in eliciting expected responses and willingness to pay for any change towards a given hypothetical situation. However, earlier studies have pointed out that responses are very sensitive to the manner in which the questions are phrased and upon the timing of such a survey vis-a-vis the household's recent outage experience (Sanghvi). Given these difficulties with CV surveys, we propose to use an econometric model to estimate the impact of policy reforms. 1.23 In examining the impact of policy reforms it is often useful to distinguish between the short and the medium run. In the ensuing analysis on the micro aspects, it is assumed that the short run is the period in which the capital stock representing the technology imbedded in the production process, remains constant. On the other hand, in the medium run, the capital stock is allowed to respond to changes in conditions of electricity supply. However, over the medium run it is assumed that everything else in the farm economy, such as output/ input prices and the overall regulatory framework with respect to the agricultural sector, remains constant. Thus for instance, in the short run, farmers may respond to unexpected power outages by say, rescheduling production activities and changing the allocation of variable inputs. In the medium run (a period of about 4 to 6years), if it is expected that these power outages will continue then farmers may shift to alternative fuel source (say, shift to use of diesel), install larger capacity pumps or install backup generation capability. In his survey of the literature on optimal electricity supply reliability, Sanghvi points out that almost the entire literature so far has focused on short-run cost of power outages. As he argues, in the medium run, with shift in the capital stock the demand curve itself can shift. Since the policy changes being proposed are likely to result in major changes in the supply of electricity, assuming the demand curve to remain constant would assume away the essence of the problem at hand. An important objective of the present study is to examine how farmers respond to the current problem in electricity supply and to assess the cost of the backup technologies that they invest in. Thus the model has two related parts. The first part consist of estimating the input and output elasticity in the short run, keeping the technology as constant. The second part models the choice of technology in the medium run. 1.24 To model the choice of technology, it is important to consider the entire spectrum of irrigation options currently in use in the selected states. Thus the sample used for the study includes not only the users of electric pumps but the entire farming population ( diesel pumpset owners, rainfed, canal and water purchasers). This is important for several reasons. Firstly, restricting the sample to only electric 'This is the main difference between medium and long run Long run effects have not been analyzed right now. - 10- users would result in selectivity bias in the estimates derived from the econometric model. Secondly, it is necessary to estimate how cropping patterns, input allocations, yields and incomes differ between those who own wells with electnc pumps as compared to all other categories of farmers. In particular, the returns currently associated with use of electricity in pumping groundwater are compared with other options. Some earlier studies have compared input intensities and yields between canal and groundwater irrigated areas. However, very few of these analysis have been conducted within a multivariate regression framework and so it is difficult to assess the extent to which the differences found in input intensities and yields can be uniquely attributed to the use of groundwater (see Dhawan, Shah for a survey). Thirdly, the impact of policy reforms on changes in irrigation technology in the short to medium run need assessing. It is likely, for instance, that some non-well owners might decide to invest in electric pumps or buy water from electric pump owners as a consequence of the policy change. Thus it is important to establish what factors determine farmer's choice of technology and how 1.25 The data to be used for this study was obtained through a farm household level survey for the agricultural year 1999-2000 in the states of Haryana and Andhra Pradesh. Details of the sampling design for the present study are given inpart II. Using this data, the econometric model described in section F was developed. Estimates derived from this econometric model were used to do a partial equilibrium analysis of policy reforms. An important advantage of the partial equilibrium approach is its empirical simplicity and also the fact that the first round effects are, in general, an acceptable first-order approximation of the total effects (Sadoulet and deJanvry). However, it is important to keep in mind that the partial equilibrium analysis does not take into account several important effects such as the income and cost changes that might shift the demand and supply curves and the interaction across markets with products or factors that are close substitutes or complements in consumption or production. For example, it is likely that policy reforms that would affect agricultural production and hence lead to a change in the prices of major crops produced in these states. The partial equilibrium analysis does not take into account this second round -effect. To take into account such indirect effects, the analysis of policy reform would possibly be extended to a general equilibrium framework. 1.26 In the next section, the set of questions that need to be addressed are listed. This provides an overall perspective and is followed by a detailed discussion on the methodology. E. Questions to be addressed Part I: Analysis of the current situation with subsidized fixed tariffs and rationed supply of electricity A. What are the different sources of mrrigation (both surface and groundwater) used by different categories of farmers? B. What are the different technologies used for pumping groundwater (Type of well, depth of well, type of pump, source of power, use of backup strategies etc.) For the purposes of this study, four broad categories of technological options for irrigation are distinguished. 1) Use of electric pumps to withdraw groundwater from own well 2) Use of electric pumps (with back up strategies such as use of diesel pump or tractor) to withdraw groundwater from own well 3) Use of diesel pumps to withdraw groundwater from own well 4) Use of neither electricity nor diesel for irrigation. This includes rainfed farmers and those that rely solely on surface water sources and/or purchase of water from neighboring well owners. C. What are the direct and indirect costs (such as costs of motor burnouts in case of electric pump users) associated with the adoption and use of the above technological options? - 1 - D. What are the cropping patterns, input use intensities and yields associated with each of these options? E. What are the input demand (including demand for power) and output supply elasticities associated with these different options? F. What are the various farm and village-specific characteristics that determine the choice of technology used for pumping groundwater? G. What is the pattern of electricity use by electric well owners? In particular, for each crop, what are the peak and off peak periods of demand for pumped water and hence for electricity? H. How do farmers perceive the different qualitative aspects of supply (i.e. reliability, flexibility in supply) associated with the current supply of electricity? I. What kind of coping strategies are currently being used by farmers to deal with problems of electricity supply? What are the costs of adopting these strategies? J. For electric well owners who do not have any backup strategies, what is the estimated loss in production in the short run? K. Do well owners also sell water to neighboring farmers? If so, how much water is contracted out and what are the terms of the contract (fixed price or crop share)? How are the terms of these contracts framed in order to deal with uncertainties in electricity supply? Do the terms of the contract differ for water purchased from electric pump owners as opposed to diesel pump owners? Part II: Partial equilibrium analysis of policy changes A. What is the impact of alternative policy changes on technology used for pumping: (shift to diesel pumps or pumps with higher efficiency, use of water conserving methods of irrigation, use of coping strategies), cropping patterns, total demand for electricity, total amount of groundwater withdrawn, yields, input intensities, costs and incomes. In particular, what is the impact of policy reforms on the small and marginal farmers? B. What is the willingness to pay for an extra hour of electricity at prevailing quality levels9 C. What is the willingness to pay for an improvement in reliability and quality of electric supply? The conceptual model underlying the analysis of the above questions in outlined in the next section. - 12 - F. The Conceptual Model 1 27 Basic assumptions Production function Consider an agricultural production function given by Y = f(W, X; Z, H) (1) where W = water input X = vector of variable inputs employed in production such as land, seeds, labor, manure, fertilizers, pesticides, hours of tractor and machine use Z = farm specific characteristics 0 = random factor denoting the effect of weather (rainfall, temperature etc.) We assume that f(.) is twice continuously differentiable and concave in all of its arguments. In addition we assume that fw 4 -o as W - 0, and similarly for X. Water input, W, in the production process is subject to the following constraint W < WR + WC + We + Wd (2) where W1z is the amount of rain water, Wc is the exogenously allocated amount of canal water, We is the amount of water pumped using own electric pumps and Wd is the amount of water pumped using own diesel pumps2. To begin with, we assume that there is no buying or selling of water. This assumption is relaxed later on. Pumping technology Water from electric pumps is pumped using the following technology We = We (he, HPe, E, Vavg, G) (3) where he denotes hours of pumping, RIPe is the horsepower of the pump, E is efficiency of pump, Vayg is average voltage during season, G denotes characteristics of groundwater aquifer (e.g depth of water table and rate of natural recharge). We is assumed to be increasing in he, HPe, E and Vavg- Similarly, water from diesel pumps is pumped using the following technology Wd = Wd (hd, HPd, E; G) (4) where hd denotes hours of pumping and HPd is the horsepower of the diesel pump. Wd is assumed to be increasing in hd , HIPd, and E. Electricity rationing Electricity is available for only a limited number of hours during the season given by Her = AHse (5) 2 We assume here that water used through these alternative sources is equivalent in terms of their effect on production It might be more realistic to put different weights on these different sources with the highest weight on water pumped by diesel pumps because it is "on demand" while the lowest weight is put on rain water since the farmer has no control over its application - 13 - where H,, is the scheduled hours of supply (known before the start of the season) and A is the availability index defined as A = Hours of actual supply/ hours of scheduled supply (6) We assume the uncertainty about A is resolved during the course of the season. Groundwater availability There is an upper bound on the amount of total groundwater that can be withdrawn through electric and diesel pumps. This upper bound WO is given by factors such as: aquifer characteristics G, rainfall during the season R, availability of canal water, Wc and density of wells, D, in the cluster WO = Wo( G, WR, Wc, D) (7) Costs of pumped and canal water a) Fixed costs of pumped water: In order to extract groundwater, there are sunk costs of digging the well and installing the pumps. Let Qd (HPd) and Qe(HPe) be the sunk costs of installing diesel and electric pumps of horsepower HPd and HPe respectively3. In case of electric pumps, Q(HPe) includes, in addition, a one-time electricity connection charge. In most regions, a flat tariff of T(HPe) is charged on electric pumps which has to be paid every season b) Variable costs of pumped water: In addition to these sunk costs, we assume that there is a constant per hour cost of pumping with a diesel pump qd, which is a function of the horsepower of the pump and is given by qd = Pd 8(HPd) + md (HPd,, Fd) (8) where Pd iS price of diesel and 8(IHd) is the consumption of diesel per hour by a pump of horsepower HPd. md denotes the non-fuel cost of operation of diesel pumps and relates to expenses incurred in oiling, replacement of bearings etc. These non-fuel costs of operation are a function of the horsepower of the pump and other characteristics such as age and brand, denoted by Fd. Similarly for electric pumps we assume that there is a constant per hour cost of pumping, q,. It includes fuel cost (in cases where a metered tariff is in place) and the non-fuel costs of operation of pumps and relates to expenses incurred in oiling, replacement of bearings and motor rewindings due to motor bumouts. Apart from normal wear and tear, motor burnouts often arise because of voltage fluctuations. Therefore, the per hour cost of operation of electric pumps, q, can be given as qe =PeHPe + m(HP, Fe, Vfc ) (9) where Pe is price of electricity consumption per HP per hour(for metered pumps), Vnf, is an index of voltage fluctuations during the season and Fe is a vector of pump specific characteristics such as age and brand 4. In general, the marginal cost of a unit of water pumped through electric pumps is much smaller than that through diesel pumps. This is so even with respect to farmers who currently pay on the basis of metered tariff, because the use of electricity in agriculture is more heavily subsidized than the use of diesel (see figure 2). 3This cost includes the cost of digging a well, installing a motor and applying for an electricity connection ( in case of electric pumps) 4 We are still working on defining these indices using the available data. - 14 - In comparison to the costs of pumped water given above, the total costs of canal water (which includes costs of digging and maintaining field channels plus the seasonal tariff) are very low. Canal water is available in only a few regions, wherein, farmers have an exogenously given quota denoted as Wc and are charged a seasonal tariff of PcWc Prices- prices of output and variable inputs (other than water) are denoted by PQ and Px respectively. 1.28 Farm household's optimization problem: two stage formulation The farm household's decision problem has two stages: First, households choose the irrigation technology. Here we will consider the main choice variables to be the installed electric and diesel pumping capacity, HPe and HPd, respectively. Next, households observe the amount of rainfall, availability of canal water and conditions of electricity supply (i.e. incidence of unscheduled cuts, and the duration and magnitude of voltage fluctuations). They then choose the level of application of variable inputs (X) and hours of pumping for electric and diesel pumps ( he and hd, respectively)5. The two stage optimization problem presented in this section is summarized in Figure 3. 5 In the presentation of the optimuzation problem we assume that households are not credit constrained In a later section we discuss the implications of credit constraints. - 15 - Figure 3 - Determinants of Technology Choices and Farm Incomes Past conditions of power supply Farm and region specific characteristics Pumping technology \ choices Current conditions of ower supply Input, output choices Current farm income 1.29 Derivation of short run profit and input (including energy) demandffunctions We start with the second stage, wherein given HPe, and HPd, households solve the following problem to maximize expected short run profits Problem PI Max: EBlS = PQY- PxX - qdhd - qehe - T(HPe)-PcWc (P1) with respect to: X, hd, he subject to. Y S f(W, X; Z) Production Techonology W S WR + WC + We + Wd Total Water availability We = We(he, HPe, E, Vavg, G) Electric pump technology Wd = Wd(hd, HPd, E, G) Diesel pump technology he > 0;, hd 2 0, X > 0; Non-negativity constraints he < Her; Electricity rationing We+Wd S WO Groundwater availability It would be helpful to distinguish between the following regimes. (Table 1 below shows the upper bound on water availability for each of these regimes) Regime 1: Farmers with no pumps HPe = 0 and HPd = 0 Regime 2: Farmers with only diesel pumps HPe = 0 and HPd > 0 Regime 3 Farmers with only electric pumps HP, > 0 and HPd = 0 Regime 4: Farmers with electric and diesel pumps HPe > 0 and HPd > 0 For each of the above four regimes, let us examine the input demand equations. - 16 - Regime 1: Here given HPe = 0 and HPd = 0, the amount of water available is fixed in the second stage and given by the availability of rain and canal water. Given our assumptions about the production function in (1), the output supply and variable input demands are given by the interior solution of problem P1 and can be written as Y, = Y, (PX, PQ, WR, WC, Z) Xi* = X (PX, PQ,,Pc WR, Wc, Z) Table 1 - Effect of Irrigation Technology Choices on the Upper Bound on Water Available Regime - Description Upper Bound-on Water Available - - Non-Well Owners Rain water + Allocated Canal Water Well Owners with Diesel Groundwater Availability Pump only 111 Well Owners: with Electric Mm {Groundwater Availability, Electricity Rationing*) Pump only IV Well Owners with Electnc Groundwater Availability and Diesel Pumps .(The higher is the horsepower of the pump the higher is the upper bound posed by electncity rationing) Regime 2: Here given HPe = 0 and HPd > 0, farmers have to choose the hours of diesel pump use (hd) and level of output supply and variable inputs (Y,X). In the absence of the upper bound on hd given by groundwater availability in (7), let h'2 and X' be the solution to the problem P1. These can be written as hu2 = h"2 (PX, PQ, qd, HP,,, E, G, WR, W., Z) X X2 (PX, PQ, qd, HPd, E, G, WR, WC, Z) Y.," Y'2 (Px, PQ,qd,HPd, E,G, WR, WC, Z) In the presence of the groundwater constraint, there is an upper bound on the number of diesel hours given as H = Hd (WO, HPd, E, G) Given this upper bound, the effective demands for diesel hours and other variable inputs are given as hd hd"2 X = X2 if hdu < Hd = H8', X*= Xg otherwise - 17 - where X2' is the solution to the problem P1 when hd is fixed at Hd 6 2d Regime 3: Here given HPe > 0 and HPd = 0, farmers have to choose the hours of electric pump use (he) and level of output supply and variable inputs (Y,X). There are two upper bounds on he. First, given by the electricity rationing constraint, He in (6). Second, given by groundwater availability in (7), which can be written as Heg = H S (WO, HPe, E, Vavg, G) In the absence of either of these constraints, let he and Xu be the solution to the problem P1. These can be written as Y3 = Y3] (Px, PQ,qd,I-Pd, E,G, Vavg, WR, W., Z) hU3= h1 3 (PX, PQ, qC, HPe, E, G, Vavg, WR, WC, Z) X3 U X3 (PX, PQ, qd, TPd, E, G, Vavg, WR, WC, Z) In the presence of the two upper bounds, the effective demands for electricity and other variable inputs are given as hU= he, X*= X3' andY*= y3u if he3 < Min (H', HS') = Min (Her, He,) X* = X3 and Y* = Y3r otherwise where X3 and Y3r are the solution to the problem P1 when he is fixed at Min (H r, H'). Regime 4: In this case, farmers have to choose the hours of electric pump use (he), the hours of diesel pump use (hd)and level of output supply and variable inputs (Y,X). Note that in our model, water pumped through electric pumps and diesel pumps are perfect substitutes. Therefore, given that in general the marginal cost of a unit of water pumped through electric pumps is much smaller than that through diesel pumps, it follows that farmers will not use diesel pumps unless they are bounded from above in the use of electric pumps due to electricity rationing. Therefore, if h' and Xu are the solutions to the problem P1 in case 3 then h = 0 if h'< Min (Her H,g)or H%< hC < hd = hU >0 otherwise where hu is the solution to problem P1, when he is constrained to be equal to H r Output supply and input demand in this regime are therefore given by W = y4u (Px, PQ, qd, HPd, E, G, Va,g, WR, WC, Z) 6We assume here that when the upper bound is binding, the optimal amount of water used is given by the upper bound This may not be true if water is used in discrete quantities This assumption is quite common in the rationing literature. - 18 - X4 = X4" (Px, PQ, qd, HPd, E, G, Vavg, WR, WC, Z) Choice of irrigation technology From the above input demand functions for each of the 4 cases above we can get the restricted profit functions (for fixed HPd and HPe). Thus the optimization problem in the first stage entails choosing HPd and HP, so as to maximuze the present discounted value of future profits, net of the fixed costs of installation Problem P2 Max lffEi7(HPdHHP X P Q PtQ R EA V Hr W W, W Z)-T(HP)dt-Q(HP)-Qd(HPd) 0 with respect to: HPd, HPe subject to: (HPd, HPe) 0 Non-negativity constraints where subscript t denotes the time period, T denotes the expected lifetime of the irrigation equipment and E( ) denotes the expectations operator. The solution to the problem P2 gives the medium run profit function as a function of the expected future values of the explanatory variables that can be written as Il = IL (PX, PQ, q., qd, Qd, Qe, T, E, G, Vavg, Her, WR, WC, WO, Z) It also gives us the demand for installed electric and diesel pumping capacities HPe and HPd, that can be expressed as HPe = HPe (Px, PQ, qe, qdQd QeT,E, G, Vavg, Her, WR, WC, WO, Z), HPd = HPd (Px, PQ, qe, qd, Qd, Qe, T, E, G, Vavg, Kr, WR, WC, WO, Z). We are particularly interested in the impact of the policy variables q, and T on installed capacities BPe and HPd, and, subsequently, on output supply and input demand he, h, ,X*, and Y*. 1.30 Impact of policy changes We wish to estimate the impact of policy reforms both over the short run (when the capital stock, particularly in the form of installed irrigation capacity is held constant) and the medium run (when capital stock is allowed to adjust). 1. Increase in flat tariff charged for electricity: in the short run this affects only the farmers in regimes 3 and 4. Increase in flat tariff does not change input and output allocations in the short run so it effect is trivial since a = HPe (from the problem Pl).7 In the medium run, it would lead to change in technology choice (if the increase is high enough) as farmers in regime 3 and 4, either retire or stop using existing electric pumps and shift to lower horsepower electric or diesel pumps. Note that in explaining the choice of technology across farmers, the relevant variable of interest is not the flat tariff perse (this shows little variation across the sample) but the implicit per unit cost of pumping water which differs significantly across clusters because of differences in aquifer conditions (groundwater depth and recharge rate) and conditions of electricity supply. 7 If farmers are credit constrained then increase in fixed tariff would lead to changes in input and output choices - 19 - After econometrically estimating the parameters of the model above, we would be able to compute medium run output supply (input demand) elasticities with respect to an increase in tariff, which is given by L In_Y_ alnYe aInHP, alnY, alnHPd alnT ailnHPe DInT aInHPd alnT =ES + lnY alnHPe +anY, alnHPd E_ +~ + DlnHPJ aInT alnHPd DInT where ES - =a In is the short run output supply (input demand) elasticity with respect to the flat tariff DT- InT T.8 A similar expression for the elasticity with respect to other power supply characteristics can be derived. 2. Shift from flat rate to per unit tariff for all users: In the short run this would affect only farmers in regime 3 and 4. Since the per unit cost of pumping has increased, it is likely to lead in fall in pumping hours and changes in other input and output allocations. The short run effect on profits for those formerly paying flat tariffs would be would be given by ( E7sq + T(HP,). In the medium aq, dP e run there would be some changes in technology choice depending on the relative magnitudes of the per hour cost of pumping by diesel and electric pumps. Important changes in cropping patterns and water transactions are also likely. 3. Increase in availability (A) and quality of supply: In the short-run it affects only the farmers in regime 3 and 4 who use electric pumps. Even amongst this category of farmers, increase in availability affects only those who were formerly constrained by electricity availability in the short- run while improvement in quality of supply affects all farmers. The marginal willingness to pay for a unit increase in availability of supply is given as9 WTP = aA Figure 5 is useful to understand the estimation of the willingness to pay estimate from the estimation of the farm income equation in the previous section. Consider, for instance, what happens if quality of power supply is varied (the analysis of other characteristics of power supply follows analogously). 8 Note that a priori this short run elasticity should be zero. However, this may be tested empirically. 9 Note that in our model we do not distinguish between peak and off peak hours of availability - 20 - Figure 4 - Relation between Ouality of Power Supply and Farm Income Farm Income AL l __ A Q] ~Q2 Quality of power supply - 21 - In Figure 4, quality of power supply is shown along the horizontal axis and farm income is shown along the vertical axis. The curve AB shows the relation between quality of power supply and farm incomes, assuming that everything else remains constant. Suppose that in the initial situation, quality of power supply is at point Q, and thus farm income is I If quality of supply increases to point Q2 then income would increase to 12 as show in the figure. The increase in income, 12 -I, can be interpreted as the willingness to pay for increase in quality of supply from Q2 to Ql. For a unit change in quality, the coefficient on the quality variable in table 6 gives an estimate of how much incomes increase in the short run and thus how much tariffs can be increased without making farmers any worse off. Note the effect of electricity supply characteristics may be different across farmers depending on the amount of land they own. Thus for instance, for larger farmers, the curve showing the relation between farm income and availability might be much flatter (shown as curve CD in figure 5) than for the smaller farmers (shown as curve AB in figure 5). If this is true then this implies that smaller farriers gain more than the larger farmers do with any given improvement in supply conditions In the medium run, increase in scheduled hours of supply will also affect technology choices as one might expect some farmers in regimes 1 and 2 to adopt electric pumps, if the tariff structure remains the same. Those already using electric pumps might shift to lower horsepower pumps and feel less compelled to use backups (such as diesel pumps and generators), if the tariff structure remains the same. - 22 - Appendix 1.1 The Econometric model In the previous section, we classified farmers into four regimes depending on their installed irrigation capacity and showed how the upper bound on water availability is dependent on the regime to which they belong. To allow for the possibility that the effect of the various explanatory variables may be different across these different regimes, it would be useful to estimate a separate short-run profit function for each regime, r, in the following way: ris = Mrj3r + En r = 1, 2 ...4 (10) where the subsrcipt i indexes the observation number (i = 1,2 .n), Ilr5 is the short-run profit function under regime r, Mr is the set of exogenous explanatory variables under regime r (based on the derivation of the short-run profit function in section I above) and Er is the error term associated with the rh regime. Several points need to be noted in the estimation of the above equation. First note that the choice of regime is endogenous so that estimation of above equation by OLS would result in inconsistent estimates. Note that it follows from our theoretical model that the individual chooses to be in regime r if the expected medium-run profits from this regime are at least as large as that under the other regimes. To formalize this idea, let I denote a polychotomous variable that takes on the values I to 4. We observe I = r if the rth regime is chosen I = r iff Ir > Max I (j =1,2, ..4; j r) (11) where, 1, denotes the expected medium run profit from choosing the rth regime and is given as Ii= Nn,y+ lri i= 1,2 .....n (12) where Nr is the set of exogenous explanatory variables (based on the derivation of the medium-run profit function in section I above). To estimate the model given by (10) to (12) we need to make assumptions regarding the distribution of the error terms. We assume that Er are distributed as N (0, cT2r). We also assume that Tr (r=1, 2, .4) are independently and identically distributed with type I extreme value distribution with cumulative distribution function F(llr< c) = exp [- exp (-c)] Let ur= Max Ir - lr (j =1, 2, ..4; j r) It then follows that I=r iff ur