WATER RESOURCES RESEARCH, VOL. 40, W12505, doi:10.1029/2004WR003332, 2004
Calculating exchange rates for water trading in the Murray-Darling Basin, Australia Teri Etchells, Hector Malano, and Thomas A. McMahon Department of Civil and Environmental Engineering, University of Melbourne, Melbourne, Victoria, Australia
Barry James Water Resource Management, Victorian Department of Sustainability and Environment, East Melbourne, Victoria, Australia Received 12 May 2004; revised 28 August 2004; accepted 28 September 2004; published 7 December 2004.
[1] Water markets have the potential to greatly improve the productive use of water by
reallocating entitlements to where they are most highly valued. However, trading can actually reduce the volumetric reliability of other parties’ entitlements if relatively more water needs to be supplied to the transferred entitlement after the trade. Exchange rates are a conversion factor applied to the traded entitlement volume to account for third party impacts caused when the water is consumed in a new location. The calculation of exchange rates must consider the inherent uncertainties associated with the volume supplied between years and across valleys. This paper explains the application of exchange rates in overcoming third party effects from trade and demonstrates the calculation of exchange rates for a case study of permanent intervalley trade between four valleys in the Murray-Darling Basin, Australia. Also, it identifies the ‘‘seller matched’’ method as the most desirable system for determining the volume of water to be INDEX TERMS: 1842 Hydrology: transferred each season to supply the traded entitlement. Irrigation; 1869 Hydrology: Stochastic processes; 6309 Policy Sciences: Decision making under uncertainty; 6344 Policy Sciences: System operation and management; KEYWORDS: entitlements, exchange rates, security of supply, third party effects, water trading Citation: Etchells, T., H. Malano, T. A. McMahon, and B. James (2004), Calculating exchange rates for water trading in the MurrayDarling Basin, Australia, Water Resour. Res., 40, W12505, doi:10.1029/2004WR003332.
1. Introduction [2] The Murray-Darling Basin (MDB) traverses four states in eastern Australia including Queensland, New South Wales, Victoria and South Australia. Each state holds constitutional powers for managing land and water, although cooperative governance is facilitated through the MurrayDarling Basin Ministerial Council (consisting of representatives of each state and the federal government). Most major irrigation infrastructure in the MDB is publicly owned and operated, and therefore the state regulatory bodies have a large degree of control over management and operating policies. For instance, after introducing the framework for water reform, the Murray-Darling Basin Ministerial Council ‘‘capped’’ the volume of water that could be diverted at 1993/1994 levels of development. As a result, each state regulator must now ensure diversions are less than their state ‘‘Cap’’ limit. Over 8.6 106 m3 of water is diverted in the Murray Darling Basin, representing an estimated 70% of divertible resources [Australian Water Resources Council, 1988]. Of this, around 88% of water entitlements in the MDB are used for irrigation, making adequate management of irrigation entitlements a critical priority. [3] In most of the regulated valleys in the MDB, an irrigator holds a specific type of entitlement for a nominal volume of surface water. In this paper, the term entitlement Copyright 2004 by the American Geophysical Union. 0043-1397/04/2004WR003332
refers to a ‘‘nominal’’ or ‘‘paper’’ entitlement. (Entitlement types vary between uses and between states; each confers slightly different attributes.) The actual volume that can be ordered though is the amount governed by a proportional allocation (which can be greater than 100% in some valleys), announced by the local managing authority at the beginning of a season and updated during the season, based on available supplies. Therefore the effective entitlement is equal to the paper entitlement multiplied by the allocation announced in any particular season. There is no requirement for an irrigator to use their full effective entitlement, and, on average, the volume utilized by each irrigator is less than the possible allocation. [4] Irrigators in most states of the MDB have been able to supplement their allocations through trade since the 1980s. However, despite steady increases, trading activity is still dominated by intravalley, temporary trade between irrigation users [Crase et al., 2000]. This means a large opportunity still exists to increase efficiency by permanently reallocating entitlements, specifically, through increased intervalley, interstate and intersectoral trading. However, creating large-scale water markets that are efficient, equitable and sustainable is difficult because of the presence of third party effects. [5] The problems associated with third party effects from water trade have been recognized for over 2 decades since Randall [1981] advocated transferable water entitlements as an effective reallocation mechanism in a mature water
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Figure 1. Map showing case study irrigation areas. economy. However, robust and practical tools for addressing these effects have not yet been developed and tested [Lund and Israel, 1995]. There has been an implicit expectation that practitioners and stakeholders will overcome these problems as water markets evolve. The recognized presence of these failures, without corresponding solutions has slowed the expansion of water trading. [6] There are three possible types of impacts which can affect the entitlements of third party irrigators, namely, volumetric reliability, where seasonal allocations to a particular valley are reduced, delivery reliability and water quality [Etchells et al., 2003]. For irrigators, the potential for ongoing reductions in allocations is of paramount concern, and with good reason. In order to be efficient, irrigators need to manage their exposure to the risks associated with variable water allocations and, therefore, they depend on having reasonable expectations of their security of supply. Exchange rates offer a robust and practical tool to mitigate external impacts from trade on third parties’ volumetric reliability. Ensuring the ongoing volumetric reliability of entitlements is critical to underpin confidence and investment in irrigation-dependent industries, where an irreversible investment can be delayed, increased uncertainty will lead to decreased investment. [7] Exchange rates are a conversion factor applied to the traded entitlement volume to account for impacts caused when the water is consumed in a new location. Exchange rates could adjust (reduce or increase) the nominal entitlement volume to ensure that the traded entitlement can be adequately supplied, and to minimize third party impacts. Exchange rates can effectively address volumetric reliability effects since they can adjust the volume of the nominal entitlement so that the same volume is released before and after the trade. [8] The application of exchange rates is most effectively demonstrated using a simplified example. Imagine a farmer in the Sunraysia district (Figure 1) sells his 100,000 m3 entitlement to another farmer in the Goulburn valley and assume transmission losses in supplying the traded entitlement are negligible both before and after the trade. (In practice, physical limits on the volume that is available for transfer means that this trade can only occur after an equivalent trade from Goulburn to Sunraysia.) Sunraysia entitlements have a maximum possible allocation of 100%, and the average utilization in Sunraysia is 80%.
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This means that for a 100,000 m3 entitlement, on average, 80,000 m3 will be released. Goulburn valley entitlements can exceed 100% and average utilization in that valley is 133%, meaning 133,000 m3 needs to be released to supply a 100,000 m3 entitlement. [9] With no exchange rates (or an exchange rate equal to unity), it would be expected that a trade of 100,000 m3 from Sunraysia to Goulburn, would result in an additional 53,000 m3 (133,000 less 80,000 m3) to be released from storage supplying the Goulburn farmer in order to supply the traded entitlement. The additional water released from storage will reduce the volume of water available for allocation across all users supplied from that source. This means that, if no exchange rates are applied, the trade will directly reduce the volumetric reliability (and value) of third parties’ entitlements. Obviously, the impacts of a single trade spread across all third parties will be negligible, but accumulated impacts of water reallocation could undermine the ongoing security of entitlements. [10] In order that no negative third party effects occur, the volume released for the initial entitlement should be consistent before and after the trade: the 80,000 m3 initially released should continue to be released to the buyer after the sale. So, if the utilization of the sold entitlement was 80% and the utilization of the purchased entitlement was 133%, the individual exchange rate would need to be 80% divided by 133%, which equals 0.60. In other words, in order to avoid third party volumetric effects, an individual exchange rate of 0.60 would need to be applied to the sold entitlement (assuming that historical utilization rates continue into the future). [11] Other authors, such as Howe et al. [1986], Delforce et al. [1990] and Brennan and Scoccimarro [1999], have noted the presence of return flow externalities from trade. These effects are not discussed here since most allocation regimes in the Murray-Darling Basin assume no return flows from their entitlements. Therefore there should be no third party effects from changes in the return flows of upstream users since there should be sufficient water released to supply any allocated water. [12] This paper aims to explain the application of exchange rates in overcoming third party effects from trade and demonstrate the calculation of preferred exchange rates for a case study of permanent intervalley trade between four valleys across two states in the MDB. In particular, this paper demonstrates how uncertainty can be incorporated into calculations using stochastic modeling techniques.
2. Key Decisions in Water Transfers [13] A permanent intervalley transfer requires two decisions to be made by valley authorities: the exchange rates to be applied to the trade and the exchange system which dictates the volume of water and Cap to be transferred each season to supply the traded entitlement. The selection of exchange rate and exchange system should be based on minimizing the third party volumetric effects. However, the selection of exchange rates is constrained by two requirements. First, that exchange rates are fixed over the medium term to reduce uncertainty and transaction costs, and second, that bilateral exchange rates need to be reciprocals to prevent agents accumulating entitlements, water or Cap by trading backward and forward. In any particular year, exchange rates
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would have to vary in order to perfectly mitigate third party effects. However, the level of allocations and usage cannot be determined ahead of time when farmers need to make trading decisions. Therefore exchange rates will never perfectly prevent third party effects. It is more feasible to fix exchange rates over the medium term in order to decrease sources of uncertainty and to reduce transaction costs. [14] The selection of an exchange system should be based on the question of whether the potential third party effects should be borne by the selling valley or the buying valley (or whether they should be shared), and whether the volume ceded or Cap transferred should be fixed or variable. Three exchange systems have been assessed for this paper. They have been selected since they represent plausible policy alternatives and represent a range of decisions currently being addressed by policymakers. The three exchange systems are: (1) fixed, where the volume of water ceded and Cap transferred equals a fixed volume each year based on the average volume supplied by the selling valley to the untraded entitlement; (2) matched, where the volume of water ceded and Cap transferred equals the annual volume that the selling valley would have supplied to the entitlement had it not been traded (varies each year) (more accurately called ‘‘Seller Matched’’); and (3) averaged, where the volume of water ceded and Cap transferred equals the annual average of the volume the selling valley would have supplied and the volume the buying valley requires to supply the traded entitlement (varies each year).
3. Assessing Water Transfer Systems [15] There are many potential approaches for assessing exchange rate systems including institutional, legal, economic and scientific approaches. Each of these broad disciplines offers analytical methods and tools to understand the impact of particular exchange rate systems. Indeed, the practical implementation of any exchange rate system needs to incorporate analyses from all of these fields. However, an exchange rate is a quantity, and a methodology to calculate one must be quantitative and based on measurable data. In this paper, a hydrologic approach has been adopted which models water-trading scenarios as volumetric changes in water demand and supply characteristics, and assess the impacts on third parties’ allocations. Implicitly, the hydrologic approach seeks to ensure social welfare is increased as well as private welfare by assuming that the economic or social impacts in different valleys are proportional to the third party volumetric reliability impacts. [16] A model was developed which takes inputs describing the supply profile of buyers and sellers, utilization and loss parameters, and produces metrics that quantify the magnitude of third party impacts. The impacts were determined using 108 years of simulated allocation and supply results (from 1891 to 1999) based on actual streamflow and climate data. Permanent trading scenarios were modeled relative to the unmodified base case (i.e., no trade) by transferring a volume of entitlements from the selling valley to the buying valley in 1891 at a prescribed exchange rate. Then, in each ensuing season, an amount of water corresponding to the transferred entitlement was ceded from the selling valley to the buying valley according to the exchange system option under consideration.
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[17] The model compares for each year in the time series the before-trade and after-trade measures of the ratio of supplied volume to required volume for irrigation across the entire valley. Where the ratio declines for a particular year, this means there is less water available in the valley and negative third party volumetric effects will result. The basic structure of the assessment model utilizes three main time series inputs from the detailed basin water allocation models: allocation, volume supplied and storage content time series. Each of these time series is required for each valley and/or irrigation district along with the values of storage capacities and entitlements from the basin models. Examples of water allocation models used in the Murray-Darling Basin include network routing models such as Resource Allocation Model (REALM) [Victoria University of Technology, 2001] and regressionbased models such as the Murray Simulation Model (MSM) [Close, 2003]. [18] The modeling approach has been designed to demonstrate the efficacy of various exchange systems and exchange rates for water trading in the MDB. To assess the efficacy, it is necessary to test the exchange systems for trading scenarios at different scales and for different entitlements within the MDB. Rather than analyzing all possible trading permutations within the MDB, which would be timeconsuming and duplicate insights, a case study approach has been adopted. The case study incorporates four types of entitlements across three valleys and includes trading at three scales: intravalley, intervalley and interstate trade. [19] The four types of entitlements come from Goulburn, Murray Valley from the Victorian Murray system, Sunraysia also from the Victorian Murray system and Deniliquin (Figure 1). Six potential combinations of trade are possible between the four valleys. For instance, a trade between Goulburn and Deniliquin clearly constitutes an interstate trade, whereas trade between the Murray Valley and Sunraysia can be defined as an intravalley trade since they are both part of the Victorian Murray subbasin and are subject to the same allocations. However, Sunraysia entitlements have a maximum possible allocation (and hence utilization) of 100% whereas Murray Valley entitlements have access to additional water (called ‘‘sales’’ water) allowing potential utilization of up to 200%. [20] The key characteristics of these four valleys vary substantially (Table 1), with Goulburn and Deniliquin with around 3 – 4 times more total nominal entitlements than Murray Valley and Sunraysia. Additionally, the average annual volume used (supplied) in each valley varies significantly, with the Goulburn typically consuming almost twice the volume of Deniliquin per nominal entitlement, reflecting the higher security of entitlements in the Goulburn. This paper concentrates on mitigating third party volumetric effects measured at the annual scale since water allocations are defined on an annual basis and the availability of water to supply entitlements on an annual basis is being assessed. Supply differences between valleys also exist at shorter timescales, but are automatically factored into the annual allocations. The difference in supply characteristics between valleys is demonstrated most clearly through the average utilization per cubic meter of nominal entitlement, which is calculated as the average annual volume supplied to the valley (at the farm gate) divided by the total nominal
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Table 1. Key Valley Characteristics Valley
Total Nominal Entitlements, 106 m3
Average Annual Volume Supplied, 106 m3
Average Utilization per Nominal Entitlement, %
Goulburn Murray Valley Sunraysia Deniliquin
1054 255 347 1192
1399 359 277 741
133 141 80 62
entitlements in the valley (i.e., column four in Table 1 equals column three divided by column two). [21] The magnitude of third party effects is driven by the differences in the buyer and seller’s types of entitlement and, in particular, from discrepancies in the volume utilized per cubic meter of nominal entitlement. Therefore the exchange rate that is expected to be most effective is the ratio of the seller and buyer’s average utilization. Using the average utilizations, these expected exchange rates can be calculated where the expected exchange rate is equal to the ratio of the seller’s average utilization to the buyer’s average utilization. The results for the four valleys are shown below in Table 2. [22] It is important to note that these exchange rates are based on the average ratios of utilizations and do not reflect the time series differences between valleys. Once the time series effects are considered the expected exchange rate may not actually be selected as the preferred exchange rate. The water-trading analysis herein has been designed to quantify and assess these temporal effects of exchange rates and exchange rate systems. The analysis assumes that average utilization in the selling valley remains unchanged by trade: The utilization of the seller is equal to the average in the valley. While this is unlikely to be true, insufficient information is available to make more accurate assumptions. This is one example of the model uncertainty which is addressed later in the paper using stochastic techniques. [23] In order to assess the exchange rate systems, an objective function or metric is required. This metric must reflect the overall objective of exchange rates: to minimize volumetric reliability third party effects. The measure adopted was based on the ratio of actual volume supplied to required supply ( j) for each year, in other words, the ratio of available water posttrade (per cubic meter of nominal entitlement) after water exchange commitments to the volume that would have been demanded prior to the trade. The third party impacts on the seller can be measured by determining the factor, js, which is a ratio of two ratios: the ratio of available water to requirements before the trade, divided by the ratio of water to requirements after the trade. Where there are no third party effects, js will equal 1. The same measure can be determined for the buying valley, where the deviation of a constant, jb, from unity indicates the magnitude of third party effects. [24] Over the length of the available utilization series, the best j result should meet three criteria: a mean closest to 1, the lowest possible standard deviation around this and the least cumulative negative effects where j falls below 1. If these three criteria are weighted according to corresponding constants, then an impact measure (IM) can be defined to summarize the result for each trade type, and for the buyer and the seller. To find the optimal exchange system, a combination of the individual impact measures can be used
(equation (1)), where the lowest impact measure value is preferred. IMTot ¼ IMs;v1;v2 þ IMb;v1;v2 þ IMs;v2;v1 þ IMb;v2;v1 ;
ð1Þ
where IMs,v1,v2 equals the impact measure for the selling valley when valley 1 sells to valley 2 and IMb,v1,v2 equals the impact measure for the buying valley when valley 1 sells to valley 2. IMs,v1,v2 is defined as in equation (2) thus IMs;v1;v2 ¼ fðmðjs Þ 1Þ þ ksðjs Þ þ l
n 1 js;y 1X if js;y < 1; n y1 as;p;y ð2Þ
where f, k, l constants used to weight each term; js,y ratio of actual volume supplied to required supply in the selling valley in year y; m( js) mean of js,y; s( js) standard deviation of js,y; as,p,y posttrade allocation in the selling valley in season y; n number of years, [25] The impact measure for an individual trade for the selling valley is defined in equation (2) (for an individual trade for the buying valley the selling terms in equation (2) are replaced with equivalent terms for the buying valley). Equation (2) consists of three major terms, with the first term measuring the deviation over time of that valley’s j value from 1, the second term measuring the standard deviation of j around the mean, and the third term quantifying the cumulative negative effects in years where j falls below 1 weighted relative to the allocation in that year. This third term is important since the impact measure increases in inverse proportions to the allocation. So, if negative effects occur in a year with an extremely low allocation, the impact measure will rise significantly, reflecting the critical nature of adverse impacts at such a time. These three major terms are respectively weighted by f, k and l, which are all assumed to equal 1 for the base case analysis presented here.
Table 2. Expected Exchange Rates Buying Valley Selling Valley
Goulburn
Murray Valley
Sunraysia
Deniliquin
Goulburn Murray Valley Sunraysia Deniliquin
1.00 1.06 0.60 0.47
0.94 1.00 0.57 0.44
1.66 1.76 1.00 0.78
2.15 2.27 1.29 1.00
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Figure 2. Impact measure for exchange rates by exchange system (50 GL traded). Expected exchange rate (r) corresponds to calculated exchange rates in Table 2. [26] The assessment itself is based on analyzing a variety of conditions and trading scenarios to determine which set of exchange decisions minimizes the total impact measure (IMTot). The most simple and direct analysis is presented here, comparing the total impact measure for various exchange rates for each of the three exchange systems (‘‘fixed’’, ‘‘matched’’ and ‘‘averaged’’). This analysis is presented for the six potential trading scenarios between the four valleys.
4. Preferred Exchange System [27] The assessment model was applied to the six potential trades between Goulburn, Murray Valley, Sunraysia and Deniliquin for each of the three exchange systems, fixed, matched and averaged. In each of these 18 cases, many exchange rates were tested based around the expected exchange rates given in Table 2. In all of these examples, the volume of entitlement traded was
50 GL (reflecting a large enough volume to expect some significant results for large valleys as well as small valleys), the length of time series was 108 years (from 1891 to 1999) and the weighting factors, f, k and l, were all set to equal 1. [28] The impact measure of overall performance has been plotted against the exchange rates (Figure 2) for each of the exchange systems to show which exchange system yields the least third party effects (the lowest impact measure) and which exchange rate is most appropriate for each trade. The exchange rate on the x axis is defined in terms of a particular direction of trade, and automatically implies the reciprocal exchange rate for trades in the alternate direction. In all cases, the exchange rate that has been presented is that which is less than 1.00. The expected exchange rates (r) correspond to the calculated values in Table 2 and are shown on each graph. [29] This analysis is designed to yield insights on two issues: which exchange system is most effective and what is
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the best exchange rate for each trade. On this first question, the six graphs presented in Figure 2 show clearly that the fixed system is the poorest of the three options since it has the highest impact measure across the spectrum. The averaged system performs reasonably well, although the impact measure is consistently higher than the matched system. For this reason, the matched system is assumed to be the preferred system, an assumption which is confirmed through sensitivity testing. [30] Sensitivity analyses were conducted to understand the impact of assumptions on the preferred exchange system. In particular, analyses were constructed to understand the performance of exchange systems in relation to four key variables: the weighting of components (f, k, l) of the impact measure, the volume of trade, assumptions about the buyer’s utilization of the traded entitlement and the relative size of the trading valleys. [31] The first sensitivity test focused on understanding how the weighting of the three criteria within the impact measure affects the relative performance of exchange systems. In particular, the most critical outcome from a water user’s perspective is minimizing negative effects in low allocation periods since these negative effects could jeopardize the ongoing viability of enterprises. Given the importance of avoiding these negative impacts, the impact measures presented in Figure 2 were repeated with the weighting of the negative impacts component tripled (i.e., in equation (2), l = 3 while f = 1 and k = 1). This analysis shows that the matched system is preferred for all trades when negative impacts in low allocation years are weighted more heavily, giving further credence to the conclusion that the matched exchange system is preferable. [32] The second sensitivity test focused on the volume of trade. The analyses discussed so far in this section were based on 50 GL of entitlements being traded, which is only likely to be achieved over the longer term if trade moves in a particular direction. The magnitude of volumetric third party effects increases with the volume of entitlements traded, although the minimum does not shift unless the volume traded results in increased reservoir spillages. [33] The analysis so far assumes that the level of utilization by the buyer in any particular year is the same as the average utilization within the buying valley in that same year. It is possible that buyers of entitlements will have different utilization profiles to the average user level, because of different management practices or more vigorous trading behavior. To understand the potential effects of different utilization by buyers, the impact measure was recalculated for various exchange rates with a matched exchange system when the buyer has a different utilization (expressed as percentage change on current) to the average user in the buying valley. This analysis shows that changes in the buyer’s utilization can significantly change the preferred exchange rate since the volume supplied (on average) to the buying valley will change. The direction of the change in exchange rate will be most heavily influenced by the larger valley’s supply profile. For example, if the larger valley utilizes more as a buying valley and this increases the supply deficit between the two valleys, the preferred exchange rate will move further away from 1. If, by utilizing more water, the larger valley decreases the gap in supply profiles (i.e., the larger valley has a lower initial
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average utilization than the smaller valley), the preferred exchange rate will move toward 1. [34] Despite the importance of the larger valley (in relative terms) in determining the impact of buyer utilization changes on exchange rates, the actual size of the valley itself does not change the preferred exchange rate. This is demonstrated by the final sensitivity analysis, which shows that although the absolute level of the impact measure changes when the relative valley sizes change, the location of the minimum does not change. Therefore the preferred exchange system and preferred exchange rate is insensitive to the relative valley size. [35] These sensitivity analyses confirmed that the matched system is the most effective exchange system. Even when parameters were changed in sensitivity testing, the matched system consistently delivered relatively low levels of third party effects as measured by the impact measure. [36] Apart from being the most effective exchange system, it is likely that the matched system would be easier for stakeholders to agree on as a method for determining water and Cap transfer commitments. This is because the selling valley can limit its potential liability at a particularly sensitive time when the entitlements are leaving the valley and potentially adverse externalities are being experienced by the local community and economy. In contrast, the buying valley is likely to be generating positive social and economic externalities associated with the use of more water and may be more amenable to accepting the supply risks. Also, the matched system offers advantages by being simple to communicate and monitor.
5. Preferred Exchange Rate [37] As well as determining the preferred exchange system, the assessment analysis was used to determine which exchange rates are preferable. The graphs in Figure 2 show that there is a preferred exchange rate for each trading scenario under the modeled conditions corresponding to the minimum impact measure for each curve. Not surprisingly, the minimum exchange rate in most cases corresponds to the expected value presented in Table 2. [38] In terms of the preferred exchange rate, the analyses showed that, under most circumstances, the expected optimal exchange rate does indeed lead to the lowest third party effects. However, there are several exceptions to this rule, in particular, when spills from storages due to capacity constraints reduce the available water (as in the case of the Goulburn-Deniliquin trading scenario in Figure 2) and when it is assumed that the buyer’s utilization is different from the average buying valley user. This means that practitioners who are responsible for calculating exchange rates should focus on three key issues: determining the expected exchange rate (on the basis of the ratio of the expected selling valley utilization to the expected buying valley utilization); estimating the impact of trading on spills in the buying and selling valleys (which may require deterministic modeling of additional inflows or reduced outflows); and developing reasonable assumptions regarding the buyer’s utilization behavior. [39] Another important observation is that the sensitivity of selecting the correct exchange rate varies dramatically
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for different trading scenarios. For example, an exchange rate for trade between Sunraysia and Deniliquin would yield a similar result for any value between 0.70 and 0.80 (where the exchange rate here is expressed as from Deniliquin to Sunraysia). In contrast, the impact measure for trades between Goulburn and Sunraysia or Murray Valley and Sunraysia can change dramatically in response to relatively small deviations in the exchange rate. The impacts can be seen to rise dramatically, because of the relatively small size of Sunraysia, resulting in an amplification of impacts. [40] Overall, the assessment shows that the expected exchange rate is indeed the preferred exchange rate as long as there is storage capacity for the ceded volumes of water each season. These conclusions, however, assume that all of the supply and trading conditions are known and that the historical utilization series represent future utilization behavior.
6. Incorporating Uncertainty [41] The calculation of exchange rates is dependent on several random variables, which makes the exchange rate itself, also a random variable. As Bouchart and Goulter [1998] note, the irrigation environment is one characterized by uncertainty, and management decisions need to be made without complete information about future events. [42] The objective for exchange rates is to mitigate third party volumetric effects, but in the face of uncertainty the best exchange rate should be selected based on broader considerations. In addition to the efficacy of particular exchange rates, it is important to consider the impact that exchange rate choices will have on transaction costs and on perceptions by traders which might impact their likelihood of becoming active in the market [Challen, 2000]. There are larger costs associated with implementing nonunity exchange rates compared with unity exchange rates. It is difficult to estimate the difference in these costs, although components are likely to include costs in education, negotiation and system changes. Nonunity exchange rates would increase the perceived complexity of the market, increasing the need for assistance or service providers and thus increase transaction costs. Therefore the simpler the rules for trading, the lower the transaction costs. If the objective is to allow socially optimal and privately optimal deals to take place, and, if there is a reasonable probability that a particular exchange rate could equal 1, then unity should be selected. [43] Given the importance of understanding if an exchange rate of unity is appropriate, it is necessary to consider the potential impacts of uncertainty on the calculation of the expected exchange rate. The calculation of exchange rates depends on having an accurate understanding of the volume of water utilized by buyers and sellers for each cubic meter of their water entitlement. Currently, the estimates of utilization are derived from water allocation models that use streamflow and climate data, along with many programmed rules, constraints and relationships, to determine deliveries to each district. These models have evolved over the past decades but do not necessarily reflect future system behavior. Also, these time series are developed at an aggregated level for irrigation districts or diversion reaches
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and it is assumed that individual buyers and sellers have utilization behavior equal to that of the average for the district if the model output is used to calculate exchange rates. [44] These factors mean that utilization time series provided by the water allocation models are not robust enough to constitute the sole source for calculating exchange rates, although they are the best source available. If they are to be used as inputs, uncertainty needs to be incorporated into modeling, in order that a recommended methodology for exchange rates is sufficiently robust. To achieve this, stochastic modeling was used to synthetically generate a distribution of potential exchange rates, allowing the robust estimation of the probability of the exchange rate equaling 1 for each of the six trading scenarios. Given the uncertainty surrounding the original utilization time series, and given that these series are modeled output and not historical records, parameter uncertainty was incorporated into each valley model using Stedinger and Taylor’s [1982] method. [45] Significant short-term persistence was seen at lag 1 in the Goulburn, Murray Valley and Deniliquin districts and so an autoregressive (AR) type model was estimated for each of the four valleys based on the rapid decaying nature of their respective correlograms [Salas et al., 1980]. Also, significant cross correlation was observed at lag zero for four of the six trading scenarios. Overall, a lag-1 autocorrelation term and a lag-zero cross-correlation term were required for most of these relationships. This means that the most appropriate modeling approach was to use a multisite model with autocorrelation at lag 1 and cross correlation at lag zero. One thousand replacements were generated for each of the districts using a multisite Matalas residual approach [Matalas, 1967; McMahon and Mein, 1986]. [46] The first step in modeling the trading scenarios was to ensure that all of the time series were stationary. (The Sunraysia and Deniliquin series’ both exhibited significant trends, which were removed before standardization and added back after simulation.) The next prerequisite in applying the residual approach was to have a standardized, normally distributed series, meaning that the skewness needed to be removed. The series, at all four sites, were standardized using the Wilson-Hilferty transformation. McMahon and Miller [1971] showed that the WilsonHilferty transformation is valid for coefficients of skewness between negative two up to positive two. Since all of the coefficients of skewness fit within this range, it is valid that this transformation is applied to the four utilization time series. Additionally, in order to incorporate parameter uncertainty into the residual approach, the mean, standard deviation, autocorrelation and level of skewness were treated as random variables based on a gamma-based posterior distribution. The cross correlation between sites was held constant within the estimated model, although the stochastic variability driven by other parameters did lead to variability in the cross correlations observed between the simulated series. A comparison of the original and stochastic characterizing measures shows that the characteristics of the series with parameter uncertainty were very similar for the mean and, as was expected, the standard deviations of the stochastic series were higher than the original and the coefficient of skewness was consistently lower.
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Figure 3. Distribution of preferred exchange rates with parameter uncertainty (on the basis of 1000 replacements). E(r) refers to the expected exchange rate, and s(r) refers to the standard deviation of the distribution.
[47] Using the stochastically generated time series, 1000 preferred exchange rates were calculated for each trading scenario. The results of the simulation are shown in Figure 3, with histograms of exchange rates reflecting the distributions. Overall, it can be seen that the expected exchange rate is the median; however, the tails cover a wide range of exchange rates. [48] Previously, it was argued that an exchange rate of unity is preferable where there is a reasonable likelihood that unity could be the preferred exchange rate. Using this logic, the distributions of exchange rates shown as histograms in Figure 3 can be analyzed to determine whether any exchange rates of unity can be justified. Overall, these distributions show that only the Goulburn – Murray Valley trading scenario contains unity within a single standard deviation of the expected exchange rate. Therefore the preferred exchange rate should be selected as unity for
Goulburn – Murray Valley trades. Where there is a lower probability of a unity exchange rate (i.e., where unity only occurs in the tails of the distribution), the expected exchange rate should be selected, since that is the best available estimate.
7. Conclusion [49] Intervalley water trading requires that the buying and selling valleys agree on an exchange system: the volume of water and Cap transferred each season to supply the traded entitlement. This paper demonstrates that of three distinct exchange systems (fixed, matched and averaged systems), the matched system (or ‘‘seller matched’’ system, where the volume of water ceded and Cap transferred equals the annual volume that the selling valley would have supplied to the entitlement had it not been traded) is the preferred
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exchange system since it most effectively mitigates third party effects related to volumetric reliability of supply. This exchange system offers the additional advantage of being relatively simple to communicate with stakeholders and limiting the potential risks to the selling valley. [50] The key lever in mitigating third party volumetric effects from trade is the exchange rate applied to the traded entitlement. This paper demonstrates that the preferred exchange rate is almost always equal to the expected exchange rate: the ratio of the seller’s average utilization to the buyer’s average utilization. The exception to this is where there is insufficient storage capacity for ceded water or where the utilization behavior of buyers varies significantly from the buying valley average. [51] The calculation of exchange rates depends on inputs with significant sources of uncertainty, and the selection of exchange rates should prioritize the selection of unity over nonunity values to minimize trading costs, as in the case of Goulburn – Murray Valley trades. This uncertainty can be incorporated into the calculation of exchange rates by using stochastic data generation techniques to create distributions of exchange rates. [52] Several institutional conditions are required to enable the application of exchange rates, such as well-defined entitlements, robust estimates of the utilizations of various types of entitlements and an ability to control water transfers through time. This methodology has been developed for the conditions in the Murray-Darling Basin where entitlements are defined and allocated at the valley scale and utilizations are able to be calculated at the valley scale. However, the methodology could readily be applied in other circumstances where individual entitlements have differing allocations and utilizations.
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Brennan, D., and M. Scoccimarro (1999), Issues in defining property rights to improve Australian water markets, Aust. J. Agric. Resour. Econ., 43(1), 69 – 89. Challen, R. (2000), Institutions, Transaction Costs, and Environmental Policy: Institutional Reform for Water Resources, Edward Elgar, Cheltenham, UK. Close, A. (2003), Current conditions benchmark run 30-1-2003, software, Murray-Darling Basin Comm., Canberra, ACT. Crase, L., L. O’Reilly, and B. Dollery (2000), Water markets as a vehicle for water reform: The case of New South Wales, Aust. J. Agric. Resour. Econ., 44(2), 299 – 321. Delforce, R. J., J. J. Pigram, W. F. Musgrave, and R. L. Anderson (1990), Impediments to free market water transfers in Australia, in Transferability of Water Entitlements: Proceedings of An International Seminar and Workshop, the Centre for Water Policy Research, Univ. of New England, July 4th – 6th 1990, pp. 51 – 64, Cent. for Water Policy Res., Univ. of New England, Armidale, N. S. W., Australia. Etchells, T., H. Malano, and T. McMahon (2003), Developing a methodology to calculate water trading exchange rates, Aust. J. Water Resour., 7(1), 41 – 48. Howe, C. W., D. R. Schurmeier, and W. D. Shaw Jr. (1986), Innovative approaches to water allocation: The potential for water markets, Water Resour. Res., 22(4), 439 – 445. Lund, J. R., and M. Israel (1995), Water transfers in water resource systems, J. Water Resour. Plann. Manage., 121(2), 193 – 204. Matalas, N. C. (1967), Mathematical assessment of synthetic hydrology, Water Resour. Res., 3(4), 937 – 945. McMahon, T. A., and R. G. Mein (1986), River and Reservoir Yield, Water Resour. Publ., Highlands Ranch, Colo. McMahon, T. A., and A. J. Miller (1971), Application of the Thomas and Fiering model to skewed hydrologic data, Water Resour. Res., 7(5), 1338 – 1340. Randall, A. (1981), Property entitlements and pricing policies for a maturing water economy, Aust. J. Agric. Econ., 25(3), 195 – 219. Salas, J. D., J. W. Delleur, V. Yevjevich, and W. L. Lane (1980), Applied Modeling of Hydrologic Time Series, Water Resour. Publ., Highlands Ranch, Colo. Stedinger, J. R., and M. R. Taylor (1982), Synthetic streamflow generation: 2. Effect of parameter uncertainty, Water Resour. Res., 18(4), 919 – 924. Victoria University of Technology (2001), Realm user’s manual: Realm version W1.4h, report, Melbourne, Victoria, Australia.
References
Australian Water Resources Council (1988), 1985 review of Australia’s water resources and water use, report, Aust. Gov. Publ. Serv., Canberra, ACT. Bouchart, F. J. C., and I. C. Goulter (1998), Is rational decision making appropriate for management of irrigation reservoirs, J. Water Resour. Plann. Manage., 124(6), 301 – 309.
T. Etchells, H. Malano, and T. A. McMahon, Department of Civil and Environmental Engineering, University of Melbourne, Parkville Campus, Melbourne, Victoria 3010, Australia. (
[email protected]) B. James, Water Resource Management, Victorian Department of Sustainability and Environment, 240-250 Victoria Parade, East Melbourne, Victoria 3002, Australia.
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