Water Market Functionality: Evidence From the Australian Experience

Market approaches to natural resource management have gained popularity over the last few decades. This study provides an encompassing analysis of the water market in the southern Murray‐Darling Basin (sMDB), Australia, in order to evaluate its performance and the importance of having various types of water rights traded in the market. We do so by investigating a set of market attributes, including price and price volatility, traded volume, number and the average size of transactions, and net import across a number of trading zones in the southern Murray‐Darling Basin. Our findings show that the price mechanism in the water market functions as intended, as the water prices signal the level of scarcity and reflect value that can be derived from water resources. Other factors like crop structure and institutional settings also play important roles in explaining differences in water market outcomes across the considered trading zones within the sMDB market. Overall, our findings document that water markets serve well their fundamental purpose in water resource management to allocate water toward its economically‐highest‐valued uses, and that various types of water rights traded in the market are meeting heterogenous needs of market participants in managing water supply and use.


Water Resources Research
ZHAO ET AL. 10.1029/2022WR033938 2 of 37 regions.These investigations are conducted utilizing market transaction data over a fourteen-year period between 2007 and 2021.As one of the largest, most active and most advanced water markets in the world with abundant transaction data, the sMDB water market can serve as a template for understanding water markets more generally.Through this investigation, we aim to answer questions about the performance of the sMDB water market in terms of serving its fundamental purpose of directing water to its highest value uses; distinct roles that the permanent versus the temporary market and security-differentiated water use rights play; and the level of heterogeneity/ homogeneity of the set of highly connected yet segmented local water markets (trading zones) in the sMDB.
Despite the significance of the sMDB water market, existing literature has tended to focus on a single region (de Bonviller et al., 2020;Qureshi et al., 2010) or a few regions within the sMDB, especially the Goulburn-Murray Irrigation District (e.g., Bjornlund & Rossini, 2005;Wheeler et al., 2008;Wheeler et al., 2016).Studies across multiple regions (e.g., Haensch, 2022;Qureshi et al., 2009;Wheeler, Bjornlund, & Loch, 2014;Wheeler, Loch, et al., 2014) rely on stated preference surveys on water trading, rather than market transactions data as we do here.Existing literature also has been focused on prices and trading volumes of water, and their drivers (e.g., Bjornlund & Rossini, 2005;Brown, 2006;Colby et al., 1993;Connor et al., 2013;Jones & Colby, 2010;Michelsen et al., 2000;Wheeler et al., 2008), while the other attributes of the market, such as the frequency of trading and price volatility have been under-studied.The only study that statistically examined the price volatility of water products in the sMDB is Zuo et al. (2019), in their investigation of the impacts of government buybacks on the water market in a major trading zone.
The key market attributes that we study exhibit temporal variation, necessitating an analysis over a relatively extended time series.We therefore aim to understand the characteristics of the sMDB water market across different trading zones but also to trace the evolutionary path of these characteristics and identify factors influencing their changes over time.Overall, there is currently a deficit of cross-trading zone studies (especially those crossing state borders) in the sMDB, that delves into the characteristics of local water markets and their evolutionary trends based on historical transactions of both allocations and entitlements.The current study fills this gap in the literature.In addition, documenting market performance across a number of individual trading zones within sMDB brings a more general significance to this study.If water markets in individual trading zones of the sMDB are found to function similarly well, despite the notable differences between them characterized by trading constraints, differences in jurisdictional and geographic attributes, and heterogeneous crop structure, it will provide encouraging empirical indication that the water market could be an effective way to manage water resources in other regions of the world.
The benefit of implementing security-differentiated water rights has been hypothesized by previous studies (e.g., Brent, 2017;Lefebvre et al., 2012).Young andMcColl (2003a, 2003b) hypothesized that two types of security are optimal since water users can then achieve different levels of reliability by mixing the two types of entitlements.Nevertheless, there remains an empirical research gap in documenting the distinctive roles these rights might play in the water markets, and their subsequent impact on market efficiency.Empirical studies focusing on the U.S. water markets have assessed the impact of the reliability, or seniority, of entitlements on water prices (Colby et al., 1993;Goodman & Howe, 1997;Payne et al., 2014), while such investigation in the MDB water market is missing.Moreover, the existing literature has primarily concentrated on the effects of reliability on water prices, neglecting other critical attributes such as the volume of trade and price volatility.This study fills these gaps by statistically comparing the price difference between the high and lower-security entitlements and then examining the response of the security-differentiated entitlements to important market fundamentals such as water availability through regression analysis.The findings contribute to a better understanding of the multifaceted roles these entitlements play in the market, particularly in satisfying heterogeneous demands for water usage and managing water supply.We also analyze the inherent distinctions between the entitlement market which is supposed to reflect long-term water demand, and the allocation market which is designed to reflect short-term demand, and the unique roles they each fulfill.Previous U.S. research, such as Brewer et al. (2008) and Brown (2006), has drawn comparisons between the leasing market-temporary transfer of water access rights, akin to the allocation market in the MDB-and the water rights market, which involves permanent transfer of water access rights, similar to the entitlement market in the MDB.While these studies provided insights into transaction characteristics that differ between temporary and permanent markets, thus hinting at their potentially diverse roles, they did not perform statistical tests to determine if these attributes respond differently to market fundamentals.This leaves the question of whether the markets for entitlements and allocations operate fundamentally differently unanswered.Furthermore, previous studies have only offered a static comparison between allocation and entitlement markets.In contrast, our research examines the temporal dynamics of these market types, thereby adding a valuable dimension of understanding to the field.
The paper proceeds as follows: in Section 2, we give a brief background and overview of the water market in the sMDB.Section 3 presents the data sources and summary statistics.Section 4 describes our empirical strategy and model specifications.Sections 5 and 6 present our findings and discussions of the findings.Section 7 offers conclusions.

Background
The MDB water market was formally established in 1980s and water trading has since been growing.There are two types of markets in the MDB: permanent water rights (entitlements) market and temporary water allocation (the actual water) market (National Water Commission, 2011).The entitlements, which represent permanent rights to certain shares of available water in a river or dam, vary in terms of security levels (Ancev, 2015).High-security entitlements (HSEs) have priority to receive water allocations before the lower-security entitlements when water supply is limited (Freebairn & Quiggin, 2006).The long-term average annual yield (LTAAY) of HSEs is 90%-95%, which means that holders of HSEs can expect to receive an average of 90%-95% allocation of actual water (Wheeler et al., 2016).In contrast, the LTAAY of general-security entitlements (GSEs, applicable only to NSW) is approximately 70%, and it is only 30% for the low-reliability entitlements (LREs, applicable only to VIC) (Wheeler et al., 2016).The seasonal allocations of water to entitlements are announced progressively during a water year (which starts in July) by local authorities based on water availability.The allocated water stays accessible to be withdrawn or traded by the entitlement holders throughout the water year, and unused water would be lost at the end of the water year unless it is "carried-over" (Loch et al., 2012).Carryover can be used or traded in the next season but it is not identifiable in the transaction records, so it is not directly analyzed in this study using water trading data.On the other hand, carrying-over unused allocation requires carryover capacities under a license, sometimes referred to as "empty parking space" for water.Entitlements of lower securities such as GSEs and LREs are often entitled for more carryover capacity than HSEs and are therefore used and traded as carryover products (Seidl, 2020).This is especially the case for LREs in the study regions that historically receive no water allocation and are exclusively traded for their carryover capacity.Because of this, transactions of LREs can reflect the demand of carryover capacity, even though carryover trades are not directly identifiable in trading records.
During the early stages of the market, water entitlements were tied to agricultural land, which meant that only agricultural landholders were allowed to own water entitlements.Water trading therefore was limited to only between irrigators, which impeded the efficiency of the market (Wheeler et al., 2013).Aimed at facilitating efficient water allocation towards its highest-valued uses and reducing the barriers to trade, a series of water reforms took place since the 1990s (Lee & Ancev, 2009).The unbundling of land and water, and other policy reforms created preconditions for the rapid development of the water market (Hanemann & Young, 2020).This resulted in non-land-holding investors participating in the market, which has greatly intensified water trading in the MDB (Wheeler & Garrick, 2020).With the increased level of market participation, some derivative products such as forward contracts, entitlement leasing, and carryover capacity leasing have been developed (Seidl, 2020).Various stakeholders view the water market like other financial markets, applying sophisticated investment management (Seidl, 2020).There have also been debates over the impacts of non-land holders, especially large institutional investors, on the market.Some suspect that the speculative activities by financial investors drive up the entitlement and allocation prices (see Wheeler, 2022).However, previous literature found that water scarcity is the fundamental driver of water prices (Seidl et al., 2020;Zuo et al., 2019).The Australian Competition and Consumer Commission (ACCC) conducted an inquiry into the MDB water market and reported no evidence of market power or market manipulation by financial investors (ACCC, 2020).

Study Area
This study focuses on the surface water markets in the southern MDB (sMDB) where water trading is the most active.The sMDB covers parts of New South Wales (NSW), Victoria (VIC), South Australia (SA) and the Australian Capital Territory (ACT).While the trading zones in the sMDB are mostly hydrologically connected and enjoy a similar climate, there are some important differences, such as trading restrictions, crop structure and institutional differences across jurisdictions.These differences could lead to development of diverging water market outcomes across trading zones.It is therefore important to consider and control for the trading zone heterogeneities when analyzing the characteristics of the water market.Here, we study in total eight major trading zones from both NSW and VIC, covering some 80% of all water market transactions in the sMDB.
We study five major trading zones for both the entitlement and allocation market: NSW Murray and NSW Murrumbidgee, VIC Murray 6 above Barmah Choke, VIC Murray 7 Barmah Choke to SA, and VIC 1A Greater Goulburn.These five trading zones are the largest ones in the sMDB for both entitlement and allocation trading, constituting over 70% of transactions.They are also important regions for irrigated agriculture, including high-value crops like cotton and almonds, as discussed below in Section 3.3.The locations of these trading zones are shown in Figure 1.NSW Murray actually consists of two trading zones, NSW 10 Murray above Barmah Choke and NSW 11 Murray below Barmah Choke.The entitlement transaction data obtained from NSW water register does not distinguish between these two trading zones-transactions from both zones are listed under the NSW Murray Regulated River.Given that these two trading zones are geographically close to each other, and they share the same water source and thus the same water allocation announcements, we combine NSW 10 and NSW 11 in our analysis, referring to them together as NSW Murray.
We study additional three trading zones for the allocation markets: VIC 1B Boort, VIC 3 Lower Goulburn and VIC 6B Lower Broken Creek with locations also shown in Figure 1.These trading zones are among largest trading zones in terms of trading frequency and were investigated in ACCC (2020).However, the frequencies of trading are in general too low to generate reliable estimates of the key attributes for the entitlement market in these zones.Specifically, these three trading zones on average have less than 10 entitlement transactions per quarter with non-zero prices, or even no transaction at all in some quarters.The frequencies of allocation trading in these three trading zones, on the other hand, are sufficient for our analysis.Additionally, SA Murray, which is a relatively large and active trading zone, is not included in this study due to transactional-level data not being accessible.Benefiting from the highly interconnected hydrological systems in the sMDB, water trading across jurisdictions is relatively unhampered.This contributes to the market efficiency in allocating scarce water resources (Young & Macdonald, 2001).Nevertheless, there are existing limitations on interregional water trading in allocations, such as the predetermined limits applied between specific trading zones (Hughes et al., 2023).In cases of binding restrictions on interregional trading of allocations, price differentials emerge between regions (Hughes et al., 2023).Here, we are interested in analyzing factors influencing the direction of price differences between trading zones.Water entitlements, on the other hand, are inherently linked to their sources.The mechanism of "tagged trading" allows a change in the point of use of an entitlement to a different region while the entitlement is still subject to the allocation conditions of the source zone and inter-regional allocation trading restrictions (Victorian Water Register, 2023a).Consequently, tagged trading of entitlements mirrors interregional allocation trading and therefore entitlements may be considered as essentially not being tradable inter-regionally.Based on the analysis of market transactions data, we can see that the practice of tagged trading is fairly rare and only represents a very small proportion of total trading.

Data Sources
We use data on historical allocation announcements, transactions in allocations and entitlements, and water usage by certain crops.The data spans the period from 2007 to 2021 water year, in an attempt to utilize all available transactional market data.All transaction data on prices and volumes, and water allocation announcement records were sourced from NSW and VIC state water registers.The data set on irrigated crop water use was obtained from the Australian Bureau of Statistics (ABS, 2007(ABS, -2021)), which reports the application of irrigation water by crop in each natural resource management (NRM) region on an annual basis.The cumulative rainfall data was based on monthly rainfall provided by the Bureau of Metrology (BoM) and subsequently processed by the Australian Bureau of Agricultural and Resource Economics and Sciences (ABARES) to suit catchment-level analysis.The data set was processed and models were estimated using Stata (StataCorp, 2017).

Quarterly Rainfall
We use cumulative rainfall as an indicator of water availability.It is expected that at times of higher rainfall the irrigation water demand and allocation purchases will be lower.Limited by the level of disaggregation of the rainfall data, trading zone VIC 1B and 3 are assumed to receive the same rainfall as VIC 1A, and VIC 6B the same rainfall as VIC 6.These regions are geographically close and follow the same allocation schemes (see Section 3.4).As shown in Figure 2, the rainfall in the study regions exhibited highly aligned movements but differed in absolute values.Overall, VIC 6 received the highest rainfall while VIC 7 received the lowest rainfall during the study period.

Historical Allocation Announcement
Historical allocation announcements by trading zone are shown in Figure 3. VIC 1B and VIC 3 share the same allocation determinations with VIC 1A as they belong to the same water source (Victorian Water Register, 2023b).Similarly, VIC 6B share the same allocation determinations with VIC 6 (Victorian Water Register, 2023b).Historical allocations for LREs in the studied VIC trading zones are not presented in Figure 2, because they have historically received zero allocation.
HSEs, especially those in NSW, received a full allocation (or at least 95%) even during the driest years (Figure 3).In contrast, GSEs did not receive a full allocation almost half the time.This is because HSEs have priority to receive a full allocation when the water supply is insufficient (Freebairn & Quiggin, 2006).GSEs only receive allocation after all water demand from HSEs has been met.Therefore, the allocation made available to GSEs in NSW trading zones is much more sensitive to water availability than the allocation given to HSEs.

Summary Statistics for the Transaction and Key Crop Data
Tables 1-3 show the quarterly summary statistics for HSEs, GSEs and LREs, respectively.The transaction prices are expressed in real terms using 2020 as the base year.Traded volumes are shown from the origin.We analyze quarterly data for three reasons: (a) to analyze attributes like traded volume or price volatility, we have to group individual transactional data over a period of time.The frequencies of entitlement trading are in general relatively low, so the values for the attributes averaged weekly or even monthly would often be based on too few observations to be reliable; (b) agricultural production plans, which drive the water demand of irrigators, usually do not vary at time intervals shorter than a quarter; (c) the crop water use data are only available on annual basis.For the crop water use data, we match the NRM regions with water trading zones based on their geographic location with correspondences shown in Appendix B (Table B1).Our study focuses on cotton and fruit and nut trees as key crops due to their high economic value and quick expansion in the study regions over the studied period.For instance, cotton cultivation, which was historically absent in the sMDB, has experienced rapid expansion in the Murrumbidgee region over the past two decades.By 2016, Riverina (which aligns with the Murrumbidgee water trading zone) emerged as the third largest cotton-growing region in Australia in terms of gross value produced (GVP), contributing 20% of the cotton GVP in NSW (NSW DPI, 2016).As shown in Figure 4, the percentage of total irrigation water applied to cotton in Murrumbidgee has increased significantly since 2010.At the same time, the percentage of irrigation applied to fruit and nut trees has grown in NSW Murray, NSW Murrumbidgee and especially significantly in VIC Murray 7. The significant increases can be attributed to the expansion of the almond industry in these regions (MDBA, 2023).As shown in Figure 5, large acreage of almond trees has been newly planted in Australia during the past five years, indicated by the "non-fruit-bearing" trees as they are young and not yet productive.These new trees are predominately planted in southern NSW and northern VIC (Almond Board of Australia, 2021).ABARES predicts that the maturing of these new almond trees will have further effects on the water market in sMDB and will intensify the impacts of inter-regional trade restrictions (Gupta et al., 2020).We are interested in investigating if the quick expansion of these high-value crop industries is correlated with the divergence in entitlement and allocation prices across trading zones, as described and presented in Section 3.6.Other high-value crops such as grapevines are not included because there have not been significant changes in the acreage of these crops in the studied trading zones over the study period.
Table 4 shows summary statistics for the allocation market.Price averages (VWAPs) for water allocation are similar across studied trading zones.The markets in VIC 1B, 3, and 6B are significantly smaller than the others, in terms of traded volume and number of transactions per quarter.

Volume-Weighted-Average Prices
Entitlement prices have long been a focus of the literature on water markets.As summarized in Section 1, numerous studies in the U.S. have investigated the influence of seniority/priority on entitlement prices (Colby     et al., 1993;Goodman & Howe, 1997;Payne et al., 2014).We provide a t-test in Appendix A for the price difference between HSEs and lower-security entitlements in the same state.The t-statistics suggest that HSEs have significantly higher prices than lower-security entitlements.
We are also interested in price movements of entitlements of the same reliability category over time and across trading zones.As shown in Figure 6, the movements of HSEs prices across five major trading zones were highly aligned over the period 2010 to 2016.More recently (since 2016), however, the prices started to diverge across trading zones.The differences across zones kept increasing between 2016 and 2021.At the end of the 2021 water year, the quarterly VWAP for HSEs in NSW Murray was above $8000/ML, about twice the price of HSEs in VIC Goulburn at that time.Divergences also occurred in the prices of GSEs and LREs across trading zones, though to a less notable extent than for the HSEs (Figure 6).Similar observations can be made for allocation trading (Figure 6).The allocation prices across eight trading zones from both NSW and VIC were mostly aligned during 2010-2019.The prices diverged during 2019 and then quickly converged back together at the beginning of 2020.The allocation prices exhibited again minor divergences during 2020 and then converged in early 2021.
Overall, entitlement and allocation prices across different trading zones appear to be following each other closely during the first part of the study period (2010)(2011)(2012)(2013)(2014)(2015), and then show various levels of divergence during the second half, from 2015 to 2021.Given the highly connected river system, similar climate and water availability conditions that these trading zones share, it is worth investigating the drivers behind the price divergence across trading zones.

Price Volatility
We measure price volatility by the standard deviation of the prices of water products.As shown in Figure 7, HSEs on average exhibited higher price volatilities during the later period (2018-2021), while this was not the case for the lower-security entitlements.The allocation price volatilities in all trading zones exhibited some large spikes caused by a small number of transactions with prices significantly higher or lower than the prevailing spot price.
The allocation price volatilities showed smaller differences across trading zones during the latter half of the studied period, especially from 2018 to 2021.

Traded Volume
Traded volumes of entitlements and allocations are shown in Figure 8.On average, a larger volume of HSEs and GSEs were traded during the early years, from 2010 to around 2016, despite one large spike in VIC 7 in 2019 for HSEs.In general, traded volumes of entitlements did not exhibit seasonality.This is expected since entitlements are regarded as long-term investments, in contrast to allocations which are mostly used to meet seasonal water demand that display some level of seasonality (Figure 8), with peaks usually occurring during the first quarter.
The traded volume in NSW Murrumbidgee shows a somewhat different pattern, which can be attributed to the inter-valley trade (IVT) restrictions that limits trade between the Murrumbidgee and the other major trading zones (Wheeler et al., 2020).

Number of Transactions and Average Transaction Size
Figure 9 shows the number of transactions for entitlements and allocations and Figure 10 shows the average transaction sizes.The number of transactions of entitlements did not show clear seasonality, consistent with the pattern for traded volumes.The number of transactions in the allocation market showed clear seasonality, peaking around the first or second quarter and plunging during the third quarter (Figure 9).Allocation trading took place in VIC 1A and VIC 7 in the form of more frequent and, on average, smaller transactions, while Murrumbidgee tended to have on average larger transaction sizes (Figure 10), again similar to the pattern for entitlement trading.
It is possibly a result of the IVT restrictions: once the trading restriction is removed temporarily, traders may rush to trade on limited quota by placing large orders.

Empirical Design-Fixed-Effects Model
Our empirical analysis aims to investigate differences in key market attributes across trading zones and factors that influence changes in these key attributes over time.While the trading zones in sMDB are in general similar and hydrologically connected to each other, there are some important differences that can lead to heterogeneity in the local market characteristics.This includes differences in time-invariant zone-specific characteristics such as climate, size of the market, geographic characteristics, historical crop type and irrigation infrastructure that may influence key market attributes.While ignoring these time-invariant zone-specific characteristics may lead to omitted variable bias in estimation, the effects of these characteristics are fixed over time and are not useful for understanding the observed changes in key market attributes over the study period.We therefore use fixed-effects to control for the effects of these time-invariant zone-specific factors on the set of market attributes we study.On the other hand, time-varying zone-specific characteristics such as the composition of market participants (e.g., proportion of financial investors vs. traditional water users), market liquidity, and the level of market maturity have important effects on the key attributes of the water market.However, it is not possible to directly estimate and separate the effects of these time-varying characteristics at this stage due to lack of data (e.g., identification of trader types in the transaction data is not currently possible) or due to difficulties in measuring and quantifying the stages of market development.We include a time trend for each zone in the model, in an attempt to capture the joint effects of these time-varying characteristics.
We present the model for each attribute in the following subsections.Each model is estimated separately for allocations, and for entitlements of three reliabilities: high-security, general-security (NSW trading zones only) and low-reliability (VIC trading zones only).All models use the Newey-West estimator to produce estimates of standard errors robust to heteroskedasticity and serial correlation.The maximum lag order of auto- correlation specified for the Newey-West estimator is two, based on the approach proposed by Greene (2018) who suggested a rule of thumb for the estimation of maximum lag order of autocorrelation for Newey-West standard error: m = int(T^(1/4)), where m is the optimal lag order and T is the number of periods in the data set.

Volume-Weighted-Average Prices
To understand the major drivers of entitlement prices and to formally test if the observed price divergences across trading zones are statistically significant, we focus on the fixed-effect model with interaction terms between trading-zone and time.The model is specified as follows: where the outcome variable VWAP it is the volume-weighted-average price of the studied water product (allocation or entitlement) in the ith trading zone in quarter t.The explanatory variable Allo it records the cumulative allocation of the studied entitlement in the ith trading zone in period t (only used in the model for entitlements).
Variable Rainfall t measures the cumulative rainfall in millimeters during the tth quarter in the ith trading zone, while Rainfall t−1 represents rainfall in the previous quarter.
The key crop water usage variables, Fruit_nut it and Cotton it , measure the percentage of total volume of water applied to fruit and nut trees and cotton, respectively, in the ith trading zone.Note that the crop water usage data are only available on an annual level while we use quarterly data for the other variables.The percentage of water applied to fruit &nut trees and cotton reflects the crop structure in each trading zone as well as the demand for irrigation water.A higher proportion of irrigation water devoted to these high-value crops indicates a more inelastic water demand in a given zone, and may affect water prices of both permanent water rights and water allocations in that zone.Potential endogeneity between price and quantity (i.e., water use in this case) is a common concern.However, percentage of water applied to high-value crops is not used in this model to identify a causal relationship between crop water use and entitlement prices, but to control for the changing cropping pattern in studied trading zones.The almond and cotton industries have been growing very fast in some of the sMDB trading zones (e.g., VIC Murray 7 and NSW 13 Murrumbidgee) and have been identified as factors contributing to the price gaps between regions (e.g., see ACCC, 2020; Hughes et al., 2023), which is why we include the water use of these high-value crops as control variables in the VWAP model.
The fixed effects,   ∑ =2  , capture the impacts of trading-zone-specific time-invariant factors.This specification allows the intercept α i of each trading zone, indicated by the dummy variable D i , to be explicitly estimated in the model (except for one baseline zone, Goulburn in this case, that is dropped to avoid collinearity).The term measures the impacts of the zone-time interaction terms on the outcome variable, where the time trend variable t is measured in quarters and is estimated as a continuous variable.The interaction terms enable model to estimate a different time trend for each trading zone to evaluate the effects of some time-varying, zone-specific factors.
Price series can exhibit a high degree of autocorrelation as the current prices may be highly correlated with prices observed in immediately preceding time periods.To assess the possible bias and to incorporate the dynamic aspect of the data, we use an alternative model with lagged dependent variable for robustness check.The procedures and results of this alternative model based on the Arellano-Bond estimator are presented in Appendix C.

Price Divergence
To further investigate the drivers behind the divergence in prices of water products, we employ the following model: While the variables are defined similarly as in Equation 1, the prefix DF_ means the variable measures the difference between the values of that variable in the ith trading zone and that in VIC 1A Greater Goulburn during the same period.VIC 1A Goulburn is used as the baseline trading zone for two reasons: (a) it is the largest trading zone in terms of entitlement volume on issue and one of the most active trading zones in terms of traded volume in sMDB; (b) the entitlement prices are consistently the lowest in Goulburn compared to other trading zones, making it easier to compare the price divergences between zones.Since the dependent variable already measures the differences in VWAP between zones, it is no longer appropriate to include trading-zone-fixed effects.We thus estimate this model using OLS.
The additional variable Volume_onissue it represents the total volume on issue of the studied entitlement in ith trading zone (i.e., total volume of entitlement linked to the ith trading zone) in period t.This variable is used as a proxy for the size of the water market in a trading zone.This variable is not included in the FE models because it is time invariant for the VIC trading zones and slowly varying for the NSW trading zones.It therefore cannot be estimated under the within transformation in FE models.
We use the difference between the percentage of volume applied to fruit and nut trees (the same for cotton) in the ith trading zone and that in VIC Goulburn, denoted by DF_Fruit_nut it (DF_Cotton it for cotton), to reflect the differences in the relative importance of these high value crops in irrigation between different zones.The hypothesis is that water prices are likely to increase more dramatically in those trading zones where there have been notable increases of the acreage under these crops during the study period.The model given in Equation 2formally tests the significance and magnitude of the effects of these high-value crops in driving water price differences among trading zones.
The fundamental value of an entitlement lies in its ability to generate water allocation.The differences in allocation received by entitlements of the same reliability between trading zones, denoted by DF_Allo it , is therefore expected to influence price differences.We also include the water availability variable Rainfall it in this model to test if the price divergences among zones are enlarged during relatively dry periods.Increases in the water use by high-value and perennial crops like fruit and nut trees are likely to drive up water prices, which could be further intensified during drought period as the perennial irrigators have high willingness to pay for water to keep the plants alive.

Price Volatility
The price volatility reflects the riskiness in a market.In the water market, price volatility reflect the fluctuations in the cost of water allocation purchases in meeting irrigation needs and in the return on investment in permanent water rights (entitlements).We measure volatility in this model by the standard deviations of prices.The model of price volatility that we estimate is as follows: where Price_sd it is the standard deviation of the price of water products in the ith trading zone during the tth quarter, so it reflects price dispersion within a quarter for each trading zone.We keep entitlement allocation Allo it and Rainfall it in the model to study the impact of water supply on the volatility of water prices.
We include two additional variables in the price volatility model: total traded volume of the studied water product, Volume_traded it , and the average transaction size (in terms of volume), Trans_size it .The volume-volatility relation has long been debated in finance literature, with most studies finding positive correlation between traded volume and stock return volatility (Kyröläinen, 2008).The average size of transactions is calculated by dividing total traded volume by the number of transactions in a quarter.By including this variable, we aim to study the impacts of large-volume transactions, the so-called bulk trading, on the volatility of prices.

Total Traded Volume and Number of Transactions
Traded volume is an important indicator for how active the water market is in a trading zone.We use the number of transactions as an alternative measure of how frequent transactions happen in the market and thus how active the water market is in a trading zone.The models are specified as follows: where total traded volume Volume_traded it and total number of transactions Num_transactions it are the outcome variables and the explanatory variables are defined above.

Models of Water Allocations
All models for the allocation market are constructed similarly as those for the entitlement market, except for two differences: (a) two variables, total volume on issue and cumulative allocation for each entitlement, are excluded from the allocation models because they are only relevant for the entitlements; (b) We include additional quarter dummies in the allocation models to control for the seasonality exhibited in the allocation market but not in the entitlement market.The models are specified as follows: Volume-weighted price model: All the variables are defined as in the entitlement price model (Equation 1).The additional quarter dummies, Quarter t , indicate if the tth quarter in the data set is the first (base category), second, third or the fourth quarter in the calendar year.We expect the allocation prices to show seasonality, which should be reflected by the estimated coefficient on Quarter t .
Price volatility model: All the variables are defined as in the entitlement price volatility model (Equation 3).
Total traded volume model: Number of transactions model: All variables are defined similarly as in Equations 4 and 5.Both total traded volume and number of transactions of water allocations reflect how active the allocation market is.We expect the market to be more active during irrigation season which extends from November to mid-May.
We present an additional model for the net import of allocations in a trading zone in Appendix D.

Volume-Weighted-Average Prices
The regression results for entitlement prices are shown in Table 5.There is strong evidence that allocation made available to HSEs is negatively associated with their VWAPs, while there is only weak evidence showing a positive relationship between rainfall in the current quarter and HSE prices.These results indicate that HSE prices are more responsive to water supply specifically made available for HSE holders to withdraw rather than to rainfall as such.The percentage of water applied to fruit and nut trees is positively associated with VWAPs in the HSE model.The estimated coefficient indicates that if the percentage of water applied to fruit and nut trees increases by 1%, the price of HSEs will increase by AUD 108.1 in that trading zone, corresponding to a 3.3% increase based on the overall average HSE price.The estimated slopes of the zone-specific time trends indicate an overall increasing trend in HSE prices and possible explanations are discussed in Section 6.
The regression results for the GSE model are similar to those for HSEs.Percentages of the allocation made available to GSEs are negatively associated with their prices (p < 0.05).The percentages of water applied to fruit and nut trees positively contribute to GSE prices.A 1% increase in the percentage of water applied to fruit and nut trees in a trading zone increases GSE price in that zone by AUD 32.2, corresponding to 2.3% increase based on the average price in Table 4.For the LRE, allocation level and percentage of water applied to cotton in a trading zone are dropped out of the model, because all the studied LREs in Victoria receive zero allocation and grow no cotton, as discussed in Section 3. The prices of LREs are negatively associated with the contemporaneous and lagged rainfall.There is also evidence (p < 0.05) indicating that water applied to fruit and nut trees positively affect the prices of LREs.We also found that prices of LREs and GSEs exhibit scale diseconomies, based on the positive correlations estimated between monthly VWAP and average size of transactions (see Appendix E).
Estimation results from the alternative Arellano-Bond model (see Appendix C) are consistent with the FE models, confirming the robustness of the FE models and that the inclusion of lagged dependent variable does not change our major findings.

Price Divergence
The results of the price divergence model (Equation 2) by entitlement reliability are shown in Table 6.The negative coefficient on rainfall indicates that the price gaps of HSEs among trading zones are enlarged during relatively dry periods.The results also show that HSE price differences (between each trading zone and the baseline VIC Goulburn) are positively correlated with allocation differences.The differences between the proportion of irrigation water devoted to cotton (p < 0.05) and fruit and nut trees (p < 0.1), among trading zones are also positively correlated with the price differences.The implication is that entitlement prices diverge based on the  ability to yield water allocation and the value that can be derived from the usage of the water.The differences in total volume on issue are negatively associated with price differences.The baseline trading zone, VIC Goulburn, is the largest zone analyzed in this study for HSEs in terms of total volume on issue and also the zone with the lowest entitlement prices.So, the negative coefficient sign here suggests that the larger the trading zone is (closer in size to the Goulburn), the smaller the price difference will be.This result reflects that HSE prices tend to be lower in larger trading zones.The estimated coefficient on the time trend suggests that the differences between prices in different trading zones are increasing over time.
The results of the GSE models are similar.The allocation differences (p < 0.1) and the differences in the proportion of irrigation water applied to cotton (p < 0.001) are positively associated with entitlement price differences.This result is not surprising since cotton has recently become a major high-value crop in the two NSW trading zones, especially in Murrumbidgee.The time trend variable also has a significant and positive coefficient, indicating increased divergence in VWAPs over time.For the model of LREs, the differences in percentage of water applied to fruit and nut trees are positively correlated with the price differences of entitlements (p < 0.05).Similar to the HSE model, the negative coefficient on the difference in total volume on issue indicates that the prices of LREs are lower in larger trading zones.The significant and positive coefficient of the time trend also indicates increasing differences between the LRE prices over time.

Price Volatility
The results on price volatility of entitlements, measured by the standard deviation of the prices, are shown in Table 7.Total traded volume is negatively correlated with the price volatility in both HSE and LRE models, which suggests that entitlement prices are relatively less volatile in more active trading zones.Allocation is negatively associated with price volatility in the HSE model, indicating higher price volatility for HSEs during relatively dry periods when allocations are lower.The result also suggests that HSE prices are more volatile in regions with a higher proportion of water devoted to high-value crops, that is, fruit and nut trees and cotton.The percentage of water applied to fruit and nut trees is also positively associated with price volatility of LREs.

Total Traded Volume
The estimation results for total traded volume of entitlements are shown in  to be −220.01,indicating a decreasing trend in traded volume over time and the slope of the time trend for NSW Murray can be calculated as −220.01 + 182.84 = −37.17,which also indicates a decline in traded volume over time but at a slower rate.The flatter time trends combined with the lower intercepts mean that differences in traded volume caused by zone-specific characteristics are diminishing over time among these trading zones.The percentage of water devoted to fruit and nut trees in an area is positively associated with the traded volume of HSEs, while both percentages of water applied to cotton and fruit and nut trees are negatively associated the total traded volume of GSEs (p < 0.05).

Number of Transactions
The estimated results for the number of transactions in the entitlement market are shown in Table 9.In the model for HSEs, allocation is positively associated with the number of transactions, indicating HSEs with higher allo-  cation are traded more frequently.Like in the model for traded volume, the number of transactions shows a decreasing trend over time for HSEs but not for the lower-security entitlements.
For GSEs, the percentage of water applied to fruit and nut trees is negatively associated with the number of transactions in a quarter, suggesting that a higher proportion of high-value crops irrigated in a trading zone has a depressing effect on the trading activities of GSEs.

Volume-Weighted-Average Prices
Table 10 presents the regression results for key attributes of the allocation market.There is strong evidence that the allocation prices are negatively associated with both contemporaneous rainfall and rainfall from the previous period.The proportion of irrigation water applied to fruit and nut trees exhibits a positive association with the allocation price, which is consistency observed within the HSE and GSE price models.Additionally, there is a weak evidence suggesting a positive association between the percentage of water dedicated to cotton and the allocation price.The findings also indicate a clear seasonality in allocation prices, with peaks during the first and fourth quarters-these correspond to the summer growing season in the sMDB, when irrigation demand also reaches its peak.Estimation results from the alternative model using Arellano-Bond estimator (presented in Appendix C) are again similar to those from the FE models, confirming the robustness of the FE models.We also found evidence of scale economies in allocation prices (see Appendix E).

Price Volatility
The volatility of water allocation prices is negatively associated with traded volume (Table 10), similar to the results for entitlements.This result reflects the importance of more active trading in terms of reducing price volatility and uncertainty in the market.The percentage of water applied to fruit and nut trees is positively associated with price volatility.The estimated coefficients of the quarter dummies indicate that price volatility is higher during the first and fourth quarters.

Traded Volume
There is strong evidence that rainfall is negatively associated with the traded volume of allocation (Table 10), which can be expected since rainfall is a substitute for irrigation water.The traded volume of water allocation also exhibits clear seasonality that it peaks during the first quarter, again the growing season in the sMDB.Traded allocation volume is negatively associated with the percentage of volume applied to fruit and nut trees, and the magnitude of the coefficient is large.A possible explanation is that irrigators growing these high-value perennial crops tend to rely on their own entitlements for water supply instead of relying on the allocation market.

Number of Transactions
Consistent with the regression results for total traded volume, the number of transactions per quarter for allocation trading is negatively correlated with the percentage of water applied to fruit &nut trees (Table 10).While the total traded volume during the first quarter is significantly higher than all the other quarters, the number of transactions in the first quarter is not statis tically higher than in the second quarter.This result suggests that allocation transactions during the second quarter are still frequent but with smaller trade size on average.

Water Availability and Water Prices
Water availability is a central determinant of pricing within water markets (Bjornlund & Rossini, 2005;Wheeler et al., 2008), yet its relationship has not been thoroughly investigated across the sMDB and existing evidence remains fragmented.Bjornlund and Rossini (2005) identified a significant negative correlation between allocation levels and allocation prices in the Goulburn-Murray Irrigation District (GMID).However, their regression analysis did not factor in rainfall.Wheeler et al. (2008) incorporated a monthly water deficit variable (NDKyab) and allocation level into their examination of allocation and entitlement prices in the GMID.However, they discovered no statistically significant connection between entitlement price, water deficit, or allocation level.Zuo et al. (2019) considered only allocation level, omitting rainfall in their scrutiny of allocation and entitlement price within VIC Goulburn.
In our comprehensive analysis spanning multiple trading zones in the sMDB, both rainfall and allocation percentages serve as water availability indicators.The FE price models reveal compelling evidence that HSEs and GSEs are more strongly influenced by the allocation level than by rainfall.This outcome, although intriguing, is to be expected since entitlements' inherent value is linked to the rights of water allocation, while rainfall does not necessarily (or at least not in a linear fashion) contribute to streamflow or available water in dams (Vervoort et al., 2021).Achieving water allocation from rainfall necessitates a specific intensity to form runoff, influencing dam storage or river flow (Fowler et al., 2022;Vervoort et al., 2021).Conversely, LREs prices appear to be negatively related to rainfall.This variation reflects the distinct nature of the three entitlement types: HSEs and GSEs are valued for their capacity to supply water via actual water allocations, while LREs function primarily as carryover products tied to seasonal irrigation needs.Interestingly, the results of the LRE model closely resemble the findings of the allocation market, which is primarily steered by seasonal irrigation demands.Our study further substantiates that allocation prices are inversely tied to both current and prior quarter rainfall.An increase in rainfall increases irrigation water supply and curtails irrigation demand, leading to a negative effect on allocation prices.Overall, the findings of this study provide robust evidence that the price mechanism in the sMDB water market functions well in terms of signaling the level of water scarcity/supply in the region across multiple important trading zones.

Effects of High-Value Crops on the Local Water Markets
The burgeoning industries of almond and cotton within the study regions have come into focus due to their prospective influence on entitlement and allocation prices.Government report, such as Westwood et al. (2019) has linked the sharp rise in water prices in recent years with the rapid expansion of the almond industry but did not empirically examine this relationship.The FE price models in this study show that the proportional significance of fruit and nut trees in irrigation within a trading zone has a substantial and positive effect on allocation  prices and on all three types of entitlements.This positive correlation can be expected, as growers of perennial crops such as almonds, which necessitate significant initial capital investment, are apt to show higher willingness to pay for water and water rights to maintain their vitality and productivity during dry periods.In contrast, when examining cotton, the percentage of water allocated to this crop within a region does not exhibit a strong correlation with entitlement prices but does influence allocation prices.This finding underscores that the demand for entitlements, notably HSEs and GSEs, aligns more with the need to secure long-term water supplies for perennial crops with extended production plans and inelastic water demand, rather than merely satisfying short-term, seasonal irrigation needs.Crops like cotton, which possess high economic value but display flexibility in water demand between seasons (allowing for suspension during dry years), exert a positive effect on allocation prices but a limited impact on entitlement prices.
In addition to the influence of high-value crops on water prices, they also exert impacts on price volatility and trade volume.A positive correlation is identified between the percentages of irrigation water devoted to fruit and nut trees in a trading zone and the price volatility of HSEs, LREs, and water allocation.Simultaneously, evidence suggests that a higher proportion of water consumption by high-value crops, particularly fruit and nut trees, has a suppressive effect on the traded volume of GSEs and water allocations, although findings for the HSE model are contradictory.While the transfer of water to uses with high economic value may indicate efficiency gains through trading, we note that a water market within a region containing a higher concentration of high-value, and particularly perennial crops, may exhibit characteristics of being both thinner and more volatile.This complex interplay offers essential insights into water market dynamics and the multifaceted effects of specific crop industries.

Uncertainty in the Market
Price volatility in the water market presents an important source of uncertainty for irrigators in terms of access to water, management of production costs, or assessing investment risks, especially for those who regard entitlements as assets.Zuo et al. (2014) investigated price clustering and bidding behavior within the Murray-Darling Basin (MDB) allocation market and identified two primary drivers: uncertainty for buyers and strategic behavior for sellers.The research emphasized that buyer clustering behavior is often propelled by heightened market uncertainty, especially during hotter and drier conditions.This insight illuminates buyers' primary focus on risk management and securing access to water resources during difficult periods.Regression results in this study dovetail on the findings of Zuo et al. (2014), showing that the prices of HSEs and LREs tend to become more volatile during drier spells.The factors behind this observation differ, as the volatility correlates with allocation level for HSEs and lagged rainfall for LREs.Such effects can be further amplified by the positive correlation between the presence of fruit and nut trees in irrigation within a region and water price volatilities.These results highlight the potential risk of escalated uncertainty in the entitlement market during extreme drought, particularly in areas with a high concentration of perennial crops.
Our study also unveils that the price volatilities of HSEs, LREs (though the evidence for LREs is weak) and allocations are inversely related to traded volume.This finding stands in contrast to findings of financial literature, where a positive correlation between volume and volatility has generally been observed (Kyröläinen, 2008).However, it is worth noting that the water market exhibits unique characteristics compared to financial markets.The water market, particularly the entitlement market, tends to be quite thin, featuring sometimes only a handful of transactions within a month or even a quarter.With infrequent transactions, the prices can be highly scattered.
As such, an increase in trading volume may actually contribute to decreased volatility.This insight underscores the critical importance of fostering and enabling more active entitlement trading and the potential benefit of trading activities performed by non-land-holding investors in terms of reducing uncertainty in the market, and the investment and management risk that irrigators bear.

Distinct Nature of the Allocation Versus Entitlement Market in the sMDB
The allocation market generally demonstrates a higher level of homogeneity across trading zones compared to the entitlement market, as can be expected.Water allocations are largely homogenous products and can be traded relatively freely across trading zones while entitlements are tied to their water sources.Our models incorporate zone-specific time trends to assess the influence of potentially significant, yet unobserved, time-variant factors on key market attributes.These estimates illuminate the evolutionary paths of the examined market attributes in each trading zone, going beyond the impacts of control variables.The zone-specific factors, particularly the time-variant ones, appear to exert minimal influence on allocation price volatility and the number of transactions.However, there are notable differences across trading zones within the entitlement market as indicated by the significance of the zone-specific terms.The estimation results reveal an increasing trend in entitlement prices over time across all trading zones, but especially significant in the two NSW trading zones.Notably, the price disparities among trading zones are also widening over time, particularly for HSEs, as suggested by the price difference model.A plausible explanation for this trend, and one that has been widely debated, is the potential influence of large institutional investors driving up entitlement prices for speculative gains (as summarized by Wheeler, 2022).If this were true, prices in zones with a larger share of entitlements held or traded by financial investors would be higher.Since the data required to directly test this hypothesis is not publicly available, it is not possible to control for them directly in our models.Nevertheless, the unobserved impacts of financial investors on water prices may still be reflected in our zone-time interaction terms (or the time trend variable in the price divergence model), given that investor activities are likely time-varying.The ACCC water market inquiry report (2021) suggests that the largest four institutional investors predominantly hold entitlements in VIC while we see faster growth of entitlement prices over time in NSW trading zones, controlling for water availability and crop structure in our models.Our empirical findings therefore do not support the notion that large financial investors are driving up entitlement prices, subject to aforementioned limitations.
An alternative explanation for the overall upward trend in entitlement prices across all trading zones may be rooted in the expectations of market participants concerning future water supply and demand.If there is a prevailing belief that future climate conditions will be drier or that future water demand will escalate (as being projected and reported by BoM & CSIRO, 2022), entitlement prices will likely follow an upward trajectory.This consideration is particularly pertinent with the rapid growth of the almond industry in southern NSW and VIC over the last five years.The expanses of newly planted, yet unproductive, almond trees foreshadow a substantial increase in future water demand in these regions (Gupta et al., 2020).As the trees reach maturity, this anticipation may evolve, contributing to widening price disparities across trading zones.Such dynamics may interplay with existing differences in crop structure, adding complexity to our understanding of market behavior.
Another finding in the entitlement market pertains to the indication of decreasing trends in traded volume and the number of transactions for all three types of entitlements (with the exception of the number of transactions model for GREs) beyond the impact of factors controlled for in the models (Tables 8 and 9).This trend is particularly pronounced for HSEs.There are at least two potential explanations for these decreasing trends: (a) the presence of factors that inhibit entitlement trading, with their negative impacts intensifying over time; (b) a shift towards long-term ownership of entitlements, especially HSEs, as opposed to shortterm trading.It is worth noting that there is only weak evidence for these trends in the GSE and LRE models, making it unlikely that any factor would discriminatorily impede HSE trading.Furthermore, prior literature has documented a rise in market participation and enhancements in institutional and governance structures, promoting active trading in the southern Murray-Darling Basin (sMDB) water market over the last decade (Loch et al., 2018;Seidl, 2020;Wheeler & Garrick, 2020;Zuo et al., 2019).Therefore, these declining trends in trading volume and frequency may signify a shift in HSE ownership towards long-term holders, possibly high-value users such as horticultural irrigators.Seidl et al. (2020) reported that owning excessive water entitlements (especially HSEs) as a buffer is a dominant strategy for many irrigators.Although their study did not analyze such behavior of irrigators by industry (e.g., broadacre, dairy vs. horticulture), it can expected that such strategy is especially important for irrigators with perennial horticulture crops since their water demand is generally more inelastic.In addition, Seidl et al. (2021) pointed out based on a survey with 1,000 irrigators in the sMDB that more irrigators prefer expansive adaptation strategies in response to climate change, which include increasing entitlement holdings.The decreasing trend estimated in entitlement volume traded in our analysis also run counter to recent suggestions that investors have been manipulating the market through abusive behaviors such as high-frequency trading (see Wheeler, 2022).The results also imply a maturation of the entitlement market, reflecting progress toward the fundamental goal of channeling water resources to their most valuable uses.
In summary, we found that the allocation markets in the set of eight trading zones in sMDB exhibit a relatively high level of homogeneity while the characteristics of the entitlement markets are complicated by various zone-specific factors.Our findings also indicate that the trading activities in the entitlement market are more profoundly shaped by long-term factors and production planning, whereas the allocation market responds mainly to seasonal irrigation needs.The allocation models reveal robust seasonal patterns, with the first quarter of the year marked by more frequent transactions, greater trading volumes, higher prices, and increased volatility.Given that irrigation activities in the sMDB are typically concentrated in the summer months, it is logical to observe more intense allocation trading, with corresponding higher prices during this period.

Conclusions
Market approaches have become increasingly used for efficient allocation of scarce resources in natural resource management, including fisheries, forestry and water (Wheeler & Xu, 2021;Young & McCay, 1995).
Highly developed natural resource markets can be similar to other asset markets in terms of their sophistication, but may also exhibit distinct characteristics, for example, that they are often much thinner than financial markets and trading activities are usually subject to more restrictions.The findings from this study document that the water market in the sMDB is, by and large, functioning well.We conclude that the price mechanism in sMDB water market is working well as the prices are highly responsive to the level of scarcity of water resources and reflect the value that can be derived from the use of the water.Other key market attributes including price volatility, volume and frequency of trading also respond to market fundamentals, for example, supply and demand of irrigation water.In addition, the decreasing trends in price volatilities found in our models may be a sign of maturing of the sMDB water market.Our findings stress the importance of encouraging more active water trading that could contribute to reducing uncertainty in the water market.We also conclude that the water market is functioning well in the sense that water rights suitable for long-term investment purposes like HSEs seem to be increasingly owned by long-term users while products designed to meet temporary and seasonal demand like allocations have been traded increasingly actively, indicating increased adoption of water market by irrigators.
Overall, we find that the allocation market is relatively more homogenous across different trading zones than the entitlement market.The dynamics in the various market attributes of allocation market mostly reflect seasonal demand for irrigation water and the variations in most of the market attributes are largely explained by the explanatory variables included in our models.The entitlement market, on the other hand, exhibits no seasonality and a higher level of heterogeneity across trading zones, which adds additional complexity to understanding the operation and functionality of the entitlement market.Our results indicate that there are still unobserved factors influencing the entitlement markets.While data necessary to directly test and separate the impacts of various unobserved factors are not currently available (e.g., data on financial investor activities), the zone-specific time trends estimated in our models could be largely explained by theoretical expectations, as discussed in Section 6.
Market-based approaches to natural resource management should not be regarded as a panacea since markets have their limitations and successful operation of the markets requires a set of enabling conditions.Numerous studies discussed market failure or third-party impacts associated with water markets (e.g., Bourgeon et al., 2008;Hanak, 2003;Wheeler et al., 2020) and failures in the institutional arrangements of water rights and markets in Australia (Young & McColl, 2003a, 2003b).Young and McColl (2005) defined the robustness of a system for tradable entitlements and allocations based on reforms and institutional arrangements.Wheeler (2021) proposed a framework to assess the prerequisite conditions for establishing water markets.Nevertheless, the findings of our study point to the more general benefits of water markets, as they seem to perform well in serving its fundamental purpose of directing scarce water resource toward its highest valued uses and facilitating irrigators to effectively manage water supply risks in agricultural production.Note.Ho: there is no significant price difference.Ha: The VWAPs of HSEs are significantly higher than that of the lower-security entitlements.

Table A1
T-Tests for the Difference in VWAP Between the HSEs and the Lower-Security Entitlements in the Studied States

Appendix C: Arellano-Bond Models
We present an alternative model using the Arellano-Bond estimator to assess the possible omitted variable bias associated with the exclusion of lagged dependent variable and as a robustness check of the FE models.
The inclusion of both fixed-effect terms and lagged dependent variable in the same model may give raise to endogeneity problem, resulting in estimation bias known as the Nickell's bias (Nickell, 1981).The Arellano-Bond (1991) estimator, one of the commonly used GMM estimators, is often employed to solve such endogeneity issue.The Arellano-Bond (1991) estimator utilizes the orthogonality conditions between lagged dependent variables and the disturbance term, producing consistent and efficient estimation for dynamic panel data.There are however, two major shortcomings in the use of the Arellano-Bond estimator: (a).This GMM estimator eliminates all fixed-effect and zone-time interaction terms that we are interested in by first differencing the equation; (b).The inclusion of lagged dependent variable takes over a large part of the explanatory power given the autoregressive nature of prices, while the lagged dependent variable does not provide helpful information in terms of the drivers of the prices.Therefore, we believe that the FE model provides better insight into the fundamental drivers of water prices, but we present this alternative model to test if the inclusion of lagged dependent variable will change our main conclusions.The following model is estimated using the Arellano-Bond estimator: All the variables are defined similarly as in Equation 1.Without the fixed-effect and zone-time interaction terms, we now include a constant term ρ 0 and a single time trend t in the model.Note that with the lagged dependent variable VWAP i,t−1 in Equation C1, the coefficients now estimate the short-run impacts of corresponding explanatory variables on the dependent variable instead of the long-run impacts as estimated in Equation 1.The long-run impact of one variable in this case can be recovered by dividing its estimated coefficient by one minus the estimated coefficient of the autoregressive term.For example, the long-run impact of Allo it is 2 1 − 1 .

C1. Arellano-Bond Model Estimation Results
Table C1 shows estimation result for the Arellano-Bond model on entitlement prices by reliability level.There is a positive and significant correlation between the lagged prices and current prices in all three models, as expected.The significance of allocation percentage and the percentage of water applied to fruit and nut trees are in general weaker in the Arellano-Bond models compared to the FE models.The percentage of water applied to fruit and nut trees becomes insignificant for GSEs and LREs in the AB model.The allocation level is negatively correlated with entitlement prices in the HSE and GRE models, but with a slightly weaker significance in the former (p < 0.05).The in-general weaker significance of explanatory variables in the Arellano-Bond model compared to the FE model is to be expected since the high correlation between the dependent variable and lagged dependent variable has taken over most of the explanatory power (one of the shortcomings in the use of Arellano-Bond estimator as discussed).The results of the Arellano-Bond model confirm that the inclusion of lagged dependent variable does not change our major conclusions, albeit the weaker statistical significance.
Table C2 presents the results of the model using the Arellano-Bond estimator for allocation prices.The estimation results are similar to the FE model that allocation prices are negatively associated with rainfall and positively with water applied to fruit and nut trees (p < 0.05) and cotton (p < 0.1).These results again confirm the robustness of the FE models we focus on.The other variables are defined similarly as in the previous models.We expect that trading zones with higher allocation prices and higher proportion of water devoted to high value crops (cotton and fruit and nut trees) to import more allocation from other zones.

D2. Estimation Results
The estimated model fits poorly, and it is difficult to see any patterns for the volume of net import (Table D1).
Net import seems to be not influenced by trading restrictions between zones rather than these included factors in the model.

Data Availability Statement
Data used in this study are available in the Sydney eScholarship Repository (Zhao et al., 2023).

Figure 2 .
Figure 2. Historical quarterly rainfall (in mm) in study regions.

Figure 3 .
Figure 3. Historical allocation for HSEs and GSEs in the study regions.

Figure 4 .
Figure 4. Percentage of total volume of water applied to cotton and fruit and nut trees in major sMDB trading zones.

Figure 6 .
Figure 6.Quarterly volume-weighted average prices of entitlements by reliability level and water allocation in major sMDB trading zones.

Figure 7 .
Figure 7. Within-quarter price volatilities (measured by standard deviations) of entitlements by reliability level and water allocation in major sMDB trading zones.

Figure 8 .
Figure 8. Quarterly traded volume (GL) of entitlements by reliability level and water allocation in major sMDB trading zones.

Figure 9 .
Figure 9. Quarterly number of transactions for entitlements by reliability level and water allocation in major sMDB trading zones.

Figure 10 .
Figure 10.Quarterly average size of transactions for entitlements by reliability level and water allocation in major sMDB trading zones.
the econometric model for net import.The dependent variable Net_import it represents the net volume of water imported (import volume net export volume) into the ith trading zone during the tth quarter.

Figure D1 .
Figure D1.Quarterly net import of allocation in major sMDB trading zones.

Table 1
Total volume on issue (ML) Quarterly Summary Statistics of Key Variables by Trading Zone for HSEs

Table 3
Quarterly Summary Statistics of Key Variables by Trading Zone for LREs

Table 4 Quarterly
Summary Statistics of Key Variables by Trading Zone for Allocation

Table 5
Fixed-Effects Estimation Results on Entitlement VWAP by Reliability Level

Table 6
Estimation Results on Entitlement VWAP Differences (Price Divergence Across Trading Zone) by Reliability Level

Table 8
. The trading zones, NSW Murray, Murrumbidgee, and VIC Murray 6 which are smaller than the baseline zone VIC Goulburn, have lower estimated intercepts.The estimated coefficients of the zone-specific time trends indicate a decline of traded volume over time in all trading zones.For example, the slope of the time trend for the baseline zone is estimated

Table 7
Fixed-Effects Estimation Results on Entitlement Price Volatility by Reliability Level

Table 8
Fixed-Effects Estimation Results on Entitlement Traded Volume by Reliability Level

Table 9
Fixed-Effects Estimation Results on Entitlement Number of Transactions by Reliability Level

Table 10
Fixed-Effects Estimation Results for Allocation Market

Table 10 Continued
TableB1below shows summary statistics of water use by crop type in each NRM (natural resource management) region.We match the NRM regions with water trading zones based on their geographic location with correspondences shown in Appendix B (TableB1).The NRM region "Murrumbidgee" in the data set during 2010-2015 has been replaced by "Riverina" since 2016.The trading zone VIC Murray 7 geographically extends across two NRM regions "Mallee" and "North Central."To better reflect the crop structure in VIC Murray 7, we use the weighted sum of the key crop water usage data of the two NRM regions, weighted by the total volume applied.

Table D1
Fixed-Effects Estimation Results on Allocation Net Import