Do Agricultural Pumping Restrictions Hold Water? General Equilibrium Cost Impacts of Regulated Groundwater Withdrawals ∗ Andrew Schreiber†‡ ‡

Department of Agricultural and Applied Economics, University of Wisconsin-Madison, US

November 20, 2017

Abstract Throughout the United States, agricultural irrigation contributes to growing groundwater scarcity concerns. In this paper, I quantify the regional consequences of groundwater withdrawal restrictions for agricultural sectors, basing the analysis on a calibrated multi-sectoral, multiregional computable general equilibrium model. I provide a methodology for ex ante regional analysis of supply restrictions of a non-market good and use the model to evaluate economic mechanisms which could improve water and factor utilization in the production of agricultural goods. To achieve this purpose, I use county level economic data and spatial data on groundwater withdrawals for the Central Sands of Wisconsin. Restrictions produce heterogeneous impacts on employment and welfare across counties, depending both on the level of agricultural activity and the policy instruments used to ration water use. Command and control regulation is expensive relative to market based mechanisms, though overall costs are small. Long run losses in aggregate GDP range up to approximately 0.1%, or $10 million across simulations which achieve reduced water withdrawals comparable to levels observed in 1985. JEL Codes: D58, Q25, Q58, R13 Keywords: Computable General Equilibrium, Water, Command and Control, Tradable Permits, Regional Welfare

∗

Preliminary; do not circulate or cite without permission. Support for this research is gratefully acknowledged from the Single Step Foundation through the CIAS mini-grant program. For helpful comments, I would like to thank Thomas Rutherford, Corbett Grainger, Ian Coxhead, Steven Deller, Nick Parker, George Kraft, Robert Smail, participants of seminars hosted by the Department of Agricultural and Applied Economics at the University of Wisconsin-Madison, seminar participants at the Water Research Conference at University of Wisconsin-Whitewater, and two anonymous reviewers. All errors are my own. † Email: [email protected]

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Schreiber (2017)

1

Introduction Prolonged periods of drought are a predicted consequence of global warming (Trenberth et al.

2014; Dai 2013). The United States faces this challenge in an environment that is regionally heterogeneous in both fresh water availability and withdrawal patterns (Karl 2009). A survey conducted by the GAO in 2014 found that 80% of statewide water resource managers cite concern for below average fresh water availability within a decade.1 Though fresh water supply concerns are increasing, the price of fresh water doesn’t often reflect its true level of scarcity (in many cases, the price is zero). As a result, many parts of the country (and world) engage in a groundwater “free for all” (Famiglietti 2014). This is particularly true for agricultural irrigation, which accounts for nearly 70% of all groundwater withdrawals in the United States in 2010. In this paper, I assess the general equilibrium costliness of restricting agricultural rights for groundwater on the regional economy and provide a methodology for ex ante regional analysis of supply restrictions of a nonmarket good using data from the Central Sands of Wisconsin. The analysis examines channels for improvements in water utilization by agricultural irrigators facing prospective reductions in groundwater allocations. Property right allocations for fresh water is under state jurisdiction and depends on whether water is withdrawn from surface or ground sources in the United States.2 Fresh water sources can be linked hydrologically, meaning high levels of withdrawals from one source can have external impacts on another. Barlow and Leake (2012) estimates that groundwater contributes up to 90% of annual streamflow volume in parts of the country. However, groundwater and surface waters are typically regulated separately, limiting use of both to a “reasonable” level (Joshi 2005). Externalities may exist in regions where property rights structures fail to account for fresh water use across sources. In an environment of competing water users, cost-benefit analysis can provide a method for assessing whether policies designed to re-allocate water across the economy are more beneficial to society relative to the status quo. The benefits of water allocation restrictions on irrigators in a region without other sector level competition for the resource would fall under the non-market valuation category (e.g. recreation benefits of lakes and streams, capitalization into housing prices). The costs, if restrictions fall on sector level use, would constrain production, inducing feedback effects across other sectors and agents in the economy. In the Central Sands of Wisconsin (see figure 1), large levels of groundwater pumping sustain a $180 million potato farming industry but has stressed local lakes and streams.3 Recent decades have witnessed both increasing groundwater use in agricultural production and falling water levels in regional lakes and streams. The causal link between increased irrigation and lower lake/stream 1

See the report: Freshwater: Supply Concerns Continue, and Uncertainties Complicate Planning (GAO-14-430). Surface water access is typically tied to land ownership or dictated through prior use, while groundwater access is either similarly based on land ownership or unregulated. 3 Wisconsin ranks third amongst states for potato production, generating roughly $260 million in sales in 2015 (according to the National Agricultural Statistical Survey, State Agriculture Overview in 2015). The Central Sands accounts for the majority of this output, with approximately 70% of the total harvested area for potato production in the state for 2011 (calculated using the USDA Cropland Data Layer). 2

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Figure 1: Wisconsin’s Central Sands is comprised of Adams, Marquette, Portage, Waupaca, Waushara and Wood counties, located in the center of the state with county borders outlined in black. Dots denote water withdrawal sites registered with the Department of Natural Resources in Wisconsin from 2011-2014.

levels is controversial. The perceptions of property owners (and others that value amenities offered by the lakes and streams) differ from those of farmers, whose livelihood partially depends on crop irrigation. Implicitly (or explicitly) the public debate on water use in Wisconsin concerns determining an equitable allocation of property rights between farmers, property owners and all others valuing the environmental amenities in the region. The only constraints on agricultural groundwater use are the cost of capital for irrigation (e.g. well installation, center pivots) and the electricity required to pump water to the surface.4 Under Wisconsin’s Public Trust Doctrine, the state’s lakes and rivers are declared a public resource. However, access to the groundwater system for irrigation is virtually unrestricted. A permit is required to install a high capacity well for groundwater pumping, though limits on allowable water withdrawals are typically nonbinding. This paper considers one side of the cost-benefit equation: the costs of restricting agricultural regional fresh water use. I quantify the impacts of regulated water allocation restrictions on the regional economy and assess who bears the economic costs, basing the analysis on numerical simulations from a multi-regional, multi-sectoral computable general equilibrium (CGE) model. Setting aside the more complex question of what constitutes the optimal level of irrigation in an envi4

In the Central Sands, court rulings and legislation thus far have been concerned with the provision of high capacity wells, or wells that exceed 100,000 gallons pumped per day. Decisions on whether the Wisconsin Department of Natural Resources approval should be required for re-purposing well water uses and to what extent cumulative effects of installed wells in a region should be considered when allocating new permits are pending.

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ronment of competing water users, I consider groundwater allocation reductions of up to 40% by agricultural irrigators. A 40% reduction relative to 2011 water withdrawals in the Central Sands is roughly equivalent to withdrawal levels in 1985, while smaller restriction levels of 10%-30% roughly correspond to withdrawals throughout the 1990s.5 A water allocation mandate adds an additional constraint on the economy, generating shadow values for sector level water use. In these calculations, I study scarcity rent implications by comparing command and control regulation with cap and trade permitting schemes. Though markets for water have had mixed success in the United States, the Central Sands presents a scenario where water transfers would occur between rural counties and irrigators, with potentially limited transactions costs. I use permits to investigate the impacts of inter-sectoral and inter-regional water allocation trade, and the extent to which recycling permit revenues affect the distributional outcomes of policy. Relative to command and control type regulation, market based mechanisms provide firms a least cost channel to satisfy environmental restrictions by re-allocating water to sectors with the highest value for the resource (Hahn and Stavins 1992). Revenue recycling in permitting scenarios is studied either through lump sum payments or through lowering other distortionary taxes in the regional economy. Permitting policy flexibility is analyzed through three schemes differing in rent allocation and restrictions on trade. The most restrictive is similar to the basic command and control mandate by enforcing permits to be non-tradable. All agricultural users are required to restrict withdrawals by a fixed percentage, allowing scarcity rents to accrue to households. The other two schemes consider fully tradable permits between sectors and counties. In the fully tradable case, those who can reduce water withdrawals at the lowest cost will do so, and agricultural irrigators for who the equivalent costs are greater will buy more permits (Stavins 1998). This represents a transfer of water allocations between sectors and regions.6 Scarcity rents are accrued either at the household or firm level. An output based allocation of fully tradable permits to agricultural water users is used for the firm case. While the economics literature advocates the use of scarcity rents in revenue recycling schemes to reduce other distortionary taxes, a common theme in United States environmental policy using market based mechanisms is to forgo possible double dividends in favor of allocating permits, and the resulting scarcity rents, directly to affected firms (Fischer and Fox 2007). I find that overall economic costs are small, though they differ across counties. Economic impacts are driven by the underlying farming intensity in the region as well as by the policy implementation. Command and control regulation is relatively more expensive than the tradable permitting cases. In permitting schemes, economic outcomes depend on revenue recycling. The model provides a guide to assess the orders of magnitude of regional water restrictions. The benchmark dataset, a snapshot of economic transactions in the region, suggests that water conservation 5

These comparisons are made using water withdrawal data from the United States Geological Survey and the Wisconsin Department of Natural Resources. 6 Note that allowing for fully tradable permits could be problematic from a hydrological perspective. Because water is a local resource, potentially concentrating water withdrawals to a given region due to efficiency criteria for tradable rights could potentially reduce the effectiveness of water allocation restrictions for fresh water recharge.

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is unlikely to have a significant effect. In what follows, I provide background on the core issues and underlying economic mechanisms involved in section 2. Data used in the analysis is described to illustrate key parameters in the policy experiment in section 3, followed by discussion of the CGE model in section 4 concerning model structure and closure rules. I present main results in section 5 along with sensitivity considerations on the importance of revenue recycling and budget balancing assumptions. A brief discussion concludes the paper in section 6.

2

Background Fresh water is withdrawn from ground and surfaces sources for different reasons. In 2010, the

top three categories for total fresh water withdrawals in the United States were thermoelectric power (39%), irrigation (38%) and public supply (14%).7 The impact of water withdrawals on the hydrological system depends on how water is distributed across competing uses. For instance, while thermoelectric power generation represents the largest use category, most of the withdrawn water is returned to its original source once used for cooling purposes.8 The USGS estimated that in 1995, water withdrawn for agricultural irrigation had the highest consumptive rate of roughly 61% (as opposed to 2% for thermoelectric power generation). In other words, approximately 61% of water withdrawn for agricultural irrigation is either embedded in the product or lost in transit and no longer contributes to recharge for the groundwater system. However, the profile of water withdrawals is locally specific, and its impact on a region’s ability to regenerate water supplies varies. Water is regulated at the state level due in part to the uneven distribution of resources across the country. The level of irrigated crop production that can be supported locally depends on access to and availability of fresh water and the costliness of irrigation technologies (Green et al. 1996; Caswell and Zilberman 1986). States with the largest water withdrawals for agricultural irrigation in 2010 are California (8.4 trillion gallons) and Idaho (5.1 trillion gallons), with the majority of withdrawals from surface water sources. The upper Midwest, conversely, is composed of states with relatively small totals for withdrawals for irrigation. This region is unique, however, because an overwhelming majority of irrigation related water withdrawals are pumped from groundwater aquifers (e.g. 68% in Wisconsin, 92% in Illinois, 86% in Minnesota).9 In Wisconsin, free groundwater access is a product of past regulatory decisions. Mid-20th century hydrological research on groundwater pumping (Weeks et al. 1965) sparked interest amongst public officials concerning expanded irrigation levels. The popular opinion at the time that groundwater resources were sufficiently great such that any pumping would be negligible prompted unregulated access, favoring economic growth rather than environmental conservation. From 1960 to 7

Estimates come from the United States Geological Survey (USGS) water use reports. Notably, this is not without externalities. Instances of rising water temperatures exist which impact the ecosystem and the ability to continue to use water as a cooling agent. 9 The groundwater share of irrigation related water withdrawals is historically higher for Wisconsin. Recent expansions in cranberry production in the state has lowered this statistic. 8

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Figure 2: Left side: Potato production and groundwater use trends in Wisconsin and the Central Sands. Source: National Agricultural Statistical Service (NASS) and the United States Geological Survey (USGS). Right side: Yearling trout re-stocking in the Central Sands and annual fishing licenses issued in Wisconsin. Source: Wisconsin Department of Natural Resources (DNR).

2000, irrigated land coverage in the Central Sands grew from 37,000 acres to 180,000 acres (Kraft et al. 2012). The shallow aquifer in the Central Sands supplies the region’s roughly 80 lakes and 620 miles of headwater streams which hosts ecosystems and contributes to recreational amenities. Evidence of atypical drying of regional lakes exists, along with anecdotes of reduced fishing levels and aesthetic appeal (Kraft and Mechenich 2010).10 For instance, the right side of figure 2 describes the number of yearling trout added to lakes and rivers in the Central Sands from the 1970s along with the total number of issued fishing licenses per year across the state. Yearling sized trout are typically stocked in areas with large fishing demand for a put and take type fishery. Though the number of licenses in the state have remained approximately constant over time, the number of re-stocked yearling trout in the Central Sands have declined, providing some partial evidence for a decline in surface water amenity demands in the area. The aquifer also supports more than 198,000 acres of irrigated land primarily consisting of potatoes, canning vegetables, soybeans, and field corn crops. Kraft et al. (2012) provides hydrological evidence for the link between irrigation use of groundwater and lower surface waters in the Central Sands.11 Irrigation advocates, however, claim that lake and stream depletion is not directly caused by expanded use of irrigation in the region, which is typically justified by the complexity of hydrological processes and uncertainty in climate induced impacts. Moreover, in recent years, an increasing number of groundwater wells in the Central Sands is associated with decreasing levels of water withdrawals, which can be rationalized by cost minimizing farmers taking advantage of 10 Notably, it is unclear, as a result, the extent to which property values are impacted through surface water level changes. Government property tax revenues are also subject to change. 11 Specifically, the authors find large amounts of estimated evapotranspiration (the sum of plant transpiration and evaportation) in irrigated land relative to pre-irrigated land cover. This is significant because as more water navigates its way into the atmosphere, less is available for groundwater recharge.

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off-peak electricity pricing.12 Nevertheless, water use for irrigation in the area has substantially increased over time from 1985-2005. The left side of figure 2 compares trends in potato production in Wisconsin with groundwater withdrawals for irrigation in the Central Sands from 1972-2005 (USGS data only available from 1985 onward). Potato production and use of groundwater for irrigation are closely correlated.13 High capacity wells, or wells exceeding 100,000 gallons of water pumped daily, are the focus of current public interest. A 2016 attorney general’s opinion supported restricting the Wisconsin Department of Natural Resources (DNR) ability to consider cumulative effects of pre-existing wells in review of new state-wide well applications (Schimel 2016). It was found that without explicit permission by state statute, the Wisconsin DNR is limited in its oversight.14 The Central Sands alone accounts for roughly half of all wells in the state, corresponding to nearly two-thirds of all groundwater withdrawals for agricultural irrigation. The local implications on future ground and surface water resources are uncertain and if policies were imposed to restrict water use, there exists considerable ambiguity surrounding the magnitude of associated costs and the benefits of recharged lakes and streams.

2.1

Economic Motivation

Financial incentives are often advocated for by economists as a means of reducing water withdrawals for agriculture (Dinar and Letey 1991; Johansson et al. 2002). The theory suggests that optimal groundwater management policies should consider external effects of water withdrawals (Provencher and Burt 1993) and the conjunctive use between ground and surface sources (Noel and Howitt 1982; Provencher and Burt 1994; Pongkijvorasin and Roumasset 2007). However, in practice, the price of water rarely reflects its true level of scarcity. Reluctance to raise water prices, even in times of significant shortage, is socially and politically constructed because fresh water is a basic human need and an essential input to production. Drought and population induced water shortages have, however, necessitated regional water allocation mechanisms in some instances across the United States, particularly in the American West (Olmstead 2010). Creating a water market or raising the marginal price of water can align incentives for water con12

From 2012-2014, the number of high capacity groundwater wells used for agricultural irrigation increased from 1,641 to 1,812 while total groundwater withdrawals decreased from 80.2 to 51.3 billion gallons (see table 20 in appendix E for aggregate water withdrawals across all use categories). Though annual water withdrawals fluctuate significantly after 2005, I consider the economic rationale for such an observation in appendix F by developing a simple cost minimization model. The model jointly considers the use of electricity and the installation of wells and pivots for irrigation. 12 hour peak ($0.15 per kWh) and off-peak ($0.061 per kWh) electricity pricing is offered in the area. An average of $22,822.5 is assumed for installation of a high capacity well and pivot with sprinkler (data from UW-Extension), with 40 kWhs required for pumping an acre-foot of water. Holding water use in the region fixed and using estimates of capacity limits per pump from DNR data, I find that the optimal response to off-peak pricing is to approximately double the number of wells for use during the off-peak period. 13 Moreover, on average, annual rainfall has been increasing over the past few decades in the region (Motew and Kucharik (2013), Kniffin (2013)). 14 As a result of the opinion, the DNR will still be responsible for determining if the well applicant is within a protected area, impact springs with flow greater than one cubic foot per second, result in 10 or more feet of water level reductions in public utility wells, or reduce water quality. Applicants may also be subject to environmental review. For more information, see http://dnr.wi.gov/topic/wells/HighCapacity.html.

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servation. Increases in the price of irrigation water can prompt a farmer to substitute management efforts for water withdrawals, switch to less water-intensive crops due to decreases in profitability or adopt precision (water conserving) irrigation technologies (Schoengold et al. 2006; Caswell and Zilberman 1985; Shah et al. 1995). Allocation markets, in particular, can enforce conservation through property rights regimes (Provencher 1993).15 Empirically, markets for water in the United States have been associated with price responsiveness to weather conditions and gains from trade between regions and sectors (Brookshire et al. 2004; Chang and Griffin 1992). However, though efficiency improvements due to flexible trading schemes are apparent, so too are equity concerns. Flexibility in water trade when its relative valuation across regions and use categories can lead to large shifts away from agriculture (Griffin and Boadu 1992; Brewer et al. 2008). Equitable outcomes are impacted by high transactions costs (Carey et al. 2002), potential consolidation of market power and improper revenue recycling (Johansson et al. 2002). The Central Sands presents a circumstance in which affected irrigators are large landowners in rural counties. Competition for fresh water resources isn’t solely amongst producers (as, for instance, in the race to fish in ocean fisheries). Rather, this property rights struggle pits environmental amenity consumers against agricultural water users in a rural setting. As is common across the United States for groundwater use, a market for agricultural water withdrawals does not exist in the Central Sands, leading to free access barring any capital or electricity costs associated with pumping (Glennon 2004). Abstracting away from benefit calculations, the economic costs of reductions in groundwater pumping can be simulated using equilibrium modeling.16 Though water used for irrigation is typically a non-market good, simulating a restriction on the level of water use would serve to raise its shadow price in the farmer’s production decision, reflecting an imposed level of scarcity of the resource (Roe et al. 2005; Tsur, Yacov 2004).17 Computable general equilibrium models have been used to study water policy in both domestic and international settings. Models studying water policy in an international setting have focused on single countries or trade issues. For trade related modeling, a series of papers have extended the GTAP (Global Trade and Analysis Project) model to include water accounts.18 Topics include 15 Note that water markets can have additional positive externalities aside from conservation benefits. It can reduce incentives to over use water for irrigation, which can reduce the likelihood polluted agricultural drainage. 16 While I focus on the cost side of the cost-benefit equation, examples of methodologies used to estimate benefits can be found in the literature. For instance, Phaneuf et al. (2013) considers how amenity values are capitalized in housing prices, and Loomis and Creel (1992) studies the benefits of increased river flow in California’s San Joaquin and Stanislaus rivers through survey methods. 17 In this setting, water restrictions can be modeled either as a partial or general equilibrium problem. A partial equilibrium model would be appropriate if the secondary impacts of a given policy shock are negligible. Because water is an important resource for a variety of farming and non-farming sectors in the Central Sands, I adopt a general equilibrium framework which simultaneously determines supplies, demands, prices and incomes of all sectors and agents. Restrictions in water withdrawals for farming sectors would affect the profitability of different crop types depending on their relative level of water-intensity. Downstream sectors in the area are impacted through changes in supply and price levels for locally produced inputs (e.g. food processing plants using locally grown vegetables). Indeed, 36% of all produced agricultural goods are used locally in the Central Sands as opposed to being exported to the national or foreign markets. Food and milk processing sectors in the study area alone (of which make up 2% of total value added in the Central Sands, or $200 million) account for 70% of domestically sourced agricultural input demand, which encompasses locally sourced goods. 18 For a representation of the standard model in GAMS, see Rutherford and Paltsev (2000).

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implications of national level restrictions in water withdrawals and water tariffs on virtual water (Berrittella et al. 2007; Berrittella et al. 2008), water trade in China (Berrittella et al. 2006), and trade liberalization (Berrittella et al. 2008). Theoretical updates to the production structure in the baseline GTAP water model are used to study the effects of sustainable water use in agriculture finding a general trade off between environmental conservation and economic well-being (Calzadilla et al. 2010) and comparative advantage shifts due to irrigation efficiency (Calzadilla et al. 2011).19 National models outside of the United States have been formulated for South Africa and Uganda to consider water management policies and the possibilities for a double dividend in revenue recycling schemes (Letsoalo et al. 2007; Hassan and Thurlow 2011; Kilimani et al. 2015). Country level analyses, however, don’t capture regional effects of policy given the heterogeneity in water availability and use patterns across space. Regional models have been built for historically water stressed parts of the world with an emphasis on drought resiliency and water trading (Morocco: (Diao and Roe 2003; Roe et al. 2005; Diao et al. 2005; Diao et al. 2008) and Australia: (Horridge et al. 2005; Wittwer 2012; Wittwer and Griffith 2011)). Domestic studies are relatively more scarce and tend focus on arid or large agricultural producing regions of the United States. Berck et al. (1991) simulate the inter-sectoral and border price implications of reductions in water inputs for agricultural production in the San Joaquin Valley of California. Simulations restrict water supply for farmers by a fixed percentage, finding that the results depend on the allowed substitutability between inputs to production. Other general equilibrium studies consider the American Southwest. Water shortages in Colorado have prompted policy debate on temporary water transfers (Goodman 2000) and the implications of population growth (Watson and Davies 2011). In a similar context to the Central Sands, reallocation of water between competing users is considered in Nevada, generally finding that the benefits of increased recreational use do not outweigh costs from lost agricultural output (Seung et al. 2000; Seung et al. 1998).20

3

Data The primary dataset used for the analysis is provided by IMPLAN Group LLC. and describes

a snapshot of all regional economic exchanges in the Central Sands for 2010. The core dataset consists of a series of constructed county level social accounting matrices, each with 440 sectors, 9 household types based on income groups, federal and state/local government types, and investment accounts. County level economic data are constructed using national level BEA (Bureau of 19

In a similar vein, Debaere (2014) finds that fresh water access acts as a source of comparative advantage. It is worth noting that few papers have attempted to explicitly link hydrological frameworks with computable general equilibrium models. For instance, in previous studies, new levels of water withdrawals are calculated in a postpolicy equilibrium, yet, the impact of changing withdrawal levels on the hydrological system (e.g. groundwater table, surface water stream-flows) is largely unconsidered. In areas with relatively straightforward hydrological systems like the surrounding regions of the Nile River with two seasons of crop production, papers have used a top-down bottom-up approaches, embedding a linear program to select non-substitutable land-water bundles in each period (Strzepek et al. 2008; Robinson et al. 2008). The only paper to have attempted to interact a hydrological model with a CGE model explicitly to my knowledge is Robinson and Gueneau (2013), which considers the investment decision of constructing a dam in Pakistan. However, given the uncertainty in how irrigation affects surface waters in the Central Sands, I refrain from considering this system jointly. 20

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Economic Analysis) tables along with data on local economic characteristics. Sectors in the dataset are accompanied by a profile of the value of inputs used in production, output by-products, indirect business tax flows to the various levels of government, and supply to the regional, national or foreign markets. Demand accounts (households, governments, etc.) provide the value of expenditures on produced commodities both from domestic and foreign markets, along with the value of incomes denominated by source (e.g. wages, capital rent, transfers). Inter-regional trade flows for all commodity types are also provided and used to explicitly link counties in the Central Sands and capture terms of trade effects. Trade flows are estimated using a gravity model of trade, relying on Commodity Flow Survey data and computed impedances by Oak Ridge National Laboratory (Alward et al. 2000). Default three-dimensional social accounts provided by IMPLAN are rearranged into a CGE compatible format using routines outlined in Rutherford and Schreiber (2016). The programs construct two-dimensional matrices with additional satellite tables for transfer accounts. Embedded in these routines is a matrix balancing least squares optimization framework for enforcing key accounting identities in each region while inducing sparsity in the dataset. The core economic data set provides capital rental accounts for proprietary and non-propriety incomes. However, for agricultural studies, additional information on land rental rates is useful for a more comprehensive representation of sector level trade offs. To reconcile, I aggregate core social accounts to approximately match the GTAP 8 sectoring scheme to 53 distinct sectors.21 National level land value shares from GTAP are used to create a separate capital category for land in production decisions of agricultural sectors. Land ownership is shared out to household types following the distribution of aggregate factor endowments in each region. Water withdrawals by sector are computed using data compiled by the Wisconsin DNR of all registered high capacity wells for the state of Wisconsin. High capacity well data describes water withdrawals at each registered pump from 2011-2014. Each site includes withdrawals from groundwater, non-great lake surface water, and great lake sources, along with associated water basins representing the end drainage point for water runoff. Because the economic data comes from 2010, I use estimates for 2011.22 The water withdrawal dataset provides estimates for the total number of gallons per year (and month) as well as the category of the water’s intended use. Aggregate well water withdrawal categories are irrigation, other agriculture, public supply, domestic supply (household wells), electricity generation, industrial use, recreation and non-agricultural irrigation. Water withdrawal data did not, however, include information on the intended type of irrigated 21

The GTAP 8 sectoring scheme provides data on 57 sectors (Aguiar et al. 2012). 6 of these sectors lacked an appropriate mapping to the IMPLAN sectoring scheme, and were therefore aggregated. Paddy rice, wheat, cereal grains, other animal products, wool and silk-worm cocoons and processed rice were aggregated to either grains or animal products. 22 Note that there were differences in the levels of average precipitation in Wisconsin between 2010 and 2011. According to NOAAs Climate at a Glance dataset, average precipitation fell from 39.02 inches in 2010 to 31.04 inches in 2011 in Wisconsin. While average precipitation levels increased closer to 2010 levels in 2014, farm output and the number of irrigated acres has been increasing over time. NASS estimates from the 2012 agricultural census report an increase in the market value of total sales of agricultural products from 705 million dollars in 2007 to 925 million dollars in 2012 for the Central Sands counties. Additionally, the number of irrigated acres increased from 187 thousand to 198 thousand acres for the comparison years. As such, water withdrawal data for the closest year relative to the economic data is used.

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crop. To estimate water withdrawals by crop type following the GTAP 8 sectoring scheme, I use the Cropland Data Layer (CDL) from the National Agricultural Statistical Service (NASS) for 2011. Table 1 describes the distribution of cropped area by county and crop type provided in percentage of total land attributed to farming. Crop types are aggregated to match the GTAP sectoring scheme. Table 1: Percentage of Total Farmed Land in 2011 GTAP Sector

Crop Type

Adams

Marquette

Portage

Waupaca

Waushara

Wood

Grains

Corn Winter Wheat Oats Sweet Corn Barley Rye

44.1 3.5 0.2 6.1

60.4 2.2 0.3 0.1

51.6 3.8 0.7 0.3

0.1

41.5 3.7 0.3 6.8 0.1 0.2

34.9 1.8 1.6 0.3

0.2

30.7 1.5 0.6 10.0 0.1 0.4

Potatoes Dry Beans Peas Carrots Cranberries Misc Vegs & Fruits

10.6 9.2 0.3 0.3 0.2 0.1

1.2 0.8

10.0 7.9 1.1 0.5 0.2 1.0

0.6 0.5 0.2

9.9 8.8 1.3 0.7

0.9 1.2 0.1

0.2

0.6

Oil seeds

Soybeans

12.9

12.4

7.5

14.9

12.4

14.2

Other crops

Alfalfa Herbs Fallow/Idle Cropland

12.0 0.1

20.4 1.9 0.1

27.9

27.0

44.3

0.5

0.3

13.2 0.2 0.3

Vegetables and fruits

0.0

0.1

0.2

0.3

Notes: Figures are given in percentages. Total areas may not add to 100% due to rounding. Source: USDA Cropland Data Layer.

Well sites are mapped to crop types by joining the two data sets in GIS (Geographical Information System) software. If a well site existed within the boundaries of a cropped field and far enough away from other cropped fields, I assign total water withdrawals to the singular crop type. If the active well is not within a cropped area, I assign water withdrawals to the nearest type of crop. Finally if the site was within a cropped area, though bordering closely another cropped area of a different type, I split the water use between crops allowing for the possibility that the groundwater well services multiple center pivots. Figure 3a describes the distribution of water withdrawal sites and cropped areas in the Central Sands. Differently shaded plots denote different types of crops provided by the CDL. Dots denote groundwater withdrawal sites.23 Non-agricultural well withdrawals are mapped to GTAP sectors according to the listed use category. In instances where a non-agricultural well was defined as an aggregate category (food production, manufacturing, non-manufacturing industrial use and animal use), I use IMPLAN data 23 The algorithm used to extract crop information at the point of withdrawal consisted of drawing a buffer around each site of a radius similar to the average length of a center pivot in the area. Crop types that intersect this circle get water allocations according to the area of intersection. An average pivot length of 400m was used as the buffer. Of the roughly 1800 withdrawal sites, only 3 weren’t mapped to crop types. Conversely, using the same average length of a center pivot around irrigation wells, I calculate the total percentage of cropped farmland falling within the boundaries of a pivot’s path. I use this information to separate the use of irrigated versus non-irrigated land in the various forms of agricultural production in the economic model.

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(a) Crop Type and Groundwater Withdrawal Distribution

(b) Data Merge Between Well Location and Crop Type

Figure 3: Central Sands crop and withdrawal site distribution. Dots denote water withdrawal sites registered with the Department of Natural Resources in Wisconsin from 2011-2014. Plots of farmland are from the Cropland Data Layer from the National Agricultural Statistical Service. An average length of 400m was used for the center pivot arm around each withdrawal site. The bottom layer consists of crop plots.

along with national water use averages found in Blackhurst et al. (2010) to share out aggregate water withdrawals for each sector in each region. Notably, missing data entries in category designation exists. I add missing entries to the agricultural withdrawal classification if the only water withdrawals are during growing season. Non-mapped water withdrawals make up at most 0.002% of total water withdrawals in a given county.24 Data on the value of capital requirements for pumping water and use of center pivot sprinkling systems for irrigation is taken from the University of Wisconsin-Extension program, which provides tables for calculating the costs of water related capital for farmers in Wisconsin. Average values for the rental cost of pumps and pivots are used which are comprised of depreciation and repair 24

Using the alloted withdrawal limit prescribed by the DNR at non-mapped sites, these 0.002% of water withdrawals translates to 4.7% of total capacity across all registered sites that is not-categorized, representing an upper bound if misreported.

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costs, and interest and insurance payouts. I assume that only farmers incur both pump and pivot costs, while all other groundwater using sectors incur just pump costs.25 Additional information on associated electricity costs of pumping an acre-foot of water is also given.

3.1

Descriptive Statistics

The following tables provide descriptive statistics on characteristics of the regional county level economies in the Central Sands. Table 2 enumerates total regional gross domestic product (GDP) along with magnitudes of its components. Regional GDP indicates a measure for the total value of goods and services produced in a given county. Wood and Portage counties are the largest, both with over 3 billion dollars in regional GDP, while Adams, Marquette and Waushara are the smallest counties, each with less than a billion dollars in GDP. Table 2: Regional Benchmark Gross Domestic Product in 2010

Total GDP (billions of $)

Adams

Marquette

Portage

Waupaca

Waushara

Wood

0.9

0.5

3.1

1.9

0.7

3.5

Income Approach (% of total)

L K N Tax Other

26 17 1 6 51

29 13 1 4 53

52 18 1 6 23

47 15 1 6 31

30 15 2 5 48

57 15 1 5 22

Expenditure Approach (% of total)

C G I X-M

65 18 54 -37

75 12 52 -39

67 13 48 -27

80 15 46 -42

79 13 50 -43

69 12 48 -28

Notes: Regional GDP (Gross Domestic Product) is listed in billions of dollars. Income and expenditure approach data are denominated as percentage of total regional GDP attributed to sub-categories. The income approach is composed of labor (L), capital (K), land (N ), taxes and other incomes. Expenditures are divided into household consumption (C), government expenditures (G), investment (I) and net exports (X − M ). Source: IMPLAN.

GDP can be calculated using the income, expenditure or value added approaches. Because the social accounting matrix compiled for the Central Sands is micro-consistent (satisfying basic accounting identities), incomes must equal expenditures and the income and expenditure approaches yield the same value for regional GDP. Table 2 provides the percentage of regional GDP that is attributed to each individual category. Labor and other incomes represent the largest components of regional GDP using the income approach, accounting for 26-57% and 22-53% respectively. Other incomes are composed of returns to housing ownership, investment income and resource rents. The smallest income category, N , represents the returns to agricultural lands (other land types in the Other category). On the expenditure side, the largest components of GDP are household consumption (65-80%) and investment (48-52%). Large trade imbalances exist in the Central Sands, with 25

A 7% interest rate is assumed on pump and pivot investments. The assumed depreciation lifespan is 20 years, with a salvage value of both a pump and pivot of $10,000 or $5,000 for just a pump. Additional assumptions include the cost of repairs to be 3.5% of the original cost and insurance payments of 0.5% the average investment value.

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net imports ranging from 27.5% in Portage county, to 42.7% in Waushara county of total regional GDP. The sector level composition of regional GDP is provided in the first tier of table 3. Agricultural sectors, or water intensive sectors of interest, are listed first. These sectors represent aggregated categories of crop types and raw milk production. The vegetable, fruit and nuts sector accounts for potatoes, sweet potatoes, other vegetables and cranberries. Grain farming encompasses corn, wheat, barley, oats and other cereals. Oil seeds represents soy bean production, and other crops consist of alfalfa, herbs, and fallow cropland. Refer to table 1. Vegetable and fruit production is the largest agricultural sector in the Central Sands, accounting for between 0.4-5.8% of the given county’s regional GDP. The value of grain production, conversely, is quite small, ranging from 0.10.7%. Sectors downstream from crop production including dairy production and food processing account for between 0.4-3% of county level value added. Other sectors listed provide indicators for the composition of each county’s economic activity. Most value added is produced by recreation activities (7-19%), public administration which includes health, education and defense (16-38%), owner occupied dwellings (6-10%) and trade and retail (7-13%). The next sections of table 3 describe crop production by type. The labor percentage of value added provides a measure of how labor intensive crop types are relative to other agricultural activities. Vegetable and fruit farming and other crop production are more labor intensive relative to grain and oil seed (e.g. soybeans) production. In aggregate across the Central Sands, vegetable and fruit farming account for the largest labor share of total value added, totaling roughly $51 million.26 The bottom two tiers indicate the level of farming in each county of the Central Sands and their relative reliance on irrigation. Irrigated land is defined as land within a 400m radius of a registered high capacity well with positive levels of water withdrawals. The number of acres farmed (in 2012) for vegetable and fruit production across the Central Sands are concentrated in Adams, Portage and Waushara counties, accounting for nearly 140 thousand acres. Of those farmed acres, approximately 100 thousand are irrigated. Grain farming occupies roughly 280 thousand acres, the most land attributed to farming in the area, though with smaller proportions of irrigation. Despite small levels of regional GDP attributed to grain farming activities, large levels of groundwater withdrawals exist in the dataset. Table 4 describes estimated groundwater withdrawals by county for sectors with at least 10 million gallons withdrawn in 2011. The largest groundwater withdrawals are for vegetable and fruits (21 billion gallons), grain (19 billion gallons) and oil seed farming (3 billions gallons). Adams, Portage and Waushara counties account for the majority of these withdrawals. Notably, groundwater withdrawals for public administration contribute to the public supply of freshwater, and are provided as reference. Withdrawals from household wells are small in the region. The second tier provides the number of gallons per dollar of output in the reference dataset. Across counties, grain farming ranks highest and amongst the largest agricultural producing counties, Portage county is the most efficient for all four land intensive agricultural activ26 As discussed later, however, only one type of labor is denominated in the dataset. I therefore cannot be sure whether the majority of these labor receipts accrue to wealthier farm owners or low-skilled laborers.

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Table 3: Benchmark Statistics (2010) Sector % of regional value added

Adams

Marquette

Portage

Waupaca

Waushara

Wood

0.3 0.1 4.4 0.3 0.4 0.1 0.2

0.7 0.8 1.8 0.7 0.8 0.2 2.8 15.5

0.1 0.2 1.9 0.1 0.1 0.1 0.5

0.2 0.2 0.4 0.2 0.3 0.1 2.0

0.5 0.7 5.8 0.4 0.7 0.1 1.4

0.1 0.1 0.6 0.1 0.3 0.0 0.6

2.3 0.8 4.7 3.4 7.8 1.6 3.1 0.9 2.4 2.7 13.2 2.5 3.2 3.8 1.0 1.2 10.4 19.6 8.2

3.1 0.0 2.3 0.6 3.7 2.7 6.3 2.4 4.0 10.2 3.6 1.3 2.3 1.8 0.9 13.8 19.0 10.0

0.7 0.6 12.3 0.6 0.1 1.0 0.1 0.2 0.6 3.1 8.1 5.7 4.9 2.9 0.3 1.8 7.2 38.2 5.8

Grains Animal products Vegetables, fruit, and nuts Oil seeds Other crops Bovine cattle Raw milk Other meat products Dairy products Other food processing Paper products, publishing Chemical products Ferrous metals Metal products Motor vehicles and parts Electronic equipment Electricity Construction Trade/retail Other transport Communication Other financial services Insurance Other business services Recreational and other services Public administration Dwellings

0.4 1.6 0.2

0.0 1.4

19.7

1.4

5.5 4.3 6.6 5.3 0.7 1.4 0.2 1.2 19.5 18.5 8.0

1.6 4.2 2.9 6.6 2.4 2.2 3.7 1.1 1.3 16.6 16.1 10.5

0.2 2.8 4.1 0.6 0.0 1.2 0.2 0.9 0.7 2.1 9.8 6.1 1.5 2.8 21.7 2.5 12.9 16.0 5.9

Labor % of value added

Grains Vegetables, fruit, and nuts Oil seeds Other crops Raw milk

18.7 37.4 2.1 51.0 16.0

16.1 40.7 1.8 35.8 13.7

18.1 37.1 2.0 70.0 15.4

18.5 38.9 2.1 69.1 15.8

13.4 28.2 1.5 58.6 11.5

19.6 36.4 2.2 40.6 16.8

Acres Farmed (1000s)

Grains Vegetables, fruit, and nuts Oil seeds

12.1 35.0 11.0

16.2 2.5 14.8

46.6 73.0 12.2

18.2 1.6 20.2

16.9 30.1 14.9

45.8 0.1 22.0

% of farm area irrigated

Grains Vegetables, fruit, and nuts Oil seeds Other crops

37.8 80.5 25.9 11.7

2.8 13.5 2.0 3.0

39.0 71.5 26.2 7.5

4.3 45.9 4.2 1.4

26.1 66.7 23.4 12.0

1.2 43.6 0.8 0.6

Notes: Percentage share of value added by sector will not add to 100% due to small omitted sectors. Area farmed by GTAP sector in thousands of acres is taken from the 2012 Agricultural Census. Sources: IMPLAN, NASS, USDA Cropland Data Layer, Wisconsin DNR.

ities. Adams county is associated with the largest water withdrawals in aggregate, while Waushara is relatively more efficient.27 27

Table 4 does not report surface water withdrawals for each sector. Many sectors were omitted because of negligible groundwater withdrawals, though are associated with larger surface water withdrawals. For instance, large levels of surface waters are used in the production of cranberries as well as industrial uses like pulp and paper and chemical and plastic production in the region (see table 21 in appendix E). I refrain from allowing for substitution possibilities between surface and groundwater sources in the model at the regional level by not including a surface water withdrawal category. Only groundwater withdrawals are used and it is assumed that groundwater is pumped due to limited access to surface waters. Notably, while I use regional data on water withdrawals, studies do exist which provide average

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Table 4: Groundwater Withdrawals

Withdrawals (bill. gallons)

Gallons per dollar output

Adams

Marquette

Portage

Waupaca

Waushara

Wood

Grains Vegetables, fruit, and nuts Oil seeds Other crops Raw milk Public administration

6.7 6.8 1.1 0.4

0.5 0.1 0.1 0.1

0.2 0.9

0.1

0.5 0.2 0.1 0.1 0.1 1.4

5.0 5.9 1.1 0.6

0.3

6.0 7.0 0.7 0.7 0.1 2.7

0.2

1.6

Grains Vegetables, fruit, and nuts Oil seeds Other crops Raw milk Public administration

850.2 127.4 313.1 97.7

53.5 6 16.3 19.1 1.1 2.1

389 57.9 149.6 68.3 2.4 4.4

29.9 17.7 18.3 12 0.6 3.4

421.5 102.6 244.8 97.9 0.3 1.6

17.4 21.9 8.1 3.4

2.4

0.1

0.8

Notes: Groundwater withdrawals are provided in billions of gallons for the year 2011. Empty elements in tier 1 are associated with non-empty elements of tier 2 due to rounding. Some sectors were omitted due to negligible levels of withdrawals. Surface water withdrawals are excluded from the table. See table 21 in appendix E for more information. Sources: Wisconsin DNR, USDA Cropland Data Layer.

The general equilibrium framework allows us to consider indirect effects of policy changes. Most sectors with significant use of domestically sourced agricultural goods are other agricultural sectors, or sectors immediately downstream from raw crop production. Roughly 15% of the total cost of production for grains, vegetables and fruits, and oil seeds comes from domestically produced agricultural goods. Raw milk production also requires large levels of domestically produced agricultural goods for things like animal feed (approximately 13% of the total cost of production). Large levels of domestically produced agricultural goods are also used as intermediate inputs in downstream sectors such as dairy products, food processing and bovine cattle. The dataset also describe the local composition of the county level goods markets. Across the Central Sands counties, only up to 5% of total demand for grains, oil seeds and other crops come from local counties. The proportion of vegetable and fruit commodity demand produced in the area, however, ranges from 40-65%, and the proportion of total demand for raw milk is almost entirely sourced locally. Most of the produced agricultural goods in the area are exported out of the region, with the exception of raw milk and to some extent, vegetables and fruits. However, the share is much smaller than for input demand (see table 12 in appendix A). Household consumption expenditures by income group are also captured by the dataset. Though the ranking of expenditures (see table 13 in appendix A) on goods depends on income group, in aggregate, the largest consumption categories are public administration (e.g. education and health, for $1.6 billion), recreational activities ($1.4 billion), retail and trade services ($0.9 billion), and dwellings ($0.8 billion). Expenditures on raw crop production are relatively small. Of the 53 total number of goods categories, vegetables and fruits are ranked 22nd ($34 million), dairy products water use per dollar of output by sector for the United States (Blackhurst et al. 2010). However, such measures aggregate across source type and therefore, in the Central Sands, would overestimate the level of withdrawals for industrial uses (e.g. pulp and paper) or underestimate based on levels of output in the benchmark dataset (e.g. grain farming).

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Table 5: Tax Flows in Central Sands Counties (millions of $)

Federal government

State/local government

Incidence

Tax Type

Revenue

Indirect business taxes

Excise tax Custom duties Federal fines

Transfers

Corporate profits tax Personal income tax

229.8 626.4

Indirect business taxes

Business sales tax Business property tax Business vehicle licensing Severance tax Other taxes State/local fines

214.3 287.3 5.6 0.1 21.3 36.5

Household taxes

Personal property tax Personal sales tax Personal income tax

7.1 94.5 269.3

Transfers

Corporate profits tax Other fines Household vehicle licensing Fishing/hunting fees

37.8 14.8 25.3

36.3 29.5 11.6 13.0

Notes: Incidence describes how the tax is applied in the computable general equilibrium model. Indirect business taxes are applied as an output tax on production, household taxes are applied as a tax on household consumption and transfers describe lump sum bilateral transfer payments, not denominated through explicit tax rates in the model. Transfers between governments and investment revenues are suppressed in the table. Source: IMPLAN.

are ranked 23rd ($34 million), other crops are ranked 39th ($1 million) and grain is ranked 40th ($1 million). The majority of agricultural good demand is sourced domestically. Households accrue income from different sources. The dataset describes 7 aggregate categories (bottom portion of table 13 in appendix A), with a variety of explicitly designated subcategories. The most income is derived through wage payments, accounting for roughly $4.2 billion in the region, with additional transfer payments between institutions accounting for approximately $2.1 billion (weighted toward poorer households and reflecting transfers amongst household types, interest payments, or personal income tax payouts). Capital and land ownership total $0.5 billion (weighted toward richer households). Housing ownership represents an imputed category based on a 25% tax rate on housing for household property tax payments. Table 5 provides tax revenues for both federal and state/local government levels by tax type. Incidence describes how a particular tax is applied in the general equilibrium model. IMPLAN provides aggregate indirect business tax flows and lump sum transfer payments for household taxes. Because revenue recycling from water permit schemes are of interest, some effective tax rates are calculated from benchmark tax payments and explicitly represented. I assume that revenue recycling occurs at the state/local level given the policy dimensions. Explicit individual tax rates are used for household taxes, whereas a single effective output tax on production aggregates all indirect business tax types. Transfers describe lump sum payments denominated as bilateral transfers to the government. Governmental income through transfers between government types and investment Page 17 of 59

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related revenues are suppressed from the table. Indirect business taxes which accrue to the federal government include excise taxes, duty taxes and federal fines, all three of which account for $78 million in total. 92% of total federal tax revenues from the Central Sands is derived from personal income taxes and corporate profit taxes. The state/local government collects tax revenue through indirect business taxes: business sales taxes, business property taxes, business motor vehicle taxes, severance taxes, other taxes, and state and local fines. Of these, business property and sales taxes make up 49% of total state/local tax collections. Effective tax rates are used for household sales taxes, property taxes and income taxes. The sales tax rate paid for final consumption is computed by separating total sales tax paid using relative weights for household final demand and intermediate input demand. Effective property and personal income tax rates are calculated based on the total amount of transfer payments between households and governments for each type of tax. Personal property tax payments are the smallest, representing only 0.7% of total state and local government tax receipts. Public good expenditures are largest for public services like health care, education and infrastructure improvements.

4

Model The analysis is based on a static multi-regional, multi-sectoral computable general equilibrium

model, calibrated to county level data for the Central Sands. A multi-regional setting is important in the context of water related issues. Fresh water access and supply is an inherently localized problem, depending on withdrawal patterns, hydrological conditions and climate. The spatial consequences of water restriction policies depend upon the regional configuration of water users. Prospective policies which are flexible in water trading could promote a spatial re-allocation of water withdrawal rights. Hydrological concerns for the potential consolidation of rights in regions with the most productive sectors may be warranted. The model is formulated using the small open economy assumption: regional price fluctuations are assumed not to affect national and world prices. Labor is mobile across sectors and counties in the Central Sands. Capital and land are assumed to be mobile across sectors, but not counties. Water related capital such as high capacity wells, for instance, are fixed to a given location after installation, though could be used for farming other crop types or pumping uses (e.g. public supply). Alternative factor closures are considered in sensitivity simulations. A perfectly competitive framework in the production of commodities is assumed and modeled with nested constant elasticity of substitution (CES) cost functions. Nested input decisions describe price dependent tradeoffs between factors, water resources, and material inputs. Figure 4 graphically depicts production nested tradeoffs in the form of a tree diagram. The top level nest describes a Leontief composite between intermediate material inputs and the value added and resource composite (i.e. used in fixed proportions, or σ S =0). Material inputs can come from either domestic or foreign sources. Willingness to substitute between sources is characterized through the Armington elasticity of substitution, σgARM , for each commodity g which introduces product

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heterogeneity across producing regions (Armington 1969). National level Armington elasticities between foreign and domestic sources are taken from GTAP 8 and are provided in table 16 in appendix C. The value added and resource composite combines labor, an aggregate land composite which includes water use, and non-water capital according to GTAP 8 elasticities of substitution, σsV A , which vary by sector s (also see table 16 in appendix C). Land dependent sectors either require non-irrigated or irrigated land types. The model restricts the ability to transform non-irrigated land into irrigated land, and vice versa through an assumed elasticity of transformation. For agricultural goods which require irrigated land for production (vegetable and fruits, grains, oil seeds, and other crops), both types of land enter production level input choices. Other land intensive sectors (raw milk, bovine cattle and other animal products) require only non-irrigated land. The top level nest of the land composite decision describes the choice between non-irrigated land and an irrigation aggregate. The tradeoff is governed by an elasticity of substitution, σ N IR set to 0.5, reflecting some level of substitution possibility between irrigated land and non-irrigated land use. The irrigation composite is formed by combining irrigated land with a water composite, describing the necessary inputs needed to withdraw water from high capacity groundwater pumps and apply it to the fields.28 For all sectors with positive groundwater withdrawals in the benchmark dataset, water withdrawals require payments for water related capital (high capacity well pumps and, for irrigating sectors, center pivots), electricity and the physical water resource used in fixed proportions (σ W = 0). Substitution away from water use yields less water related capital use and electricity input demand. Note that in the absence of water supply restrictions, the shadow price for water, pW rs , in region r and sector s is zero. The land composite becomes the water composite for sectors with positive groundwater withdrawals and no land input demand. The regional output structure is defined in figure 5. Produced commodities are allocated to either the local market (supplying the county in which the good was produced, or other counties in the Central Sands), national market or foreign market according to an elasticity of transformation, η Y , set to 4. Inter-regional trade flows between Central Sands counties are used to describe an aggregate regional supply according to local Armington elasticities, σgLAR . Regional supply is combined with national imports using domestic Armington elasticities, σgN AR , to create the domestic composite good used as material inputs in production and in final demand. While I lack appropriately estimated values for σgLAR and σgN AR , regional research has provided some evidence that subnational Armington elasticities tend to be smaller than foreign elasticities (Turner et al. 2012; Bilgic et al. 2002), suggesting that the composition of demand for goods or inputs in regional CGE models should be less sensitive to intraregional price fluctuations, relative to interregional price changes possibly driven more by regionally specific non-price barriers. As such, baseline GTAP foreign Armington elasticities (σgARM ) are scaled such that σgARM > σgN AR > σgLAR .29 The consumer side of the model is characterized by regional representative household agents 28 Without estimated elasticities for σsIR which represents the tradeoff between land and water use, I scale GTAP value added elasticities such that σsIR = γσsV A where γ is set to 0.5 for the main policy runs. 29 In the model, regional Armington elasticities are defined as σgN AR = 0.8σgARM and σgLAR = 0.5σgARM .

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Figure 4: Production structure for land dependent agricultural goods. For sectors with no demand for land but withdraw water through the use of high capacity wells, the land composite becomes the water composite. The tree diagram represents the level of substitution between material inputs, resources, and factors used in the production of output. The nests characterize these trade-offs according to listed elasticities of substitution. See model equations in appendix B and variable descriptions in table 14.

who maximize utilities subject to budget constraints. Total endowment income follows table 13, consisting primarily of factor income, transfers and fixed investment. Consumption is modeled using nested CES functions for each household type. The top level nest assumes Cobb-Douglas preferences between housing demand and all other goods, implicitly assuming constant income shares. Housing demand represents an imputed category based on the level of property taxes paid to the state/local government. Demand for all other goods is given by a CES composite between imports and domestically produced goods. GTAP Armington substitution elasticities are used. Reference prices for housing and goods are net of property and sales taxes. The model also features two levels of government: federal and state/local, which aggregates county and state level government expenditures and tax revenues. Tax revenues accruing at the federal level are treated as leaving the regional economy, and denominated as foreign exchange. Government expenditures on public goods and services is modeled as a Leontief composite between

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Figure 5: Output structure for the regional economy. The regional output structure follows the Armington assumption: people’s preferences depend on where the good was produced. See model equations in appendix B and variable descriptions in table 14.

domestic and imported sources. Aside from tax revenues described in table 5, governments receive income through inter-governmental transfers, fixed investments, and production (e.g. recreation, real-estate). Public expenditures are assumed to balance with revenues. The constraint is enforced by allowing the federal government to buy and sell foreign exchange through a rationing instrument. The state/local government balances their budget by endogenizing a chosen state/local tax rates. Each region is equipped with an entrepreneurial agent who demands aggregate transfers for enterprises, investment and inventory. The rest of world agent (including the rest of the United States) demands foreign exchange with income endowments based on ownership of capital, labor endowments, net domestic and international transfers payments (through factor trades and surplus or deficit payments) and benchmark levels of national and foreign exchange. I use a New York Stock Exchange parameter to provide a means of describing capital owned locally or outside of the Central Sands. The default share of domestic and foreign capital ownership is 50%. Unemployment is introduced into the model through a regional level wage curve (Blanchflower and Oswald 1994; Blanchflower and Oswald 1990). The wage curve is an empirically tested result that describes a negative correlation between the level of unemployment and the real wage in a region. Econometric studies on the wage curve estimate the elasticity of the real wage with respect to the unemployment rate. Deller (2011) estimates county level elasticities using a geographically weighted regression. Point estimates show that county level elasticities in the Central Sands tend

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to be larger in absolute value than the national average.30 County and household level unemployment rates are used, calculated by combining county level unemployment rates from the Wisconsin Department of Workforce Development along with national level estimates on unemployment by household group found in Sum et al. (2010). County-household unemployment rates are calculated as a weighted average according to labor endowments found in the economic dataset. Resulting unemployment rates are found in table 18 in appendix C. Finally, I fix the price of foreign exchange as the numeraire. Restrictions for water withdrawals in production are implemented through exogenous withdrawal constraints, or through permit prices. Water use abatement can occur either through water-land substitution or through a reduction in production levels. Permit revenues are recycled either lump sum back to households through a per-capita re-allocation scheme, or to the state/local government for two-step redistribution policies. Two-step redistribution represents initial scarcity rent accrual at the state/local government level, recycled through lessening other distortionary taxes in the regional economy following the fixed budget assumption. Following Rutherford (1995), the general equilibrium model is formulated and solved as a mixed complementarity problem (MCP). In this format, an equilibrium is characterized by three classes of equilibrium conditions: zero profit, market clearance and income balance. No production activity makes positive pure profits, supply must satisfy demand with excess supply being non-negative, and expenditures cannot exceed incomes. A complete description of model equations is given in Appendix B. Refer to tables 14 and 15 for notation.

5

Results

5.1

Policy Scenarios

Alternative water allocation restriction scenarios are considered to explore differential impacts due to policy flexibility and permit revenue re-distribution schemes. While the economics literature provides examples of the benefits of market based mechanisms, more complex regulation often requires additional expenditures on enforcement. Small communities like the Central Sands may benefit more from easily implemented policies. Though the modeling framework does not capture fixed and variable costs associated with the implementation of water restrictions, understanding the relative difference in the magnitude of impacts is informative for policy makers. I consider restricting water withdrawals for agricultural sectors by up to 40%. Note that the amount of the reduction is largely arbitrary, given the premature state of prospective policy. Rather, a distribution of reductions is considered to understand the variability in how the regional economy responds to water reductions in agricultural production. Table 6 describes six scenarios that are constructed to explore the effects of policy flexibility and revenue re-distribution. Policies can be 30

The standard result in the literature places the national average elasticity around −0.1, meaning a 1% increase in the unemployment rate is associated with a 0.1% decrease in the real wage. Estimates for Wisconsin use data from 2006. The point estimate for Adams county is -0.2023, for Marquette is -0.1946, for Portage is -0.1816, for Waupaca is -0.1652, for Waushara is -0.1833, and for Wood county is -0.1984

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Table 6: Policy Scenarios

Scenario

Permit

Tradable

Allocation

Lump Sum

CaC HH nt lump HH nt tax HH t lump HH t tax Firm t oba

No Yes Yes Yes Yes Yes

n/a No No Yes Yes Yes

n/a Household Household Household Household Firm

n/a Yes No Yes No Yes

Notes: In the main simulation results, lump =per capita, for equal per capita lump sum payments and tax =personal property tax. In sensitivity simulations, lump ∈ {per capita, land, fgovt} adding payments on the basis of revenue from land rents or to the federal government. tax ∈ {property tax, income tax, agricultural indirect business taxes} where the first two are applied on the household side and the third on the supply side of the model.

differentiated on the basis of whether exogenous mandates or permits are used to regulate water allocations across users. Scenario CaC denotes the command and control case where agricultural water users (vegetables, grains, oil seeds, other crops and raw milk production) are subject to restricted water withdrawals per unit of output. Shadow scarcity rents are generated, though retained by affected firms. Five separate permitting schemes are subsequently considered, using the equilibrium level water demands from the mandate scenario as a reference point. Permitting schemes are differentiated on the basis of whether permits are non-tradable (nt) or fully tradable (t) across sectors and regions in the Central Sands. Generated permit revenues from agricultural sector level water demand are allocated to households (HH ) or firms (Firm) either through lump sum payments (lump) or the state/local tax system (tax ). Lump sum payments to households are modeled by allocating groundwater property rights on an equal per capita basis in the main simulation results. Table 7 provides the distribution of total households across each income category by county in the Central Sands. Most households locate towards the middle income groups. Two-step re-distribution through the state/local tax system occurs through the property tax in the main simulation results. Property taxes and transfers from the federal government are the main sources of revenue for local governments across the United States (The Urban Institute-Brookings Institution Tax Policy Center 2017). They also represent a form of tax where it is relatively simple to characterize the local beneficiaries of revenue redistribution geographically. Household income taxes and agricultural indirect business taxes (a supply side tax on output) are also considered in sensitivity. Lump sum payments to firms follow an output based allocation (oba). Sectors are allocated permits on the basis of benchmark water use and their subsequent activity levels, and are tradable between agricultural sectors in the Central Sands. If a recycling identifier is not specified in the scenario descriptor, no change is computed across recycling methods (e.g. if HH nt is listed, effects across lump sum and two-step redistribution are identical).

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Table 7: Lump Sum Permit Revenue Distribution Shares (%) Households Per Capita

<10k 10-15k 15-25k 25-35k 35-50k 50-75k 75-100k 100-150k >150k

Adams

Marquette

Portage

Waupaca

Waushara

Wood

7.0 6.1 14.2 15.6 19.4 20.6 9.1 5.8 2.4

6.1 6.1 13.6 11.5 18.7 23.2 11.3 6.9 2.6

6.7 5.7 11.5 10.5 14.2 21.5 14.4 10.6 5.1

5.5 7.3 11.8 13.2 15.2 22.7 13.1 8.7 2.4

6.4 6.6 12.1 14.9 18.6 20.4 12.7 5.9 2.4

5.2 5.8 12.7 12.6 16.7 21.6 12.8 9.1 3.5

Notes: Number ranges indicate household types. All figures are denominated in percentage form. Source: IMPLAN and ACS (American Community Survey).

5.2

Simulation Results

The main simulation results explore the long run implications of water allocation restrictions. Following the nomenclature provided in table 6, figure 6 reports the total percentage change in aggregate GDP (totaling changes across all counties in the Central Sands) due to different policy designs across a range of water restriction levels (labeled here as cutbacks). The ranking of policy performance is consistent across levels of water restrictions. Moreover, differential revenue recycling allocations in the household permitting scenarios have no impact on GDP outcomes. Rather, the role of lump sum equal per capita payments relative to two-step re-distribution is purely a distributional effect.31 Command and control policy is associated with the largest losses, ranging up to 0.096% or approximately $10.1 million. Permit allocations to households of non-tradable and tradable water rights are the best performing mechanisms for water reductions in terms of aggregate GDP. Non-tradable permits results in GDP losses of up to 0.052% (roughly $5.5 million). Trading permits across agricultural sectors and regions leads to lower shadow values for water by allocating water to its most productive uses. As such, allocating households tradable permits leads to smaller losses, or approximately a $2.38 million reduction in aggregate GDP.32 Table 8 gives the value change in millions of dollars for each component of aggregate GDP either from income or expenditure accounts for a 30% reduction in water allocations. The largest percentage change in income comes from reductions in the returns to agricultural land (N ), given that water is assumed to be capitalized into land values. This component, however, represents the smallest income related sub-category of GDP (see table 2), and for household non-tradable permits, the reduction in agricultural land rents totals approximately $29 million (or a 31% change). 31 For subsequently reported production related impacts where revenue recycling has no effect, the lump or tax is similarly removed to reduce the number of displayed elements. However, differential welfare and tax implications for revenue recycling exist and are reported accordingly. 32 Sensitivity simulations which consider recycling revenue through other taxes in the regional economy show that no differences in GDP impacts exist when recycling through the household income tax relative to the property tax. Small changes in GDP are calculated when considering a supply side tax in the model. Recycling permit revenue through agricultural indirect business taxes is associated with larger GDP impacts in absolute value. The magnitude of the difference relative to lump sum payments, however, is only at most 0.03% of GDP for a 40% reduction in water allocations.

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Figure 6: % Change in Total GDP. Impacts for restrictions in water use for agricultural sectors. Total GDP denotes the aggregated change across all counties in the Central Sands. Table 8: Disaggregate GDP Impacts for a 30% Reduction in Water Allocations CaC

Firm t oba

HH nt percapita

HH nt propertytax

HH t percapita

HH t propertytax

Expenditure approach (millions of $)

C G I X-M

-5.4 0.1 -0.4 0.0

-4.1 -0.2 0.4 0.1

-2.8 0.0 -0.3 0.0

-2.8 0.0 -0.3 0.0

-0.8 0.1 -0.1 0.0

-0.8 0.1 -0.1 0.0

Income approach (millions of $)

L K N Other Tax

0.2 -0.4 -7.1 1.5 0.0

1.1 0.3 -6.2 13.0 -11.9

-0.4 -0.2 -28.9 26.6 0.0

-0.4 -0.2 -28.9 51.2 -24.6

0.1 -0.1 -6.1 5.2 0.0

0.1 -0.1 -6.1 10.4 -5.1

Regional GDP (millions of $)

Adams Marquette Portage Waupaca Waushara Wood

-1.7 -0.3 -1.6 -0.2 -1.6 -0.5

-0.3 -0.2 -0.7 0.0 -2.2 -0.3

-1.0 -0.2 -0.1 -0.2 -1.1 -0.4

-1.0 -0.2 -0.1 -0.2 -1.1 -0.4

-0.1 0.0 -0.3 0.0 -0.3 -0.1

-0.1 0.0 -0.3 0.0 -0.3 -0.1

Notes: The income approach is composed of labor (L), capital (K), land (N ), taxes and other incomes. Expenditures are divided into household consumption (C), government expenditures (G), investment (I) and net exports (X − M ). Source: IMPLAN.

Reductions in income from agricultural land rents are not as large for other policy mechanisms. Instances where permits separate water and land property rights lead to transfers in income related effects to other accounting categories. Water permit revenues accrue in the Other category of GDP. Page 25 of 59

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Table 9: Tax Impacts for the State/Local Government: 30% Reduction (millions of $)

Indirect Business Tax Personal Income Tax Personal Property Tax Personal Sales Tax Permit Revenues

CaC

Firm t oba

HH nt percapita

HH nt propertytax

HH t percapita

HH t propertytax

3.7 0.01 -3.4 -0.2

1.7 0.1 -1.8 -0.1 23.8

4.3 -0.04 -4.2 -0.1

4.3 -0.04 -53.4 -0.1 49.2

0.4

0.4

-0.3 0.0

-10.6 0.0 10.3

Negligible tax related impacts exist in cases where permit revenues are recycled back to households through per capita lump sum payments. In scenarios designed for two-step redistribution, the net effect of increases in the Other category (which includes permit revenues received by the state and local government) and subsequent reductions in tax related income due to reductions in the personal property tax approximately equal the per capita case. Table 9 details the tax impacts of a 30% water allocation reduction for the state/local government. Permit revenues are highest for the non-tradable permit case. Notably, output based allocation scenarios are modeled as a subsidy on output, leading to tax related impacts. Permit revenues are recycled to firms rather than through other regional taxes. Indirect business taxes increase given production shifts to sectors with higher tax rates on output in the dataset (agricultural sectors tend to have lower tax rates on production). All policies lead to negligible changes in labor and capital related income, ranging between -0.02% - 0.02%. Price effects captured on the expenditure side of GDP accounting are modest. The largest percentage changes across policy types are captured in the household consumption category, and in particular the CaC scenario with a -0.07% change. Agricultural production affects local downstream production of food processing and dairy products, both of which represent more significant domestic household expenditures relative to raw agricultural goods. Regional GDP is captured in the final tier of table 8. Regional changes in GDP depend on the distribution and magnitude of sector level activity. Adams, Portage, and Waushara counties account for the largest groundwater withdrawals in the Central Sands, and correspondingly are associated with the largest changes in regional GDP, denominated in millions of dollars. Across policy scenarios, command and control tends to lead to the largest reductions in each region with the exception of Waushara county under the OBA mechanism, providing evidence that the gains from trade are not evenly distributed in all tradable permit cases across counties. While tradable household permitting cases lead to unanimously better outcomes in terms of regional GDP relative to command and control and non-tradable permits, granting firms tradable permits on the basis of water use and output levels leads to the largest changes in GDP in Waushara county across scenarios. The gains from trade depend on the extent of inter-regional and inter-sectoral trade of water allocation rights. In simulations where permits are tradable across regions and agricultural sectors, large groundwater withdrawals for grain farming shift into other agricultural activities. Figure 7 displays the percentage change in regional and agricultural sector level water use. Histogram bars Page 26 of 59

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denote reductions for a 30% water allocation reduction. Error bars indicate the range of effects between a 10-40% restriction. Non-tradable permits and command and control policies are omitted. Such policies produce a uniform reduction in water use across counties and sectors according to the cutback level specified. The OBA mechanism shifts water withdrawals from grain farming in Waushara county to other sectors and counties in the Central Sands, primarily reallocated to vegetable and fruit farming. The household allocation of tradable permits (both lump sum and through two-step redistribution), conversely, shifts groundwater withdrawals away from grain farming in Adams county. Note that most water is re-allocated to Adams, Portage and Waushara counties for vegetable and fruit farming. These counties represent the three largest water users for vegetable and fruit farming though in terms of percentage change, smaller farming counties see the largest relative shift. Re-allocations into other sectors are similar across firm based or household based policy scenarios. In both cases, grain farming is associated with high levels of water use per dollar of output relative to other agricultural activities in the benchmark dataset. Restrictions in water withdrawals produces smaller losses in production value relative to other farming types, allowing for beneficial trade between sectors and regions if the permit price is less than the cost of abating water withdrawals (either through substitution effects or lost output). The difference in abating counties between firm or household based allocations is a consequence of who retains scarcity rents and subsequent water rights trade. In both instances, beneficial transfers between low value, water intensive sectors and relatively higher value, water intensive sectors is apparent. The difference, however, is the distribution of permit allocations across counties. In the household permitting case, lacking any subsidy or retainment of shadow scarcity rents, agricultural sectors are less inclined to limit output losses through factor substitution because of inexpensive permit prices. The highest levels of water use per dollar of output across agricultural sectors and counties in the Central Sands is for grain farming in Adams county. Beneficial terms of (a) Regional Percentage Change in Water Demands (b) Agricultural Sectoral Percentage Change in Water with Tradable Permits Demands with Tradable Permits

Figure 7: Changes in aggregate water demands for agricultural sectors with tradable permits. Baseline magnitudes are reported for a 30% reduction. Error bars indicate the interval of changes ranging from 10-40% reductions in water allocations.

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trade result in a complete transfer of water rights away from this sector. However, more of this trade is retained within county agricultural sectors relative to the OBA mechanism. The output based allocation scenario, conversely, is associated with a per unit revenue adjustment for sectors granted water rights. Adams county is a relatively larger water user for grain farming in the reference data set than Waushara county and therefore gets a larger allocation of permits under the output based allocation. This acts as a subsidy per unit of output. Consequently, results for the output based allocation indicate more trade away from relatively less subsidized sectors and regions.33 Regional and sectoral changes in agricultural factor demands and production due to a 30% reduction in water allocations are reported in figure 8 for vegetable and fruits, grains and raw milk for Adams, Portage and Waushara counties. Note that reported percentage change in capital aggregates both water related and non-water related capital. In policies where water allocation rights are tradable, losses in output can be mitigated through buying more permits or through substitution effects, as is evident in both the household tradable permit and OBA cases in the large shift in production away from grain farming into vegetable and fruit farming. Relative to the benchmark and averaged across counties, losses in vegetable farming output range from 2.21% to -1.65% when permits are tradable. Losses in output are mitigated differently across policy mechanisms. Small levels of factor substitution are evident in the household tradable permit scheme where water permit transfers between regions and sectors dominate. In comparison, the OBA subsidizes agricultural water use allowing sectors to increase their labor demand relative to capital to limit output losses. Indeed, the average increase in the value of labor per dollar of output for grain farming across counties is 11%. This is compared to a 1% increase in the household permitting case. In more restrictive policies where a mandate is used or household permits are not tradable, losses in output can only be mitigated through substitution between factors of production. Across the Central Sands, loss in output for vegetable farming ranges from -19.13% in the non-tradable permit case to -13.33% for command and control for a 30% reduction in water allocations. The command and control case is associated with larger levels of substitution between water related capital and labor demand. Vegetables and fruit farming has a larger share of its total value added attributed to labor in the benchmark relative to grain farming, leading to, on average, a larger substitution shift towards labor relative to grains. Raw milk is included due to the downstream dependence for dairy products. Low water withdrawals in the benchmark and small levels of water related capital expenditures on high capacity wells lead to small shifts in factors and levels of production. The non-tradable permitting case is associated with less factor substitution. Even 33

Trade between sectors follows the same general pattern if fixing water permits to a region, and only allowing for trade between sectors. Transfers in water allocations occur between grain and vegetable farming (and to some extent the other farming sectors). However, a complete reduction in water allocations for grain farming is only calculated for the household tradable case in Adams and Portage counties. Impacts to aggregate GDP are similar to those reported in figure 6, though slightly larger in absolute value for household tradable permit case (by at most 0.01%) and smaller in the OBA scenario by up to 0.08%. Because trade is restricted to within region only, Waushara county doesn’t suffer as large of GDP costs under the OBA scenario, shifting more of the burden to Portage county, whom benefited from less restricted trade.

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though the shadow price for water is higher in the command and control scenario, the non-tradable permitting scenario transfers water scarcity rents to households. This creates an additional burden on sectors who are no longer able to retain shadow resource rents, contributing to larger losses in output in the permitting case. Loss in output for land intensive agricultural activities can additionally be mitigated through substituting between irrigated and non-irrigated land. Table 10 shows the level of substitution between irrigated and non-irrigated land across sectors, counties and policy types for a 30% reduction in water allocations. Restrictions in water withdrawals leads to reductions in the total water composite. Sectors are able to either substitute more irrigated land for water (spreading water withdrawals more thinly across cropped land) or to substitute for non-irrigated land and transition to rain-fed irrigation. Command and control and non-tradable household permits are associated with the same levels of substitution between land types. The largest substitution shift denominated in percent change from the benchmark comes from vegetable and fruit farming in Adams, Portage and Waushara counties. However, note that vegetable farming has lower levels of non-irrigated land production relative to other farming types in the benchmark. Small levels of substitution are present for the tradable permit cases outside of grain farming where a total loss of production is evident for Adams county in the household case, or Waushara county in the firm case.34 The model captures long run structural unemployment through the use of a wage curve. Changes to unemployment result from changes to the real regional wage rate which is only marginally affected across policy changes, where the percentage change fluctuates between -0.02-0.03%. Figure 9 reports the total long run employment impacts across cutbacks in water allocations and policies. The percentage change in aggregate agricultural labor demand is highest in absolute value for nontradable permitting cases due to lower levels of factor substitution, ranging up to a 20% decrease. However, agricultural labor demand only makes up 1.5% of the value of total labor demand across the Central Sands in the reference dataset. Across agricultural sectors, only vegetable and fruit farming contribute to more than 1% of the value of total regional employment, with Adams and Waushara having the highest regional percentages of 4.3% and 3.6% respectively. Aggregating across all employment impacts in each sector and region, the percentage change from the benchmark for aggregate labor demand in the Central Sands is negligible, reflected in figure 9b for each policy scenario.35 34

This result is sensitive to the elasticity of substitution assumed for irrigated versus non-irrigated land demand in the production of agricultural goods. The main simulation results considers a case of setting the elasticity to 0.5 or slight substitutability between rain-fed and center pivot irrigation. Reducing this elasticity serves to treat these closer to compliments in the production process. If the elasticity is cut in half, GDP costs increase by a factor of 2 and the percentage change in irrigated land and non-irrigated land is approximately halved. Moreover, in the tradable permit cases, the percent change in total non-irrigated land is negative. Production responses are more sensitive when reducing the ability to substitute between irrigation techniques. These sensitivity calculations find a larger shift away from grain farming into vegetables and fruits, particularly so in Portage county in addition to Adams and Waushara counties. 35 Using data from GTAP on the proportion of labor demand in production attributed to different labor types (managers, technicians, clerks, service/shop workers, and unskilled labor), simulations are conducted to characterize transitional employment effects in the short run by restricting labor to be fixed to a given sector and labor type (though mobile across Central Sands counties). I use a constant elasticity of transformation function to allocate regional labor supply to labor types following an elasticity of transformation of 4. Labor types are demanded in

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(a) Command and Control

(b) Household Non-tradable Permits

(c) Household Tradable Permits

(d) Firm Output Based Allocation

Schreiber (2017)

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Figure 8: Percentage changes in agricultural factor demand and production in Adams, Portage and Waushara counties. Marker size indicates the percentage change in a given agricultural sector’s production level as a result of a 30% reduction in water allocations (relative to other data points within each plot).

Table 10: Irrigated vs. Non-irrigated Land Demand: 30% Reduction Adams Irrigated Non-irrigated

Marquette Irrigated Non-irrigated

Portage Irrigated Non-irrigated

Waupaca Irrigated Non-irrigated

Waushara Irrigated Non-irrigated

Irrigated

Wood Non-irrigated

Grain

CaC Firm t oba HH nt HH t

-17.8 -30.8 -17.8 -100.0

11.2 20.0 11.2 -100.0

-21.8 -13.9 -21.8 -6.9

0.7 0.4 0.7 0.2

-17.6 -29.9 -17.6 -29.5

11.7 20.4 11.7 20.1

-21.6 -8.2 -21.6 -4.1

1.0 0.4 1.0 0.2

-19.3 -100.0 -19.3 -33.3

7.0 -100.0 7.0 12.5

-21.9 -5.1 -21.9 -2.7

0.3 0.1 0.3 0.0

Other Crops

CaC Firm t oba HH nt HH t

-23.2 -10.3 -23.2 -8.7

3.2 1.4 3.2 1.2

-23.9 -6.1 -23.9 -2.9

0.8 0.2 0.8 0.1

-23.6 -19.6 -23.6 -14.9

2.0 1.6 2.0 1.2

-24.0 -5.4 -24.0 -2.8

0.4 0.1 0.4 0.0

-23.2 -17.5 -23.2 -9.0

3.3 2.4 3.3 1.2

-24.0 -2.6 -24.0 -1.2

0.1 0.0 0.1 0.0

Oil Seeds

CaC Firm t oba HH nt HH t

-21.8 -14.8 -21.8 -13.7

7.9 5.3 7.9 4.9

-23.9 -3.4 -23.9 -1.6

0.5 0.1 0.5 0.0

-21.8 -9.9 -21.8 -6.7

8.0 3.6 8.0 2.4

-23.8 -2.6 -23.8 -1.3

1.1 0.1 1.1 0.1

-22.1 -21.7 -22.1 -10.9

7.0 6.9 7.0 3.4

-24.1 -1.7 -24.1 -0.8

0.2 0.0 0.2 0.0

Vegetables and fruits

CaC Firm t oba HH nt HH t

-12.4 -1.9 -12.4 -1.5

55.1 7.8 55.1 6.4

-21.0 -2.2 -21.0 -1.0

3.4 0.3 3.4 0.2

-14.9 -1.5 -14.9 -1.0

39.8 3.9 39.8 2.5

-19.4 -1.4 -19.4 -0.7

17.3 1.2 17.3 0.6

-16.0 -4.1 -16.0 -1.8

34.1 8.3 34.1 3.7

-16.9 -2.3 -16.9 -1.1

13.6 1.8 13.6 0.9

Total

CaC Firm t oba HH nt HH t

-12.9 -3.3 -12.9 -5.4

25.1 6.1 25.1 -7.0

-21.5 -3.6 -21.5 -1.7

0.7 0.1 0.7 0.1

-15.1 -2.7 -15.1 -2.1

13.4 2.3 13.4 1.9

-19.9 -2.0 -19.9 -1.0

1.0 0.1 1.0 0.0

-16.4 -8.3 -16.4 -3.4

13.0 -4.5 13.0 2.6

-17.0 -2.3 -17.0 -1.1

2.6 0.3 2.6 0.2

Notes: Figures included in this table represent percentage changes corresponding to a 30% reduction in water allocations.

Schreiber (2017)

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Production level implications of a policy translates to the household side of the economy through price and income changes. Most income related effects come from the changes in the value of agricultural land endowments, permit revenue re-distribution and through endogenizing tax rates to satisfy a fixed state/local government budget constraint (especially in scenarios when permit revenues accrue at the state level). Expenditure effects can be traced both to changes in the price for agricultural supply as well as through downstream sectors. The percent increase in the local supply price for vegetable and fruit farming goods across policy scenarios for a 30% reduction in water allocations ranges from 0.02% to 4.3%, with the larger impacts for mandated cutbacks or for non-tradable permit simulations. Household demand for other farming sectors’ supply is small. The most affected local downstream sectors (defined as downstream if a given sector has greater than 2% of total production costs attributed to domestic intermediate demand of agricultural goods) are other food processing and dairy production, both of which represent more significant household expenditure categories. Given the increase in the price of local agricultural goods and restrictions in supply, food processing and dairy plants in the study region are able to substitute local intermediate inputs with other domestic or foreign sources to mitigate reductions in production according to the Armington trade framework embedded in the model. Portage county has the largest food processing sector in the region, accounting for approximately 3% of regional value added in the benchmark. Correspondingly for a 30% reduction in water allocations, the largest output effect for the other food processing sector is in Portage county, with reductions up $70 million (18% change from the benchmark) for the non-tradable household permitting scenario, and $48 million (12% change from the benchmark) for command and control, with relatively higher levels of import substitution for the mandate scenario. This contrasts with a reduction of $1 million in production for household tradable permits and a $2 million increase in production for the OBA scenario. The dairy sector is similarly affected most in Portage. The associated change in prices for the local supply of other food processing range from -.29% to 2.73%. Other marginally affected downstream sectors are the bovine cattle and animal products sectors. Changes to the local and foreign/domestic supply of agricultural goods drive the percent change in domestic input demand for downstream sectors (notably, the percent change in the real regional capital rental rate fluctuates between −0.04% to 0.04% across policy scenarios). Table 11 represents the percentage change in local and foreign/domestic supply relative to the benchmark for a 30% reduction in water allocations. Larger percent changes are reported for the foreign/domestic market relative to supply to the Central Sands counties due to the Armington elasticity assumption that local elasticities are larger than domestic or foreign substitution elasticities. The largest percent production according to an additional nest governed by an elasticity of substitution of 0.5 indicating that labor substitution between types is small. For up to a 40% reduction in water allocations, the percentage change in the total number of unemployed workers relative to the benchmark is at most 0.8% (household non-tradable permits) and as little as -0.03% (OBA) in the short run. Adams and Waushara counties are most affected in the non-tradable permitting scenario with unemployment changes of 1.8% and 1.9% for a 40% reduction in water allocations. The two largest labor types employed across agricultural sectors are managers (53% of total labor payments) and unskilled workers (19% of total labor payments) and as such are most affected by water restrictions in the short run. The largest labor demand decreases are calculated for managers, ranging down to -0.18% across all sectors and regions in the non-tradable permit scenario.

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(a) Aggregate Agricultural Employment (%)

(b) Aggregate Employment (%)

Figure 9: Agricultural vs. Aggregate Labor Demand Changes (%) Table 11: % Change in Local and Foreign/Domestic Supply: 30% Reduction CaC

Firm t oba

HH nt

HH t

Local market

Grain Other Crops Oil Seeds Raw Milk Vegetables and fruits

-10.1 -8.8 -13.2 -0.2 -8.0

-29.1 -5.2 -5.3 0.0 0.0

-12.6 -12.2 -14.4 -0.3 -11.8

-22.5 -4.0 -3.1 0.0 -0.8

Foreign/ domestic market

Grain Other Crops Oil Seeds Raw Milk Vegetables and fruits

-16.1 -9.8 -13.0 -0.4 -14.5

-29.4 -5.6 -5.0 -0.3 -2.7

-18.7 -13.2 -14.0 -0.5 -20.8

-25.0 -4.1 -3.1 -0.1 -1.8

reduction is for grain farming, especially in scenarios with tradable permits. In terms of absolute magnitudes, command and control and the non-tradable permit case are associated with the largest reductions in the supply of vegetables and fruits across both markets. Household final demand is composed of both imported goods and Armington composite goods which combine local and other national goods. The extent to which changes in the local supply price of agricultural and affected downstream goods impact household welfare depends on changes to the domestic Armington composite price in each region and sector. While there are significant local production effects in downstream sectors, the value share on local versus the rest of the national market for each affected sector is small. The percentage change in the Armington composite price as a result of each policy scenario is, consequently, also small. For instance, the largest change comes from the composite price of vegetables and fruits, ranging from a 0.04% - 2.9% increase across counties and policy scenarios for a 30% reduction in water allocations. For downstream sectors, the other food processing sector is affected most, with impacts ranging from a -0.03%-0.34% change in its Armington price.36 36 Sensitivity is conducted considering the size of the proposed elasticities of substitution in the Armington formulation. Notably, reducing or increasing the elasticities have no effect on supply to the foreign/domestic market. If the national and local elasticities are restricted to be even smaller (σ LAR = 0.2σ ARM and σ N AR = 0.5σ ARM ), then

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The percent change in aggregate welfare across water reduction levels and policy types is provided in figure 10. The metric, measured in the percent change in equivalent variation in income relative to the benchmark, represents a utilitarian metric of welfare, negating distributional differences across household types by equally weighting expenditures. Similar to aggregate GDP impacts, reductions in aggregate household welfare is largest for the command and control scenarios, with exception to the largest cutback scenario. CaC scenarios range between $0.2-9.7 million in aggregate household welfare losses. In contrast to aggregate GDP impacts, there are welfare consequences to two step redistribution relative to lump payments in the household non-tradable permit scenario. Recycling revenue through the property tax is associated with larger welfare losses relative to per capita lump sum payments, with the difference for a 40% reduction in water allocations equivalent to $1.7 million in losses.37 The welfare effects of each policy can be decomposed into income and expenditure effects following the decomposition derivation in appendix D.1. Similar to GDP impacts, income decomposition reveals that the largest impacts are concentrated on agricultural land returns for property owners, especially in instances when households are granted non-tradable permits. In lump sum permitting payments, welfare improvements come from permit income adjustments. Most expenditure related welfare losses come from increases in the price for Armington composite goods. Even in two-step redistribution scenarios where property taxes are reduced, only marginal welfare gains are calculated through housing expenditure changes. More welfare improvements occur through income related housing ownership due to higher equilibrium housing prices relative to expenditure effects of reducing property tax payments.38 for a 30% reduction in water allocations, the percentage change in supply to the local market is smaller in absolute value for the command and control and non-tradable permitting cases, though only by 0.5-2%. Tradable permits result in roughly doubling the reductions to local supply for grain farming (due to large production responses across regions and smaller elasticities in defining the total local supply), though other sectors’ supply changes remain similar across elasticity specifications. If I assume an elasticity structure where local and national Armington elasticities are larger than foreign elasticiies (σ LAR = 4σ ARM and σ N AR = 2σ ARM ) meaning local and nationally produced goods are more substitutable, then the percentage change in the supply to the local market is larger in absolute value with exception to grain. Impacts to the change in the Armington price of downstream goods are, however, negligible across sensitivity simulations considering alternative elasticity specifications, with changes of at most 0.02%. 37 Welfare losses are still small even when considering distributional concerns across income groups. Using a social welfare aggregation function developed in appendix D.2 encompassing different distributional assumptions on the relative weights different households should receive when aggregating at the county level, welfare losses for the Rawlsian case (putting more weight on the poorest income group) are at most 1% across counties, policy scenarios and water allocation restrictions up to 40%. Losses are larger because poorer household groups spend a larger proportion of their budget on food items. 38 Additional revenue recycling is explored in sensitivity. Lump sum payments on the basis of agricultural land ownership (see appendix C.3) yield negligible changes in total welfare losses relative to the per-capita case as well as in decomposition. Land based revenue recycling relative to the per capita scenario differs only on distributional outcomes between household income groups, more heavily favoring richer income tiers. Additionally a scenario where revenues are not recycled locally, but rather accrue to the federal government is considered. Relatively large differences are computed. Aggregate welfare losses range up to $28 million for a 30% reduction in water allocations, providing evidence for the importance of permit revenue retainment in the regional economy. Results for other twostep redistribution mechanisms either through the household income tax or agricultural indirect business tax show negligible differences in welfare. Reductions in the regional income tax is associated with identical welfare impacts as the per-capita lump sum payments whereas reductions in regional agricultural business taxes lead to larger welfare costs relative to lump sum payments, with at most a difference in impacts of 0.04% in aggregate welfare for the non-tradable permitting case.

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Figure 10: % Change in Aggregate Welfare (Utilitarian Metric)

6

Concluding Remarks The implications of fresh water scarcity across the United States will depend on the regional

heterogeneity of surface and ground water availability and use. In Wisconsin, groundwater is primarily used in the irrigation of agricultural goods. Groundwater withdrawals can lead to externalities when surface waters are dependent on groundwaters for recharge in the regional hydrological system. Drying lakes and streams with recreational amenity value may be the consequence of increased levels of groundwater withdrawals from irrigators in the Central Sands. This paper considers the economic costs of restrictions in groundwater allocations. Using a static, multi-regional, multi-sectoral general equilibrium model, I investigate scenarios which correspond to alternative policy frameworks for regulating water use for agricultural water users. The results suggest that reducing allocations by up to 40% of 2011 groundwater withdrawal levels (post reduction levels similar to 1985 withdrawals) is unlikely to have significant economic costs. Permit revenue recycling only plays a distributional role. Household types are impacted differently depending on the revenue recycling mechanism used, though overall welfare impacts are largely unaffected across mechanisms. However, this is only true when revenues are recycled locally. If permit revenues are allocated to the federal government, welfare costs are larger by a factor of three. Market based mechanisms provide the least costly channel to satisfy water restriction requirements, though the gains from tradable permits are not evenly distributed across counties in all cases. Moreover, while tradable water rights reduces costs, the regional distribution of water use changes and therefore the reductions in regional water withdrawals are not uniform. The extent Page 35 of 59

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to which this may impact the hydrological system is subject to future research. The optimal economic/hydrological policy would require knowledge on the recharge implications of regional lakes and streams. In this paper, I illustrate what the post policy equilibrium looks like if sectors and demanding agents respond purely to economic incentives. This paper aims to structure discussion of the costliness of groundwater regulation on a model based framework. Cost-benefit analysis is appropriate for understanding the likelihood of whether water restrictions are likely to improve or harm aggregate social well-being in the Central Sands. The model described in this paper relies on optimal economic responses following a policy shock. These sets of assumptions produce the basic result that the costliness of groundwater allocation restrictions can be reduced given flexibility in policy design. However, it should be noted that often times different crop types are planted for non-economic reasons. Optimal crop rotations are contingent not only on market prices, but on growing conditions. In the Central Sands, farmers cannot grow potatoes each year without depleting their land’s soil nutrients. A carefully constructed policy would reconcile both sets of insights. Estimating the benefits of water conservation would require reducing the uncertainty in the impact reductions in agricultural water withdrawals have on regional lakes and stream levels. The benefits of a water restriction policy would be derived from lake and stream recharge through increases in fishing and recreation demand (similar to Loomis and Creel (1992)) and increases in water front housing prices (both from a home owner perspective and government perspective collecting property tax). An additional limitation suffered in the analysis is the level of sectoral aggregation in the reference dataset. Given economic data restrictions on agricultural sectors, crop types are aggregated to match the GTAP sectoring scheme, and therefore, so are water withdrawals. Grain farming is reported to have the largest per dollar of output water requirements for production, though a majority of this is due to corn farming. Similarly, groundwater withdrawals for vegetable and fruits is dominated by potato and dry bean production. The model provides an averaged perspective across aggregated sectors, though the extent to which crop type substitution is a consequence of groundwater allocation restrictions will depend on within category crop types. This analysis presumes some degree of substitutability between factors and inputs in production. This is evident in the simulation results with smaller reductions in output relative to water withdrawal demands. This differs from fixed price frameworks such as input output analysis where production is modeled as a Leontief input nest of fixed coefficients. I consider an instance where a resource is not priced in the benchmark dataset and consequently has a small value share in production for agricultural sectors. Small elasticities of substitution could lead to larger than estimated costs. However, Hogan et al. (1977) provide a metaphor using elephant and rabbit stew: a stew made from one rabbit and one elephant will still very much taste like elephant stew. This suggests that impacts in agricultural sectors with relatively small levels of value added as in the Central Sands is likely to have limited impacts to the overall regional economy.

Page 36 of 59

References

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Provencher, B. and O. Burt (1993). The Externalities Associated with the Common Property Exploitation of Groundwater. Journal of Environmental Economics and Management 24 (2), 139–158. Provencher, B. and O. Burt (1994). Approximating the Optimal Groundwater Pumping Policy in a Multi-aquifer Stochastic Conjunctive Use Setting. Water Resources Research 30 (3), 833– 843. Robinson, S. and A. Gueneau (2013). CGE-W: An Integrated Modeling Framework for Analyzing Water-economy Links Applied to Pakistan. In Proceedings of the 16th Annual Conference on Global Economic Analysis, Shanghai, China, Volume 1214. Robinson, S., K. Strzepek, M. El-Said, and H. Lofgren (2008). The High Dam at Aswan. In Indirect Impact of Dams: Case Studies from India, Egypt, and Brazil. Washington, DC, and New Delhi, India, pp. 227–273. World Bank and Academic Foundation. Roe, T., A. Dinar, Y. Tsur, and X. Diao (2005). Feedback Links Between Economy-wide and Farm-level Policies: With Application to Irrigation Water Management in Morocco. Journal of Policy Modeling 27 (8), 905–928. Rutherford, T. F. (1995). Extension of GAMS for Complementarity Problems Arising in Applied Economics. Journal of Economic Dynamics and Control 19 (8), 1299–1324. Rutherford, T. F. and S. V. Paltsev (2000). GTAPinGAMS and GTAP-EG: Global Datasets for Economic Research and Illustrative Models. Working Paper, 1–64. Rutherford, T. F. and A. Schreiber (2016). Using IMPLAN Social Accounts for Applied General Equilibrium Modeling. Technical Manual , 1–31. Schimel, B. D. (2016, May). AG Opinion - 2011 WI Act 21. Schoengold, K., D. L. Sunding, and G. Moreno (2006). Price Elasticity Reconsidered: Panel Estimation of an Agricultural Water Demand Function. Water Resources Research 42 (9). Seung, C. K., T. R. Harris, J. E. Englin, and N. R. Netusil (2000). Impacts of Water Reallocation: A Combined Computable General Equilibrium and Recreation Demand Model Approach. The Annals of Regional Science 34 (4), 473–487. Seung, C. K., T. R. Harris, T. R. MacDiarmid, and W. D. Shaw (1998). Economic Impacts of Water Reallocation: A CGE Analysis for Walker River Basin of Nevada and California. Journal of Regional Analysis and Policy 28, 13–34. Shah, F. A., D. Zilberman, and U. Chakravorty (1995). Technology Adoption in the Presence of an Exhaustible Resource: The Case of Groundwater Extraction. American Journal of Agricultural Economics 77 (2), 291–299. Stavins, R. N. (1998). What Can We Learn From the Grand Policy Experiment? Lessons From SO2 Allowance Trading. The Journal of Economic Perspectives 12 (3), 69–88. Strzepek, K. M., G. W. Yohe, R. S. J. Tol, and M. W. Rosegrant (2008, May). The Value of the High Aswan Dam to the Egyptian Economy. Ecological Economics 66 (1), 117–126. Sum, A., I. Khatiwada, and S. Palma (2010). Labor Underutilization Problems of US Workers Across Household Income Groups at the End of the Great Recession: A Truly Great Depression Among the Nation’s Low Income Workers Amidst Full Employment Among the Most Affluent. Center for Labor Market Studies Publications. Paper 26. The Urban Institute-Brookings Institution Tax Policy Center (2017). State & local government finance data query system. http://slfdqs.taxpolicycenter.org/pages.cfm. Data from Page 40 of 59

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References

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Additional Data Tables Table 12: Local Demand for Agricultural Goods Sector

Adams

Marquette

Portage

Waupaca

Waushara

Wood

Grains Animal products Vegetables, fruit, and nuts Oil seeds Other crops Bovine cattle Raw milk Forestry Fishing Dairy products Other food processing Beverages/tobacco products

17.0 8.5 14.9 15.5 10.4 20.4 13.2 1.6 1.3

16.7 9.0 14.5 15.1 15.9 20.2 12.9 2.4 1.7

17.0 9.6 14.8 15.5 10.0 20.4 13.2 3.6 1.9 27.8 10.7 3.2

16.8 8.6 14.6 15.3 11.3 20.3 13.0 2.0 1.6 38.7 14.2

16.8 9.1 14.3 15.2 6.7 20.2 13.0 2.6 1.7 14.6

17.0 8.8 18.3 15.5 9.8 20.4 13.2 8.3 1.6 37.8 6.9

Local % of total input demand

Grains Vegetables, fruit, and nuts Oil seeds Other crops Raw milk Dairy products Other food processing

0.2 56.7 2.5 4.9 99.7 9.0 7.9

0.2 40.4 2.5 3.1 99.7 7.5 7.8

0.2 64.7 3.7 5.7 99.1 34.7 17.9

0.2 44.0 4.1 2.9 76.0 26.7 15.1

0.2 55.0 3.6 5.5 99.5 21.1 29.4

0.2 51.1 3.0 4.4 61.4 30.4 8.3

Local % of total supply

Grains Vegetables, fruit, and nuts Oil seeds Other crops Raw milk Dairy products Other food processing

0.1 5.7 0.2 6.4 43.1

0.1 8.0 0.2 1.7 2.7 97.8

0.1 22.5 0.3 8.1 98.9 8.4 6.2

0.1 4.8 0.3 11.9 84.6

2.4

0.1 23.5 0.3 9.9 79.1 25.8 5.7

0.1 36.3 0.2 7.8 100.0 10.2 2.9

Domestic ag input % of total production

6.3

36.5

Notes: Excluded sectors in the domestic input share of total production attributed to agricultural sectors averaged less than 1% of total production value. Source: IMPLAN.

Table 13: Household Expenditures and Income Sources (millions of $)

<10k

10-15k

15-25k

Household Income Groups 25-35k 35-50k 50-75k 75-100k

100-150k

>150k

Top 15 expenditures

Public administration Recreational and other services Trade/retail Dwellings Other financial services Chemical products Insurance Communication Other food processing Other manufactures Petroleum, coal products Electronic equipment Beverages/tobacco products Motor vehicles/parts Electricity

58.1 52.4 23.5 21.5 8.6 6.9 3.9 6.4 6.1 4.6 6.6 4.6 4.3 0.5 3.3

56.7 44.4 18.0 16.2 17.9 12.3 4.7 7.1 7.6 5.3 5.9 3.9 5.4 2.8 4.3

154.9 108.3 54.4 53.9 25.4 32.4 13.1 15.2 15.9 14.2 14.8 10.6 10.9 6.1 9.7

174.3 141.5 57.6 64.8 47.4 37.2 17.6 18.4 22.2 17.3 19.0 10.2 14.4 8.7 11.5

258.3 242.1 149.1 105.2 87.1 47.9 32.9 31.7 34.9 29.6 30.0 21.1 23.4 18.9 16.8

424.2 363.3 240.1 216.5 138.1 60.2 56.7 51.5 48.3 50.0 48.7 31.2 32.1 30.8 23.3

185.3 171.2 147.6 111.5 79.7 29.2 31.4 28.0 24.7 25.4 23.4 18.9 16.4 18.0 10.6

122.4 104.2 98.7 84.2 44.1 16.6 22.1 17.2 13.8 15.1 14.8 11.1 8.9 10.6 6.4

164.3 131.8 94.3 112.9 41.7 15.1 28.5 16.3 13.1 15.8 13.5 12.6 7.8 13.5 5.6

Domestic agricultural expenditures

Vegetables, fruits, and nuts Grains Other crops Dairy products Other food processing

0.8 0.0 0.0 1.1 5.7

0.9 0.0 0.0 1.4 7.1

2.1 0.1 0.1 2.9 14.9

2.8 0.1 0.1 4.0 20.8

4.6 0.1 0.1 6.3 32.7

6.5 0.2 0.2 8.7 45.2

3.2 0.1 0.1 4.5 23.2

2.0 0.1 0.1 2.5 12.9

2.2 0.0 0.1 2.3 12.2

Income

Labor Transfers Dividends Capital ownership Household production Land ownership Housing ownership

18.7 160.2 40.8 0.4 10.7 3.8 0.6

31.8 181.3 6.3 1.1 7.6 6.3 1.0

171.3 362.7 24.2 13.7 16.3 7.2 2.3

302.8 340.9 36.8 23.9 16.1 8.4 2.7

643.5 445.2 75.2 50.9 21.6 9.9 4.3

1344.6 395.9 126.7 86.5 25.8 11.6 6.8

705.6 162.1 72.4 53.3 9.3 11.3 4.0

500.6 38.5 44.5 48.8 5.5 12.1 2.9

453.2 12.7 124.0 139.5 3.5 23.1 2.1

Source: IMPLAN.

Page 42 of 59

References

B

Schreiber (2017)

Equilibrium Conditions I formulate the model as a mixed complementarity problem.39 Three sets of conditions char-

acterize a competitive equilibrium: firms must earn zero profit, markets clear and incomes balance with expenditures. I let Πprg denote the unit profit function of activity p in region r for good g. Complementarity conditions are represented by the ⊥ symbol. Using Shepard’s Lemma, netput coefficients are calculated by differentiating the associated unit profit function with respect to input and output prices. Variable notation for prices, activity levels, and auxiliary multipliers is provided in Table 14. Descriptions of value share and elasticity notation is given in Table 15.

B.1

Zero Profit

Zero pure profits require that unit revenues must not exceed unit costs. If so, complementarity implies that the activity level (e.g. production, exports) for the associated sector and region is zero. 1. Sectoral production: OBA Y W W −ΠYrs = − φYrs (1 − tYrsF − tYrsL − τrAG tYrsA + τrs )prs − φW rs ψrs (1 + µrs )prs

+

X

MI VA θrsg P IMrsg + θrs CV Ars ≥ 0

⊥

Yrs ≥ 0

g

where the composite price for material inputs is:   1 A A 1−σgARM A 1−σgARM 1−σgARM P IMrsg = θrgs prg + (1 − θrgs )pM rg and the unit cost of the composite of value added and water use, CV Ars , is:  CV Ars =

L L 1−σgV A θrs p

+

K K 1−σgV A θrs pr

+

1−σ V A N θrs CLNrs g



1 VA 1−σg

CLNrs represents the unit cost of land use. Land use decisions are nested based on the composite cost of irrigating irrigable land (CIRrs ) relative to the price of non-irrigated land IR (pN rs ).

CLNrs

  1N IR N IR 1−σ N IR N IR N IR 1−σ N IR 1−σ = θrs CIRrs + (1 − θrs )prs

CIRrs

  1IR IR IR 1−σ IR IR W W KW K E A 1−σ IN 1−σ = θrs prs + (1 − θrs )(θrs prs + θrs prs + θrs pr,ele )

39 A mixed complementarity problem can be represented generally using the definitions found in Ferris and Munson (2000) and Rutherford (1995). Given a function F : Rn → Rn , find z ∈ Rn such that zi Fi (z) = 0. This can equivalently be written using the ⊥ symbol: F (z) ≥ 0 ⊥ z ≥ 0. In our model however, many of the inequalities are set to equalities, creating a large system of nonlinear equations.

Page 43 of 59

References

Schreiber (2017)

2. Exports:  1Y  F X F X 1+η Y F X D 1+η Y 1+η = − θrg p + (1 − θrg )prg

−ΠX rg

+ pYrg ≥ 0

⊥

Xrg ≥ 0

3. Armington composite: N AR

−ΠA rg

1 X  1−σgLAR  N  1−σg 1−σg AR N AR LAR N AR A N AR F X 1−σg LAR D 1−σg + (1 − θrg ) = −prg + θrg p θrr0 g pr0 g

r0

≥0

⊥

Arg ≥ 0

4. Imports: M FX −ΠM ≥0 rg = −prg + p

⊥

Mrg ≥ 0

5. Land transformation into irrigable or non-irrigable land types: X  1 E NT 1+η N 1+ηN + pN ≥0 −ΠN = − θ RN rs r r rs

⊥

Nr ≥ 0

s

where the revenue from regional and sector level land use, RNrs , depends on the price of irrigable and non-irrigable land: RNrs

  1IR GN IR 1+η IR GN N IR 1+η IR 1+η = θrs prs + (1 − θrs )prs

6. Water (tradable permits): W WT −ΠW ≥0 rs = −prs + p

⊥

Wrs ≥ 0

7. Household consumption: −ΠC rh

=

−pC rh

 +

p p pH r (1 + τr trh )

phrh



H θrh

Y

θHA

rhg CDMrhg ≥0

⊥

Crh ≥ 0

g

where the unit cost of demanding domestically or foreign produced goods other than housing is: CDMrhg

  A   M   1 prg (1 + τrs tsrgh ) 1−σRA prg (1 + τrs tsrgh ) 1−σRA (1−σgRA ) AC AC g g = θrgh + (1 − θrgh ) pA pM rg rg

Page 44 of 59

References

B.2

Schreiber (2017)

Market Clearance

I first specify the unit expenditure functions for the representative state/local and federal governments. 7. Federal government unit expenditure function: X

eFr,fED g =

F FA A FA M θr,g,f g θr,g,f g prg + (1 − θr,g,f g )prg




g

8. State/local government unit expenditure function: X

eSLG r,sg =

S SA SA M θr,g,sg θr,g,sg pA rg + (1 − θr,g,sg )prg




g

Market clearance requires that supply must not exceed demand. If so, the complementarity condition implies that the associated price is zero. 9. Local demand: Xrg

∂ΠX ∂ΠA rg rg ≥ A rg D ∂pD ∂p rg rg

pD rg ≥ 0

⊥

10. Output: X

Yrs

s

∂ΠX ∂ΠYrs rg ≥ X rg Y Y ∂prg ∂prg

⊥

pYrg ≥ 0

11. Armington composite: Arg + Arg

X ∂ΠA ∂ΠC ∂ΠYrs X rg rh ≥ + C Y rs rh A A ∂pA ∂p ∂p rg rg rg s h

+

X

SLGr,sg

sg

X ∂eFr,fED ∂eSLG r,sg g + F ED r,f g A ∂pA ∂p rg rg

⊥

pA rg ≥ 0

⊥

pM rg ≥ 0

fg

12. Imports: M rg + Mrg

X ∂ΠM ∂ΠC ∂ΠYrs X rg rh ≥ Y + C rs rh M M ∂pM ∂p ∂p rg rg rg s h

+

X

SLGr,sg

sg

X ∂eFr,fED ∂eSLG r,sg g + F ED r,f g M ∂pM ∂p rg rg fg

13. Transfers: T Rr ≥

F IRMr pTr

⊥

pTr ≥ 0 Page 45 of 59

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14. Consumption: Crh

∂ΠC RArh rh ≥ C C ∂prh prh

pC rh ≥ 0

⊥

15. Housing: X

Hrh ≥

X

Crh

h

h

∂ΠC rh p p ∂pH r (1 + τr trh )

⊥

pH r ≥0

Yrs

∂ΠYrs ∂pL r

⊥

pL ≥ 0

∂ΠYrs ∂pK r

⊥

16. Labor: X

Lri −

X

ur Ur ≥

X

r

ir

rs

17. Capital: X

K ri ≥

X

Yrs

s

i

pK r ≥0

18. Irrigable land (sector level use): Nr

∂ΠYrs ∂ΠN r ≥ Y rs ∂pIR ∂pIR rs rs

pIR rs ≥ 0

⊥

19. Non-irrigable land (sector level use): Nr

∂ΠN ∂ΠYrs r ≥ Y rs IR IR ∂pN ∂pN rs rs

⊥

IR pN ≥0 rs

⊥

E pN ≥0 r

20. Land endowments (ownership rent): X

X

N ri ≥

Nr

s

i

∂ΠN r N ∂pr E

21. Water (sector level use): X

W E ris + Wrs

i

∂ΠW ∂ΠYrs rs + Yrs W ≥0 W ∂prs ∂prs

⊥

pW rs ≥ 0

22. Water endowments with tradable permits: X i

W ri ≥

X s

Wrs

∂ΠW rs ∂pW T

⊥

pW T ≥ 0

Page 46 of 59

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23. Foreign exchange: FE +

X

F EDBr,f g +

X rg

r,f g

Xrg

∂ΠX ROW rg ≥ FX F X ∂p p

∂ΠM ∂ΠA F EDT AXr X rg rg M + + A + rg rg F X F X F p ∂p ∂p X rg

! ⊥

pF X ≥ 0

24. Local tax collections: X

T AX r,sg ≥

sg

B.3

LOCT AXr pTr AX

pTr AX ≥ 0

⊥

Income Balance

Income balance conditions define each representative agent’s budget constraint. 24. Households: RArh =

X

  L K FX p ) pYrg Y rgh + (1 − tpit L + p (1 − nyse)K + p nyseK ri rh rh r rh

g

+ pF X

X

E W WT BT rth + pTr BT r,f rm,h + pN W rh r N rh + prs W E rhs + p

t L + pH r H rh − p ur Ur

25. Federal government: F EDr,f g =

X

T pYrg Y r,g,f g + pL Lr,f g + pK r (1 − nyse)K r,f g + pr BT r,f rm,f g

g

  X + pF X F EDBr,f g + T AX r,f g + BT r,t,f g + nyse K r,f g t E W WT + pN r N r,f g + prs W E r,f g,s + pr W r,f g

Page 47 of 59

References

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26. State/local government: SLGr,sg =pTr AX T AX r,sg +

X

pYrg Y r,g,sg + pL Lr,sg + pK r (1 − nyse)K r,sg

g

FX

+p

X

 BT r,t,sg + nyseK r,sg

+ pTr BT r,f rm,sg

t W WT E + pN r N r,sg + prs W E r,sg,s + pr W r,sg

27. Entrepreneur: F IRMr =

XX

 X F RM A F RM M prg Arg − + prg M rg g

g

f rm

+

pYrg Y r,g,f rm

pK r (1

FX



− nyse)K r,f rm + p

pTr BT r,f rm,f rm

 BT r,t,f rm + nyseK r,f rm +



28. Federal taxing agent: F EDT AXr =

X

tYrsF pYrs Yrs

s

29. Local taxing agent: LOCT AXr =

X

tYrsL pYrs Yrs +

s

+

X

τrp tprh pH r

h

X

τrpit tpit rh

∂ΠC rh ∂pH (1 + τrp tprh ) r

  L K FX p Lrh + pr (1 − nyse)K ri + p nyseK rh

h

30. Rest of the world: ! ROW =

X

L

p Lr,row +

pK r (K r,row

+ nyseK r,row ) +

r

X

pTr BT r,f rm,t

−

t

! FX

p

X

(BRrit + nyseK r,row ) − F E

rit

B.4

Auxiliary Constraints

Auxiliary constraints are used to enforce budget balance restrictions for representative governments. I endogenize state/local tax rates (property, sales, personal income, and indirect business

Page 48 of 59

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taxes) to satisfy the state and local budget balance restriction. The federal government is permitted to buy foreign exchange to satisfy its budget. 31. Federal government budget balance: F EDr,f g ≥

X

pA r,g DD r,g,f g

+

pM r,g M D r,g,f g

 ⊥

F EDBr,f g ≥ 0

g

32. State/local government budget balance: SLGr,sln ≥

X

pA r,g DD r,g,sln

+

pM r,g M D r,g,sln

 ⊥

τrtax ≥ 0

g

where τrtax denotes the tax multiplier for the chosen budget balance restriction and sln denotes state/local spending on goods other than education and investment. Finally, I use a wage curve to characterize regional structural unemployment based on elasticities estimated by Deller (2011). 33. Wage curve:  log

pL pCI r

 = r log (Ur )

Page 49 of 59

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Table 14: Model Variables

Set Indices

Symbol

Description

r g, s i

Regions Goods/Sectors Aggregate institutional index Households Federal government State/local government Entrepreneur institutions Trade (domestic and foreign)

h fg sg f rm t Variables

Yrg Xrg Arg Mrg Wrg Nr Crh pD rg pYrg pA rg pM rg pTr pL r pK r pW rg pW T pIR rg IR pN rg E pN r F X p pTr AX pC rh pCI r pH r RArh F EDr,f g SLGr,sg F IRMr ROW F EDT AXr LOCT AXr Ur F EDBr,f g ls τr,sg τrp τrpit τrAG τrs OBA τrs µrs

Sectoral production Exports Demand for domestic goods Foreign imports Water trade Land allocation Household consumption Price of local goods Price of sectoral output Price of domestic goods Price of foreign imports Price of bilateral transfers Wage rate Rental rate of capital Shadow price of water (sectoral use) Returns to water endowments (tradable permits) Rental rate of irrigated land (sectoral use) Rental rate of non-irrigated land (sectoral use) Returns to regional land endowments Foreign exchange State/local tax revenue return Composite consumption price Consumer price index Rental rate of housing Representative household income Federal government income State/local government income Entrepreneurial income Rest of world Federal tax collections State/local tax collections Unemployment multiplier Federal budget closure rationing instrument State/local budget closure rationing instrument (education and investment) Endogenous personal property tax multiplier Endogenous personal income tax multiplier Endogenous agricultural indirect business tax multiplier Endogenous household consumption sales tax multiplier Output based allocation rent multiplier Command and control restriction multiplier

Page 50 of 59

References

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Table 15: Data Parameters Symbol

Description

Value Shares

φYrs φW rs MI θrsg V θrsA A θrg∗ L θrs K θrs N θrs N IR θrs IR θrs W θrs KW θrs E θrs FX θrg N AR θrg LAR θrr 0g NT θrs GN θrs H θrh HA θrhg AC θrs FA θr,g,f g SA θr,g,sg F θr,g,f g S θrs

Revenue share of output in sectoral production Revenue share of water allocation rents in sectoral production Cost share of material inputs to sectoral production Cost share of value added to sectoral production Cost share of Armington intermediate input to sectoral production Cost share of labor as input to sectoral production Cost share of capital as input to sectoral production Cost share of land composite as input to sectoral production Cost share of irrigable land composite as input to sectoral production Cost share of land in irrigation composite as input to sectoral production Cost share of water in water pumping composite as input to sectoral production Cost share of capital in water pumping composite as input to sectoral production Cost share of electricity in water pumping composite as input to sectoral production Cost share of foreign and national exports Cost share of national market goods for Armington aggregate Cost share of local regions for Armington aggregate Revenue share of sector level land transformation Revenue share of irrigated land transformation Cost share of housing in household consumption Cost share of good g in household consumption Cost share of Armington good in household consumption Cost share of Armington good in federal government expenditure Cost share of Armington good in state/local government expenditure Cost share of good g in federal government expenditure Cost share of good g in state/local government expenditure

Elasticities

σgV A σ N IR σ IR σgARM σgN AR σgLAR σgRA ηY ηN η IR

Substitution between factors and water composite (GTAP 8) Substitution between land types for sectoral production Substitution between irrigable land and water composite for sectoral production Substitution between foreign and domestic intermediate inputs for sectoral production (GTAP 8) Armington substitution between national market and local goods Armington substitution between regional local goods Substitution between Armington and imported goods for household consumption Transformation between local, national and foreign exports Transformation of land for sectoral use Transformation of irrigable and non-irrigable land

Benchmark Parameters

tYrsF tYrsL tYrsA tprh tsrgh tpit rh phrh pA rh pM rh Arg M rg T Rr H rh Lri K ri N ri W E ris W ri FE T AX ri Y rgi nyse BT rii0 r Ur

Federal indirect business tax rate on sectoral production Local indirect business tax rate on sectoral production (non-agricultural) Local agricultural indirect business tax rate Household property tax rate Household sales tax rate on domestic and foreign demand Household personal income tax rate Benchmark housing price Benchmark household consumption of domestic demand price Benchmark household consumption of imported demand price Benchmark domestic goods endowments Benchmark imported goods endowments Benchmark transfer endowments Benchmark housing endowments Benchmark labor endowments Benchmark capital endowments Benchmark land endowments Benchmark water endowments (sector specific) Benchmark water endowments Benchmark foreign exchange endowments Benchmark tax income for governments Benchmark household sectoral output Portion of capital endowments outside of region Benchmark bilateral transfers Elasticity of the real wage with respect to unemployment Benchmark unemployment

Policy

W ψrs

Water restriction policy lever

Notes: Value shares denote shares calculated from the benchmark dataset on relative proportion of the respective value of output/input choice. Cost shares (input choices) are represented by θ and revenue shares are represented by φ. Substitution elasticities are denoted by σ and transformation elasticities are denoted by η.

Page 51 of 59

References

C

Schreiber (2017)

Additional Assumptions

C.1

GTAP Elasticities

Without information on county level elasticities, I make use of national estimates from GTAP 8. I assume that county level elasticities roughly follow national estimates for factors and domestic use of goods. Table 16: GTAP 8 Elasticities

Sector Insurance Business services nec Recreational and other services Public Administration, Defense, Education, Health Dwellings Vegetables, fruit, nuts Oil seeds Sugar cane, sugar beet Plant-based fibers Crops nec Bovine cattle, sheep and goats, horses Raw milk Forestry Fishing Petroleum, coal products Gas Minerals nec Bovine meat products Meat products nec Vegetable oils and fats Dairy products Sugar Food products nec Beverages and tobacco products Textiles Wearing apparel Leather products Wood products Paper products, publishing Chemical, rubber, plastic products Mineral products nec Ferrous metals Metals nec Metal products Motor vehicles and parts Transport equipment nec Electricity Machinery and equipment nec Manufactures nec Gas manufacture, distribution Water Construction Trade Transport nec Water transport Air transport Communication Financial services nec Coal Crude Oil Electronic equipment Grains Animal Products

Factor Elasticity of Substitution

Domestic Elasticity of Substitution

1.26 1.26 1.26 1.26 1.26 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.2 0.2 1.26 0.2 0.2 1.12 1.12 1.12 1.12 1.12 1.12 1.12 1.26 1.26 1.26 1.26 1.26 1.26 1.26 1.26 1.26 1.26 1.26 1.26 1.26 1.26 1.26 1.26 1.26 1.4 1.68 1.68 1.68 1.68 1.26 1.26 0.2 0.2 1.26 0.33 0.25

1.9 1.9 1.9 1.9 1.9 1.85 2.45 2.7 2.5 3.25 2 3.65 2.5 1.25 2.1 17.2 0.9 3.85 4.4 3.3 3.65 2.7 2 1.15 3.75 3.7 4.05 3.4 2.95 3.3 2.9 2.95 4.2 3.75 2.8 4.3 2.8 4.05 3.75 2.8 2.8 1.9 1.9 1.9 1.9 1.9 1.9 1.9 3.05 5.2 4.4 3.22 1.58

Notes: All elasticity values here are taken from the GTAP 8 dataset and should be treated as estimated nationwide averages. The factor elasticities of substitution are used in the value added nest of the production structure and the domestic elasticity of substitution values are used in the output structure of the model in forming the Armington composite.

Page 52 of 59

References

C.2

Schreiber (2017)

Unemployment Rates by Household Type

In order to get a sense of how unemployment rates vary by household and region, regional unemployment rates are taken from the Wisconsin Department of Workforce Development, listed in table 17. Heterogeneity of unemployment across household types is introduced by taking national average estimates from Sum et al. (2010) of unemployment rates by household decile. I compute effective rates of unemployment for each household group for each region in the model, provided in table 18. The second and third groupings are averaged to form the unemployment rate for household group two in the IMPLAN data. Table 17: Unemployment Rates (%) 2010 Unemployment Rate County

Adams Marquette Portage Waupaca Waushara Wood

11.1 10.5 7.2 9.1 10 8.7

Household Type

<10k 10-15k 15-25k 25-35k 35-50k 50-75k 75-100k 100-150k >150k

30.8 17.2 12.2 9 7.8 6.4 5 4 3.2

Notes: County level unemployment rates are taken from the Wisconsin Department of Workforce Development. Each rate represents a seasonally unadjusted annual average. Household level unemployment rates come from Sum et al. (2010) and were derived via Consumer Expenditure Survey data. In order to map deciles to IMPLAN’s nine household classification, the second and third deciles in Sum et al. (2010) are averaged.

Table 18: Unemployment Rates by Region and Household

<10k 10-15k 15-25k 25-35k 35-50k 50-75k 75-100k 100-150k >150k

Adams

Marquette

Portage

Waupaca

Waushara

Wood

19.3 10.8 7.6 5.6 4.9 4.0 3.1 2.5 2.0

20.4 11.4 8.1 6.0 5.2 4.2 3.3 2.7 2.1

26.3 14.7 10.4 7.7 6.7 5.5 4.3 3.4 2.7

21.9 12.2 8.7 6.4 5.6 4.6 3.6 2.8 2.3

20.7 11.5 8.2 6.0 5.2 4.3 3.4 2.7 2.1

22.3 12.5 8.8 6.5 5.7 4.6 3.6 2.9 2.3

Notes: These figures represent weighted rates based on each region’s and household’s labor endowment. Represented as percentages.

Page 53 of 59

References

C.3

Schreiber (2017)

Revenue Allocation Distribution

Main policy revenue recycling is assumed either through lump sum payments on the basis of equal per capita payments across households or through the local tax system. Two additional revenue re-allocation payments are considered in sensitivity: lump sum payments based on agricultural land ownership (weighted more toward richer households, see table 19) or to the federal government, negating recycling effects by assuming permit revenues leave the regional economy. Table 19: Lump Sum Sensitivity Permit Revenue Distribution (%) Households Land Endowment

<10k 10-15k 15-25k 25-35k 35-50k 50-75k 75-100k 100-150k >150k

Adams

Marquette

Portage

Waupaca

Waushara

Wood

4.5 8.2 8.9 9.0 9.4 11.3 13.1 12.9 22.7

5.3 8.0 9.0 12.3 11.7 12.2 10.5 10.4 20.6

3.4 6.8 7.2 9.9 11.3 12.9 13.9 13.3 21.3

4.0 5.3 8.2 7.5 11.3 11.9 11.8 12.5 27.5

4.2 6.3 7.9 8.4 9.8 12.2 9.5 13.0 28.7

4.3 6.9 6.7 7.9 9.7 12.8 12.0 13.7 26.0

Notes: Household types are denominated through income groupings. All figures are provided in percentage form. Source: IMPLAN.

D

Welfare Derivations

D.1

Welfare Decomposition

Changes in welfare induced by a policy simulation can be decomposed into expenditure or income related effects. Notably, because budgets must necessarily balance, the changes in welfare e denote the expenditure due to both income or expenditure effects must be the same. Let θrhgp i value share for household h in region r for good g at price p in the benchmark. Similarly, let θrhgp

denote the equivalent value share on income endowments. The post policy aggregate income index is defined as: Irh =

X  Prgp  pg

prgp

i θrhgp

where Prgp denotes the post policy equilibrium price level for region r, good g and price p with the associated benchmark price equaling prgp . Similarly, the post policy aggregate expenditure index is defined as: Erh

X  (1 + τrhgp )Prgp  e = θrhgp p rgp pg

Page 54 of 59

References

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where τrhgp denotes tax rates on expenditures in the model (sales and property taxes). The decomposition is calculated for changes in expenditures (e) and income (i) as: ∆eprh

=

X

e θrhgp

g

∆iprh

=

X

i θrhgp

    (1 + τrhgp )Prgp 1− /Irh prgp 

g

D.2

  Prgp /Erh − 1 prgp

Welfare Index

The conventional equivalent variation change in welfare provides a regional and household specific measure enumerating the change in income necessary to achieve the new level of utility at old prices. In order to aggregate this information to a regional level, an index is developed which accounts for inequalities between income groups. Let SWr denote the value of aggregate social welfare in region r. We aggregate consumption levels using a CES function. Let nrh represent the number of households in category h in region r, Crh represent the new equilibrium level of consumption, and σ an elasticity of substitution between household groups characterizing the level of inequality in a given region. SWr is defined as: SWr =

X

1−1/σ nrh Crh



1 1−1/σ

h

If σ → ∞, this measure represents a Utilitarian social welfare aggregation function which values a dollar equally amongst all income groups. If σ → 0, a Rawlsian perspective is adopted which values welfare according to the least well off income group. From this welfare aggregation function, an index is derived which describes changes in aggregate social welfare following water restriction policy scenarios. Let σw denote the elasticity of substitution between income groups using welfare aggregation denomination w, where w ∈ {Rawlsian, Low, Medium, Utilitarian}40 . Let crh denote the reference level of consumption. The index allows comparison between benchmark consumption levels and new equilibrium consumption levels and is derived as follows: SWrw =

X

1−1/σ nrh crh w



h

Crh crh

1−1/σw 

This is rewritten as: SWrw = κrw

X h

 θrhw

Crh crh

1−1/σw 

1 1−1/σw

1 1−1/σw

40

In practice, I set σw = 0.01 for Rawlsian, σw = 0.5 for Low, σw = 2 for Medium, and σw = 50 for the Utilitarian case.

Page 55 of 59

References

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where: κrw =

X

1−1/σ nrh crh w



1 1−1/σw

1−1/σw

and θrhw = P

nrh crh

h0

h

1−1/σw

nrh0 crh0

Let SW Irw be the social welfare aggregation index. The level of social welfare can then be calculated as: SWrw = κrw SW Irw with: SW Irw =

X h

E

 θrhw

Crh crh

1−1/σw 

1 1−1/σw

Water Data Accounting High capacity well data for the state of Wisconsin is compiled by the Wisconsin DNR for each

registered pump from 2011-2014. Withdrawals are classified by source (ground, non-great lake surface, and great lake surface waters), drainage basin (Lake Michigan Basin, Lake Superior Basin or Mississippi River Basin) and category of intended use. See table 20 for aggregate water withdrawals for the Central Sands and all of Wisconsin, along with the number of high capacity wells registered by source type. Examples of aggregate well water withdrawal categories include irrigation, public supply and industrial use, with additional subclassifications for industrial withdrawals. Table 21 describes aggregate water withdrawals by category for the Central Sands. DNR documentation notes that illegal installation and use of a high capacity well is likely to be rare. There are, however, instances in the dataset where zeros are entered for all listed years. These are treated as inactive sites, though it is possible the registered user failed to report water usage for the duration of observation. Wisconsin law mandates that all high capacity well owners annually report their monthly withdrawals. Penalties for failing to report are listed in Chapter 281 of the Wisconsin Statutes. Failure to comply with the conditions listed under an approved well application can result in rescinded access. Moreover, water allocations are based on previously approved well applications and not historical withdrawals, limiting incentives to over/under report.

Page 56 of 59

References

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Table 20: Aggregate Water Withdrawals in the Central Sands

Central Sands

All of Wisconsin

Source

Year

Total Witdrawals

Available Capacity

% of Capacity

N

GW

2011 2012 2013 2014

56.6 95.1 76.8 65.9

882.5 970.9 1020.5 1054.9

6.4 9.8 7.5 6.2

2334 2631 2755 2843

SW

2011 2012 2013 2014

67.0 101.5 97.3 84.6

1226.6 1406.8 1244.2 1397.8

5.5 7.2 7.8 6.0

168 195 176 204

GW

2011 2012 2013 2014

154.5 180.6 169.0 159.1

1346.4 1470.2 1515.9 1588.8

11.5 12.3 11.1 10.0

6869 7788 7857 8209

SW

2011 2012 2013 2014

466.7 461.1 463.1 404.2

4769.2 4926.6 4884.3 4964.4

9.8 9.4 9.5 8.1

396 487 491 507

GL

2011 2012 2013 2014

1404.4 1391.9 1309.3 1236.9

3440.3 3444.3 3143.4 3432.0

40.8 40.4 41.7 36.0

40 41 38 38

Withdrawal and capacity data are enumerated in billions of gallons. N denotes the annual number of registered high capacity well sites in the Central Sands or all of Wisconsin for either groundwater (GW), non-great lake surface waters (SW) or great lakes waters (GL). Available capacity describes the total annual regulated limit on water withdrawals.

F

Well Demand Optimization Problem The cost minimization problem seeks to minimize the total cost of irrigation composed of both

electricity use and capital rent per well and pivot (the combination will subsequently be referred to as a unit of capital) installed subject to fixed water withdrawal requirements. Let s denote the set of electricity load segments offered to agricultural producers throughout the day. In the Central Sands, s ∈ {peak, off-peak}, where the price of electricity in each segment, ps is defined as $0.15 per kWh during peak hours and $0.061 per kWh during off-peak hours.41 The duration of each segment, ds is 12 hours. The cost of capital, pk , is $20,822.5 per unit of capital (data from UW-Extension). The estimate is calculated by assuming that the total costs for a high capacity well and center pivot with sprinkler system is $171,000. I assume a rate of return of 7%, repair costs of 3.5%, insurance payments equaling 0.5% and depreciation calculated with a lifespan of 20 years. Average daily groundwater well pumping limits imposed by the Wisconsin DNR during the permitting process are used (calculated from DNR data) equaling 1,412,062 gallons of groundwater. Capacity is divided equally amongst load segments (Ωs ). Daily water withdrawal requirements, W , are calculated as total annual water demands for agricultural irrigators in the Central Sands divided 41

See, http://www.acecwi.com/Portals/0/Billing/Rate%20Schedule%20updated%204.1.16.pdf

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References

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Table 21: Average annual water withdrawals by category in the Central Sands Source

Growing Season

Winter Season

N (avg.)

Irrigation (agricultural)

GW SW

60.75 23.68

0.57 13.85

1866 151.75

Other agricultural use

GW SW

1.63 0.00

1.11 0.00

150.75 1.25

Public supply

GW SW

4.14 0.02

2.48

287.75 0.5

Domestic supply

GW

0.02

0.01

177.75

Electricity generation

GW

0.02

0.01

1

Industrial use

GW SW

1.47 32.58

0.77 17.20

58 22.5

Recreation

GW

0.01

0.02

28.25

Non-agricultural irrigation

GW SW

0.60 0.23

0.01 0.00

71.25 9.75

Reported water withdrawals are in billions of gallons. Each figure represents an average value over four years of data, ranging from 2011-2014. Growing season is assumed to be from May-October, while Winter is the rest of the year. N denotes the average number of registered sites per category annually.

by the number of days in the growing season (here assumed to be from May to October or 183 days). The aggregate annual water withdrawals for 2012 was 80.152 billion gallons for agricultural irrigation. Furthermore, I assume it requires 40 kWh of electricity to pump an acre-foot of water (or 27,154 gallons), or 0.0015 kWh to pump one gallon of water (α). The optimization problem can be formulated as a linear program.

min C =

X

ps Es + pk N

s

s.t. Es = αXs Xs ≤ ds Ωs N X W ≤ Xs

∀s ∀s

s

The variables of the problem represent endogenous components of the irrigation process in a partial equilibrium framework. C denotes the total cost of irrigating in the Central Sands, Es represents the total amount of electricity in kWhs required to satisfy water withdrawals in each load segment s, Xs represents the total number of gallons withdrawn during each segment s, and N denotes the number of units of capital installed. The total cost of irrigation is composed of both Page 58 of 59

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Schreiber (2017)

the cost of electricity used across load segments and the cost of capital. Electricity requirements translates the number of gallons withdrawn to kWhs. The total amount of water withdrawals must be less than or equal to maximum capacity limits of each installed high capacity well, and water withdrawals must at least satisfy a fixed water level. The optimal number of wells decreases by a factor of 2 when changing the exogenous price level to reflect a flat price rather than block pricing.

Page 59 of 59